An original and insightful account of nature and our place in it from one of France’s preeminent historians of philosophy. One of France’s preeminent historians of philosophy, Marcel Conche has written and translated more than thirty-five books and is recognized for his groundbreaking and authoritative work in Greek philosophy, as well as on Montaigne. In Philosophizing ad Infinitum, one of his most remarkable and daring books, Conche articulates a unique and powerful understanding of nature, inclusive of humanity, as infinite (...) in time and space—ever self-renewing, eternal, and beyond complete understanding or control. In today’s world the notion of infinity is at the core of the crisis humanity faces understanding nature. For the last two hundred years economies have been running at full speed, fueled by the implicit belief that natural resources are infinite; however, it is clear that they are not and that humanity needs to radically rethink the foundations of environmental and economic systems. Conche seeks to begin this rethinking, illustrating along the way insightful and sometimes unorthodox ideas about Plato, Aristotle, Epicurus, Montaigne, Nietzsche, Bergson, and others. “Philosophizing ad Infinitum: this book paints a perfect picture of the life of Marcel Conche, a natural-born philosopher. His aptitude to question absolutely everything drove him to the pre-Socratics, even at an early age, in his relentless quest for the truth. With Montaigne, the thinker to whom he feels most akin, Marcel Conche stands tall as an exceptional figure in contemporary French philosophy, renewing and enriching a great philosophical tradition.” — Françoise Dastur, University of Nice Sophia Antipolis. (shrink)

In 1928, Friedrich Solmsen argued that Aristotle'sPosterior Analyticswas largely composed before thePrior Analytics. Ross rejected Solmsen's position in 1939, and a rather lengthy series of rebuttals and counter-attacks between the two scholars followed. Quite recently, Jonathan Barnes has revived this issue with arguments in favour of something very close to Solmsen's thesis: that Aristotle first developed a theory of demonstration (‘apodeictic’) before he had worked out the syllogistic, and that thePosterior Analyticswas originally conceived against this background. Subsequently, when Aristotle formulated (...) a syllogistic, he is supposed by Barnes to have revised or added to the contents of thePosterior Analyticsso as to make syllogistic the logic of Aristotelian science. Thus, Barnes says: ‘the syllogism is in fact an incidental adjunct to the theory of demonstration: the theory can be formulated without reference, explicit or implicit, to Syllogistic, and itcould havebeen discovered by someone who knew nothing whatever about the Syllogism’ (pp. 33–4). (shrink)

In his 1910 book On the principle of contradiction in Aristotle, Jan Łukasiewicz claims that syllogistic is independent of the principle of contradiction . He also argues that Aristotle would have defended such a thesis in the Posterior Analytics. In this paper, we first show that Łukasiewicz's arguments for these two claims have to be rejected. Then, we show that the thesis of the independence of assertoric syllogistic vis-à-vis PC is nevertheless true. For that purpose, we first establish that there (...) is no possibility to account for Aristotle's original views on syllogistic without using per impossibile deductions. At last, following an idea due to Smith 1983, we prove that there is a complete reconstruction of assertoric syllogistic using ecthesis instead of reductio ad absurdum. Contrary to what is claimed in Smith 1983, we show that Smith's system SE has to be improved for such a reconstruction. This results in an ecthetic system which is complete with respect to syllogistic arguments, not explosi.. (shrink)

Mencius, a prominent Confucian philosopher in the Warring States period of ancient China, is well-known for his argumentative skills, including his refutational skills used to maintain his own standpoints. This paper attempts to reveal how Mencius refuted his opponents argumentatively and strategically on the issue of human nature. To this end, the pragma-dialectical approach to argumentation is adopted to first reconstruct Mencius’s argumentative discourse on human nature according to the four stages in critical discussion—the confrontation, opening, argumentation and concluding stages. (...) Under the ancient Chinese historical and cultural context, Mencius’s argumentative discourse about human nature was developed in three critical discussions, between Mencius the protagonist, and his explicit interlocutors and implicit adversaries who held different views on human nature—the antagonists. The discussions were undertaken around three single mixed differences of opinion concerning three propositions, with resolution of the first difference of opinion serving as a starting point of the second, and the resolution of the second as a starting point of the third. Then based on the reconstruction, the paper elaborates the refutational strategies that Mencius employed in various stages, such as dissociation, reductio ad absurdum based on refutational analogy, and conciliation. It further points out that the employment of these strategies is strategic maneuvering undertaken by Mencius in an attempt to realize both dialectical and rhetorical aims. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called 'Reductio ad Hitlerum (RAH)'. RAH is a species of the reductio ad hominem genre of logically fallacious reasoning. It is clear that ad hominem arguments, such as RAH, may be understood as “fallacies of relevance”. The most notorious example of the RAH in philosophy is the association of Martin Heidegger with Hitler and the Nazi Party. The RAH makes it seem as though philosophically critiquing the (...) Cartesian worldview or providing proofs of valid inference in a formal logic course would be tantamount to being desirous of perpetrating the Holocaust. Thus, the logical question regarding the truth‐value of Heidegger's philosophical claims is separate from the moral question of whether actions perpetrated by “Nazis”, or in the name of “Nazism”, were evil. (shrink)

In the present article I attribute to the common topic in the Rhetoric a two-fold suggestive function and a guarantee function. These three functions are possible because this type of topic, while often quite abstract, nevertheless contains thought-steering, substantial terms, and formulates a generally empirical or normative endoxon. Assuming that according to Aristotle an enthymeme has at least two premises, it would appear that a common topic is the abstract principle behind the often implicit major premise. This means that (...) the topic may be regarded as the – generalizing – if-then statement in a modern argumentation scheme. Therefore it should be possible to see the enthymemes of Rhetoric 2.23 as a combination of a logical argument form (which can usually be reconstructed as modus ponens) and an argumentation scheme – even though we may not attribute this idea to Aristotle himself. (shrink)

Ghazālī’s The Incoherence of the Philosophers is an unusual philosophical work for a number of reasons, not the least of which is the author’s explicit disavowalof any of the conclusions contained within it. The present essay examines some of the hermeneutical challenges that face readers of the work and offers anexegetical account of the much-neglected Third Discussion, which examines a key point of Neoplatonic metaphysics. The paper argues that Ghazālī’s maintaining of the incompatibility of metaphysical creationism and Neoplatonic emanationism should (...) not be viewed as simply a rhetorical or dialectical argument, but rather is best understood, to use Ghazālī’s words, as a philosophical “proof.” Essential to this proof in the solution to the argument of the Third Discussion is an implicit theory of metaphorical predication that can be pieced together from several of Ghazālī’s remarks as well as a reductio ad absurdum argument about the very possibility of ethical discourse. (shrink)

The ‘Private Language’ sections of the Philosophical Investigations §§ 243–315 serve to undermine the idea that our ordinary felt sensations, e.g., of heat, or cold, or pain, together with our experienced impressions of colour or of sound, are ‘private’ or ‘inner’ objects, where an object mirrors in the mental realm what we associate with that of the physical. This paper explores Wittgenstein's method in these sections, together with the work of several of his commentators who agree with his ‘therapeutic’ approach (...) to the denial of a possible private language. More significantly, however, it discovers a paradox in the fact that a number of philosophers who claim that his ‘Argument Against Private Language’ is unsuccessful point in reaching this conclusion to the very features concerning first-person sensation ascription that Wittgenstein employs to reveal that our ordinary sensations are not ‘private’ to us in that sense identified in § 243, which talks of ‘a language used to refer to what only its speaker can know’, viz, ‘his immediate private sensations’. This helps to explain why there is still no general agreement on the significance of §§ 243–315. (shrink)

Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. Lukasiewicz (...) evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof. This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted. This paper points out that if Aristotle had not been establishing an underlying logic but he was instead axiomatizing a theory of terms, Aristotelians could not claim for Aristotle the title Founder of Logic. People who take Euclid, Peano, and Zermelo to have first axiomatized geometry, arithmetic, and set theory, respectively, do not think that this qualifies them for the titles Founder of Geometry, Founder of Arithmetic, and Founder of Set Theory, respectively. Such people do think that this would qualify the three for the titles Founder of Axiomatic Geometry, Founder of Axiomatic Arithmetic, and Founder of Axiomatic Set Theory, respectively: titles that carry no honors in logic. Being the Founder of Axiomatic Term Theory would likewise carry no honors in the field of logic. CORRECTION: The paper inadvertently implied that Euclid was the first to axiomatize geometry. In order to understand Aristotle’s Analytics as a treatise on demonstration it helps to realize that axiomatized geometry was studied in Plato’s Academy when Aristotle was a student. Euclid was the author of the only ancient axiomatized geometry now available. (shrink)

Aristotle's Categories can easily seem to be a statement of a naïve, pre-philosophical ontology, centered around ordinary items. Wolfgang-Rainer Mann argues that the treatise, in fact, presents a revolutionary metaphysical picture, one Aristotle arrives at by (implicitly) criticizing Plato and Plato's strange counterparts, the "Late-Learners" of the Sophist. As Mann shows, the Categories reflects Aristotle's discovery that ordinary items are things (objects with properties). Put most starkly, Mann contends that there were no things before Aristotle. The author's (...) class='Hi'>argument consists of two main elements. First, a careful investigation of Plato which aims to make sense of the odd-sounding suggestion that things do not show up as things in his ontology. Secondly, an exposition of the theoretical apparatus Aristotle introduces in the Categories--an exposition which shows how Plato's and the Late-Learners' metaphysical pictures cannot help but seem inadequate in light of that apparatus. In doing so, Mann reveals that Aristotle's conception of things--now so engrained in Western thought as to seem a natural expression of common sense--was really a hard-won philosophical achievement. Clear, subtle, and rigorously argued, The Discovery of Things will reshape our understanding of some of Aristotle's--and Plato's--most basic ideas. (shrink)

The uses and interpretation of reductio ad absurdum argumentation in mathematical proof and discovery are examined, illustrated with elementary and progressively sophisticated examples, and explained. Against Arthur Schopenhauer’s objections, reductio reasoning is defended as a method of uncovering new mathematical truths, and not merely of confirming independently grasped mathematical intuitions. The application of reductio argument is contrasted with purely mechanical brute algorithmic inferences as an art requiring skill and intelligent intervention in the choice of hypotheses and (...) attribution of contradictions deduced to a particular assumption in a contradiction’s derivation base within a reductio proof structure. (shrink)

Which properties are characteristic of the enthymeme in Aristotle's Rhetoric? There is no consensus on this point. The present discussion centres on three properties. 1. Is there always an implicit premise? (Answer: Above all, a pragmatic level and a logical level must be distinguished.) 2. Do the premises consist by definition of probabilities and signs? (Answer: No.). 3. Are all enthymemes reducible to a syllogistic form? (Answer: The literature pertaining to this question is dominated by a false dilemma: (...) an enthymeme does not have either a topical or a syllogistic structure). In general, Aristotle's approach to the enthymeme in the Rhetoric appears to shift from argumentation theory to logic. (shrink)

This paper argues that Aristotle’s Metaphysics Z.3 deploys a reductio against the claim that ‘substances underlie by being the subjects of predication’, in order to demonstrate the need for a new explanation of how substances underlie. Z.13 and H.1 corroborate this reading: both allude to an argument originally contained in Z.3, but now lost from our text, that form, matter and compound ‘underlie’ in different ways. This helps explain some of Z’s peculiarities—and it avoids committing Aristotle to self-contradiction (...) about whether matter is substance, a claim denied in the reductio but endorsed elsewhere. (shrink)

In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises (contrary and contradictory) (...) studied by the Stagerian in the Analytica Priora (B15). According to him, the following syllogisms are valid from opposite premises, in which small Latin letters stand for terms such as subject and predicate, and capital Latin letters stand for the categorical propositions such as in the traditional notation: (i) in the second figure, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), and Aba,Oba ` Oaa (Baroco); (ii) in the third one, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) and Eab, Iab ` Oaa (Ferison). Finally, we discuss the passage from the Analytica Posteriora (A11) in which Aristotle states that the Principle of Non-Contradiction is not generally presupposed in all demonstrations (scientific syllogisms), but only in those in which the conclusion must be proved from the Principle; the Stagerian states that if a syllogism of the first figure has the major term consistent, the other terms of the demonstration can be each one separately inconsistent. These results allow us to propose an interpretation of his deductive theory as a broad sense paraconsistent theory. Firstly, we proceed to a hermeneutical analysis, evaluating its logical significance and the interplay of the results with some other points of Aristotle’s philosophy. Secondly, we point to a logical interpretation of the Aristotelian syllogisms from opposite premises in the antilogisms method proposed by Christine Ladd-Franklin in 1883, and we also present a logical treatment of the Aristotelian demonstration with inconsistent material in the paraconsistent logics Cn, 1 _ n _!, introduced by da Costa in 1963. These two issues seem having not yet been analysed in detail in the literature. (shrink)

This paper considers some aspects of the early conception and use of the infinite in ancient Greece, in the spirit of recent results in the history of ancient mathematics. It follows aspects of the practice of reasoning ad infinitum from the extant corpus of and about Zeno of Elea up to early Hellenistic examples in Aristotle and Euclid. Starting with the idea of ‘reasoning from indefinite iteration’, based on the metalogical recognition of the unachievability of an inference process, it (...) identifies several different classes of more or less sophisticated arguments that make use of this idea, and examines the logical devices and notions required for their acceptance in the philosophical practice. Those include ‘Infinite regress’ properly speaking, where Non-Contradiction is used in the formation of indirect infinitary arguments. (shrink)

In Plato’s Parmenides 132a-133b, the widely known Third Man Paradox is stated, which has special interest for the history of logical reasoning. It is important for philosophers because it is often thought to be a devastating argument to Plato’s theory of Forms. Some philosophers have even viewed Aristotle’s theory of predication and the categories as inspired by reflection on it [Owen 1966]. For the historians of logic it is attractive, because of the phenomenon of self-reference that involves. Bocheński denies (...) any possibility of correct logical reasoning before Aristotle. In particular, he flatly declares of Plato that “correct logic we find none in his work” [1951, 15]. In this line, many papers have been written that call attention to the violation of a metalogical principle – the type rules – because of the Third Man Paradox. The problem of interpretation of the paradox raised many discussions, since the 50’s, and the literature devoted to this topic is today enormous. Nevertheless, many points in Plato’s reasoning remain obscure. Hitherto, it is commonly believed that the paradox was simply stated by Plato in his "Parmenides", but not actually solved. Even more, it is believed that it is hardly possible for Plato to have suggested a solution, because he confused the categories of substance and attribute. B. Russell has also argued that Plato violates in his arguments the restrictions imposed on language by the theory of logical types. This view is encouraged by the linguistic difficulties, which Plato has faced in his attempt to formulate an ontology of abstract entities, i.e. that in Greek language abstract and concrete terms are formally indistinguishable [Kneales 1984]. In this paper, we analyse the logical structure of the argument in an attempt to give a systematic consistent reconstruction of the text appealing to methods and concepts of modern logic and semantics. Already in 1954 G. Vlastos had noted in his seminal paper “The ‘Third Man’ Argument in the Parmenides” that “if any progress … is to be made at this juncture it must come from some advance in understanding the logical structure of the Argument”. Accordingly, our analysis is primarily focused on the line of logical reasoning, rather than the metaphysical underpinnings and philosophical implications of the paradox for Plato’s theory of Forms. We divide the Platonic text into three parts, presenting apparent thematic coherence: a) Formulation of the Third Man Paradox (132a-132b). The central issue of this part is a step-like generation of Forms that can continue ad infinitum. b) Discussion of the paradoxical situation (132b-c), by passing to the use of terminology echoing Eleatic philosophy. The concept of “thought” and the underlying semantics of Eleatic origin are central in this passage. c) Solution of the paradox (132d-133a). In our view, this part contains not only a resemblance regress, as most interpretators con-sider, but also the solution of the paradox by the introduction of a sound definition of the concept of “similarity”. We should note that the name ‘Third Man Paradox’ never occurs in Plato, who, strictly speaking, formulates a ‘Third Large Paradox’. The name ‘Third Man Paradox’ appears in the works of Aristotle and the commentators of the Peripatetic tradition. Later commentators have identified Aristotle’s Third Man with Plato’s Third Large Argument. In our paper, we also examine other testimonies about the Third Man Paradox found in the works of commentators in order to illuminate the logical structure of the argument. Although the vocabulary used in these versions is different, they do not affect its logical structure, but rather reveal different understandings by the ancient authors. These testimonies are divided into two main categories: those met in Neo-Platonic authors, notably in Proclus’ "Commentary on Plato’s Parmenides", and the versions of the Third Man Paradox found in texts of the Peripatetic tradition (Eudemus, Aristotle, Alexander). From our discussion, it becomes clear that the approaches to the paradox by the various scholars of antiquity are different, depending also on their participation in the one or the other campus of philosophical thought. We show that the Peripatetic authors are aware of the source of the paradox. However, the first scholar of antiquity who explicitly ascribes a solution to Plato seems to be Proclus. (shrink)

본 논문의 목적은 아리스토텔레스가 『니코마코스 윤리학』 3권 5장에서 초반부에 제시한 악덕의 자발성 논증을 고찰하는 것이다. 이 논증은 성격과 행동을 개념적으로 혼동했을 뿐만 아니라, 다른 곳에서 제시된 아리스토텔레스의 입장과 상충한다는 비판을 받았다. 이 논증에 선행하는 덕의 자발성 논증 또한 덕행의 자발성을 입증할 뿐인데 덕의 자발성을 결론으로 도출했다는 비판을 받았다. 우리는 이러한 비판에 맞서 우선 선행 논증에서 일종의 생략추론(enthymeme)이 사용되었고, 논증에서 생략된 전제는 3권 5장의 후속 논의에서 완전히 몰지각한 사람 외에 누구나 아는 것으로 간주된 것이라는 해석을 제안한다. 다음으로 우리는 악덕의 자발성 논증을 (...) 소크라테스를 겨냥한 대인 논증(ad-hominem argument)으로 재구성하길 시도한다. 특히, 위(僞)-플라톤의 대화편 『정의에 관하여』에서 소크라테스가 악덕의 비자발성을 옹호하면서 유덕하게 행동하는 것과 유덕한 것을 등치시킨 점에 주목할 것이다. 우리는 아리스토텔레스가 이 점을 자신의 대인 논증에서 이용했지만, 이 점을 스스로 인정할 필요가 없었고, 자신의 입장을 일관적으로 유지하길 바라는 이상, 그럴 수도 없었다고 주장한다. (shrink)

Cicero, Lucullus 38: ‘…non potest animal ullum non adpetere id quod accommodatum ad naturam adpareat …’ From earliest childhood every man wants to possess something. One man collects horses. Another wants gold. Socrates has a passion for companions. He would rather have a good friend than a quail or a rooster. In this way, Socrates begins his interrogation of Menexenus. He then congratulates Menexenus and Lysis for each having what he himself still does not possess. How is it that one (...) gets a friend, Socrates asks? Since the nineteenth century many who have read these lines have found them repulsive. Scholars have damned the Lysis for its selfish egoism, for regarding persons as personal belongings. At the turn of the century some sought to discredit the dialogue as a forgery and a calumny. Others debated the dating of the dialogue as Socratic or Platonic, seeking whom to blame rather than whom to credit. And those who have regarded the dialogue as Platonic have tried to redeem it by detecting hints of Plato's theory of Forms. A few have attempted to salvage reputations by understanding the argument of the Lysis as a reductio of egoism, or else by invoking the loyalty of Socrates' friends and the history of Plato's friendship for Dion of Syracuse to speak up for their defence. Guthrie has condemned the dialogue as a failure of method and presentation , and Vlastos has pronounced it a failure of love: ‘The lover Socrates has in view seems positively incapable of loving others for their own sake, else why must he feel no affection for anyone whose good-producing qualities he did not happen to need?’ The Lysis appears to make no positive contribution to the Greek tradition on friendship when compared to the Symposium or the Phaedrus. And in the subsequent tradition, whatever Aristotle might have borrowed from the dialogue he uses for his own purposes. Aristotle too is quite critical of specific points raised in the Lysis. Now it might seem that Aristotle made a place for the selfish love of the Lysis in his own theory, as an inferior grade of utility love. But even this cannot be so, if we are to agree with recent studies of Aristotle's ethics. According to Aristotle, if a client is friendly to his benefactor because of the latter's usefulness, this utilitarian motive must accompany a genuine concern for the benefactor's own interest in that relation, if they are to be friends. Inferior and genuine friendship may differ in purpose but not in regard for the well-being of the beloved. This respect for the object of one's love has no parallel in the Lysis, according to the standard reading of the dialogue. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Ad Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematics and Putting the Body Back InTony E. JacksonAd Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematics and Putting the Body Back In, by Brian Rotman; xii & 203 pp. Stanford: Stanford University Press, 1993, $39.50 cloth, $12.95 paper.Brian Rotman’s book attempts to pull mathematics—the last, most solid home of metaphysical thought—off (...) its absolutist foundations and into the roiling current of postmodernism. His argument works in what has by now become a rather standard manner. He shows how the grounding ideas of mathematics rest upon the insupportable assumption of a realm of absolute truth, “truth perfect, truth outside time, outside space, outside the material world of matter, energy, and entropy, truth somehow able to be discovered or apprehended but never invented” (p. 19). Rotman questions this Platonic grounding in a number of ways.First, with the help of linguistics (de Saussure, Benveniste, Wittgenstein, and Peirce) he provides a semiotic analysis of mathematical arguments as real-world linguistic events. Proof he looks at “not as a form of inference engaged in preserving eternal truths, but as an historically conditioned species of rhetoric” (p. 35). Secondly, Rotman argues that one idea has most secured the fortress-like solidity of mathematical Platonism: the idea of ad infinitum or infinite iteration. Mathematics takes off from the givenness of the natural numbers, our everyday 1, 2, 3 and so on to infinity. It is the “so on to infinity” that frames up the house of arithmetic as it has stood since Euclid. (Euclidean in this context is equivalent to Platonic in the context of philosophy.) But what is the referent of these numbers? Ultimately they are said to be the symbolic representation of the action of counting, which is the “mathematical ur-cognition” (p. 51). And yet we cannot imagine any material human situation in which counting could actually go on to infinity. Therefore, some impossible, supernatural agent (the ghost of the title) must be projected in order for this conception to exist. Similarly, Rotman argues against the assumption of “perfect repeatability” because this notion depends upon some purely imaginary, ideal identity of object or action that could possibly be repeated. Ad infinitum requires and assumes both a disembodied, metaphysical counter and a disembodied, metaphysical counted.So Rotman sets about putting the body back into this symbolic system by rejecting the idea of ad infinitum. Instead of assuming the existence of counting activities that run, in principle, out to infinity without changing their nature, Rotman posits what he calls “realizable iteration,” that is, counting that admits the necessary dissolution or change of whatever repetitive function you begin with. Put simply, he includes the fact that quantitative accumulation or repetition always eventually brings about a qualitative change: at some point in everyday life a difference of degree of the “same” thing or action inevitably becomes a difference of kind. The natural numbers and the ad infinitum [End Page 390] remain blissfully sheltered from this inescapable real world truth, but Rotman reformulates mathematics so as to include this truth in the very idea of numbering.In fact (and he acknowledges this) he theorizes counting after the model of chaos or complexity theory in the physical sciences. Realizable iteration, he says, will bring in the “qualitative differences” forgotten or repressed (the language of Nietzsche, Heidegger, and Freud runs throughout) in the metaphysical version of number, and “display [the qualitative differences] as the emergent effects of repetition” (p. 131). Even numerical addition, for instance, which had been the most linearly continuous of activities, now will be linear beginning from some initial point, but will become increasingly nonlinear as quantitative increase tends towards some point of qualitative discontinuity with what had come before. The point of discontinuity, though certain to appear, is by its nature not specifiable beyond a horizon of probability, and in this, Rotman aligns his arithmetic not only with chaos theory, but also with quantum mechanics. In an appendix, Rotman elaborates at least to a degree the “pre-elements” of his non-Euclidean arithmetic.As chaos theory does not destroy everyday cause... (shrink)

St. Thomas’s Third Way to prove the existence of God, “Of Possibility and Necessity” (ST 1, q.2, art. 3, response) is one of the most controverted passages in the entire Thomistic corpus. The central point of dispute is that if there were only possible beings, each at some time would cease to exist and, therefore, at some point in time nothing would exist, and because something cannot come from nothing, in such an eventuality, nothing would exist now—a reductio ad (...) absurdum conclusion. Therefore, at least one necessary being must exist. Generations of critics and defenders have contended over St. Thomas’s proof. This article argues that the principle of pros hen analogy is implicit in the Third Way and that once identified explains the ontological dependency of possible beings, as secondary analogates, on the first necessary being, as primary analogate. Thus, without the necessary being as primary analogate, possible beings simply could not exist. The fact that they do exist is evidence for the existence of the necessary being. St. Thomas makes synthesizes the principle of pros hen analogy, as found in Aristotle’s Metaphysics, with the Neoplatonic principle of participation. Aristotle develops pros hen analogy in contradistinction to univocal and equivocal predication as well as to genus in Metaphysics 4.2, 11.3, 12.3-5. Since Scotus and re-enforced by modern analytic logic, philosophers have almost universally regarded any kind of analogical predication as a sub-category of equivocal predication and, thus, implicitly occlude the possibility of considering pros hen analogy in their readings of the Third Way. Distinction of per se and per accidens infinite regress and of radical and natural contingency are also central to understanding the Third Way. While resolving apparent problems in the Third Way, the article also seeks to rehabilitate the doctrine of pros hen analogy as a basic principle in Thomistic and, indeed, Aristotelian metaphysics. (shrink)

For Aristotle and other Greek thinkers, philosophy is itself a rethinking. There are other branches of knowledge, like medicine and mathematics, that each grasp some particular subject matter. Since philosophy or, as it has come to be called, metaphysics is the highest science, its job is to grasp somehow all the other sciences and all their subjects. If the science of a subject requires a type of thinking proper to the subject, then the science of that science requires a rethinking (...) of this and all other subjects. In this paper I explore some of Aristotle’s modes of rethinking philosophy. I am interested in the connection between rethinking philosophy and the kinds of philosophical principles that emerge from this rethinking. I argue that reflexive principles are implicit in rethinking but that theyare projected onto things for systematic reasons. Because my time is short, my discussion is limited to broad brush strokes, but there are so many textual details and so much that is contentious about them that a broad sketch may be the best way to set out my point. It is plausible to proceed this way because Aristotle’s main themes are often much clearer than the details of his discussions and my argument relies only on the broad lines of his organization. (shrink)

What good is logic? -- Seventeen ways this book is different -- The two logics -- All of logic in two pages : an overview -- The three acts of the mind -- I. The first act of the mind : understanding -- Understanding : the thing that distinguishes man from both beast and computer -- Concepts, terms and words -- The problem of universals -- The comprehension and extension of terms -- II. Terms -- Classifying terms -- Categories -- (...) Predicables -- Division -- III. Material fallacies -- Fallacies of language -- Fallacies of diversion -- Fallacies of oversimplification -- Fallacies of argumentation -- Inductive fallacies -- Procedural fallacies -- Metaphysical fallacies -- Short story : love is a fallacy -- IV. Definition -- The nature of definition -- The rules of definition -- The kinds of definition -- The limits of definition -- V. Second act of the mind : judgment -- Judgments, propositions, and sentences -- What is truth? -- The four kinds of categorical propositions -- Logical form -- Euler's circles -- Tricky propositions -- The distribution of terms -- VI. Changing propositions -- Immediate inference -- Conversion -- Obversion -- Contraposition -- VII. Contradiction -- What is contradiction? -- The square of opposition -- Existential import -- Tricky propositions on the square -- Some practical uses of the square of opposition -- VIII. The third act of the mind : reasoning -- What does reason mean? -- The ultimate foundations of the syllogism -- How to detect arguments -- Arguments vs. explanations -- Truth and validity -- IX. Different kinds of arguments -- Three meanings of because -- The four causes -- A classification of arguments -- Simple argument maps -- Deductive and inductive arguments -- Combining deduction and induction : socratic method -- X. Syllogisms -- The structure and strategy of the syllogism -- The skeptics objection to the syllogism -- The empiricist's objection to the syllogism -- Demonstrative syllogisms -- How to construct convincing syllogisms -- XI. Checking syllogisms for validity -- By Euler's circles -- By Aristotle's six rules -- Barbara Celarent : mood and figure -- Venn diagrams -- XII. More difficult syllogisms -- Enthymemes : abbreviated syllogisms -- Sorites : chain syllogisms -- Epicheiremas : multiple syllogisms -- Complex argument maps -- XIII. Compound syllogisms -- Hypothetical syllogisms -- Reductio ad absurdum arguments -- The practical syllogism : arguing about means and ends -- Disjunctive syllogisms -- Conjunctive syllogisms -- Dilemmas -- XIV. Induction -- What is induction? -- Generalization -- Causal induction : Mill's methods -- Scientific hypotheses -- Statistical probability -- Arguments from analogy -- A fortiori and a minore arguments -- XV. Some practical applications of logic -- How to write a logical essay -- How to write a socratic dialogue -- How to have a socratic debate -- How to use socratic method on difficult people -- How to read a book socratically -- XVI. Some philosophical applications of logic -- Logic and theology -- Logic and metaphysics -- Logic and cosmology -- Logic and philosophical anthropology -- Logic and epistemology -- Logic and ethics. (shrink)

Crispin Wright tried to refute classical 'Cartesian' skepticism contending that its core argument is extendible to a reductio ad absurdum (_Mind<D>, 100, 87-116, 1991). We show both that Wright is mistaken and that his mistakes are philosophically illuminating. Wright's 'best version' of skepticism turns on a concept of warranted belief. By his definition, many of our well-founded beliefs about the external world and mathematics would not be warranted. Wright's position worsens if we take 'warranted belief' to be implicitly (...) defined by the general principles governing it. Those principles are inconsistent, as shown by a variant of Godel's argument. Thus the inconsistency Wright found has nothing to do with the special premises of Cartesian skepticism, but is embedded in his own conceptual apparatus. Lastly, we show how a Cartesian skeptic could avoid Wright's critique by reconstructing a skeptical argument that does not use the claims Wright ultimately finds objectionable. (shrink)

Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...) middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. -/- Keywords Plato; early dialogues; middle dialogues; being; knowledge; development -/- Introduction The differences between two groups of the early and middle period dialogues have always been a matter of dispute. Whereas the developmentalists like Vlastos, Silverman (2002), Teloh (1981), Dancy (2004) and Rickless (2007) think that from the early to the middle dialogues Plato’s philosophy changes, at least in some essential points, the unitarists like Kahn, Cherniss and Shorey believe that there happens no development and the differences must be taken as natural, ignorable and even pedagogic. In his well-known article, Socrates contra Socrates in PLATO, Vlastos lists ten theses of difference between two groups of dialogues. The first group which includes Plato’s early dialogues he divides to 'elenctic' (Apology, Charmides, Crito, Euthyphro, Gorgias, Hippias Minor, Ion, Laches, Protagoras and Republic I) and 'transitional' (Euthydemus, Hippias Major, Lysis, Menexenus and Meno) dialogues. These transitional come after all the elenctic dialogues and before all the dialogues of the second group which compose Plato’s middle period dialogues, including (with Vlastos' chronological order) Cratylus, Phaedo, Symposium, Republic II-X, Phaedrus, Parmenides and Theaetetus (1991, 46-49). Vlastos asserts strictly that his list of differences are 'so diverse in content and method that they contrast as sharply with one another as with any third philosophy you care to mention, beginning with Aristotole’s' (ibid, 46). Vlastos’ list of differences between two Socrateses is considered a view breaking sharply between the early and the middle dialogues. Besides all ten differences between the two Socrateses in Vlastos’ list that can be supportive for our doctrine here, we intend to focus on some ontological as well as epistemological distinctions that have not completely been discussed hitherto. Contrary to the developmentalist theory of Vlastos, unitarian theory of Charles Kahn wishes to eliminate any substantial difference between the early and the middle dialogues. He distinguishes seven 'pre-middle' or 'threshold' dialogues including Laches, Charmides, Euthyphro, Protagoras, Meno, Lysis and Euthydemus from the other Socratic dialogues which he calls 'earliest group' (1996, 41). The threshold dialogues, Kahn thinks, 'embarke upon a sustained project' that is to reach to its climax in the middle period dialogues, namely Phaedo, Symposium and Republic. Believing in that there is no 'fundamental shift'between the early and middle dialogues (ibid, 40), Kahn thinks the Socratic dialogues are just the 'first stage' with a 'deliberate silence' towards the theories of later periods (ibid, 339). One of the reasons of the surprising fact that Plato gives no hint of the metaphysics and epistemology of the Forms in the early dialogues, he thinks, is the pedagogical advantages of aporia. He thinks that Plato 'obscurely', and mostly because of education, hinted to some doctrines and conceptions in his early dialogues and with the aim of clarifying them only in the later ones (ibid, 66). The seven threshold dialogues, Kahn asserts, 'had been designed from the first' to prepare the pupils and readers for the views expounded in the middle period dialogues (ibid, 59-60). To show that the differences of the two Socrateses of the early and middle period dialogue are in their onto-epistemological grounds and thence cannot be explained by a unitaristic view, we try to draw the ontological and epistemological principles of the early dialogues in the first part below in order to show, in the second part, that those principles have been developed in the middle period dialogues. -/- A. The Onto-Epistemologic Principles of the Early Dialogues Socratic dialogues are paradoxical about knowledge because while being knowledge-oriented always searching for knowledge, they deny it and even never discuss it directly. Three elements of Socrates’ way of searching Knowledge throughout the early dialogues, i.e. Socratic 'what is X?' question, his disavowal of knowledge and his elenctic method combined together produce something like a circle which works, more or less, in the same way in these dialogues. Though this circle is an embaressing inquiry always resulting in ignorance instead of knowledge, its motivation is surprisingly Socrates’ passionate enthusiasm for knowledge, an intensive love of wisdom. The starting point of this circle is Socrates’ confession of having no knowledge which might be explicitly asserted or presupposed, maybe because it was one of the famous characteristics of Socrates; a confession always paradoxically accompanied with his intense longing for knowledge (e.g., Gorgias 505e4-5). Every time Socrates encounters with someone who thinks he knows something (οἴεταί τι εἰδέναι) (Apology 21d5) and tries to examine him. This examination seems to be the simplest one asking just what it is that he knows. Socrates’ elenchus, therefore, is always connected with 'what is X?' (τίς ποτέ ἐστιν) question, a question that most of the early dialogues of Plato are concerned with; 'what is courage?' in the Laches, 'what is piety?' in Euthydemus, 'what is temperance?' in Charmides and 'what is beauty?' in Hippias Major. This question we call here 'Socratic question' and probably is the very question the historical Socrates used to employ, is tightly interrelated with both his disavowal and his elenchus. He disclaims knowledge because he cannot find the answer to the question himself and he rejects others’ since they cannot offer the correct answer too. Every interlocutor can claim he knows X, if and only if he can answer the Socratic question. Otherwise, he is more of an ignorant than of a knower of τί ποτέ ἐστι X. Knowing the answer to this question is, thus, knowledge’s criterion for Socrates. Having found out that he cannot answer what it is which he would claim to know, the interlocutor comes to the point Socrates was there at the beginning. The least advantage of this circle is that he becomes as wise as Socrates does about the subject, becoming aware that he does not know it. At the end of the circle they are both still at the beginning, not knowing what X is. So let us first take a glance at these three elements. Socratic disavowal of knowledge is strictly asserted in some passages. At Apology 21b4-5, Socrates says: -/- I do not know of myself being wise at all (οὔτε μέγα οὔτε σμικρὸν σύνοιδα ἐμαυτῷ σοφὸς ὤν) -/- Moreover, at 21d4-6: -/- None of us knows anything worthwhile (καλὸν κἀγαθὸν εἰδέναι) …. I do not know (οἶδα) neither do I think I know. -/- In Charmides Socrates speaks about a fear about his probable mistake of thinking that he knows (εἰδέναι) something when he does not (166d1-2). The somehow generalization of this disavowal can be seen in Gorgias. After calling his disavowal 'an account that is always the same' (509a4-5), Socrates continues (a5-7): -/- I say that I do not know (οἶδα) how these things are, but no one I have ever met, like now, who can say anything else without being absurd. -/- At the end of Hippias Major (304d7-8), Socrates affirms his disavowal of knowledge of 'what is X?' this time about the fine: -/- I do not know (οἶδα) what that is itself (αὐτὸ τοῦτο ὅτι ποτέ ἐστιν). Some other passages, however, made a number of scholars dubious about Socrates’ disavowal. Vlastos mentions Apology 29b6-7 as an evidence : 'that to do wrong and to disobey one’s master, both god and men, I know (οἶδα) to be evil and shameful'. He thinks that if we give this single text 'its full weight' it can suffice to show that Socrates does claim knowledge of a moral truth (1985, 7). Vlastos’ claim is not admittable since it would be too strange, I think, for a man like Socrates to violate his disavowal claim just after emphasizing it. We can see his claim just before the already mentioned passage: -/- And surely it is the most blameworthy ignorance to believe that one knows what one does not know. It is perhaps on this point and in this respect, gentlemen, that I differ from the majority of men and if I were to claim that I am wiser than anyone in anything it world be in this, that, as I have no adequate knowledge (οὐκ εἰδὼς ἱκανῶς) of things in the underworld, so I do not think I have (οὐκ εἰδέναι) (Apology 29b1-6) Vlastos tries to solve what he calls the 'paradox' of Socrates’ disavowal of knowledge distinguishing the 'certain' knowledge from 'elenctic' knowledge (1985, 11) and thinking that when Socrates avows knowledge, we must perceive it as an elenctic knowledge, a knowledge its content 'must be propositions he thinks elenctically justifiable' (ibid, 18). Irwin’s solution is the distinction of knowledge and belief. He approves that Socrates does not 'explicitly' make such a distinction, but still thinks that Socrates’ 'test for knowledge would make it reasonable for him to recognize true belief without knowledge, and his own claims are easily understood if they are claims to true belief alone' (1977, 40). While I agree with Vlastos up to a point, I strongly disagree with Irwin about the early dialogues. As I will try to show below, we are not permitted to consider any kind of distinction within knowledge in Socratic dialogues because only one category of knowledge is alluded to there and the distinction of knowledge and belief thoroughly belongs to the second Sorcates. Although no kind of distinction can be admittable here, I think Vlastos’ distinction can be accepted only if we regard it as a distinction between knowledge, which is unique and without any, even incomparable, rival, and a semi-idiomatic and ordinary one that is a necessary requirement for any argument, and thus, unavoidable even for someone who does not claim any kind of knowledge. An apparent evidence of this is Gorgias 505e6-506a4: -/- I go through the discussion as I think it is (ὡς ἄν μοι δοκῇ ἔχειν), if any of you do not agree with admissions I am making to myself, you must object and refute me. For I do not say what I say as I know (οὐδὲ γάρ τοι ἔγωγε εἰδὼς λέγω ἃ λέγω) but as searching jointly with you (ζητῶ κοινῇ μεθ᾽ ὑμῶν). -/- The minimal degree of knowledge everyone must have to take part in an argument, conduct it and use the phrase "I know" when it is necessary is what Socrates cannot deny. We can call it elenctic knowledge only if we agree that it is not the kind of knowledge that Socrates has always been searching, the one that can be accepted as the answer of Socratic 'what is X?' question. His disavowal of knowledge is applied only to the knowledge which can truly be the answer of Socratic question and pass the elenctic exam; a knowledge that, I believe, is never claimed by first Socrates. Socrates conducts his method of examining his interlocutors’ knowledge, our second element here, by almost the same method repeated in Socratic dialogues. That whether we are allowed to regard all the examinations of Socrates in the early dialogues as based on the same or not has been a matter of dispute. Vlastos himself (1994, 31) distinguished Euthydemas, Lysis, Menexenns and Hippias Major from the other Socratic dialogues because he thinks Socrates has lost his faith to elenchus in there. Irwin (1977, 38) distinguishes Apology and Crito where Socrates’ own convictions is present. Contrary to some scholars like Benson (2002, 107) who take elenchus in all the Socratic dialogues as a unique method, Michelle Carpenter and Ronald M. Polansky (2002, 89-100) argue pro the variety of methods of elenchus. Thomas C. Brickhouse and Nicholas D. Smith (2002, 145-160) even reject such a thing as Socratic elenchus which can gather all of the Socrates’ various arguments under such a heading. There can be no solution for the problem of elenchus, they think, is due to 'the simple reason that there is no such thing as 'the Socratic elenchos"'(p.147). Though we consider elenchus a somehow determined process and a part of Socratic circle in the early dialogues, all we assume is that whatever differences it might have in different dialogues, it has the same onto-epistemological principles and, thus, we are not going to take it necessarily as a unique method. This method sets out to prove that the interlocutors are as ignorant as Socrates himself is. That whether elenchus is constructive, capable of establishing doctrines as Vlastos (1994) or Brickhouse and Smith (1994, 20-21) believe or not is another issue to which this paper is not to claim anything. What is crucial for our discussion here is that elenchus does not reach to the very knowledge Socrates is looking for. This is strictly against Irwin who thinks that not only elenchus leads to positive results, 'it should even yield knowledge to match Socrates’ conditions'(1977, 68, cf. 48). He does not explain where and how they really yield to that kind of knowledge. He explains his elenctic method in his apology in the court (Apology 21-22), that how he used to examine wise men, politicians, poets and all those who had the highest reputation for their knowledge and every time found that they have no knowledge. If we accept, as I strongly do, that Socrates’ disavowal of his knowledge is not irony, it might seem more reasonable to agree that the process that has that disavowal as its first step cannot be irony as well. The key of the circle which can explain why Socrates disclaims knowledge and how he can reject others’ claim of having any kind of knowledge lies in the third element, Socratic question. In Hippias Major (287c1-2), Socrates asks: 'Is it not by Justice that just people are Just? (ἆρ᾽ οὐ δικαιοσύνῃ δίκαιοί εἰσιν οἱ δίκαιοι). He insists at 294b1 that they were searching for that by which (ᾧ) all beautiful things are beautiful (cf. b4-5, 8). At Euthyphro 6d10-11 it is said that the Socratic question is waiting for 'the form itself (αὐτὸ τὸ εἶδος) by which (ᾧ) all the pious actions are pious; and at 6d11-e1: -/- Through one form (που μιᾷ ἰδέᾳ) impious actions are impious and pious actions pious. -/- Since the X itself is that by which X is X, knowing 'X itself' is the only way of knowing X. It is probably because of this that Socrates makes the distinction between the ousia as a right answer to the question and effect as a wrong one: -/- I am afraid, Euthyphro, that when you were asked what piety is (τὸ ὅσιον ὅτι ποτ᾽ ἐστίν) you did not wish to make clear its nature itself (οὐσίαν … αὐτοῦ) to me, but you said some effect (πάθος) about it. (Euthp. 11a6-9) -/- 1. Knowledge of what X is Now it is time to look for the onto-epistemological principles of Socratic circle and its three elements. It cannot reasonably be expected from the first Socrates to present us explicitly and clearly formulated principles of his onto-epistemology when such explications cannot be found even in the second Socrates who has some obviously positive theoris. Since there must be some principles underlying this first systematic inqury of knowledge, we must seek to them and be satisfied with elicitation of the first Socratas’ principle. What will be drawn out as his principles cannot and must not, thus, be taken as very fix and dogmatic principles. Some very slightest principles and grounds suffice for our purposes here. The first principle that is the prima facie significance of the Socratic question and his implementation of all those elenctic arguments I call the principle of 'Knowledge of What X is' (KWX): -/- KWX To know X, it is required to know what X is. -/- Aristotle (Metaphysics 1078b23-25, 27-29, 987b4-8) takes Plato’s τί ἐστι question as seeking the definition of a thing that is the same as historical Socrates’ search but applying to a different field. That Plato’s 'what is X?' question was a search for definition became the prevailed understanding of this question up to now. I am going neither to discuss the answer of Socratic question nor to challenge taking it as definition. What I am to insist is that knowledge is attached firmly to the answer of the question: Knowledge of X is not anything but the knowledge of what X is. It entails, certainly, the priority of this knowledge to any other kind of knowledge about X but it also has something more fundamental about the relation of knowledge and Socratic question. Socrates’ exclusive focus on the answer of his question can authorize the consideration of such an essential role for KWX in his epistemolgoy. The total rejection of his interlocutors’ knowledge when they are unable to answer the question can be regarded as a strong evidence for it. Socrates’ elenctic method and his rejection of others’ knowledge in the early dialogues, which all end aporetically with no one accepted as knower and nothing as knowledge, prevent us from finding any positive evidence for this. We have to be content, therefore, of negative evidences which, I think, can be found wherever Socrates rejects his interlocutors’ knowledge when they are not able to give an acceptable answer to his 'what is X?' question. 2. Bipolar Epistemology Socrates’ rejection of his interlocutors’ knowledge has another epistemological principle as its basis. Let me call this principle Bipolar Epistemology' (BE): BE There is no third way besides knowledge and Ignorance. -/- BE says that about every object of knowledge there are only two subjective statuses: knowledge and Ignorance. Socrates’ disavowal, however, says nothing but that he is ignorant of knowledge of X because he does not know what X is. This means that BE is presupposed here. Socrates’ elenchus and his rejection of interlocutors’ having any kind of knowledge are the necessary results of the fact that he does not let any third way besides knowledge and ignorance. The first Socrates never let anyone partly know X or have a true opinion about it, as he would not let anyone know anything about X when he did not know what X is. -/- 3. Bipolar Ontology The principle of BE in first Socrates’ epistemology is parallel to another principle in his ontology. Plato’s bipolar distinction between being and not being is as strict and perfect as his distinction between knowledge and ignorance. This principle I shall call the principle of 'Bipolar Ontology' (BO): BO Being is and not being is not. BO is apparently the same with the well-known Parmenidean Principle of being and not being (cf. Diels-Kranz (DK) Fr. 2.2-5). Euthydemus’ statement against the possibility of false knowledge can be good evidence for this principle: -/- The things which are not surely do not exist (τὰ δὲ μὴ ὄντα … ἄλλο τι ἢ οὐκ ἔστιν). (Euthydemus 284b3-4) -/- He continues (b4-5): -/- There is nowhere for not being to be there (οὖν οὐδαμοῦ τά γε μὴ ὄντα ὄντα ἐστίν). -/- That BE does not let true opinion as a third option besides knowledge and ignorance seems to be related to BO’s rejecting a third option besides being and not being, which is itself the basis of the impossibility of false belief. Socrates’ elaborate discussion of the problem of false belief in Theatetus that leads to a more decisive discussion and finally to some solutions in Sophist can make our consideration of BO for the first group of dialogues authentive. -/- 4. &5. Split Knowledge and Split Being The fourth principle I shall call the principle of 'Split Knowledge' (SK): -/- SK Knowledge of X is separated from any other knowledge (of anything else) as if the whole knowledge is split to various parts. -/- This Principle is hinted and criticized as Socrates’ way of treating with knowledge in Hippias Major: -/- But Socrates, you do not contemplate the entireties of things, nor do people you have used to talk with (τὰ μὲν ὅλα τῶν πραγμάτων οὐ σκοπεῖς, οὐδ᾽ ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). (301b2-4) -/- Contrary to Rankin who regards the passage as 'antilogical, almost eristic in tone rather than presenting a serious philosophy of being' (1983, 54), I think it can be taken as serious. Hippias criticizes Sorcates that he does not contemplate (σκοπεῖς) the entireties of things (ὅλα τῶν πραγμάτων), a critique which Socrates is not its only subject but all those whom Socrates accustomed to talk with (ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). This last phrase, I think, extends this critic beyond this dialogue to other Socratic dialogues. Hippias’ use of the perfect tense of the verb ἔθω (to be accustomed) is a good evidence of this extension. We can get, thus, these ἐκεῖνοι as Socrates’ interlocutors in his other dialogues that hints that this criticism has the epistemological groundings of the previous dialogues as its subject. What ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι points to is that Hippias does not have in mind Socrates’ way of treating things only in this dialogue, but he is also criticizing Socrates’ way throughout his dialogues. At 301b4-5, Socrates and his interlocutors’ way of beholding things is described as such: -/- You people knock (κρούετε) at the fine and each of the beings (ἕκαστον τῶν ὄντων) by taking each being cut up in pieces (κατατέμνοντες) in words (ἐν τοῖς λόγοις). This leads us to our next principle that is parallel to, and the ontological side of, SK, the principle of 'Split Being'(SB): -/- SB Everything (being) is separated from any other thing as if the whole being is split to many beings. -/- Socrates and his interlocutors and thus, as we saw, the Socratic dialogues are accused to regard everything as it is separated from all other things. This separation is en tois logois that, I think, can reasonably be taken as saying that Socratic dialogues (it refers of course to the dialogues before Hippias Major) cut up all things which have the same name/definition from all other things and try to understand them separately, without considering other things that are not in their logos. They, for example in Hippias Major, are cutting up to kalon and try to understand what it and all others inside this logos are by separating it from all other things. This is directed straightly against Socratic question and the way Socratic dialogues follow to find its answer, every time separating one logos. As Meyer (1995, 85) points out, every question 'presupposes that the X in question in a logos is something' and 'every answer to every question aims at unity' (84). The critique of Hippias Major is, therefore, at the same time a critique of SK and SB. It is also a critique of KWX because it is only based on KWX that Socratic dialogues could search for the answer of 'what is X' question supposing that knowing what X is is enough for the knowledge of X. SK and KWX are absolutely interdependent. What Socrates and all his previous interlocutors have neglected in Socratic dialogues, Hippias says, was 'continuous bodies of being' (διανεκῆ σώματα τῆς οὐσίας) (301b6). Either this theory actually belongs to the historical Hippias as it is being said or not, it is strictly criticizing SB. We have the same phrase with changing sūma to logos some lines later at 301e3-4: διανεκεῖ λόγῳ τῆς οὐσίας. Although this theory that can be observed as both an ontological and an epistemological theory is rejected by Socrates (301cff.), it is still against first Socrates’ onto-epistemological principles and might let us look at what is rejected as Socratic prineple. -/- 6. Knowledge is of Being The sixth principle that I think is presupposed by the first Socrates, is the 'Knowledge of Being' Principle (KB): -/- KB Knowledge is of Being. -/- This principle is obviously the source of the problem of false knowledge, a very important problem throughout Plato’s philosophy. We face this problem maybe for the first time in Euthydemus. In less than 20 Stephanus’ pages, 276-295, we are encountered with different interwoven problems about knowledge , all grounded in the problem of false opinion. Having challenged the obvious possibility of telling lies at 283e, at 284 Euthydemus discusses it saying that the man who speaks is speaking about 'one of those things that are (ἓν μὴν κἀκεῖνό γ᾽ ἐστὶν τῶν ὄντων)' (284a3) and thus speaks what is (λέγων τὸ ὄν) (a5). He must necessarily be saying truth when he is speaking what is because he who speaks what is (τὸ ὄν) and the things that are (τὰ ὄντα) speaks truth (τἀληθῆ λέγει) (a5-6). This is based on Parmenidean principle of the impossibility of being of not being which Euthydemus restates (284b3-4) and we mentioned discussing BO principle above. The things that are not are nowhere (οὐδαμοῦ) and there is no possibility for anyone to do (πράξειεν) anything with them because they must be made as being before anything else can be done, which is impossible (b5-7). The words, then, are of things that exist (εἰσὶν ἑκάστῳ τῶν ὄντων λόγοι) (285e9) and as they are (ὡς ἔστιν) (e10). The result is that no one can speak of things as they are not. It is this impossibility of false speach that is extended to thinking (δοξάζειν) at 286d1 and leads to the impossibility of false opinion (ψευδής … δόξα) (286d4). The general conclusion is asserted at 287a extending this impossibility to actions and making any kind of mistake. Not only knowledge is of being but speech, thought and action are of being simply because of the fact that nothing can be of not being. -/- B. First Socrates’ Principles in the Middle Period Dialogues Out of what were presupposed or criticized mostly in five dialogues, Euthyphro, Euthydemus, Hippias Major, Laches and Charmides, we tried to draw the first Socrates’ principles. Our inquiry here is directed to find out the fate of these principles in the three dialogues of the middle period, Meno, Phaedo and Republic. To do this, first we ought to check the situation of Socratic circle in these dialogues. The Socratic circle that was predominant in the early dialogues, does not look like a circle here anymore though they certainly have some features in common. Meno, Phaedo and Republic II-X are not committed to the principles of the circle and the whole circle in disrupted in them. The difference of the two Socrateses towards acquiring knowledge is obvious. The Socrates of Meno, Phaedo and Republic is evidently more self-confident that he can get to some truths during his arguments as he does. They are in their first appearance, as almost all other dialogues, committed to Socrates’ disavowal. All of them try to keep the shape of the Socratikoi Logoi genre, which is committed to the historical Socrates’ way of discussion; a dramatic personage who is to challenge his interlocutors, ask them and refuse the answers. Nevertheless, the fact is that what we have in common between two groups of dialogues is mostly a dramatic structure. Whereas the first group’s arguments are based on Socrates’ disavowal and lead to no positive results, the second group is decisively going to achieve some positive results. The aim of the first Socrates was to show others that they are ignorant of what they thought they knew. The new Socrates of Meno, on the opposite, makes so much efforts to show that the slave boy has within himself true opinions (ἀληθεῖς δόξαι) about the things that he does not know (οἶδε) (85c6-7). Despite his lack of knowledge, he has true opinions nevertheless. The way from these true opinions to knowledge, as Socrates states, is not so long. These true opinions are now like a dream but 'can become knowledge of the same things not less accurate than anyone’s' (οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων) (c11-d1), if they be repeated by asking the same questions. The most outstanding text regarding Socrates’ disavowal is Meno 98b where he explicitly claims knowledge: -/- And indeed I also speak as (ὡς) one who does not know (εἰδὼς) but is guessing (εἰκάζων). However, [about the fact] that true opinion and knowledge are different, I do not altogether expect (δοκῶ) myself to be guessing (εἰκάζειν), but if I say about anything that I know (εἰδέναι) -which about few things I say- this is one of the things that I know (οἶδα). (98b1-5) This passage is very significant about Plato’s disavowal of knowledge. There can hardly be found, I think, anywhere else in Plato’s corpus where Socrates speaks about his knowledge of something as such. He says first that he speaks as someone who does not know. This ὡς οὐκ εἰδὼς λέγω comparing with what he used to say in the first group, οὐκ οἶδα, has this added ὡς. Socrates does not claim strongly anymore that he does not know anything but speaks only as someone who does not know. He needs this ὡς not only because he is going to accept that he does know some, though few, things immediately after this sentence, but also because he needs his previous disavowal to be loosened from Meno on. He does not merely say here that he knows something. It is then different from the examples mentioned before which could be taken as idiomatic or at least not emphatic. Socrates’ remarkable emphasis on distinguishing εἰδέναι from εἰκάζειν departs it from all other passages where he says only he knows something. Moreover, he claims definitely that he has knowledge about few (ὀλίγα) things. From the early to the middle dialogues, Socrates’ attitude to knowledge has totally renewed its face. He brings forth a new concept, true opinion, and he does not speak of knowledge as he used to before; the rough, perfect and unachievable knowledge of the first group has turned to something more smooth, realistic and achievable. Comparing with the early dialogues that did not set out from the first to reach positive results, the middle ones are extraordinarily and surprisingly positive and hence destroy the basis of the Socratic circle. The questions and answers are purposely directed to some specific new theories; most of them are not directly related to the topics or the main questions of the dialogues. They are suggested when Socrates draws the attention of the interlocutor away from the main question because of the necessity of another discussion. Even if the main question remains unanswered, we have still many positive theories, prominently of metaphysical type. These theories are so abundant and dominant in these dialogues, especially Phaedo and Republic, that one might think that they may appear to be arbitrarily sandwiched in there. This helps dialogues to keep their original Socratic structure while they are suggesting new theories. Hence, the Socratic question of 'what is X?', though is still used to launch the discussion, is loosened and is forgotten for most part of the dialogues. Meno that has first a differently formulated question, 'can virtue be taught?', leads finally to the Socratic question of 'What is virtue?'. Phaedo is dedicated to the demonstration of the immortality of soul and the life after death without having a central Socratic question. The case of Republic is more complicated. The first book, on the one hand, has all the criteria of a Socratic circle: its 'what is justice?' question, Socrates’ strong disavowal (e.g. 337d-e), his rejection of all answers and coming back to the first point without finding out any answer. This Book, considered alone, is a perfect Socratic dialogue, as many scholars regard it as early and separated from other books. The books II-X are, on the other hand, far from implementing a Socratic circle. They have still the 'what is justice?' question as their incentive leading question, but they are, in most of the positive doctrines and methods that encompass the main parts, ignoring the question. Even these books that, I believe, are the farthest discussions from the Socratic circle are so cautious not to break the Socratic structure of the dialogue as long as it is possible. What is changed is not the structure of the dialogue but the ontological and epistemological grounds based on which new theories are suggested. -/- 1. Knowledge of the Good We can clearly see in the second group of dialogues that the KWX principle loses the place it had before in our first group. It is not, of course, rejected, but still we cannot say that it has the same situation. KWX that was based on Socratic question, as we discussed before, was the leading principle of the first Socrates’ epistemology and of the highest position. Other epistemological principles, SK directly and BE indirectly, were relying on Socratic question and therefore on KWX. Such a position does not belong to KWX from Meno on. What makes it different in the second Socrates is another principle that is needed it not only as its complementary principle but also as what is more fundamental. Plato, then, does not reject KWX in this period, but, it seems, he transcends to another more basic principle; a principle we shall call the principle of 'Knowledge of the Good' (KG): -/- KG Knowledge of X requires knowledge of the Good. -/- Whereas all the dialogues of our first group are free from any discuscon about KG, it bears a very important role in the second group so as becomes the superior principle of knowledge in Republic. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). What let us discuss KG as an epistemological principle for the second Secrates is the relation he tries to establish between knowledge and the Good which, though is alongside with the mentioned thesis and the idea of virtue as knowledge, goes much deeper inside epistemology asking to regard the Good as the basis of knowledge. The effort of Phaedo cannot succeed in establishing the Good as the criterion of explanation and knowledge since, I think, it needs a far more complicated ontology of Republic where Socrates can finally announce KG. What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: -/- The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) -/- Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: -/- That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). KG, which had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. As what was quoted clearly proves, this principle is the very one which we can observe as the most fundamental principle of the second Socrates in Republic, corresponding to the role KWX had in the first Socrates. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). -/- 2. Tripartite Epistemology BE is thoroughy rejected in the second Socrates and substituted by its opposite, the principle of 'Tripartite Epistemolgy' (TE): -/- TE Opinion is an epistemological status between knowledge and ignorance. BE of the first Socrates was denying any third way besides knowledge and ignorance which was the foundation of Socratic circle without which Socrates could not reject his interlocutors’ possessing any kind of knowledge. We cannot say, however, that the first Socrates had a third epistemological status in mind but rejected it. Such a status was unacceptable for him so that one can say that he would reject any kind of such status if suggested. There were only two possibilities about knowledge: either one knows something or he does not know it. TE, thus, was not the first Socrates’ discovery and, I think it is not the second Socrates’discovery. All we can see in our second group of dialouges is that he uses this principle as an already demonstrated one. Having examined the slave boy in Meno for the prupose of showing the working of recollection, it truns out that he has some opinions in him while he still does not know. Without trying to prove it, Socrates takes this as the distinction between knowledge and opinion: -/- So, he who does not know (οὐκ εἰδότι) about what he does not know (περὶ ὧν ἂν μὴ εἰδῇ) has within himself true opinions (ἀληθεῖς δόξαι) about the same things he did not know (περὶ τούτων ὧν οὐκ οἶδε) (85c6-7). -/- The same distinction is set between ὀρθὴν δόξαν and ἐπιστήμην at 97b5-6 ff. (also cf. 97b1-2: ὀρθῶς μὲν δοξάζων … ἐπιστάμενος). He connects then their difference to the myth of Daedalus, the statue that would run away and escape. So are true opinions, not willing to remain long in mind and thus not worthy until one ties them down by αἰτίας λογισμῷ (98a3-4). Socrates says that this tying down is anamnesis. We face, in Phaedo, the same relation is settled between knowledge as the process of being tied down and getting the capability to give an account, on the one hand, and anamnesis, on the other hand. When a man knows, he must be able to give an account of what he knows (Phaedo 76b5-6) and since not all people are able to give such an account, those who recollect, recollect what once they learned (76c4). Although the distinction between knowledge and opinion is not explicitly used in Phaedo, referring to the parallel link between knowledge plus account and anamnesis in Phaedo and Meno, one can say that those who cannot recollect are not able to give account and, thus, are in a state of opinion. What is said at Phaedo 84a, though not yet a definite distinction between knowledge and opinion, makes a distinction between their objects so as we can agree that it is presupposed. The soul of the philosopher, Socrates says, follows reason, stays with it forever and contemplates the divine, which is not the object of opinoin (ἀδόξαστον) (84a8, cf. Meno 98b2-5). The distinction of knowledge and belief in Republic has a significant difference with what we discussed in Meno and Phaedo since the distinction of Meno was based on anamnesis and thus more an epistemological distinction. Even in Phaedo that we do not have any elaborate discussion about the distinction, the only hint to the matter at 76 is bound to the theory of anamnesis. In addition to the relation of the distinction with this theory, there is another evidence that does not permit us to consider the distinction as an ontological distinction. Let’s see Meno 85c6-7: -/- So, he who does not know about what he does not know has within himself true opinions about the same things he did not know (τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε). (85c6-7) -/- This last sentence persists that the objects of knowledge and true opinion are the same. What Socrates is to say here is that whereas he does not know X he has true opinion about the same X. I think Socrates’ sentence that the slave boy οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ and his restatement of it by saying περὶ τούτων ὧν οὐκ οἶδε is because he wants to emphasize that the slave boy who does not know, has true opinion about the same thing. Socrates could say this just with using τούτων and there would be no necessity to bring περὶ ὧν ἂν μὴ εἰδῇ for οὐκ εἰδότι if he did not want to emphasize. -/- 3. Tripartite Ontology The distinction between knowledge and true opinion in Republic, on other side, has nothing to do with recollection, but is based on an ontological principle, 'Tripartite Ontology' (TO): -/- TO There are things that both are and are not. -/- This principle I confine, among our three dialogues of the second group, to Republic not extended to Meno and Phaedo, is obviously the opposite of BO. Speaking about the lovers of sights and sounds in the fifth book, Socrates distinguishes them from philosophers because their thought is unable to understand the nature of beautiful itself besides beautiful things (476a6-8) and hence they can only have opinions. The philosopher who, on the contrary, believes in beautiful itself and can distinguish it from beautiful things (476c9-d3), has knowledge because he knows, contrasting others who have opinion because they only opine (d5-6). Since those whose knowledge were degraded as opinion will complain about Socrates’ such calling their thought, he provides them the following argument (476e7-477b1): -/- - Does the person who knows, knows (γιγνώσκει) something (τὶ) or nothing (οὐδέν)? - He knows something (τί). - Something that is (ὂν) or is not (οὐκ ὄν)? - Something that is (ὂν) for how could something that is not be known (πῶς γὰρ ἂν μὴ ὄν γέ τι γνωσθείη)? - Then we have an adequate grasp of this: No matter how many ways we examine it, what completely is (παντελῶς ὂν) is completely knowable (παντελῶς γνωστόν) and what is in no way (μὴ ὂν δὲ μηδαμῇ) is in every way unknowable (πάντῃ ἄγνωστον). - A most adequate one. - Good. Now, if anything is such as to be and also not to be (ὡς εἶναί τε καὶ μὴ εἶναι), won’t it be intermediate (μεταξὺ) between what purely is (εἰλικρινῶς ὄντος) and what in no way is (μηδαμῇ ὄντος)? - Yes, it’s intermediate. - Then as knowledge (γνῶσις) is set over what is (τῷ ὄντι), while ignorance (ἀγνωσία) is of necessity set over what is not (μὴ ὄντι) mustn’t we find an intermediate between ignorance (ἀγνοίας) and knowledge (ἐπιστήμης) to be set over the intermediate, if there is such a thing? -/- From the third status of being we must reach to the third status of knowledge. The simple reading of this text can be an existential reading, taking the "is" of the mentioned sentences as existence. The problem is that when it is said that there is something that both is and is not reading "is" existentially, it sounds too bizarre to be acceptable. It cannot easily be understandable to have something as both existent and non-existent at the same time. This problem arose so many debates and led many scholars to reject the existential reading of "is" and suggest some other readings like predicative or veridical readings. I think though Plato’s complicated ontology of Republic cannot be correctly understood by a simple existential reading, this "is" cannot be free from existential sense of being and, thus, cannot be reduced to just a predicative or veridical sense of being. -/- 4. Bound Knowledges In addition to KG, the Good is also the basis of another principle in the second Socrates, namely the principle of 'Bound Knowledge' (BK): -/- BK Knowledge of everything is bound to the knowledge of the Good. -/- We distinguished BK from KG because we want to insist, in BK, on what had not been insisted upon in KG, that is, the binding role that the Good plays in the second Socrates, contrasting the absence of such a role in the first Socrates. Socrates remembers, in Phaedo, his wonderful keen on natural philosophers' wisdom when he was young. The origin of this enthusiasm was Socrates’ hope to know the cause of everything as they used to claim. When he was searching the matters of his interest on their basis, Socrates says, he became convinced he can get no acceptable answer from them and found himself blind even to the things he thought he knew before. One day he hears Anaxagoras’ theory that 'it is Mind that arranges and is the cause of everything (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (Phd. 97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14) and thinks that he can finally find what he has always expected, i.e. something which can explain all things. What I intend to show here is that what makes Socrates hopeful is that Anaxagoras’ theory tries 1) to explain all things by one thing and 2) this explanation is understood by Socrates as if it is based on the concept of the Good. That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing on the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by one thing. Another reason was that Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge we pointed to above are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: -/- I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. We must insist that we are discussing what Socrates thought that Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good we chose as the name of BK principle: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) -/- Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty which is precisely confirmed in Republic (504e-505a, 506d-e). Moreover, BK is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, as was noted above discussing KG, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)', he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This binding aspect of the Good is by no means a simple binding of all knowledges or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledges of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g., ibid, 988b11-13) the relation between the Good and unity may become more understandable. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledges. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledges by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. -/- 5. Bound Beings The ontological aspect of BK we shall call the principle of 'Bound Beings' (BB): -/- BB Being of all things are bound by the Good. -/- We saw in our principle of Split Being (SB) how the first Socrates was criticized because of his approach to split being and separate each thing from other things. The principle of Bound Beings intends to make the things more related, a duty which is done again by the Good. In the allegory of Sun, there are two paragraphs that evidently and deliberately extend the binding role of the Good to the ontological scene: -/- You will say that the sun not only makes the visible things have the ability of being seen but also coming to be, growth and nourishment. (509b2-4) -/- This clearly intends to remind the ontological role the sun plays in bringing to being all the sensible things in order to display how its counterpart has the same role in the intelligible realm (b6-10): -/- Not only the objects of knowledge (γιγνωσκομένοις) owe their being known (γιγνώσκεσθαι) to the Good, but also their existence (τὸ εἶναί) and their being (οὐσίαν) are due to it, though the Good is not being but superior to it in rank and power. That the Good is here represented as responsible for being of things in addition to their being known means, in my opinion, that Plato wants to posit BB in addition to BK. The allegory of Cave at the very beginning of the seventh Book (514aff.) can be taken as another evidence. The role of the Good, one might say, is confined to the intelligible realm because it is asserted that the role the Good plays in this realm is corresponding to that of the sun in the visible realm. The fact that Plato wants to observe the Good also as the ontological cause of the sensible things is obvious from his saying, in the allegory of Cave, that the Form of the Good 'produces light and its source (τὸν τούτου κύριον) [i.e. the sun] in the visible realm' (517c3). We can conclude, then, that the ontological function of the Good is not confined to the intelligible realm in which it is the lord and provides truth and understanding (c3-4) because it is also responsible to produce τὸν κύριον of light. 6. Proportionality of Being and Knowledge Insofaras BE and BO principles of the first Socrates gave way to TE and TO principles of the second Socrates, we cannot expect him to preserve KB in the same way as it was in the first Socrates. The new tripartite ontology and epistemology necessitates some modifications in KB which results in the principle of 'Proportionality of Being and Knowledge' (PBK): -/- PBK To every class of being there is a proportionate category of knowledge. -/- This principle, of course, does not entail the refutation of KB and thus is not kind of rejecting PBK but only a more complicated version of it. Based on PBK, we can still agree that knowledge is of being (KB) but the issue is that since none of the concepts of knowledge and being in the second Socrates are as simple as they were for the first Socrates, we need a more complicated principle for their relation here. Although from Meno 97a where the distinction of knowledge and true opinion is drawn out in the second group of the dialogues, we can expect a new relation, it is articulated in its most complete way in Republic and specifically in the allegory of Line. All the beings are divided there hierarchically to four classes, to each of them belongs a class of knowledge: imagination to images, belief to the sensible things (more correctly: the things of which they[in previous class] were images (ᾧ τοῦτο ἔοικεν)), thought to mathematical objects (?) and understanding to the Forms and the first principle. The degree of clarity that each of the classes of knowledge shares in (σαφηνείας ἡγησάμενος μετέχειν) is proportionate to the degree that its object shares in truth (ἀληθείας μετέχει). (511e2-4) -/- Conclusion From the six onto-epistemilogical principles of the first Socrates, four principles turn to their opposite in the middle period dialogues. While bipolar epistemology and ontology of the early dialogues give place to tripartite epistemology in the middle period dialogues and tripartite ontology in Republic, the split knowledge and being of the first Socrates are inclined to be substituted by bound knowledges and bound beings in the second Socrates and specifically in Republic. Not all our system of principles in this article is necessarily determinative. Either they are rightly formulated or not, our result would not be vulnerable if we accept that 1) making the distinction of knowledge and belief, 2) accepting the being of not being and 3) trying to bind both being and knowledge by the concept of the Good happens only in middle period dialogues, having been absent in the early ones. These are the favourite results all those somehow arbitrary and even oversimplified principles were to illustrate; that there is kind of a development in the epistemological as well as the ontological grounds of Plato’s philosophy. -/- Notes . (shrink)

Perelman’s view of the role of persons in argument is one of the most distinctive features of his break with Cartesian assumptions about reasoning. Whereas the rationalist paradigm sought to minimize or eliminate personal considerations by dismissing them as distracting and irrelevant, Perelman insists that argumentation inevitably does and ought to place stress on the specific persons engaged in an argument and that the relationship between speaker and what is spoken is always relevant and important. In taking this (...) position, Perelman implicitly revives the classical conception of proof by character (ethos or “ethotic” argument), but despite an extended discussion of act and person in argument, The New Rhetoric does not give much consideration to the classical concept and confuses differing approaches to it within the tradition. The result is that Perelman treats the role of the speaker in argument only by reference to abstract techniques and does not recognize the importance of examining particular cases in order to thicken understanding of how ethotic argument works in the complex, situated context of its actual use. Consequently, Perelman’s account of the role of persons in argument should be supplement by reference to case studies, and to that end, I consider ethotic argument in W.E.B. Du Bois’ famous essay “Of Mr. Booker T. Washington and Others”. (shrink)

Peter Klein has taken Aristotle’s regress argument for foundationalism as a point of departure for developing a view he calls ‘infinitism’. In this paper, I offer a critique of Klein’s view. I argue for three main conclusions. First, Klein’s response to the regress argument for foundationalism is neither infinitism nor foundationalism but a distinct position I call the “unjustified foundations” view. Second, Klein’s “unjustified foundations” view is subject to some serious problems that make it inferior to foundationalism. Third, (...) Klein’s objections to foundationalism fail to knock it from its place of superiority over the “unjustified foundations” view. Before defending these three conclusions in sections 3-5, I begin with an account of the regress argument for foundationalism in section 1 and with a brief presentation of Klein’s views in section 2. (shrink)

In the De Generatione et Corruptione II 9, Aristotle aims to achieve the confirmation of his theory of the necessity of the efficient cause. In this chapter he sets out his criticism on the one hand of those who wrongly attributed the efficient cause to other kinds of causality and on the other, of those who ignored the efficient cause. More specifically Aristotle divides all preceding theories which attempted to explain generation and corruption into two groups: i) those which offered (...) an explanation by using the formal cause ii) those which provided an explanation by using the material or the instrumental causes. According to Philopo­nus, when Aristotle reproaches the other philosophers for adducing no proper notion of the efficient cause he alludes to both Anaxagoras and Plato. Regarding Anaxagoras, in our view this cannot be confirmed by internal textual evidence. In terms of Plato, in this chapter we trace an explicit and an implicit criticism of the Platonic Forms as causes. Aris­totle’s implicit criticism is that the Forms are not at all active causes. We can understand better the grounds for this criticism if we also consider his relevant arguments in Book Lambda of his Metaphysics. His explicit criticism, articulated in two arguments, is formulated in GC 335b18–24. We examine the different lines of its interpretation in the second­ary literature, but primarily we focus on Philoponus’ exegesis, which contributes significantly, not only to the clarification of Aristotle’s thinking, but also to the manifestation of the arguments articulated in defence of the Platonic theory of the Forms. In this paper, through the analysis of Philoponus’ exegesis we set out to prove that Aristotle’s criticism of the Platonic causes can be construed from the perspective of either Aristo­telian theory or the Platonic and Neoplatonic influence. Finally, based on Philoponus’ exegesis, we examine Aristotle’s criticism of those who posited matter or instrumental causes as efficient causes. (shrink)

This is an exploration of what Locke and Whately said about the Argumentatum ad Hominem, especially in the context of what they said about the other ad arguments, and with a view to ascertaining whether what they said lends support to the understanding of this argument implicit in Johnstone's thesis that all valid philosophical arguments are ad hominem. It is concluded that this support is forthcoming insofar as Locke and Whately had in mind an argument concerned with (...) principles.The essay ends with a brief reformulation of Johnstone's generalization regarding philosophical arguments. (shrink)

Aristotle argues that the soul and body are non-identical substances; the soul is an immaterial particular form, while the body is a diachronic material continuant. Despite their immateriality, Aristotle argues that souls are not separable from bodies, and so implicitly rejects any version of Cartesian dualism. But because of his commitment to immaterialism, Aristotle's position cannot be assimilated to any contemporary materialist theory in the philosophy of mind. We need not, however, regard him as inconsistent in rejecting both Cartesian (...) dualism and materialism: Aristotle rightly recognizes that the soul can be a substantial immaterial particular form which supervenes on the body. Aristotle is, then, a supervenient dualist, who holds that there are nomological relations between physical and psychic states, but who denies that psychic states are token identical with material states. ;But Aristotle notoriously does not regard the supervenience of the soul as sufficient for the supervenience of each of its capacities. He provides an interesting but unsuccessful a priori argument for the claim that nous, or mind, is a capacity of the soul which does not supervene on any bodily state. Thus, he concludes that nous can survive the destruction of the body; but post mortem survival of nous need not be regarded as sufficient for a commitment to post mortem personal identity in Aristotle. (shrink)

The symbolism introduced earlier provides a convenient vehicle for examining the status and consistency of Aristotle's three diverse justifications and for explaining how he means to avoid Protagorean relativism without embracing Platonic absolutism. When the variables ‘ x ’ and ‘ y ’ are allowed to range over the groups of free men in a given polis as well as over individual free men, the formula for the Aristotelian conception of justice expresses the major premiss of Aristotle's three (...) justifications: (1) (∀ x )(∀ y ) (P(x)·W(x)/P(y)·W(y)=V(T(x))/V(T(y)))Democracy is justified by adding a minor premiss to the effect that as a group the many ( m ) are superior (>) in virtue and wealth to the few best men ( f ): 85 (2 d ) (P(m) · W(m)) > (P(f) · W(f)) (3 d ) V(T(m))>V(T(f))Absolute kingship is justified when a godlike man ( g ) appears in a polis who is incommensurably superior (≫) in virtue and wealth to all the remaining free men ( r ): (2 k ) (P(g) · W(g)) ≫ (P(r) · W(r)) (3 k ) V(T(g)) ≫ V(T(r))True aristocracy requires a more complex justification, which was symbolized in Section 4. These justifications are compatible with each other since they apply to different situations. The polises where democracy and true aristocracy are justified contain no godlike men, and the polis in which democracy is justified differs from that in which true aristocracy is justified in containing a large group of free men who individually have little virtue ( Pol. III.11.1281b23-25, 1282a25-26). Each of the justifications is a valid deductive argument. Aristotle affirms the major premiss they share on the basis of a twofold appeal to nature. The principle of distributive justice, the concept as distinguished from the various conceptions of distributive justice, is itself according to nature ( Pol. VII.3.1325b7-10) and so too is one particular standard of worth, the standard of the best polis. Consequently, the question of the status of these three justifications, whether they are purely hypothetical or not, is a question about the minor premiss or premisses of each. In the case of the democratic premiss Aristotle's answer is straightforward: it is sometimes but not always true ( Pol. III.11.1281bl5-21). Hence the justification of democracy is not purely hypothetical. Nor is the justification of absolute kingship. The man who is “like a god among men” ( Pol. III.13.1284a10-11) would be a man of heroic virtue (see VII.14.1332bl6-27); and such a man, Aristotle says, is “rare” ( σπávιoη ) (not nonexistent) ( E.N. VII.1.1145a27-28). The minor premisses of the aristocratic argument describe a situation where all of the free men in a given polis have sufficient wealth for the exercise of the moral and intellectual virtues and where all of the older free men of the polis are men of practical wisdom. In the Politics Aristotle makes only the modest claim that such a situation is possible: It is not possible for the best constitution to come into being without appropriate equipment [that is, the appropriate quality and quantity of territory and of citizens and noncitizens]. Hence one must presuppose many things as one would wish them to be, though none of them must be impossible ( Pol. VII.4.1325b37-38; see also II.6.1265al7-18). But Aristotle appears to subscribe to the principle that every possibility is realized at some moment of time ( Top. 11.11.115bl7-18, Met. Θ.4.1047b3-6, N.2.1088b23-25). This principle together with the claim that the situation described is possible entails that the situation sometimes occurs. Thus even Aristotle's justification of true aristocracy is not purely hypothetical. The final question is Aristotle's way of avoiding Protagorean relativism without embracing Platonic absolutism. The relativist, along with everyone else ( E.N. V.3.1131a13-14, Pol. III.12.1282bl8), can accept the principle of distributive justice: Q(x)/Q(y) = V(T(x))/V(T(y)) And he can concede that particular instances of this principle, particular conceptions of justice, accurately describe the modes of distributing political authority that appear just to particular polises and to particular philosophers. What he denies is that there is any basis for ranking these various conceptions of justice or for singling one out as the best (Plato, Theaet. 172A-B). Aristotle, following in Plato's track ( Laws X.888D7-890D8), maintains against the relativist that nature provides such a basis. But he departs from Plato in his conception of nature. For Plato “the just by nature” ( τó ρυσει δίκ↑oν }) ( Rep. VI.501B2) is the Form of justice, an incorporeal entity ( Phdo. 65D4-5, Soph. 246B8) that exists beyond time and space ( Tim. 37C6-38C3, 51E6-52B2), whereas for Aristotle the sensible world is the realm of nature ( Met. A.1.1069a30-b2). Thus in appealing to nature Aristotle does not appeal to a transcendent standard. Nor does he appeal to his main criterion of the natural, namely, happening always or for the most part. Aristotle's theory of justice is anchored to nature by means of the polis described in Politics VII and VIII, and he regards this polis as natural because it fosters the true end of human life and because its social and political structure reflects the natural hierarchy of human beings and the natural stages of life. Thus the nature that Aristotle's theory of justice is ultimately founded on is human nature. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions ARISTOTLE'S ALLEGED "REVOLT" AGAINST PLATO Hermippus' most conspicuous contribution to Aristotle's biography probably was his determined effort to depict Aristotle as the founder of an original school of philosophy which was wholly independent of Plato and Platonic teachings. Among the several and, in all likelihood, fanciful stories about Aristotle he invented or propagated, the most startling was the account, subsequently widely accepted (and widely (...) exploited by the detractors of Aristotle), that after having been a disciple of Plato for a while, he seceded from the Academy and from Plato's philosophic teachings while Plato was still alive. 1 Accordingly, he owed little to Plato and to the Academy. This story, invented and propagated by an inveterate Peripatetic (Hermippus), was intended to demonstrate the original philosophic genius of Aristotle which developed in complete independence of Plato and necessitated a break with the master's teachings. In devising his argument, Hermippus might have made use of a report, found in some of Aristotle's ancient biographers, that a few brash young men (members of the Academy?) revolted against Plato and, in a spirit of independence, defiance and antagonism, attempted to start a school of their own which would rival the intellectual standing of the Academy. 2 Hermippus, it appears, subsequently identified these young "rebels" with Aristotle, a substitution convenient to Hermippus" aim to depict Aristotle as a wholly independent and totally original philosopher who owed nothing whatever to Plato and his teachings. In all likelihood, Diogenes Laertius' statement that Aristotle "seceded from the Academy while Plato was still alive," a is just an echo either of a statement made by Hermippus himself or is a conclusion drawn from the several unpleasant stories about Aristotle invented and reported by some of Aristotle's detractors. According to these derogatory stories, there existed many serious personal as well as doctrinal 4 disagreements or rifts between Plato and the Stagirite--disagreeDiogenes Laertius, V. 2. See also Eusebius, Praeparatio Evangelica, XV. 2. 3, and ibid., XV. 2. 13 (Aristoxenus); Aelian, Varia Historia, IV. 9; Theodoretus, Graecorum Affectionum Curatio, IV. 46; St. Augustine, De Civitate Dei, VIII. 12; Philoponus, Comment. in Aristotelis Analytica Posteriora, CIAG, vol. XIII, part 3, pp. 133, 30 ft. 2 See Aelius Aristides, Oratio XLVI, 249. 10. See also note 1, supra. s Diogenes Laertius, V. 2. See also Vita Aristotelis Marciana 9; Vita Aristotelis Latina 9. 9 See, for instance, Plutarch, Adversus Coloten 14 (Moralia, III5A); Cicero, Academica I. 9. 33; Eusebius, op. cir., XV. 2, passim; Diogenes Laertius III. 37; Justin Martyr, Cohortatio ad Graecos 5 (Migne, PG. vol. VI. p. 247); Cyrillus, Contra Julianum II. 47; Proclus, [91] 92 HISTORY OF PHILOSOPHY ments whichmarred the relations between these two men and which were indicative of Aristotle's ingratitude, bad taste and unwarranted conceit. The report of Diogenes Laertius, in an oblique manner, may also refer to the fact that already during his active association with the Platonic Academy (367-348 B.c.), that is, in his On (the) Ideas and On the Good, Aristotle had begun to disagree with, and criticize, some of Plato's fundamental teachings. It may also, in a distorted form, refer to the following specific incident which, however, cannot be verified: According to Aristoxenus, during the absence of Plato in Syracuse (and while Heracleides of Pontus was the "acting scholarch" of the Academy),5 some unnamed young members of the Academy, or "students" or, perhaps, some "outsiders " attempted to start a rival school (within the Academy?).6 As a matter of fact, Aelian, who apparently dramatizes this incident, reports that during Plato's last years, that is, some time after Plato's return from his third and last voyage to Syracuse, a serious conflict or confrontation arose within the Academy. Aristotle, together with some of his friends, or "conspirators," we are told, harrassed and molested the aging Plato by constantly putting questions to him, by arguing with him in an insolent manner, by contradicting him on every point, and by attempting to involve him in hair-splitting dialectics. At the time Xenocrates was in Chalcedon, and Speusippus was gravely ill. Hence, neither of them could come to the succor of Plato. In... (shrink)

In the field of philosophy, Plato's view of rhetoric as a potentially treacherous craft has long overshadowed Aristotle's view, which focuses on rhetoric as an independent discipline that relates in complex ways to dialectic and logic and to ethics and moral psychology. This volume, composed of essays by internationally renowned philosophers and classicists, provides the first extensive examination of Aristotle's Rhetoric and its subject matter in many years. One aim is to locate both Aristotle's treatise and its (...) subject within the more general context of his philosophical treatment of other disciplines, including moral and political theory as well as poetics. The contributors also seek to illuminate the structure of Aristotle's own conception of rhetoric as presented in his treatise. The first section of the book, which deals with the arguments of rhetoric, contains essays by M. F. Burnyeat and Jacques Brunschwig. A section treating the status of the art of rhetoric features pieces by Eckart Schütrumpf, Jürgen Sprute, M. M. McCabe, and Glenn W. Most. Essays by John M. Cooper, Stephen Halliwell, and Jean-Louis Labarrière address topics related to rhetoric, ethics, and politics. The final section, on rhetoric and literary art, comprises essays by Alexander Nehamas and André Laks. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.1 (2000) 19-37 [Access article in PDF] Eudaimonism and Theology in Stoic Accounts of Virtue Michael Gass The Stoics were unique among the major schools in the ancient world for maintaining that both virtue and happiness consist solely of "living in agreement with nature" (homologoumenos tei phusei zen). We know from a variety of texts that both Cleanthes and Chrysippus, if not also (...) Zeno, characterized such conduct both in essentialist terms, as a matter of living purposively in a manner natural for the human species, and in cosmological terms, as a matter of living in agreement with the purposes of nature as a whole, this being regarded as identical to Zeus. This is not to suggest, however, that cosmo-theological speculation figured prominently in the ethical systems of the early Stoics. Judging from extant summaries and discussions of Stoic ethical doctrines, those doctrines were justified in a dialectical fashion, not by appeal to facts about the purposive order of nature but simply from an analysis of ethical concepts patterned after similar analyses by earlier philosophers (most notably, Aristotle). It is this kind of learning that Chrysippus apparently had in mind when he maintained that ethics should be studied prior to undertaking a systematic investigation of nature: [T]here are three kinds of philosopher's theorems, logical, ethical and physical.... [W]hat should be ranked first of these are the logical, next the ethical, third the physical; and what should come last in the physical theorems is theology. 1On the other hand, as we learn from the testimony of Plutarch (and also from other indirect textual evidence examined recently by Jacques Brunschwig), 2 [End Page 19] Chrysippus also believed that physics in general and theology in particular yield a quite distinct, demonstrative knowledge of the matters first studied in ethics. A. A. Long and others have suggested that such knowledge was regarded by the Stoics as encompassing not just information about the ways in which virtuous living is encouraged by, and fits into, the wider aims of nature at large but also a deeper understanding of the very essence of virtue. 3 Specifically, virtue is revealed to consist in a conscious and deliberate harmonization of one's actions with the purposes of the divine architect. Thus, under this interpretation of their ethical intentions, the Stoics thought of the initial, analytical approach to ethics as necessarily incomplete even in its treatment of strictly ethical topics; the systematic study of nature was thought to impart additional wisdom regarding ethical matters.In her recent study of ancient ethical theories, Julia Annas seeks to counter this view of the place of cosmo-theological speculation in early Stoicism by arguing that such a religious characterization of virtue is incompatible with the eudaimonism to which all schools of ancient philosophy, including Stoicism, were committed. 4 She concedes that first Cleanthes and then much later the Roman Stoics did regard virtue in religious terms, but in her assessment this represents a radical departure from mainstream Stoic thinking on this subject (which is identified mostly with the views of Chrysippus and his disciples, all of whom were clearly and consistently committed to the eudaimonistic model of ethical inquiry). Annas argues that whereas the Stoic sage was traditionally depicted as a person whose commitment to morally appropriate conduct stems from his own rational reflection on his own needs and interests, a person who identified completely with the aims of the divine architect in his purposive activity would be someone who surrendered his right to decide for himself what his needs and interests are, and who therefore could even be required to act in violation of what he might judge by himself to be crucial to his happiness.In what follows I demonstrate that this argument, often advanced in the literature as a reductio ad absurdum of divine command theories of morality, falls wide of the mark in the present case due to the fact that those Stoics who characterized virtue in religious terms did so apparently because they regarded a complete identification with... (shrink)

In an earlier article (see J Gen Philos Sci (2009) 40: 357-372) I have discussed the arguments brought forward by Michael Wolff against the interpretation given in the commentary by Ebert and Nortmann on Aristotle's syllogistic theory (Aristoteles Analytica Priora Buch I, übersetzt und erläutert von Theodor Ebert und Ulrich Nortmann. Berlin 2007) and against the critique of Kant's adaption of the syllogistic logic. I have dealt with Wolff's arguments concerning (Ebert/Nortmann's interpretation of) Aristotle in the paper mentioned and (...) with his attempts to defend his critique in this subsequent article (part 1; see J Gen Philos Sci (2010) 41: 215-231). Part 2 (the paper below) is concerned with Wolffs renewed attempts to defend Kant as a logician. In particular I point out that if, as Wolff claims, the nota notae relation in Kant is restricted to subordinated concepts, then it can hardly serve as a principle for syllogistic logic, as Kant claims. Against Wolff's attempts to defend Kant's claim that o-propositions are simpliciter convertible, I point out two arguments: (1) Even if Kant, following the Vernunftlehre by Meier, has assumed that an o-proposition can be turned into an i-proposition (by adding the negation sign to the predicate), this conversion is useless for the reduction to first figure syllogisms since we are no longer dealing with three syllogistic terms but with four. (2) It is quite unlikely that Kant has a conversion of this type in mind since the texts of his students always talk of the group of either the particular propositions or else of the negative propositions. Given Kant's mistakes concerning the convertibility simpliciter of o-propositions, it is no wonder that he overlooks the special status of the moods Baroco and Bocardo. Wolffs attempts to provide Kant with what he claims are direct proofs for these moods can be shown to rely on a reductio ad impossibile. Kant mistook what are parts of the proofs for the validity of moods in figures two to four as parts of these moods themselves. Wolff—who tries to defend Kant on this point—is forced to an artificial and unconvincing reading of the Kantian texts. (shrink)

Thomas Kuhn has argued that scientists never reject a paradigm without simultaneously accepting a new paradigm. Coupled with Kuhn's claim that it is paradigms as a whole, and not individual theories, that are accepted or rejected, this thesis is seen as one of Kuhn's main challenges to the rationality of science. I argue that Kuhn is mistaken in this claim; at least in some instances, science rejects a paradigm despite the absence of a successor. In particular, such a description best (...) fits Kuhn's most discussed example, the Copernican Revolution. By differentiating scientific discoveries into three types, spontaneous, implicit, and directed, we see that Kuhn's thesis holds for spontaneous and implicit discoveries, but not directed discoveries. Directed discoveries must be understood by an alternative account of falsifiability, based on argument by reductio ad absurdum rather than argument by modus tollens as traditional accounts of falsifiability would have it. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on (...) the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

At APr 2.4 57a36–13, Aristotle presents a notorious reductio argument in which he derives the claim ‘If B is not large, B is large’ and calls that result impossible. Aristotle is thus committed to some form of connexivity and this paper argues that his commitment is to a strong form of connexivity which excludes even cases in which ‘B is large’ is necessary. It is further argued that Aristotle’s view of connexivity is best understood as arising from his (...) analysis of affirmation and negation in terms of combination and separation: a proposition that separates two terms cannot entail a proposition that combines the same two terms. In order to motivate this account of connexivity, this paper interprets Aristotle as emphasising the predicative structure, especially the copulae, of the argument’s component propositions. The arguments for this are based on a consideration of the larger context of APr 2.2–4. A reconstruction of the argument using propositional variables does not fully capture Aristotle’s intentions. (shrink)

Sense experience, naïvely conceived, is a way of knowing perceptible properties: the colors, sounds, smells, flavors, and textures in our perceptual environment. So conceived, ordinary experience presents the perceiver with the essential nature of a property like Sky Blue or Middle C, such that how the property appears in experience is identical to how it essentially is. In antiquity, as today, it was controversial whether sense experience could meet the conditions for knowledge implicit in this naïve conception. Aristotle was (...) a partisan in this debate, but his position is poorly understood. This dissertation examines how Aristotle’s perceptual psychology responds to ancient challenges to the naïve conception, and so articulates his defense of perceptual knowledge. -/- Aristotle’s defense relies on an ontology of “perceptual qualities"—a core class of perceptible properties—according to which those qualities, despite having a perceiver-independent essence rooted in the physics of causation and affection, nevertheless can be present in experience as they essentially are. Chapter 1 defends this realist and objectivist reading against competing interpretations, which overlook a crucial distinction between perceptual qualities and perceptual objects. Chapter 2 presents Aristotle’s ontology as a physicalism that uncharacteristically allows for perceptual qualities to appear in experience as they essentially are. -/- This ontology informs Aristotle’s account of the psychological conditions under which perceivers actually are presented with the essence of perceptual qualities. The locus of this account is an obscure passage where Aristotle purports to show that the senses “discriminate” perceptual qualities because the senses are “mean states” (An. 2.11, 424a5–7). Chapter 3 develops a comprehensive interpretation of the sensory mean state, which Chapter 4 uses to elucidate Aristotle’s argument for sensory discrimination. Sensory discrimination turns out to be a process in which the essence of a perceptual quality comes to be present in the affection it produces in a perceiver. For Aristotle, this shows that sense perception meets a condition for knowledge that his predecessors, including Plato, thought it could not meet. For in his view, but not in theirs, sense experience shares in both the truth and the essence of the qualities it perceives. (shrink)

This article offers a reconstruction of an argument against infinite regress formulated by Aristotle in Posterior Analytics I 22. I argue against the traditional interpretation of the chapter, according to which singular terms and summa genera, in virtue of having restrict logical roles, provide limits for predicative chains, preventing them from proceeding ad infinitum. As I intend to show, this traditional reading is at odds with some important aspects of Aristotle’s theory of demonstration. More importantly, it fails to (...) explain how his proof is connected to a defence of the existence of ultimate explanations, a connection that must be the case if I 19-22 is advancing a foundationalist way-out to a sceptical challenge raised in I 3. (shrink)

Everyman’s Library commemorates its fiftieth anniversary very aptly with this issue as its thousandth volume of a classic text of some 2,300 years of age, which through varying fortunes has been a major influence in European culture. As a transcendental science Metaphysics makes no concession to the semi-curious; Aristotle’s inaugurating textbook is understandably concentrated and obscure. A literal version of this formidable text would have no appeal to the general reader, innocent largely of the Greek idiom and of philosophical jargon, (...) while a personal paraphrase could not carry the authentic voice of a past master. Mr. Warrington simply takes the existing Oxford version, retranslating it into easier, more fluent English and rearranging its fourteen books into a free, logical order. In this he is guided by their matter and by the critico-historical views of Jaeger and Ross, outlined in a short Introduction by Sir David himself. He has added chapter titles, numbered sections, prefixing their main groups with a short summary of contents and has courageously kept clear the main line of Aristotle’s argument by relegating all parentheses to footnotes, to which he adds his own identification of historical references. Radical re-arrangement justifies itself by success—here a forbidding classic is presented with the immediate, systematic clarity of a modern text. (shrink)

Alexander of Aphrodisias's commentary (about AD 200) is the earliest extant commentary on Aristotle's Metaphysics, and it is the most valuable indirect witness to the Metaphysics text and its transmission. Mirjam Kotwick's study is a systematic investigation into the version of the Metaphysics that Alexander used when writing his commentary, and into the various ways his text, his commentary, and the texts transmitted through our manuscripts relate to one another. Through a careful analysis of lemmata, quotations, and Alexander's discussion (...) of Aristotle's argument Kotwick shows how to uncover and partly reconstruct a Metaphysics version from the second century AD. Kotwick then uses this version for improving the text that came down to us by the direct manuscript tradition and for finding solutions to some of the puzzles in this tradition. Through a side-by-side examination of Alexander's text, his interpretation of Aristotle's thought, and the directly transmitted versions of the Metaphysics, Kotwick reveals how Alexander's commentary may have influenced the text of our manuscripts at different stages of the transmission process. This study is the first book-length examination of a commentary as a witness to an ancient philosophical text. This blend of textual criticism and philosophical analysis both expands on existing methodologies in classical scholarship and develops new ones. (shrink)

ABSTRACT William Hurlbut, a Stanford University bioethicist and member of the President's Council on Bioethics, recently proposed a solution to the current impasse over human embryonic stem cell research in the United States. He suggested that researchers could use genetic engineering and somatic cell nuclear transfer (i.e. cloning) to develop human ‘pseudo‐embryos’ that have no potential to develop fully into human persons. According to Hurlbut, even thinkers who typically ascribe high moral status to human embryos could approve of destroying these (...) ‘pseudo‐embryos’ for the sake of harvesting human embryonic stem cells. This essay argues, first, that an argument based on the ‘paradox of the heap’ (an argument that many ‘pro‐life’ thinkers employ in order to defend the notion that human embryos have high moral value from the moment of conception) challenges the ethical legitimacy of Hurlbut's proposal. Second, the paper argues that this conflict may illustrate a reductio ad absurdum for this ‘pro‐life’ argument itself rather than being a problem for Hurlbut's proposal. As a result, the paper challenges the ‘pro‐life’ strategy of arguing that one should respond to uncertainty about the moral status of developing embryos by being morally ‘cautious’ and granting all human embryos full moral status from the moment of conception. It appears that one is faced with a complex series of choices (about where to draw the moral line between entities that are human persons and entities that are not), and a strict moral ‘cautiousness’ about this series of choices may ultimately lead to absurdity. (shrink)

This argues for a reading of PA I.1, 639b11-640a9 as a continuous argument, which I divide into 3 main sections. Aristotle’s point in the first section is that teleological explanations should precede non-teleological explanations in the order of exposition. His reasoning is that the ends cited in teleological explanations are definitions, and definitions—which are not subject to further explanation—are appropriate starting points, insofar as they prevent explanations from going on ad infinitum. Moreover, I argue that Aristotle proceeds in (...) the following two sections to criticize certain non-teleological accounts offered by his predecessors on the grounds that they are explanatorily defective: I take Aristotle’s complaints to be that those accounts—unlike teleological explanations—neither begin from appropriate starting points nor entail the phenomena that they purport to explain. Along the way, I am defending an alternative way of understanding what "hypothetical necessity" refers to, for Aristotle. Comments are welcome! (shrink)

By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation (...) and the reality it represents. I further show that the argument seeks to undermine core commitments of Frege’s and Russell’s. But the reductio, as I read it, is not intended to establish the falsity of any of their specific assumptions. Rather, its aim is to make manifest the indeterminacies that underlie the language in which these assumptions are framed, and establish the need for a transformation of that language. So understood, Wittgenstein’s argument exemplifies his idea that philosophy is not a theory, but an activity of elucidation. The interpretation I propose bears on one of the central debates in the literature, namely how we should understand Wittgenstein’s contention that his elucidations succeed despite being nonsensical. (shrink)

Using print ads and recognizing the role of visual images in argument (Groarke) and the presence of arguments in ads (Slade), this paper argues that the work of argumentation theorists from Aristotle to van Eemeren and Grootendorst can be used to support the thesis that ads are arguments. I cite as evidence definitions, demarcations, delineations, and descriptions of argument put forth by leading scholars in the field of argumentation. This includes Aristotle, Informal Logic, Toulmin (Claim, Data, Warrant, Backing, (...) Qualifier, Rebuttal), Johnson and Blair (argument as “reasons or evidence as grounds or support for an opinion”), Gilbert (Multi-Modal Argumentation), and van Eemeren and Grootendorst (argumentation as a social activity and pragma-dialectics). I show how, although just fitting a particular advertisement to someone’s definition does not mean that all ads are arguments, nevertheless, the fact that we can find in an ad all these elements from this variety of scholars over time, leaves us reasonably secure in stating that an ad is indeed an argument. Since my argument would be the same for practically any ad, I am using only one ad. I do, however, use the kind of ad that is least likely to seem to be an argument: an ad with few words, an ad which is mostly visual. If I can show how even an almost entirely visual ad can be analyzed as an argument using the terms of all these scholars of argumentation, I will maintain that most ads could be analyzed in the same way. (shrink)

Many interpreters have noted that §§138–242 of Wittgenstein's Philosophical Investigations is dominated by an attack on a platonist or classical realist conception of rules and meaning. In this paper, I address the lack of clarity that still exists concerning the nature and strength of the arguments in those sections. I argue that Wittgenstein's attack is genuinely compelling if viewed as an intricate reductio ad absurdum argument that runs all the way through §§138–201. On my reading, the well-known regress-of-interpretations (...) argument is merely one stage in the overall reductio and is not sufficient on its own to generate the rule-following paradox. (shrink)

Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and negation in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the Sophistical Refutations—goes (...) far beyond any of these. (shrink)

Attempts to characterise time seem to throw up paradox at every turn. Some of the most famous of the paradoxes are also the oldest—those due to Aristotle (384–322 BC) and Zeno (b. c. 488 BC), as described in Aristotle’s Physics. For example, Zeno argued that in order to traverse any distance, one must always first traverse half that distance; but since this half is itself a distance to be traversed, one must in turn first traverse half of the half, and (...) so on ad infinitum. Since it is impossible to traverse an infinite number of distances in a finite time, all motion must be impossible—indeed, incoherent. A similar argument can be used to show that a line cannot be composed of a set of points, a problem which was only satisfactorily resolved with the development of the modern mathematics of infinity. A central question for the philosophy of time, then, becomes whether (and how) the mathematics of infinity applies to time. (shrink)