I thoroughly enjoyed this work. I think this enjoyment will be shared by anyone who appreciates the difficulty of writing a summa of the theology of the Church today. We have been standing so close to Vatican II that many find it hard to see anything behind and beyond it. The merit of this work is that it is comprehensive and clear. It deals with nova and vetera and even vetera noviter. It seems to me to represent what abides when (...) the dust which has been stirred up has blown away. (shrink)

Informational conceptions of logic are barely novel. We find them in the work of John Corcoran, in several papers on substructural and constructive logics by Heinrich Wansing, and in the interpretation of the Routley-Meyer semantics for relevant logics in terms of Barwises and Perrys theory of situations. Allo & Mares [2] present an informational account of logical consequence that is based on the content-nonexpantion platitude, but that also relies on a double inversion of the standard direction of explanation (in- (...) formation doesnt depend on a prior notion of meaning, but is used to naturalize meaning, and informational content is not defined relative to a pre-existing logical space, but that space is constructed relative to the level of abstraction at which information is assessed). In this paper I focus directly on one of the main ideas introduced in that paper, namely the contrast between logical discrimination and deductive strength, and use this contrast to (1) illustrate a number of open problems for an informational conception of logical consequence, (2) review its connection with the dynamic turn in logic, and (3) situate it relative to the research agenda of the philosophy of information. (shrink)

CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI’S COLLECTED PAPERS Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but (...) most of the Aristotelian corpus is not about logic, whereas virtually everything written by Tarski concerns logic more or less directly. There is no doubt that Tarski wrote more on logic than any other author; he started publishing on logic in 1921 at the age of 20 and continued until his death at the age of 82. (shrink)

It is widely agreed by philosophers that the so-called “Frege-Russell definition of natural number” is actually an assertion concerning the nature of the numbers and that it cannot be regarded as a definition in the ordinary mathematical sense. On the basis of the reasoning in this paper it is clear that the Frege-Russell definition contradicts the following three principles (taken together): (1) each number is the same entity in each possible world, (2) each number exists in each possible world, (3) (...) some entities existing in the actual world do not exist in every possible world. Since these principles seem to be true, the paper is a refutation of the Frege-Russell definition. The paper does more. It shows that the contradictory of the Frege-Russell definition follows even when principles 2 and 3 are replaced by one considerably weaker principle. The ideas contained in the paper are related to two earlier objections to the definition. The first, sometimes attributed to the mathematician, C. S. Keyser, is that existence of the numbers as defined implies the existence of infinitely many particulars in each possible world. The second is, in effect, an idea which is said to have led Whitehead to reject the definition of number to which he had subscribed in Principia Mathematica. Whitehead is supposed to have said that he could not believe that the number two changes every “time twins are born”. The mathematician H. Jeffreys expressed similar ideas [Philos. of Sci. 5 (1938), 434–451]. One of the merits of the author’s work is that it refutes the Frege-Russell definition without the need to take sides on controversial points presupposed by the Keyser and Whitehead objections. The objections made by the author are therefore not to be identified with the Keyser and Whitehead objections. Even if the author’s work is to be regarded as a refinement and integration of previous ideas, it is nevertheless a contribution—not only because the basic points are well worth repeating but also because the refinements are logically significant improvements and because the author has stated them clearly and concisely in the idiom of contemporary philosophy. (shrink)

PUTNAM has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) is largely correct as far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary (...) science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers, scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. The book can be recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the literature of the 1950’s and before, when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. QUINE’S book is not easy to read, partly because the level of sophistication fluctuates at high frequency between remote extremes and partly because of convoluted English prose style and devilish terminology. Almost all of the minor but troublesome technical errata in the first printing have been corrected [see reviews, e.g., the reviewer, Philos. Sci. 39 (1972), no. 1, 97–99]. In the opinion of the reviewer the book is not suitable for undergraduate instruction, and without external motivation few mathematicians are likely to have the patience to appreciate it. Nevertheless, a careful study of the book will more than repay the effort and one should expect to find frequent references to this book in coming years. (shrink)

This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo period first reporting his original results. It ends with works published (...) in 2015. Some items are annotated as listed or with endnotes connecting them with other work and pointing out passages that, in retrospect, are seen to be misleading and in a few places erroneous. In addition, Section V, “Discussions”, is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 10 items published in the 1970s, 24 in the 1980s, 42 in the 1990s, 60 in the 2000s, and 70 in the current decade. The secondary bibliography is also annotated as listed or with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. Section VI, “Alternatives”, lists recent works on Aristotle’s logic oblivious of Corcoran’s research and, more generally in some cases, even of the Łukasiewicz-initiated tradition. As is evident from Section VII, “Acknowledgements”, Corcoran’s publications benefited from consultation with other scholars, most notably George Boger, Charles Kahn, John Mulhern, Mary Mulhern, Anthony Preus, Timothy Smiley, Michael Scanlan, Roberto Torretti, and Kevin Tracy. All of Corcoran’s Greek translations were done in collaboration with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for a (...) wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

The Hong and Page ‘diversity trumps ability’ result has been used to argue for the more general claim that a diverse set of agents is epistemically superior to a comparable group of experts. Here we extend Hong and Page’s model to landscapes of different degrees of randomness and demonstrate the sensitivity of the ‘diversity trumps ability’ result. This analysis offers a more nuanced picture of how diversity, ability, and expertise may relate. Although models of this sort can indeed be suggestive (...) for diversity policies, we advise against interpreting such results overly broadly. (shrink)

As well as disagreeing about how much one should donate to charity, moral theories also disagree about where one should donate. In light of this disagreement, how should the morally uncertain philanthropist allocate her donations? In many cases, one intuitively attractive option is for the philanthropist to split her donations across all of the charities that are recommended by moral views in which she has positive credence, with each charity’s share being proportional to her credence in the moral theories that (...) recommend that particular charity. Despite the fact that something like this approach is already being used by real-world philanthropists to distribute billions of dollars of donations, it is not supported by any of the approaches to moral uncertainty that have been proposed thus-far in the philosophical literature. In this paper, we will develop a bargaining-based approach to moral uncertainty that honors the proportionality intuition in favor of splitting one’s donations. We also show how this bargaining-based approach has several further advantages over the best alternative proposals. (shrink)

What is the function of cognition? On one influential account, cognition evolved to co-ordinate behaviour with environmental change or complexity. Liberal interpretations of this view ascribe cognition to an extraordinarily broad set of biological systems—even bacteria, which modulate their activity in response to salient external cues, would seem to qualify as cognitive agents. However, equating cognition with adaptive flexibility per se glosses over important distinctions in the way biological organisms deal with environmental complexity. Drawing on contemporary advances in theoretical biology (...) and computational neuroscience, we cash these distinctions out in terms of different kinds of generative models, and the representational and uncertainty-resolving capacities they afford. This analysis leads us to propose a formal criterion for delineating cognition from other, more pervasive forms of adaptive plasticity. On this view, biological cognition is rooted in a particular kind of functional organisation; namely, that which enables the agent to detach from the present and engage in counterfactual inference. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

ABSTRACT The aim of this paper is to elucidate Schopenhauer’s moral philosophy in terms of an ethics of virtue. This paper consists of four sections. In the first section I outline three major objections Schopenhauer raises for Kant’s moral philosophy. In section two I extract from these criticisms a framework for Schopenhauer’s own position, identifying how his moral psychology underpins a unified and hierarchical conception of virtue and vice. I then ascertain some strengths of this view. In section three I (...) focus in upon the issue of fixed character and moral education as at least one major point of divergence between Schopenhauer’s virtue ethics and typical trends within the tradition. In the fourth and final section, I consider and respond to this ethical framework’s possible susceptibility to the charge of egoism, and adjudicate among competing solutions in the secondary literature. I conclude that refined forms of Schopenhauer’s ethical views offer rich and plausible insights into both virtue and vice which have received less attention than they deserve. Hence, Schopenhauer warrants more serious concern in contemporary discussions of virtue ethics alongside the likes of Aristotle, Hume and Nietzsche. (shrink)

Definition of the problemOrganisations play a vital role in modern societies. This article presumes a lack of sufficient organisational reflection of well-established forms of ethics and ethics counselling in institutions belonging to the health sector or sees particular challenges where it is implemented.ArgumentsWe have therefore conceived a procedural type of organisational ethics which critically examines the organisational fit of processes in terms of ethical reflection, leading to practicable suggestions.ConclusionsOn the one hand they relate to where differences are established when asking (...) for the good; on the other hand they are concerned with background theories and the organisational fit of the reflection settings. (shrink)

The Naked Self explores Søren Kierkegaard's understanding of selfhood by situating his work in relation to central problems in contemporary philosophy of personal identity: the role of memory in selfhood, the relationship between the notional and actual subjects of memory and anticipation, the phenomenology of diachronic self-experience, affective alienation from our past and future, psychological continuity, practical and narrative approaches to identity, and the intelligibility of posthumous survival. By bringing his thought into dialogue with major living and recent philosophers of (...) identity, Stokes reveals Kierkegaard as a philosopher with a significant--if challenging--contribution to make to philosophy of self and identity. (shrink)

Is childhood valuable? And is childhood as, less, or more, valuable than adulthood? In this article I first delineate several different questions that we might be asking when we think about the ‘value of childhood’, and I explore some difficulties of doing so. I then focus on the question of whether childhood is good for the person who experiences it. I argue for two key claims. First, if childhood wellbeing is measured by the same standards as adulthood, then children are (...) worse off than adults. Second, if childhood and adulthood wellbeing are measured by different standards, then we cannot compare them, and children are neither better off nor worse off than adults. This has some counter-intuitive implications, such as that we do not harm persons by depriving them of a childhood, nor by keeping them as children for elongated periods. (shrink)

In this paper, I articulate an argument for incompatibilism about moral responsibility and determinism. My argument comes in the form of an extended story, modeled loosely on Peter van Inwagen’s “rollback argument” scenario. I thus call it “the replication argument.” As I aim to bring out, though the argument is inspired by so-called “manipulation” and “original design” arguments, the argument is not a version of either such argument—and plausibly has advantages over both. The result, I believe, is a more convincing (...) incompatibilist argument than those we have considered previously. (shrink)

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...) by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

In his lectures, Kant suggested to his students that the freedom of a divine holy will is “easier to comprehend than that of the human will,”(28:609) but this suggestion has remained neglected. After a review of some of Kant’s familiar claims about the will (in general), and about the divine holy will in particular, I consider how these claims give rise to some initial objections to that conception. Then I defend an interpretation of Kant’s conception of the divine will, and (...) of its historical development in relation to Leibniz and Spinoza, that identifies the content, origin, and role of God’s representations in a way that is responsive to some of the historical and contemporary problems. Finally, I trace a few of the implications of this account of the divine will for our understanding Kant’s account of freedom more generally, including human freedom. (shrink)

Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore.

It remains controversial whether touch is a truly spatial sense or not. Many philosophers suggest that, if touch is indeed spatial, it is only through its alliances with exploratory movement, and with proprioception. Here we develop the notion that a minimal yet important form of spatial perception may occur in purely passive touch. We do this by showing that the array of tactile receptive fields in the skin, and appropriately relayed to the cortex, may contain the same basic informational building (...) blocks that a creature navigating around its environment uses to build up a perception of space. We illustrate this point with preliminary evidence that perception of spatiotemporal patterns on the human skin shows some of the same features as spatial navigation in animals. We argue (a) that the receptor array defines a ‘tactile field’, (b) that this field exists in a minimal form in ‘skin space’, logically prior to any transformation into bodily or external spatial coordinates, and (c) that this field supports tactile perception without integration of concurrent proprioceptive or motor information. The basic cognitive elements of space perception may begin at lower levels of neural and perceptual organisation than previously thought. (shrink)

One of the central tasks for naturalistic theories of representation is to say what it takes for something to be a representation, and some leading theories have been criticised for being too liberal. Prominent discussions of this problem have proposed a producer-oriented solution; it is argued that representations must be produced by systems employing perceptual constancy mechanisms. However, representations may be produced by simple transducers if they are consumed in the right way. It is characteristic of representations to be consumed (...) by systems which are capable of independent action. This paper defends this claim; discusses more precise, naturalistic formulations; and shows how it can illuminate the explanatory payoffs which science achieves by appealing to representation. (shrink)

‘The problem with simulations is that they are doomed to succeed.’ So runs a common criticism of simulations—that they can be used to ‘prove’ anything and are thus of little or no scientific value. While this particular objection represents a minority view, especially among those who work with simulations in a scientific context, it raises a difficult question: what standards should we use to differentiate a simulation that fails from one that succeeds? In this paper we build on a structural (...) analysis of simulation developed in previous work to provide an evaluative account of the variety of ways in which simulations do fail. We expand the structural analysis in terms of the relationship between a simulation and its real-world target emphasizing the important role of aspects intended to correspond and also those specifically intended not to correspond to reality. The result is an outline both of the ways in which simulations can fail and the scientific importance of those various forms of failure. (shrink)

In this paper we critically evaluate Trenton Merricks’s recent attempt to provide a “new” way of defending compatibilism about divine foreknowledge and human freedom. We take issue with Merricks’s claim that his approach is fundamentally different from Ockhamism. We also seek to highlight the implausibility of Merricks’s rejection of the assumption of the fixity of the past, and we also develop a critique of the Merricks’s crucial notion of “dependence.”.

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

Kant’s claims about supersensible objects, and his account of the epistemic status of such claims, remain poorly understood, to the detriment of our understanding of Kant’s metaphysical and epistemological system. In the Critique of Practical Reason, and again in the Critique of Judgment, Kant claims that we have practical cognition (Erkenntnis) and knowledge (Wissen) of the moral law and of our supersensible freedom; that this cognition and knowledge cohere with, yet go beyond the limits of, our theoretical cognition; and that (...) this knowledge grounds rational belief (Vernunftglaube) in the existence of God, the immortality of our soul, and the real possibility of the “highest good.” This essay untangles some of these claims about practical cognition, practical knowledge, and practical belief and their relation to Kant’s account of theoretical cognition and theoretical knowledge. There is a core conception of cognition and knowledge underlying the accounts of theoretical cognition and practical cognition, which allows for a principled distinction between cases of practical knowledge and practical belief. Kant’s doctrine of the “fact of reason” turns out to be crucial to his claims about legitimacy of and distinction between the two forms of practical cognition, one which constitutes knowledge and another which cannot. (shrink)

This article revisits Karl Popper’s falsificationist methodology with respect to three tasks. The first is to illuminate and systematize Popper’s methodological views in light of his core epistemological commitments. A second and related objective is to gauge which aspects of falsificationism should be identified as “conventionalist”—a label that Popper himself uses (albeit with qualifications) but that is compromised by and, thus, stands in need of elucidation because of Popper’s idiosyncratic understanding of conventionalism. Third, by elaborating Popper’s virtue-epistemological, dialogical model of (...) rationality, I show how Popper’s conventionalism, fallibilism, and critical rationalism form a coherent system. This system allows Popper to accord science the status of a privileged source of knowledge—without naïve appeal to authority. My systematization of Popper’s views yields an intrinsically and exegetically more satisfactory reading of Popper’s falsificationism than usual presentations. Thanks to its marked flexibility and methodological liberalism, it bypasses many standard objections but still offers sound and relevant methodological advice. With its “virtue-methodological” thrust, Popper sketches an original and promising approach to methodology, the fertility of which deserves further exploration for contemporary debates. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

Ethics consultation in institutions of the healthcare system has been given a standard form based on three pillars: education, the development of guidelines and concrete ethics consultation in case conferences. The spread of ethics committees, which perform these tasks on an organizational level, is a remarkable historic achievement. At the same time it cannot be denied that modern ethics consultation neglects relevant aspects of care ethics approaches. In our essay we present an “ethics of care” approach as well as an (...) empirical pilot project—“Ethics from the bottom up”—which organizes ethics consultation based on this focus. Findings and philosophy of the project will be discussed as far as relevant for ethics consultation in the healthcare system. (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)

The iterated Prisoner’s Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 198Ob, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that finally triumphs in (...) an ecological model based on population percentages (Axelrod and Hamilton 1981), but ‘generous tit for tat’ (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of l/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner’s Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GIFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of ‘bending over backwards’, which returns cooperation for defection with a probability of 2/3 - a rate twice as generous as GTFT. (shrink)

Aristotelian substance theory tells us that substances have structures (read: forms) as proper parts. This claim has recently been defended by Kathrin Koslicki who dubbed it the ‘Neo-Aristotelian Thesis.’ Strangely, Aristotelianism has not yet been universally embraced by philosophers – partly because some of its claims, such as the Neo-Aristotelian Thesis – are viewed by some as counterintuitive at best. In this paper, I argue for Aristotelianism by showing its philosophical usefulness: specifically, I put it to use in saving the (...) metaphysical doctrine of endurantism and some central mereological doctrines (such as Transitivity) from recent attacks. This utility gives us reason to endorse Aristotelianism. Along the way, I defend Koslicki's argument for the Neo-Aristotelian Thesis from a recent criticism, thus helping provide still more reason to endorse Aristotelianism: namely, Koslicki's vindicated argument. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and (...) his understanding of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis (...) of Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

This article examines the debate about the normative relevance of social constructivism, arguing that the criticisms of Winner, Radder, and others are fundamentally accurate. The article argues that a combination of Radder's notion of nonlocal values and Martin's concern for deliberative interventions may offer a theoretical exit from the normative irrelevance that marks constructivism. The article goes on to suggest that theoretical and praxeological developments in two other literatures, participatory public policy analysis and deliberative democracy, may provide fruitful initiatives for (...) constructivist scholars eager to address normative concerns. The article next reviews a range of problems facing deliberative and participatory practices and suggests ways in which constructivist insights might help to advance deliberative theory. (shrink)

Interpersonal disagreement happens all the time. How to properly characterize interpersonal disagreement and how to respond to it are important problems, but the existence of such disagreements at least is obvious. The existence of intrapersonal disagreement, however, is another matter. On the one hand, we do change our minds sometimes, especially when new evidence comes in, and so there is a clear enough sense in which we can be characterized as having disagreements with our past selves. But what about synchronic (...) disagreements with ourselves? Are such cases possible, or is there something about the nature of belief that rules out the possibility of knowingly holding beliefs which cannot be rationally held at the same time? In this paper, I argue that there can be cases of intrapersonal synchronic disagreement, and that such disagreements can be deep, in the same way that interpersonal disagreements can be deep. For intrapersonal disagreements, just like interpersonal disagreements, can be grounded in conflicting frameworks for interpreting and reasoning about the world. I also argue that synchronic intrapersonal disagreements are peer disagreements. The paper ends with a discussion of four possible responses to interpersonal deep disagreements, concluding that if those responses are sometimes rational responses in the interpersonal case, then they are also sometimes rational responses in the intrapersonal case. (shrink)

This paper lays out the moral theory of philosopher and educator Maria Montessori (1870–1952). Based on a moral epistemology wherein moral concepts are grounded in a well-cultivated moral sense, Montessori develops a threefold account of moral life. She starts with an account of character as an ideal of individual self-perfection through concentrated attention on effortful work. She shows how respect for others grows from and supplements individual character, and she further develops a notion of social solidarity that goes beyond cooperation (...) toward shared agency. Partly because she attends to children's ethical lives, Montessori highlights how character, respect, and solidarity all appear first as prereflective, embodied orientations of agency. Full moral virtue takes up prereflective orientations reflectively and extends them through moral concepts. Overall, Montessori's ethic improves on features similar to some in Nietzschean, Kantian, Hegelian, or Aristotelian ethical theories while situating these within a developmental and perfectionist ethics. (shrink)

This paper attempts to identify a principle of equal treatment that gives specific structure to our widely shared judgments about the circumstances in which we have moral reason to object to the differential adverse treatment of others. I formulate what I call a “substantive” principle of equal treatment (to be distinguished from principles of formal equality) that describes a moral constraint on the reasons we can have for picking out individuals for differentially adverse action. I argue that this constraint is (...) violated when an action, in view of its rationale, expresses lesser respect for the moral status of an individual under some differentiating description, compared to the respect reserved to another class of individuals who are not picked out by that description. I show that this substantive demand of equal treatment is not morally otiose and reveal the fallacy underlying accounts that have concluded otherwise. (shrink)

Subjects estimated the time of intentions to perform an action, of the action itself, or of an auditory effect of the action. A perceptual attraction or binding effect occurred between actions and the effects that followed them. Judgements of intentions did not show this binding, suggesting they are represented independently of actions and their effects. In additional unpredictable judgement conditions, subjects were instructed only after each trial which of these events to judge, thus discouraging focussed attention to a specific event. (...) Stronger binding effects were found, with intention, action and effect fusing to a single central point in time. In a control task, subjects reported the time of the first or second tone in sequence. Tone sequences showed no binding at all when subjects knew in advance which tone to judge, but showed the same fusion as actions when the event to be judged was not predictable. Binding of actions and effects, but not of tone sequences, occurs pre-attentively, and automatically. The data are consistent with a reconstructive process, implemented after actions, which generates a coherent sense of agency. However, this process should only be triggered only when our actions make it appropriate. We suggest that this mechanism is triggered in advance by efferent processing. This conclusion was supported by a further study in deafferented subject IW. This subject showed the normal binding of a tone towards an action, although his experience of the action was of pre-motor, rather than peripheral origin. The experience of intentional action involves an interplay between pre-motor and reconstructive processes. (shrink)

Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of scientific researchers, auditors, financial analysts, air crash investigators, and forensic art experts are increasingly important in our complex and interdependent society. This comprehensive textbook--the first of its kind in decades--presents important theories and experimental research about group problem solving. The book focuses on tasks that have demonstrably correct solutions within mathematical, logical, scientific, or verbal (...) systems, including algebra problems, analogies, vocabulary, and logical reasoning problems.The book explores basic concepts in group problem solving, social combination models, group memory, group ability and world knowledge tasks, rule induction problems, letters-to-numbers problems, evidence for positive group-to-individual transfer, and social choice theory. The conclusion proposes ten generalizations that are supported by the theory and research on group problem solving. Group Problem Solving is an essential resource for decision-making research in social and cognitive psychology, but also extremely relevant to multidisciplinary and multicultural problem-solving teams in organizational behavior, business administration, management, and behavioral economics. (shrink)

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

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)

Theological fatalists contend that if God knows everything, then no human action is free, and that since God does know everything, no human action is free. One reply to such arguments that has become popular recently— a way favored by William Hasker and Peter van Inwagen—agrees that if God knows everything, no human action is free. The distinctive response of these philosophers is simply to say that therefore God does not know everything. On this view, what the fatalist arguments in (...) fact bring out is that it was logically impossible for God to have known the truths about what we would freely do in the future. And this is no defect in God’s knowledge, for infallible foreknowledge of such truths is a logical impossibility. It has commonly been assumed that this position constitutes an explanation of where the fatalist argument goes wrong. My first goal is to argue that any such assumption has in fact been a mistake; Hasker and van Inwagen have in effect said only that something does go wrong with the argument, but they have not explained what goes wrong with it. Once we see this result, we’ll see, I think, that they need such an account—and that no such account has in fact been provided. The second goal of this paper is therefore to develop— and to criticize— what seems to be the most promising such account they might offer. As I see it, this account will in fact highlight in an intuitively compelling new way what many regard to be the view’s chief liability, namely, that the truths about the future which God is said not to know will now appear even more clearly (and problematically)‘ungrounded’. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

What is the relationship between harm and disease? Discussions of the relationship between harm and disease typically suffer from two shortcomings. First, they offer relatively little analysis of the concept of harm itself, focusing instead on examples of clear cases of harm such as death and dismemberment. This makes it difficult to evaluate such accounts in borderline cases, where the putative harms are less severe. Second, they assume that harm-based accounts of disease must be understood normatively rather than naturalistically, in (...) the sense that they are inherently value based. This makes such accounts vulnerable to more general objections of normative accounts of disease. Here we draw on an influential account of harm from the philosophy of law to develop a harm-based account of disease that overcomes both of these shortcomings. (shrink)

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...) better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)

In this paper, I take it to be uncontroversial that increasingly into his philosophical career, Nietzsche believed human greatness to be an appropriately valuable goal, at least for certain types of people. But while Nietzsche's repeated paradigms of greatness include figures as seemingly diverse as Beethoven, Goethe, Shakespeare, Cesare Borgia, Julius Caesar, it is unclear precisely what great-making property (or properties) Nietzsche considers these figures to share. I consider two possible approaches which have shaped the terrain of the secondary literature (...) on this controversial matter: greatness as a matter of internal properties (character traits); or external properties (achievements). I discuss the arguments for each view here, resulting with my own view being that both achievements and traits of character are at least necessary for what Nietzsche understands greatness to consist in. I then consider a distinction between actual and potential greatness in order to explore further necessary and perhaps sufficient conditions of Nietzsche's positive ideal. While my aim in this paper is primarily exegetical, I hope to draw upon contemporary issues in value theory surrounding the nature of achievement which are of interest to ethicists more broadly. (shrink)

Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...) of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.Paul Rosenbloom 1950. (shrink)

For several decades, public political discourses on ‘welfare dependency’ have failed to recognise that welfare states are not the source of economic dependence, but rather reconfigure economic dependencies in a specific way. This article distinguishes four senses of ‘economic dependence’ that can help to clarify what is missing from these discourses, and what is at stake in political and legal decisions about how we may economically depend upon one another. While feminist, republican and egalitarian philosophical work has examined the problems (...) of dependence on states, in families and in markets, the present approach adds a further dimension to our cultural and political concerns with economic dependence: it argues that it is reasonable and useful to consider the economic dependence of the economically powerful. Doing so requires a clarification of the ‘varieties of dependence’ that exist in contemporary societies and economies, and the recognition that legal and political choices regarding social and economic justice are often about choosing between varieties of dependence, not about escaping dependence entirely. (shrink)