AUGUSTINE WISHED TO DEFEND AND MAKE AS INTELLIGIBLE AS POSSIBLE THE CHRISTIAN DOCTRINE OF THE TRINITY. I SHOW HOW AUGUSTINE WORKS WITH AN ARISTOTELIAN MODEL OF PREDICATION, DERIVES AN INCOMPLETENESS RESULT WITHIN THE STANDARD FORMS OF PREDICATION, AND ACCEPTS, WITH SOME QUALIFICATION, A NONSTANDARD FORM OF PREDICATION USED BY ARISTOTLE FOR PREDICATING PRIMARY SUBSTANCE OF MATTER.

Reading through the Corpus Aristotelicum we come across a group of expressions meant to indicate predicative relations, which lead us to think that Aristotle connected predication to a part-whole relation. He frequently calls the ‘εἴδη’, “species”, ‘μέρη’, “parts”, of their genera. More generally, the universal is said to contain that of which it is true. In a parallel way, what is contained by something is also what is under something else. Again, it is quite common for him to consider (...) the species as partaking of their genera. Although the relation of partaking is normally used to qualify the way in which species are related to their genera, sometimes also the relation between particulars and species or even genera is expressed in terms of partaking. (shrink)

In Predication and Ontology A. Kalbarczyk provides the first monograph-length study of the Arabic reception of Aristotle’s Categories. At the center of attention is the critical reappraisal of that treatise by Ibn Sīnā, better known in the Latin West as Avicenna. Ibn Sīnā’s reading of the Categories is examined in the context of his wider project of rearranging the transmitted body of philosophical knowledge. Against the background of the late ancient commentary tradition and subsequent exegetical efforts, Ibn Sīnā’s Kitāb (...) al-Maqūlāt of the Šifāʾ is interpreted as a milestone in the gradual reshuffle of the relationship between logic proper and ontology. In order to assess the philosophical impact of this realignment, some of the subsequent developments in Ibn Sīnā’s writings and in the emerging post-Avicennian tradition are also taken into account. The thematic focus lies on the two fundamental classification schemes which Aristotle introduces in the treatise: the fourfold division of Cat. 2 and the tenfold scheme of Cat. 4. They both pose the question of whether and how the manner in which an expression is predicated relates to extra-linguistic reality. As the study intends to show, this question is one of the driving forces of Ibn Sīnā’s momentous reform of the Aristotelian curriculum. (shrink)

What in Aristotle corresponds, in whole or (more likely) in part, to our contemporary notion of predication? This paper sketches counterparts in Aristotle's text to our theories of expression and of truth, and on this basis inquires into his treatment of sentences assigning an individual to its kinds. In some recent accounts, the Metaphysics offers a fresh look at such sentences in terms of matter and form, in contrast to the simpler theory on offer in the Categories . I (...) argue that the Metaphysics initiates no change in this regard over the Categories . The point that form is (metaphysically) predicated of matter is a contribution, not to the account of statement predication, but to the analysis of compound material substances. Otherwise put, in our terms Aristotelian form is not - in particular, is not also - a propositional function, but a function from matter to compound material substances. (shrink)

The article proposes a renewed analysis of the texts in which Aristotle claims that the term ‘good’ is spoken of in many ways and more precisely in as many ways as there are categories. After a revision of the traditional interpretations, a new reading of the texts is advanced in the light of the theory of predication described in Top. 103 b20-38 and Metaph. 1017 a7-30. The conclusion is that in the Aristotelian passages on the multivocity of ‘good’, (...) the word ‘good’ should not be meant as the predicate of categorially distinct realities, and therefore as a qualifying adjective, but itself as the subject of the question what is it? (τί ἐστι;) In this way, it is possible to advance the hypothesis that the homonymous notion of ‘good’ performs a predicative function, useful to the formulation of practical and prescriptive propositions. (shrink)

ON A GENERAL READING of the Metaphysics and the treatises of the so-called Organon, the types of assertion which Aristotle would allow as genuine predications seem relatively straightforward. According to the Categories, for instance, a species is characteristically predicated of the individuals falling under it, while genera and differentiae are predicated both of the relevant species and their associated individuals. The predicates are, in these instances, universals in a familiar Aristotelian sense. Furthermore, these intra-categorial predications, such as "Socrates is (...) a man" and "white is a color," are not the only instances of categorial acts. Aristotle also admits certain cross-categorial predications as logically well-formed; for example, "Socrates is white" and "Socrates is in the marketplace". These latter predications are at first glance also intelligible enough, though there are in both cases questions yet to be faced about the logical structure and ontological commitments of such ways of speaking. For Aristotle, one metaphysical theme presented even on the face of these linguistic appearances is the possibility that being a substrate for predication counts as a criterion for ontological primacy or, more generally, that being an ultimate substrate for meaningful discourse is grounds for being primarily real. An obvious corollary to this line of thought is the thesis that whatever might be said of or predicated of such primary substrata is ontologically dependent upon them. Just such a criterion seems to be at work in disqualifying universals from their claim to be substance in a significant sense. Therefore, it would be somewhat surprising to find primary substance appearing anywhere as a predicate. (shrink)

Abstractionist programs in the philosophy of mathematics have focused on abstraction principles, taken as implicit definitions of the objects in the range of their operators. In second-order logic (SOL) with predicative comprehension, such principles are consistent but also (individually) mathematically weak. This paper, inspired by the work of Boolos (Proceedings of the Aristotelian Society 87, 137–151, 1986) and Zalta (Abstract Objects, vol. 160 of Synthese Library, 1983), examines explicit definitions of abstract objects. These axioms state that there is a (...) unique abstract encoding all concepts satisfying a given formula $$\phi (F)$$, with F a concept variable. Such a system is inconsistent in full SOL. It can be made consistent with several intricate tweaks, as Zalta has shown. Our approach in this article is simpler: we use a novel method to establish consistency in a restrictive version of predicative SOL. The resulting system, RPEAO, interprets first-order PA in extensional contexts, and has a natural extension delivering a peculiar interpretation of PA $$^2$$. (shrink)

The Aristotelian double characterization of a primary substanceexploits the difference between the part-whole relation and the non-linguisticrelation of predication. A problem arises whether and how the second relationcould be reduced to something else. Such a reduction is explicitly declared orat least implicitly assumed in all version of conceptualism and nominalism.The moderate realism is often interpreted as a reductionism of this kindbut such interpretations do not seem corect. Only the so called resemblancetheory can be regarded as a successful attempt (...) at the reduction in question.However, it seems that the predication per se cannot be disposed of even inthis way. If so, then the nature of the relation of predication still waits fora precise analysia and description. This would provide an insight into theessence of a universal being. (shrink)

Geach's account of the Aristotelian logic of categorical sentences supplemented the views shared by Frege, Russell, Quine and others. I argue that this particular predicate logic approach and Geach's points apply to only one variety of natural language categorical sentences. For example, it takes the universal categorical as a universal conditional “If anything is a man, then it is mortal”. A different natural language form can and should be invoked: “Every man is a mortal.” Employing special restricted quantifiers in (...) a version of predicate logic, we justify a full square of opposition and the rules of quality and quantity that Geach rejected. (shrink)

ABSTRACTI offer a simple‐minded analysis of presupposition in which if a sentence has a presupposition, then both that sentence and its negation logically entail the presupposition; and in which sentence with failed presuppositions are neither true nor false. This account naturally generates an analysis of what it takes to disagree and what it takes to be at fault in a disagreement. A simple generalization gives rise to the possibility of disagreements in which no party is at fault, as is required (...) by leading theories on predicates of taste. (shrink)

Michael-John Turp | : There is little consensus concerning the truth or reference conditions for evaluative terms such as “good” and “bad.” In his paper “Good and Evil,” Geach proposed that we distinguish between attributive and predicative uses of “good.” Foot, Thomson, Kraut, and others have put this distinction to use when discussing basic questions of value theory. In §§1-2, I outline Geach’s proposal and argue that attributive evaluation depends on a prior grasp of the kind of thing that is (...) evaluated, which is another way of saying a prior grasp of a thing’s nature. In §§3-4, I discuss the evaluation of artifacts, which provide the clearest examples of attributive evaluation. This allows me to address a series of problems apparently facing the idea of attributive goodness. In §5, I consider the neo-Aristotelian idea that we can extend attributive accounts of goodness to human lives, and I pay attention to Foot’s account of natural goodness. This leads me to consider the goodness of human life as a whole in §6. At this point. I depart from Geach’s approach and argue that questions of attributive goodness finally give rise to questions of predicative or absolute goodness. | : Il y a peu de consensus sur la vérité ou les conditions de référence pour les termes évaluatifs tels que « bon » et « mauvais ». Dans son article « Good and Evil », Geach a proposé de distinguer les usages attributif et prédicatif du « bon ». Foot, Thomson, Kraut et d’autres considèrent qu’il faut utiliser cette distinction lorsqu’il s’agit des questions fondamentales de la théorie de la valeur. Dans les parties 1-2, je décris ici la proposition de Geach et je prétends que l’évaluation attributive dépend d’une compréhension préalable du genre de chose qui est évaluée, ce qui est une autre façon de dire une compréhension préalable de la nature d’une chose. Dans les parties 3-4, je discute de l’évaluation des artefacts, qui fournissent les exemples les plus clairs d’évaluation attributive. Cela me permet d’illustrer une série de problèmes apparemment liés à l’idée de la bonté attributive. Dans la partie 5, je considère l’idée néo-aristotélicienne voulant que nous puissions étendre notre compréhension de la bonté attributive aux vies humaines, et je me penche sur l’idée de bonté naturelle selon Foot. Cela me conduit à considérer la bonté de la vie humaine comme un tout, dans la partie 6. De là, je m’éloigne de l’approche de Geach pour affirmer que les questions de bonté attributive suscitent finalement des questions de bonté prédicative ou absolue. (shrink)

Those who believe that ordinary things have temporal as well as spatial parts must give an account of the truth conditions of temporally modified predications of the form ‘a is F at t ’ in terms of temporal parts. I will argue that the friend of temporal parts is committed to an account of temporal predication that is incompatible with the classical principle of predicate abstraction.

According to Aristotelian logic, in categorical logic, there are three kinds of judgements (qaḍīyya): affirmative, negative, and metathetic (ma‘dūla). Khūnajī, a famous Muslim logician in the 13th century, introduces a different judgement (or statement) entitled “affirmative judgement with the negative predicate” (mūjiba al-sāliba al-maḥmūl; henceforth, ANP judgement). Although in the Arabic language, formally, ANP judgement is similar to definite negative (sāliba muḥaṣṣala) and also metathetic judgements, the way of its construction is different from both of them and its truth (...) conditions are different from metathetic ones. From a modern logic viewpoint, ANP may indicate equality judgement; however, attributing it to Muslim logicians is questionable, although some of their wordings may implicitly show it. According to Ḥāʾirī, an Iranian contemporary philosopher and logician, the new judgement is supposed to solve some problems, especially logical explanation of the division of modalities into necessity, impossibility, and contingency (imkān khāṣṣ). However, Ṭabāṭabāʾī, another Iranian contemporary philosopher, disagrees with Ḥāʾirī and regards ANP judgement the same as an affirmative metathetic one. In this paper, while examining Ṭabāṭabāʾī’s and Ḥāʾirī’s reasons, by using some insights into modern logic, I will try to strengthen Ṭabāṭabāʾī’s views, although it may be confronted with some questions or deficiencies. (shrink)

The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed.GraphicThe photo shows a prototype sculpture for the cube.

One of the perennial questions of philosophy concerns the simple statements which say that an object is so and so or that such and such objects are so and so related: simple predicative statements. Do such statements have an ontological basis, and if so, what is that basis? The answer to this question determines—or in any case, is expressive of—a specific fundamental outlook on the world. In the course of the history of Western philosophy, various philosophers have given various answers (...) to the question of predication. This essay presents the main, crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. In addition, the essay follows (to some extent) the most influential—the Aristotelian or mereological—paradigm of predication in its continuity and modification through the many centuries of its reign. However, the essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, there was no philosophically adequate theory of predication, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication theory considered in it. Frege, in the nineteenth century, brought the philosophy of predication on the right track, but his own theory of predication has its own deficits. The essay ends with the presentation of a theory of predication that the author himself considers adequate. (shrink)

In the past four or five years I have been especially dependent on Aristotle's writings as I have initiated a series of experiments that can legitimately be called empirical efforts to prove Aristotelian conceptions to be true. In actuality, of course, I am trying to prove my own theory to be true—that is, worthy of consideration because it is consistent with observed human actions. However, by extension, I am surely seeking evidence for Aristotle's image of human cognition. There are (...) two Aristotlelian conceptions that underwrite my theoretical and empirical efforts: predication and opposition. When we speak of a "predication" in cognition we refer to a process that is fundamentally creative. Predications deal in meanings; and the way in which we align meanings, lending the meaning of one concept to another is what predication is all about. Predication is the act of affirming, denying, or qualifying certain patterns of meaning in relation to other patterns of meaning. The second Aristotelian conception that I have been employing theoretically and investigating empirically is "opposition." Although association through frequent contact was recognized by Aristotle , he also appreciated that there is often an intrinsic tie of opposite meanings to be seen in human reason. In my own interpretation of Aristotle, I believe that we can see the ultimate necessity of predication stemming from the opositional ties of meanings like this. If I am cognizing within a congerie of interlacing meanings which relate to and, indeed, delimit the definitions of their opposite meanings, then it is up to me as a cognizer to continually "take a position" on just what I am going to affirm—or not! 2012 APA, all rights reserved). (shrink)

Glenn Langford; XI—Rules, Moral Rules and the Subjects of Moral Predicates, Proceedings of the Aristotelian Society, Volume 69, Issue 1, 1 June 1969, Pages 187–.

Nexuses such as exemplification are the fundamental ties that structure reality as a whole. They are “formal” in the sense of constituting the form, not the matter of reality and they are “transcendental” inasmuch as they transcend the categorial distinctions between the denizens of reality, including that between existents and non-existents. I shall advocate a moderately particularist view about (external) nexuses and argue that it provides not only the best solution to Bradley’s regress, but also an elegant account of symmetrical (...) relations (both formal and material), as well as of temporal and modal change. These advantages are illustrated by the reconstruction of an Aristotelian ontology of exemplification involving substances, kinds and material attributes. (shrink)

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are (...) elaborated, and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

On several critical occasions in his philosophical and theological musings, we find Abelard having recourse to what is at heart the same philosophical simile -- in one instance drawing comparison to a stone statue, in another to a bronze statue, in a third to a wax image. The common point of comparison is obvious; each of these examples gives us a case where some physical material has come to receive some manner of shape. The doctrine illustrated by these means is (...) not, as might be supposed, a conventional Aristotelian form/matter metaphysics. (shrink)

This paper deals with Aristotelian and Stoic logic. In the first part the author writes about the history of logic and shows, why Stoic logic had not been studied properly from the Middle Ages up to the beginning of the 20th century, when an increasing interest in the study of Stoic logic is visible. The paper describes the character of Aristotelian and Stoic logic respectively. Stoic logic is first introduced as a system of propositional logic. On this basis (...) a complementarity between the two logical systems of Antiquity is stated. The ways to support the thesis that Stoic logic involved some features of predicative logic are shown at the end of the first part. The ways in which the two rival logical systems were perceived by the authors of the first centuries A. D., namely Galen and Boethius, is described in the second part. Galen is seen as the first to develop an objective synthesis of the two systems. In his Eisagogé dialektiké he tries to show the goals of both rival logical systems. Boethius, in his De hypotheticis syllogismis, is also combining the Aristotelian and the Stoic logic. However, his synthesis is different from Galen's because Boethius probably forms the synthesis unknowingly and indirectly through compiling his confused sources. (shrink)

Peters and Westerståhl (Quantifiers in Language and Logic, 2006), and Westerståhl (New Perspectives on the Square of Opposition, 2011) draw a crucial distinction between the “classical” Aristotelian squares of opposition and the “modern” Duality squares of opposition. The classical square involves four opposition relations, whereas the modern one only involves three of them: the two horizontal connections are fundamentally distinct in the Aristotelian case (contrariety, CR vs. subcontrariety, SCR) but express the same Duality relation of internal negation (SNEG). (...) Furthermore, the vertical relations in the classical square are unidirectional, whereas in the modern square they are bidirectional. The present paper argues that these differences become even bigger when two more operators are added, namely the U ( ${{\equiv} {\rm A}\,{\vee} \,{\rm E} }$ , all or no) and Y ( ${\equiv{\rm I} \,{\wedge} \,{\rm O}}$ , some but not all) of Blanché (Structures Intellectuelles, 1969). In the resulting Aristotelian hexagon the two extra nodes are perfectly integrated, yielding two interlocking triangles of CR and SCR. In the duality hexagon by contrast, they do not enter into any relation with the original square, but constitute a independent pair of their own, since they are their own SNEGs. Hence, they not only stand in a relation of external NEG, but also in one of duality. This reflexive nature of the SNEG will be shown to result in defective monotonicity configurations for the pair, namely the absence of right-monotonicity (on the predicate argument). In the second half of the paper, we present an overview of those hexagonal structures which are both Aristotelian and Duality configurations, and those which are only Aristotelian. (shrink)

This paper consists roughly of three parts. In the first part, an attempt has been made to find some tenable interpretation of Hamilton's logic. This results in accepting that Hamilton's logic can be "saved" if it is understood as being an everday language version of Euler's relations, i.e., extensional relations between terms. In the second part, the propositions of Euler and the propositions of Aristotle are compared and found to be interdefinable: every proposition of Aristotle can be defined by a (...) disjunction of Euler's propositions, and every proposition of Euler can be defined by a conjunction of Aristotle's propositions. In the third part, extensional interpretation is applied to the traditional logic. As a result the 19 traditional syllogisms are reduced to 11. (shrink)

The purpose of this paper is to point out that some mathematical doctrines attributed by Aristotle to Plato find their origin in a threefold order of problems: first, in some allusions contained in the dialogues, which might create ambiguities within the so-called standard model of ideas; second, in the Aristotelian interpretation of ideal entities as universals or predicates, an interpretation in turn partly authorized by Plato himself; third, in the tendency not to emphasize the possibility of understanding participation and (...) the whole-part relationship from a non-quantitative point of view. In this paper I will disregard the complex debate about whether or not to attribute the unwritten doctrines of the Aristotelian account to Plato, but I will appraise in what sense some Aristotelian objections to participation may arise from the fact of conceiving of numbers and magnitudes as ideas. (shrink)

Throughout the greater part of the twentieth century, both in the analytic and continental traditions, metaphysics was deemed to be passé. The last few decades, however, have witnessed a remarkable growth of interest among analytic philosophers in various traditional metaphysical topics, such as modality, truth, causality, etc. which resulted in the emergence of various forms of analytic metaphysics. The new forms of metaphysics differ from its traditional forms mostly in their methodology and in the range of proposed solutions to particular (...) problems. Besides these and other differences, however, there are also many similarities and there are even some who intentionally develop traditional metaphysical themes using the contemporary analytical methods. All these developments call for detailed exploration, which is the general goal of the present publication Metaphysics: Aristotelian, Scholastic, Analytic. The publication is the fruit of the conference which took place in Prague in 2010 and which had for its aim to bring together those willing to explore relations between the traditional and contemporary concerns, both from among the leading analytic philosophers working in metaphysics and the historians of philosophy devoted to the study of the metaphysical tradition. The specific focus of the conference was a re-examination of topics such as categories, metaphysical structure, substance and accident, existence, modalities, and predication. (shrink)

The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.

Must we choose between reducing material substances to collections of properties, a’ la Berkeley and Hume or positing bare particulars, in the manner of Locke? Having repudiated the notion that a substance could simply be a collection of properties existing on their own, is there a viable alternative to the Lockean notion of a substratum, a being essentially devoid of character? E.J. Lowe and Michael Loux would answer here in the affirmative. Both recommend hylomorphism as an upgrade on the metaphysics (...) of the British empiricists: treating a material substance as its essential 'form,' this embodied 'substance' universal being, in turn, the substratum in which its 'accidents' inhere. Here, I evaluate this Aristotelian metaphysics, identifying the advantages it enjoys over the empiricist's alternatives pertaining to dependence, unity, identity, change, and the distinction between essential and accidental properties. I also develop solutions to the two problems that Loux sees it posing. (shrink)

Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the _A, E, I _and_ O_ forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional logic as it existed (...) in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation. (shrink)

A theory purporting to solve the problem of universals must be able to explain predication, recurrence, and classification. How Platonism does this is well known. Here I take a hard look at an attempt by M.J. Cresswell to give an Aristotelian answer and show it to be a complete and utter failure. The answer does not eliminate commitment to universals and it is only half an answer anyway because it does not cover relational predicates, an omission that Russell (...) noted dooms answers by other philosophers as well. (shrink)

In some of the Aristotelian accounts, Parmenides’ thesis is construed in opposition to the philosophy of nature; on the other hand, he is also depicted, in a different context, as a cosmologist, to whom the Stagirite (and a long tradition afterwards, ending with Simplicius) ascribes a theory of becoming and its principles. In this paper, I exhibit and analyse the relevant passages from Physics I 1-3, Metaphysics I 3 and 5 and On generation and corruption I 3, providing an (...) interpretation that aims to solve the apparent paradox, making sense of the information we can gather from Aristotle’s and Simplicius’ testimonies. Eventually, I propose a construal of the Two Ways of fr. 2 with an emphasis on the predicative reading of einai, which could hint at the Parmenidean approach to cosmology that runs in parallel with the argument on Being. (shrink)

This paper analyzes and compares the doctrines of categories of Aristotle, Kant and Hegel, each of which is first discussed separately. The paper explains the essential double perspective of the problem, showing how a logico-linguistic analysis of the form of rational discourse serves for them as an important clue to ontological problems. Although Aristotle and Kant’s doctrines differ significantly, they both endorse a kind of isomorphism between language/thought and reality. By contrast, Hegel, who takes a critical attitude toward the capability (...) of human language and discursive thinking, rejects the possibility of deriving the structure of reality from the forms of predication or judgment. Nevertheless, the forms of judgment do play an equally crucial role in Hegel’s doctrine, though in a very different way from his predecessors. It is the structural “deficiency” of the judgmental form that turns out to be the driving force for the dialectical movement of the Concept. By shifting the primary concern from the categories themselves to the transitions between them, Hegel opens up the possibility of a dynamic system of categories. (shrink)

This paper addresses the question of what existential assumptions are needed for the Aristotelian interpretation of the relationships between the four categorical propositions. The particular relationships in question are those unique to the Aristotelian logic, namely, contrariety, subcontrariety, subaltemation, conversion by limitation, and contraposition by limitation. The views of several recent authors of logic textbooks are surveyed. While most construe the Aristotelian logic as capable of being preserved by assuming that the subject class has a member, Irving (...) Copi construes that logic as requiring that four assumptions about class membership be made. These are that the subject, predicate, complement of subject, and complement of predicate classes all have members. It is argued that only three assumptions about class membership are needed, viz., that subject, predicate, and complement of predicate classes have members. (shrink)

The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status (...) over the other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:188 BOOK REVIEWS work. Certainly, there is much in this book to honor the memory and continue the scholarly tradition of Beryl Smalley. University of Pennsylvania Philadelphia, Pennsylvania E. ANN MATTER Logic: An Aristotelian Approach. By MARY MICHAEL SPANGLER, 0.P. Lanham, Maryland: University Press of America, 1986. Pp. 270. $16.75 (paper). Certain fields of knowledge periodically require updated textbooks since new material is added and new issues arise. (...) One thinks of liturgical textbooks or those in moral theology. Why would we need a new text in Aristotelian logic 7 vVe still have the classic breakthrough text of the late John Oesterle, Logic: The Art of Defining and Reasoning. Five years later in 1957 appeared the brilliant volume of the late Vincent Edward Smith, The Elements of Logic. Still available is Dennis Kane's Logic: The Art of Predication and Inference. In one way or other all three present splendidly the basics of Aristotelian logic and Kane's book has a section on symbolic logic. However, another factor for publishing a new text even in a stable field of knowledge is the change in the student population. Oesterle's text is almost cryptic by comparison with the Spangler volume. Many, perhaps most, of today's students would find the clear, clipped style of Oesterle too bare for them. Smith's erudite case problems probably would intimidate many in our present logic classes. Spangler knows today's students. She has written a text that is developed in the same outline as the texts cited but in a language and style suited to our present student population. Indeed, Spangler, from her years of college teaching, is aware that many an otherwise competent student still lacks skills in reading and writing. Consequently this text, though primarily setting forth the principles of Aristotelian logic, at the same time provides optional exercises which relate logic to comprehension skills of reading. The result is an admirable textbook which brings together something of the Middle Ages' famous trivium of logic, grammar, and rhetoric. Repetition is the mother of learning but if done poorly repetition can be a total bore. Spangler has the gift for repeating the doctrine on each point of logic over and over but in such a pleasant and even entertaining way that the ~tudent is not bored but delighted at the almost effortless BOOK REVIEWS 189 progress achieved in each chapter. Further, the text includes study questions at the end of each chapter that make for a challenging review plus exercises at the back of the book which test the studrnt's skills. The teacher will find this text a imist useful tool of instruction. One can lecture on the material in one's own words. The student can read the text. Then teacher and student can discuss the material as well as have interesting sessions based on the various exercises provided. ]'or those with the time, the reading· exercises offer another rich area for intellectual growth. This text is suited for superior high school seniors, college students, and excellent as a review course at the seminary level. The latter is important. Many Catholic seminaries are providing a year or at most two years of philosophy. Some subjects are given less time than needed and logic often is ignored or has a small share in the curriculum schedule. The Spangler text is ideal for such situations. Her explanations of each point in logic are crystal clear, her illustrations abundant, and her skillful use of charts to give a comprehensive picture of the whole and parts of logic is outstanding. As one who has used the text for three years in its manuscript form, the verdict is: Try it. For students interested in a further development of logic a series of appendices is provided, including a fine one on symbolic logic. Dominican House of Studies Washington, D.C. RAYMOND SMITH, O.P. The View from Nowhere. By THOMAS NAGEL. New York: Oxford University Press, 1986. Pp. 244. $19.95. With the opening words of his Introduction, Thomas Nagel, Professor of Philosophy at New York University, makes clear the probll'rn that his book will treat: This book is about a single problem: how to... (shrink)

Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was (...) originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic. (shrink)

In this paper, I focus on the important semantic components involved in analogy in hopes of providing an epistemic ground for predicating names of God analogously. To this task, I address a semantic/epistemic problem, which concludes that the doctrine of analogy lacks epistemological grounding insofar as it presupposes a prior understanding of God in order to sufficiently alter a given concept to be proportionate to God. In hopes of avoiding this conclusion, I introduce Aquinas’s specifically semantic aspects that follow after (...) the real distinction between a thing’s esse and its essence or form in the context of analogy and show that the ratio of a term can be altered in a way proportionate to a consideration of the mode of being of God. (shrink)

Professor Veatch's writings have a special significance here. In recent years he has been more concerned than most to accept this responsibility, and more concerned than many to insist upon its importance. Drawing out some of the implications of his earlier Intentional Logic and still—as then—relatively unconcerned about the fate of any particular necessary truth, he has attempted to relate a realistic doctrine of necessity to some non-realistic doctrines. His is, it should be remarked, not a realism which for its (...) logical inspiration finds anything of use in such random realists as Peirce or Cook Wilson; rather, there are muffled echoes of the early Russell and Moore, confident quotations from Aquinas, and a very firm reliance on the finality of the Aristotelian predicables. (shrink)

Dummett defines a ‘predicate’ as that which combines with one or more singular terms to form a sentence. His account of ‘singular term’ is syntactical, involving three necessary conditions. He discusses a fourth, ‘Aristotelian’, criterion before propounding a criterion of predicate quantification which he claims to be superior to it. He tentatively proposes that the three necessary conditions plus the criterion of predicate quantification yield sufficient conditions for being a singular term. I show that Dummett’s necessary conditions fail with (...) regard to referentially opaque contexts, negative existentials and wide-scope negations, and that he overlooks an important class of predicative expressions that satisfy his three supposedly necessary conditions for singular terms, namely, those that may appear either as adjectives or as nouns. I argue that Dummett cannot use the ‘Aristotelian’ criterion without circularity; and that, in any case, the ‘Aristotelian’ criterion fails dramatically. I also show that his criterion of predicate quantification fails with regard to expressions for colours. I end by casting doubts on the adequacy of any purely syntactical approach. (shrink)

The Aristotelian tradition in a sense is constituted by the history of Aristotelianism, i. e. by the philosophies of those who declared themselves Aristotle’s followers, even if in fact they hardly ever have been completely such. But in another sense the Aristotelian tradition is formed by the patrimony of concepts, distinctions, definitions, of which not only the philosophy, but also the culture in general, and even the common language, made use for millennia and of which still now they (...) make use: category, subject-predicate, square of oppositions, syllogism, induction, refutation, contradiction, matter-form, potency-act, essence, substance-accident, types of cause, types of change, nature-art, time, place, infinite, chance, luck, soul-body, sensation, memory, fantasy, experience, intellect, desire, analogy, mean-end, action- production, choice, deliberation, virtue, happiness, justice, friendship, city, family, slavery, constitution, revolution, persuasion, character, passion, poetry, tragedy, myth, catharsis, etc. (shrink)

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of (...) opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)