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This paper explores the influence of Aristotle's work "The Categories" on the philosophical doctrine of objective coherentism, analyzing the comparative modalism present in both Aristotle's concepts and the contemporary interpretations by figures like David K. Lewis. It critiques Lewis's multi-conditional framework and discusses the role of contraries in Aristotle’s philosophy, proposing that these elements serve as fundamental definitions in both systems, ultimately positing that Aristotle’s modal definitions can inform and improve categorical systems.
pfeifer-research.de
Two experiments (N 1 = 141, N 2 = 40) investigate two versions of Aristotle's Thesis for the first time. Aristotle's Thesis is a negated conditional, which consists of one propositional variable with a negation either in the antecedent (version 1) or in the consequent (version 2). This task allows to infer if people interpret indicative conditionals as material conditionals or as conditional events. In the first experiment I investigate between-participants the two versions of Aristotle's Thesis crossed with abstract versus concrete task material. The modal response for all four groups is consistent with the conditional event and inconsistent with the material conditional interpretation. This observation is replicated in the second experiment. Moreover, the second experiment rules out scope ambiguities of the negation of conditionals. Both experiments provide new evidence against the material conditional interpretation of conditionals and support the conditional event interpretation. Finally, I discuss implications for modeling indicative conditionals and the relevance of this work for experimental philosophy.
Journal of the History of Philosophy 53, 2015
Aristotle presents a formal logic in the Prior Analytics in which the premises and conclusions are never conditionals. In this paper I argue that he did not simply overlook conditionals, nor does their absence reflect a metaphysical prejudice on his part. Instead, he thinks that arguments with conditionals cannot be syllogisms because of the way he understands the explanatory requirement in the definition of a syllogism: the requirement that the conclusion follow because of the premises. The key passage is Prior Analytics I.32, 47a22-40, where Aristotle considers an argument with conditionals that we would consider valid, but which he denies is a syllogism. I argue that Aristotle thinks that, to meet the explanatory requirement, a syllogism must draw its conclusion through the way its terms are predicated of one another. Because arguments with conditionals do not, in general, draw their conclusions through predications, he did not include them in his logic.
This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle’s syllo- gistic and the Stoic doctrine of conditionals,
Documenti e studi sulla tradizione filosofica medievale, 2016
In this paper I investigate Aristotle’s account of predication in Topics I 9. I argue that in this chapter Aristotle (i) presents two systems of predication cutting across each other, in order to distinguish them and explore their mutual relationship. I propose a semantic interpretation of this relationship. Further, Aristotle (ii) explains the connection between these two systems and the ten items listed in Chapter 4 of the Categories.
Essential Predication in Aristotle’s Categories: A Defence”, in: David Bronstein, Thomas Johanson, Michael Peramatzis (eds.), Essays in Honour of David Charles, Oxford: Oxford University Press 2024, 143-167., 2024
Aristotle's Categories is a treatise that is mostly concerned with classifications. Many ancient commentators saw the Categories as closely connected with the Topics and some of the earliest mentions of this treatise in antiquity even used the title Before the Topics instead of Categories, thus indicating that it was seen as a sort of propaedeutic to the Topics, and thus as closely related to Aristotle's method of dialectic. Still, the Categories offers a series of claims, most notably claims associated with the concept of substance (ousia) that we would rate as straightforwardly 'metaphysical' ones. This is the reason why the Categories' claims about substance are regularly and inevitably compared to the presumably most authoritative treatise on all questions concerning Aristotelian metaphysics, namely Aristotle's Metaphysics-even though this latter treatise is dedicated to an entirely different project. Far from the Categories' mostly classificatory interest (and far from, perhaps, merely contributing to the art of dialectic), the Metaphysics is meant to unfold Aristotle's most ambitious project of first philosophy, aiming at the identification of the first principles and causes of everything.
1988
According to the traditional view of the Categories, the ten "categories" are the highest genera of beings. Each of them stands at the head of a tree-like division of the the items falling under it; this division is also sometimes called a "category". The metaphysical structure made up of these ten divisions is the "system of the categories". According to the traditional view, the system of the categories is very rigidly laid out. Not only is every being included in the structure, but every being has exactly one location. Each being is predicated essentially of those below it along the lines of division. Each being is related to those above it, if any, as a determination of them, and to those below it, if any, as a determinable. Because of these facts, the full analysis of the essence of any being can be gotten by stringing together the names of all the beings superior to it in the division, along with a final differentia. But this traditional view is very widely off the mark. In the first place, it is important to realize what a remarkable achievement the system of the categories as traditionally conceived would have been, if Aristotle had in fact achieved it. Plato in the late dialogues raises the specter that division leads to chaos: dismayingly many Forms are closely interwoven with dismayingly many others; some Forms are interwoven with all others. The number of different divisions which lead to any given Form is dismayingly large. Clearly, one óf the tasks the early Academy faced was to make order of this mess. The distinction in the Sophist between essential and non-essential predication was one tool invented for this purpose; the Academic distinction between the categories ti and prosti was another. For Aristotle to have developed criteria powerful enough to uniquely determine a single structure of divisions of everything there is-to have solved this problem completelywould have been extraordinary. Moreover, on the traditional view Aristotle's achievement is even more extraordinary than this. Since the work of Emst Kapp in the first half of this century it has been recognized that a major source of Aristotle's theory of categories is his research into "topics"-into classes of terms-or things-such that the members of each class share certain logical properties which are useful in constructing arguments. Armed with a theory of topics, one need only determine into which class a thing belongs in order to know what its most important properties are. Topics 1,9 introduces a theory of categories as part of the theory of topics. As Michael Frede has shown, the categories in the Topics are kinds of predicates or predications, whereas in the Categories we have to do with kinds of thing. But in the Categories Aristotle is careful to discuss the logical properties of each "category": whether it admits of contraries or not, whether it varies in degree, and so on. Somehow, the theory of kinds of thing in the Categories seems to be a development of the theory of kinds of predicate or predication in the Topics. If this is accepted, then, when it is combined with the traditional interpretation, we get the following thesis: the project of organizing beings in terms of genus and species into their ultimate divisions, and the project of groupings things according to their basic logical properties, coincide in their results. The same ultimate classes are arrived at by these two very different inquiries. If Aristotle did claim this for his theory of categories, then he claimed a very strong and remarkable result Of course, Aristotle was an extraordinary man. But one important sign that he did not take himself to have accomplished all that the traditional interpretation ascribed to him is his famous uncertainty over the number of categories. Sometimes Aristotle gives the number of categories as ten, smetimes as eight, and sometimes as six. It is unlikely that a person who was in a position to be certain that all being can be fitted into one unique division could be so unsure of how many basic divisions there are. Apart from this general misgiving, the traditional interpretation of the Categories faces obstacles in the text itself. The first of these is the well-known problem of the status of the differentiae. At Categories 3a21-28 and a33-b9, we are told that not only substances but also differentiae are said of, but not in their subjects. From this it follows, we are told, that the definitions, not only of substances, but also of their differentiae, are predicated of their subjects. Despite their similarity to substance, however, differentiae are ¡¡Q l substances; the text is clear on this. What are the implications of these remarks? First, they prove that the said of/present in distinction was not intended by Aristotle as by itself sufficient for the construction of the system of categories. Being said of a subject, being present in a subject, and their negations give one sufficient criterion to distinguish primary substance from secondary substance, and provide a help toward distinguishing substance from non-substance. But that is all. Differentiae are not substances, so they are not in the category of substance. But differentiae are beings, and many if not all of them are uncompounded, so they must be in some category or other. So many, if not all, differentiae will be in non-substance categories: perhaps chiefly quality, but others as well. Presumably items in other categories are defined in a manner similar to substance, through genus and differentia. Pale=penetrative color is a favorite Aristotelian example. But if the definitions of differentiae are predicable of whatever they are said of, and they are said of substances, then the definitions of substances are expandable in two ways: by further definitional analysis of the genus, and by further definitional analysis of the differentiae. The differentiae mentioned in the definitions of the differentiae must themselves have a place in the structure of the categories, presumably a rather different place from that of what they help to define, and they must themselves be definable. So a complete analysis of the definition of any item, substantial or not, while 12 Since substance is not divided into kinds in this text, it is unsafe to say how it would have been divided. Given the changes which Aristotle's view of substance underwent in the meantime. Metaphysics Delta 8 is not a safe guide. In Chapter 15 "having" does seem to be divided into kinds by means of differentiae. But as these differentiae include substance, defenders of the traditional interpretation will not want to count it as a discussion of the category "having".
2015
Aristotle’s Categoriae, or the Categories, is a comprehensive classification system for every object of human understanding that can be either a subject or a predicate of a proposition. There are ten categories: Substance, Quantity, Qualification, Relative/Relation, Place, Time, Position, State (Condition), Action, and Affection. The first part of this paper will explain each of the categories in the order in which they are presented in the chapters of Categoriae. The second half of the paper will discuss the question of ambiguity in the approach Aristotle uses to both construct and find meaning in these categories. Fr. Joseph Owens examines the use of metaphysical, logical and grammatical ways in which Aristotle presents the categories. Owens observes the benefits and disadvantages of Aristotle’s mixed approach, and questions the usefulness of the system as a whole. This paper will argue that Aristotle successfully uses all three approaches, sometimes separately and sometimes in co...
2018
According to the traditional view of the Categories, the ten "categories" are the highest genera of beings. Each of them stands at the head of a tree-like division of the the items falling under it; this division is also sometimes called a "category". The metaphysical structure made up of these ten divisions is the "system of the categories". According to the traditional view, the system of the categories is very rigidly laid out. Not only is every being included in the structure, but every being has exactly one location. Each being is predicated essentially of those below it along the lines of division. Each being is related to those above it, if any, as a determination of them, and to those below it, if any, as a determinable. Because of these facts, the full analysis of the essence of any being can be gotten by stringing together the names of all the beings superior to it in the division, along with a final differentia. But this traditional view is very widely off the mark. In the first place, it is important to realize what a remarkable achievement the system of the categories as traditionally conceived would have been, if Aristotle had in fact achieved it. Plato in the late dialogues raises the specter that division leads to chaos: dismayingly many Forms are closely interwoven with dismayingly many others; some Forms are interwoven with all others. The number of different divisions which lead to any given Form is dismayingly large. Clearly, one óf the tasks the early Academy faced was to make order of this mess. The distinction in the Sophist between essential and non-essential predication was one tool invented for this purpose; the Academic distinction between the categories ti and prosti was another. For Aristotle to have developed criteria powerful enough to uniquely determine a single structure of divisions of everything there is-to have solved this problem completelywould have been extraordinary. Moreover, on the traditional view Aristotle's achievement is even more extraordinary than this. Since the work of Emst Kapp in the first half of this century it has been recognized that a major source of Aristotle's theory of categories is his research into "topics"-into classes of terms-or things-such that the members of each class share certain logical properties which are useful in constructing arguments. Armed with a theory of topics, one need only determine into which class a thing belongs in order to know what its most important properties are. Topics 1,9 introduces a theory of categories as part of the theory of topics. As Michael Frede has shown, the categories in the Topics are kinds of predicates or predications, whereas in the Categories we have to do with kinds of thing. But in the Categories Aristotle is careful to discuss the logical properties of each "category": whether it admits of contraries or not, whether it varies in degree, and so on. Somehow, the theory of kinds of thing in the Categories seems to be a development of the theory of kinds of predicate or predication in the Topics. If this is accepted, then, when it is combined with the traditional interpretation, we get the following thesis: the project of organizing beings in terms of genus and species into their ultimate divisions, and the project of groupings things according to their basic logical properties, coincide in their results. The same ultimate classes are arrived at by these two very different inquiries. If Aristotle did claim this for his theory of categories, then he claimed a very strong and remarkable result Of course, Aristotle was an extraordinary man. But one important sign that he did not take himself to have accomplished all that the traditional interpretation ascribed to him is his famous uncertainty over the number of categories. Sometimes Aristotle gives the number of categories as ten, smetimes as eight, and sometimes as six. It is unlikely that a person who was in a position to be certain that all being can be fitted into one unique division could be so unsure of how many basic divisions there are. Apart from this general misgiving, the traditional interpretation of the Categories faces obstacles in the text itself. The first of these is the well-known problem of the status of the differentiae. At Categories 3a21-28 and a33-b9, we are told that not only substances but also differentiae are said of, but not in their subjects. From this it follows, we are told, that the definitions, not only of substances, but also of their differentiae, are predicated of their subjects. Despite their similarity to substance, however, differentiae are ¡¡Q l substances; the text is clear on this. What are the implications of these remarks? First, they prove that the said of/present in distinction was not intended by Aristotle as by itself sufficient for the construction of the system of categories. Being said of a subject, being present in a subject, and their negations give one sufficient criterion to distinguish primary substance from secondary substance, and provide a help toward distinguishing substance from non-substance. But that is all. Differentiae are not substances, so they are not in the category of substance. But differentiae are beings, and many if not all of them are uncompounded, so they must be in some category or other. So many, if not all, differentiae will be in non-substance categories: perhaps chiefly quality, but others as well. Presumably items in other categories are defined in a manner similar to substance, through genus and differentia. Pale=penetrative color is a favorite Aristotelian example. But if the definitions of differentiae are predicable of whatever they are said of, and they are said of substances, then the definitions of substances are expandable in two ways: by further definitional analysis of the genus, and by further definitional analysis of the differentiae. The differentiae mentioned in the definitions of the differentiae must themselves have a place in the structure of the categories, presumably a rather different place from that of what they help to define, and they must themselves be definable. So a complete analysis of the definition of any item, substantial or not, while 12 Since substance is not divided into kinds in this text, it is unsafe to say how it would have been divided. Given the changes which Aristotle's view of substance underwent in the meantime. Metaphysics Delta 8 is not a safe guide. In Chapter 15 "having" does seem to be divided into kinds by means of differentiae. But as these differentiae include substance, defenders of the traditional interpretation will not want to count it as a discussion of the category "having".
John Corcoran. 1973. A Mathematical Model of Aristotle's Syllogistic, Archiv f"ur Geschichte der Philosophie 55, 191–219. This article presents a mathematical model designed to reflect certain structural aspects of Aristotle's logic. Accompanying the presentation is an interpretation of certain scattered parts of the Prior and Posterior Analytics. Although our interpretation does not agree in all respects with those previously put forth, the present work would have been impossible without the enormous ground work of previous scholars—especially Łukasiewicz and Ross—to whom we are deeply grateful. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several attributions of shortcomings and logical errors to Aristotle are seen to be without merit. Aristotle's logic is found to be self-sufficient in several senses. In the first place, his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) In the second place, Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. (His deductions were falsely alleged to have gaps only correctable using propositional logic.) In the third place, the Aristotelian system is seen to be complete in the sense that every valid argument statable in his system admits of a deduction within his deductive system, i. e. every conclusion that follows from given premises is deducible from them using Aristotle’s explicitly described methods: in short, every valid argument is deducible. This result, stated but not proved by Aristotle, connects logical ontology to logical epistemology: every argument that in fact is valid can be known to be valid. It is not clear whether Aristotle appreciated the epistemic significance of his own completeness claim.
Logik, Naturphilosophie, Dialektik. Neue internationale Beiträge zur modernen Deutung der Aristotelischen Logik (N. Öffenberger & A. Vigo, eds.), 2014
The aim of this paper is rather modest: we do not intend to reconstruct Aristotle’s theory of truth (although we are convinced that there is such a thing), and we will not try to settle the issue concerning Bivalence in Aristotle. We merely want, on the one hand, to argue for the consistency between the main Aristotelian texts on truth and a possible rejection of Bivalence; and on the other hand, to investigate the conditions of a possible counterexample to Bivalence. The motivation for this research is also very specific. We are interested in the apparent violation of Bivalence introduced by vague predicates, and in particular we want to respond to a family of arguments put forward by T. Williamson in support of the idea that allowing for exceptions to Bivalence would be incoherent. We have focused on these arguments for two reasons. On the one hand, what is allegedly threatened by a denial of Bivalence is no less than the very “nature of truth or falsity”. On the other hand, Aristotle is explicitly mentioned as one of the defendants of this “natural” conception of truth, and we are reminded about the connection between Aristotle’s theory and Tarski’s semantic conception. These arguments, therefore, give us an occasion to explore Aristotle’s analysis of the nature of truth and falsity, and to examine its connection with the Tarskian conception of truth. In particular, we would like to question the assumption, which has become a commonplace in the field of analytical philosophy, that Aristotle’s notion of truth can be encoded in the pair of disquotational biconditionals that derive from Tarski’s “T schema”.
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