4,056 research outputs found
Greek and Roman Logic
In ancient philosophy, there is no discipline called ālogicā in the contemporary sense of āthe study of formally valid arguments.ā Rather, once a subfield of philosophy comes to be called ālogic,ā namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the āsyllogismā in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning ādemonstration.ā Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises āOn Logic,ā where the topic would be what today counts as logic. Instead, arguments and theories that count as ālogicā by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each otherās views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry
Kant, Bolzano, and the Formality of Logic
In Ā§12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that āIn the new logic textbooks one reads almost constantly that āin logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal scienceāā (WL Ā§12, 46).1 The sentence Bolzano quotes is his own summary of othersā philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers who held that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that āpure general logicā, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is ājustified in abstracting ā is indeed obliged to abstract ā from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own formā (KrV, Bix).
Explanation and Essence in Posterior Analytics II 16-17
In Posterior Analytics II 16-17, Aristotle seems to claim that there cannot be more than one explanans of the same scientific explanandum. However, this seems to be true only for āprimary-universalā demonstrations, in which the major term belongs to the minor āin itselfā and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second problem in II 16-17: the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotleās solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which suggests that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstration
Kant on the Logical Form of Singular Judgments
At A71/B96ā7 Kant explains that singular judgements are āspecialā because
they stand to the general ones as Einheit to Unendlichkeit. The reference to
Einheit brings to mind the category of unity and hence raises a spectre of
circularity in Kantās explanation. I aim to remove this spectre by interpreting
the Einheit-Unendlichkeit contrast in light of the logical distinctions
among universal, particular and singular judgments shared by Kant and
his logician predecessors. This interpretation has a further implication for
resolving a controversy over the correlation between the logical moments
of quantity (universal, particular, singular) and the categorial ones (unity,
plurality, totality)
The Object of Aristotleās Godās ĪĻĪ·ĻĪ¹Ļ in Metaphysics Ī.9
In this paper I attempt to discover the object of Aristotleās Godās Ī½ĻĪ·ĻĪ¹Ļ in MetĪ±physics Ī.9. In Section I, I catalogue existing interpretations and mention the two key concepts of (i) Godās substancehood and (ii) his metaphysical simplicity. In Section II, I explore the first two aporiae of Ī.9 ā namely (1) what Godās Īæį½ĻĪÆĪ± is and (2) what God intelligizes. In Section III, I show how Aristotle solves these aporiae by contending that Godās Īæį½ĻĪÆĪ± is actually intelligizing, and being determined to do so by himself, and that the object of his Ī½ĻĪ·ĻĪ¹Ļ is himself, such that he intelligizes his own Īæį½ĻĪÆĪ±, and I explain what this means. In Section IV, I present the second pair of aporiae in Ī.9 and show how, by solving these, Aristotle clarifies the position arrived at in Section III. Lastly, in Section V, I present the final aporia and its solution, and conclude that Aristotleās God is a radically-unified Narcissus-God who intelligizes his own Īæį½ĻĪÆĪ±
Hegelian and syllogistic logic compared
Thesis (M.A.)--Boston University, 1947. This item was digitized by the Internet Archive
From Logical Calculus to Logical FormalityāWhat Kant Did with Eulerās Circles
John Venn has the āuneasy suspicionā that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kantās ādisastrous effect on logical method,ā namely the āstrictest preservation [of logic] from mathematical encroachment.ā Kantās actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Eulerās circles and comparing it with Eulerās own use. I do so in light of the developments in logical calculus from G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations
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