Syllogistic reasoning lies at the intriguing intersection of natural and formal reasoning, of language and logic. Syllogisms comprise a formal system of reasoning yet use natural language quantifiers, and invite natural language conclusions. How can we make sense of the interplay between logic and language? We develop a computational-level theory that considers reasoning over concrete situation...

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This paper undertakes a re-examination of Sir William Hamilton’s doctrine of the quantification of the predicate. Hamilton’s doctrine comprises two theses. First, the predicates of traditional syllogistic sentence-forms contain implicit existential quantifiers, so that, for example, All p are q is to be understood as All p are some q. Second, these implicit quantifiers can be meaningfully duali...

We extend the language of the classical syllogisms with the sentenceforms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.

Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other one, the so-called conditional interpretation, assumes that quantified propositions talk about conditional propositions and how strong are the links between t...

The goal of natural logic is to present and study logical systems for reasoning with sentences of (or which are reasonably close to) ordinary language. This paper explores simple systems of natural logic which make use of intersecting adjectives; these are adjectives whose interpretation does not vary with the noun they modify. Our project in this paper is to take one of the simplest syllogisti...

In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prio...

Syllogisms and syllogistic reasoning has been the subject of research and scientific discourse for more than two millennia. Syllogisms sum quantified assertions into an overall statement, usually consisting of two premises and one conclusion. While syllogistic reasoning can be modeled by classical first-order logic in a straightforward manner, it is an open question which of the possible syllog...

Recent research on syllogistic reasoning suggests that the logical status (valid vs. invalid) of even difficult syllogisms can be intuitively detected via differences in conceptual fluency between logically valid and invalid syllogisms when participants are asked to rate how much they like a conclusion following from a syllogism (Morsanyi & Handley, 2012). These claims of an intuitive logic are...

Existing accounts of syllogistic reasoning oppose rule-based and model-based methods. Stenning and Oberlander (1995) show that the latter are isomorphic to well-known graphical methods, when these are correctly interpreted. We here extend these results by showing that equivalent sentential implementations exist, thus revealing that all these theories are members of a family of abstract individu...