Online research in philosophy

Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov’s approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 ed. Exercises.

Montague’s analysis of the well-known temperature paradox poses a problem for Gupta’s syllogism, whose surface syntax differs from the temperature syllogism in the addition of the intensional adverb necessarily. Lasersohn (2005) argues that the puzzle arising from these syllogisms can be solved if one adopts the Fregean presuppositional treatment of definite descriptions, and concludes that the temperature-Gupta puzzle provides an argument in favor of such treatment. This paper shows that the analysis of definite descriptions is in fact orthogonal to the puzzle. Instead, it will be shown that the differences between the two syllogisms stem from the temporal interpretation of their premises.

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments. The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed. The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented.

This article tackles a number of puzzles related to Aristotle’s practical syllogism, notably the relationship between deliberation and the practical syllogism, the distinction between deliberative and reconstructive practical syllogisms, and the nature of the conclusion of the practical syllogism.

It is well-known that the Arab philosophers of the Aristotelian tradition, like some of their Alexandrian predecessors, attached rhetoric and poetics to logic, and supported this inclusion by the idea that the principal poetic procedure - that is, essentially, metaphor - is a kind of syllogism: the poetic syllogism. However, until now, no texts prior to those of Avicenna had been identified which render the structure of this syllogism explicit. In the present contribution, we present and translate a passage from al-Farabi which shows that for him, the poetic syllogism is an incorrect syllogism of the second figure - a different interpretation from that which will be given by Avicenna.