# Logic, philosophy of

Philosophy of logic can be roughly characterized as those philosophical topics which have emerged either from the technical development of symbolic (mathematical) logic, or from the motivations that ...

Overview

Philosophy of logic can be roughly characterized as those philosophical topics which have emerged either from the technical development of symbolic (mathematical) logic, or from the motivations that ...

Overview

Conceived of philosophically, the foundations of mathematics concern various metaphysical and epistemological problems raised by mathematical practice, its results and applications. Most of these problems are of ancient ...

Thematic

How is it known that every number has a successor, that straight lines can intersect each other no more than once, that causes precede their events, and that ...

Thematic

The term ‘probability’ and its cognates occur frequently in both everyday and philosophical discourse. Unlike many other concepts, it is unprofitable to view ‘probability’ as having a unique ...

Thematic

Logical positivism (logical empiricism, neo-positivism) originated in Austria and Germany in the 1920s. Inspired by late nineteenth- and early twentieth-century revolutions in logic, mathematics and mathematical physics, it ...

Thematic

The law of excluded middle (LEM) says that every sentence of the form A∨¬A (‘A or not A’) is logically true. This law is accepted in classical logic, ...

Thematic

The first philosophically-motivated use of many-valued truth tables arose with Jan Łukasiewicz in the 1920s. What exercised Łukasiewicz was a worry that the principle of bivalence, ‘every statement ...

Thematic

The Roman general Julius Caesar was assassinated on 14 March 44 bc by conspirators led by Brutus and Cassius. It is a remarkable fact that, in so ...

Thematic

A sentence is a string of words formed according to the syntactic rules of a language. But a sentence has semantic as well as syntactic properties: the words ...

Thematic

Generalized quantifiers are logical tools with a wide range of uses. As the term indicates, they generalize the ordinary universal and existential quantifiers from first-order logic, ‘∀x’ and ...

Thematic

Quantificational reasoning in natural languages contains occurrences of expressions which, though name-like from a syntactic perspective, intuitively seem to be importantly different from ordinary names. For example, in ...

Thematic

The quantifiers ‘some’ and ‘every’ were the object of the very first logical theory, Aristotelian syllogistic. An example of a syllogism is ‘Every Spartan is Greek, every Greek ...

Thematic

Understood substitutionally, ‘Something is F’ is true provided one of its substitution instances (a sentence of the form ‘a is F’) is true. This contrasts with the objectual ...

Thematic

The ‘reference’ of an expression is the entity the expression designates or applies to. The ‘sense’ of an expression is the way in which the expression presents that ...

Thematic

Speakers ‘use’ the expressions they utter and ‘mention’ the individuals they talk about. Connected with the roles of used expressions and mentioned individuals is a way of uniting ...

Thematic

It seems obvious that there are vague ways of speaking and vague ways of thinking – saying that the weather is hot, for example. Common sense also has ...

Thematic

Fallacies are common types of arguments that have a strong tendency to go badly wrong, or to be used as deceptive tricks when two parties reason together. In ...

Thematic

Imperatives lie at the heart of both practical and moral reasoning, yet they have been overshadowed by propositions and relegated by many philosophers to the status of exclamations. ...

Thematic

The type/token distinction is related to that between universals and particulars. C.S. Peirce introduced the terms ‘type’ and ‘token’, and illustrated the distinction by pointing to two senses ...

Thematic

Necessary truths have always seemed problematic, particularly to empiricists and other naturalistically-minded philosophers. Our knowledge here is a priori - grounded in appeals to what we can imagine ...

Thematic

Plural phenomena are significant and inescapable. Granted, the plural idiom is sometimes reducible to the singular, e.g. ‘2 and 3 are prime is equivalent to ‘2 is prime ...

Thematic

The effective calculability of number-theoretic functions such as addition and multiplication has always been recognized, and for that judgment a rigorous notion of ‘computable function’ is not required. ...

Thematic

An algorithm or mechanical procedure A is said to ‘compute’ a function f if, for any n in the domain of f, when given n as input, A ...

Thematic

Church’s theorem, published in 1936, states that the set of valid formulas of first-order logic is not effectively decidable: there is no method or algorithm for deciding which ...

Thematic

According to Herbrand’s theorem, each formula F of quantification theory can be associated with a sequence F_{1}, F_{2}, F_{3},… of quantifier-free formulas such that F is provable just ...