Philosophy of logic

Reason is the capacity to consciously apply logic by drawing valid conclusions from new or existing information, with the aim of seeking truth. It is associated with activities considered characteristic of humans, including philosophy, religion, science, language, and mathematics, and is generally considered a distinguishing ability possessed by humans. The term "reason" is sometimes used to refer to rationality, although the latter is more about its application.

thumb|right|upright=1.25|Painting depicting a lecture in a knight academy, painted by [[Pieter Isaacsz or Reinhold Timm for Rosenborg Castle as part of a series of seven paintings depicting the seven independent arts. This painting illustrates rhetoric.]] thumb|upright|Jesus was a preacher in 1st-century Judea.

thumb|Adriaen van Ostade, "Analysis" (1666)

1781 philosophical work by Immanuel Kant

application of logical methods to philosophical problems

statement which is true regardless of the truth or falsity of its constituent parts

study of the scope and nature of logic

non-fiction work by Noam Chomsky

semantic distinction, used primarily in philosophy to distinguish propositions (in particular, statements that are affirmative subject–predicate judgments) into two types: analytic propositions and synthetic propositions

impossibility for separate objects to have all their properties in common

Begriffsschrift (German for, roughly, "concept-writing") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.

undefined term motivated informally, usually by an appeal to intuition and everyday experience, or introduced axiomatically and eventually generated only by a series of elementary operations

formal systems of logic that significantly differ from standard logical systems

distinction that separates a concept from the objects which are particular instances of the concept

type of logic whose elements are concepts

rules used for constructing or transforming the symbols of a formal language

In linguistics, grammaticality is conformity to grammar. The notion of grammaticality rose alongside the theory of generative grammar, the goal of which is to formulate rules that define well-formed, grammatical sentences. These rules of grammaticality also provide explanations of ill-formed, ungrammatical sentences.

theorem that truth in the standard model of a formal system cannot be defined within the system

In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, x+3=3+x is valid over the integers, but x+3=y is not.

the use of reason to decide how to act

interpretation of intuitionistic logic

Reasoning that is rationally compelling, though not deductively valid

principle governing approaches to logical semantics