Concept
Theory (mathematical logic)
Overview
set of sentences in a formal language
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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It is probably in some such manner as this, that almost all verbs have become personal, and that mankind have learned by degrees to split and divide almost every event into a great number of metaphysical parts, expressed by the different parts of speech, variously combined in the different members of every phrase and sentence.[29] The same sort of progress seems to have been made in the art of speaking as in the art…
Adam Smith, The Theory of Moral Sentiments
The book is titled for Theory.
Normally formed, the section offers a central group of seven sentences, preceded and followed by three groups of five: the first section of each part reduces to three sentences three of its groups, symmetrically placed; the last section gives seven sentences to each of its extreme groups. These rules of composition make prose approach to the regularity of poetry, when combined with my previous reduction of the…
John Stuart Mill, Auguste Comte and Positivism
Close in meaning to Theory; the term itself is not named.
Wundt defines a theory as a hypothesis taken together with the facts for whose elucidation it was invented. In thus establishing a connection between the facts which the hypothesis merely suggested, the theory furnishes at the same time partly the foundation (_Begründung_) and partly the confirmation (_Bestätigung_) of the hypothesis.[79] These aspects, Wundt insists, must be sharply distinguished. Every hypothesis…
John Dewey, Studies in Logical Theory
Names Theory several times; states what Theory is.
Philosophers who discussed Theory (mathematical logic)
Related ideas
- Method of analytic tableaux
- Formal language
- First-order logic
- Gödel's completeness theorem
- Axiomatic system
- Mathematical logic
- Peano axioms
- Rule of inference
- Sequent calculus
- Recursion
- Theorem
- Second-order logic
- Löwenheim–Skolem theorem
- Logical consequence
- Formal system
- Well-formed formula
- Structure (mathematical logic)
- Natural deduction
- Principle of explosion
- Decidability (logic)
- Axiom
- Complete theory
Place in the tradition
Part of Philosophy of mathematics.
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