Concept
Substitution (logic)
Overview
concept in logic; syntactic transformation on formal expressions
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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The idea of annihilation or of partial nothingness is therefore formed here in the course of the substitution of one thing for another, whenever this substitution is thought by a mind that would prefer to keep the old thing in the place of the new, or at least conceives this preference as possible. The idea implies on the subjective side a preference, on the objective side a substitution, and is nothing else but a…
Henri Bergson, Creative Evolution
Names Substitution several times; states what Substitution is.
In this case, however, the predicate and subject are not merely reversed, but one of them is changed. Instead of [A] and [B], the terms of the new proposition are [a thing which is not B], and [A]. The original proposition, Some A _is not_ B, is first changed into a proposition æquipollent with it, Some A _is_ "a thing which is not B;" and the proposition, being now no longer a particular negative, but a particular…
John Stuart Mill, A System of Logic
States what Substitution is.
They are such as supply information, where the senses are entirely deficient, and we therefore have recourse to them when appropriate instances cannot be obtained. This substitution is twofold, either by approximation or by analogy. For instance, there is no known medium which entirely prevents the effect of the magnet in attracting iron--neither gold, nor silver, nor stone, nor glass, wood, water, oil, cloth, or…
Francis Bacon, Novum organum
States what Substitution is; names Substitution twice.
Related ideas
- Formal language
- First-order logic
- Philosophy
- Interpretation (logic)
- Free variables and bound variables
- If and only if
- Zermelo–Fraenkel set theory
- Propositional variable
- Propositional logic
- Function (mathematics)
- Algebra
- Mathematics
- Axiomatic system
- Mathematical induction
- Mathematical logic
- Parameter
- Rule of inference
- Variable (mathematics)
- Well-formed formula
- Tautology (logic)
- Identity of indiscernibles
- Proposition
- Contraposition
- Universal instantiation
Place in the tradition
Part of Outline of logic.