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Argument

Tautology (rule of inference)

Overview

In propositional logic, tautology is either of two commonly used rules of replacement. The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are:

The principle of idempotency of disjunction:

P

∨

P

⇔

P

{\displaystyle P\lor P\Leftrightarrow P}

and the principle of idempotency of conjunction:

P

∧

P

⇔

P

{\displaystyle P\land P\Leftrightarrow P}

Where "

⇔

{\displaystyle \Leftrightarrow }

" is a metalogical symbol representing "can be replaced in a logical proof with".

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

Found by search and not yet checked by a person; they may only mention the idea in passing.

  1. And if the reader rebels at the iteration of such obvious tautology, I can only reiterate that the realization of the _meaning_ of this tautology is the key to the whole question of the objectivity of experience, as that stands to the empiricist. The lines of _that_ experience _are_ divergent; not merely _seem_ so.

    John Dewey, The Influence of Darwin on Philosophy, and other essays in contemporary thought

    States what Tautology is; names Tautology twice.

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  2. Every proposition consists of three parts: the Subject, the Predicate, and the Copula. The predicate is the name denoting that which is affirmed or denied. The subject is the name denoting the person or thing which something is affirmed or denied of.

    John Stuart Mill, A System of Logic, Ratiocinative and Inductive

    States what Tautology is.

    Read the chapter · Open in the reader

  3. Instead of mercury put a mere letter which is the name of some undetermined thing: we get-- The specific heat of _x_ is 0·033. This is not a proposition; it has been called by Russell a propositional function. It is the logical analogy of an algebraic expression. Let us write ƒ(_x_) for any propositional function. We could also generalise still further, and say, The specific heat of _x_ is _y_.

    Alfred North Whitehead, The organisation of thought, educational and scientific

    States what Tautology is; the author is tied to Tautology in the knowledge graph.

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Related ideas

Place in the tradition

Part of Propositional logic.

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