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These sentences may contain quantifiers, unlike sentences of propositional logic. In the context of first-order logic, a distinction is maintained between logical validities, sentences that are true in every model, and tautologies (or, tautological validities), which are a proper subset of the first-order logical validities. In the context of ...
The use of tautologies, however, is usually unintentional. For example, the phrases "mental telepathy", "planned conspiracies", and "small dwarfs" imply that there are such things as physical telepathy, spontaneous conspiracies, and giant dwarfs, which are oxymorons. [8] Parallelism is not tautology, but rather a particular stylistic device.
In propositional logic, tautology is either of two commonly used rules of replacement. [1] [2] [3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs.
Verificationism, also known as the verification principle or the verifiability criterion of meaning, is a doctrine in philosophy which asserts that a statement is meaningful only if it is either empirically verifiable (can be confirmed through the senses) or a tautology (true by virtue of its own meaning or its own logical form).
Tautological consequence can also be defined as ∧ ∧ ... ∧ → is a substitution instance of a tautology, with the same effect. [2]It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.
Instead, Quine argues by using examples that although there are tautological statements in a formal theory, like "all squares are rectangles", a formal theory necessarily contains references to objects that are not tautological, but have external connections. That is, there is an ontological commitment to such external objects. In addition, the ...
This example argument will be reused when ... This is more common in computer science than in philosophy. [54] It can be done ... false, tautological, or ...
Instead, philosophy is seen as an activity of defining and clarifying the logical relationships of empirical propositions. In considering how to distinguish between a conscious man and an unconscious machine, [ 2 ] Ayer also anticipates the development in 1950 of the Turing test to test a machine's capability to demonstrate intelligence ...