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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 ...
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.
Philosophy of psychology also closely monitors contemporary work conducted in cognitive neuroscience, cognitive psychology, and artificial intelligence, for example questioning whether psychological phenomena can be explained using the methods of neuroscience, evolutionary theory, and computational modeling, respectively.
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).
Circular reasoning (Latin: circulus in probando, "circle in proving"; [1] also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. [2]
Theorems are those logical formulas where is the conclusion of a valid proof, [4] while the equivalent semantic consequence indicates a tautology.. The tautology rule may be expressed as a sequent:
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
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.