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For example, because is a tautology of propositional logic, ((=)) ((=)) is a tautology in first order logic. Similarly, in a first-order language with a unary relation symbols R , S , T , the following sentence is a tautology:
In literary criticism and rhetoric, a tautology is a statement that repeats an idea using near-synonymous morphemes, words or phrases, effectively "saying the same thing twice". [1] [2] Tautology and pleonasm are not consistently differentiated in literature. [3] Like pleonasm, tautology is often considered a fault of style when
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 .
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. [1] [2] It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens ...
('I [have] put it on the table.') This example further shows that the effect, whether pleonastic or only pseudo-pleonastic, can apply to words and word-parts, and multi-word phrases, given that the fullest rendition would be "I am after putting it on the table". "Have a look at your man there." ('Have a look at that man there.')
In modern usage, it has come to refer to an argument in which the premises assume the conclusion without supporting it. This makes it an example of circular reasoning. [1] [2] Some examples are: "People have known for thousands of years that the earth is round. Therefore, the earth is round." "Drugs are illegal so they must be bad for you.
Tautology may refer to: Tautology (language), a redundant statement in literature and rhetoric; Tautology (logic), in formal logic, a statement that is true in every ...
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.