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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.
The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...
For example, given a formula such as ~S 1 V S 2 and an assignment of K 1 to S 1 and K 2 to S 2 one can evaluate the formula and place its outcome in one or the other of the classes. The assignment of K 1 to S 1 places ~S 1 in K 2, and now we can see that our assignment causes the formula to fall into class K 2. Thus by definition our formula is ...
A half-truth is a deceptive statement that includes some element of truth.The statement might be partly true, the statement may be totally true, but only part of the whole truth, or it may use some deceptive element, such as improper punctuation, or double meaning, especially if the intent is to deceive, evade, blame or misrepresent the truth.
(3) "Either you tell the truth, or you lie". Therefore "[y]ou are an immoral person (whatever choice you make in the given situation)". [1] This example constitutes a false dilemma because there are other choices besides telling the truth and lying, like keeping silent. A false dilemma can also occur in the form of a disjunctive syllogism: [6]
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A logical form such as "A and B" is independent of any particular conjunction of meaningful propositions. Logical form alone can guarantee that, given true premises, a true conclusion must follow. However, formal logic makes no such guarantee if any premise is false; the conclusion can be either true or false.
The paradox is of concern for verificationist or anti-realist accounts of truth, for which the knowability thesis is very plausible, [1] but the omniscience principle is very implausible. The paradox appeared as a minor theorem in a 1963 paper by Frederic Fitch , "A Logical Analysis of Some Value Concepts".