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15 Cards in this Set

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 Validity An argument is valid if the conclusion must be true in any circumstances in which the premises are true. Soundness A valid argument with all true premises (and hence a true conclusion) is said to be a sound argument. Indiscernibility of Identicals =Elim, =Intro, Symmetry of Identity, Transitivity of Identity Tautology A logical consequence of an empty set of premises. If all under the connective are T, then it is a tautology. If at least one is T, it is TT-possible. Tautological Consequence Q is a tautological consequence of P if in the joint truth table for the two sentences there is no row on which P is true and Q is false. Logical Consequence 1. If a claim or a conclusion is not a logical consequence of a set of premises, then the argument is invalid. 2.If there is some possible scenario where the premises are true and the conclusion is false, then the conclusion is not a logical consequence of the premises, and the argument is invalid. Logical Necessity A logical truth is a sentence that is a logical consequence of any set of premises. That is, no matter what the premises may be, it is impossible for the conclusion to be false. That is also called a logical necessity. Individual constant Individual constants, or names, are those symbols of FOL that stand for objects or individuals. In FOL it is assumed that each individual constant of the language names one and only one object. = Elim If b = c, then whatever holds of b holds of c. This is also known as the indiscernibility of identicals. = Intro: Sentences of the form b = b are always true (in fol). This is also known as the reflexivity of identity. Symmetry of Identity If b = c, then c = b Transitivity of Identity If a = b and b = c, then a = c. Translation ~(Home(john) v Home(mary)) SameAs ~ Home(john) & ~ Home(mary) Antecedent of a conditional P OnlyIf Q...this is P in this sentence Consequent of a conditional P OnlyIf Q...this is Q in this sentence