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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 ...
Alternatively, a person might look at a number line, and notice that the number 1 is a square number; 3 is a prime number, 5 is a prime number, and 7 is a prime number; 9 is a square number; 11 is a prime number, and 13 is a prime number. From these observations, the person might claim that all odd numbers are either prime or square, while in ...
The rational consequence relation is non-monotonic, and the relation is intended to carry the meaning theta usually implies phi or phi usually follows from theta.In this sense it is more useful for modeling some everyday situations than a monotone consequence relation because the latter relation models facts in a more strict boolean fashion—something either follows under all circumstances or ...
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. [1] [2] The structure, argument form and formal form of a proof by example generally proceeds as follows ...
Argument from fallacy is the formal fallacy of analyzing an argument and inferring that, since it contains a fallacy, its conclusion must be false. [1] It is also called argument to logic (argumentum ad logicam), the fallacy fallacy, [2] the fallacist's fallacy, [3] and the bad reasons fallacy.
The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus.It was originally proved by Gerhard Gentzen in part I of his landmark 1935 paper "Investigations in Logical Deduction" [1] for the systems LJ and LK formalising intuitionistic and classical logic respectively.
Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR). The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively.