Abstract
When on the basis of my being convinced that today is Saturday I arrive at the conviction that tomorrow is Sunday, then it means that from the fact of today being Saturday I have inferred that tomorrow is Sunday. Inference is the intellectual process whereby someone accepts a proposition or a set of propositions as true, and arrives on that basis at a conviction about the truth of another proposition. Those propositions on the basis of which we recognize the truth of other propositions; or—in other words—those propositions from which the inference is drawn, are called the premises of the inference. The proposition which is regarded as true as a result of the inference process is called the conclusion. In the example quoted above the premise was the proposition: Today is Saturday’, while the conclusion was the proposition: ‘Tomorrow is Sunday’. More precisely, in the inference there was still another premise, not explicit but assumptive, that the conditional sentence: ‘If today is Saturday, then tomorrow is Sunday’ is true. This premise has not been expressed, because everybody knows that if today is Saturday, then tomorrow is Sunday; so there is no need of repeating it. An assumptive premise of somebody’s inference is called an enthymematic premise (retained in mind, in Greek: en thymo).
Keywords
Propositional Variable Major Premise Deductive Inference Propositional Function False PropositionPreview
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References
- 1.Some deductive inferences based on the modus ponendo ponens may also be presented as inferences carried out according to the formula: ‘For every x: if x is A, then x is B, and x 1 is A, therefore X 1 is B’, where x 1 stands for some definite specimen among x’s. Then we take into account the internal structure of the propositions comprising the premises by utilizing the logical law about the name variables called dictum de omni. In an inference of this kind one of the premises is a formal implication tied by a quantifier, but not an implication built of propositions p and q as is the case in modus ponendo ponens. Google Scholar
- 2.Let us recall that to show negation of the whole proposition we use the sign while to show that some name is negative in relation to the given name, we procede it by the suffix non-.Google Scholar
- 3.3 Cf. J. Lukasiewicz, Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, 2nd ed., Oxford, 1957, pp. 1–76.Google Scholar
- 4.It must be noticed that the words ‘premises’ and ‘conclusion’ are used traditionally as the names for the propositions, which are the components of the antecedent, and the name of the consequent in a syllogistic formula. But this usage is not strictly accurate. It is only after making substitutions for the variables contained in the formula, that the resulting propositions may finally become the premises and conclusion of somebody’s act of inferring.Google Scholar
- 5.The valid moods of the syllogism may be written out, consequently, in the same ways as other logical laws, for example: II S, M, P: (M a P . S a M) ? S a P, but we shall use the traditional notation.Google Scholar