premise

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premise

Logic a statement that is assumed to be true for the purpose of an argument from which a conclusion is drawn

Premise

 

in the broad sense, that on the basis of which an inference or conclusion is drawn. Premises may be facts or judgments of facts, principles, axioms, postulates, or any events or propositions that are raw data from which some information that is new to us can be extracted directly or through reasoning. In this sense we may speak equally of premises of induction and premises of deduction.

In the narrow sense, premises proper in formally deductive logical constructs are propositions to which is applied some rule of inference or formulas symbolizing the propositions and comprising statements of the rules of inference in the investigator’s language. The concept of logical corollary is symmetrical to the concept of premise. These concepts are generally relative: a proposition may be a premise in one application of a rule of inference and a corollary in another. In logical formalisms of the axiomatic type, the premises of the first steps of deduction are stated in advance in the form of axioms and thus play the role of absolute premises, or prerequisites: the deductive procedure must necessarily begin with them. In natural calculi, in which reasoning follows the principle of assumptions that was known even in antiquity, there are no absolute premises.

Whatever their character, premises are a necessary condition for logical argumentation or proof. Here the question of the nonextraneous character of premises turns out to be essential. A premise that is extraneous to a given argument may always be replaced by the contradictory premise without damage to the argument. A law of logic that may be called the law of the extraneous premise corresponds to the rule

(A & BC) & (AC)) ⊃ (A & ┐ BC)

The fundamental task of logic is to investigate the corollaries of given premises and to find nonextraneous premises corresponding to given consequences. Within the limits of the formalism of the algebra of propositions, these problems have an exhaustive solution.

M. M. NOVOSELOV

References in periodicals archive ?
that introduces the premisses is 'doubly' translated: first as 'if' (at the head of the first antecedent) and then as 'since' (at the head of the second antecedent).
Cornford-Wicksteed take both premisses to be counterfactuals and so translate the Greek indicative in them by the English subjunctive:
the modal status of the premisses of the Flying Arrow argument.
This information is used to evaluate the premisses of the rules that the knowledge base contains and, depending on what premisses test out to be true, the conclusions are then returned to the working memory.
Any stained proof will be disabled anyway when its stained premisses are thrown out in the final throes of contraction.
But if the pedigrees involve premisses that themselves in turn require justification, the process will have to be repeated as often as is necessary to climb all the way up the branches of the justificatory tree.
We could try representing a theory instead more economically by means of entries with justifiers invoking as premisses previously justified claims (but without their justifications).
91) Both he and the Gnostics would have agreed, though on different bases, on the truth of the two premisses in this argument and the conclusion derived from them.
an argument which from pre-evident premisses deduces something nonevident.
The basis for asserting that Paul later became a son of God is then shown in two additional demonstrative arguments, both of which take the words of the biblical text used in the first argument in the series as their premisses, the first implicitly, the second explicitly.
Tenders are invited for Lease holds right of Photography in front of Temple Premisses
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