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 ?
the modal status of the premisses A and B can hardly be ignored.
(15) So, by distinguishing 'if' from 'since' in the manner indicated above, we obtain the following nine materially different variants of T2 (the translation of the Flying Arrow in which Zeno's argument, understood as a syllogism or inference from two premisses, is formulated as a conditional with an embedded conditional as consequent): (16)
The point of this classification is to enable translators to make clear, by choosing from among the nine variants, their considered judgment concerning the modal status of each of Zeno's premisses or, more precisely, what they think Aristotle thought that Zeno had intended the modal status of each premiss to be.
For precisely this reason some scholars have insisted on the retention or preservation of the original text proposed by Bekker, tolerating appeal to tacit premisses only for its interpretation.
In order to render the argument complete, Hamelin invokes two allegedly tacit premisses:
Interestingly, insertion of these two alleged tacit premisses leads to the same interpretation as the one obtained by the aforementioned textual changes.
But might there not be some as yet undiscovered justification for S, one of whose premisses should also be stained in this way, but which will escape staining simply because the justification in question is not within purview at this finite stage?
Any deducibility relation generated by proofs of conclusions from premisses will do.
With upward staining, the proofs whose premisses are to be stained do not have to be deductive proofs.
The only complication attending our method arises from the possibility of distinct choices of least entrenched premisses for staining.
The problem of multiple results could be avoided altogether, of course, simply by staining all least entrenched premisses of any unstained proof of a stained sentence.(42) But as pointed out above, this would in a certain sense maximize the minimum mutilation being inflicted on the theory] It turns a Sophie's choice into a Hobson's choice.
This is because the premisses of such II might survive the method of staining.