Sentence examples for propositional principles from inspiring English sources

Besides discussing differences between the classical and intuitionistic conceptions of logic, it gives a list of some propositional principles that are intuitionistically valid, as well as a list of some propositional principles that are classically valid but not intuitionistically.

In its propositional form, this principle says that a person can deserve something in virtue of a certain fact only if that fact is a fact "about the person".

Both in grammar and in propositional content, the principle's gerundive "is-to-be" is neither imperative nor predictive, but rationally directive — an ought — in the way that gets its fully developed and central sense and normativity in the more specified ought of moral standards.

The intuitionistic calculus aims at presenting in axiomatic form those and only those principles of propositional logic that are accepted as sound in intuitionist mathematics.

Thus, propositional PCK presents general principles of effective subject-specific teaching.

The principles of propositional modal logic, found in Prior Analytics I.15, were generally expressed as follows: if the antecedent of a valid consequence is possible/necessary, the consequent is possible/necessary (Abelard, Dialectica 202.6 8).

The use of variable functors with liberal substitution enables a number of principles of propositional logic to be given startlingly compressed and elegant formulations, for example the principle of bivalence in the form which can be read as "if something is true of a false proposition then if it true of a true proposition, it is true of any proposition" (C00 is a true proposition).

In practice, of course, this test is unworkable for formulae containing a large number of propositional variables, but in principle one could apply it successfully to any formula of the propositional calculus, given sufficient time, tenacity, paper, and pencils.

For Aristotle, LNC is understood primarily not as the principle of propositional logic that no statement can be true simultaneously with its negation, but as a prima facie rejection of the possibility that any predicate F could both hold and not hold of a given subject (at the same time, and in the same respect).

On this view, propositions and propositional functions have an order.

One would simply add the standard (or classical) rules for quantifiers to the principles of whichever propositional modal logic one chooses.