Sentence examples for terms of logical from inspiring English sources

Instead, he defined the basic notions of "number", "successor" and "0" and proposed to show, with carefully chosen definitions of their basic notions in terms of logical notions, that those axioms could be derived from principles of logic alone.

Tarski (1923) noted that in the context of higher-order logic, one can define propositional connectives in terms of logical equivalence and quantifiers.

It presents a system of symbolic logic and then turns to the foundations of mathematics to carry out the logicist project of defining mathematical notions in terms of logical notions and proving the fundamental axioms of mathematics as theorems of logic.

Simplicity ranks are defined in terms of logical entailment relations, hence are language-invariant.

He regarded reality, the world, not in terms of logical order, but as manifesting aesthetic order.

Similarity is defined solely in terms of logical notions of quantifiers and identity.

Indeed, some logicians have attempted to spell out the logic of direct inferences in terms of the logical form of the sentences involved.[6] But regardless of whether that project succeeds, it seems reasonable to take likelihoods of this sort to have highly objective or intersubjectively agreed values.

Using the logical system containing Basic Law V (1893/1903), he attempted to demonstrate the truth of the philosophical thesis known as logicism, i.e., the idea not only that mathematical concepts can be defined in terms of purely logical concepts but also that mathematical principles can be derived from the laws of logic alone.

Certain things could be expressed in language, and these were best understood in terms of the logical techniques developed by Russell, he maintained.

One of the significant achievements of philosophy in the 20th century was the development of rigorous ways of characterizing such arguments in terms of the logical form of the sentences they comprise.

All these interstratal one-many or many-one relations are then analyzed in terms of the logical notions of conjunction and disjunction (AND-relations versus OR-relations), of ordering (x precedes y in an AND-relationship, x is selected in preference to y in an OR-relationship), and the directionality ("upward" towards meaning, or "downward" towards sound).