Sentence examples for weaker principle from inspiring English sources

The unrestricted principle of comprehension is then replaced by the weaker principle that for every condition there is a class the members of which are the individuals or sets that fulfill that condition.

The problem with this justification is that it establishes a weaker principle than Strong Convexity.

The difference becomes important if proponents of the weaker principle also allow that syntactic rules may have context-dependent meanings.

Thus, (LIV) amounts to the assumption that there is a finite number of generator properties, and the weaker principle (LIV*) to the assumption of positive probability, in any case of interest, that the number of relevant generator properties is finite.

This was first pointed out by Patrick Maher (2002), who noted that Joyce's justification in fact motivates the following weaker principle: Weak Convexity Suppose \(\mathfrak{I}\) is a legitimate inaccuracy measure.

In support of taking Descartes to be employing the weaker principle that includes the fourth condition, it could be pointed out that, at least at this early point in the Meditations, Descartes does have a reason for thinking that whatever is causally responsible for his "state of being," is not sufficiently "perfect" so as to have made that equipment reliable.

In the context of constructive set theories like CZF, power set and separation are replaced by intuitionistically weaker principles.

In particular, one would like to obtain a foundational theory compatible with those contexts (e.g. categorical models of set theory) in which even these weaker principles of choice may not be validated.

The latter is motivated by (1) the observation that weaker principles appear to suffice for the constructive mathematical practice and (2) the desire to adhere to a form of predicativity (see the next section for a clarification of this notion of predicativity).

Galileo was also the first to show by experiment that bodies fall with the same acceleration whatever their composition (the weak principle of equivalence).

By the start of the 21st century, all observations and experiments on gravitation had detected that there are no deviations from the deductions of general relativity, that the weak principle of equivalence is valid, and that the inverse square law holds over distances from a few centimetres to thousands of kilometres.