Sentence examples for foundational point of view from inspiring English sources
This has been taken by many to be a vindication of the foundational point of view of mathematical intuitionism.
Since the last step guarantees the consistency of the original theory, from a foundational point of view one is interested in the methods used to prove normalization.
Indeed, from a foundational point of view it does not make much sense to understand the 'proofs' above as proofs in an intuitionistic system which these conditions are supposed to be specifying.
What is important, from a foundational point of view, is that the set-theoretic version of $\mathbb{R}$, together with the usual algebraic operations, satisfies the categorical axioms that the real numbers satisfy, namely those of a complete ordered field.
Bernays has written (see Bernays' entry on David Hilbert in Edwards 1967) that this result of Gödel's drew the attention of the Hilbert school to two observations: first, that intuitionistic logic goes beyond finitism, and secondly, that finitist systems may not be the only acceptable ones from the foundational point of view.
Develop your point-of-view.
Consistently remain in one point-of-view.
Tell from the proper point-of-view.
From a conceptual point of view, the transition from kinetic gas theory to statistical mechanics poses two main foundational questions.
