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Sometimes this worry is expressed as whether Spinoza can "derive" the finite from the infinite, but it is not really a question of logical deduction.
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Bethe contended that the developments which led to the successful Teller Ulam design were a matter of serendipity and not a question of manpower or logical development of previously existing ideas.
Although, as Russell and Whitehead acknowledge in their preface to Principia Mathematica, "In all questions of logical analysis, our chief debt is to Frege" (PM, viii), Russell's own advance lay in extending logical analysis and in suggesting the possibilities of eliminativism.
A more appropriate departing point for this issue is not the question of logical priority but rather Einstein's distinction between 'constructive theories' and 'principle theories'.
Dr. Gale added that he is not just being querulous when he raises the question of logical impossibility.
On this view, psychological genesis (or the context of discovery) was irrelevant to the question of logical justification (or the context of justification).
It is simply a question of mental and conceptual exercises incorporated with systemic and logical thinking.
The extensive use of analytic methods, the incorporation of applied subjects, and the adoption of a pragmatic attitude to questions of logical rigour distinguished the new mathematics from traditional geometry.
Or do questions of logical consistency simply matter less to them?
Hintikka (1996: 194 210) discusses mathematical theories (or mathematical axiomatizations) and mathematical problems (or questions of logical consequence) separately.
On the face of it, it appears that questions of logical form leave the existential issue undecided, at least insofar as an event-committing analysis automatically turns into an eliminativist paraphrase when read in the opposite direction (and vice versa).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com