By Ralph Krömer
The most aim of the e-book below evaluation is to supply a scientific and profound research of numerous vital historic and epistemological features of class conception. The important subject of the booklet is to offer an research of the impressive undeniable fact that class thought received place in day-by-day arithmetic as an invaluable and legit conceptual innovation, despite the problems of its set-theoretical foundations and the problem it brought on to this previously well-established mathematical origin and to a couple epistemological positions.
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Extra info for Tool and Object: A History and Philosophy of Category Theory
This approach relates history (to understand a course) and philosophy (to understand a piece of knowledge in its justiﬁedness). The claim is that the understanding of a principle of knowledge acquisition ﬂows from the understanding of the progress of knowledge24—as manifest in the transformation of concepts—, while the reduction of knowledge to basic insights, because it is retrograde, is not very likely to participate in the promotion of new knowledge. This means in particular that philosophical questions are to be asked anew for each stage of historical development of a discipline, and that the respective answers have to be compared with each other25 .
What are the criteria to choose the “reasonable” uses among the “correct” uses). I will subsume problems of this type under the label “criterion problem”. 1, these criteria cannot at any rate be formal ones. We have to discuss the criterion problem since we want to analyze the historical development of a theory. It is to be noted ﬁrst that the term “theory” is used in (talk about) mathematics in diﬀerent manners: • in naive use, the term denotes most often a collection of results and methods around a certain concept (examples: number theory, group theory, knot theory, game theory, proof theory .
Some thirty books on mathematics constituting a small reference library used by Eilenberg; 2. a substantial part of Eilenberg’s scientiﬁc correspondence; 3. several unpublished manuscripts19 ; 4. materials from Eilenberg’s time as a student in Poland (lecture notes, diploma, enrollments at foreign universities); 17 This notwithstanding, one will need to consult this article for exact bibliographical references to the unpublished material, and for more ample information concerning the internal functioning of Bourbaki which will be needed in order to appreciate fully the signiﬁcance of the conclusions drawn from this material.