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Single Idea 21224
[filed under theme 6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
]
Full Idea
Pure mathematics is the science of the relations between any object whatever (relation of whole to part, relation of equality, property, unity etc.). In this sense, pure mathematics is seen by Husserl as formal ontology.
Gist of Idea
Pure mathematics is the relations between all possible objects, and is thus formal ontology
Source
report of Edmund Husserl (Formal and Transcendental Logic [1929]) by Victor Velarde-Mayol - On Husserl 4.5.2
Book Ref
Velarde-Mayol,Victor: 'On Husserl' [Wadsworth 2000], p.69
A Reaction
I would expect most modern analytic philosophers to agree with this. Modern mathematics (e.g. category theory) seems to have moved beyond this stage, but I still like this idea.
The
15 ideas
with the same theme
[existence of fundamentals as a basis for mathematics]:
18271
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We can't prove everything, but we can spell out the unproved, so that foundations are clear
[Frege]
|
21224
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Pure mathematics is the relations between all possible objects, and is thus formal ontology
[Husserl, by Velarde-Mayol]
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17880
|
Integers and induction are clear as foundations, but set-theory axioms certainly aren't
[Skolem]
|
17810
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The study of mathematical foundations needs new non-mathematical concepts
[Kreisel]
|
9937
|
I do not believe mathematics either has or needs 'foundations'
[Putnam]
|
12688
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Mathematics is the formal study of the categorical dimensions of things
[Ellis]
|
17776
|
The ultimate principles and concepts of mathematics are presumed, or grasped directly
[Mayberry]
|
17775
|
If proof and definition are central, then mathematics needs and possesses foundations
[Mayberry]
|
17777
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Foundations need concepts, definition rules, premises, and proof rules
[Mayberry]
|
17804
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Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms
[Mayberry]
|
10236
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There is no grounding for mathematics that is more secure than mathematics
[Shapiro]
|
8764
|
Categories are the best foundation for mathematics
[Shapiro]
|
8676
|
Is mathematics based on sets, types, categories, models or topology?
[Friend]
|
17922
|
Reducing real numbers to rationals suggested arithmetic as the foundation of maths
[Colyvan]
|
18846
|
Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry)
[Rumfitt]
|