21222
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Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
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Full Idea:
Husserl maintained that because most logicians have not studied the connection between logic and the world, logic did not achieve its status of purity. Even more, their logic implicitly presupposed a world.
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From:
report of Edmund Husserl (Formal and Transcendental Logic [1929]) by Victor Velarde-Mayol - On Husserl 4.5.1
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A reaction:
The point here is that the bracketing of phenomenology, to reach an understanding with no presuppositions, is impossible if you don't realise what your are presupposing. I think the logic/world relationship is badly neglected, thanks to Frege.
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14235
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Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
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Full Idea:
If the rule is asserted 'Given any well-determined objects, they can be collected into a set by an application of the 'set of' operation', then on the usual account of 'they' this is a tautology. Collection comes automatically with this form of reference.
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From:
James Cargile (Paradoxes: Form and Predication [1979], p.115), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? Intro
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A reaction:
Is this a problem? Given they are well-determined (presumably implying countable) there just is a set of them. That's what set theory is, I thought. Of course, the iterative view talks of 'constructing' the sets, but the construction looks unstoppable.
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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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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.
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From:
report of Edmund Husserl (Formal and Transcendental Logic [1929]) by Victor Velarde-Mayol - On Husserl 4.5.2
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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.
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