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4 votes

Is Frege's axiom of unrestricted comprehension actually true after all?

There is a problem with representing the comprehension principle as a single axiom. It is more accurately read as an axiom scheme. So the specific formula that gives rise to the Russell set is an ...
Kristian Berry's user avatar
7 votes

Is Frege's axiom of unrestricted comprehension actually true after all?

∀F∃y ∀x[x ∈ y iff F(x)] [OSC1] ∀F∃y [α ∈ y iff F(α)] [UI] ∃y [α ∈ y iff α ∉ α] [UI] α ∈ x1 iff α ∉ α [EI] Step 2 is not how universal instantiation works. It only lets you remove the outermost ∀, but ...
causative's user avatar
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0 votes

Are Fregian abstract objects Kantian noumena?

According to Kant if, however, I suppose that there be things that are merely objects of the understanding and that, nevertheless, can be given to an intuition, although not to sensible intuition (as ...
lee pappas's user avatar
3 votes

Are Fregian abstract objects Kantian noumena?

Kant doesn't think that mathematics is concerned solely with concepts. He in fact thinks that mathematics is concerned with constructing objects in intuition (which is a view that people like Brouwer ...
abracadabra's user avatar
4 votes
Accepted

Are Fregian abstract objects Kantian noumena?

At one point in the first Critique, Kant says: For if I cogitate an understanding which was itself intuitive (as, for example, a divine understanding which should not represent given objects, but by ...
Kristian Berry's user avatar
4 votes
Accepted

Frege's implication theory

There is an link. The key-point of the Russell-MacColl's debate about the boolean formula 0A=0 is that for MacColl the symbol 0 means "the class of non-existents" while for Russell the ...
Mauro ALLEGRANZA's user avatar

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