[FRIAM] square land math question

[uǝlƃ ↙↙↙]

Spot on! And my cognitive disability prevents me from remembering who or where someone used that as an argument against the law of the excluded middle ... arguing for intuitionist logic. 

On 7/23/20 3:32 PM, Jon Zingale wrote:
> SDG is a rather cool example of where the point notion can be radically
> different than classically handled by Euclid. From the man himself, Anders
> Kock[1]:
> 
> "Euclid maintained further that R was not just a commutative ring,
> but actually a field. This follows because of his assumption: for any two
> points in the plane, either they are equal, or they determine a unique
> line.
> 
> We cannot agree with Euclid on this point. For that would imply that
> the set D defined by
> 
> D := [[x ∈ R | x^2 = 0]] ⊆ R
> 
> consists of 0 alone, and that would immediately contradict our
> 
> Axiom 1. For any g : D → R, there exists a unique b ∈ R such that
> ∀d ∈ D : g(d) = g(0) + d · b"
> 
> Gotta love Kock.
> 
> [1] Synthetic Differential Geometry: https://users-math.au.dk/kock/sdg99.pdf
> Also, the paper of his I am currently entrenched in to investigate further
> some
> ideas in the Instrumental Goal versus Evolutionary Function discussion:
> https://arxiv.org/pdf/1105.3405.pdf

-- 
↙↙↙ uǝlƃ