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/sci/ - Science & Math

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File: 33 KB, 315x499, intuitionistic_proof_vs_classical_truth.jpg [View same] [iqdb] [saucenao] [google]
10738211 No.10738211 [Reply] [Original]

Intuitionism vs classical logic. Which is better? Why?

>> No.10738255

>>10738211
why don't you make up your own mind and go read the classics of antiquity you brainlet.

>> No.10738275
File: 29 KB, 600x900, PaulTaylor.jpg [View same] [iqdb] [saucenao] [google]
10738275

>>10738211
Read pic related and find out for yourself.

>> No.10738300
File: 301 KB, 413x549, spooky.png [View same] [iqdb] [saucenao] [google]
10738300

>>10738211
Intuitionistic logic is more interesting right now.

>>10738275
I like that book but it's not like it convinced me towards either answer.

On that note, I recently started reviewing a set theory book and drop some views on the subject

https://youtu.be/IR0GkYoRzeE

>> No.10738367

>>10738300
>On that note, I recently started reviewing a set theory book and drop some views on the subject
This is pretty based, desu. Thanks for the review, I'll watch the full thing later.

Also props for honestly introducing yourself as a 'sadistical physicist'.

>> No.10738396

>>10738300
>On that note, I recently started reviewing a set theory book and drop some views on the subject
Ah, got to the part about the Paul Taylor book. Yeah, he goes pretty hard in the category theory direction, lol.

>> No.10739093

>>10738211
Brouwer is a moronic asswipe, but Godel is legit genius and one of the three greatest mathematicians that ever lived. Hmmmmm.

>> No.10739122
File: 221 KB, 1590x1916, 1554405171698.png [View same] [iqdb] [saucenao] [google]
10739122

A Theory of Particular Sets

>> No.10739127

Is it possible to summarize what intuitionistic proof means? I only know classical.

>> No.10739241

>>10739127
A better name for it might be "constructive proof". A proof of "for all x there exists y such that blah blah blah" is constructive if given x you can actually tell us what y is. This generally disallows proof by contradiction, since proving "there can't NOT be a y" doesn't get you far towards actually constructing it.

An example of a nonconstructive theorem is, and this takes some getting used to, that every real is either <0, =0, or >0. A simple ""proof"" of this is that when you write down x as a string of digits, even if we examine the first one-trillion decimal places of x and they are all zero, x could still be positive if the next digit is a 1.

You could call this point of view "Bishop-style constructive mathematics" because I've avoided writing down autistic axioms or even specifying exactly what I mean by "tell us what y is". There are also autistic versions that lay out specific axioms, and these have applications in computer science, but Brouwer would probably kick my ass if I called those intuitionism.

>> No.10739268

>>10739241
Oh I see. Much obliged, Anon.
Seems I need to get into proofs a lot more.