>The interesting conception of the propositions-as-types principle is what I call Brouwer’s Dictum, which states that all of mathematics, including the concept of a proof, is to be derived from the concept of a construction, a computation classified by a type. In intuitionistic mathematics proofs are themselves “first-class” mathematical objects that inhabit types that may as well be identified with the proposition that they prove. Proving a proposition is no different than constructing a program of a type. In this sense logic is a branch of mathematics, the branch concerned with those constructions that are proofs. And mathematics is itself a branch of computer science.
Veeky Forums eternally BTFOd. Please post the SICP guy gif to try and seem less assblasted. Math is a subset of Computer Science, come to terms with it.
>>The interesting conception of the propositions-as-types principle is what I call Brouwer’s Dictum, which states that all of mathematics, including the concept of a proof, is to be derived from the concept of a construction, a computation classified by a type. In intuitionistic mathematics proofs are themselves “first-class” mathematical objects that inhabit types that may as well be identified with the proposition that they prove. Proving a proposition is no different than constructing a program of a type. In this sense logic is a branch of mathematics, the branch concerned with those constructions that are proofs. And mathematics is itself a branch of computer science. Who are you quoting?
>Mathematicians of classical Egypt were computer scientists
k.
Tyler Myers
Many researchers have blogs, my underage friend. Do look up Terence Tao's blog, Scott Aaronson and many other popular high quality blogs published by our contemporary geniuses!
John Taylor
also >he doesn't know ncatlab Kys
Nicholas Bell
>inb4 poor methematicians bring up """proof""" by contradiction and the """axiom""" of choice as defenses
Sebastian Myers
>Many researchers have blogs, my underage friend. Do look up Terence Tao's blog, Scott Aaronson and many other popular high quality blogs published by our contemporary geniuses! What's your point?
>>he doesn't know ncatlab False presupposition.
And I'm not a "he".
Julian Hughes
The point is that serious and respected researchers engage in blogging and ncatlab is a great resource for all things categories.
Julian Smith
>Logic >Intension, extension, etc. >nCatCafe - a shity blog wherein a good portion of the posts refer to logic and philosophy
Nice try hijacking Veeky Forums, humanities fag, but I'm afraid you're gonna have to do better than that - and if you want to talk about stupid bullshit like "logic" or "semantics" how about you discuss it with your brainlet history or sociology professor so you guys can be retards together and leave the real science and math to people more intellectually capable.
Daniel Mitchell
Spotted the freshman. ncat is very popular amongst mathematicians.
Easton Flores
>In this sense logic is a branch of mathematics No. Logic gates are the foundation of logical reasoning, which includes mathematics.
Liam Edwards
>logic gates t. Computer Engineering fag
Jason Lopez
Both Math and CS are subsets of Logic, which is a subset of philosophy. Also, Kant basically first penned the idea of computer science long after Mathematics was a thing for thousands of years.
Andrew Cox
>Check your CIS Privlege
You're not a girl, so why don't you clean your room and sort yourself out.
Ryder Smith
>Mathematics is a subset of Computer Science i cant imagine being this autistic desu i thank the gods every day
Nolan Reyes
>t. Retards that dont know there are multiple logics and type theory is superior to classical logic
Joshua Stewart
Obviously a troll thread but most CS courses focus on preparing students for industry. When most people think 'CS' they think 'programming' or at best 'machine learning'. I went to a top 5 uni in the UK and had to teach myself type theory.
Brody Ross
Well my CS curriculum was pretty much theoretical stuff only, I never even had a programming class, that's something we were supposed to learn by ourselves (if we cared to). Our only programming project was a SAT-solver. Courses ranged from algorithms, graphs, cryptography, game theory, to automata and formal languages, logic, set theory, type theory and lambda calculus, semantics, category theory
Hudson Russell
>CS courses >preparing students for industry I think you mean "programming courses".
Jaxson Fisher
>What most people >CS Degrees Who cares? We're talking computer science here, not university curriculum and courses.
Jack Torres
>Mathematicians of ancient Egypt were KANGZ 'N SHIET FTFY
William Foster
Thats kind of my point Exactly
Ayden Foster
This only applies to people who dont actually know computer science
Andrew Collins
Yes >Curry–Howard correspondence nailed it.
Adam Fisher
No. All reasoning is by virtue of physical Boolean logic gates, biological or otherwise. All three primitive logic gates are two dimensional physical devices. All mathematics, "multiple logics" and "superior theories" can be expressed in terms of these devices.
Jason Hill
>And I'm not a "he". You are right. We should have different pronouns to identify niggers like you.
Cameron Roberts
>formalist virgin vs >intuitionalist chad
Xavier Campbell
OK, prove that if f(a) and f(b) have opposite signs and f is continuous then there exists c between a and b such that f(c) = 0 using a computation.
Hudson Myers
Sweetie, you're obviously confusing expressive adequacy with logics, a testament to how little you know you think all logics deal in truth tables! Truly pathetic, stop posting!
Chase Phillips
>niggers Why the racism?
Grayson Stewart
There is also non-constructive mathematics.
Asher Carter
Aka formalized nonsense that leads to stupid as fuck theorems like Banach Tarski.
Brandon Brooks
It's the easy way to trigger faggots like you. Get used to it or get back to ledit.
Luke Jones
>faggots Why the homophobia?
Oliver Brown
Which can still be done in type theory.
Matthew Lee
Anything which assumes LEM globally can't really be called "mathematics".
Sebastian Adams
WE
Josiah Nguyen
You're awfully annoying, do you happen to be a gay?
Robert Rogers
>intuitionalist instead of "intuitionist" Fuck off to
Isaiah Harris
>You're awfully annoying, do you happen to be a gay? Why does it matter?
There are real numbers that cannot be approximated by any computer program. If math is a subset of comp.sci, then how did mathematics discover the existence of these numbers?
Henry Turner
>They are vermin which should be euthanized. Why would you euthanize homosexuals?
Blake Morales
Because they are vermin.
Logan Gonzalez
>There are real numbers that cannot be approximated by any computer program They can't be shown to exist constructively. Which means that their existence is not refuted, not that they can actually be shown to exist.
Levi Sullivan
>47 replies
Stop falling for obvious baito.
Nolan King
Could you elaborate on what exactly is bait in this post?
Blake King
>threads are bait because of tone and not because of content We got a brainlet over here
Gavin Wilson
>Because they are vermin. What makes them vermin?
Isaac King
>>threads are bait because of tone and not because of content Who are you quoting?
