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/sci/ - Science & Math

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7430324 No.7430324 [Reply] [Original]

There are people on this board RIGHT NOW who would unironically call themselves mathematical logicists

>> No.7430418
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7430418

>there are people on this board right now unironically

>> No.7430429
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7430429

>>7430324
>There are people on this board RIGHT NOW

>> No.7430451

>>7430429
THERE ARE PEOPLE

...right...

>NOW!

>> No.7430456

>>7430324

I'm mathematically and physically autologistic.

>> No.7430598

>>7430324

>There right this on now board are people

>> No.7430600

Do you mean logicians?

>> No.7430847

I study logic in the math department, would say I qualify yeah? You probably don't even know of the subfields of logic I study.

>> No.7430865

Math is nothing more than an extremely inflated sub-discipline of logic.

Numbers don't actually exist in real life; you can't find a "pi" in real life. You can't grab a fistful of "12". Numbers only exist as a side effect of the application of the rules of logic upon the axioms of mathematics. Math is only so popular because it's easily applicable to modeling real life in an abstract sense.

>> No.7430875

>>7430865
You haven't done much math or logic in your life, right ?

>> No.7430880

>>7430875
Are you denying that all of math is derived from a small number of axioms?

It is simply the truth that all of math is derived logically from a small number of axioms. It is just applied logic.

>> No.7430907

>>7430880
>Are you denying that all of math is derived from a small number of axioms?

Yes. All parts of maths have existed before their first axiomatization (there was geometry before Euclid, analysis before Weierstrass, arithmetic before Frege). There isn't a single axiomatization of maths, a lot of maths is axiomatized under set theory but other approaches like category theory and intuitionist logic have grown traction over the past decades.
And even if you're talking about the classical ZFC axiomatic (probably still the most commonly used though that is changing) you actually have an infinity of axioms.

Also iirc the first axiomatic treaty on math predates the first treatise on logic.

>It is simply the truth that all of math is derived logically from a small number of axioms.

And how do you choose the axioms ? "Logically" ? Logic doesn't tell you how to choose your axioms, it can only give you an idea of what happens once you've done so. In order to choose our axioms you must first want to axiomatize, and in most cases you axiomatize because you want to do something, and to understand something, using that axiomatic. And that "doing something" and that "understanding something" is where math is derived from. Logic simply allow you to play around with formal statements. Maths involve a lot of that, but first arises from intuition and observation, from daily activities like counting and drawing figures (on sand, paper, or mentally), from intuitions of mathematicals objects and from concepts about structure, relation, independance.

>> No.7430910

Logic insofar as it is used by mathematician comes later, it's a way to formalize and make more rigorous the mathematical practice, but it can only formalize if there is something you want to formalize in the first place. You don't think the technical terms of masonery, or the standardized procedures for building, were invented before the first primitive rope, hammer and nail, do you ?

>It is simply the truth

It's not an uncontroversial truth, it's a hotly debated topic among experts, and it has been for more than a century. If you're considering the history of mathematics, logic is a later development, if you're considering the current mathematical practice nowadays, mathematical logic is mostly a tiny subfield of maths. That's not even considering the question of wether mathematics can entirely be translated into a form of logic (again, still a controversial topic in the field). The best you can say is that the history of modern logic is very much tied to the history of modern math, and that mathematician nowadays use a loose logical framework to the extent that it suits them.

TL;DR: Logic is to math as to math is to physics, a useful tool that you'll often need, except physicist quickly use pretty advanced math while mathematician mostly use rather simple logic.

>> No.7430939

>>7430907
>>7430910
I should add that logic wasn't developed for mathematics at first, although a lot of the earlier problems for 19th century logicians were related to axiomatization of arithmetic. I'm talking mainly about the part of logic that mathematician care about.

>> No.7430960

>>7430847
>You probably don't even know of the subfields of logic I study.
Literally the most autistic sentence I have ever heard.

>> No.7430969

>>7430865
Mathematics and logic are equivalent, given by the inclusions taking every mathematical theory to its model-theoretic foundations, and the map taking every logical system to its mathematical realization. Obviously composition left or right yields an automorphism that is isomorphic to the identity on these fields of study. The sooner you children realize this, the sooner these shit threads can come to a halt.

>> No.7431003

>>7430600
>>7430847
>>7430865
>>7430910
I was obviously talking about the logicism of Frege & friends (the doctrine that math is reducible to logic, if you somehow still don't know what I'm talking about), which was pretty much single handily destroyed by the nice man in the OP (along with "muh axioms" fags in general)

>> No.7431031

>>7431003
Let's pretend you're not a moron undergrad who recently got out of his intermediate-level symbolic logic course. The fact of the matter is that logic is simply the prescriptive study of how we ought to reason. That's it. The fact that axioms cannot be decided on using logic alone and must be obtained through other means is fine. Yes, Goedel's incompleteness theorems regarding arithmetic were a huge wake-up call. But your OP is retarded. Logic just tells us how we should reason. What we base our reasoning on is an entirely different story. That doesn't somehow invalidate the entire field.

Sure is summer in here.

>> No.7431050

>>7431031
What field am I invalidating, exactly? I'm fine with set theory and higher order logic (though I don't think it has the beauty of continues math or much in the way of pragmatic value), I'm just making fun of a position in philosophy of math.

>> No.7431051

>>7430324
>Let's pretend you're not a moron undergrad who recently got out of his intermediate-level symbolic logic course. The fact of the matter is that logic is simply the prescriptive study of how we ought to reason. That's it. The fact that axioms cannot be decided on using logic alone and must be obtained through other means is fine. Yes, Goedel's incompleteness theorems regarding arithmetic were a huge wake-up call. But your OP is retarded. Logic just tells us how we should reason. What we base our reasoning on is an entirely different story. That doesn't somehow invalidate the entire field.

>Sure is summer in here.

bump

>> No.7431077

>>7430910
>Logic is to math as to math is to physics \

Completely wrong. Logic is a sub-field of mathematics as is topology, algebra, geometry, combinatorics, etc.

Mathematical Logicians study shit like model theory, set theory, category theory, proof theory, recursion theory and sub-fields within those sub-fields and often these areas have applications to other areas of math like combinatorics, graph theory, topology, and the like.

You obviously never studied higher level math, least not higher level logic.

>> No.7431106

>>7431077
Well, formal logic is also applicable to philosophy so that's a specious argument. But yeah, mathematical logic is a subfield, not a superset.

>> No.7431145

>>7430907
>And how do you choose the axioms ? "Logically" ? Logic doesn't tell you how to choose your axioms, it can only give you an idea of what happens once you've done so. In order to choose our axioms you must first want to axiomatize, and in most cases you axiomatize because you want to do something, and to understand something, using that axiomatic. And that "doing something" and that "understanding something" is where math is derived from. Logic simply allow you to play around with formal statements. Maths involve a lot of that, but first arises from intuition and observation, from daily activities like counting and drawing figures (on sand, paper, or mentally), from intuitions of mathematicals objects and from concepts about structure, relation, independance.
I am glad to read this. Every undergrade in math must understand this [and there is nothing to understand really]

>> No.7431612

>>7430324
>there are people
>UNIRONICALLY