/sci/ - Science & Math

>>10502045
>mathematical logic
>posts a logic for philosophy brainlets book

>>10502045
There is more to that anon

>>10503332
they are essentially intertwined though? You can't delve fully into mathematical logic without dipping your feet in analytical philosophy and vice versa

>>10504802
>they are essentially intertwined though
No.
>You can't delve fully into mathematical logic without dipping your feet in analytical philosophy
You can and do.

>>10504813
I disagree 100% just because something is in a non literal form does not make not philosphical and logic of mathematics delves straight into alot of assumption based questions that can and have been asserted into analytical philosophy

>>10504827
>people who do x care about the philosophy of x

>>10504813
This is just plain wrong, it has been known for years mathematical logic and modal logic has helped philosophy progress substantially. The success of formal methods in mathematical logic has led philosophers to try to formalize many other kinds of reasoning.

>>10504835
So my point still stand that they are intertwined? And what makes you so upset to immediately start green texting?

>>10504839
you have not shown that they are intertwined
you've shown that philosophy has a dependence on mathematical logic but not the other way around

>>10504827
>logic of mathematics delves straight into alot of assumption based questions that can and have been asserted into analytical philosophy
no one cares that you can ask the same question in a different subject
you can delve into mathematical logic without touching analytical philosophy in the same way you can listen to a song without listening to covers of that song

>>10504841
>So my point still stand that they are intertwined?
you didnt make a justified point

>>10504856
so they are intertwined you continue to prove the same point?

lol brainlet

>>10504856
logic is essentially a discussion of philosophical terms especially in math based presumption

This is why /sci/ sucks at discussing mathematical logic. /mg/ dismisses it, and anytime a thread about it appears the philosotards show up.

>>10504877
>This is why /sci/ sucks, the philosotards show up.
ftfy

What is a nice first book for mathematical logic? I'm still in lower-level courses if that matters.

>>10504877
/lit/ discusses wittgenstein and russel often with alot of back up mathematical logic but that board is a fucking mess

>>10504859
>so they are intertwined
no, what in my post even remotely resembles a definition of intertwined
one depends on the other, not the other way
so they are not intertwined you fucking idiot

>>10504904
analytical philosophy and pure logical ideas are dependant on mathematical logic is what your saying but there not they often advance making great leaps of assumption and use mathematical logic to continue these notions and as>>10504860 says mathematical logic is a technically a philosophy itself. As mathematical logic is a formal mathematical dissertation of logic. Logic alongside metaphysics,ethics,rhetoric etc etc all fall into the definition of philosophy, maybe not exactly the philosophy your use to-Western Philosophy- but the cold logic,linguistical and language game based analytical philosophy which in itself is a field ignored by western philosophers as a whole, what your failing to see is mathematical logic is even exchanged with being philosophy of mathematics consistently.

>>10504904

>>10504877
>/mg/ dismisses it
Literally no one will complain if you go to /mg/ and try to discuss topoi and model theory.

>>10504904
retard look here --->>>10504927
>>10504927
on this note since logic is being discussed

/thread/

>>10504827
>retard can't follow direction
You don't need AP for mathematical logic. I don't give a fuck what AP losers do.
>>10504839
>it has been known for years mathematical logic and modal logic has helped philosophy progress substantially
Not math, don't give a shit. And you still haven't shown you need AP for any mathematical logic work (because you don't).

>>10505605
The foundations of mathematics, and how they can be composed with logic, is in itself a philosophical topic. The logicians who founded and developed the subject were all philosophers heavily involved in dialogue with other philosophers. You can't just cast away the philosophy and act like all the logic was just magicked out of nowhere by pure mathematicians who weren't interested in how reason might be grounded.

>>10505605
Are you autistic? The guy has been trying to tell you that mathematical logic is founded on logic and both analytical philosophy and mathematical logic have a mutualistic relationship, both help eachother... how is it not hard to understand its literally one fucking google search

I love how you skip over this >>10504927

>Not math, don't give a shit. And you still haven't shown you need AP for any mathematical logic work

Is this what /sci/ has become? Arguing to argue;autism full blown out muting anyone elses opinion?(pic related)

>>10505605
>whats that your arguing a valid point thats been regarded as facts for years? No your not your dumb, im right your wrong because im right

>>10506517
>The guy has been trying to tell you that mathematical logic is founded on logic
No. Mathematical Logic is independent
>and both analytical philosophy and mathematical logic have a mutualistic relationship
No. AP just steals ideas from ML.
>I love how you skip over this >>10504927
Random words placed randomly and some autist wrote his name in the corner. Not an argument.
>>10506525
>your wrong because you contradict infallible dogma promulgated by self-important philosophers
Not an argument.

>>10506474
Philosophical logic is dead and replaced by mathematical logic just like alchemy is dead and replaced by chemistry.

>>10506678
>Philosophical logic is dead and replaced by mathematical logic

In what universe? I'm not even asking that rhetorically, since modal logic is a core topic developed in philosophy that has influenced other fields. Logic is and has always been philosophically motivated, and your ignorance of it and its aim of modeling reason doesn't change this.

>>10506674
philosphers have invented over half of the shit>>10504927 in this chart is what your over looking, and mathematicians used those ideas to expand onto mathematical logic.

are you blind? read,understand than respond. Originally you said they did not intertwine when presented evidence they did you moved your argument to mathematical logic not being affected by philosophy but mathematical logic is based on logic,a philosophical term. Hence why philosophical concepts are implimented into mathematical logic through mathematical language by analytical philosphers and vice versa(mathematicians create mathematical proofs that can be implemented in philosophy).

Are you slow or something?

>>10506731
>inb4 "Mathematical Logic is independent" "No. AP just steals ideas from ML."

>>10504839
>>10504920
>modal logic has helped philosophy progress
If you consider people believing that Kripke frames are real and there are universes nearby where kangaroos fall over because they have no tails, sure, I guess

>>10506731
Take some courses in mathematical logic or read some books, philosophy is never brought up. Mathematical logic doesn't even care if T stands for some concept of "true" or not. It's all symbols and math.

>>10506759
analytical philosophy and courses on logic are all nearly symbols aswell i hope you know this...you do realise just because its labeled philosophy doesent mean they dont use symbols. I've taken a course in both mathematical logic and logic majoring in both philosophy and mathematical logic. My professor reccomended that I take more courses in mathematics to under kripke more as I was having immense trouble with him at the time.

Do you really think analytical philosophy doesent use numbers and symbols? Every person in that field originated from a mathematical background and or studied both fields......

>>10506703
Logic was garbage in philosophy and had to be saved by mathematics. In less than 200 years, mathematicians have achieved way more than over 2300 years of philoshitters getting nowhere.

>b-but they invented the word they used so they deserve half the credit!

>>10506774
no mathematical logic is dead if anything being slowly replaced by computability theory's and complexity theorys.. but I don't even think either field is dead if anything they all help each other. But I understand how some people can't see the obvious relationship?

>>10504839
>modal logic has helped philosophy progress substantially

>>10504927
>implying philosophy is intertwined with math
>implying comp sci is intertwined with math

Top kek. The only field intertwined with math is physics (and engineering on rare occasions).

>>10506847
>circles modal logic, philosophy of mathematics,philosophy of set theory,foundations,temporal logic and non classical logic

>>10506953
>thinks meta-mathematics is not math

>>10506963
>doesent notice the argument was whether it was intertwined or not....not if its mathematics or not

>>10507006
It's not intertwined. Mathematicians don't pay the least bit attention to anything the philotards do nor do philotards contribute mathematics.

Take your "we wuz mathematicians and shieet" back to >>>/lit/ and >>>/g/

>>10507027
>>>>/lit/
*>>>/his/

>>10506773
way to completely miss his fucking point

>>10507027
no convincing autism
>>10507006
go home its bait

>>10507027
tfw russel tfw kripke tfw hintikka tfw bernard williams tfw scruton tfw charles taylor

tfw when theres like 1000 more
tfw autism

>>10507027
>Mathematicians don't pay the least bit attention to anything the philotards do nor do philotards contribute mathematics.
That's why mathematics has turned into illogical bullshit.

>>10507281
The logic you create to make a game or other piece of software isn't non-existent, it simply does not conform to reality at a high rate of incidence.

>>10507300
>it simply does not conform to reality at a high rate of incidence.

brainlet.

>>10507300
The logic is represented physically as electromagnetic pulses. That logic being formal logic.

>>10507273
>russel
Literally a meme only brought up to mock.

>>10507300
>"bick wurd mak me smar"
this thread can't be serious?right?

>>10507281
>That's why mathematics has turned into illogical bullshit.
cope harder retard

>>10507594
>thinks zero is a number

You know, someone could just post a syllabus of a graduate level philosophy logic course

You know, someone could just post a syllabus of a graduate level mathematical logic course

>>10507645
>>10507616
course description for mathematical logic in a uni near me

>>10507645
my impression is straight logic isn't very common but where i went the logic classes were an introduction to formal systems then into completeness/incompleteness

>>10507670
Philosophy

Mathematics is a branch of philosophy.

>>10507770
Mathematicians can easily go into philosophical discussions about the metaphysical or epistemological aspects of numbers, mathematical operations, signs, and the relationship between mathematical probability and possibility, but philosophers might have a much greater difficulty getting into the specifics of the validity of a certain mathematical proof.

>>10507878
thats whwere the sperg analytical philosophers are lumped in i.e wittgenstein,kripke,russell. Hard cold analytical philosphers are a completely seperate branch of philosophy as a whole, and albeit its an extremely beneficial branch its hard for them to discuss with other philosophers the cold hard math side of their philosophy.

>>10507770
It might be true that mathematics and philosophy do overlap to some extent, but I'd like to believe that people were adding and subtracting berries, tree branches, and pieces of meat thousands of years before Thales of Miletus or the ancient Indian brahmani who first recited the Upanishads were born.

>>10507670
>no soundness, completeness, compactness, etc

Sounds like a mathematical logic course for cs brainlets who want to gawk at incompleteness

>>10507906
Kripke might actually be a literal autist

>>10507311
>>10507447
Literally "illogical" isn't a valid criticism of math.

>>10507878
>Mathematicians can easily go into philosophical discussions about the metaphysical or epistemological aspects of numbers, mathematical operations, signs, and the relationship between mathematical probability and possibility
Provide an example.

>>10507914
>I'd like to believe that people were adding and subtracting berries, tree branches, and pieces of meat thousands of years before Thales of Miletus or the ancient Indian brahmani
Yes they would have been, but the "adding" and "subtracting" of such physical things wouldn't need to be done as a separate mathematical calculation, as the inherent nature of the objects themselves would've been enough. Just like a baby doesn't need to know the mathematical concept of 'one' in order to breast feed upon one breast.

>>10508061
not him but read any of the people mentioned here>>10507273

It's not a hard concept to grasp, and its obvious your lacking knowledge in both fields(if your the guy continuing to reply ignorantly).

>>10508079
Those people are philosophers, not "mathematicians" as they like to call themselves.

>>10507770
>philosophers need a total of 16 (SIXTEEN) binary operations
>mathematicians use 2 binary operations and a unary operation on variables in a commutative ring with 2 elements
>somehow philosophonies consider themselves just as smart as mathematicians

>>10508117
>Mathefagitions are extremely limited

>>10508152
No, we just don't need to make up a bunch of extra shit that's just more of the same to overcomplicate our work and make ourselves seem deep. Our work is deep and worth paying for.

>>10508159
>Mathematicunts use numbers, binary and unary operations etc not realising these are philosophical concepts

>>10508171
kill yourself

>>10508171
no, no. All these things are well-defined, precise constructs that are applications of first-order logic. No need for any philosophy, just OR, AND, ~, and whatever symbolic language to make things less complicated.

>>10508173
What does mathemashitics tell you about death?

>>10508177
>applications of first-order logic. No need for any philosophy, just OR, AND, ~, and whatever symbolic language to make things less complicated.
First-order logic is philosophy you insufferable swine.

>>10508187
kill yourself

>>10508189
Death is merely illusory, but being a mathefaggotician you wouldn't know that.

>>10508100
pretty sure all of them have a plethora of accolades associated with mathematics

>>10508195
i thought kripke was purely a philosophy fag, i guess i stand corrected

>>10508195
They all call themselves philosophers. I want a pure mathematician.

>>10508198
see here -->>>10508196
kripke graduated with a mathematics degree from harvard
Russel to quote wikipedia directly "Russell won a scholarship to read for the Mathematical Tripos at Trinity College, Cambridge, and commenced his studies there in 1890,[94]"
As for Scruton"He left school with three A-levels, in pure and applied mathematics, physics and chemistry, which he passed with distinction. The results won him an open scholarship in natural sciences to Jesus College, Cambridge, as well as a state scholarship"
As for Frege well... frege has too much shit to list so I'll leave it to you to check it out:https://en.m.wikipedia.org/wiki/Gottlob_Frege

If you don't think graduating from top universitys with mathematics degrees and winning multiple accolades in mathematics before moving onto analytical philosophy in interest doesent make you a mathematician...then I can't help you.

>btw frege is the founder of analytical philosophy and the guy studied mathematics like no other

>>10508230
>kripke graduated with a mathematics degree from harvard
Saul Aaron Kripke is an American philosopher and logician. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York
>Bertrand Arthur William Russell, 3rd Earl Russell, OM FRS was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate
Bertrand Arthur William Russell, 3rd Earl Russell, OM FRS was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate
>As for Scruton"He left school with three A-levels, in pure and applied mathematics, physics and chemistry, which he passed with distinction. The results won him an open scholarship in natural sciences to Jesus College, Cambridge, as well as a state scholarship
Sir Roger Vernon Scruton FBA FRSL is an English philosopher and writer who specialises in aesthetics and political philosophy, particularly in the furtherance of traditionalist conservative views.
>As for Frege well... frege has too much shit to list so I'll leave it to you to check it out
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language and mathematics.

They all identify as philosophers, funny that... can you find a mathecuckician who does not identify as a philosopher but can profoundly analyse mathematics at a level philosophers can?

>>10508245
wow buddy calm down, their named philosophers because they worked on mathematical logic, logic a philosophical term, making them philosophers and mathematicians especially when they worked in very math heavy fields such as Frege and Kripke(modal logic). So, all that copy and pasting for your argument to male no sense? Just because their called philosophers does not me their not mathematicians. Frege was a mathematician his whole life without being labeled a "philosopher" only later did they realise the emphasis of work he put into a "philosophical field"(AP).

>>10508261
>Just because their called philosophers does not me their not mathematicians.

Which nobody is claiming. The ancient Greek philosophers were heavily involved in mathematics too, but they don't suddenly not count because of that. I mean, are you aware of the contributions CS Peirce made to logic, or do you think that he somehow "doesn't count" because he was a scientist?

>>10508271
if we go by your example
>Charles Sanders Peirce (/pɜːrs/,[9] PURSS; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".

>>10508261
Based upon what you've just said, does one agree with the below statement that began this argument in the first place?
>Mathematicians can easily go into philosophical discussions about the metaphysical or epistemological aspects of numbers, mathematical operations, signs, and the relationship between mathematical probability and possibility

>>10508271
peirce was, at least in part, a scientist tho. doesn't mean he wasn't an archaic dummy

>>10508261
>worked in very math heavy fields such as Frege and Kripke(modal logic)
Also modal logic is philosophy.

reminder that philosophers not only can't into physics, but also, even if they read physics, they misinterpret it very badly. example:
>The theory of Einstein is a marvelous proof of the harmonious multiplicity of all possible points of view. If the idea is extended to morals and aesthetics, we shall come to experience history and life in a new way.
total philosopher brainletism

>>10508284
yes, why are we arguing?

lets hug it out

>>10508292
>doesn't realise that the theory of relativity is just bad metaphysics that uses mathematics instead of modal logic so that it doesn't need to be logically sound in reality

>>10508284
>>10508295
this fucking thread

>>10508295
>yes, why are we arguing?
That's called philosophy - mathematicians don't need it apparently, so you mustn't be a mathematician.
>lets hug it out
Do you believe you can be a good mathematician without being a philosopher?

>>10508315
kill yourself

>>10508187
I would agree with you, but philosophy has deviated from the old wisdom so much and has turned into such a load of liberal arts bullshit that I'm inclined to consider first-order logic as an element in the domain of mathematics. Sort of an absorption by superior intellect, if you will.

>>10508319
>Philosophy is shit because only the shit parts of it count now

>>10508316
i tried but ur mom stopped me and then i made love to her

>>10508312
this whole thread is delving into the logic of mathematics and philosophy whilst delving into the logic of the logic if philosophy or mathematics are both logical???????

t.graduated with a BA in mathematics...(pic related is me)

>>10508319
>has turned into such a load of liberal arts bullshit
Like what?

>this fucking thread
Don't insult philosophy by trying to intertwine it with mathematics.

>>10508329
o lord, this thread started the other way around don't start this shit again

>>10508325
>graduated with a BA in mathematics
More like a BA in philosophical axiomatic logic

>>10508182
your cells stop interacting in a structured enough way to maintain a mind so you stop existing. what the fuck beyond that did your philosophy classes tell you about death?

>>10508171
>not realising these are philosophical concepts
This is stupid. You don't have to navelgaze about mathematics to shuffle symbols according to rules any more than a fisherman needs to determine when a ship has officially turned into another ship.

Humans almost all agree on what it means to shuffle symbols according to rules. And now we can even officially declare we're actually looking at patterns of bit manipulation (that happen to correspond to what everyone means by shuffling symbols) by physical logic gates. So if there's any disagreement we can just see what the bit flipping logic gates say about it. That's all we need for mathematicians to do math; no philosophizing is required.

Whether philosophy is helpful to professional symbol shufflers by providing intuition or whatever is a separate more interesting question but I see no reason to assume the answer is yes.

Anyways it's substanceless to claim people don't understand what they're doing is a "philosophical concept". I don't even know what that means or what a non-philosophical concept is. If you want to start thinking about your thought process it's probably reasonable to call that philosophy but that doesn't mean that introspection is relevant to every task requiring thought.

>>10508321
>>10508328
Modern philosophy has a number of applications: political science, theology, criticism, lawyering and judgement, policy setting, but all of them non rigorous bullshit that never seems to come up with a definitive answer, and always guaranteeing a philosopher's employment. One could say that statistical analysis is also in the domain of philosophy, but that has just as much math and computer modeling in it that you might as well consider it an interdisciplinary study: math for the rigor and the accurate, reasonable conclusions, code-monkeying for the number crunching computing power, and philosophy in case you were missing common sense. First-order logic might as well be known as mathematical foundation, as math has co-opted it since philosophers have ceased using it. After all, when George Boole invented it, he was being a mathematician, not a philosopher.

>>10508384
>your cells stop interacting in a structured enough way to maintain a mind so you stop existing
Cute story but essentially meaningless.
>what the fuck beyond that did your philosophy classes tell you about death?
That one can never BE dead, because to BE something requires being alive.
>This is stupid. You don't have to navelgaze about mathematics to shuffle symbols according to rules any more than a fisherman needs to determine when a ship has officially turned into another ship.
Then you are not a fully fledged mathematician.
>Humans almost all agree on what it means to shuffle symbols according to rules. And now we can even officially declare we're actually looking at patterns of bit manipulation (that happen to correspond to what everyone means by shuffling symbols) by physical logic gates. So if there's any disagreement we can just see what the bit flipping logic gates say about it. That's all we need for mathematicians to do math; no philosophizing is required.
But you don't even know what numbers are.
>Whether philosophy is helpful to professional symbol shufflers by providing intuition or whatever is a separate more interesting question but I see no reason to assume the answer is yes.
And thus you will remain stagnant.
>Anyways it's substanceless to claim people don't understand what they're doing is a "philosophical concept". I don't even know what that means or what a non-philosophical concept is. If you want to start thinking about your thought process it's probably reasonable to call that philosophy but that doesn't mean that introspection is relevant to every task requiring thought.
If you want to improve mathematics you better start analysing it philosophically. NOW.

>>10508385
>but all of them non rigorous bullshit that never seems to come up with a definitive answer,
That's life - not everything can have a definitive answer.
>math for the rigor and the accurate, reasonable conclusions
Just being rigorous doesn't mean it is correct/true in "reality".
>First-order logic might as well be known as mathematical foundation, as math has co-opted it since philosophers have ceased using it.
Mathematicians have ceased calling themselves philosophers while still using philosophical logic.
>After all, when George Boole invented it, he was being a mathematician, not a philosopher.
False, he was a philosopher hiding behind the name mathematician. Just as theoretical physicists are actually metaphysicists.

>>10508410
>That one can never BE dead, because to BE something requires being alive.
That is stupid. I see inanimate objects being things all the time.

>Then you are not a fully fledged mathematician.
If I can shuffle symbols in ways that excite the other people doing mathematics I don't see why your opinion should matter.

>But you don't even know what numbers are.
They're symbols that are shuffled by particular rules.

>And thus you will remain stagnant.
People still make mathematical discoveries. Stagnation seems to mean being in a state you don't like.

>If you want to improve mathematics you better start analysing it philosophically. NOW.
Maybe that could improve mathematics, whatever that means. But you seem unreasonably certain about the effect 'analyzing it philosophically' (whatever that means) will have on symbol shuffling for someone that presumably doesn't shuffle many symbols.

>>10508410
>But you don't even know what numbers are.
you dont need to know what they are to use them you fucking clown
ever hear of Peano?
>If you want to improve mathematics you better start analysing it philosophically. NOW.
>t doesn't actually do mathematics

>>10508429
>not everything can have a definitive answer
[citation needed]
>muh "reality"
we live in reality. mathematical reality is true on its own
>philosophical logic
nice oxymoron
>philosophy is math. theoretical physics is metaphysics
lmao

>>10508430
>That is stupid. I see inanimate objects being things all the time.
Death by its very nature cannot exist, it is the opposite of existence, therefore you never be dead if you already exist.
>If I can shuffle symbols in ways that excite the other people doing mathematics I don't see why your opinion should matter.
You may enjoy arousing people by shuffling symbols, but you could give full blown orgasms if you changed mathematics foundationally.
>They're symbols that are shuffled by particular rules.
Is that it?
>People still make mathematical discoveries. Stagnation seems to mean being in a state you don't like.
Useless "discoveries".
>Maybe that could improve mathematics, whatever that means. But you seem unreasonably certain about the effect 'analyzing it philosophically' (whatever that means) will have on symbol shuffling for someone that presumably doesn't shuffle many symbols.
It doesn't matter how many "symbols" you shuffle when you don't understand the symbols at a deep level.

>>10508438
>you dont need to know what they are to use them you fucking clown
That's the problem you fucking clown.

>mathematical logic = logic = philosophy of logic

>mathematician=mathematician

>philosopher=philosopher

>mathematical logician(very wide and vast field=analytical philosopher

/thread

>>10508441
>[citation needed]
What is the tastiest meal?
>we live in reality. mathematical reality is true on its own
Show me a perfect circle.
>nice oxymoron
What?
>lmao
No argument?

>>10508456
>>They're symbols that are shuffled by particular rules.
>Is that it?
Yes.

As an aside the symbols seem to be getting shuffled in a way that corresponds to how some other systems work. As long as correspondence holds up I guess theorems about the symbols could be useful for counting and shit.

>It doesn't matter how many "symbols" you shuffle when you don't understand the symbols at a deep level.
Sure it does. Nice patterns of symbol shuffling will allow me to shuffle even more symbols.

Also occasionally someone else notices a correspondence between symbols and something they care about.

>Useless "discoveries".
Wait are you trying to make math more applied? Fuck off faggot.

>>10508471
opinions are definitely answers. Perfect circles exist in the reality of our imaginations, and as a mathematical concept.
>philosophical logic
oxymoron
>he thinks he can co opt physics into some kind of philosophy
It's like everyone is in this big brain club and you dumb philosophers are trying to fit in, but you can't.

>>10508461
there is no problem, atleast outside your head

>>10508475
>As an aside the symbols seem to be getting shuffled in a way that corresponds to how some other systems work. As long as correspondence holds up I guess theorems about the symbols could be useful for counting and shit.
What separates numbers?
>Sure it does. Nice patterns of symbol shuffling will allow me to shuffle even more symbols.
With no end in sight.
>Also occasionally someone else notices a correspondence between symbols and something they care about.
They don't care.
>Wait are you trying to make math more applied? Fuck off faggot.
Are you trying to make it shittier?

>>10508482
>opinions are definitely answers.
Definitive answers?
>Perfect circles exist in the reality of our imaginations, and as a mathematical concept.
Can you show me one?
>oxymoron
Do you mean redundant?
>It's like everyone is in this big brain club and you dumb philosophers are trying to fit in, but you can't.
Physics already co-opted philosophy.

>>10508493
you have nothing to contribute

>>10508475
>Also occasionally someone else notices a correspondence between symbols and something they care about.

This is the crux of the issue. In your model, people come up with ways to shuffle around symbols, and then maybe someone notices how the patterns involved in the symbol shuffling correspond to some other aspect of reality. The problem with this is that it ignores that the development of logic, in both modern and ancient times, was motivated by people aiming to specifically capture aspects of *reason* in their formal systems, and that this is a philosophical activity.

Now, of course, you can pluck these formalisms and treat them purely as formalisms, and there's nothing wrong with doing this or calling it mathematical logic. But when you deny or ignore that these formal systems came about because of people's introspection into the nature of reasoning and inference and how these might be aptly modeled, you are being dishonest and doing a disservice to yourself.

>>10508498
Are you referring to your own post there?

>>10508496
no no no and no. retart

>>10508501

>>10508500
Well said.

You might then ask, why has this philosophical reasoning disappeared from these intellectual pursuits? Is it deliberate?

>>10508514
Okay retart.

>>10506847
>>implying comp sci is intertwined with math
...have you read any comp sci theory papers recently? The connection has been there for a long time

>>10506847
>he didn't bundle computer science in with complexity theory
Anon, I hate to break it to you, but complexity is studied in TCS departments, and no, the majority of people in those departments don't hold math PhD's.

>>10506847
Also, Hamkins is an absolute beast, but I disagree with his classification of complexity adjacent to computability since it's more like an refinement of computability; we're still talking about the conceptual and computational realization of mathematics, but it's in the context of feasible realization. So while the open problems start from computability, they're really only fully examined when you talk about complexity

>>10502045
Anybody else here like Proof by Induction? I can make a mean Hypothesis

>>10508500
The reality is people started looking at specific systems of symbol shuffling because they correspond to something else they care about. However that still doesn't mean introspection is actually vital to that process. Especially after a correspondence you like has already been established all you need to do is act on your mental model in ways that correspond to legal shufflings of symbols. Despite being mental this is just your consciousness acting on a system it is perceiving; like deciding when to move your arm to swing a stick to hit a ball.

It's conceivable philosophy might have something to say about the details of when your mental actions correspond to legal symbolic actions and external systems. And even that this knowledge might somehow inform which sequences of actions are likely to get you results you want. However it's not obvious to me how exactly that would happen and people claiming that philosophy is vital to doing math should probably find a specific example of philosophizing making a mathematician produce better math for a fixed system before making that claim.

The more supported claim is that philosophy is helpful for deciding which new systems to look at. But even here it's not completely apparent that's true. Maybe looking at your box of mental systems and pulling one out that matches the situation is just instinctive. Maybe finding a list of axioms that shuffles symbols similarly to your mental system is a learned skill that doesn't require self analysis to optimize.

Furthermore how often is looking for new systems necessary? People are still mining the old systems for new discoveries (and these new discoveries are still useful in surprising ways to homos that want to influence the real world). It's not even obvious that more undiscovered but useful systems still exist, or that they aren't just immediately discoverable from shuffling symbols in one of the systems we already have.