My last name is pipes but I'm not a plumber
also, consider the problem of logical omniscience. suppose you have some axioms and some inference rules. then why dont you already know all there is to be inferred? why is mathematics something difficult that needs to be done? if logic is pure why is there a process?
there is a process because your mind is an imperfect instrument that slowly does mathematical-like things via some underlying processes. i dont mind if you pretend the axioms and inference rules exist. but its clear to see your mind fails to access them perfectly, because otherwise youd already know everything. the axioms and inference rules end up in your head probably because you read a book about it and it induced a particular brainstate, and through cognition you find a compelling and communicable meme that you write down in a book to induce brainstates in others. thats human mathematics. the metaphysical abstraction is an idea that helps you think about mathematics better.
Same and fucking based thread go hbotz
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you could also imagine a "mathematician" who shuffles formal symbols around and outputs proofs of things. that's you, but you have a powerful brain with built-in heuristics and heuristics developed through experience and training so in general you try the better shufflings first. and from the inside it feels like you have insight into the metaphysics. do you actually have insight? well if you think you do you do i guess. drugged mathematician.
That's not how this fucking works. Whether you access it or not, a well-formed natural language necessarily accesses the real, metaphysical mathematical objects it's able to prove the existence of.
You are.
That's because you're not using a well-founded formal language and constructing first or second order logical proofs in that language.
What? This is irrelevant: there are valid, rigorous methods to asses the validity of proofs. That's why there's peer review: Wiles's first proof of Fermat's Last Theorem required a huge amount of mathematicians to check it because it utilized so many mathematical specializations. It wouldn't be accepted as a proof until the review completed (it took about a year), but the proof was proven to have a flaw. It then took another year to fix that flaw, and another 2 years for review and acceptance.
You don't get to claim that mathematical results are flawed when they can be completely verified and the verification is done by many other mathematicians to ensure that it is correct.
You can't keep asserting this when it's provably false.
No you cannot. It's inherently contradictory
There are theorems that are computed. The issues are the length of time it takes and that the resulting proof is not often verifiable by a human, so it can't be considered true.
This makes no sense. There's a process because there's a logical process and strict rules, so every step must be verified and manner of getting from premise to predicate may involve thousands of intermediary premise to predicate proofs.
It's not fucking pretending when it's provable from the assumptions you make.
You fucking moron, we talked about this. Mathematics is a process of discovery for realists. Discovery is not instantaneous. There is zero reason to assert that we should intuitively know all of mathematics. Every single fucking field of epistemology proves you wrong here, including the empiricism you masturbate to while failing to understand it.
That doesn't fucking matter. The mathematical objects are real and metaphysical. For you to access it at all, cognition must also be metaphysical. This is fucking empiricism 101. If you deny that, you deny all of science.
You provably do
READ A CITATION YOU UNINFORMED, BRAINDEAD, MORONIC BRAINLET HOLY SHIT HOW ARE YOU THIS FUCKING STUPID
natural language is not well-formed. why do you think it is well formed?
if you need the metaphysical abstraction for science to make sense to you, then go ahead and take it. if you assert the metaphysical abstraction is necessary for science to make sense to anybody, then you are wrong because science makes sense to me. if you are saying i am delusional and not thinking clearly or not doing logic, what makes you think you are?
does the automated theorem prover that shuffles formal symbols around have insight?
ok lets try something else. apparently you think i am thinking wrong, or not thinking at all. model me in terms of someone accessing metaphysical objects, with the understanding that i am coming to the wrong conclusions, or non-conclusions that i think are meaningful.
I never fucking claimed this. I claimed the existence of mathematical structures as real and metaphysical objects combined with our ability to access them means that cognition is metaphysical. This implies that language is metaphysical.
Because there are verified proofs in first and second order logic that show I'm right.
I never claimed any of this. You made the claims about abstractions, which are provably metaphysical objects.
Gödel proved these results already under the assumptions of adding extrinsic axioms, but which you advocate. I don't have to prove them over again and cannot because Gödel was one of the greatest geniuses of all time and far beyond me.
i dont see how natural language can be well formed in a way that captures the meaning of "build a wall". unless you include all the biological and social and psychological and political context into natural language. which is totally fine with me. at that point it being well-formed doesnt mean much besides "well obviously it happened that way so it must be well-formed".
i want to read this thread but i also feel like shit and have a headache so that's gonna be a hard pass
READ THE FUCKING SHORT SUBSECTION OF THE ARTICLE I CITED AND LINKED
I HAVE NECW FUCKING CLAIMED IT IS BECAUSE NATURAL LANGUAGE CAN'T BE WELL-FORMED BY FUCKING DEFINITION
@hbotz stop typing your post and answer this question. What's your educational background with respect to science, math, philosophy of science, and philosophy of mathematics? Not just formal, but self-education as well. And what form did the self-education take?
ok thats good. then theres no disagreement, why are you yelling?
i read the subsection about the axiom of constructability you linked. it seems you wanted me to read all the way to the end. okay. i see godel thinks materialism is false and concepts have an objective existence.
It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions and in both cases it is impossible to interpret the propositions one wants to assert about these entities as propositions about the “data,” i.e., in the latter case the actually occurring sense perceptions.
okay. this is good motivation to suppose they exist, when youre doing mathematics. because it helps make mathematics make more sense. but wherein must you necessarily conclude thought is metaphysical? what im saying is that people dont "do math" for such a naive definition of "do math" humans are not mathematical objects, they are physical ones, and so are human brains, which are the thing doing the mathematics.
godel also wrote about how he thinks math facts have some inherent truth even if they are undecideable in the current axiomatic system and gives some ways to analyze them despite that. okay. sounds plausible to me.
No fucking shit that's the basis of mathematical objects being real: the objects have truth value even outside our set-theoretic universe, justifying extrinsic axioms. I explained this. It's the whole fucking point
The formal language proof doesn't suppose they exist: it proves they do
Because they have no spatiotemporal location. This isn't explained there because it's literally not contested and never has been, even by constructivists, because they believe if they are real, they must be metaphysical. This goes all the way back to Plato and no one has ever been able to critique the idea that actually existing mathematical objects must be metaphysical.
Yes they do.
No, fucking cognition is the process behind discovering mathematics. And it is provably not contained in the brain if mathematical objects are real
What's your educational background with respect to science, math, philosophy of science, and philosophy of mathematics? Not just formal, but self-education as well. And what form did the self-education take?
I did Khan academy pre algebra and algebra 1 and received a 100%
ok. lets try something else. suppose its not "contained in the brain". are there any experiments you can use to distinguish whether or not its "contained in the brain"? if not, why should i care?