/lit/ - Literature

>>14262840
also like liebniz's monadology

>>14262840
literally any book about imaginary numbers

>>14262848
huh?

>>14262910
wiikkipediai dot orog dumbrainlet

>>14262840

>>14262840
>The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation.

>>14262971
8 categories of existence, 27 categories of explanation, and nine cateogrical obligations. Autism confirmed.

This is pretty much what the latter half of 20th century analytic metaphysics is, e.g. Armstrong, Dummett, Lewis, Quine.

>>14262848
Most upper-level Mathematics books, as a matter of fact.

Critque of pure reason. Essentaily Kant the autist was being moderately autistic, then Hume, the chad, came along and made him super autistic.

>>14262848
>>14262925
>>14263184
not sure what any of you idiots are saying, pure mathematics has no relation or correspondence to the physical/material world we live in. sure, you can use mathematics to describe the world, but most books on mathematics are not at all concerned with doing so.

>>14263040
Davidson destroyed all of them

Wittgenstein, Tractatus

>>14263743
And yet math is used all the time in physics while metaphysics is laughed at by working physicists. Metaphysics is all the fantasy of math with none of the rigor or even just empirical evidence.

>>14262848
Lmao this

Any recommendations for further reading on the topic?

>>14264432
There is no empirical evidence for math either yet it is indispensable to physics, brainlet. Quine, who was a hardcore physicalist, had to posit the existence sets and abstract objects to resolve this issue. Sure, you can deny their existence, but that would also require some kind of a metaphysical explication. Ever wondered why/how math even applies to objects at all? There are a lot of these meta-questions that physics can't answer. Try reading some metaphysics, faggot. Also, most physicists nowadays are brainlets. Chad physicists like Bohr, Schrödinger, Poincaré, Heisenberg, etc. all engaged with metaphysics.

>>14264735
This.
Math and Logic are dependent on metaphysics.

>>14264735
>no empirical evidence for math
Math is not justified using empirical evidence but there is a ton of empirical evidence for it. Saying metaphysics is closer to reality that math is retard shit.

>>14264799
It is a matter of point of view you retard. Metaphysics comprises Reality in all its degrees.

>>14264812
Metaphysics is make believe for philosophy majors. OP wanted a system worked out from logical principles which is exactly math in all its different fields.

>>14264799
I demand that you show me empirical evidence for the Banach-Tarski theorem! Mathematics is a priori, moron.

>>14264788
>Math and Logic are dependent on metaphysics.
In what aspect is that true?

>>14264980
You are missing his point.
Mathematics is empirically validated in the sense that there never has been a mathematical theorem with a correct proof that had a counterexample.

>>14263743
>pure mathematics has no relation or correspondence to the physical/material world we live in
That seems intuitively false. Mathematics is incredibly concerned with basic principles of how the universe works.
Look at ZFC, all the Axioms make intuitive sense (even though they cause counter intuitive results) and mathematicians very often rely on geometric intuition, how shapes behave in our world, when thinking about certain things.

>>14264985
They follow principles

>>14265020
Everything follows principles.

>>14265042
Exactly.

>>14264980
Math is proven using deductive reasoning but there is plenty of inductive evidence for its truth. Am I really arguing with someone who doesn't think that if you have a stone in each hand then you have 2 stones?

>>14265064
But then metaphysics is just "everything" at which points it becomes nothing.

everyone in this thread is talking at cross purposes

the mathematicians ITT are ultimately wrong but if they understood the ground they're standing on, they would realize that they don't want to be standing on that ground anyway, and that they have only done so inadvertently. the mathfags are taking the anti-mathfags as denying any reality or real reference in the natural world to ideal mathematical entities, and the anti-mathfags are taking the mathfags as the most naive possible mathematical platonists with a logical positivist outlook. again, i highly doubt either party subscribes to the outlook they are being seen as holding, respectively.

it's a shame neither of them will clarify their respective positions and have an interesting discussion about the metaphysical implications of math

>>14265155
>the anti-mathfags as denying any reality or real >reference in the natural world to ideal >mathematical entities

>pure mathematics has no relation or >correspondence to the physical/material world >we live in

>There is no empirical evidence for math either

That is exactly what the anit-mathfags said

>>14265148
Everything depends on it, its principles; even nothingness.

>>14264997
>>14265115
Pure mathematics makes no claims regarding empirical objects, it is only concerned with mathematical objects. We can apply mathematical concepts to objects in our experience, but these concepts cannot be found in experience. You can never find the concept of 2 in experience, you can only find instantiations of it. The instantiation of the concept is not the same as the concept. This can be said about any mathematical concept.

Inductive evidence can never be used to show the truth of a mathematical statement. Mathematical statements are universal and necessary, while inductive statements are particular/general and contingent.

>>14265011
That's not the concern of pure mathematics, that's the concern of the natural sciences.

>>14265704
>Inductive evidence can never be used to show the truth of a mathematical statement. Mathematical statements are universal and necessary, while inductive statements are particular/general and contingent.

Again let me repeat what I've said twice at this point, math is deductively or logically proven from axioms or postulates. But that does not mean that empirical evidence for math does not exist 1+1=2 is something people get daily evidence for.

>Pure mathematics makes no claims regarding empirical objects, it is only concerned with mathematical objects. We can apply mathematical concepts to objects in our experience, but these concepts cannot be found in experience. You can never find the concept of 2 in experience, you can only find instantiations of it. The instantiation of the concept is not the same as the concept. This can be said about any mathematical concept.

Do you believe there can be inductive evidence for anything? Seeing a white swan is inductive evidence for all swans being white but from your argument swans is a category that can never be found in experience only instantiated in a particular swan.

>>14265780
>But that does not mean that empirical evidence for math does not exist 1+1=2 is something people get daily evidence for.

That's not evidence for math, it is just an application of mathematical concepts.

>Seeing a white swan is inductive evidence for all swans being white but from your argument swans is a category that can never be found in experience only instantiated in a particular swan.

Not sure what you're trying to say here to be honest. The concept of a swan is distinct from this or that swan. Concepts are usually thought to be mental or abstract.

>>14265957
>Not sure what you're trying to say here to be honest. The concept of a swan is distinct from this or that swan. Concepts are usually thought to be mental or abstract.

The universal of swaness is an abstract just like the concept of number. If we can gather inductive evidence about the category swan we can gather inductive evidence about the concept of number. In particular in grade school teachers frequently give children collections of objects to split up and count then gather together and count. This empirical example gives inductive evidence to the validity of addition since no kid is going to be able to follow the logical argument from the Peano axioms or whatever is in the Principia. It is not logical proof but it is inductive evidence. Mathematicians require deductive reasoning but that does not mean there can not be empirical evidence in addition to the logical proof.

Or even better say that someday somebody counts up papers and finds that the two piles they have don't combine to the sum or 1+1=3. That would be inductive evidence against math. Would mathematicians care? no since math is deductively proven but the point is there can definitely be inductive evidence for or against math it just happens that all of the evidence happens to be for it see https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

I can't help but read some of this insistence that math is totally disconnected from reality as an attempt to steal some of its prestige for whatever made up metaphysics people are hawking. For after all if math has no way of being inductively verified it's just the same as my metaphysical fantasy. But math can and is inductively verified in addition to be derived with a logical rigor that metaphysicians can only gape at

irrefutable

>>14266208
it's actually a way of protecting math

it's amazing to me how few mathematicians know the history of their own discipline. the "crisis of mathematical foundations" ca. the late 19th-early 20th century almost drove the best minds of several generations mad. when the dust settled, the set theorists won over the intuitionists and others, but only just barely, and effectively out of mutual fatigue.

math can of course be related to reality but the question is in how it's done and who does it. the logical and formalist mathematicians want to keep mathematics isolated from reality because it protects them from metaphysics, meaning also philosophies of mind, it allows their deductive certainty and structural cohesion to be maintained without asking questions e.g. whence the fundamental axioms or axiomatic "intuitions" in math come from. the alternative is a return to j.s. mill trying to put math on an empirical basis, decades of intuitionists trying to put it on a neo-kantian or phenomenological intuitionist basis, neo-kantian logicists trying to put it on a non-phenomenal kantian basis, etc., etc., etc. insulating mathematics from such questions is largely why theoretical mathematics has been so successful in the past century. it became a walled garden.

if you want to open it back up to such questions, great, i agree with you, let's have a new crisis of mathematical foundations, or rather let's continue the old one since it was never resolved. but my reasons for doing this are because i actually want to radically tear down a century of shitty mathematical dogmas and set theory occultism, and begin from scratch. i doubt that's why you want to do it.

>>14266461
>isolated from reality because it protects them from metaphysics

This is a joke right? Metaphysics is an academic ghetto the only thing that needs to be protected from it is people who practice it.

> whence the fundamental axioms or axiomatic "intuitions" in math come from

Fundamental misunderstanding math is what is done after the axioms are chosen, if you choose different axioms it doesn't invalidate the math founded on the other axioms.

>math can of course be related to reality
This is bizarre every time someone buys something in a store you have a empirical confirmation of math.

>set theory occultism
Spoken like a brainlet, set theory is just as deductively founded as any other branch if you can show an inconsistency based on the ZFC axioms you'll be famous otherwise the occultism is in these ridiculous fantasy metaphysics made up for aesthetic or religious reasons. See all the Guenon shit on this board that dude hated calculus

>>14266036
>If we can gather inductive evidence about the category swan we can gather inductive evidence about the concept of number.

You can gather inductive evidence about swans being white, two-legged, or whatever, but you can't gather inductive evidence about the properties of prime numbers or how they're distributed.

>In particular in grade school teachers frequently give children collections of objects to split up and count then gather together and count. This empirical example gives inductive evidence to the validity of addition since no kid is going to be able to follow the logical argument from the Peano axioms or whatever is in the Principia. It is not logical proof but it is inductive evidence.

No, that's just analogy. There are no empirical examples of infinite sets. The best you can do is use analogy to explain it. That does not mean that infinite sets are contained in these analogies or that the analogies are inductive evidence for the existence of infinite sets.

>>14266146
That paper says nothing about the inductive evidence for or against mathematical objects. He's only talking about the application of mathematics to physics, I think. This is only inductive evidence that mathematics works in our universe. Nothing else. Inductive evidence for mathematical objects would be like encountering a set of natural numbers on your way home, which is absurd. Counting or whatever is just an application of mathematical concepts, not inductive evidence for or against mathematics.

>>14266208
>I can't help but read some of this insistence that math is totally disconnected from reality as an attempt to steal some of its prestige for whatever made up metaphysics people are hawking.

Mathematics is independent of our minds and spatiotemporal world. It might seem like a controversial position today, but this position has been argued for by mathematicians and logicians like Frege, Gödel, G.H. Hardy, etc. Even Russell showed some inclination towards platonism with respect to mathematical objects. It is nothing new. Maybe read Frege.

>For after all if math has no way of being inductively verified it's just the same as my metaphysical fantasy.

So would you discard mathematical results that have no way of being inductively verified (whatever that means)?

>But math can and is inductively verified in addition to be derived with a logical rigor that metaphysicians can only gape at

Again, metaphysics deals with questions that mathematics and physics do not even ask and cannot answer.

The World as Will and Representation

>>14266657
>
Mathematics is independent of our minds and spatiotemporal world. It might seem like a controversial position today, but this position has been argued for by mathematicians and logicians like Frege, Gödel, G.H. Hardy, etc. Even Russell showed some inclination towards platonism with respect to mathematical objects. It is nothing new. Maybe read Frege.

>So would you discard mathematical results that have no way of being inductively verified (whatever that means)?

I've said this multiple times at this point so you're obviously too stupid to understand but math being deductively founded does not mean there is inductive evidence to support it. You don't need the inductive evidence and inductive evidence by itself is not mathematical proof but that does not mean there can be no inductive evidence for math.

>
You can gather inductive evidence about swans being white, two-legged, or whatever, but you can't gather inductive evidence about the properties of prime numbers or how they're distributed.

>
You can gather inductive evidence about swans being white, two-legged, or whatever, but you can't gather inductive evidence about the properties of prime numbers or how they're distributed.

Swaness is the same type of thing as primeness. If you can have inductive evidence about swans you can have inductive evidence about primes.


>No, that's just analogy. There are no empirical examples of infinite sets.

There are no empirical examples of the ideal swan. There are particular instantiations that we can reason analogically from to the category of swans.

>>14266657
>This is only inductive evidence that mathematics works in our universe

This is gibberish of course it's only evidence of math working in our universe all inductive evidence only applies to our universe. When you have inductive evidence of something it means the facts of this universe agree with the predictions of a theory. Wtf do you think inductive evidence means?

So let me get this straight, there is an indubitable metaphysical presence within mathematics which act more so as principles than actual quantity.

I know almost nothing beyond the practical mathematical functions which I failed in high school but have recently developed an interest in mathematics specifically in its relation to philosophy and aesthetics. Qrd? Any books?