/lit/ - Literature

[Anonymous No.16304065]

how does one reconcile mathematics and metaphysics?

[Anonymous No.16304069]

>>16304065
Plato and Jung, but then in reality Husserl and Heidegger.

[Anonymous No.16304071]

what is there to reconcile?

[Anonymous No.16304080]

>>16304069
>in reality
elaborate?

>>16304071
they're two opposite things. the former is discrete while the latter is monistic.

[Anonymous No.16304401]

>>16304080

what do you mean by maths being discrete?

t. mathematician

[Anonymous No.16304420]

All mathematical structures exist, our universe just being one.

[Anonymous No.16304429]

It was done decades ago. Get ready to see a lot of coping brainlets try to debunk this.

[Anonymous No.16304436]

[Anonymous No.16304439]

>>16304401
Not him but it's particular to quantification solutions but doesn't, as it is rn, refer back to more universal objects like logic or ontology yet

[Anonymous No.16304444]

>>16304401
this >>16304420

>>16304429
Sure anon, physics taking quantification and it's most developed field as an axiom is also its (math's) axiom. That makes perfect sense

[Anonymous No.16304451]

>>16304444
>he wasted his trips by replying before I could post all 6 pages
Pathetic.

[Anonymous No.16304454]

>>16304451
>cucked
That doesn't reconcile metaphysics w math just because it uses the term pan psychic energy field slit experiment logical fallacy consciousness. None of those are defined or pragmatically prior to math

[Anonymous No.16304455]

>>16304065
I dunno man how do you reconcile pizza and me eating it?

[Anonymous No.16304460]

>>16304455
by making pizza available so you, the derivative aspect, can eat it.

[Anonymous No.16304471]

>>16304065
>>16304080
this discussion makes no sense.
mathematics is intrinsically metaphysics but wierdly enough this missunderstanding is commonplace even in /sci/ too

if mathematics is the soul (the logos) physics is the physical body of the same coin (the coin being reality the universe)

for the people that don't understand read this text, it explains why math is methaphysics or a form of poetry... it has always been!!! :
https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

[Anonymous No.16304474]

>>16304460
now what have we learned?

[Anonymous No.16304485]

>>16304474
that you're a moron that doesn't know where his pizza comes from

>>16304471
Math doesn't account for ontology or epistemology. How can it then be metaphysics

[Anonymous No.16304501]

>>16304080
What on earth are you talking about? Mathematics is just the metaphysics of quantity.

[Anonymous No.16304515]

>>16304439

Ah well, it won't ever refer to ontology. It's a formal discipline, it doesn't claim anything about reality. Sure, there are applied fields, but that's mostly analysis, not things like say algebraic geometry or quantum groups. It occasionally takes ideas from "reality" and defines things like representation theory, but these are also very intrinsic from the pov of modules. To return to my point about referal to ontology, currently maths all formulated in terms of categories, which is again more of an operational framework than "logic". One could and has argued about logic being a topos, but I'm not really referring to that, again.

t. same guy

[Anonymous No.16304526]

>>16304485
>Math doesn't account for ontology or epistemology. How can it then be metaphysics
Epistemology is not a part of metaphysics. The ontology of mathematics includes various algebraic structures. Mathematics is the metaphysics of succession (arithmetic) and part-whole relations (geometry, topology, analysis) and their abstract generalizations.

[Anonymous No.16304529]

>>16304515
yeah fair enough. Ig the goal is to link it back so you can say this is where we've gone in math, we can change these axioms or allow these new operations etc to get something new foundationally or that's the goal.

[Anonymous No.16304543]

>>16304526
read >>16304515
math takes numbers, and how we have them linearly, as axioms and metaphysics encompasses a framework for reality entirely much like physics claims to be a framework for material reality. It needs to account for us just derivatively. Plus math takes axioms of truth or I could say any math equation and it would be true if math was foundational to everything

[Anonymous No.16304545]

>>16304515
Generally all formal mathematical systems have an ontology. Only purely logical systems lack ontological commitments.

[Anonymous No.16304549]

https://ncatlab.org/nlab/show/Science+of+Logic

[Anonymous No.16304554]

>>16304543
Not following anything you're saying. Math differs from logic specifically by having an ontology.

[Anonymous No.16304559]

>>16304545
Where tf are you getting these ideas. Ontology or the study of being defines numbers and relationships are defined in logic. You can't not take an axiom from ontology unless the object referred to is truth or Being (existence)

[Anonymous No.16304564]

>>16304429
What the fuck are you talking about? What does high school physics have to do with the metaphysics of mathematics?

[Anonymous No.16304568]

>>16304554
What do you think ontology means. How can math define numbers itself? It doesn't even define the law of identity it takes (=) it doesn't define associativity or commutativity. How it can it define it then too and godel showed you can't define math w math

[Anonymous No.16304579]

>>16304559
You sound like someone who has never studied either mathematics or philosophy. The line between mathematics and logic is drawn based on the fact that mathematical axiomatic systems entail existentially quantified statements (i.e., have ontological commitments) whereas logic applies even to an empty universe.

[Anonymous No.16304590]

>>16304568
You have no idea what you're talking about. The ontology of a theory is the set of things that must exist in order for the theory to be true. ZFC, for example, requires that a hierarchy of sets exist. The axioms of FOL, on the other hand, do not assert the existence of anything.

[Anonymous No.16304592]

>>16304579
Asserting logic applies to an empty universe is modal logic. It's not all logic languages.
That's not what existential operators are in mathematical logic. ∃x∀y mean there exists (at least one) x and for all y.

[Anonymous No.16304595]

>>16304590
You're divorcing sets from math logic? That's pretty ballsy

[Anonymous No.16304599]

>>16304592
Are you drunk? Your posts make no sense at all. FOL is completely free of ontological commitments.

[Anonymous No.16304601]

>>16304579
Also axioms are inherently logical terms.

[Anonymous No.16304604]

>>16304080
>>in reality
>elaborate?
Plato and Pythagoras and Jung look at numbers in a mythico-symbolic religious sense, while Heidegger and Husserl look at it in a much more realistic place in reality. As different parts of reality. But that is not to say the mythifying of numbers is gone.

[Anonymous No.16304605]

>>16304599
What about the relationship between objects? Are logical relationships not an ontological commitment? Does it make them formalist?

[Anonymous No.16304607]

>>16304595
It's the standard dividing line: mathematical axioms make existential assertions, logical axioms don't. Logic holds true regardless of what exists, or whether anything exists. Set theory, in contrast, cannot be true unless sets exist.

[Anonymous No.16304626]

>>16304607
what mathematical axiom asserts numbers? They're always taken as an axiom in the structure of a logic language. They aren't proved in it. Even the Cantor Peano etc sets assert that "one follows the other", the unary operator S, but doesn't define numbers or what following means and why saying that must make them linearly arranged. If they try to build up a set it's based on intuition of numbers and structure of them. It doesn't define numbers, it just tries to make it valid in math.

[Anonymous No.16304644]

>>16304420
relativity isn't proven and it never will be

[Anonymous No.16304894]

>>16304529

I see a lot of other comments I have no idea how to reply to.

I just wanna say that nobody really "changes axioms and looks at how things change" anymore, at least not with respect to fundamental maths. The only "foundational" axiom one regularly invokes is the axiom of choice, because one wants split epi morphism, i.e. sections.

Again, I can talk about some advanced stuff, say, toric Deligne-Mumford stacks, without ever bothering about the foundations, the same way as I can do algebra on a piece of paper. It's a formal procedure.

t. same guy

[Anonymous No.16305104]

>>16304894
Yeah it's coherent enough but I'm a foundationalist and I have a different conception of how numbers should be structured etc. It's not an attack on the field at all just meant to attach it correctly in logic etc. There are a ton of logic languages and no ability to contradict any without tying it to ontology. I think the 1+1=3 thing can be done on hegelian logical terms. It's just fun

[Anonymous No.16305180]

>>16304626
Peano axioms are the most common, but you can construct the natural using set theory. Basic mathematical objects are often defined by the way they interact with other objects. We are not that interested in what numbers actually "are", and instead focus on how they relate to each other. This has been true for millenia. Take Euclid's Elements, lines are defined in how they interact with other objects. If you replaced the words "line" and "circle" with "table" and "chair" and kept everything else the same, all the logical deductions would still be valid.

The short answer is, a number is anything that acts like a number.

[Anonymous No.16305189]

>>16305180
Holy shit cope the post. Then don't claim its ontological claims are covered in math. In fact gtfo this thread

[Anonymous No.16305195]

>>16305189
I'm not the same guy you initially replied to. You asked how mathematicians defined numbers, and I answered.

[Anonymous No.16305205]

>>16305195
No I didn't but appreciate the response. I was saying math isn't a metaphysics.

[Anonymous No.16305259]

>>16304065
you just have to get them in a room together to talk it out

[Anonymous No.16305599]

[Anonymous No.16305606]

>>16305599

[Anonymous No.16305625]

>>16305104

I'm just telling you how the field works. To me, maths is more than a system, it's also the people, their relations, how they do correspondences and advance in careers. A real question about mathematics would be, for me, something like: why did it take 70+ years to find a counterexample to Hilbert's 21st problem, and why was it exactly by Bolibruch.

But the questions about logic don't fit in the more abstract as well, at least to me, since you can do everything on topoi by replacing topology by Grothendieck sites, so you get funny logic systems too, higher-order. No idea how those things fit in the usual type theory approach.

How do you logicians view those kinds of foundations? Especially HoTT?

t. same dude (wish /lit/ did IDs)

[Anonymous No.16306368]

>>16304065

[Anonymous No.16307051]

>>16305625
In logic or in math? Also I appreciate the responses, I don't think I'm sounding antagonistic with you.
In math if you accept axioms you're taking from another subject. I'm not into type theory because I think starting from the particular to get a universal, or at least setsn, is about as backwards as you can get. That being said Russell opened up math a lot to more interpretations so I appreciate that.

In logic it's clear it takes axioms simply in the bald king of France example. I could be referring to a video game or real life. We can't know until it's defined in ontology and type theory simply can't handle Being so it shouldn't try. Until then it's valid. I think logic needs its foundations formalized.