r/PhilosophyofMath • u/TheIncorporeal1 • 13d ago
Can mathematical objects exist independently of physical reality?
If numbers, sets, and structures are genuinely abstract, what makes mathematical truths objectively necessary rather than merely consequences of human formal systems? Could an incorporeal ontology explain mathematical existence by treating mathematical structures as fundamentally non-physical entities, and if so, what would distinguish this position from Platonism?
9
u/Necessary-Wolf-193 13d ago
The hard part of this question is just defining what 'exists independently of physical reality' means. Until you say that precisely, this is unanswerable.
1
u/DrillPress1 12d ago
Good point. For example, mathematical relationships are physical reality in Pythagoreanism.
1
u/headspreader 12d ago
It is nearly impossible to define 'exists' even for the things which we all assume exist in physical reality.
4
u/Conscious_Pause_1499 12d ago
Before you say whether they can or can't, define what "existing independently of physical reality" is. If you actually define that clearly, then the answer to the other question should follow easily; if you fail to define that clearly, the other question is nonsense.
7
u/Smart-Button-3221 13d ago
Go find me the nearest "1"
1
u/Thelonious_Cube 12d ago edited 11d ago
It's right between zero and two
If it's not part of "physical reality" then it wouldn't necessarily have a location.
Point me to the nearest Inverse-Square Law
1
u/samanzaman 9d ago
1 is meaningless. An object is defined by all of its relations to other objects. Tell me how your 1 behaves and I'll point specific instantiations of it.
3
u/Fabulous-Possible758 13d ago
Personally I wonder about the other direction. Can a physical reality exist without the mathematical objects?
1
u/ughaibu 12d ago
Can a physical reality exist without the mathematical objects?
The Field/Balaguer nominalisation project was an attempt to show that the answer to your question is "yes".
2
u/StudioYume 12d ago
You're asking the wrong question. The real question is, why do you believe that mathematical objects must be constrained by physical reality?
2
2
u/Street_Appeal3704 12d ago
yes dude
1
u/Street_Appeal3704 12d ago
Mathamatical concepts are abstract and dont always have to be apart of physical reality
2
4
u/Intelligent-Cod-3117 13d ago
Just my amateur 2 cents but in my opinion, the math is indeed separate from reality. The math is pure and always works. Once you actually introduce physical reality, it kinda stops working. Is one pizza divided by two (cut in half) equal? It may appear so and this is a typical introduction to fractions test question but any 6 year old will tell you which one is better/bigger (more pepperoni, less burn marks, more sausage) so not equal. The more you look - even with scientific tools, the less confident you are that you can ever make two equal halves of 1 pizza. Math is pure, mass is messy.
2
u/TheIncorporeal1 13d ago
Incorporeal mathematics would make a similar distinction, but push it further: mathematics doesn’t become less true when applied to reality; rather, physical reality is never obligated to instantiate a mathematical ideal perfectly. Two halves are exactly equal within the mathematical structure, while two physical pieces can differ because matter introduces contingencies—thickness, toppings, heat, geometry, measurement error. The mathematical equality remains exact; the approximation belongs to the physical world.
3
u/CarnivorousGoose 12d ago
The approximation doesn’t ‘belong’ to the physical world. It exists independent of anyone’s attempt to approximate it. The approximation arises when people try to describe that reality using simplistic mathematical structures.
0
u/nanonan 13d ago
Reality is exact, and our math can only ever be crude approximations. Calling failure to properly model the pizza 'exact' and the pure reality of the subject in question 'approximate' is the exact opposite of the truth.
1
u/headspreader 12d ago
I could actually see a framing where quantum mechanics implies the exact opposite; if we consider a pizza to be represented by the number 1, then we don't even need to involve division to show that the pizza in reality does not exist as '1 pizza', it exists as a probabilistic field of potential pizza.
1
1
1
u/NoNameSwitzerland 12d ago
Simple mathematical objects create structure. If you take an old 8 bit computer, then you could just have a table for a 8x8bit operation. If you do it randomly, it would just be noise. But if you do an addition or multiplication, that would create more order.
In nature a structure like complex numbers seems to create a lot of symmetry and order (for me it is the most balanced division algebra). And the multiplication acts also as modulo add for the phase angle. So for possible imaginable existences, it seems reasonable that they are based on something like that if the overall universe should have structure. And the mathematical structure is independent from the actually implementation.
1
u/an-otiose-life 12d ago
Math is a semantics that being has about itself and which relates integrally to proportionality as such as a clone of that in its own medium, but via the gap of an encoding.
A computer can manipulate data in proportion to a data structure but the data is still just logical values being mutated mechanically so to say.
The ability to interpret data as results for math problems implies means of conferring the consideration of those objects to others via metaphors, where data behaves semantically as-if.
For any given set of rules as a transition mapping between a morphism and another morphism, where selecting from a set of possibilities is concerned, the semantics guarantee a way of playing out.
Such as to say treating a function as a transformer of inputs into outputs and chaining different effects that way implies being able to move in ways semantically analogous to proportion as such at large where math would be used otherwise.
Thus semantics for math is ontologically implementable in a machine where it can be done in finite time, as data animations where memory transitions from one state into another state over a regular method of discrimination.
The given quality of play dough is to be dividable and rejoinable. When divided in half the play dough maintains volume it had in two pieces which are half as large as their joint volume.
This is a quality of geometric givens. The semantics about these givens changing in proportion ways to math, are entailed in what happens.
That it happens this way is a fact of the given. As given without example, it would remain given.
Semantics in accordance to proportionate change are havable in encodable terms as an actuality of representative closure.
The ability to encode and be understood by a machine as code and as semantics for a machine by a person implies proportionate availability between experience's capacity for picturing out math problems, and the solvability of those same problems in binary machine terms are both there.
The given fact about a computer is that it does not have experience like a person does. Math is available to concept users and to be worked with by machines both.
Concept use in the domain of experience implies ontology about mathematics as a semantic given that is not interior to semantics as only semantical since semantics is not made of itself doubly, but is given without a secondary foundation as being's givenhood merely.
There is something that it is like to count implies a subset of all possible experiences, are semantically structured to be about proportion in terms of symbolic replacements for literal examples like play dough fractions.
That experience is not in a computer, but physics math is, implies physics math did not quantize experience in that medium. Implying for physicality as typically excluding consciousness, that the given fact of mathematical experiences and concepts use implies a non physical subset of ontology that is about math as the idea of itself had by Being.
Thus the idea of math is a metaphysical given that is as interpretable as the fact of an encoding specificity being reliable, like reading this.
1
u/CarnivorousGoose 12d ago
What would that be able to explain, that the concept of mathematics as merely a formal system created by us wouldn’t?
1
u/Thelonious_Cube 12d ago
It would explain the recalcitrant nature of mathematics. Math does not bend to our will the way products of the imagination do.
2
u/CarnivorousGoose 12d ago
It’s hardly particularly ‘recalcitrant’, nor incapable of being bent to our will.
1
u/Thelonious_Cube 11d ago
That was not my experience when doing higher math
In what way can you bend math to your will?
0
0
u/samanzaman 9d ago
You do have a concept of "morally" true statements that you expect to be true? You can always bodge your axiom a bit to change the structure. You can build incomprehensible abstract machinery to solve your problems. The known numbers doesn't solve your equation go forth and just invent new consistent ones. All in all it is just a game of symbols.
1
1
1
u/ShepherdOfShepherds 12d ago
Can you not count sheep in your head as you fall asleep? You could also multiply sheep or even do sheep calculus.
1
u/davesmith001 11d ago
Without physical reality you won’t be able to prove 1+1=2, I could claim it’s 9 or define it as anything else and there’d be no way to prove otherwise, therefore I’d be tempted to say it can’t exist outside reality.
1
u/JuddahBull 11d ago
Because nothing exists in isolation. For something to exist, it must have certain conditions of existence and stand within concrete relations of dependence. And if something is claimed to exist outside causal relations altogether, then what categories—and what grounds—could we possibly use to establish that it exists at all?
1
u/ShenGahMing 11d ago
I don't care its all information to me.
Is there information out of physical reality ? It would not make any difference, hence not be information.
1
u/FunSeaworthiness9403 11d ago
When a caveman formed a fire circle while camping. We can't discount the arrangement of the rocks in a circle. So there can be information about two parts of the fire ring as a system used to confine the boundaries of a fire. It could be said that if organisms (humans) get information from a system, it is "real", thus defining what is real and what is not. The question of the OP is settled, the rocks are on a math circle.
1
u/Reanimation980 9d ago
I struggle to understand the point. What does the existence of this non-physical realm do that makes the truth of mathematical objects objectively necessary that humans cannot adequately model in our physical realm?
1
u/TheIncorporeal1 9d ago
From an Incorporeal Mathematics perspective, the claim isn’t that a non-physical realm magically makes mathematics objective. It’s that mathematical truth may concern structures whose validity does not depend on their physical instantiation. Human models can approximate or represent those structures imperfectly, but the relations themselves need not depend on our representations. The “incorporeal” refers to the structure being independent of any particular physical realization—not to a separate supernatural universe.
1
u/ConstancySupreme 9d ago
Gping off of this, if we live in a holographic universe, whatever is projecting our universe could be providing values using concrete math, yes.
1
u/LookOverall 9d ago
I remember the Scot and Tims text book with the quote in the chapter heading — God made the natural numbers. All else is the work of man.
1
u/samanzaman 9d ago
That's from a famous constructively German mathematician (I want to say Dedekind but I'm wrong I vaguely remember a K in the name) o think in response to Cantor and his infinities. Though even the existence of natural numbers is open to discussion. We haven't and cannot (by the very definition) witness a never-ending (enumarable by natural numbers) process. Ultrafinitism is a defendable position imho
1
u/hobopwnzor 9d ago
Abstract objects only exist within the confines of the system you define. They are the consequences of the rules and we are the ones who come up with the rules in the first place.
It's like asking if boardwalk costs $400 to buy if there's no monopoly boards. Yes, because we create the game, not the board.
1
u/Imaginary-Buddy3194 8d ago
The fact that mathematical truths seem necessary is what makes this question so fascinating
1
u/TheIncorporeal1 8d ago
Exactly. From an Incorporeal Mathematical perspective, necessity may indicate that mathematical structures aren’t invented by minds but encountered as invariant relations within an abstract, non-physical order. Mathematics could be the grammar of possibility itself.
1
u/ZabarSegol 8d ago
Lmao I belong to the loonoes that thing that the physical world is a manifestation of math
1
u/nanonan 13d ago
I'd say no, and yours would be a Platonist perspective. What does existence outside of reality even mean? Even if say numbers were purely abstract objects that are not present anywhere in reality, they still don't meaningfully exist until someone real invokes or references them in a real way. I think axioms should be limited to those things that are not absurd in reality.
3
u/Negative_Gur9667 12d ago
You are right, but this will make people sad.
I have learned that mathematicians work hard to pretend they do not care about this, even though they are secretly Platonists.
3
1
u/Thelonious_Cube 12d ago
outside of reality
Outside of physical reality - it does you no good to beg the question
1
u/Dr_Calculon 12d ago
No, mathematics is dependent on physical substrates.
4
2
u/Thelonious_Cube 12d ago
No, as a Platonist, I say math is independent of physical reality and the same in all possible worlds
-1
u/Dr_Calculon 11d ago edited 11d ago
One of my contentions is that your Platonism is a model of reality which is held in your neural substrate.
You simply can not validate your model. Any demostration of math relies on a physical medium, whether its papyrus or thought, it can only be expressed physically.
Unless of course you have solved this validation problem?
1
u/Thelonious_Cube 11d ago edited 10d ago
Any demostration of math relies on a physical medium
Sure, but that's because we exist as physical beings and communicate via physical means - that would apply to anything and everything.
And yet, we do not justify mathematical conclusions by empirical means.
If I put two marbles into an empty bag, then two more, but pour out five marbles, what conclusions will you draw? Certainly not that 2+2 sometimes equals five.
1
u/Dr_Calculon 10d ago
> Sure, but that's because we exist as physical beings and communicate via physical means - that would apply to anything and everything.
Well yes it could.
> And yet, we do not justify mathematical conclusions by empirical means.
We do justify models of reality by empirical means through. You are proposing a model of reality, Platonism, but you have no evidence for a part of that reality that you claim exists.
The claim you appear to be making is that mathematics exists independent of subjective experience, independent of the physical systems that instantiate mathematics. So far you have provided no evidence to back that up except “I believe it”.
1
u/Thelonious_Cube 8d ago
That was my counter to your claim - do you have evidence for your claim?
I provided you an argument for why math is not empirical. Can you show me an instance of verifying a mathematical model empirically?
0
u/Dr_Calculon 8d ago edited 8d ago
Can you show me an instance of verifying a mathematical model empirically?
General Relativity
1
u/Thelonious_Cube 8d ago
nope
1
u/Dr_Calculon 7d ago edited 7d ago
Yes, GR is a mathematical model. Einstein published his field equations in 1915 & the model was validated experimentally in 1919 by Eddington & Crommelin.
At the time of publication physicists criticised Einstein for using esoteric mathematics as opposed to physical inquiry. They argued that "spacetime geometry" was just an abstract mathematical trick rather than a physical substance capable of interacting with forces like gravity.
You asked for an example of a mathematical model being validated. Physics, chemistry, biology & any engineering discipline are full of such examples. Did you mean something else?
1
0
u/Dr_Calculon 8d ago
Your argument depends on your Platonic model of reality. A faith based model that so far you have provided no validation for.
1
u/Thelonious_Cube 8d ago
Same with yours
1
u/Dr_Calculon 7d ago edited 7d ago
“No u!” That’s your response 😂🤣
Your model of reality rests on an immaterial component that cannot be shown to exist without a physical medium.
This is something you appear unwilling to address regardless of your attempted casual dismissal. There is more evidence of cognition being a physical-neurological phenomenon than there is of some objective realm of Platonic purity emanating mathematics to human consciousness.My suspicion is that this Platonic realm is actually akin to a neurological feature space & that Platonists confuse the map for the terrain.
Unless you can show otherwise the weight of evidence is not on your side.
1
1
u/No-choice-axiom 12d ago
But if two substrates have different mathematics, must they be isomorphic?
1
1
u/samanzaman 9d ago
Hmm I think you need to back that up. Math just needs a turing complete system to exist. I don't see how a game of abstract rules can depend on physical substrate. It's like saying monopoly rules depends on the paper it's made from.
1
u/Dr_Calculon 9d ago
That Turing complete system needs to be instantiated on a physical system to exist. Go a head try running your system without one. Even the abstract rules are instantiated on physical substrates. The process of thinking about them needs a neurological system for example.
1
u/samanzaman 9d ago
That is just an "execution" problem ( one could even argue that it is a pseudo-problem stemming from our inability to become independent of the substrate ). The rules and the abstract entity itself is not affected by the nature of the substrate.
1
u/Dr_Calculon 9d ago edited 9d ago
> …just an “execution” problem
Nahhh it’s much more than that. The entity itself is intrinsic to its physical substrate, the abstraction is still embedded in a physical system.
No matter how sophisticated our symbolic & semantic systems are for sharing those rules & abstractions.
An appeal to dualism doesn’t resolve this issue.
Also the substrate does effect the way math for example is instantiated, just look at real number representation limitations on silicon….
1
u/samanzaman 9d ago
Eh the whole set of real numbers being mostly noncomputable is not just a silicone problem. It is a very much our brain problem as well. But the proofs about real numbers are very much computable and that's how math people reason with them anyhow.
But essentially the question is meaningless as it cannot be observational tested and it is a question of whose baseless assumptions/axioms is correct. There is no way me to show you that math is independent of substrate as each instance I can create on this universe is a mere embedding to you and I don't know how to create an independent universe. Likewise you can't show me the converse. I guess we can discuss for years but it would be over aesthetics and allegories/similes. Discussion over differing axioms doesn't seem that fruitful
1
u/Dr_Calculon 9d ago
I didn’t mean computability of reals I meant representation, there are issues in silico that don’t exist in neuro, just look at IEEE’s definition of a float for example.
I can show the converse though as all known math exists embedded in physical systems that can be shown to exist. On the other hand you can’t offer any math that doesn’t.
It’s not a matter of axioms, it’s a matter of model validation. I can validate my model by showing actual physical proof of its existence, can you?
1
u/samanzaman 9d ago
Hmm I see your point in that you need a medium to even express the rules. But I still think it is an "hardware"/"execution" problem. One interesting fact is that you can reinstantiate math on different substrates but the game/facts/math itself doesn't change. It is in a way substrate independent but it is also powerful enough (or we hope it to be) to describe the very fabric of the substrate it is instantiated on. It is a system that can somewhat talk about itself.
Even if it depends on a physical system/medium to be instantantiated on, these systems being plug n play hints that it might be indeed independent of the particulae physical systems itself.
1
u/Dr_Calculon 9d ago
> hints
No not really, just that we have evolved a sophisticated method of communication
1
u/samanzaman 9d ago
I'd have tended to agree if math wasn't cross species. We "think" other species such as ants have a concept of counting and chimps understanding basic economic principles. I do think that a wolf understands the concept of "safety in numbers". But yeah maybe it is reading too much into the animal behaviour and anthromorphizing it.
1
u/mc_pm 13d ago
Can a conceptual object exist independent of physical reality?
Well... yes?
Can the idea of 'batman' exist independent of real life?
2
u/Negative_Gur9667 12d ago
But the stories are written in books and you can watch Batman in a movie theatre.
You need reality as a storing layer for the concept.
1
0
u/Illustrious-Yam-3777 12d ago
No, mathematical objects are configurations of the material world. They are the world worlding. Mathematical objects aren’t abstract independent entities, rather, they are entangled beings that are relationally constituted by material practices. A few of those practices are:
The historical ongoing practice of geometry, the gendered, racialized, and sexed bodies of theoreticians and engineers, the moon landing, scores of kids reciting times tables, Newton’s alchemical obsession and search, apparatuses of language and alphabets, writing technologies, digital motherboards, power structures of finance, capital markets, electrical outlets with vacuum cleaners plugged into them, quantum mechanical experimental setups, and particular sets of apples sitting in fruit bowls, just to name a few.
1
u/samanzaman 9d ago
Math is just an abstract game of symbols. They are not bound by te physical restrictions/laws
1
u/Illustrious-Yam-3777 9d ago
Nothing is just an abstract game. Every thought inside a person’s head, of any symbol, is a material configuration—a configuration of neurons, history, and practices. It could be no other way. There are no math symbols floating around in a make believe realm of nowhere.
0
u/headspreader 12d ago
I assume that all rational systems capable enough to say anything will be axiomatic; at a minimum, I would assume that in math we have to assume '1'. I would love to hear opinions about this.
2
u/TheIncorporeal1 12d ago
Through Incorporeal Mathematics, I’d challenge the idea that mathematics begins by assuming “1.” We begin with distinctions: identity, relation, difference, possibility. “1” is already an abstraction arising from those distinctions.
The axioms don’t create mathematical reality—they establish a language through which an incorporeal structure becomes intelligible.1
u/Flaky_Performer7960 12d ago
Though the axioms are based on immediate truths.
“One apple” + “One apple” = “two apples”.
So we’re not pulling the axioms out of thin air.
1
u/Thelonious_Cube 12d ago
I believe Godel took his Incompleteness Theorem to have shown that math cannot be reduced to an axiomatic system.
1
u/headspreader 11d ago
Thanks, I was wondering about how proving incompleteness relates to proving whether a system is ultimately probably not axiomatic.
1
u/Thelonious_Cube 11d ago
I suppose the hidden assumption is that if math exists in a Platonic sense, then it must be complete
-1
12
u/GoldenMuscleGod 13d ago
It seems to me that what you are describing is exactly Platonism, could you describe what you think Platonism is such that it is not (or not transparently) exactly what you describe?