I noticed that in nature (i.e. in the physical universe) there appears to be no logic. There are not even two things exactly the same, as far as I can tell. So that lead me to believe that "counting" (or abstraction) is not even a property of the universe, but possibly only a human (or animal, or Turing machine) construct. To me, logic only starts to occur when a very complex amalgam of matter comes together [1] to realize a discrete switch. Using these discrete switches, organisms build memory and abstraction mechanisms, start counting, and do mathematics.
So my thesis is that things that are considered to be "basic" by most, such as logic or mathematics, are in fact quite specific systems built on top of chaos. From there, it remains to be proven that all physical laws that we observe are no more than projections of the chaos onto such a system.
Perhaps a metaphor that helps to take on my perspective, is to look at a screen filled with random noise, and then observe some patterns in there. Now replace the screen with an infinite dimensional set of chaos, and then observe a pattern that is our universe. With the added twist that we are part of this chaos, and observing the pattern, possibly in the form of physical laws.
Of course, there are many problems with this theory. What does the chaos reside in? How can there be discernible parts in the chaos? Is time an emergent property inside the chaos? How can it be that the patterns that we observe are so consistent?
However, to me this theory seems more fruitful than merely accepting that we cannot say anything about things that science cannot observe, or that some deity created all this.
[1] With "comes together" I do not refer to a dynamic process, but to the accidental occurrence of stuff in such a shape or form. Obviously, my ridiculous theory asserts a chaos chock full of dimensions, where time and space are but supporting actors.
I don't think you've taken on the full force of the argument that regularity in human activity (such as building systems) requires a source of order for it not to simply dissolve into chaos itself.
> How can it be that the patterns that we observe are so consistent?
How can we claim to discern consistency (or inconsistency) without the ability to follow a rule correctly? And how can we follow a rule without a source of order or regularity in the cosmos? Wouldn't it be like trying to build a the Eiffel tower out of live slugs?
If you insist on an absence of order in the physical universe, the onus is on you to explain how regularity in human activity (required for mathematics of any kind) can be achieved without it.
This is not an argument for Platonic realism, BTW, or against intuitionism, roughly construed as the view that "mathematics is a creation of the mind" as per [1], or in your formulation that 'mathematical abstractions are not part of the physical universe' (if I understand what you're saying). You can perfectly well believe that mathematics is a mental construct and at the same time acknowledge that it's possible to observe regularities and order in the cosmos. If you want to insist that the regularity doesn't come from physical law, then I find it hard to see how you'll escape from some kind of Platonic belief in a non-physical realm that serves as the source of order :)
In your TV screen dots analogy, isn't it usually thought that patterns appear only because of the structured, generative activity of law-observing physical components, specifically the neurons comprising your grey matter?
This argument completely ignores the observer which is bound by the same limits of our processing - indeed they are paired together.
Entering purely theoretical space here: On the timescale of eternity this might be a local pocket of some logical organization but there is no fundamental logic governing everything. Our observation is limited so we can’t perceive chaos, instead evolved to only recognize patterns. Over infinity, pure chaos does not preclude long pockets of what looks like order. What we consider fundamental rules could very well be local phenomenon, which we are a product of.
Of course this purely theoretical - all I’m saying is that intuitism could be true while also math being useful to predict things right now. We could also only exist for an instant and all our memories just construct, but that’s not very useful. It’s more useful to believe in scientific method because what’s repeatable is provable, whereas chaos is by its nature unprovable - which doesn’t make it impossible.
Well, not a possibility I considered, but nothing in the argument depends on the regularity being a permanent feature of the cosmos, just that systematic human endeavours, such as mathematics or indeed meaningful debate, depend on it, so when it goes they go. In that sense, if you wish to consider this conversation meaningful you are kind of ceding the point that for now chaos doesn't, in fact, reign. If you don't consider it meaningful, then why are you having it? :)
Not arguing anything - it's more an interesting thought experiment. This view doesn't change much other than never finding the "true unified theory of everything", which I'm not sure how many people think is truly possible (at least anytime soon) anyway.
It is useful to focus on repeating things, and useless to focus on randomness. But I don't think it's necessarily true that randomness (probably a better word than chaotic since chaotic systems are complex mathematical interactions) doesn't reign. We evolved to take advantage of repeatable things, our sense organs and perception are all focused on things that are repeatable. Our definition of usefulness (what is useful/what isn't) depends on repeatable things. I believe there's a pretty high likelihood that we are blind to anything outside of that, such as true randomness. IE, we literally cannot conceive of true randomness since we are products of an environment that rewarded it.
To your point, I guess this isn't exactly Intuitionism, since Intuitionism says it's a totally human construct, and mathematics has provenly predicted things in nature from purely theoretical models, whereas I just find the part that supposes mathematics isn't a fundamental part of objective reality possible.
Either way, I don't think it changes anything about how we do math or science or anything - how could you even study this? By definition understanding and using things depends on repeatability. If there truly were cracks in it, they by definition couldn't be repeatable. It certainly won't help us get food.
EDIT
> If you don't consider it meaningful, then why are you having it?
I just find it interesting since I've had this thought before and seeing what other people think of it.
Something to consider in the context of "repetition", is that it requires abstraction, and possibly memory. As noted before, I do not see any kind of repetition (identical things, counting) in nature. I think abstraction and memory are both emergent properties from human brains (or machines, brains in other mammals, octopuses, etc.) My pet theory also initially discards "things", because that again requires abstraction.
For reference, my views are somewhat related to "emergentism", "connectionism", and "realism", but I haven't found a school of philosophy that I feel comfortable with.
> how could you even study this?
This is indeed the biggest challenge. I am currently studying this from a conceptual art perspective, because philosophy and science do not seem adequately equipped for this kind of problem.
Thanks again for taking the time for a thoughtful reply. I am aware that I'm using terminology very loosely, and I omit many details that may be required for a full understanding.
With respect to the full force of the argument: I assume that the "regularity" stems from the physical systems that make up our brain. Just as replication through DNA offers some stability in life, the shape of our neurons (and perhaps the dynamics of space-time, and the laws of physics) offer some regularity in the chaotic universe.
In my view, this regularity is but an accidental blip in the totality of existence, but to us, who cannot observe the rest of the chaos, it seems fundamental -- which from the universal context, it isn't.
The biggest problem that I cannot get around is that I somehow assume this chaos exists, and allows for things to exist inside of it. I do not know how to provide arguments for that, other than the negative one that it seems highly unlikely that "there is something rather than nothing". Likeliness, and the fact that I can define these abstract concepts, only make sense in the realm of human thought, so I am sort of stuck in a recursive loop there.
With regards to the second part of your reply, again it is us humans who do the discerning. It is an emergent property of our brain (or possibly of slightly simpler, but still rather complex "discrete switches") that we can discern things. In the underlying universe of total chaos, there is no context, no logic, no measure to discern things.
So, the source of order does arise through physical constructs, that happen to have a certain structure that allows observation. It is humans, mammals, octopuses, computers, that can use this universal form of observation to process input, and then do observation as we know it. So I suppose my idea is some kind of realism, but my reality is nothing more than pure and utter, unbounded chaos. And we live in some corner of that.
The grand claim is that mathematics is nothing more than the result of some self-observing shapes in the chaos that is existence.
Again, I feel sorry for all the readers who try to make sense of all my overloaded concepts. I wish I had the skills to write down my thoughts more rigorously. Or perhaps someone can save me a lot of time [1].
The first link is an article that explains that all electrons are exactly identical, suggesting that there are indeed things in the universe that are exactly the same. However, the second link discusses the one-electron idea by Wheeler, which suggests the exact opposite :)
> There are not even two things exactly the same, as far as I can tell
Aren’t all basic particles defined by the fact that they are exactly the same? And countable things rely on some difference, such as different spatial locations — or else they wouldn’t be countable, they’d just be the same.
While two neutron stars are distinguishable they are also classifiable as a real type of star in a manner that seems to go beyond human perceptual idiosyncrasy.
But I'm a deep Platonist/Pythagorean — so my bias is that "all is number" and the world is made of math. Math is real :)
If the world is made of math, do new physical objects pop into being whenever a mathematician writes down or thinks of a structure or a proof? Or does only some math get to become physical?
In general, your view seems like a definitional issue to me. If you want to call what the world is made of “math”, then what you and I mean by math are two different things, and using the same word to describe them only leads to confusion.
> "mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."
I take the brevity and lack of commitment to a position in your reply as an indication that you're not really willing or able to defend your position. That's fine, it's a complex topic, as the many articles on the SEP linked above attest. But if you want to claim "the world is made of math", then the onus is on you to define what you mean by that. To me, it looks a little incoherent.
Take the brevity as a lack of hubris. The notion that “the world is made of math” is one of the oldest and most influential ideas of all time. If you find Pythagoras, Plato and Newton a little incoherent, that’s not unusual. But the onus doesn’t lie with them (or me). In any case, I remain interested in your ideas!
None of Pythagoras, Plato, or Newton claimed that the “world is made of math”. Also, Aristotle’s philosophy of mathematics is considered an alternative to Plato’s, so trying to seek solace in both at the same time seems inconsistent.
Plato described math as a realm distinct from both the physical world and the world of consciousness. This doesn’t support the idea the “the world is made of math”.
Newton described the world as operating in accordance with the rules of math, but that’s not the same as being “made of math.” Plato’s view is compatible with this: what Frege described as the “third realm”, the realm of abstract objects, can have a relationship with the physical realm without requiring that the latter be “made of” the former.
Aristotle explicitly distinguished between physics and mathematics, saying in his Metaphysics that physics is concerned with things that change, whereas mathematics encompasses things that are eternal, do not change, and are not substances. So Aristotle seems to explicitly reject your view.
As such, I don’t accept your claim that your position is “one of the oldest and most influential ideas of all time.”
> But the onus doesn’t lie with them (or me).
If you make a claim, the onus certainly lies on you to support that claim.
Pythagoras said “all is number.” So, where some claimed that “fire” was the primary constituent of all things and others “earth,” Pythagoreanism held that numbers were the underlying principle. Do you accept this claim?
Newton was a Pythagorean. He even attributed the inverse square law to Pythagoras.
Plato is always hard to pin down, but he describes the immaterial world as crafted by number, prior to the material world.
There are not even two things exactly the same, as far as I can tell.
That is a common definition of identity, two things are the same if all their properties are the same. So by definition there can not be two different things with all their properties the same as this would make them indistinguishable and therefore the same thing. But if you relax this a bit, then for example elementary particles like electrons are - as far as we know - all completely identical up to their position, momentum and spin.
I've seen statistics proposed as the force that makes reality, that would be fundamentally random, coherent. But statistics laws are themselves very strong when numbers get big.
I noticed that in nature (i.e. in the physical universe) there appears to be no logic. There are not even two things exactly the same, as far as I can tell. So that lead me to believe that "counting" (or abstraction) is not even a property of the universe, but possibly only a human (or animal, or Turing machine) construct. To me, logic only starts to occur when a very complex amalgam of matter comes together [1] to realize a discrete switch. Using these discrete switches, organisms build memory and abstraction mechanisms, start counting, and do mathematics.
So my thesis is that things that are considered to be "basic" by most, such as logic or mathematics, are in fact quite specific systems built on top of chaos. From there, it remains to be proven that all physical laws that we observe are no more than projections of the chaos onto such a system.
Perhaps a metaphor that helps to take on my perspective, is to look at a screen filled with random noise, and then observe some patterns in there. Now replace the screen with an infinite dimensional set of chaos, and then observe a pattern that is our universe. With the added twist that we are part of this chaos, and observing the pattern, possibly in the form of physical laws.
Of course, there are many problems with this theory. What does the chaos reside in? How can there be discernible parts in the chaos? Is time an emergent property inside the chaos? How can it be that the patterns that we observe are so consistent?
However, to me this theory seems more fruitful than merely accepting that we cannot say anything about things that science cannot observe, or that some deity created all this.
[1] With "comes together" I do not refer to a dynamic process, but to the accidental occurrence of stuff in such a shape or form. Obviously, my ridiculous theory asserts a chaos chock full of dimensions, where time and space are but supporting actors.