71–80 of 179 posts
We model the world and the world follows the model and the exceptions add to our refinement of the model and that’s what makes it true.
Perception and reality are yin and yang and that is about as deep as my philosophy needs to go here
I have liked intuitionism from the very moment I first heard about it. I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences". It may also help to guide us away from the "why is there something rather than nothing" problem. If existence is total chaos, then we a…
The physical world is a persistent system that exhibits highly consistent behaviour. Because the behaviour is consistent we can describe it in a highly consistent formal language, mathematics. What Plato called forms are just descriptions. We have a description of what a circle is, and anything that matches that description is a circle.
Thats because chemicals shape/influence our personalities and emotions. You'll see the same consistent behaviours in animals as you do in humans, when given the same chemicals.
Earlier quoted context omitted.
> I think mathematics is a human construction and doesn't have a real substance. Instead, mathematics is a system of assumptions and generative rules, and more generally a discipline around creating and operating such systems. But "truth" within a system of assumptions and generative rules is not subjective, it's mechanically provable. Mathematics is a human construction, but it certainly has a real substance. What d…
>What does "mechanically provable" even mean, if there is no absolute truth? Do you believe in the definition of a proof or not? Different Axioms lead to different provable statements. Believing in standard mathematics basically means that you can not believe in absolute truth. Unless you also believe that some guys a hundred years ago figured the sole and completely perfect rules which totally correspond to reality.
Even your comment references “perfect rules which totally correspond to reality” which seems to be another way to say “absolute truth”.
Earlier quoted context omitted.
Wow, you excavated an ocean to cover a puddle. how this: "something which follows rules, with no independent thinking or homunculus" can be easier to prove and reason than the initial rules? For example, what is simpler to reason out: does a chess move violate chess rules, or, there exist a method to construct an electomechanical device, that will Correctly determine whether this chess move is legal?
The reason I brought up a machine explain something as being mechanical is to clarify that it doesn't require intuition. We can make machines that count. A trivial example: pebbles in a bucket. Neither the pebbles nor the bucket need intelligence to act as (have a correspondence with) a counter.
Without having proof for the machine itself that machine is declared axiomatic. It is a valid way to go about things of course, but I would hesitate calling it "not requiring intuition".
"In theory, mathematics is all pure & abstract logic, with no connection whatsoever to the real world.
"In practice, if you want funding for your mathematical research, or for more than a puny handful of people to ever look at what you did, then you had best pay plenty of attention to the real-world usefulness of it."
If anyone feels compelled by this you should probably start by learning about the many rock-solid antipsychologistic arguments out there that are at least 130 years old:
Paraphrasing a math professor I had [mumble] decades ago: "In theory, mathematics is all pure & abstract logic, with no connection whatsoever to the real world. "In practice, if you want funding for your mathematical research, or for more than a puny handful of people to ever look at what you did, then you had best pay plenty of attention to the real-world usefulness of it."
I understand what your math professor was trying to communicate, but at the same time, I think framing things this way begs the question that mathematical entities are not "real". It's more accurate (or at least less question begging) to say something like "mathematics, or mathematical objects, doesn't seem to have any obvious or direct connection to the material or physical world". Putting things this way doesn't reify mathematical entities, but it also doesn't presume that they don't exist.
I have liked intuitionism from the very moment I first heard about it. I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences". It may also help to guide us away from the "why is there something rather than nothing" problem. If existence is total chaos, then we a…
It's not chaos, it's infinitely ordered order most would rather die than accept.
The article seems poorly written, or at least self-contradictory in a way that makes me uncertain what it means. The introduction talks about the intuitionism framing mathematics as a human construction, in opposition to an objective reality. But the subsequent paragraph talks about the truth of proofs themselves as being subjective. It seems to me that these are two different claims. I think mathematics is a human c…
Earlier quoted context omitted.
Thank you for your reply. I'll try some more! :) 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…
> built on top of chaos. 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 follo…
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].