101–110 of 179 posts
The older I get the more I feel like pursuing these trains of thought will lead to mental instability and sadness. 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
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So you consistently perceive streams, the world, have a body, a life, a wife, a kitchen with a flaw that has persisted over time, an order in to fix it. Also the world is consistent enough that you could predict that argument in advance. That sounds like an awful lot of consistency :)
Yes, I've already conceded that some things are consistent. Will you concede that we tend to glom onto them or will I interpret your reply where you once again glommed onto them as a concession? ;)
You haven't really come to grips with what a world that was mostly inconsistent would look like.
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 Metamath system lets you specify the axioms you want to use, and then can verify that your proofs only use those axioms (directly or indirectly). There's a Metamath database specifically for intuitionistic logic:
https://us.metamath.org/ileuni/mmil.html
More things have been proven using intuitionistic logic over time.
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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…
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 co…
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.
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…
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". I have a similar but somewhat different take on this. The universe comes first, it behaves - for what ever reasons - in the way it does. Than we humans show up and invent logic, a set of rules that is usefu…
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> fools us into thinking there is some inherent order -- which there isn't. Bold claim :) Even while maintaining a willful agnosticism about Platonic realism, it seems clear that the business of doing mathematics - intuitionistic or otherwise - depends on the ability to state and follow unambiguous rules, or else how to establish a proof within some axiomatic system or other? But if mathematicians have this ability,…
In other words, the Cartesian principle extended to two parties? Cogito sicut tu cogitas, ergo sum sicut structus es : I think as you think (at least for a moment); therefore, I am, at some level, structured as you are (at least for a moment); and therefore, there is order in the universe, at least in the temporary alignment of our structures that enables us to think along these same lines? (Saying nothing, of course…
There's something truly evil about psychologizing math. 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: https://plato.stanford.edu/entries/psychologism/#FreAntArg
In the same way that psychology can be harmful to the pursuit of truth, there is an evil or deformity in what pure mathematics represents (or became), as Cantor and Gödel both discovered trying to eliminate its paradoxes. Mathematics as practiced by, e.g., Leibniz and Euler, was much more interested in calculation, i.e., mechanization. It is this form of "mathematics", as the thing has come to be called, that should have been developed, instead of trying to axiomatize infinite sets, explain the continuum, or fix impredicativity.
But despite the many paradoxes of mathematics (e.g., AoC, LEM) and machines (i.e., bugs), computer science has happily chugged along and made many practical contributions which explain the universe and shed light into people's minds, fulfilling the role that pure mathematics once served. Today, we are very close to mechanizing both minds and mathematics, and can replicate many aspects of reality (i.e., mathematical or otherwise) inside computers. It is not unimaginable that one day, computer science as it is practiced today will be seen as a kind of telescope for revealing the nature of mathematics and/or reality, which the mind alone cannot fathom.
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…
If universe was total chaos, then we would observe it, because absence of chaos isn't required by anthropic principle, but instead we observe universe to have at most pseudorandom processes, therefore universe isn't total chaos.
(Yes I know that one cannot use "reasonable" as an argument for a context in which human arguments do not apply. The entire thing is a thought experiment, nothing more.)
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Yes, I've already conceded that some things are consistent. Will you concede that we tend to glom onto them or will I interpret your reply where you once again glommed onto them as a concession? ;)
It's not glomming on when these things are basically the core aspects of reality. You haven't really come to grips with what a world that was mostly inconsistent would look like.
Probably one that had trouble evolving high-order lifeforms, aka anthropic principle.