121–130 of 322 posts
Earlier quoted context omitted.
>It matters for philosophical inquiry. I was thinking more of tangible implications. Maybe there are some.
Philosophical implications are perhaps the most tangible implications there are: they shape the conception of reality and society that you live in. They only seem intangible because they are subtle and pervasive.
Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…
I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a species who has no sense of vision will not develop geometry the same way we would. A species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of ge…
Earlier quoted context omitted.
"two of our own species [discovered calculus]"..? Which two species are those? I assume by "own own" you mean Terran species, and one of them is Homo Sapiens, which is the other one? Really curious...
Leibniz and Newton. Two [members] of our own species.
Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…
I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a species who has no sense of vision will not develop geometry the same way we would. A species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of ge…
Except once axioms have been fixed, the resulting geometry will be the same wether you perceive reality via visible light or echolocation.
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> I'll never understand how someone otherwise so apparently intelligent can be so religious. Why not? Religious people believe that God is the Most Wise. Mathematics in nature attest to that attribute of God (as well as to other attributes of Him). An intelligent and religious person would recognize that, knowing it is God who came up with all the rules that keep the universe in balance. I'll never understand why som…
And who/what created God -- e.g. who is God's God? And so on? It seems like humans trying to understand a hypothetical God are not unlike ants trying to understand quantum physics.
Of course this is hard to understand, but what would you expect? We can't even comprehend the tiny amount of His wisdom He has given us, let alone comprehend all of it.
If you're in the sahara desert you basically have all materials you need to create an iPhone. Not in a million billion years will there ever come an iPhone into existence by mere accident of natural forces in that desert, would there? Yet you believe that living things, which are not even comparable in complexity to an iPhone, were formed by a chain of coincidental events in the universe?
You can see God if you are willing to, unfortunately most atheists keep their hearts closed...
Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…
Tell me more about the difference between "potential infinity" and "actual infinity". Recursive functions in computer programming, or fractals in maths, are infinite but can be described. Each small part looks like the whole, but the whole can never be fully known within a finite universe. Is that "potential" or "actual" infinity? I've been thinking a lot about infinity this past week, mostly because of Conway's lect…
There's no reason why universal determinism and free will need to be related. So trying to "prove" free will with math makes as much sense as "proving" free will with weather forecasting.
Even if that weren't true you still can't get to Conway's Step 3, because "free will" could just be statistical noise, and not willed in any sense at all.
Earlier quoted context omitted.
I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a species who has no sense of vision will not develop geometry the same way we would. A species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of ge…
And yet, most blind mathematicians are geometers, which suggests your theory is incorrect.
Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…
Tell me more about the difference between "potential infinity" and "actual infinity". Recursive functions in computer programming, or fractals in maths, are infinite but can be described. Each small part looks like the whole, but the whole can never be fully known within a finite universe. Is that "potential" or "actual" infinity? I've been thinking a lot about infinity this past week, mostly because of Conway's lect…
Eg, the “natural numbers” are a recipe to make as many as you want (by taking the successor of the last one) but not an actual (as in existing) infinite collection — the only ones which exist are the ones you construct, and the “potential infinity” refers to the fact that you can always make a new one.
Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…
The reason why intuitionist mathematics is useful in QM is because it can be viewed as resource based logic. But remember that (as far as I know) you can do intuitionist mathematics in classical mathematics, but not the other way around. So you can think of intuitionist mathematics as being embedded in classical mathematics.
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Isn't that simply because axioms that don't lead to consistent conclusions are rejected?
You can invent and pick axioms in many ways that (probably) won't lead to inconsistencies. But they won't all be powerful enough or relevant in the real world.
Or in other words: the constraints on maths are imposed from outside of maths.