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Roger Penrose – Is Mathematics Invented or Discovered? [video]

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Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#181
post #132

A vaguely, but tangentially related fact, is that Stephen King actually considers the stories in his books as discovered, rather than invented. He talks about it in his book 'On Writing'. He considers the stories to be sort of preexisting things, and his job as a writer to unearth and discover them, rather than invent them. It's about his frame of mind while writing, I guess, but still.

To me this sounds like an echo of the view that free will is an illusion. The stories that King is going to write are already predetermined by the laws of physics applied to the initial conditions of the system. In a sense, he's really just "along for the ride".

We're all slaves to ka.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#183

There's one thing I cannot wrap my head around. Math is purely abstract science yet it describes the world around us to the utmost precision. Does that mean that this world is simply ... a math model which means everything around us is ... not real? I've long stopped believing in free will because everything points at it being an illusion of our brain because we're a product of this world and we had no chance of infl…

>I've long stopped believing in free will because everything points at it being an illusion of our brain because we're a product of this world and we had no chance of influencing the conditions which brought us to life

Free will doesn't depend on the universe being deterministic or not. Things that haven't happened yet are likely going to happen in a certain way based on the trajectory, but it doesn't mean that you can't change your own path in a meaningful way, you're free to take a harder path vs. an easier or more obvious one.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#184
The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery. The apparent distinction arises from our separation of physical and mental processes. But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes are physical processes. Specifically, mental processes are computational processes, which are physical. So it's not surprising that the structure of the physical world should be reflected back on itself in the structure of mental processes. It's universal Turing machines all the way down.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#185
post #176

Same question also answered by Max Tegmark: https://www.youtube.com/watch?v=ybIxWQKZss8 Stephen Wolfram: https://www.youtube.com/watch?v=nUCwtLTUPQ4 Steven Weinberg: https://www.youtube.com/watch?v=NpMk9G-ddiM I particularly liked Max's answer who neatly makes the distinction between the structure (we discover) and the language (we invent). We're free to invent the names, but not the structures.

Entire playlist:

* https://www.closertotruth.com/series/mathematics-invented-or...

Gregory Chaitin was interesting as well:

* https://www.youtube.com/watch?v=1RLdSvQ-OF0

The (apocryphal?) story about Godel not believing in empirical science and only in a priori truths was interesting.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#186

Earlier quoted context omitted.

If you want to understand why some people believe that science and creationism don't go hand in hand, then studying epistemology would help you do that. Most introductory texts will cover what you need.

Sounds like I got something new to learn during this lockdown, thank you. After a quick look at the wikipedia page on epistemology (very interesting), I'm not sure how this explains why some people believe that science and creationism don't go hand in hand.

A super super short version is about the question "how do you know X?" Its generally (although not universally) agreed that there are two types of knowledge, a priori and a posteriori. Roughly, in the first case, all you can deduce is implications from assumptions. For example, "if X and Y are true then Z is true." Such things don't require experience. The second case requires evidence gained from experience. Mathematical knowledge is of the first type, scientific knowledge is of the second type. The school of rationalism prioritizes the first type and the school of empericism emphasizes the second. That the universe was created by an omnipotent omniscient and benevolent god is not an emperical fact but requires some kind of a priori supports. Thats why you see so called proofs of god rather than scientific theories of god. There are other options of couree like mysticism, the claim that knowledge can be gained outside of these methods, or an emphasis on faith, that we don't take these things to be justifiable.

I probably butchered this but it gives you some starting points to research and hopefully shows a model of the debate. Huge topic. Check out https://plato.stanford.edu/entries/epistemology/ as a hardcore crashcourse or check "crash course philosophy" on youtube for the relavent sections at a more HS level. SEP has entries on god, faith and mysticism as well as rationalism and empericism too.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#187

The expression is invented but the underlying relationships are discovered. It's silly to think that the sqaure root of negative one is something real to be discovered. It's just a stand-in to express complex relationships more succinctly. The same for negative numbers, for that matter. It would be equally silly to think that the underlying relationships are invented. Nobody invented prime numbers, they were discover…

> The same for negative numbers, for that matter. It might be expressed differently, but the concept of addition seems very fundemental, and additive inverses (negative numbers) are a very real part of addition. > It's silly to think that the sqaure root of negative one is something real to be discovered If we assume the aliens also have a need for multiplication, combining it with multiplication we get polynomials,…

"additive inverses (negative numbers) are a very real part of addition"

Inverses are just an abstraction that helps you rearrange operations.

You'd think something like accounting would need negative numbers, but nope, it gets along just fine without them.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#188
post #184

The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery. The apparent distinction arises from our separation of physical and mental processes. But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes are physical processes. Specifically, mental processes are computational processes, which are…

This all seems like semantic masturbation.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#189

Earlier quoted context omitted.

You think logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does?

There is a distinction between logic, which is just the study of formal systems where you can prove theorems as in any other area of mathematics, and the philosophy of maths and particularly of mathematical logic. The same applies for set theory. The first one can assert that (in classical first order logic) e.g. there are uncountable models of the natural numbers; this is irrefutable. The second one asks things like…

Irrefutable and "unequivically" true if you take some classical FOL as a productive method of producing knowledge, a philosophical assumption. Philosophy came first, mathematical logic is just a formalization of that and the reason it was formalized at all and not somethimg else is epistemological.

Your entire argument attempting dismiss philosophy is philosophy.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#190
post #78

Earlier quoted context omitted.

Yes, that's my point. It applies to anything that is creative and dismisses the original point through abstraction.

You didn't make a point. You asked a loaded question. It backfired on you.

My question asking if you value products of philosophy that have become essential to our society neither contains an unjustified assumption and thus is not a loaded question and still stands and thus has not backfired.
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