Mathematical and logical truths exist before we have discovered them, so

[Chrisc]

Hi, I don't know if you read my more recent post, which is slightly different to my original idea, here it is:

Our universe follows rules, these rules (as far as we can see) have always been obeyed. All of these rules so far can be defined through mathematics, so I presume that the fundamental rules of the universe are 'written' in a language similar to maths.

You are not recognizing a fundamental assumption you hold as true without reason, in order to claim this.
Humans are made of the stuff we are trying to define with the language of mathematics.
As Carl Segan said, "we are space dust".
This means we are the universe trying to understand itself.
The meaning we attribute to observation is perhaps more thorough than the meaning
a turtle might attribute to the same event, but it is still the meaning arising from the
reasoning of humans.
Turtles could have the discussion we are having now and be just as certain that the
universe "follows" their rules or reason, and none of us could dispute it unless we
could reason their way and find fault with their axioms.
Our axioms are what "ALL" of mathematics must stand on, and are considered "self evident".
Think about that term, does that "self" mean you, me, all of us humans or the universe?

What is "self evident" to turtles MUST by definition be true reason and will be as
true to turtles as ours are to us. The universe will always, by definition, follow self evident truths.
But as the universe follows the truths of turtles and humans, we should at least
recognize these truths say nothing about the universe and everything they do
say is reflection of humans (or turtles).

 

[Pythagorean]

Ok, since we've been getting personal, we should separate our personal arguments from the factual arguments. Anytime you question somebodies motives you're always going to be at least partially wrong (not finger-pointing here, it's a natural result of debate when people have the genuine interest that you spoke of).

So we'll retain your format and do personal first, then topic. I don't think the personal is irrelevant to the topic, but it would be nice to keep them separate.

Now, hopefully you're clear that "One math works in one frame, the other math works in another frame" is an argument against attitudes like this:

Our universe follows rules, these rules (as far as we can see) have always been obeyed. All of these rules so far can be defined through mathematics, so I presume that the fundamental rules of the universe are 'written' in a language similar to maths.

I'm not making an argument about whether or not math is compatible. The argument is that we could have easily designed it to be compatible with our descriptions of reality (which wouldn't be a stretch, considering math arose from studying reality). I also stead in the previous thread we had this discussion that a TOE might convince me (as long as it's not a makeshift pack of algorithms, utilizing math as a tool bag of random tools that you can get a lock open with) that the universe is fundamentally mathematical, which would also show that mathematics is discovered.

It isn't my imagination or some sort of bias that makes me think that you and turbo and others say things like this. You actually say such things.

non-sequitur. I never claimed that I don't "say things like this". We're talking about your interpretation of my the words. By further interpreting them the way you have been, you don't really make the point that you aren't.

Okay, so we're again back to a complaint about the nature of mathematics that is based upon its utility to physicists and difficulties that physicists encounter when trying to apply mathematics.

We've now come full circle back to the first thing I was saying in this thread, "But physicists erroneously applying mathematics to a problem of science isn't the same thing as a flaw or limitation in mathematics itself" which you [post=1980511]quoted and asserted was bias[/post].

You see, the bias is that physicist's are "erroneously applying mathematics". That's assuming your conclusion, since mathematics would have to be necessarily discovered, and not invented for there to be a wrong way to apply mathematics.

The way I use mathematics is like a sculpture, cutting my function to fit reality. I chip away from functions with other functions and approximate. There's no "erroneous application" since what I do works to the degree I need it to. If I need more accuracy, I cut more and approximate to a higher order.

The claims I make about the sort of things that physicists say, which you keep claiming is some sort of biased view or assumption on my part, you actually keep repeatedly saying.

Or... you keep repeatedly interpreting with a bias...? We could argue circles all day about this, really.

I understand that you were mistaken in what you thought I was saying but that doesn't mean that I'm somehow biased - I am describing the way that you and (some) other physicists do actually behave. When it serves your purpose, in discussing the fundamental nature of mathematics you will very readily blur the line between mathematics and applied mathematics within physics, and imply that some problem that physicists run into in applying mathematics extends to being a general problem with mathematics itself.

But you were interpreting my posts as absolutes, such as "math does not work" when I was the argument really has to do more with are humans the ones making mathematics work?. You were taking my arguments to be me extreme than I intended them.

Bah, I've been responding to the wrong post. I'm going to try do this competently, later.

 

[Georgepowell]

Now, hopefully you're clear that "One math works in one frame, the other math works in another frame" is an argument against attitudes like this:

Our universe follows rules, these rules (as far as we can see) have always been obeyed. All of these rules so far can be defined through mathematics, so I presume that the fundamental rules of the universe are 'written' in a language similar to maths.​

What do you mean exactly by ""One math works in one frame, the other math works in another frame"

 

[Pythagorean]

I'm just going to continue this as if it's part of my last post. But my views have changed a bit since even then, or at last become more clear to me.

When physicists tried to apply the mathematics they used in classical physics at the quantum level, that was an erroneous application of mathematics. But despite the context in which you brought it up, it has no bearing on whether or not mathematics is discovered nor invented. Nor even were someone proposing that there's some matrix-like mathematical substrate to the universe, would it have anything to do with that.

These are your words, not mine. I have no idea what that means. But If you'll look at the author of this thread, and where I quoted him in my last post, maybe you'll see where you're wrong if you consider what I'm actually saying (in fact, look at the first sentence in this whole thread) and not how you took it in and spat it back out (unless that's actually what you meant... compared to GeorgePowell's statement). I honestly thought you were defending GP's views.

However, I still hold that the axioms of mathematics are invented. I cannot deny that there's lots of discovery involved in pi and e, but constant values hardly represent all of mathematics, so it's not basis for "mathematics is discovered" it's basis for "constants are discovered".

So the argument "mathematics is invented" is equally invalid, since you can't bullpen mathematics into a simple little category; There's a lot of elements to mathematics and I find it hard to believe that you and I share the same set of elements everytime we hear the word mathematics. My focus is on the axioms.

I've been looking to counter two arguments of yours:
"mathematics is not invented"
"mathematics is discovered"

Which I still hold are false statements. However, I also realize the approach I've been using is to prove two things by counter-example:
"mathematics is not discovered"
"mathematics is invented"

which is equally false because we're both assuming that mathematics is something we can just lump into a generalization like that.

I will reply to your organized argument eventually if it's necessary, but I still have things to think about for it.

What do you mean exactly by ""One math works in one frame, the other math works in another frame"

by "works" I mean 'is useful in making predictions in physics'

by "one math" and an "other math" I mean this equation or that equation. This model or that model. There's no ultimate equation that's fundamental to all reality. There's several ways you can go about doing it.

Mathematics is a language. You can use it to describe anything you want, only quantitatively instead of qualitatively. You have some creative license with how you mathematically describe physical things, so long as the predictions work within a given confidence and accuracy.

Language, qualitatively, is the same way: you can't say a fish is a boot. Some people may argue that you can, but if they refine the accuracy of their argument, they might say "a fish-shape can be made out of a boot" or "a boot can be made of a fish". But we all know that a fish is not a boot, so there's still false and true statements and accuracy associated with qualitative description.

 

[Pythagorean]

Premise 1: As you yourself affirm, we agree that any intelligence, even an intelligence entirely unlike that embodied by the human brain, which could formulate and understand a particular set of mathematical axioms would arrive at the same conclusions humans arrive at based upon those axioms.

If Premise 1 is true independent of the point in history such a hypothetical scenario might occur at then in the absence of humankind, before its existence or after it perishes, the same alien intelligences would arrive at the same conclusions based upon the same axioms.

Ergo, the relationship between the set of mathematical axioms and the conclusion is a constraint that is independent of the existence of humans or human brains or human-like brains.

If something is independent of the existence of humans it would not be characterized as invented by humans; hence it would fall within the opposite of "invented", which by the conventions of this discussion has been designated "discovered".

∴ the relationship between the set of mathematical axioms and the conclusion is a constraint that is discovered rather than invented.​

I saw this movie (can't remember the name) where they make contact with aliens. Their greeting ship was fixed with lights that lit up in some "mathematical pattern". The point was made in dialogue that mathematics would be the way we'd have to communicate with aliens because it transcends language. I think this is a silly idea. Rote will always be the way to communicate with someone who's language you don't have a codec for. That's how the codec's (standard word by word translations) came about. I just wanted to put that out there. I know you haven't made the argument or anything, but you could have something to say about that.

p1 is a weak premise. The argument for invention is that mathematics comes from consciousness. It doesn't really matter which consciousness it comes from, but it's inherent to one of the ways we think about the world (specifically in series and linearly). The mathematics that tell the most accurate truth about the physical universe are the ones that say the least... that is they have infinite solutions... for then you can chose the one that fits your situation and throw away the others.

p2 is a case of p1

In your "Ergo", you've softened your stance to a point by talking about the relationship between the subject we were debating and "conclusions", then following into your next paragraph you've actually bravely avoided declaring that "mathematics is discovered"

your first post, back in our old thread:

Well, I'm inclined to try staking out the position that it's entirely discovered.

https://www.physicsforums.com/showpost.php?p=1610409&postcount=14

you even put the last two words in red. In fact you're wording is very similar to mine, you say "inclined", but then emphasize the point. It appears you have been doing what I noticed I was doing. Taking the extreme side out of ignorance. You slowly gave up parts of it, and I gave up parts of my stance.

And note that again this does not depend on any aliens actually existing. I am demonstrating that based upon a statement that you agreed with, in the way you yourself view mathematics some part of it has existence independent from humans.

I can agree to that. You have moved toward the middle as much as I have in this debate. We're at least not stating the absolutes anymore.

 

[CozmicScott]

This goes way back too the math, and reality thing again. Putting them together. What are everyones views on Heisenberg's principle that focuses on realation's between quantities which in principle are observable thus having formulation of quantum mechanics., the difference between 2piextimesp and ptimes2piex would be imaginary. right?