Civility

[pkane2001]

Just now, wgscott said:

 

Same problem:  Do those rules of physical reality have any objective existence, apart from the people who articulate and implement them?  Do the rules exist before they are discovered?

 

A formal logic system is defined by a set of axioms and derivation rules. A proof consists of showing that a statement (theorem) can be derived from the axioms through the repeated application of rules.

 

Ignoring  Gödel's unprovable theorems for a moment, the other 'truths' within such a system are recursive, i.e., computable. Does that mean that each proof has an existence before it is constructed? Probably not in the physical realm, but certainly in a mathematical sense. All such proofs come into 'mathematical existence' as soon as the formal system is defined.

 

What is curious is that the physical universe appears to be extremely adverse to violating the truths that are derivable in any internally consistent formal logic system. That's why mathematics (a formal system) is such a great tool for modeling physical sciences. Why this is so, is unknown and probably unknowable. Is it by design? By accident? My guess is that the universe itself is just a dynamic formal system trying to randomly construct instantiations of all the possible theorems. In other words, a computer. But I have no proof

 

[pkane2001]

3 minutes ago, jabbr said:

 

What is your criteria for truth? Let’s say true = 1. In your logic system does 0.99 = 1? What formal logic system are you using? 

 

A formal logic system is a well-defined construct. I'm not using any specific ones. In mathematics (a formal system)  0.99=1 is not true and can be proven.

 

[pkane2001]

9 minutes ago, jabbr said:

So you need to work your way through Heisenberg and then all of 1st half 20th century quantum mechanics before you even get to Quine. The physical world is not precisely described by formal discrete logic and the harder you try to describe it, the harder the physical universe fights back at your meager  attempts. 

 

You are jumping way deep into the physical world, where I was operating in the theoretical. But, yes, even quantum mechanics of today is based on a formal system. Whether or not we are using the correct formal system to model it, and whether or not our human intelligence is capable of deriving and proving the appropriate theorems (those that can be proven) in our chosen formalism is a very different story.

[pkane2001]

2 minutes ago, jabbr said:

So I assume you wish to modify this statement? This isn't the case from even a theoretical point of views. Essence of Heisenberg Uncertainty. I would say that at its very essence the physical universe is described by statistical probabilities. Schrodingers cat etc etc

 

Not any formal logic system: Start here: https://en.wikipedia.org/wiki/Schrödinger_equation ... can you derive a formal logic from this? (Hint: its not binary logic)

 

Nope, you're still missing the point. It's not formal logic that's derived from physical science, it is science that is derived from formal logic. 

 

What Heisenberg did was change the then prevailing formal system by adding an additional axiom about the limit of measurability of momentum and position. The rest of the axioms and rules of the formal system remained unchanged. Just like Einstein did when he introduced his relativity principle (axiom).

[pkane2001]

56 minutes ago, mansr said:

Continuing that line of thought, the entire history of the universe, to use your words, comes into mathematical existence simply through the definition of the underlying formal system. The question is then, does someone or something need to actually formulate the axioms and rules in order for a universe to "exist," or is it sufficient that they could be formulated?

 

Good question... to which I don't have a solid answer. A good book by Max Tegmark that attempts an answer:

 

https://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307599809

 

If I can summarize his idea, it is that all mathematically possible universes must and do exist.

[pkane2001]

5 minutes ago, jabbr said:

Heisenberg and Einstein et al. didn’t merely each add an axiom to the prevailing rigid, formal system, they entirely ripped apart and completely reformulated our understanding of the nature of the universe. These were not mere single axioms rather created an entirely new framework that has led to a vast number of new empirically verifiable predictions.

 

You can’t even begin to understand modern physics from a rigid formal logic approach. Not to say that mathematical equations are not critical to the description but ultimately a Bayesian type if logic is appropriate and if you fail to see the difference between Bayesian and binary logic, there is no hope.

 

That said it is incredible that Maxwell’s equations have survived essentially unscathed through this enormous sea change in world view. 

 

The so called “rationalist” school of philosophy (which is as close to the pseudo philosophical objectivist school of audiophile philosophy) has only a historical importance for the reasons I’ve outlined above (Leibniz & Descartes were remarkable for their time)

 

There @wgscott  this here is not an Reducto al Hiedeggerian but cudos and I bow down for getting that reference — the reason I made it was that the Nazis rejected modern physics as “Jewish”, “relativistic” and thus not precise, and the story of Einstein’s difficulties securing an appropriate academic position can be read in his Biography. 

 

You're still missing the point. Formal systems include Bayesian logic, binary logic, all of mathematics, physics, pretty much all of sciences and all of logic. You seem intent on arguing about specific formal systems, while I'm talking about them all. I suggest that you read up on formal systems before you argue any further. None of your points contradict anything I've said, and yet it seems that you think that they do.

 

[pkane2001]

48 minutes ago, jabbr said:

 

Look are you just being deliberately difficult or just dense? http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf

 

Russell and then Hilbert attempted at the beginning of the 20th century. Your reactionary rationalism was a 19th century activity. You need to go through Godel before you even get to Quine before you could even address the issue. 

 

This type of argument is archaic.

 

As an exersize for your personal quest, why don't you present us with a formal proof using binary logic of  Schrödinger's_equation? Show us how useful this formal proof is. Can you do it? 

 

Math is useful because it allows us to safe build bridges. Math is useful because it allows us to describe the world as it is (physics). Physics doesn't derive from math, rather the other way around. Ask Newton. 

 

Formal systems are a tool. Sometimes a sunset over the water is just that. Sometime a song is just a song.

 

A formal system is a set of symbols, axioms, and derivation rules. This applies to math, physics, and logic. I'm confused as to what part of this you see as archaic. 

 

And no, I don't need to prove Schrödinger's equation, as it's already derived using standard inference rules from more primitive constructs.

 

[pkane2001]

30 minutes ago, Ralf11 said:

pkane - I am not sure what you are proposing, but no formal system or set of systems can describe reality completely, and all need empirical observations.

 

While fine on their own, they don't contain science.

 

I actually didn't propose anything worth discussing on audio forums  

 

It was just a passing comment about the physical universe being a formal system randomly deriving ever more complex statements from some basic primitives and a set of rules.

[pkane2001]

1 hour ago, Ralf11 said:

the fundamental question about the physical universe is why god had such a fetish for differential equations 

 

Don't blame god, I suspect it's completely our fault for picking the wrong formal system to describe the universe