Is the Empirical Nature of Mathematics and Logic the Key to Understanding Truth?

[HallsofIvy]

Please do not "hi-jack" other peoples threads to tout your own pet non-sense. You have posted this same thing on two of you own threads- I don't mind that so much but don't try to take over other peoplkes threads.

 

[selfAdjoint]

Shorter Ryskamp:

Can't do relativity in economics, so much for relativity.

I like Sraffa better than Keynes, so much for Keynes.

We in the 21st century are ever so much sharper than the big names of the 20th century, so much for them.

I have a thought on Einstein's relativity which is so confused it shows I don't understand Einstein. So much for me!

I am going to keep posting this same megillah until I cover the face of the earth.

 

[Philocrat]

There is no absolute truth in mathematics and logics. There are many consistent mathematical systems, consistent in the sense that they are not breaking the basic rules. But there is no absolute way of knowing that the basic rules are true. And there are limitless basic rules that can be chosen. Different basic rules gives different systems, like the intuitionist logic,predicate logic or fuzzy logic.

So why then is mathematics/logic interesting and why are some systems studied instead of others? I would argue it is because mathematics is empirical. There are some logical and mathematical systems that are more true than others. Those systems that more closely follow the real world are more true than others.

So truth in mathematics is ultimately derived from physics. Those mathematics that gives physicists more accurate models are more true.

Yes, it is!

 

[CrankFan]

Yes, it is!

Right, so how do you derive from physics, the truth that $$\pi$$ is transcendental?

 

[honestrosewater]

Well, just to strengthen my point, do I understand correctly that the universe of discourse, x, is empty just in case $$[\exists x (Px)]$$ is false and $$[\forall x (Px)]$$ is true? BTW, I am not talking about the physical universe.

 

[CrankFan]

Well, just to strengthen my point, do I understand correctly that the universe of discourse, x, is empty just in case $$[\exists x (Px)]$$ is false and $$[\forall x (Px)]$$ is true? BTW, I am not talking about the physical universe.

In FOPL, the domain of discourse is non-empty, by definition. Have no idea what your point is.

 

[honestrosewater]

In FOPL, the domain of discourse is non-empty, by definition. Have no idea what your point is.

My question about the universe of discourse is the subject of another thread where comments about the physical universe and the applications of logic keep intruding. Now that the question is here, I'm hoping those irrelevant comments will follow it.

 

[CrankFan]

My question about the universe of discourse is the subject of another thread where comments about the physical universe and the applications of logic keep intruding. Now that the question is here, I'm hoping those irrelevant comments will follow it.

I see your initial post in that thread, and questions along the lines of: if the domain of discourse is empty, is this or that formula "true" (I think you meant, a theorem).

But before anyone can answer your question they need to know what kind of logic you're talking about. If you're talking about first order predicate logic (which seems to me to be a reasonable assumption) then the answer to your original question is: that case never arises. So there's no point in taking it any further.

 

[honestrosewater]

CrankFan, so as not to intrude here, my reply is here.

 

[Philocrat]

Right, so how do you derive from physics, the truth that $$\pi$$ is transcendental?

A Superior Logic or Mathematics is the one that CAN reconcile SEQUENTIALISM with SIMULTANEITY. The mariage between these two beasts is the very foundation or seat of reality. My prediction is that there is no logical or quantitative utterances that can transcend this spooky marriage. The fate of Logic or mathematics lies in the continual interplay of these beasts in the spooky marriage. If reality colapses so will the marriage along with its underlying sustaining quantitative and logical components! That mathematics or logic is empirically enliven is beyond dispute.

 

[Hurkyl]

All I have to say is