Mathematica Does the demand on no mathematical contradiction fix our world?

[naunzer]

Consider the following:
Postulate as FEW as possible things that seem to be necessary to make (intelligent) life possible, e.g. causality (one should be able to kill one's dad) at least at "large" scales,...?...
Let there be mathematical logic and demand that all laws of nature can be written in a mathematical language and further demand that no mathematical contradictions MUST arise in these laws.

Do you think that it is possible to get a universe as ours just out of this?

That means e.g., it turns out that one has to have just one time dimension
and let's say exactly 3 space dimensions (maybe this could have something to do with quaternions, for example; I don't claim that!)
or
that there have to be exactly 3 lepton generations as we currently observe
or ...

If you think it is a possible way, where would then God be?

 

[eighth man]

Non contradiction is an aesthetical choice. There is really nothing deep or fundamental about non-contradicton! I actually think we should embrace contradiction to further improve our research. CONTRADICTION IS A HIGHER FORM OF REASONING.

the ape

 

[quantumdude]

CONTRADICTION IS A HIGHER FORM OF REASONING.

I'm afraid you'll have to elaborate on that. It is my understanding that if you deny the excluded middle, then it is possible to prove anything. This would include proving both a statement and its negative. This would render the system completely useless, and you'd be hard pressed to convince anyone that this is a higher form of reasoning.

 

[arildno]

eighth man is possibly a Hegelian..

 

[quantumdude]

I don't see that as a problem. As I understand it, those who use dialectical logic would deny that logical variables are static (that is, they say that "A=A" is just an empty tautology, with no application to the real world). But I don't see a conflict with Hegel's logic and Aristotle's, if we recognize that logical variables are in general time dependent. That is, if we let A=A(t), then we can hold to both Hegel and Aristotle if we recognize that A(t₁)=A(t₁) always, while it is not true in general that A(t₁)=A(t₂).

 

[eighth man]

There must be contradiction somewhere in the universe at least in one point or time because contradicton generates every conceivable universe both in extent and conceptually. That is before the big bang there must have been a moment of "logical contradiction" where every conceivable thing is created.

From an artistic and metaphysical point of view, contradiction is useful in creating anything you want. You obviously won't use it for engineering (but if you are an extremist, you could use it there to, but I dont' suggest).

THE APE MEN

 

[arildno]

I don't see that as a problem. As I understand it, those who use dialectical logic would deny that logical variables are static (that is, they say that "A=A" is just an empty tautology, with no application to the real world). But I don't see a conflict with Hegel's logic and Aristotle's, if we recognize that logical variables are in general time dependent. That is, if we let A=A(t), then we can hold to both Hegel and Aristotle if we recognize that A(t₁)=A(t₁) always, while it is not true in general that A(t₁)=A(t₂).

An excellent interpretation!
Occasionally, Hegel managed to retain that notion (in particular in the "Phanomenologie des Geistes"), but in his later works (particularly, "Die Wissenschaft der Logik") is rather muddled on these issues.