# Nothing is Impossible

A disproof is sometimes more interesting than a long and repetitive argument, or even a dubious proof...

I wonder though if it can be valid if we create some restrictions? Ie. No statement that relates to reality can be impossible? ie. allow impossibility for purely internal ideas... Or is the problem still there?

Originally posted by FZ+
A disproof is sometimes more interesting than a long and repetitive argument, or even a dubious proof...

I wonder though if it can be valid if we create some restrictions? Ie. No statement that relates to reality can be impossible? ie. allow impossibility for purely internal ideas... Or is the problem still there?
Yeah, there's still a problem. You are saying that the new proposition is, "No statement that relates to external reality can be impossible", right? If so, then the problem is now the fact that you are making a statement about statements about external reality. I think (though I'm not positive) that this runs into Russel's paradox.

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by FZ+
ahrkron: I see. So you say that impossibilities exist as they are defined to be impossible? Does this then neccessarily have relation to impossibilities in reality then?
Yes. The tautology (x OR ~x) is always true by construction.

As a concrete example:

x="The light is on".

So the compound statement is:

"The light is on or it is not the case that the light is on."

or, more colloquially,

"The light is on or the light is off."

That is true, regardless of whether the light is on or not. So negating it creates a false statement, again independent of whether the light is actually on.

Originally posted by FZ+
A disproof is sometimes more interesting than a long and repetitive argument, or even a dubious proof...

I wonder though if it can be valid if we create some restrictions? Ie. No statement that relates to reality can be impossible? ie. allow impossibility for purely internal ideas... Or is the problem still there?
Again, the restrictions you can put on it is called multi-value logic and semantics. Rather than settling for true or false, you expand upon the values of a logical system by adding new catagories like the "Indeterminate" or you resort to the pragmatic semantics of natural language. These two approaches are steadily converging as we speak towards a more global rational understanding of both the physical and linguistic realms at the very least.

In other words, cutting edge philosophy today is coverging on this problem and either logisticians, mathematicians, computer scientists, or physicists will beat them to the punch or not. What has emerged in the process is that the more profoundly spare Asian philosophies have become of interest to national defense industries among others. What we don't know is of more keen interest sometimes than what we do know.