Keeping uncertainty at arm's length

[Stephen Tashi]

It seems self-evident that mathematics must keep uncertainty at arms length. For example, to deal with probability mathematics establishes a set of assumptions. The assumptions themselves are not probabilistic - i.e. the "laws" of probability are assumed to be true "all the time", not randomly true or false. As another example, consider multi-valued logics. As far as I can tell when people reason about a system of "multi-valued" logic they use ordinary logie - i.e. they prove thing about it in terms of statements that are assumed to be one of "true" or "false". So the basic framework for conducting mathematics is "classical". If it wants to deal with a a type of uncertainty, it assumes there are statements about the uncertainty that are themselves certainly true.

Mathematics can (traditionally) be discussed without discussing the mathematicians who are doing it. But in physics, the physicist might acknowledge himself as a physical system. Is there any sort of paradox or inherent limitation when physicists trying to discuss uncertainty in nature? They use mathematics, so the discussion takes place as if it were implemented by a "classical" physical system.

(I suppose an abstract mathematical paradox wouldn't disturb physicists. This is more a question of whether a mathematician could get agitated about what physicists do.)

 

[Greg Bernhardt]

I'm sorry you are not finding responses at the moment. Is there any additional information you can share with us?

 

[Stephen Tashi]

I thought this topic was too philosophical for "General Math", so it was posted to "General Discussions".

Can we study uncertainty in the physical world in any way except by using a "classical" system of mathematics - meaning the ordinary type of mathematics where logic is boolean, not "mulit-valued" and the asumptions are assumed to be true "with certainty".

For that mater, can we study multi-valued logic or various abstrations of uncertainty (probability, fuzzy sets, theories of evidence) in any way except by forcing them into a classical framework?

I'd expect the average mathematician to think "Of course not". I tend to agree. However, it would be interesting to hear dissent from someone who has more imagination that I have.

In the first post, my spelling should have been "logic" instead of "logie".