Logic as applied to the real world is just beliefs too; using probability for the math is a way to account for uncertainty, instead of rounding everything up or down to impossible standards of "true" or "false".

> Logic as applied to the real world is just beliefs too

I disagree. For example: how can humans operating on scientific principles so consistently stack hundreds of "just" beliefs on top of each other to achieve things like landing things on the moon, as just one very old example?

I suspect there is more to it....I believe that all beliefs are not equal, and I'll go even further: some beliefs are true, and some beliefs are not true.

> using probability for the math is a way to account for uncertainty

That "account for" has a different meaning than "perfectly resolve" seems highly relevant.

> instead of rounding everything up or down to impossible standards of "true" or "false"

Of the two of us, who is rounding things up or down to an artificial truth?