Maggie's Farm

Math is not the basis for logic or reason, in fact you have it backward, logic and reason are the basis for math, or at least two of them

Attempts to reduce logic to pure mathematics have in the end always failed.

No, I meant that in a technical sense.

Logic, the "science" of correct reasoning (and here science is meant in an older sense), is rather different from the broader "reasoning" you are talking about here, where rhetoric and moral valuations, metaphysics or general philosophic issues and modalities may obtain. These sort of "conclusions" that lead to "beliefs" involve other considerations than formal logic.

Thus, it is not strictly truth that " It is quite easy to reason yourself into a false belief.". In a strictly formal logical sense this is not true at all. Again, logic is not concerned with "beliefs" or even meaning, but with clearly stating and logical proving propositions, etc. Certainly, higher level discussions of ethics or other philosophical issues, or even religious issues employ logic, but other factors come into play as well. The point here is that "logic" in and of itself is unambiguous in these discussions. statements are either logical true or not, and we know why they are so in either case.

This is the problem of conflating the discipline of "logic" with the colloquial notion of its application. When we say "your logic is different than mine", we do not really mean that both "logics" are valid from a formal point of view, because they cannot be fi they reach radically differnt conclusions. What we mean is the other factors come into play, such as assumptions about values, tactic assumptions, rhetorical approaches (false metaphors, etc), and etc. This is something we run into all the time in politics, for example.

Likewise, it is quite possible to develop mathematical systems that have nothing whatsoever to do with "reality", and yet they are quite mathematical valid. Moreover, it possible to use math is such a way to confound the "mathematical logic" under consideration with the conclusions. In both of these cases, Statistics, and all the scientism and pseudo-science that can crop up around it, comes to mind.

So it is quite possible to "reach" false beliefs "employing mathematical logic" in a practical sense, if you are willing to be a sloppy about what "mathematical logic" actually is. We see this all the time in the "soft sciences" such as Political science, Sociology of Psychology.

Beyond that, when i said that attempts to make logic as subset of mathematics--the idea that math is the root of logic--I again meant this is a formal, technical sense. I was talking about people like whitehead, or, in other areas, people like Quine or Wittgenstein--and then there is always Godel.

None of these attempts is a formal sense were successful, and for various reasons.


Of course, there is a lot of debate about this, particularly in the area of proofs, but I would say from a formal POV, mathematics uses a subset of logic, which is reasonable given that it is dealing with a smaller "solution space" if you will.

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In my mind this why attempts as "computational logic" (which is an attempt to automate formal logic)so often fall short. We can come up with systems that are reasonable in lower order logic, but as we add higher levels, these systems fall apart.

This may seem like nitpicking but it is not really any such thing. We need to be clear about what we mean.