Deduction is used in a lot more than just the classes labeled "mathematics". Which makes one question just to what degree the mathematics classes are even useful. Perhaps deductive reasoning could've been taught to do more useful things than factoring polynomials.
Philosophy (at least in the Analytic tradition) involves a lot of deductive reasoning about non-mathematical things (the main difference from maths being that in maths everyone mostly agrees on the foundations, where in philosophy a lot of the reasoning is conditional: IF you believe X, Y, Z, then Q is also true).
Could you give an example of philosophers from the analytic tradition that actually build their arguments in an axiomatic way like many practices in mathematics try to? I feel like I've read more attacks on this very approach than actual examples of this approach (from both analytics folks and continental folks)
Classical logic is related to boolean logic, and has its uses.
But a lot of real world "logic" (decision theory, etc) is statistical in nature, often with a big inductive component and often based on "axioms" that only approximate the real world.
In other words, the field of Analytic Philosophy, when not using the proper amount of math and statistics (especially Bayesian statistics) tend to either lead to doubting everything (if they know what things they do not know) or drawing bad conclusions (if treating their axiomatic assumptions as absolute truths)
They have similar problems with science, and maybe Physics in particular, because of the abstraction of modern physics. By interpreting statements made by some physicist too literally, they may (falsely) end up with conclusions that go way beyond the domain of validity of the original statement.
Imho, Philosophy is fine as a side-project for people in academia, but I think philosphers who do not study math, science, psychology, etc at a level comparable to their philosophy work are at risk of ending up in lala-land.
I would estimate that if someone studies only philosophy in college, they will reach a point after about 1 year where their knowledge of philosophy come to a point that requires more understanding of math, science etc than they had when they started. Kind of like a physicist that doesn't take college level math.
I was referring to axioms when I used the term "foundations" above. Inference rules are largely agreed upon across both maths and philosophy (and they're the same ones in both disciplines).
I’ve heard people say things like, “The world is math”, but it never seemed particularly coherent to me. Sometimes I’d assume they meant, “Inference systems with mathematical languages make useful predictions about my empirical experience.”
But now I’m favoring the interpretation that experience is purely formal/syntactic with no semantic component. There is no additional meaning beyond (or behind) appearance.
There is a notion of meaning in that it encodes possibility. A situation with lots of future possibilities has meaning. A dead-end situation has little or no meaning: stagnation, death, ...
If the formal/syntactic appearance is how leads to new possibilities involving more formal/syntactic appearances, then that is its meaning.
Are you suggesting that some people hold the normative position, “One ought prefer situations with more possibilities to those with fewer, ceteris paribus.”
But isn’t that just some hidden metaphysical structure? That is, it’s unavailable as formal appearance?
