Varities of proof

Metaphysics & Epistemology
1

We tend to think of proof as making a statement undeniable, or unquestionably reaching a conclusion. Disproof likewise.

Typical proofs found in metaphysics:

  • (∃) existential proof: show the evidence, point it (the extant) out
  • (∀) disproof of universal assertion: show a counterexample

Proofs are commonplace in mathematics and logic. Deduction and contradiction:

  • (⇒) prove, or deduce, a conclusion
  • (:high_voltage:) self-contradiction, or inconsistency, is disproof

Arguably, (∃) is the most common or generally most relevant in life. It’s how toddlers show parents the monsters under their beds. Figuring out what something is exactly is another matter than merely that something is (∃), though.

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Mathematics is axiomatic (or has been axiomatized). We could think of deduction (⇒) as truth-preserving reasoning.

Proof can also be thought of as a kind of justification, but not vice versa.

My own interest here is what other kinds of proofs there may be, in the sense above. What say you?

2

I’m afraid logic hasn’t attained the level of poetry. In poetry we can have a signature, a particular style. In logic no. Perhaps one day we could talk of logic like we talk of someone singing like Mariah Carey. I hope and I hope but I hear hoping ultimately leads to doping. :grinning_cat_with_smiling_eyes:

3

I think deduction is just reliable reasoning, isn’t it? When the premises are correct and well-formed, the conclusion(s) it leads us to may be relied upon. They are logically correct.

Unfortunately, deduction is not always applicable, for all kinds of reasons. Then we have to use something less certain and less reliable instead. Such is life. :wink:

4

There is no other Proof but the mathematical and logical proof. Science itself never claims proof of cure: rather it’s an overwhelming agreement within the scientific community with a large data of support that something is highly effective, or with a high degree of certainty.

i.e. There is no proof that the big bang had occurred.

5

I wanted to include common/ordinary metaphysics; it makes the quest more interesting anyway.

An example of (∀) could be the old “All swans are white” thing. It seemed reasonable back then among those people talking about white swans, I suppose, until a counterexample was found ≈ 1700 (dam Aussieland :grin:). So, the original assertion was disproved, whether reasonable or not.