Miracles

[DavidOdden]

How can you prove that you cannot defy the laws of nature without reasoning in a circle. Musn't it always come down to an assumption ? What am I missing here ?

I think it is "identifications". We do accept as axiomatic that existence is identity, so there's no attempt to independently prove "A is A". You have to identify "nature" -- nature isn't just "out in the woods". So correctly identify "nature", which is in fact "existence". Then the notion of "law of nature" has to be identified. A particular cow is not a "law of nature", but it exists so is "part of nature". "Law of nature" refers to a particular fact, an aspect of existence that you can focus on. It might be the law of gravity, or conservation of angular momentum, or a high-level concept like Boyle's Law. A law of nature is something that is true of everything that exists. And so on. (Sorry, I have only a few moments left tonight). Eventually you will get to the "cannot" part, which again simply requires you to correctly identify what "cannot" is. The ultimate conclusion is that "cannot defy the laws of nature" is an undeniable fact, and that "miracle" implies "denies the laws of nature".

[Greebo]

I disagree: the statement is not axiomatic. It can easily be reduced to the axiomatic, but requires reasoning involving hypotheticals, the concept of "law", identity and causality, what "defy" describes. The statement "you cannot defy the laws of nature" logically depends on "cannot", and "cannot" is not an axiomatic concept.

I suppose that depends on whether you consider:

A is A

Existence is Identity

You cannot defy the laws of nature

to be saying the same thing or not.

I think to us, saying "You cannot defy the laws of nature" is saying A is A.

[DavidOdden]

I think to us, saying "You cannot defy the laws of nature" is saying A is A.

The former reduces logically to the latter, but the do not have the same cognitive status. That's what makes "you cannot defy the laws of nature" a true but non-axiomatic statement.