(September 13, 2021 at 5:04 pm)Klorophyll Wrote:(September 13, 2021 at 4:49 pm)polymath257 Wrote: No, it is exactly the other way around: causality depends on the existence of natural laws.
That's just a claim. For the third time: do you have any reference of what's above.....??
(September 13, 2021 at 4:49 pm)polymath257 Wrote: I think you are wrong here. They describe the workings of the universe, but to say it is the 'inner' workings, you must assume there is something outside of the universe. That amounts to either a multiverse or some other universe, which must have its own physical laws.
The *ultimate* laws *cannot* be caused. That is because if they are caused, there is some law that describes the process of that causality, and *that* law would be more fundamental.
It doesn't follow that there is a law that describes causality. The word "law" is simply a label we put on have we describe repeatable phenomena around us, nothing tells us that are laws outside of the universe -assuming there is an outside.
And there is nothing logically incoherent about a lawless universe.
And in such a universe, there would be no causality.
Quote:(September 13, 2021 at 4:49 pm)polymath257 Wrote: A flawed argument also used by Craig. It fails because of a lack of understanding of the nature of infinity and the non-contradictory aspects of infinite regress.
Yes, I think an actual infinite regress is possible. There is nothing contradictory about an actual infinity (in spite of what Aristotle and Aquinas thought).
It's a bit more than actual infinite regress, you have to take into account the fact that we exist, that our universe as an element of this causal chain really happened. It means an infinite duration of time (or sequences of events) preceded it -impossible.
No, the universe is NOT an element of that causal chain. The causal chain happens *within* the universe.
And what makes it impossible to have an infinite sequence of events preceding something? it seems like a perfectly sensible thing to me.
Quote:So, the argument here is the impossibility of an eternal past, not infinite regress per se.
OK, what is impossible about an eternal past?
Quote:(September 13, 2021 at 4:49 pm)polymath257 Wrote: I'll answer. Noe of the above. it is also dependent on the assumptions of mathematics. Which rules of math actually apply to our universe can only be determined based on observation.
We apply the law of excluded middle for example, do we somehow observe this law in the universe...?
The proposition: "there are infinitely many prime numbers" is clearly of a different category than empirical propositons about the universe, it can't be falsified nor verified empirically.
Yes, we absolutely observe the law of excluded middle at the classical level *and* its violation at the quantum level. it is a matter of observation whether logic with the law of excluded middle is helpful or not. There are versions of logic without it and, for example, quantum logic is found to be useful.
As for the infinity of prime numbers, that is not subject to observational testing. But it is a purely mathematical result and thereby only has truth value subject to some axioms. The axioms we choose for math determine which results are valid in that formal system. Whether that formal system is useful for understanding the universe is then a matter of observation and testing.
I know of no physics results that depend on the statement that infinitely many primes exist. Of course, since that would be an *actual* infinity, I suspect that you also have issues with it being true in the universe.