john doran said:
1a) “everything that begins to exist has a cause” is not negative.
Yes, see my edit. Prove that “everything that begins to exist has a cause”. Or prove that nothing that began to exist is not uncaused.
1b) the causal assumption is at logical rock-bottom when it comes to “proof”. just like the principle of non-contradiction. just like the existence of the real world. just like the existence of the past. you can be as sure of it as you are of these other things.
Empirically, it is a justifiable assumption, because it seems to hold with the possible exceptions of what quantum physics seems to say and the universe as such. To you, a foundational belief.
if you reject this assumption, then we’ve gone as far as we can go.
Indeed.
- well, current cosmology itself posits an initial singularity, so “the universe began to exist” is in keeping with modern science.
Science does not presume to speak absolute truth, only to model with a reasonable degree of accuracy. Theories are subject to change. Again, you consider 2 a foundational belief. In this case, the posited singularity only means that our current models break down at the initial point in time. Since time as we understand it loses meaning beyond the spatial and temporal boundaries of the observable universe, any statements about “events” “preceeding” “the beginning” of the universe seem like nothing but vague speculation. Yes, the universe could have been “created”, but whatever “happened” “then” is not something that brooks human argument.
but that is as may be. an infinite regress in causes and things caused is impossible because (A) an actual infinite cannot exist, and (B) even if it ***could ***, it couldn’t be completed by sucessive addition (i.e. by the addition of one thing after another, in series).
Isn’t the Christian god considered to be some kind of actual infinite? One that has unbounded attributes? Frankly, I have no idea what you mean with an “actual infinite”. An object of infinite size, something existing for an infinite amount of time, an unbounded set in mathematics? On what authority do you make assumptions on something that preceeds the beginning of the universe (if there is a beginning)?
it may very well differ - what exactly is your understanding of “proving a negative”?
as far as i can tell, you have to hold either:
- “you cannot prove a negative” is not a negative; or
- no proof of the principle is required.
Our understanding is significantly different and I’m actually relieved to find that you were not intentionally obtuse. I understand proving a negative in the mathematical sense:
Demonstrate that no member M of an unbounded set S has property P.
You can readily satisfy yourself that given a particular definition of S, M, and P, you will have one of the following cases:
- the problem can be solved analytically:
1a) There is direct (mathematical) proof that no such M can exist. If S is the set of even numbers and P(M) is the property of M being an odd number, we’re done.
1b) There is a constructive or non-constructive (mathematical) proof that an M exists and the demonstration failed.
- If no formal analysis is possible, we have no choice but to test exhaustively.
2a) If the set S is not recursively enumerable, we have a problem. How do you exhaustively test a property for e.g. all real numbers?
2b) If S is recursively enumerable, we may find an M that satisfies P - a counterexample, and the demonstration failed.
2c) Otherwise, if indeed no M exists that does not exhibit property P, we will continue to test indefinitely.
Actually, even this leaves plenty of unstated assumptions. If you don’t consider it frivolous to ask to prove a negative in this sense, tthen we should agree to disagree and leave it at that.