Wyman wrote:It's never a good sign in a discussion when one side constantly refers to outside authors...
In some cases, all it means is that there can be an explanation more intricate than can be handled in short posts. That should come as no surprise. But I'm pretty sure you'll see what I mean in the ensuing post.
Yes, we can understand infinity - at least in mathematics.
True only if by "understand" you mean "use as a theoretical construct." For example, we use
pi even though no person ever has or ever will calculate
pi, because it is infinite. Mathematicians do speak of "unreal numbers," values that serve within the self-referential condition of mathematics themselves, but which can have no empirical limits of calculation. That's routine. But it's also "unreal."
I don't know that there are actual infinities, but you don't know that there are not. Hilbert certainly didn't prove the latter, or even attempt to.
What he proved is that at the point of whatever infinity is, logic and science themselves break down, and we lose all ability to make any coherent empirical judgments. Impossible ideas, such as hotels that are infinitely empty and infinitely full at precisely the same time, become necessary. This undermines the very concepts themselves of "empty" and "full," so we can no longer speak intelligibly.
Material reality is linear and time-bound. It does not have the characteristics of infinity. I mentioned the 2nd Law of Thermodynamics, the Law of Entropy, which is probably THE most thoroughly-attested and predictable scientific law we have -- it shows linear decline, not infinite regress in the past. But you forgot to speak of that at all.
Science speaks very little, if at all, about causes. Descriptions of science (especially by philosophers) tend to use words like 'cause.'
It's not clear what you mean by this. Science doesn't "speak": scientists do. And they speak of practically nothing but cause-and-effect. They identify causes and posit effects, and that is fundamental to all scientific experimentation. If there are no causes-and-effects, there would be no science at all; so I can't sort out what you're trying to assert.
As for something I think of as proven, I'd take Einstein's set of assumptions and the theorems he deduced from them as a good example.
Eh? How does a "theorem" (or worse, an "assumption") suddenly turn into a fact? A "theorem" by definition, is a tentatively and provisionally advanced claim based on the available evidence, and lasts only as long as the available evidence does not increase. But as Kuhn argued, science moves forward in paradigms and undergoes "shifts" as more evidence becomes available. Even Geocentrism was a "theorem," and I'm pretty sure you're not standing on that one.
So what do you do with things like the EPR Paradox, that have come along since Einstein and indicated incompleteness in Special Relativity? Are you really absolutely certain (or do you consider it "proven," to use your wording) that science will end with Einstein in spite of such things as quantum entanglement? I'm certainly not.
But the system is still only as good as the assumptions.
Quite true.
Your assumption that there is a one finite causal chain going back to the 'beginning' is not self-evident.
Things aren't "self-evident" except within self-referential systems like maths. But it is evident that science itself will be impossible if it's not true, and we'll end up with no reliable predictions about phenomena at all. There is no coherent explanation on the assumption of an infinite universe, and the empirical data do not support that assumption.
What do I mean? Well, as an example, given the Law of Entropy, if the universe were infinitely old the entire thing would have gone into eternal heat-death long ago. How long ago? Actually an infinite amount of time ago. Even were the Law of Entropy operating at a 1/1,000, 000 the speed it is, or operating in a slower-faster, jerky-jerky way (which looks empirically untrue anyway), the same thing would be true: for infinite time, plus ANY decay would have put the universe into heat-death an infinite amount of time ago, were it infinitely old. So it can't be.
If the universe is not infinitely old, then it had a beginning, and we're back to the Kalaam Argument and shortly after, to the Argument from Design, since coherent physical order is only possible within a rule-bound system, and the existence of Laws rather than chaos invites the positing of an Intelligent Designer rather than mere accident. And that's a fact conceded by all sides: for the positing of things like Infinite Universes and String Theory is done even by its' major proponents on the hope they might allow escape from the Kalaam and the Design Argument.
Now, do you really suppose that without referring to the literature we're going to parse all that I have said above, and do it on this forum? Personally, I'm not very optimistic.