Well, we do persist in disagreeing on some points, but I think we're on the same page in others. Let's start with where we're a distance apart.
Quite simply there is no methodology within science that allows for a first cause.
This seems manifestly untrue to me. I understand your resistance to the idea of "first cause," because it can proceed from personal motivations, or from the unnecessary anxiety that the idea of God may somehow undermine science (though I think historically the situation is quite opposite). But what's manifestly incorrect, in my view, is the idea that "first cause" is somehow "unscientific."
Science clearly favours causes of all kinds. Furthermore, it depends on sequentiality and the concept of time (this happened,
then that happened, and did so repeatedly and under varying conditions, therefore hypothetically, this
caused that). Since science requires causality and depends on time, how can it evade the concept of first cause, save by positing that impossible idea of an eternal universe?
I don't see Hibert's work in relation to infinities as being relevant to this discussion. Unless you can convince me otherwise.
May I try? Hilbert shows that when we attempt to apply real conditions, empirical conditions, to the concept of infinity we instantly get unmeasurable nonsense, like hotels that are simultaneously infinitely full but can contain an infinite string of new arrivals. The very conditions we depend upon to do science, such as objects occupying particular space, fall apart at infinity. So positing infinity as the start-condition of the universe is merely to posit, literally "non-sense": nothing of which we, or science, can make sense.
I have already argued as to why this is not the case. Would you like me to go over it again?
Not necessary. See Hilbert. But as a matter of fact, I was actually strengthening your point for you, accepting that you needed no additional support for it, since the burden of proof is in science's favour there. I was conceding that science does not need to defend itself against something so irrational as infinite beginnings. I'm surprised you don't concur.
Now let's get to where we agree:
I would also agree. However, I have outlined this problem above. It is all very well for us to agree, but can we come up with a way of bridging the two ontologies? No, not at this stage of our understanding. Pseudo-science has definitely NOT bridged this gap.
Again, I would suggest there is but one "ontology": but indeed, there are two problems -- they are articulated in the fact/value divide. In a world composed entirely of empirical facts, how does one suddenly import a conception like value? That is Hume's question, actually. There are no resources in science to perform the alchemy of turning a fact into a value.
I have read Nagel's book and I agree with what he is saying.
As have I. And I like most of what he says. But like you, my hesitancy came with his conclusions. They seem to me entirely discordant with his hard-headed factuality earlier on, and smack of utopian dreaming. I see you felt the same about that, since you see the "gap" too.
So, ok, how do we bridge the gap? As I said, no one has been able to provide a credible theory, least of all Nagel. The bottom line is that to date no one has been able to do this.
Well, if Hume is right, we're barking up the wrong tree. We're expecting to derive values from empirical observations. And though we cannot generate them now, we keep hoping that additional empirical observations will somehow create legitimations for value judgments. Yet historically, as Hume knew, this has never been the case; and we have no reason to think it will now.
A different kind of
modus operandi is required, I suggest. Science can tell us what is the case: it cannot tell us why we should care, or what we should or should not do with our knowledge, or even that we ought to continue to exist. Nagel's indictments are quite accurate there, I think. Something else is needed.
But is it possible that our failing is asking science to do too much for us? Is it possible that science is a truly excellent tool, but one that is simply not adapted to working on any questions of value? Are we trying to use a hammer to install screws there? Would we be best to accept science as excellent for its purposes but incapable of helping us with value questions? And in continually looking to science to do what it simply does not try to do, and cannot do, are we in danger of creating pseudosciences-of-value like Marxism, Social Darwinism or Nazism?
Clearly we must not operate contrary to good science in avoiding such outcomes. If science yields us a result, and that result is reliable, we must accept it. But, on the other hand, why should our need for existential values permit us to mangle science by making it yield them to us? Maybe we can give science its rightful place, but still look to other rational ways of knowing to help us with values. I seen no likelihood that anything good will come out of persisting to imagine we'll eventually get science to create them for us.