> what then even is our value? Why exist at all, at that point?Well, what's the value of a chimpanzee (or their cousins the Bonobos)?
It surely can't just be their value to us, or we're left with the same problem (it's turtles all the way down).
The answer seems like it ought to be that any intrinsic value of a species (or genus, family, order, class, phylum, kingdom, domain, clade) lies in its generativity, or propensity to produce ever more complex and adaptive patterns of information over time.
> I don't know about other people, but I get my sense of purpose in believing that we're the captains of this Spaceship Earth, and that we're making progress towards something significant.
Hmm. There are two separate thoughts here. Let's take "progress towards something significant" first. Much (but not all) of what we see as "progress" is illusory. For example, a human is not "more evolved" than a slime mold, since both have just as much evolutionary history behind them. Similarly, whether a human actually is better adapted (or more adaptable), evolutionarily speaking is up for debate, as the time period we have data on is rather limited, and as a species humans still may kill themselves off (which slime molds are unlikely to do) sometime soon.
Now, all that being said, it is pretty clear that the human species has become a substrate for memetic evolution layered on top of, and in many cases hijacking, the feedback loops that genetic evolution has produced.
We don't yet have significant data on whether that adaptation is, in the long run, survival-oriented.
And now we can see the glimmers of yet another new type of replicator that will be layered on top of our culture, especially the parts we call science, technology, industry, etc.
We certainly can expect these new information patterns to hijack the evolution of our technology (and other parts of our culture) to some extent, as well as the layers below it.
Whether that obliterates the cultural, or even genetic, substrate from which it sprang is an open question.
If all this gives you existential heebie jeebies, I imagine that similar feelings were experienced by folks confronted with the evidence of heliocentrism, for example, demoting the Earth from it's privileged position as the center of the universe.
So, on to significance. We have no reason to think that we and our works are in fact at all special, at least in principle, except in the sense that we don't yet have any evidence of any other clades, much less ones that have budded off the equivalent of an intelligent, technological species.
So what? There is no reason that we should require the illusion of individual or collective significance in the greater scheme of things in order to function. There actually is no "greater scheme of things".
You ask, "what is our value?" the answer is that we have none (or none more than one of your cells has to you), except that which we create for ourselves and for our conspecifics. If the self-centered viewpoint isn't enough, consider a strictly utilitarian one: An adaptive pattern is of value simply because it does adapt, and co-opts more of the world into its own image (This is, in a sense, nothing more than the Anthropic Principle rejiggered). Those that have a symbiotic relationship with their underlying substrate (as opposed to parasitizing it) and also promote its long term survival are especially so.