They’re abstract because they are abstractions (literally speaking; they are abstracted out from our concepts or ideas of any particular concrete objects). But they absolutely are about reality. They were in large part designed to describe and investigate reality, and they yield objective, necessary truth.
I agree that our notions of cause and effect are first learned from our own experience of being causes. But we don’t need to bring everything back to that to be able to make sense of it. That would be like saying in order to understand lightning, we have to first imagine ourselves as clouds.
Most mathematicians will tell you that mathematics is not about reality.
The mathematician Kronecker famously said “God gave us the natural numbers; all else is the work of man.” Personally, I think he gave God too much credit there.
We understand lightning because we observe it, we can experiment with it and we can see lightning storms forming. By contrast, we have never seen a universe form. We observe our own universe only in a very limited way from the inside. So we have no idea of what it could mean to cause a universe.
At the risk of sounding childish, I’m just going to retort with “yes, they are,” since you didn’t reply to my reason for saying they are (they were in part designed to describe and investigate reality, and they yield objective truth) except with the quote from Kroenecker, which doesn’t contradict what I said.
And by the way, I agree that mathematics is a human invention, but also I have heard many mathematicians describe mathematical truth as something discovered, not invented. And the reason for this is that certain things follow logically from mathematical axioms of necessity; they couldn’t possibly turn out differently. And when we use math and logic to describe reality, we find such abstract implications borne out in a concrete way. Hence my claim that math and logic yield objective, necessary truth, that they are about reality, and that they are in fact a fundamental feature of reality (since anyone in any possible reality would find the same logical implications starting from the same axioms).
I think you are confusing understanding how something could cause a universe with understand what it means for something to be the cause of the universe. The former, I agree, is far beyond anything in our experience. That doesn’t say anything about the latter. The latter is simple. For a thing to be a cause of the universe means that the universe would not exist without the activity of that thing, even if we cannot understand the details of the activity.
To give an analogy: someone unschooled in biology may have no idea how drinking alcohol gets you drunk. But they can still understand what one means by “drinking alcohol makes you get drunk”.
P.s. on my last couple of posts, my apologies if anything I’m writing here comes across as arrogant or “you don’t know what you’re talking about” or such. That is not my intent. I recognize that you are a mathematician and that me making claims about math, to you, may be a bit presumptuous. (That being said, I still think my claims are true!)
I was expressing an opinion. I did not expect to be able to give a convincing proof. My opinion expressed what I, and most mathematicians, see as trivially obvious.
Yes, I omitted commenting on your reason, because I did not want to seem rude by pointing out that you did not say anything persuasive.
We invent axiom systems. And then we discover truths about those axiom systems. That, at least, is how most mathematicians would look at it.
Yes, some mathematicians also say that the axioms themselves are true. It’s mostly mathematical Platonists who say that. But I’m not a mathematical Platonist. I’m a fictionalist.
We don’t actually do that. We construct mathematical models of aspects of reality. But those models are idealizations. They are not exact descriptions. We then use mathematics and logic to describe our models. But since the models are not exact, we aren’t actually describing reality.
Nor am I, in fact. Though I lean towards figuralism over fictionalism regarding abstract objects.
That… sounds to me like describing reality, albeit inexactly. And I mean, if physicists can calculate the anomalous magnetic moment of the electron to however crazy many decimal places it is… how exact do we need to be?
The view from cosmologists, as I understand it, is that time may have had a beginning. That’s not quite the same thing as the universe having a beginning. For myself, I’m inclined to suspect that the cosmos may be far odder place than what we take it to be.
Or maybe all of space and matter, energy and time did have a true beginning, and maybe God created it. Then maybe you would be guilty of a fallacy of incredulity (and maybe also a scientism of the gaps fallacy), “I cannot imagine and/or refuse to believe that God was the Beginner, so something else has to be true.”