Immanuel Can wrote:wtf wrote:What does "causes are actual" mean? You have evidence for that claim? Or even an interpretation of the words that makes the statement sensible?
Ah. I thought so. I figured out afterward that you were unfamiliar with the phrase "actual infinite." My apologies...I thought you were aware of the term. I'll explain.
Aren't you the clever one. You use the phrase "causes are actual," and I ask what that means, and you talk about actual infinity. But that's not the meaning you intended originally nor does it respond to my question.
Are you being disingenuous? Or just not even understanding the words you wrote? What on earth does "causes are actual" have to do with Aristotle's distinction between potential and actual infinity? Which, by the way, I referred to in an earlier post. I'd complain that you didn't read my post, but I'm not even sure you read your own.
I ask again: What does "causes are actual" mean?
Immanuel Can wrote:
A "conceptual" infinite is one that doesn't really exist but can be imagined to exist. Take pi, for example: it can be thought about, but cannot actually be calculated. Nobody has ever seen all the digits in pi, and because it's infinite, nobody ever will. But we can think about the idea of pi.
Now that's funny, because it shows that you haven't got a clue about actual versus potential infinity.
The digits of pi as they are understood in modern math is an actual infinity. That is, there is a function that inputs a counting number 1, 2, 3, ... and outputs the first, second, third, etc. digit of pi. That's an
actual infinity. The idea that we have a function that consists of ALL the order pairs (n, n-th digit of pi) is exactly the content of the Axiom of Infinity, which says that there is (in math) a completed infinity.
An example of potential infinity is the denial of the Axiom of Infinity. So we can have 1, and 2, and 3, and in fact all of the natural numbers, without having a completed set of them. That's potential infinity. It's not often encountered in math since the Axiom of Infinity is one of the standard axioms. But it's possible to do parts math without it.
Immanuel Can wrote:
In contrast, an "actual" infinite is one that actually exists in the real world.
No this has nothing at all to do with the real world. The distinction between potential and actual (or completed) infinity is the distinction between the
collection of natural numbers 1, 2, 3, ... and the
set of natural numbers. To call them a set says that we have them existing all at once; whereas to deny the Axiom of Infinity says that we have them one at a time but never all at once.
In other words both potential and actual infinity are conceptual entities. Nothing at all is being said about the real world.
Immanuel Can wrote:
Such a thing cannot happen. A "causal regress" is a combination of real-world causality and an infinite timespan. That combination is just not possible, because each "cause" must happen before the next one does.
No that's not true either. I already showed you an example (the integers) where you can have an infinite causal regress yet no infinie timespan between any two points. Pick any two integers. Their difference is finite. You are missing this essential feature of this model of causality. There is infinite regress, no first cause, and only a finite interval of time between any two events.
Immanuel Can wrote:
Science. Science believes in causal explanations for every event that has a beginning.
Ken has already posted a good refutation of that point. Physics isn't about causes. It's about descriptive models that describe experiments. This is especially true in modern physics. But it was true in Newton's time too. Newton understood that his law of gravity was descriptive and not explanatory. Newton knew that he had no idea what caused gravity; only that his famous equation described it. You should read up on this point. You are misunderstanding science.
Immanuel Can wrote:
In other words, it assumes that things never "just start to happen for no reason." If we do believe such things happen, we are believers in magic, not science. Science looks for causality. If it finds none, it cannot get any grip on the thing in question, because it has to answer "why." If there is no causality, there is no "why" to ask about.
Newton EXPLICITLY rejected your point.
https://en.wikipedia.org/wiki/Hypotheses_non_fingo
He was challenged by critics saying that his theory of gravity DESCRIBED but did not EXPLAIN gravity. In fact Descartes at the time had a competing theory, his theory of vortices, that suggested a specific mechanism -- a cause -- for gravity. Newton was asked, "If Descartes has a cause for gravity, why don't you?"
Newton very clearly explained that science does NOT deal in causes, only in descriptions. He said he does not "frame hypotheses." He only describes observable phenomena. This is a very famous incident. It shows that Newton well understood that science does not deal in causes, only in descriptions and mathematical models.
Newton's language is so clear and modern on this point that it deserves repeating here.
Isaac Newton wrote:
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy.
"I have not as yet been able to discover the reason ...."
Please, give that some consideration. The greatest scientific genius who ever lived explained that he had no idea what causes gravity. Only that he could describe how it behaves. Newton did not believe in "causes" that were metaphysical or based on occult qualities. He only knew what he could observe, measure, and describe. That is science.
Immanuel Can wrote:
Fortunately for science that hasn't happened yet, so far as we know. There are things for which science does not yet know a cause; but in every case where it has assumed causality and then pursued it to an answer, it has found it. So science itself depends on causality.
On the contrary, science has no idea of the cause of anything. Science only has mathematical models that agree, up to the limits of measurement technology, with the results of experiments. Science is descriptive and not explanatory. If you are interested in the philosophy of science, as you seem to be, you should try to understand this point. Why does stuff fall down? Gravity. What is gravity? It's a distortion in spacetime caused by matter. Why does matter distort spacetime? Higgs boson. Why are there Higgs bosons? Nobody knows.
Nobody knows what "causes" gravity. We only have increasingly better mathematical models that fit increasingly sophisticated experiments.
You should reflect on these matters. Causality is a philosophical assumption. Science is about building mathematical models that describe observations.
Immanuel Can wrote:
Science does have assumptions, and causality is one of them. But causality is a very secure one. We know of nothing that has started to happen that did so without a cause.
That's a philosophical position. An opinion. And it's got no place in modern physics. Spontaneous symmetry breaking. Particles appearing out of the nothingness of quantum foam. In modern physics all kinds of things just seem to happen without cause.
Immanuel Can wrote:
wtf wrote:You're name-checking Hilbert? Please supply specific citations in support of whatever it is you are trying to say.
Google "David Hilbert mathematician," if you wish more.
Oh my. You name-checked Hilbert. Name-checking means that you dropped Hilbert's name into the conversation to try to impress people, but in fact the only thing you know about Hilbert is his name
Let's stipulate that I know who David Hilbert is.
I am asking you to tell me which quote, opinion, paper, or position of Hilbert's specifically supports whatever point you are trying to make.