This post sat unfinished in my browser for about a week because of exams so I hadn't read your posts yet Orr. But lol.
Originally Posted by Oneironaut Zero
This is quite arbitrary, for even when there is 'nothing', there is space, and that is something. I'd like an example of 'nothingness', actually. Even in the vacuum of space, the vacuum is 'something.'
I don't personally think this has any meaning... or at least, any parts of it with meaning aren't really true. It's a common misconception that the universe is expanding, in the sense of a spherical object expanding, as we would understand it. Such a spherical object is three dimensional and is expanding into empty three dimensional space. This is not at all what the universe is doing. When physicists say the universe is expanding, they mean that it is becoming more rarefied; not increasing in size. The best way to explain this is to explain that physicists do not know exactly the geometry of the universe, but none of the hypotheses involve an 'edge' to the universe. Possible geometries include an infinite flat space, or a space like the surface of a sphere. The surface of a 3D sphere is essentially a 2D space. It has nothing to do with a 3D space; it does not exist within a 3D space. It is just a special kind of 2D space in which, if you go far enough in a line, you will come back to the same point (have the arcade game Asteroids in mind). When we talk about this space expanding, we don't mean that a sphere is expanding in 3D space, or that an infinite flat space is somehow getting larger; just that things in the 2D space are getting further apart (or in the case of our universe, which is 3D and thus would be the surface of a 4D sphere, just replace 2D with 3D and 3D with 4D). Another hopefully insightful remark is that the Big Bang occurred at every point in space, including inside this full stop. And this one. There wasn't a coordinate in space (which is now at some well defined point inside the universe) at which the Big Bang occurred and then the universe bubbled outward from it, that's completely the wrong picture.
So when we say that 'even if there was nothing, space would have to exist', this isn't true. It's just our human intuition, which is entirely built for modelling the flat 3D space we live in, being extended to domains in which it has no place. Reality is not contained in a space; the space is part of reality. That sphere could shrink to nothing, and there wouldn't be any space. Like I said, the sphere was not 'in space', it was the space. Or in the case of an infinite flat space, if the universe did not exist that space would simply cease to be. The space wasn't contained 'inside' another space. That is just how we are used to things working in our parochial little backwater of reality.
Highly doubt you're going to find a suitable answer for that here, for even if you find out why our universe exists, you'll have to find out why there was (likely) a universe before that; a universe before That; and the multiple universes that are (likely) existing around our own at this very moment.
See my first post. We have no right to claim as a categorical principle that universes can't simply come into existence, without anything happening 'before' them. Indeed, very much like the case of space, time is bound up with the fabric of our universe, so it's not clear to what extent this even has any meaning.
Originally Posted by Dianeva
I've heard you say this before and I'm not doubting that you have it right, but I've always had trouble understanding why and would really like to, since the conclusion is an important one. What is our ability to reason then? I can imagine that it might be explained in terms of patterns. For example, if someone tries out the rule "if all A's are B's, and all B's are C's, then all A's are C's" and finds that it often works out, then that person might take up that rule of reasoning, and so it would be gained through experience. But that isn't what it feels is happening in the brain. It seems that the ability to reason is not experience based at all, that all deduction breaks down to the law of identity and so the logical rules have to be true. We don't just assume that they're true based on experience.
It's a great question, and it's an important one, which I've considered.
The first thing I'd say is that I think that the scientific discoveries of the 1900s should basically destroy our trust in any principle not being deduced from experience but rather being in some way universal (tangentially, this is why I also mentioned Darwin; he made clear to us our relationship with reality, as natural rather than spiritual beings. In the naturalistic paradigm, the concept of a principle not deduced from nature begs the question 'then where on Earth did the organism obtain the principle'? What form would the thought take in the physical neurons of the brain?). Logic is very basic and intuitive, yes, but, in my opinion, no more so than the concepts which were clearly struck down by the aforementioned events. For instance, our understanding of space. Take the statement, 'given a line and a point above it, there is one line through that point which never touches the first'. Or our understanding of time, 'if two events are simultaneous for me, they are simultaneous for you'. Or identity and causality, 'an object has a state, and that state determines its behaviour'. Are these statements not all just as intuitive as the logical example you gave? And yet they are all false. They are great models of reality for the domains that we normally experience, but outside of that domain they fall to pieces.
You are correct in your prediction of how I think we come to know the axioms. I actually think it's kind of obvious that we go through such steps, at least at first. I think a good analogy is with numbers. Many people put numbers on the same level that you put logic. But what actually is a number (let's consider whole numbers to keep it simple)? The number three is the thing in common between three trees and three clouds and three deer. But the idea that such disparate things have some entity in common is actually quite a high level of abstraction, and it must have taken many millennia of human history to develop it. If you asked one of these pioneers what two plus two was, how would they have gone about it? I think it's obvious you can't work with the abstraction itself. So you have to go down to the level of the physical substrate of the abstraction, either playing it out in reality or in your head, putting two objects together and finding that there are four. It only feels 'obvious' to us now because we are so used to working with the abstraction. And an important thing to note is the scope of meaning of the concept; it requires universe in which there are discrete objects, in order to think of this generalisation. But what's a discrete object..? There's not really such a thing. Stuff just clumps together in our universe and we notice the pattern.
I think the same goes through for logical axioms. You have to ask what the axioms are actually 'about'. They can't exist without reference to something; they must delineate some limited portion of reality. In the case of 'A is a B and B is a C therefore A is a C', we again need to have some model of discrete entities, and also we need to be able to put these entities into sets according to some adjective or another. And what's an adjective..? It's a pattern. And again, this statement may seem 'intuitively obvious', but perhaps there are objects which break it which we've just never been exposed to. And what is the neural process which allows us to conclude that it is true? In the naturalistic interpretation there must be one. Well, it seems to me that it must have come from observation. We observed every single object ever, from the time of babies (another tangent: read about Piaget's studies of infants, who turn out to be woefully poor at understanding basic logical concepts), behaving in this way. And so we formed an abstraction and now don't need to refer to the physical substrate, because we're so accustomed to it. I imagine clumps of neurons in our brain form from repeated exposure to the same pattern and become entities in themselves. In fact these concepts are so fundamentally basic that they probably constitute the fundamental essence of our being. But they're still not a priori.
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