Harv: "Your argument that mathematical law is true by its very nature doesn't even follow modern mathematics." Mario: I have very little doubt of that, I'm just speaking from my personal thoughts here, very little research or training I'm afraid. Of course a theorem is not true "by its nature," (all theorems and relations, though, exist as consequences of basic mathematical truth) but I am arguing that the basic axioms of mathemetics do not require an external source to be true.
What to you mean by true? What I'm saying is that if an axiom exists because it is true (inherently or due to some external source), then truth is not human conceived, but rather is a conceptual structure that has ontological existence. If a conceptual structure has existence, then what are its properties? Of course, we might have no idea, but we do have philosophical theories of truth (e.g., correspondence theories, etc), and I see no reason why we cannot use those theories as a guide to understand the conceptual structure of truth that exists. Since all the theories I know of are language based (i.e., language somehow must refer to a state of affairs), therefore the conceptual structure of truth requires some kind of cognitive property in order to fit our current understanding of truth. In other words, this conceptual structure appears to be Mind, and that can only be God.
Harv: "it presents overriding philosophical problems by trying to remove all of these concepts." Mario: Please be patient with me. :) Why would a self sustaining materialist universe eliminate the possibility of causation? Moreover, why would an external source permit it?
If I ask a physicist why a material thing (e.g., quark) does what it does, the answer would probably be a description of a physical law that they would say describes the actions of quarks. That's all fine and good for science, but when dealing with the actual ontology, we have to ask why a quark would follow a particular physical law. Why is it not permitted to act and behave as an electron (lepton)? Well, this is metaphysics. You cannot say in science if there are metaphysical laws that exist which limit the behavior of a quark, or whether the physical laws are only descriptions of behavior. For the physicist, this is outside of physics.
If we ask the question to a materialist, then the philosophy of the materialist is that there can be no metaphysical laws, everthing in the universe is material. Laws are only descriptive, they are not normative (i.e., they describe and control physical objects). That raises the problem for the materialist, if metaphysical laws do not exist, then how do you explain causation. Causation is not physical, it is metaphysical based on the ontological existence of causal relations. A materialist should not say that A and B causes C, since this assumes there is some outside causal relation (i.e., logical order) that treats A as a premise, B as a premise, and A and B causing C as a conclusion. However, if there is no outside logical order, then all you have are statistical correlations of an ensemble state A and ensemble state B which is statistically correlated with ensemble state C.
Therefore, if all there is just an infinite material universe, then the entire infinite chain is just an ensemble of states that exist. Since we are talking about infinite, we have to look at each 'moment' in time as member of an infinite set. That is, if we treat the infinite universe from our perspective, then you would never be able to reach an infinite future since you can't count to infinity. However, if you treat the universe as an infinite set composed of 'moments' (or infinitestimal moments, if you prefer), then you can just say that this infinite set just exists for no reason. However, what about the member relation of the 'moments' in this set. It is random. That is, there is no reason to treat consecutive ordering of the infinite set (e.g., 1,2,3,4,...) as preferable to a non-consecutive ordering (1,4,2,3...). If the infinite set exists as a matter of random luck, then you have a very small chance of having an consecutive ordering of the 'moment' members. This contradicts our observation of the world since we see consecutive ordering (e.g., evolutionary theory), and it would seem very improbable for such a universe to exist from pure randomn luck alone. But, this is what a materialist view would have you conclude.
This is not the case for a universe having a logical order that exists. A logical order is due to its axioms. The axioms exist because they are true. And truth and causality are inseparable (you can't talk about truth without talking about logical causal relations, and you can't talk about causality without talking about truth). Hence, the only thing that you have to justify as your primitive is just the logical order itself. The things that exist because of that logical order are 'caused' from a much simpler state, so you have to concern yourself with some basic state of the universe.
Now, I did say that this 'basic state' includes intelligence and consciousness, which is anything but trivial since it took our universe 13.7 billion years to produce us (of course, there might be intelligent life that evolved sooner than us), but suffice to say this is not a trivial matter to say it is primitive and less complex than an infinite universe - even one that has an amazing ordering to it that appears consecutive (i.e., apparent cause between events).
This is easily solvable. Let me solve it by asking you to think of one of those kitchen dish pans that you use to wash dishes. Imagine if we fill the dish pan with water, and stick a nail in a very unlikely spot in bottom of the dish pan (you can decide what is an unlikely spot). Now, if you performed the experiment properly, you will see that water will leak from that unlikely hole (don't ask me to pay for your dish pan...).
In a very similar manner, you can imagine the nature of truth being like this. Whatever 'spot' in reality that leaked water (i.e., where existence of something rather than nothing was possible), came gushing out. Of course, it's much more complicated since any explanation such as how the world took on its particular logical order requires that we consider logic to make that assessment (which is the very thing we are trying to explain). Nonetheless, you cannot apply this same reasoning to a material-based infinite chain since no logical order exists. A material solution can go no further than saying we are here, since any other reason is a non-material reason - which conflicts with the materialist premise.
A platonist such as myself is not limited to such a materialist perspective, so I can say that a logical order exists which is at the pinnacle of reality (heaven, if you wish).
Harv: "Why is a causeless infinite chain that just 'exists' just as legitimate as a simple truth tree that 'starts off' with a question (namely, "what is truth?") In the first case you have everything in the world that has no explanation " Mario: Yes, but your simple truth tree would have no explanation either, or am I missing something? If we include everything that has, or will, or caused something else to exist, or exists as a source or a fundamental set of axioms, I cannot see how you can avoid the problem of being left finally with an infinite chain of causation, or left with a causeless causer. That's not to discredit the idea of the Unmoved Mover, mind you, but just to tentatively establish other ideas as equally philosophically valid. Of course, this is just me talking.
Since the universes that proceed forth from there being a logical-truth order, I don't have to consider the universes as 'uncaused'. As for the logical-truth order itself, technically I don't have to say it is 'uncaused'. The reason is that cause does not need a cause, just like logic doesn't need a logic for being logical. However, if such was needed, I can provide one by my dish pan leaking water analogy. If you need a cause, then the cause for this particular logical order (versus the others that might be trivial and self-contradictory) is that those others, if they exist, do not produce anything - at least anything that we know of. The 'hole' in the dish pan (reality) that our water (Universe including God) came from, came gushing out of a 'hole' that necessitated the mathematical and logical order that we see evident. Perhaps there is a larger logic of reality that does allow for other 'holes' that has logic operating in the world that we cannot even conceive, or, perhaps, there are no other holes. Perhaps the logical order in our universe is just as I said, logic does not a logic for being logical. It is the top of the chain of what makes causation a valid concept, it doesn't need to justify itself.
Again, none of these options are available to the materialist. The materialist cannot justify the existence of matter. It's hard for them, I think, to justify virtual particles and my arguments with them were very interesting. They deny 'virtual particles' as real. And, of course, there's papers on LANL which talk about QED without virtual particles. Maybe that's the case, I don't know. But, you see, science is starting to have a say about this issue.