“Miguel A.: I was confused by Leonard’s point.. his ‘truths’ about math are no truths, but rather mathematical postulates; assertions without proof.. not ‘truth’ ? Ultimately, when one asks, why is 2 + 2 = 4? One cannot offer a logical explanation, but… rather simply quantify a list of definitions that seem self-evident.. unless truth is just that: self-evident, outside the realm of logic and thought? What one can conclude from truth, or postulates, are the workings of reason.Which is why I asked Leonard, does he mean to say logic offers truth of any kind? Or does it offer valid thinking, a prescription of thought if you will, that allows for clarity and coherency… one can be logical, but not be truthful.
Truth, instead, should be aspired through logical means, but is ultimately revelatory and/or self-evident in some way or another.. unless I am all wrong about this? =P”
Nor are they simply conventional, for by their nature as laws we find them unchanging.
Also, they’re not simply absent-minded things. Mathematics makes patterns predictable. Numbers actually contain real information, yet they are not material ‘things’. Logical laws make understanding and information possible, yet they are not material ‘things’. You don’t go through nature and say ‘Alas, I’ve found the Law of Noncontradiction hiding beneath this Bush,’ or ‘Here is the number 4!’. Yet they are very much real, as they are actually used. Yet they are not simply human explanations.
For regardless of how we’d wish to define or explain them, they still are. And they still function consistently, perfectly, and absolutely. Yet this ‘they’ that we speak of, which surely exists as evident by their real usage, is no real physical ‘thing’, yet it is real none-the-less. By it being true, we mean to say that such truths are correct explanations of Reality (and by reality we’re speaking in totality, not just physical reality).
In other words, it is true to say the earth revolves around the sun. It is true to say 2+2=4. It is true to say something cannot contradict itself. These are all true things found in physical nature, or the mind/logic. Just as there are physical and logical laws, there are moral laws. It is true raping kids is wrong.
Some try to say all there is is physical truth. However, that statement itself is not physically discerned, nor physically verifiable, for it is a philosophical statement, which presupposes the type of dynamic I mentioned above. Some try to say all there is are physical and logical and/or philosophical truths, yet that makes absent moral truth, which leads to a host of inconsistencies and errors.
The source of Truth, God, makes sense of these physical, logical, and moral truths, for He is the source of them (the Creator/Big Bang, the Source of Mathematics and Logic, the Lawgiver, the ‘Good’ [to quote the ancient Greeks]).
“Truth is that which corresponds with reality; it is the opposite of falsehood. Now the question arises, of course, is “from where does truth… come?” The answer is that truth comes from God. It is a mirror of his being. The notion of truth is an inherently religious idea. Only an eternal, transcendent sovereign could create everything in such a way as to make the universe knowable, personal, and understandable.” (G. A. Thornbury).
So in terms of focusing on mathematics, and what I mean when I say 2+2=4 is truth: This correctly corresponds with reality. To the very point that with mathematics, we can make accurate predictions of the physical universe, as well as alter it and create things.
Interesting. We, in His image, can create. One of the ways we do this is through using mathematics. No surprise, for God is the very author of the Physical Reality.
2+2=4 correctly (truthfully) corresponds to reality. In addition, it is fixed and absolute. It does not change. But 2+2=4 is not PHYSICALLY found in the physical universe. It is not a physical thing, but it is a truth, because it is correct in its correspondence. Where then is this thing called mathematics? It’s not a simple convention or definition, because it is fixed and is still there, and was there before us, and will be there after us, so we cannot be its source.
The difficulty then is in the naturalist to explain such truths, if they prescribe to only the physical being the source of truth, for the method of gaining the observations that currently correspond to the physical universe are not physical in themselves: laws of mathematics and the laws of logic. If anything, this hints at there being something greater than simply natural truths, given the dependence on these things.
The source of Truth, makes sense of natural, logical/mathematical, and moral truths. They are correct correspondences of reality (physically, logically, and morally), because they reflect the author of reality. They are true because they mirror Truth.