|Math: Sometimes the truth is contingent.|
In the interest of keeping up, I want to post a small update for consideration. I have been conversing with Kairosfocus on worldviews and first principles. One of the paths we took recently involved distinguishing contingent and necessary beings. To illustrate a necessary being, Kairosfocus offered this:
Any entity that is dependent for its ability to function on the particular co-ordinated physical arrangement of parts is contingent, as if the parts are moved around or separated such a composite entity will cease to be or will break down.I have been turning over this bit in my mind. Something about Kairosfocus's statements about 2 + 3 = 5 has seemed problematic to me.
Auto parts shops have a surprisingly deep philosophical significance, never mind that chilling, long low whistle from under your car when the mechanic is looking at it.
By way of contrast, the truth asserted in the structured set of symbols: 2 + 3 = 5 always was, will always be, cannot be denied on pain of absurdity, etc. It cannot break down and does not need to be repaired.
It is a necessary being.
(We need not trouble ourselves for the moment on the 2400 year old debate on whether such may only be instantiated in physical entities. Suffice to say that such mathematical or more broadly propositional truths capture assertions about reality that may or may not be true, but if true can have very powerful implications. Thence, the “unreasonable” effectiveness of mathematics in science: If X then Y, holds, once X is found.)
The problem, as I have tried to work it out, is that the truth of 2 + 3 = 5 is contingent. Let me explain:
For the truth of 2 + 3 = 5 to begin or continue, we need (1) a material universe; (2) principles of rationality, such as the law of identity; and (3) a computer, that is, a being to arbitrate between the universe and rationality so as to determine the truth of expressions. There may be additional needs, but these three factors seem essential at the least.In my estimation, then, it is incorrect to say “the truth asserted in the structured set of symbols: 2 + 3 = 5 always was, will always be, cannot be denied on pain of absurdity, etc. It cannot break down and does not need to be repaired.” Specifically, the incorrect parts are “always was” and “will always be.” The expression 2 + 3 = 5 is true only as long as we have a material universe where things are identical only to themselves and interact with one another in regular ways. As long as we have, in other words, all three factors in play: materiality, regular constraints, and a translating/computing intelligence.
We note also that the falsity of 2 + 3 = 4 depends on (1) to (3).
The truth or falsity of these expressions is an effect of the three factors of universe.
I should point out that my comments do not deny or reject necessary beings, per se. I am only saying that the specific truth of 2 + 3 = 5 is actually contingent and not necessary. I have not yet thought far and deeply enough to say what this conclusion means for the principle of cause and effect and the principle of sufficient reason.