Posted by:
Henry Bemis
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Date: March 11, 2013 02:12PM
Here are some responses to comments by Human in “The Nature of Mathematics” thread.
[HUMAN] “2+2=4 is true, whether it is described in a Hindu-Arabic script or a Roman script (ii+ii=iv) or something else. Language is a vehicle that carries something, a vessel for "content". Erase the language (vehicle) from mankind and I think we would be hard-pressed to claim that suddenly 2+2 didn't still = 4: specifically, what "2" stands for, what "+" stands for, what "=" stands for, and what "4" stands for. If this is true, then where exactly does this truth exist?”
“archytas's example above to MJ is exactly right. Pi is not arbitrary, it exists apart from the numerals that "carry" it. Math is a series of discoveries, not inventions.”
[RESPONSE] What is being confused here is the distinction between mathematics as a language and mathematics as a description of the world. And, with “language” we include the mental states that they are associated with. With some universals, like “love,” language as the spoken written word must be separated from its accompanying denoted mental state. Let’s discuss this.
Of course, the language of mathematics was invented by humans. However, the fact that the physical world is “mathematical,” i.e. that it can be described by complex mathematical relationships is, of course, a feature of the world (universe) that is independent of language. Thus, the underlying mathematical structure of reality remains to be explained, even if we can explain “mathematics” proper as a human language game.
[HUMAN] “But I have to ask . . . if we are willing to give ontological status to mathematical objects why not also to other conceptual objects? If our minds *discovered* Pi rather than invented it, why cannot we also say that our hearts *discovered* Love rather than invented it? Same with Justice, same with Mercy same with etc.............(the implication for recovery from Mormonism is clear here, this leads to, yes, God.)”
[RESPONSE] Universals are not all created equal with respect to their relationship to the external world, as determined by “evidence.” With each one it must be asked what does the term in the language denote? Clearly some such terms, e.g. “game” are nothing more that human constructs invented for convenience of discourse. There is no ideal, Platonic “game” existing somewhere that our human term relates to in some way. But what about “mathematics,” and “love.” What do they denote?
Now, if we take the term “mathematics,” we are in a bit of a dilemma. Although this term certainly carries with it a purely human language aspect, including human derived axioms, rules, theorems, etc., we also find that the world behaves in accordance with those very mathematical principles that we have described in our language. Moreover, sometimes we discover the “rules” by studying the structure of the physical world. Moreover, geometrical figures, like the circle, can be mathematically idealized through concepts like “pi,” the properties of which seem to transcend simple human construct. After all, human beings did not invent the truth that the circumference of a circle is related to the number pi and its radius; they discovered this.
Does this mean we have not invented mathematics after all? It certainly means that there is something special about the structure and order of reality that we did not invent. As such, the temptation, right or wrong, is great to conclude that “mathematics” denotes something over and above our language conventions. Again, the mathematical structure of the world does not disappear with the disappearance of human language or the human mind, even though our mathematical terms do. On the other hand, a proposed Platonic universal “games” does seem to disappear.
Considering “love,” it too is, of course, is a word of convenience in human language invented to denote a certain emotion; a mental state. (not a brain state!) If there were no humans (or more broadly minds) the notion of “love” would seem to disappear. So, if we want to claim that “love” carries ontological status, there are two options: First, we might claim that love carries its ontological status as a mental “entity,” that arises from brain states. Or, second, we might make the more radical claim that love is something ontologically separate from mind; i.e. that the mind taps into. But, if that is the claim, what could it possibly be? Here we seem to have crossed over into pure mysticism. We know that consciousness exists. We know that mental states exist. And we know that love exists as a mental state. But that does not justify a view that “love” is a Platonic universal.
As a dualist, who believes that consciousness is ontologically separate from the brain that instantiates it, I am sympathetic to the first suggestion. Perhaps love is an aspect or property of mind that somehow has ontological status separate from both brains and consciousness. But here again, when we try to unpack this notion we get into immediate trouble. We have enough difficulty with consciousness itself, do we want to add love and the other emotions as well. Why can’t the ontological status of love simply be as aspect or property of mind?
[HUMAN “I acknowledge that I am placing something into that "gaping hole in our understanding of reality" that is "a metaphysical conclusion unsupported by any evidence." But as you've said many times before, a materialist assumption which precludes the possibility of a metaphysical reality is no less an assumption.”
[RESPONSE] Well, you need to be careful here. Possibility is one thing; evidence is another. There is abundant evidence, in my view, that materialism, as a scientific worldview, is false. That I have said many times. But that does not leave us free to invent all sorts of metaphysical objects, or deem conventions of language as denoting the reality of our pet universals. Where to draw the line is, of course, difficult. But mathematics is on the credible side of this ledger, whereas love is on the more speculative, mystical side, in my view, simply because, as stated, mathematics is closely tied to the physical world, whereas love (the emotion) is dependent upon mind, which is itself ontologically elusive. This, of course, does not mean that love does not exist as a human emotion. It simply means that it probably does not exist outside of, and independent of, such emotions, and the minds that experience them.
[HUMAN] “But I still can't help *feeling* that poetry is a vehicle which carries a content that exists apart from the words that convey it. *Convey* here is an interesting, pregnant word.”
[COMMENT] Yes, but what is this “content” that is being carried or conveyed? I would say that whatever it is, it resides in consciousness, and “the self” of those who experience it, whatever that turns out to be. Call it the soul, if you will. It is, for me, an experience that strikes to the heart of who we are as conscious beings. But we do not have to insist that this content is part of the world separate from the human beings who experience it. Surely, consciousness, love, the self, etc. are not just words; they denote “something.” But the ontological status of what they denote is tied, it seems to me, to our own ontological status as mental (an autonomous) beings, of which we do have abundant evidence.
Finally, based upon some of the responses to the original post, some simplistically ignore the fact that the universe is remarkably ordered in accordance with mathematical principles. True, humans may have invented mathematics proper even if the world was not so ordered; and the world would be so ordered even if there were no humans to invent mathematics proper. But it is a huge error to conclude that there is nothing metaphysically significant by the fact that the world is fantastically ordered in mathematical ways, notwithstanding human beings. And the question remains; Why? This question relates to the cosmological anthropic principle; i.e. why does the universe appear to be fine-tuned for life. The even more fundamental question here is, Why is the universe in fact ordered in conformance with mathematical laws.