Tuesday, August 24, 2010

Circular circles…

In some cases, naming a thing necessarily entails asserting a thing's nonexistence. For example, if by W:x~W I name "the factor or set of factors which make the present state of affairs to be other than what they are at present," I am implicitly and necessarily denying the existence of W:x~W. Nothing exists or could possibly exist to make the present state of affairs other than they are at present. That's trivially true but, obviously, metaphysically complex.

Likewise, in some cases, naming a thing necessarily entails asserting a thing's existence. For example, if by W:xW I name "the factor or set of factors which make the present state of affairs to be they are at present," I am implicitly and necessarily asserting the existence of W:xW. That which makes the present state of affairs what they are at present cannot not exist. That is, again, trivially true but also metaphysically complex.

Why not see God's existence in the same way see a circle? Why not see the relationship between "deity" and "existence" in the same way we see the relationship between "circularity" and "roundness" (or "punctual equidistance")? Necessarily, either a circle is round or a circle is not possible; and, necessarily, either a necessary being exists or such a being is not possible. But the very terms involved––circle and round, necessary being and existing being––entail each other. In my view, "a necessarily existent being" is as much of a circumlocution for "God" as "a punctually equidistant set of points" is for "a circle." Something must fulfill what it is to be a circle, otherwise the term itself is incoherent; but it is not incoherent, since 'that which is circular' entails its roundness. Likewise, something must fulfill what it is to be W:xW, otherwise W is impossible; but since W is necessary, W:xW is also necessary. In the same way, something must fulfill what it is to be a necessary being, otherwise the term itself is incoherent; but it is not incoherent, since the term itself entails its own existence.

Perhaps an objector says, "But we can imagine 'deity' not existing. We can't imagine a non-round circle"?

I reply that I can imagine a non-round circle, in at least two ways. First, the circle is a thin rubber hoop. I find it jumbled into a knotted heap in a box. Nothing about it says "round" to my imagination. Yet it is round. Second, every instance of a circle we have experienced is actually not perfectly round and therefore not a circle. The imperfections in the chalk on the board, in the graphite on the paper, in the branch as it carves through the sand, etc.––in every case, a circle as we know it is just an approximation of 'what a circle is' in se. Yet I know such "circles" are circles because I, so to speak, know "what they are getting at." To deny that "the circle" is an impossible shape because we cannot present one devoid of any defects, is to fail to grasp what a circle is, not to disprove how and that circles exist. Likewise, while all arguments for (or presentations of) God may fail to capture wholly and perfectly 'what God is', yet we know "what they are getting at." Hence, to say that "the Deity" is an impossibility because we cannot articulate It devoid of any defects, is to misconceive of what the Godhead is, not to disprove how and that the Deity exists.

The objector continues, "But your conception of the Deity is just an historical accident. Had you been born in a different culture and a different time, you might have thought the Deity was born from an eternal chaos, etc."

I reply that our conception of a circle is also just an historical accident. Had our species evolved only to see straight and diagonal lines, we would have no conception of circularity. To retort that we have evolved to see circles because there really are circles in the world is but to beg the question, since there being circles in the world depends on circularity actually existing in the first place. I can just as reasonably say that we have evolved to detect the Deity in the world because the Deity really is in the world.

But the objector continues: "Ascribing a divine will to or 'behind' the world is just a massive cognitive illusion our species has developed because the illusion has tended to support survival and genetic transmission in the past. There isn't really 'the Deity' in the world; we are just programmed to think there is."

I reply that this only repeats the earlier error, which wanted to deny the existence of circles based on the fact that we don't experience perfect circles in nature. Seeing what is, at close range, a ragged trail of chalk on a board or graphite on paper and yet calling it "a circle" is just as much a cognitive 'illusion' as taking a discrete series of vibrations in air to be a coherent stream of language with a meaning. Fudging non-circles into "circles" must have tended to promote survival and reproduction, otherwise it would not have evolved (e.g. because such fudging drastically reduces computational demands and this reduces metabolic demands, or because Fudging the Forms prevents Platonic Paralysis by forestalling just pondering Circularity while Tigerness devours our Headness, etc.). We may have evolved to see what are not truly circles as circles, but this does not negate the existence of circularity per se.

It is my contention that any conception of God which admits His possible nonexistence is of the same character as a conception of circles which denies their roundness. I am well aware that St Thomas Aquinas, e.g. in SCG I, I, x–xi, admits the conceivability of the nonexistence of God, and thus I seem to be pitting myself against the Universal Doctor. As he says in capitum xi,

"For assuredly that God exists is, absolutely speaking, self-evident, since what God is is His own being. Yet, because we are not able to conceive in our minds that which God is, that God exists remains unknown in relation to us. So, too, that every whole is greater than its part is, absolutely speaking, self-evident; but it would perforce be unknown to one who could not conceive the nature of a whole. … For that He can be thought not to be does not arise either from the imperfection or the uncertainty of His own being, since this is in itself most manifest. It arises, rather, from the weakness of our intellect, which cannot behold God Himself except through His effects and which is thus led to know His existence through reasoning."

Thomas' target in these chapters is the Anselmian ontological argument and I don't think I am mounting an Anselmian ontological argument. St Anselm was arguing that a true grasp of what God is would convert the intellect into believing that God is. But as the quotation above indicates, St Thomas was more aware of the legitimate cognitive weaknesses many people have (à la illusions imbibed by our evolutionary past, as discussed above) and, thus, argued why Anselm's argument could not in itself convert the intellect to faith. I am making what I think is a more modest claim: insofar as God's essence is to exist, any argument against this notion fails to grasp what God is, and so, while this is not a rational fault of the objector, yet it is not a defeater for the notion of God as proclaimed in classical theism. A person may therefore legitimately be 'forgiven' for failing to see God's existence included in His essence and may be aided to faith by way of other (e.g. Thomistic) argumentation. Even so, this does not mean the person's failure to believe in God as necessarily existent is not an argument against God as held by the theist. By saying that St Thomas was perhaps more sensitive to humanity's endemic cognitive frailties, I do not mean to suggest St Anselm was unaware of the problem. This is why in chapter IV of Proslogium he says,

…there is more than one way in which a thing is said in the heart or conceived. For, in one sense, an object is conceived, when the word signifying it is conceived; and in another, when the very entity, which the object is, is understood.

In the former sense, then, God can be conceived not to exist; but in the latter, not at all. For no one who understands what fire and water are can conceive fire to be water, in accordance with the nature of the facts themselves, although this is possible according to the words. So, then, no one who understands what God is can conceive that God does not exist; although he says these words in his heart, either without any or with some foreign, signification. For, God is that than which a greater cannot be conceived. And he who thoroughly understands this, assuredly understands that this being so truly exists, that not even in concept can it be non-existent. Therefore, he who understands that God so exists, cannot conceive that he does not exist.

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Rough technical appendix… 

[∆ means possible, Ω means necessary, ~ means negation, : means predication]

1. It is impossible to assert the existence of a square circle (sc).
1a. ~∆P:(x:sc)

2. It is impossible to assert that a circle is not round (c~r) or that a non-circle is round (~cr).
2a. ~∆P:x(x:c•~r)•(x:~r)
2b. By 'round' I mean all points in an objects are equidistant from a single other point.

3. It is necessary to assert the circle is round.
3a. P:(x:c)ΩP:(x:r)

4. It is possible to assert the nonexistence of a square circle.
4a. ∆P:x(x:~sc)

5. It is necessary to be able to assert the nonexistence of a square circle.
5a. Ω∆P:x(x:~sc)

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