Archive

Archive for the ‘Descartes’ Category

Rene Decartes and Theological Perspectives on Logical Impossibilty

Not too long ago, I posted some thoughts on the interesting possibility of a theology of logic. One of the interesting venues that a theology of logic could explore might be the nature of the relationship between God’s omnipotence on the one hand, and logical possibilty v. impossibility on the other.

It’s apperant that most Christian intellectuals (at least in recent times, and whose writtings I’ve come across) have more or less taken for granted that the logically possible (which is the broadest and most basic category of possibility) marks the boundary of what even God, in His omnipotence, could (or could not) do. I too, have taken this for granted. And while the average person who hears such a claim may take it as an unwarranted limtation of God’s power (After all, God is omnipotent!) it is easy to illustrate why so many CHristian intellectuals have accepted this view. And indeed why so many of them haveheld this view as compatible with the belief that there is nothing that God cannot do.

One way of putting it might be to say that, these beliefs are compatible by virtue of the fact that the logically impossible does not actually refer to anything at all. If something is logically impossible, that simply means that it entails a logical contradiction (i.e., it implies a statement of the form P & ~P, or “it is the case that P is true and it is not the case that P is true”. It’s important to note here that this refers to the logical form of a proposition, not the lingustic appearance of a sentence. In other words, the so-called “law of non-contradiction” entails that for a proposition of the form P &~P to constitute a genuine contradiction, P must be used univocally in both instances. In short, if P means something slightly different each time it appears in the sentence P & ~P, then this is not a contradiction, precisely because it is an equivocal use of the term P). If a sentence entails a logical contradiction, it actually doesn’t assert anything at all. Think about this. What could any sentence with the logical form of P & ~P possibly express? The first conjunct (P) assets one thing, and the second conjunct (~P) denies precisely that which the first expresses. The net result is that nothing is said. Since the logically impossible literally means nothing, to say that God cannot perform the logically impossible is perfectly consistent with the belief that there is nothing which God cannot do.

Interestingly, the idea that the logically impossible lies outside God’s omnipotence has not been universally accepted. Recently, I came across this interesting quote from Rene Decartes, wherein he seems to take the view that the logically impossible is something, something which, though it lies outside our ability to comprehend, is perfectly within the domain of God’s possibilities:

I turn to the difficulty of conceiving how God would have been acting freely and indifferently if he had made it false that the three angles of a triangle were equal to two right angles, or in general that contradictories could not be true together. It is easy to dispel this difficulty by considering that the power of God cannot have any limits, and that our mind is finite and so created as to be able to conceive as possible the things which God has wished to be in fact possible, but not to be able to conceive as possible things which God could have made possible, but which he has nevertheless wished to make impossible. The first consideration shows us that God cannot have been determined to make it true that contradictories cannot be true together [les contradictoires ne peuvent être ensemble], and therefore that he could have done the opposite. The second consideration assures us that even if this be true, we should not try to comprehend it, since our nature is incapable of doing so.

Interesting….