A brain-squeaking romp through some questions of chaos and omnipotence
It is apparently possible to prove this fact in a rigorous mathematical way, though I remain bemused by what rendered this necessary.
Chaos is presumably the state in which 2 does not equal 2.
(I leave it to whom it amuses to determine whether, if that is taken too literally, it contradicts the principle of ex nihilo).
Which inevitably brings up the question of whether or not God can make triangles square.
I assume that the definition of a square triangle is an entity on the Euclidian plane that has some of the fixed mathematical properties of a triangle, and some of those of a square. For example, four sides and internal angles that add up to 180 instead of 360.
If chaos is the state in which 2 does not equal 2, perhaps it follows that God cannot make triangles square on the grounds that it would be chaos, and it is contrary to God’s nature to create chaos?
However, it would be equally possible to argue that square triangles under the proposed definition would normally be a different form of “order”.
Chaotic square triangles are not really possible because there has to be something about them which allows them to be recognised as both triangular and square. They are insufficiently unintelligible to be chaos.
Which brings one to the question of whether or not God can create a boulder he can’t lift.
For a start, if God is pure act, a question that enquires of his potentialities is problematic. We do predicate the language of potentiality of God a lot, as being creatures of time, we can’t really say anything without doing so. But it is presumably somewhat metaphorical: it is hardly surprising if the metaphor breaks down in some places.
Also, if one understands God’s omnipotence in terms of there being no constraint that can be laid on him outside His own nature, the question is rather thrown back to whether or not the boulder question is a chaotic paradox or a paradox created by our lack of understanding, with the odds on the latter. Does the question create a paradox regarding the possibility of omnipotence, or does the question require, in talking of God “lifting” a boulder, that this omnipotence is already denied? To “lift” implies a being with constraints which can’t be automatically assumed to apply to God.
Or one could just argue that He has in fact done it, as in the Incarnation, He does accept some of the limitations of our nature. If the Creator God is rendered powerless in the manger and on the cross, then He has created boulders he can’t lift. (However, the “if” is key. I have no idea how one would go about speculating on the subject – it’s rather out of my province. And note the fact that whatever is done with the tenses in that statement is problematic!).
On a different but related subject, I do believe in the Real Presence. People have a habit of asking me if I take it literally.
It depends what is meant by “literally”. If you mean “according to the normal workings of the physical world” then no, I don’t take it literally. I don’t think I am engaging in a cannibalistic revel! But if you mean “do I think the Communion actually is, really and truly, the Body and Blood of the Lord Jesus Christ?” then the answer is yes, I do take it literally. This is made more confusing because what I, as a Christian, think is going on ontologically in the normal rules of this world is very different from what a conventional atheist would think is going on. It is God that fundamentally defines what it is “to be”, not the laws of the material creation, which are a contingent result of His “decision” to create.
Normally I distinguish the two types of “literally” by saying “mystically” of the Real Presence. But as what I mean by this is approximately, “according to the ontology of the inbreaking of the world to come,” it is perhaps not much help as a clarification under most circumstances! The mystical, far from being merely symbolic, is as actual as – or more actual than – the literal.
(Part of the reason it is difficult to communicate Christianity in an accessible way is the extent to which the underlying assumptions are different from those of our culture. We are usually trying to communicate concepts for which our wider culture has neither language nor map).
It could also be pointed out that even the ordinary operation of the material creation has turned out not to fit into our ideas of “common sense”. Evolution and quarks (both of which I think to be true) are hardly less fantastic than the Real Presence in everyday terms.
The mystery of all three, and indeed of everything else, is, perhaps, not how God “could”, but why God “wanted” to.
Yes. It is indeed a fearful and wonderful thing that 2=2.