Some Christian apologists say 2+2=4 is more certain than God's existence. But is that true?
2+2=4 may be more evident than God's existence, but is it more certain? Usually, God's existence isn't directly evident because God provides the background conditions for everything else. Of course, there are situations where God can and does make himself directly evident.
Now, it seems to be the case that 2+2=4 is a paradigm-example of a necessary truth. Nothing can be more certain than that.
However, it's easy to imagine an evolutionary scenario in which we were arbitrarily hardwired to think 2+2=4. We can't help thinking that's the case, we can't doubt it, even if that doesn't correspond to reality. That's just how we were programmed by blind evolution.
Sure, we number things, we count things, but that's because we think they can be grouped into collections of twos and fours. But again, what if that's something we project onto physical objects (or events)?
So the deeper question is whether there's something that makes it the case that 2+2=4? And is that something God?
I don't mean in a voluntaristic sense, as if that equation is "true" by divine fiat. Rather, mathematical structures are an aspect of God's own mind.
My objective isn't to lay out the argument for that. I'm just pointing out that as a matter of principle, God's existence may be more fundamental than mathematical equations. If so, then God's existence is more certain than mathematical equations. Their certainty is derivative. It depends on God's existence. Again, that requires an argument, and there's an argument to be had for that.
Steve, without God as the foundation for mathematical truths, how would one know that 2 + 2 = 4 tomorrow or next year? Is it satisfactory to note that it was the case yesterday and today?
ReplyDeleteReminds me of Anderson and Welty's Lord of Non - Contradiction
ReplyDeleteSimilar argument made here: https://frame-poythress.org/wp-content/uploads/2016/01/PoythressVernRedeemingMathematics.pdf
ReplyDeleteThis is from Plato's Phaedo. The speaker is Socrates, and Plato casts this as the hours before his state execution, in a discussion that leads up to the topic of the immortality of the soul:
ReplyDeleteWell; but let me tell you something more. There was a time when I thought that I understood the meaning of greater and less pretty well; and when I saw a great man standing by a little one, I fancied that one was taller than the other by a head; or one horse would appear to be greater than another horse: and still more clearly did I seem to perceive that ten is two more than eight, and that two cubits are more than one, because two is the double of one.
And what is now your notion of such matters? said Cebes.
I should be far enough from imagining, he replied, that I knew the cause of any of them, by heaven I should; for I cannot satisfy myself that, when one is added to one, the one to which the addition is made becomes two, or that the two units added together make two by reason of the addition. I cannot understand how, when separated from the other, each of them was one and not two, and now, when they are brought together, the mere juxtaposition or meeting of them should be the cause of their becoming two: neither can I understand how the division of one is the way to make two; for then a different cause would produce the same effect,—as in the former instance the addition and juxtaposition of one to one was the cause of two, in this the separation and subtraction of one from the other would be the cause. Nor am I any longer satisfied that I understand the reason why one or anything else is either generated or destroyed or is at all, but I have in my mind some confused notion of a new method, and can never admit the other.