Paley’s Computer
(I could’ve sworn I wrote about this earlier, but I can’t find it in the archive now. So sorry if this is a duplicate.)
Let’s say you’re visiting a foreign country, along with a native. As you’re wandering the forest, you see a mechanical watch on the ground. You pick it up, open it, examine its mechanism, and wonder among yourselves how it might have come to be in the forest, who designed it, who manufactured it, and so on.
After walking a bit further, you see a computer in a glade, its LED lit, its fans whirring, its power supply connected to an array of solar panels, its monitor showing a CAD tool with plans for a watch. It says “Dell” on the side.
You ask your guide about this device: who designed it? Who built it? Who decided to install it in the woods, of all places, and why? He says, “It’s always been here. As far as anyone can tell, it’s been here since the beginning of time.”
Satisfied, you nod your head and move on.
This is, of course, ridiculous. A computer is a big complicated thing whose presence demands an explanation, and you can’t get around that just by saying that it’s always been there.
For those who didn’t recognize it, what I’ve done here is to combine two common Christian arguments. The first is Paley’s Watchmaker, which says that a complicated thing requires a complicated designer.
The second adapts the Kalam argument to Paley’s watch. Briefly: the First-Cause Argument says that life/the universe/everything is a big complicated thing that didn’t just happen on its own, and therefore demands an explanation. If everything has a cause, we can ask what caused life, and then ask what caused that, and what caused that, and so forth. Eventually, we’re bound to come to the Ultimate Cause, which has no cause of its own. And hey, let’s call that God because that’s what we’re trying to prove.
At some point, someone realized that if everything has a cause, then it’s fair to ask what caused God, and what caused the thing that caused God, and so forth. So the argument was modified to say that everything that begins to exist has a cause, and BTW God is eternal and therefore never began to exist, and therefore doesn’t require an explanation.
I hope I’ve demonstrated, above, that being eternal is not sufficient for not requiring an explanation. Heck, the four-color theorem, Gödel’s incompleteness theorem, Pascal’s last theorem are all eternal, yet they’re all complex entities that demand an explanation. If “it’s eternal, therefore it doesn’t require an explanation” were true, math class would be a lot shorter. In other words, Kalam is basically a very fancy and roundabout way of saying “I don’t need to explain God because shut up is why.”
(Some people might object that I’m casually using “cause” and “explanation” interchangeably. Yes, I am. Because for my purposes, they’re close enough that the distinction doesn’t matter.)
No, what short-circuits the infinite regress of explanations is when we get to something simple enough not to require further explanation. An explanation for Paley’s watch might be “the watch was designed in the same way as a ship’s rigging or a water pump, but smaller, more delicate, and more complicated.
But if “God” is the ultimate simple explanation, perhaps a principle of logic, like “0 = 0”, then that god loses a lot of the attributes that people who want God to exist really want that god to have. Like caring about their welfare. Like being aware of them, or indeed, of the Milky Way galaxy. Like being capable of noticing those sorts of things. Which “0 = 0” doesn’t. I’ve had people tell me that there are arguments to show why the Ultimate Uncaused Cause must necessarily have been a Jewish carpenter who was executed 2000 years ago, but somehow they never got around to presenting these arguments.
Side quibble: In the ontology I hew to, theorems (and indeed, mathematical concepts in general) do not exist except as mental artifacts (and by extension as cultural artifacts once they are shared among the community), and therefore do not exist until someone first thinks of them. Of course, to the extent they describe the physical world, the things they are *about* may exist; eg. it has always been the case that it takes no more than four colours to cover a genus-0 surface. I’ve forgotten the name for this school of thought.
TL;DR: I agree with Kronecker, except that God didn’t even do the integers.
Well, there are things that are true, and there’s the representation of those statements inside a mind. What’s called “the Pythagorean theorem” may be called something else in Chinese or Arabic, and may be represented by different systems of mathematical notation, different patterns of neural activation in different people, it’s still universal: any system that can be represented by a right triangle in a euclidean plane will have the property that the square of the hypotenuse is the sum of the squares of the other two sides.
There are also theorems that apply only to things that don’t exist, or can’t exist, like thousand-dimensional cubes, and yet we still consider those theorems to be true. As I see it, it’s because they’re statements of the form “if there were an object with such-and-such properties, then such-and-such would also be true.”