What grounds the laws of logic and mathematics? We know that they work, but why? The Transcendental Argument (TAG) says that they exist because of and are sustained by God.
I introduced the argument and explored the first responses in Part 1. Let’s continue.
6. You ask “why?” but I ask “why not?”
When we look at reality, we usually explain things in terms of more primitive laws or principles, but eventually you come to the bottom. These few elementary principles, which can’t be defined in terms of anything more fundamental, are called axioms.
Apologists claim that they can do better than this—they rest everything on just “God did it.”
The first problem is that this is stated as a theological claim, not as evidence. Second, they’ve simply replaced natural axioms with a supernatural one. There are still axioms at the bottom, so this is no improvement.
Like naturalists, apologists agree that you’ve got to stop somewhere; it’s just that their stopping point is based on nothing. It has no evidence to support it. Contrast that with the naturalists’ logical and mathematical axioms. Unlike God, these aren’t taken on faith but are tested continually. Why would we want to ground the one that is strongly confirmed with evidence (logic) with the one that isn’t (God)? Why demand something solid to hold up the fundamental axioms but then use faith to hold up God?
I’ll admit that “that’s just the way reality is” isn’t completely satisfying, but “God did it” resolves nothing. The apologist won’t tell us why or how God exists; he just exists. This informs us as much as “fairies did it.” But if the Christian can have a fundamental assumption about reality (God), so can the naturalist (natural axioms).
Show me that the laws of logic are optional or different in an alternate universe. Otherwise, we can presume that the logic that we have is universal.
Let’s say instead that reality just has properties. Or: properties are a consequence of reality. A universe with zero axioms is a universe without properties. Could such a universe even exist? Is that what a godless universe would look like? I await the evidence.
See also: The Parable of the Mathematician and the Theologian
7. TAG undercuts itself
Apologists jump into a TAG presentation using logic. At the end of their argument, they conclude that God exists.
But wait a minute—was that a valid argument? The apologists will certainly say so. But it was made using logic without a presumption of God! The TAG proponents themselves argue that logic can be reliably used without assuming God.
(I believe that this is Timothy Pew’s argument.)
8. Logic needs a vessel, like a mind
One variant of TAG says that logic requires a vessel. Logic can’t be just free-floating truth but must reside in a mind. Before humans, logic must still have been in force, but what held it? God’s mind, of course.
One popular example of this is the argument that gravity is a ghost in Zen and the Art of Motorcycle Maintenance. Before humans, there was no mind to hold the law of gravity. It had no mass or energy. How much more nonexistent could it be?
The problem here is that gravity and the law of gravity aren’t the same thing. Before Newton, Newton’s Law of Gravity didn’t exist. But gravity did. Similarly, you don’t need a mind for time to exist, but you do for “September” or “ten o’clock.” And you don’t need a mind for logic to exist, but you do for the laws of logic.
Said another way, logic and math are languages. We didn’t need to invent English for rocks to exist, we didn’t need to invent physics for gravity to exist, and we didn’t need to invent math for 1 + 1 to equal 2.
Gravity, time, and logic are properties of the universe, and no mind is required.
Concluded in part 3.
Atheism is the arrogant belief
that the entire Universe
was not created for our benefit.
— Michael Nugent
(This is an update of a post that originally appeared 12/4/13.)
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