Sanctuary of Faith W. Zeitler [PIANO]
Musing on “Immortal, Invisible, God Only Wise” [ORGAN]
The Order of Chivalry: Justice & the Knight’s Sword [ORGAN]
In a previous Music Box I mentioned that Kurt Gödel (1906-1978, whom Einstein said was the greatest logician since Aristotle) developed a proof for the existence of God. But first I thought I’d consider a couple of other famous proofs as a warmup.
One is ‘First Cause’. Generally, if P causes Q, then Q causes R, etc., we call that a ‘causal chain’ (a chain of causes and effects, where each effect is the next cause). In principle at least we can start with who and where we are right now, and trace the causal chain back to — how far back? The First Cause argument claims that there must be a first cause that started all this, and that First Cause is God.
I don’t find this one terribly convincing. We assume that the causal chain as of today can continue infinitely into the future — why can’t it extend infinitely into the past? (Never mind about the Big Bang: what caused THAT?)
Another is the “Argument from Design.” You’re on a beach, and you find a watch in the sand. Because of it’s intricate and intelligent design, you conclude it must have been made by a skilled watchmaker. Our cosmos itself is of intricate and intelligent design, therefore it must have been made by a Cosmic Watchmaker.
This one isn’t airtight either. Imagine an infinite number of Universes, each with slightly different laws of physics. (The idea that there are an infinite number of parallel universes is a currently proposed solution to some fundamental problems in Quantum Physics.) In the vast majority of these universes, Life is not possible. But we got lucky (people DO win the Lotto) — we happen to live in one of the few universes where Life is possible and actually came to pass. If you win the Lotto, of course you feel like that was your destiny, but actually it was just dumb luck.
There are many more proofs, but let’s consider just one more, the “Ontological Argument”, first proposed by Anselm of Canterbury (1033/4–1109). There are different versions, but they all argue something like: “Because we can imagine a perfect being, there must be a God, because existing makes a good thing better than one that’s only imaginary.” Oversimplified, but that’s the drift. Gödel’s proof is along these lines, only vastly more Symbolic Logic-ey.
I find this one the least convincing of all. Yet, some really bright folks (like Leibniz, Descartes and Gödel) have taken this argument quite seriously, so I’m probably missing something.
Maybe you’ll like Gödel’s proof better (yes, here’s the whole enchilada):
Ax. 1. {P(φ)∧□∀x[φ(x)→ψ(x)]}→P(ψ)
Ax. 2. P(¬φ)↔¬P(φ)
Th. 1. P(φ)→◊∃x[φ(x)]
Df. 1. G(x)⟺∀φ[P(φ)→φ(x)]
Ax. 3. P(G)
Th. 2. ◊∃x G(x)
Df. 2. φ ess x⟺φ(x)∧∀ψ{ψ(x)→□∀y[φ(y)→ψ(y)]}
Ax. 4. P(φ)→□P(φ)
Th. 3. G(x)→G ess x
Df. 3. E(x)⟺∀φ[φ ess x→□∃yφ(y)]
Ax. 5. P(E)
Th. 4. □∃x G(x)
Hmm. Instead, here’s one more my speed: I watch the news, and think: “if we are the apex of intelligence in the Cosmos, if we’re the most intelligent beings around, then God help us!”