The Duplication Argument

Gretchen gives the duplication argument on the Third Day. Do you think it works?

Reductio ad Absurdum arguments

Gretchen’s duplication argument has the reductio ad absurdum form. Reductio arguments are often used to disprove claims, i.e., to prove claims false. Reductio proofs rely on the assumption that if p (any meaningful statement) is true, then not-p is necessarily false, and if p is false, not-p is true. (Negation in logic works exactly like negation in math.) In other words: if you want to prove that "not-p" is true, it is sufficient to prove that p is false. These arguments are often called indirect proofs.

It’s handy to know about indirect proofs, because sometimes an indirect proof is clearer and simpler than a direct proof. Logically, the outcome is the same — an indirect proof is logically just as good as a direct proof — because showing that p must be false is the same as showing that not-p is true.

How do you prove that a claim must be false? You show that assuming if p were true, a contradiction would follow. A contradiction is a claim of the form "X AND not-X", where X is a statement and not-X is the negation of that statement. Because AND statements (conjunctions) are true only when both conjuncts are true, any statement of the form "X is true AND X is also not true" is false. In other words, assuming p leads to the absurd claim that if p is true, both X and not-X must be true. Here’s a simple example:

  1. To prove: there is no highest number.

  2. Assume there is a highest number N.

  3. If N is the highest number, it follows that you can’t add 1 to N, i.e., "N + 1" is impossible. (If you could add 1 to N, then N+1 would become the highest number and N would no longer be the highest number.)

  4. But it’s a fundamental property of numbers that you can add 1 to any number.

  5. So if N is a number, you can add 1 to N. (This follows from statement 4.)

  6. So if statement 2 is true, it must be true that you both can and can’t add 1 to N.

  7. Statement 6 is absurd. A statement can’t be both true and not true.

  8. So we must reject our assumption in statement 2: statement 2 must be false. If statement 2 is false, statement 1 must be true.

Got it?

Gretchen’s Argument

To prove: memory in the same stream is not a criterion of identity.

P1: Suppose memory in the same stream is the criterion of identity.

P2: “Same stream” must mean either “same stream of brain processes” or “same stream of information or consciousness.”

P3: “Same stream” cannot mean “same stream of brain processes,” since heavenly Gretchen no longer has her brain.

C1: “Same stream” must mean “same stream of information or consciousness.” (Disjunctive syllogism from P2 and P3)

P4: When Gretchen died, living Gretchen’s consciousness ceased to exist altogether.

P5: (Gretchen assumes for the sake of argument that she might still be conscious even if she were dead.)
With living Gretchen’s consciousness obliterated, the only way heavenly Gretchen could then have the same stream of information or consciousness is if God (or some technology) somehow duplicates her information stream or consciousness.

P6: If God (or technology) can make one duplicate, he (or it) can make more than one. If he did, then both heavenly Gretchens would remember “in the same stream.” They would both “be” Gretchen.

P7: But they can’t both be Gretchen, since personal identity means “I am the only one who is me”, i.e., uniqueness.

C2: (Gretchen now asks what would happen if God or technology did duplicate her stream of consciousness. In Dennett’s "Where Am I?", technology does exactly this.)
If God or technology did duplicate Gretchen’s stream of consciousness, then there would be two Gretchens with the same streams. Those two Gretchens must be, at the same time, both unique (since identity implies uniqueness) and not unique (since there are two of them). This is a contradiction, and the contradiction follows from the initial supposition (P1) that memory in the same stream constitutes identity. Since that initial supposition leads to absurdity, it must be false.

Q. E. D. Therefore, memory in same stream is not the criterion of identity.

Possible counter-argument: God is limited in his creation of duplicates to ONE, since identity implies uniqueness, and God can’t do anything that ends up violating the laws of logic. So God can’t create more than one heavenly Gretchen. This would solve the problem of the two Gretchens.

Gretchen rejects this counter-argument. She asks: is the creation of more than one duplicate a violation of the laws of LOGIC? It doesn’t seem so. We create duplicates of information streams all the time, e.g., when we copy computer files. Nobody thinks that’s logically impossible. After all, if it’s actual, it’s possible.

So if it’s not logically impossible for us, it can’t be logically impossible for God.

The believer might reply, well, of course, God could just limit himself to one duplication per consciousness. Maybe he doesn’t want to, or it wouldn’t be the best thing to do, or God always does the best possible thing, or whatever.

For an atheist like Gretchen, these speculations are, of course, meaningless.

 

 

Questions or comments?
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