A mistake in Gödel’s proof

A few years before her death Kurt Gödel’s mother asked her son whether they would see each other in a hereafter. He answered affirmatively and provided the following proof in a letter of July 23, 1961:

About that I can only say the following: If the world is rationally organized and has a sense, then that must be so. For what sense would it make to bring forth a being (man) who has such a wide range of possibilities of individual development and of relations to others and then allow him to achieve not one in a thousand of those?

…But do we have reason to assume that the world is rationally organized? I think so. For the world is not at all chaotic and capricious, but rather, as science shows, the greatest regularity and order prevails in all things; [and] order is but a form of rationality.

(In S. Feferman, C. Parsons & S. G. Simpson (eds.), Kurt Gödel: Essays for His Centennial: Cambridge University Press; 2010, p. 12)

It very much seems that Gödel here committed the fallacy of equivocation. The phrase “rationally organized” in his first paragraph means “has a sense” (or “has a purpose”), whereas in the second paragraph it means that it is “not chaotic”, i.e. that it is governed by law. And the fact that the world is not chaotic and capricious but governed by natural laws is not a reason to assume that it has a purpose.

Therefore Gödel’s argument is logically flawed.


A reader raised an objection:

I don’t see the equivocation. In the first paragraph Gödel writes, “if the world is rationally organized AND has a sense”. The conjunction indicates that a) being rationally organized and having a sense are different things for Gödel and b) that he doesn’t give a definition of rational organization until the second paragraph.

Before replying, here is Gödel’s proof in a nutshell:

1. If the world is rationally organized (RO) and has a sense (S), then there is afterlife (A).
2. The world is RO (i.e., not chaotic)
3. A

Now there are two possibilities here. Either (i) Gödel took RO in (1) to be essentially synonymous with S, or (ii) he took RO to mean the same (i.e. “not chaotic”) in both (1) and (2). If (i), the argument is invalid due to equivocation. If (ii), the argument is blatantly invalid. But it is more charitable to take someone’s argument to be merely invalid than blatantly invalid. Hence, (i).

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s