Monday, February 11, 2008

The Sixth Way

The Argument from Knowability

The Sixth Way is taken from the idea of knowability. (1) Now it is certain that all things which are true are capable of being known. (2) But then we find that all truths are known. (3) For if it is true that there is an unknown truth, then a being is capable not only of knowing that truth but knowing that that truth is unknown; (4) and it is impossible that a being both know something and know that it is not known, for the latter is contrary to the former. (5) Therefore, there exists a being in the Universe that possesses intelligence by which all truths are known; and this we call God.

[see Fitch's paradox of knowability; credit due to Phil Atkins and others in the grad lounge (Luke and Ian?) for the original idea and suggestions on the wording]


Joe Salerno said...

Nice! But like most of Aquinas' arguments for the existence of God, this one contains a fallacy. If the argument is sound and valid through step 4, then it shows that for each truth there is someone who knows it. It doesn't show that there is someone who knows each truth. However, the last step can be gotten once we notice that the conjunction of all truths is itself a truth. Since someone (but no human) knows it, there is at least one non-human that knows all truths. John Bigelow has a nice discussion of this last step.

Brian Rabern said...

Yeah, we thought the quantifier fallacy made it perfectly Aquinas-esque. I hadn't thought about the further move you suggest. Thanks for the reference...

Brian Rabern said...

Yeah, the Bigelow paper is cool. For those who haven't read it the basic proof (originally from Humberstone, "collective omniscience") goes like this:

Assume that for every truth p there is someone who knows it and that no being is omniscient (i.e. for each being i there is some truth p_i that i does not know). Consider the conjunction H of all the truths of the form [p_i and i does not know that p_i]. H is true. Hence, someone (say j) knows H. But one of the conjuncts of H is of the form [p_j and j does not know that p_j]. This leads to a contradiction.

Thus, if for every truth there is someone who knows it, then there is someone who knows every truth.

Now what? The Sixth Way looks like it could be turned into a valid proof that an omniscient being exists. If so, then I guess I would be tempted to deny the first premise...but haven't thought about it a lot.

Brian Rabern said...

Atkin's suggested trying to prove that if every truth is known, then there is an omniscient being in the following way.

Assume every truth is known. Consider the conjunction V of all true propositions. V is true. Thus, someone knows V. Hence, someone knows each conjunct of V. So, someone is omniscient.

The problem, it seems, is with the assumption that there is a conjunction of all true propositions. If V is the conjunction of all true propositions, then one of its conjuncts is V itself, since surely V & V is a true proposition.

This is all reminiscent of problems with the universal set. There is no "universal conjunction". Right? Or is there some trick I'm missing here.

Brian Rabern said...

I thought of a way to side step the "universal conjunction" problem (if it is really a problem).

A simple truth is a truth such that nothing follows from it by simplification (i.e. conjunction elimination). Let Z be the conjunction of all simple truths. If all truths are known, then someone knows Z. Thus, someone knows each of Z's conjuncts.

Note: Every truth follows from Z, including truths like Z & Z.