|
Proof of a negative proposition requires the following:
1) the proposition must exist within a bracketed system, and
2) I must be capable of investigating the system to the extent required by the proposition.
I can prove the statement "There are no unicorns in this room" because it meets the requirements. I've given a limit to the system (this room) and I am capable of investigating all of the physical space large enough to accommodate a unicorn.
The statement "There are no unicorns on earth" is less provable, even though the system is still bracketed. I cannot reasonably investigate the system with sufficient scope to prove the point.
Abstract (mathematical or logical) negative propositions are the easiest to prove, since the systems they use are by definition both bounded and fully investigable (great word, right?) without the need for empirical data.
The statement "There is no god" fails to be provable on both counts. First, the system is no longer bracketed, it is infinite. Second, we lack the ability to investigate the system to the extent required by the proposition. Imagine a deistic, watchmaker kind of god, who has no present activity in the universe. That kind of being would be impossible for us to investigate, observe, gather any sort of empirical evidence about, but it would still make our proposition false.
In the argument by Hales, he assumes these two conditions for a negative statement without ever stating them, shows a few proofs for negative statements that meet the conditions for provability, and then does some rhetorical slight of hand to switch to an argument from "inference" to cover the rest of his bases.
Hales is a radical relativist, so his definition of "true" is probably different than the one you're using. In some of his other articles, he argues that the word "true" isn't grounded in the idea of "real", it's only grounded in what he calls a "belief-acquiring method". For him, there is no reason for preferring one belief-acquiring method over another, and therefore there is no basis for preferring one person's use of "true" over another.
What is deeply ironic is that Hales is also an apostle of Dawkins, and has written very biting commentary about the "evils" (not sure what a relativist can possibly mean by that word, but oh well) of religion. So, in spite of his lofty talk of relativism, he himself is unable to live up to it's claims.
|