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Friday, July 25, 2008

A note on God and unsurpassable worlds

Let us say that a possible world is unsurpassable if there is no possible world which is better than it. (This allows for the epistemic possibility that there may be more than one unsurpassable world, as opposed to the term “best” which is commonly understood to presuppose uniqueness.) Now, suppose for the sake of argument that (roughly) the God of traditional theism—an incorporeal, omniscient, omnipotent, omnibenevolent (etc.) being—exists. The question I want to examine is this: If God is infinitely good, not just in the sense of being omnibenevolent but also in the sense that God is of infinite value, is every possible world in which God exists an unsurpassable world? The answer depends on what we take into account in assessing the value of possible worlds. I see at least two ways of carrying out such an evaluation.

On the first way, we ignore any weight that might be assigned to the goodness of individuals and simply regard one possible world as being better than another if and only if the set of all good things which exist in the latter is a proper subset of the set of all good things which exist in the former. In this sense a possible world which contains God and one sentient being is—assuming all sentient beings possess at least some value--better than a world which contains God alone (not counting necessarily existent abstracta), and this is so quite irrespectively of the fact that God is infinitely good. It seems to me that there is no unsurpassable world in this sense, for given any possible world w_x there is always another world w_y such that the set of all good things which exist in w_x is a proper subset of the set of all good things which exist in w_y. On this view possible worlds can only be ranked according to their goodness, one cannot say how much better one world is than another.

According to the second way one should take into account not only the number of instances of goodness but also, so to speak, their intensity. For when we say that God is infinitely good we do not (or should not) mean that God has aleph-null (or some other transfinite cardinal) units of goodness, but rather that God’s goodness is “infinitely intense” or “unsurpassably intense”. We might characterize this by saying that in our moral considerations God’s goodness ought to be given an infinite and/or unsurpassable weight. Given that God’s goodness is infinitely or unsurpassably intense in all possible worlds where God exists, it appears that taking the “intensity” of something's goodness into account in determining the value of possible worlds yields the result that all possible worlds where God exists are unsurpassable.

So it seems that if God exists either none of the worlds which God can actualize are unsurpassable or that all of them are, and in neither case is there a unique "best" world that God can actualize. The interesting question is then, if that’s so, does it follow that God must choose a world to actualize at random?

Friday, July 04, 2008

Against Hacker on the Justifiability of Grammar

Over at Methods of Projection, in the comments section of a post about Wittgenstein on meaningfulness and language games, N. N. posted the following arguments by P. M. S. Hacker, which attempt to show that the rules of grammar cannot be justified:

Justifying grammar by reference to the facts leads to an infinite regress. Any attempt to justify grammatical rules by reference to how things are in reality must employ a language in giving that justification. The form of words that purports to justify a rule of grammar must itself have a grammar. If it has the same grammar as that which it purports to justify, the justification begs the question. If it has a different grammar, then (a) it determines different concepts and so cannot be about the same thing, hence is irrelevant; and (b) that grammar too will stand in need of justification. So any attempt at grounding grammar is reality will launch us upon an infinite regress of justifications.
[...]
No description of reality can justify grammar. Any attempt to justify grammar by reference to reality must take the form of a grammatically licit description of how things are. Such a description is given by a proposition with a sense. Consequently its negation too must make sense, for the negation of a proposition with sense, which describes how things are, is itself a proposition with sense. But for such a proposition to justify a grammatical rule which delimits the sense of sentences and excludes nonsensical forms of words, the negation of the justifying description would have to be nonsense, not a falsehood. This has two corollaries, both of which were discussed by Wittgenstein.
(a) If it were possible to justify grammatical rules by reference to reality, those rules would be superfluous. One cannot say that a grammatical rule is made necessary by certain properties of things: e.g. the rule that excludes the words 'transparent white' or 'flashing black' cannot be justified by saying that white is not transparent or that black is not radiant. For if one could say this, then it would make sense, even though it would be false, to say that this white glass is transparent or that the traffic lights flashed black. But then the grammatical rule would be superfluous, since what it does is precisely to exclude such forms of words as nonsense.
(b) Any justification of grammar by reference to reality requires the possibility of describing a reality that would not justifify that grammar. A justifcation of our grammar by reference to reality should, it seems, take the form of saying that since reality is thus-and-so, the rules of grammar must be such-and-such. But one must then also be able to say that if reality were otherwise, then the rules of grammar would have to be different. However, one cannot sensibly say how reality would have to be in order for a different grammar to be justified. For in order to describe such a different reality, one would have to use the very combinations of words which our existing grammar excludes, i.e. one would have to talk nonsense. But if something counts as nonsense in the grammar which is to be justified, it cannot at the same time pass for sense in the grammar of the propositions purporting to justify it.

To this I responded as follows:

Hi n.n.,

I disagree with Hacker's arguments for the unjustifiability of grammar for the following reasons: First, it seems to me his regress argument works, if it works at all, only if we take sentences as the ultimate bearers of truth. If one believes in abstract propositions, as I'm inclined to do, one can hold that the justifications one gives for the grammar of some language, being abstract propositions which may be expressed in several languages each with a different grammar, don't have a grammar in the required sense. I'm sure Hacker would reject the existence of such propositions, but he would need to give some independent argument for doing so. Second, and more importantly, it seems to me that his arguments about nonsensicality vs. falsehood are self-referentially incoherent. Let us take, for example, the statement "No description of reality can justify grammar." Hacker takes this to be true. If it is true it certainly makes sense, but if it makes sense then (according to Hacker) so must its negation, namely "Some description of reality can justify grammar"; and if it makes sense Hacker can't rule it out a priori. On the other hand, if "Some description of reality can justify grammar" is nonsense, then (by Hacker's lights) so is the statement "No description of reality can justify grammar." Thus it appears that the conclusion Hacker wishes to establish is either false or nonsensical. Where does that leave us? One might think these considerations show that there are some statements which are meaningful but necessarily false. Personally, I think this is probably the correct conclusion. But there's another option which is often overlooked-- one could say that some meaningful statements simply don't have a meaningful negation at all.

The rest of the discussion is also quite interesting, so if you have the time by all means go check it out.