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Tuesday, November 02, 2010


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Excellent post. Need to ponder more. One quick comment. In the conclusion the following sentence appears to contain a misprint: "The key premises in both arguments -- (2) and (4) -- are necessarily true if true."

Did you mean to say premises here 2 and 4 or rather premises 2 and 5?

Thanks for catching that mistake, Peter. I have corrected it.

I wonder if you can take the Cantorian idea of there being no "largest infinity" and apply something similar to there being no Greatest Conceivable Being?

There is no greatest conceivable being in the same way that there is no largest infinity.

There may be a limit to what a human can conceive, but surely there are possible worlds where there are "greater conceivers" than us.

In fact, maybe just as there is no greatest conceivable being, there is also no greatest conceiver?


The "greatness" of the greatest conceivable being is not a quantified greatness like in the case of numbers; it's a qualitative greatness. I don't see how insights in mathematics have anything to do with whether or not the greatest conceivable being is possible.


What Steven said in reply is basically right. Also, nothing depends on what we can conceive. To avoid that misinterpretation, I could use 'maximally perfect being.'

Steve and Bill,

So I can say "the largest infinity", but this doesn't refer to anything because there is no largest infinity.

I can say "the maximally perfect being", but why should I think that this refers to anything either?

What does "maximally perfect" even mean? Perfect according to what measure?

In the unbounded space of possibility it seems conceivable to me that (regardless of your measure of perfection) for any being there could always be a "more perfect being" one world further out.

e.g.: "This perfect being has an infinity of cherries on top, but here's another *even more perfect* being with an even larger infinity of cherries!"

Here my measure of perfection is heavily influenced by the number of cherries on top of the being. On what grounds could I be proved wrong?

I'm not certain that you're wrong in saying that mathematical insights don't apply, but I'd like to hear the case made as to why they don't.


A maximally perfect being has everything that we think makes a being great to the maximal degree. So for instance, rationality makes a being great -- that is why humans are greater than worms or dirt, or at least one reason -- and so a maximally perfect being would have rationality to the maximal degree. The proponents of such a view would just respond to your question of "Perfect according to what measure?" by saying that there are just objective, non-conventional facts about what makes beings greater or lesser, and it is according to that standard, if it can be called a standard, that the maximally perfect being is maximally perfect.

You say it seems conceivable to you that there be a greater being than any one you could imagine. This doesn't show much, of course, because at best this shows whether or not you are able to find a contradiction in a certain proposition. It doesn't follow from the fact that you can conceive of there being no greatest possible being that therefore there is no greatest possible being.

But I am wondering exactly how you are conceiving of beings being greater than the other. I don't understand your talk of cherries on top of a being.

The fact that there is no greatest number doesn't have any tendency to show that there is no greatest possible being, because "greatest" is equivocal between the two. The greatest number is one that is greatest in terms of quantity; the greatest being is one that is greatest in terms of qualities, and these qualities cannot be quantified, they can't be put into numbers or measured like that.

A very quick thought on the Argument From Evil, which I'm sure is of no consequence whatsoever: I accept that you don't need the R-to-L reading of 7 in order for the argument to work. But if you were to require it, a formulation of 7 which might work would be:

7'. Necessarily, there can be gratuitous evils iff the GCB does not exist.

(presumably there could be a possible world where no GCB exists but there are no gratuitous evils, just by chance).

7', though, does leave the door open for contingent evidence to make an appearance. For, whilst it is necessary that there can be gratuitous evils iff the GCB does not exist, whether there are or not is an evidentiary matter.

I doubt there's anything of value in that, but I enjoyed the mental workout.

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