Does Knowledge have an Intrinsic Maximum?

The usual forms of the Ontological Argument require the possibility of a maximally great being.  For such a being to be possible, it seems necessary that its attributes must have intrinsic maximums, that is, that they have a fullness that is not possible to be surpassed.  If they were surpassable, then there could be a greater conceivable being for every conceivable being.  So it’s rather important to defend this thesis.

But there’s an immediate problem:  It seems that, for at least knowledge, there is no intrinsic maximum.  For there are plausibly an infinite number of propositions. So to possess omniscience, a being must know an infinite number of things. So there is no greatest conceivable knowledge.

If the last paragraph’s line of reasoning works, we’re in trouble.  Let’s see how we can escape it. A degreed property can have both infinitely many degrees and an intrinsic maximum.  Here’s an example:  Being square-like.  Being square-like has an intrinsic maximum in that a perfect square is maximally a square.  The more sides something has, the less square-like it is.  It’s possible for something to have an infinite number of sides (circles).  So it’s possible to have be infinitely more or less square-like, and yet there’s an intrinsic maximum to square-likeness.  This example shows it doesn’t follow from there being an infinite degree of some degreed property that the property does not have an intrinsic maximum.

I’m not quite sure how strong I feel about this line of response, but something does feel intuitive about the claims that “all-knowledge” is a property with an intrinsic maximum despite there being an infinite number of propositions to know. 

Here's another line of thought to support this: The idea of the largest number would clearly be a property with an intrinsic maximum. The problem is that it’s an incoherent notion, as there’s always a greater number. Is omniscience like this? It’s clearly an intrinsic maximum. But is it coherent? Knowing all truths. There isn’t a greater amount of knowledge than knowing all truths, so it doesn’t seem to suffer from the same problem as the idea of a largest number. This seems true whether or not there’s an infinite number of propositions. Knowing them all is simply unsurpassable. So despite the tension in trying to hold together the notions of maximum and infinite, I think they can in fact be held together.

I’m also not thinking that this problem, if it is a problem, is going to beset Godelian OAs.  The ‘intrinsic maximum’ response has been specifically catered to defeat Gaunilo island type parodies, but as Rasmussen shows in his presentation of a Godelian OA, Guanilo’s objection can be defeated without an appeal to intrinsic maximums.  Briefly, Guanilo’s island has properties that entail negative properties (such as physicality), and given this negative entailment, a parody argument cannot be run--at least for the Godelian form of the argument.  

Typically, there’s three responses to Gaunilo:

1. Intrinsic Maximums

2. An island’s greatness is subjective

3. An island has negative properties so cannot be a maximally great being

Useful paper: https://philpapers.org/rec/MANTDA-4