I think perhaps I do. For I know all of the following:
- 1 is a number
- 2 is a number
- 3 is a number
- 1 000 000 000 is a number
. . .
etc., ad infinitum.
There are infinitely many statements in that list, and I know every one of them, so it seems like I must have an infinite amount of knowledge. Yay for me!
Is there any problem with this reasoning? Being a bear of very little (certainly finite) brain, I presumably don't have all that knowledge actually tokened 'inside' me - how could it possibly fit? It must be merely potential, I think, and is perhaps best explained in dispositional terms: If someone were to ask me 'is X a number?', for any particular X (and there are infinitely many options they could choose from), I could answer it correctly.
I've touched on some similar issues before. I'd just like to get sampling of others' opinions here: are you happy to grant that we have infinite knowledge? Or would you rather restrict knowledge to actually-tokened thoughts, to the exclusion of 'potential' ones that we're merely disposed towards affirming?