Friday, December 16, 2016

The sharpness of the Platonic realm

I feel an intellectual pull to a view that also repels me. The view is that all contingent vague truths are grounded in contingent definite truths and necessary vague truths. For instance, that Jim is bald might be grounded in a contingent definite truth about the areal density of hair on his scalp and a necessary vague truth that anyone with that areal density of hair is bald.

On this view, any vague differences between possible worlds are grounded in definite differences between possible worlds.

But the view also repels me. I have the Platonic intuition that the realm of necessary truth should be clean, unchanging, sharp and definite. Plato would be very surprised to think that fuzziness in the physical world is grounded in fuzziness in the Platonic realm.

Epistemicism, of course, nicely reconciles the Platonic intuition about necessary truths with the intellectual pull of the grounding claim. For it is no surprise that there be things in the Platonic realm that are not accessible to us. If vagueness is merely epistemic, then there is no difficulty about vagueness in the Platonic realm.


William said...

I think the mathematical concept of an open neighborhood or open ball in topology allows a kind of Platonic vagueness to be necessary to the proper use of many definitions and concepts.

This can be used to apply classical logic to vagueness in other, more empirical realms of knowledge.

Anonymous said...

I don't think you will ever be able to understand vagueness as long as you insist that some truths are "definite" truths in such a way that they are vague in no way. Because if that is the case, then it would have to be absolutely definite when a statement stopped being that kind and started being the vague kind. Which ultimately would mean that vagueness could not exist; this is why all your arguments tend to this conclusion.

The truth is that all truths are vague truths, because they are expressed by words, which are intrinsically vague in virtue of being words.

William said...

Although terms like limit and convergence in mathematics are vague in certain ways, I would hope they are not vague in quite the way a term like "little" might be, where different people might have very different senses of the word in similar context.

Heath White said...

If there are meaningful vague predicates, there are going to be necessary truths that capture their meaning, and those truths will be vague. "People with less than X hairs per square inch are bald" "people under age Y are children" "People over Z height are tall" etc.

So either give up your (purely aesthetic) Platonic intuition, or give up the idea of meaningful vague predicates.