Arguing in the first direction, there are probably properties for which human language has no terms. So, there are probably properties that don't stand in one-to-one correspondence with predicates.
And even if there aren't any properties for which human language has no terms, rocks, cabbages, trees and things had properties before man and would have had he never risen from the ooze at all.
Infinities and Infinities and Infinities
Arguing in the second direction, by following accepted predicate formation rules, predicates can be gratuitously generated from other predicates. They can, for example, be generated from disjunctive predicates like “—is red or yellow”, “—is red or shiny”, and “—is red or aquatic”, and negative predicates like “—is not yellow“, “—is not shiny”, and “—is not aquatic”. If predicates stand in one-to-one correspondence with properties, each of those predicates corresponds to a unique property. So, if predicates stand in one-to-one correspondence with properties, there is some indefinitely large number of properties in the world1.
The one-to-one correspondence also leads to infinite regresses. For instance, “a is self-identical” would correspond to a property of self-identity. If, however, a has the property of being self-identical, it also has the property of being self-identical with itself-with-that-property-of-self-identity. And if a has the property of being self-identical with itself-with-the-first-self-identity-property, it also has the property of being self-identical with itself-with-the-self-identity-property-for-itself-being-self-identical-with-itself-with-the-first-self-identity-property. And so on, ad infinitum.
There is another regress. If predicates stand in one-to-one correspondence with properties, the truth of “a is red” necessitates that a has the property of being red. If, however, the truth of “a is red” necessitates that a has the property of being red, the truth of “a has the property of being red” necessitates that a has the second-order property of having the property of being red. And so on, ad infinitum.
There are more regresses. If predicates stand in one-to-one correspondence with properties, the previous argument applies to every property we can generate from a base predicate (e.g. red). So, if predicates stand in one-to-one correspondence with properties, there is an infinity of properties of having properties for every base predicate.
There are, however, probably not infinities of odious properties like the above. So, predicates probably don't stand in one-to-one correspondence with properties.
Contradiction
There are also paradoxical predicates like “—is a property to which no predicate corresponds”. So, predicates don't stand in one-to-one correspondence with properties, and we can abandon the disastrous conflation of predicates and properties, of language and reality, once and for all.
You will see why all this matters, if not now, in future posts.2
1. I take Ellis's word for it when he says that there is at least one infinite set corresponding to each generative operation.
2. Most of this post's arguments, as well as its title phrase, can be found in George Molnar's Powers.
I see that Armstrong rails against the same thing in his vol.2 of Universals. Dyke suggests that we can "separate ourselves" from language, and I'm not sure what I'm supposed to make of this. I'm assuming the whole analytic tradition, including Russell makes the conflation of language and reality. But I'm also kind of lost on where the Scholastics would stand here, how would Scholastics distinguish "terms," from words, where the latter serve as symbols that represent objects or ideas, and thus are subject to change, while the former isn't.
ReplyDelete