speakingwoman:
Don’t understand the expression “to be x is to identify as X” if I can’t substitute an equals sign. Don’t understand the predicate thing, plse explain. Thanks.
I will try.
[TLDR. Using '=' in place of 'is' can sometimes be confusing given different uses for 'is'. Let us try to avoid it if possible .]
Let me say first, as an aside, that the nomenclature here is not wholly settled, as often happens when we straddle overlapping areas. (Linguistics, formal semantics, model theory, philosophy, philosophical semantics, to name but a few.)
Some people call 'is' a copula wherever it appears, for instance, then distinguish different copulae; others take 'copula' to refer to the predicative use only, and go on to distinguish this from the use as identity, denying this latter the name 'copula'. And so on. A can of worms for the neophyte.
I will try to ignore such divergence of use. 'The predicative thing' is what you want to know about. I will try to explain that and why I am wary of '=' in such contexts as ours.
What follows looks complicated, but really only because of attempts at being fairly precise. The ideas are actually quite simple (honest!):
There are different uses of the verb 'to be', in English as well as other languages. Sometimes these are hidden. (Hence, in part, ' analyis ' in ' analytic philosophy'.)
Here are four such uses:
- Existence
- Predication
- Subsumption
- Identity
To help with the first three, a famous example (from Bertrand Russell, see, e.g. On Denoting ) :
Suppose someone says, 'The King of France is bald'. Is that true, false, or meaningless? There is no King of France, so 'The King of France' does not denote anything, but nevertheless the sentence seems to make sense. So?
Long story short. On analysis, 'The King of France is bald' can be seen as equivalent to this:
' There is(1) a King of France (and only one), and whatever is(2) The King of France is(3) bald. '
Seeing this equivalence allows us satisfyingly to categorise the original ' The King of France is bald ' as false, and for exactly the right reason too - because there is no King of France.
So, focusing on our own specific purpose,
- The claim there is a King of France involves an 'is' of existence: it amounts to saying the King of France is something that exists.
- Now consider the 'whatever is the King of France'. This involves an 'is' of predication. This might be more easily seen if - as is conventional - we replace the 'whatever' by a variable - 'x', say. Then we will have, simply 'x is the King of France', which we say, predicates the property of being the King of France to the (indeterminate) x.
- We can also name the property of being the King of France; call this property 'K'. Now the last part of the statement above comes out as 'Anything K is bald'. This illustrates the 'is' of subsumption. The property of being K is subsumed under the property of being bald.
[This latter 'subsumption' use/meaning for 'is' clearly relates to logical implication, and (thereby) also to set (or class) inclusion. One reason I am wary of giving exlanations in this area involving sets/classes is that similar confusions sometimes arise in doing so to those that may occur regarding '='. Best to try to do as much as possible in ordinary language.]
Now, what about the 'is' of identity? I had 'two times two is four' as an example earlier. Possible confusions with the 'is' of predication was what made me suggest we eschew using '=' as an 'is' replacement, even if in some cases it is appropriate, as in 'twice two = four'.
[People have also confused identity with existence and with subsumption, as I mentioned just above. Easy enough to do.]
In our example, 'A woman is a female' predicates 'female' of 'woman'; it says that a woman has the property of being female. An identity between being a woman and being a female? Or beween 'woman' and 'female'? Hmm.
One difference between predication and identity is that identity is a relexive relation: if x is(identically) y then y is(identically) x. Predication, not so: x is(predicatively) y does not imply y is(predicatively) x. A woman is a female, but a female is not necessarily a woman.
Or what about subsumption? Being a woman is subsumed under being female? Hmm again.
These 'Hmm's are intended to indicate that the distinctions may not be clear cut. For example in some cases we might want to generate a kind of identity using predicative 'is's. Some people talk of gaining a 'general identity' in definitions involving necessary and sufficient conditions stated in predicative terms, for instance.
But I would rather not go down that route, at least here at the start.