As regards my earlier post, Maverick asks
Can we justify a distinction between the ‘is’ of identity and the ‘is’ of predication even if we do not make an absolute distinction between names (object words) and predicates (concept words)? I think we can.
We need to look deeper at the reason for the absolute distinction between singular terms and common/concept terms, which originates with Frege, who firmly believed that we must ‘keep well apart two wholly different cases that are easily confused, because we speak of existence in both cases’.
In one case the question is whether a proper name designates (bezeichnet), names, something; in the other, whether a concept takes objects under itself (unter sich befaßt). If we use the words ‘there is a –‘ we have the latter case. Now a proper name that designates nothing has no logical justification, since in logic we are concerned with truth in the strictest sense of the word ..
For the latter relation he also uses the term ‘falls under’ (unter .. fällt). For example he says
Das Wort ‘Planet’ bezieht sich gar nicht unmittelbar auf die Erde, sondern auf einen Begriff, unter den unter anderm auch die Erde fällt. So ist die Beziehung zur Erde nur eine durch den Begriff vermittelte, und es bedarf zur Erkennung dieser Beziehung der Fällung eines Urteils, das mit der Kenntnis der Bedeutung des Wortes ‘Planet’ noch keineswegs gegeben ist. Wenn ich einen Satz ausspreche mit dem grammatischen Subjekte ‘alle Menschen’, so will ich damit durchaus nichts von einem mir ganz unbekannten Häuptlinge im Innern Afrikas aussagen.
(‘The word ‘planet’ has no direct relation at all to the Earth, but only to a concept that the Earth, among other things, falls under; thus its relation to the Earth is only an indirect one, by way of the concept; and the recognition of this relation of falling under requires a judgment that is not in the least already given along with our knowledge of what the word ‘planet’ means. If I utter a sentence with the grammatical subject ‘all men’, I do not wish to say something about some Central African chief wholly unknown to me.
This is contrary to the assumption of Aristotelian logic where the same relation of falling under (subsumption, from the Latin sumere sub) holds between objects and both common and proper names. The difference with the proper name is that only one thing can fall under the name, when used in the same sense. Thus a premise with a proper name in it can be treated as a universal proposition. As Ockham says (Summa III-1.8)
It should be known also that just as it is argued evidently by putting such an affirmative or negative universal for the major in the first figure, so also it follows evidently if the major is an affirmative or negative singular. For “Socrates is white, every man is Socrates, therefore every man is white” follows well.
This is because only one object falls under ‘Socrates’, when ‘Socrates’ has a fixed sense, so ‘Socrates is bald’ if true is true because every man who is Socrates is bald, since there is only one of him.
If this is correct (and that is an assumption) there is no need for identity. Take e.g. ‘Hesperus is Venus, Venus is Phosphorus, therefore Hesperus is Phosphorus’. This can be interpreted as a syllogism with the valid form ‘every Hesperus is Venus, every Venus is Phosphorus, therefore every Hesperus is Phosphorus’. Any identity statement whatsoever can be interpreted as a universal statement.
Maverick objects that ‘Tom is hypertensive’ can be analysed as ‘Tom instantiates hypertensiveness.’ Fine, which is similar to Frege saying that Tom falls under the concept of hypertensiveness. Indeed, Frege holds that concept names (common terms) are names of Platonic extralinguistic objects. But then he says
It appears that Sommers is mistaken in his claim that “Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read ‘a is b’ dyadically and to see in it a sign of identity.”
Well, no, because the whole point of the two term theory is that the same term (including proper names) can stand as both subject and predicate, and the whole point of the Fregean theory is that a proper name cannot stand as a predicate: we cannot interpret ‘Hesperus is Venus’ as ‘Hesperus has Venus-ness’. So the Maverick’s analysis implicitly rejects the two-term theory. He then objects to the nominalist theory that in ‘Hesperus is a planet’ both terms denote a single thing, on the grounds that while Orwell might not have fallen under ‘famous’, there is not possible situation in which he might might not have fallen under ‘Orwell’. So? According to Aristotle, and all the medieval logicians:
By the term ‘universal’ I mean that which is of such a nature as to be predicated of many subjects, by ‘individual’ that which is not thus predicated.
That is why proper names are called ‘proper names’. They are of such a nature as only to be predicated of a single individual. Every Orwell is an Orwell, and every Orwell is necessarily an Orwell: it is false that Orwell might not have been an Orwell, although he might not have been a famous person.