Metaphysical monstrosities

I have been looking at ‘Van Inwagen on Fiction, Existence, Properties, Particulars, and Method’, by Bill Vallicella (Studia Neoaristotelica Review Article 12 (2015) / 2). Bill is the famous Maverick Philosopher.

Section 3 deals with haecceity. A haecceity property is one which, unlike man or white cannot be multiply instantiated, or as Scotus said, not-predicable of several things (indicibilis de pluribus). For example, being Socrates (Socrateity) is a property which, if instantiated, is instantiated by Socrates alone in the actual world and by nothing distinct from Socrates in any possible world.

It is necessary to posit such properties, Bill argues, to support the semantic thesis of the univocity of ‘exists’ and ‘is’, and its ontological counterpart, that there are no modes of being/existence. It is essential to the thesis that number-words are univocal, and that ‘exists’ is a number-word. But it is not a number-word, for we can say of certain individual things that they exist, using referring terms.

Consider my cat Max Black. I joyously exclaim, ‘Max exists!’. My exclamation expresses a truth. Compare ‘Cats exist’. Now I agree with van Inwagen that the general ‘Cats exist’ is equivalent to ‘The number of cats is one or more’. But it is perfectly plain that the singular ‘Max exists’ is not equivalent to ‘The number of Max is one or more’. For the right-hand-side of the equivalence is nonsense, hence necessarily neither true nor false.

Right, but can’t a proper name N signify a property N* which can be instantiated, but by only one individual, and always and necessarily by the same individual? Then it makes sense to state there is only one object possessing N*, a statement which is false only if there are no (i.e. zero) objects possessing N*. Bill considers this, but thinks it a heavy price to pay for univocity across general and singular existentials.

‘Haecceity properties are metaphysical monstrosities’.

Why? His argument is that being properties, haecceities are necessary beings, and so exist at all possible times in all possible worlds. But how, before Socrates came into existence, could there have been any such property as the property of being identical to him. There would have been simply nothing to give content to the proposition that it is Socrates.

Now I agree that a haecceity predicate is essential to save the univocity of ‘exists’. And I agree, for the reasons given by Bill, that a haecceity property is absurd. But can there not be predicates, i.e. grammatical items, which have no properties corresponding to them?

More later.

What does the pronoun ‘I’ refer to?

What does the pronoun ‘I’ refer to? Wittgenstein (Philosophical Remarks, §64).

‘I have a pain’ is a sign of a completely different kind when I am using the proposition, from what it is to me on the lips of another; the reason being that it is senseless, as far as I’m concerned, on the lips of another until I know through which mouth it was expressed. The propositional sign in this case doesn’t consist in the sound alone, but in the fact that the sound came out of this mouth. Whereas in the case in which I say or think it, the sign is the sound itself.

Face blindness

Hume, Treatise Book I Part iii, section 2 (my emphasis):

We readily suppose an object may continue individually the same, though several times absent from and present to the senses; and ascribe to it an identity, notwithstanding the interruption of the perception, whenever we conclude, that if we had kept our eye or hand constantly upon it, it would have conveyed an invariable and uninterrupted perception. But this conclusion beyond the impressions of our senses can be founded only on the connexion of cause and effect; nor can we otherwise have any security, that the object is not changed upon us, however much the new object may resemble that which was formerly present to the senses.

Back-reference guarantees sameness of subject. Perception doesn’t. Think of the Bunuel film where two actresses (Carole Bouquet and Angela Molina) play the same character (Conchita). I was one of the many people who were fooled into thinking they were the same actress, because of the identity of character. Think also of the meaning of ‘persona’, namely ‘mask’. This idea comes more easily to me I suppose because I suffer from ‘face blindness’. I find it hard to tell when I am meeting the same (relatively unfamiliar) person or not, and rely on tells such as hairstyle, build, age and so on. I am often embarrassed when I meet the same person in the same day but the lighting is different or they have dressed differently and I do not recognise them. I often have to bluff my way out of it. The world of strangers is literally like a world of masks without identity. My wife and daughter guide me through film plots.

Now it might be that perceptual ‘reference’, i.e. reidentification, is some guaranteed and fail safe way of acquiring rapport with the subject, so you always know that the same person is before you. But I think not. I think other people just have better visual processing powers, meaning that a person’s face is a kind of uniquely applying description or ‘look’ that only one person can have. A sort of visual haecceitas, but which is descriptive, for all that. Think of identical twins. Their visual description is the same, so it’s a qualitative identity, not a numerical one.

Indefinite reference

14:51 And there followed him [Jesus] a certain young man (νεανίσκος) , having a linen cloth (σινδόνα) cast about his naked body; and the young men laid hold on him. 14:52 And he left the linen cloth, and fled from them naked.

The pronouns ‘he’, ‘his’, ‘him’ etc. clearly refer back to ‘a certain young man’. On the theory of extralinguistic reference, they do not refer in themselves, but inherit their reference from the antecedent. But the antecedent is an indefinite noun phrase. Can that refer? Surely not. Mark says ‘νεανίσκος τις’. The article τις (Latin quidam) means ‘a certain’, often used to suggest that the writer either cannot or will not speak more particularly. Commentators have speculated that the man was Mark himself, the author of the gospel, which if true means that ‘a certain young man’ and the pronouns, could be replaced with ‘I’, salva veritate. But Mark deliberately does not tell us. So in what sense does it refer?

Or suppose it does refer. Then as Geach argues (Reference and Generality chapter 1), the sentence ‘some man was wearing a linen cloth’ is true if some man – any man – was wearing a linen cloth. Even if the speaker has some particular man in mind, say Frank, and he means to say that Frank was wearing a linen cloth, it could have been the case that Frank wasn’t wearing a linen cloth, but some other man was, say Dick. So Dick was wearing a linen cloth, and so what the speaker actually said, i.e. ‘some man was wearing a linen cloth’, is true. But what the speaker meant to say is false.

It gets more difficult. If it is true that some man was wearing a linen cloth, whoever he was, then it is true to say that he was wearing a linen cloth. Note I use the pronoun ‘he’. I wrote ‘he was wearing a linen cloth’. But the subject of that sentence is a definite noun phrase, and so the sentence is true if and only if that man, and no other, satisfied the predicate. E.g. if that man was Frank, then the pronominal sentence is true if Frank satisfied the predicate, and false if he didn’t, even if Dick was wearing a linen cloth. Furthermore:

(1) Some man was wearing a linen cloth
(2) Sentence (1) is true if and only he – that man – was wearing a linen cloth.

How weird. Didn’t I say that sentence (1) can be true so long as someone – anyone satisfied ‘was wearing a linen cloth’? Yes, that’s still correct, because he, that man, could be any of the men. He could be Frank, Dick or Raymond. The whole point is that sentence (1) has an indefinite subject, and so doesn’t tell us which person satisfies the predicate. We know that he satisfies it, if the sentence is true. But we don’t know who he is.

Reference as target practice

Successful reference: You must not only hit something; you must hit the right thing. And what makes a thing the right thing is the intention of the one who refers.

I discussed this 'target practice' theory of reference a while ago. I am not impressed. The purpose of language is to communicate, and the role that reference plays is to communicate which individual the speaker is talking about. Or rather, when the speaker utters a sentence of subject-predicate form, with a referring term as subject, the purpose of reference is to communicate which individual the predicate is said to apply to.
 
So it's not just a matter of hitting the target on the bull's eye. The person you are communicating with has to understand too. How does he know you hit the target? Is it e.g. that he also has to have the target in his or her sights in some way?

We watched American Sniper over the weekend. At the target practice, there was a supervisor with binoculars who would check whether the trainee had hit the target successfully. If that is the analogy, how would it apply to reference? It implies the hearer has some privileged relationship with the target. What if the hearer is an atheist, and does not see, or refuses to see, the target? That implies an atheist cannot understand a Christian’s reference to God. But surely he can. I am sure there are a few atheists or agnostics following this discussion. Are they unable to follow it without binoculars? Surely not.

Who is Antichrist?

In medieval logic 'Antichrist' was a proper name frequently used as an example of reference to an individual who does not exist now, but will exist, just as 'Caesar' was the stock example of reference to an individual who does not exist now, but used to exist. This may help to illuminate the curious discussion going on at Vallicella's place. For all the following statements are (almost uncontroversially) true, in my opinion.

(1) At least some of the biblical texts (including Daniel 7, 8 and 11, Revelation 13 and 17) claim to make identifying reference to a man or creature who would rise up against God and the 'Son of Man', and who would wage war on the saints. For example, Daniel (7:8) claims to have seen the person in a dream, a direct revelation of the future ("and behold eyes like the eyes of a man were in this horn, and a mouth speaking great things"). Thus, even if the prophets weren't making an identifying reference, they thought they were.

(2) When the medieval scholars used the term 'Antichrist', they were aiming to refer to the same individual that prophets thought they were referring to. Thus the name 'Antichrist' was used, and is used, with the aim of making an identifying reference.

(3) Various descriptions of Antichrist are given in the biblical texts, in order that we might recognise him. Hence the question arises, even now, if whether certain individuals who exist now should be identified as Antichrist. Eg. Ian Paisley denounced Pope John Paul II as the Antichrist in 1988, and many people in America think that Obama is Antichrist.

(4) But the significance of the name should not be confused with any description by means of which we are told to recognise Antichrist. If the name signified the description, the identity would have the status of a logical truth, and we could not reasonably question whether anyone satisfying that description was Antichrist.

In summary, the name 'Antichrist' is a singular term used to make an identifying reference, or with the aim of doing that. Thus it makes an identifying reference to an individual who probably does not exist yet, or aims to make such a reference (in the case that Antichrist never exists). It is not a description, for there are individuals satisfying the description of whom one could reasonably deny they are Antichrist. E.g. when I say that Obama is not Antichrist, I am not denying a logical truth.

Charley’s (single) ant

And here is another interesting paper by Greg Frost-Arnold, “Too much reference”. He considers the case in some way opposite to empty singular terms: where a singular term ‘refers to’ more than thing.

He writes:

Suppose a person purchases an ant colony. There are many small ants in the colony, and two big ants, Ant A and Ant B. However, the owner of the ant colony does not realize that there are actually two big ants, because he only sees one big ant at a time. (We assume the ants’ behavior is coordinated to satisfy this condition.) The owner believes that there is one big ant in the colony, and the owner decides to name this ant ‘Charley.’ The philosophical issue such a story raises is this: what is the semantic status of sentences that include the term ‘Charley’?

This is a case I discussed, with reference to a Bunuel film, here and here. There are actually two people (Carole Bouquet and Angela Molina) playing the same character (Conchita). Does the name ‘Conchita’ refer to two people – for once you have realised the trick, it is obvious that there are really two characters – or one? Or (pace Greg) to none at all?

If the theory of reference (the ‘Frodo’-Frodo theory) I have argued for is correct, this sort of multiple reference is impossible. The meaning of a name is exhausted by its function of purporting to signify the same thing. To understand the sentences ‘Fa’ and ‘Ga’ is to understand that if they are both true, then “some F is G” is also true. And, because they do not imply that some Fs are G, they they can only imply that one F is G. To say that there are two F’s is to say that there is an F, and there is another F. The word ‘another’ is the complement of a singular term. It always means a different thing, and for there to be one different thing means there being at least two different things.

What about the ants? Can’t it plausibly said that the proper name ‘Charley’ refers both to Ant 1 and to Ant 2? No, because, as I have argued, reference is not a semantic relation between language and reality. As I have argued, we can regard the two ant images as visual proper names. I see ant 1 walking out of the colony, and entertain the visual proposition ‘Here is an ant’. Ant 1 goes back, and ant 2 now comes out. I entertain the visual proposition ‘Here is the same ant’. Since I cannot understand this visual singular as applying to more than one singular, i.e. because I understand it always as meaning ‘the same …’, I cannot understand it as multiple reference. Thus it cannot be multiple reference. Singular terms always refer to singular things.

Crane on singularity

In an earlier post I looked approvingly at Tim Crane's views on singularity, and promised to follow up with some things I don't like so much.  Now what I don't like so much is Crane's characterisation of failed reference.  He says that "a thinker can think about a particular object and yet fail to refer to that object in thought", and that “There are many cases where thinkers appear to be having singular thoughts in this sense even though the object of the thought does not exist: aiming to refer to a specific object in this case fails to ‘hit’ the target object" (my emphasis).


On the contrary.  As I have argued here, a proper name individuates: it tells us which individual a proposition is about.  It is easy to show (a) that it cannot fail to do this, once understood, and (b) that it has no other function.

Proof:

(a) A proper name individuates by telling us which sentences are verified by a single subject.  The sentences "Frodo is a hobbit ... Frodo has large feet" together say that some hobbit has large feet, i.e. a single thing is both a hobbit and has large feet, and not that some thing is a hobbit and that some thing (possibly a different thing) has large feet.  You simply haven't understood how the proper name works if you think that both sentences could be true without being true of a single thing.  I say a bit more about this here.

(b) This is all that proper names do.  (i) They have no descriptive sense.  They tell us which individual a sentence is about by telling us which individual it is the same as.  The 'Frodo' of the second sentence above tells us that if the second sentence is true, it is true of the same thing as the first sentence, if true, is true of, and no more.  This is exactly how proper names individuate in stories, and it is clear they can do no more than this.  Nor can they do any more even if the story is true, and all the names 'refer'.  (ii) They have no 'extra-linguistic' sense. As I argued here, if any piece of language has an important communication function, we should be able to tell whether it has an important communication function. One of the most important features of communicating with someone is that they should know they are being communicated to. Therefore, if non-empty proper names communicate information that empty proper names don’t, we should know this, and we should be able to tell whether a name was empty or not.  But we can't do this.  We do not know for certain whether the Christ Myth theory is true or not, and thus we don't know whether the name 'Jesus' is empty or not.

There is nothing that a proper name could try to do, that it does not do.  A proper name tells us which character is being written about, and it does this successfully whether in a story ('King Arthur found a sword') or in a piece of history ('King Albert burned the cakes').  Thus Crane's idea that it could possibly fail to accomplish anything is a mistake.

Indiscernibility of Identicals

One of the assumptions in the substitution problem was the indiscernibility of identicals:

Fa and a=b implies Fb

Is this always true? A slightly different way of expressing the law is that if Fa, and if 'a' denotes exactly what 'b' denotes then Fb. But in this form the law is clearly not valid. Suppose there is a shortage of red paint, and that only Ferraris are red. Then it follows that if Ferraris are fast, then red cars are fast, and conversely. But it does not follow that if John thinks Ferraris are fast, then he thinks that red cars are fast – perhaps he is imagining a red reliant Robin that he once saw. I.e. F = ‘John thinks that every – is fast’ and a = ‘Ferrari’ and b = ‘red car’. Then Fa and the fact that ‘a’ denotes everything that ‘b’ denotes does not entail Fb.

You will object that indiscernibility of identicals applies only when a and b are proper names. Proper names are referring terms, not common terms like ‘Ferrari’ or ‘red car’. I reply: what is a referring term? If it is defined as something to which indiscernibility of identicals necessarily applies, then the ‘Shakespeare’ arguments in the previous posts suggest that indiscernibility of identicals does not apply to ordinary proper names at all.

Object-independent semantics

Vallicella alludes here to a distinction originally made by Gareth Evans between ‘Russellian’ and ‘Fregean’ understanding of propositions. He says (to Peter Lupu)

Your understanding of Kaplan is excellent. But for him propositions are
Russellian, not Fregean. If 'Mt Blanc is snow-covered' expresses a Russellian
proposition, then Mt Blanc itself, that massive physical object, together with
its snow fields and subterranean gopher tunnels, etc. etc. is a constituent of
the proposition. But I can't swallow the Russellian view; how could a finite
mind wrap itself around such a monstrous object?

On the Russell-Kaplan view (although Russell himself probably never consistently held such a view), the semantics of singular thought is ‘object dependent’. A thought about Mont Blanc actually contains Mont Blanc – with all its snow fields. That seems absurd for a number of reasons. How can a thought contain a physical object? How can a thought even be internally related to an object when the thought remains the same whether or not the object exists? Does the proposition ‘Etna is a volcano’ cease to be meaningful even if Etna is completely destroyed in an eruption? Surely not. Is the proposition ‘Caesar was a man’ meaningful even though Caesar does not exist? Surely it is.

The problem is to explain individuation. The name ‘Mont Blanc’ individuates. It tells us which large object is the subject of the proposition 'Mt Blanc is snow-covered'. It distinguishes that object from other similar objects such as Ben Nevis, Kilimanjaro, Everest and the rest. How do we give an object-independent account of the semantics of individuation?
The key, as I shall argue, is to explain the semantics of fictional names. The name ‘Aeneas’ distinguishes a character in Virgil’s epic from all the other characters mentioned in the Aeneid. If we can explain how that is possible, it will be possible to explain individuation in general, I believe.

You will be Marcellus

In his gloss on Porphyry (Commentary on Porphyry’s Isagoge, edited by Bernhard Geyer in Beitraege zur Geschichte der Philosophie und Theologie des Mittelalters 21 (1). Aschendorff: Munster 1919), Peter Abelard quotes from Virgil's Aeneid, book VI line 865. 'Who is that, father, marching at the side of Marcellus?'. Virgil is referring to Marcellus the younger (42 BC – 23 BC) who was the eldest son of Octavia, sister of Augustus Caesar. He died young, at the age of 19, rumoured to have been poisoned by Livia, Augustus' wife.

Marcellus was one of those future Romans whom Aeneas sees in the underworld in Book VI of the Aeneid. The passage from 865-885 recounts Marcellus's life and laments his early death. The line at 882 'tu Marcellus eris', 'you will be Marcellus' supposedly caused Octavia to faint with grief when it was read to her and Augustus, and inspired many bad paintings.

Why does Abelard mention this here? The context is a discussion of Boethius' account of individuation, that individuation comes about by a set of properties that are unique to each individual. Socrates is individuated because the collection of properties ‘bald’, ‘snub-nosed’, ‘old’, ‘son of Sophroniscus’ is found in no other person except Socrates. (Saul Kripke famously criticised a very similar theory in Naming and Necessity).

Abelard says that the reply was ‘Marcellus’ not because of the substance which he was seeing, but because of the unknown quality which could not be perceived by sense - which Boethius seems to agree with when he gives the made up name of 'Platonity' (platonitatem) to the whatever property it is that individuates Plato (Non propter substantiam quam videbat, responsum est 'Marcellus' sed propter ignoratam qualitatem quam sensu percipere non poterat. Cui etiam Boethius consentire videtur in editione secunda super Perihermeneias, ubi proprietatem Platonis ficto nomine platonitatem appellat).

Perhaps Abelard also has in mind how the future Romans are those whose souls are owed a second body. It is Mind that sets all matter in motion, by infusing the material bodies with spirit. When some people die, their spirit is not wholly freed from the ills and miseries of the body. Some of these souls are stretched out to dry in the winds, or are sent over the plains of Elysium until the days remove the ingrained corruption of the body and leaves them pure ethereal sense. They are drenched by God in the river of Lethe, which removes all their memories so that they go back for a second bodily life. In that case, their identity cannot consist in any perceptible property. Perhaps Abelard is alluding to this.

What is individuation?

Later on, I shall be arguing that empty names individuate just as well as non-empty ones, and that since individuation is the primary semantic function of a proper name (as well as any other singular term), the semantics of empty names is no different from semantics of non-empty names. But what is individuation?

The concept (as with so many philosophical concepts) goes back to the medieval period. It is clearly articulated by Henry of Ghent (Quodlib. 5. quest. 8) as being a 'double negation', and by Scotus (Ordinatio II. iii. q2) as 'privatio divisionis in se et privatio identitatis ad aliud' - the privation of division, and the privation of identity with another.

Taking the first of these negations (I will discuss the second elsewhere), what does 'a privation of division' mean? It is where we get the word 'individual' - literally, the undivided or undividable. What is meant is that the division of genus into species, the division of the species into sub-species, and so on, comes to a halt when we reach the individual. We can divide a genus (e.g. animal) into different species of the same genus, such as giraffe, koala, swan, man, and so on. A species such as man can be divided into individuals of the same type, such as Socrates, Plato, Aristotle and so on. But there it ends. You cannot divide Plato into different things of the type Plato.

This is all rather medieval, but it has a simple logical consequence. It means that the inference

A man is white and a man argues, therefore something that argues is white

is invalid, for Socrates might be the only person who is white, and Plato the only person who is arguing, and so no one individual is both arguing and white. The inference fails because there can be always be different things of the same kind, for anything above the 'most specific species' (i.e. the individual). But on the other hand

Socrates is white and Socrates argues, therefore something that argues is white

is valid, for there cannot be one Socrates who is white, and another different Socrates who is arguing (at least when 'Socrates' is understood in the same sense). A name, taken in the same sense, cannot be verified of different individuals. Or rather, what we mean by 'individual term' is such that inferences of the type above are valid. If 'A is B and A is C' implies that some B is C, i.e. if it cannot be true that A is B and A is C, without it also being true that some B is C, then 'A' must be a singular or individual term. The semantics of the singular term is defined - I will argue wholly defined - by this feature.

Boethius on the Trinity

Boethius' treatise on the Trinity is one of the two key places for the medieval discussion of individuation and numerical identity (the other being distinction III of book 2 of Peter Lombard's sentences). The discussion was of fundamental theological importance, for the catholic or 'universal' faith holds that there is one God. But God is three persons.'there is one Person of the Father, another of the Son, and another of the Holy Spirit'. This seems to involve a contradiction. If God is identical with each of those three Persons, then God is identical with three different things. But there is one God - i.e. God is one thing only. Since a contradiction (in the sense of the simultaneous assertion of two contradictory statements) cannot be true, it follows that dogma requires all Christians to believe - on pain of eternal damnation and suffering - something that cannot possibly be true. This is a clear problem for the orthodox.

The sixth century Christian philosopher-theologian Boethius was one of the first to engage the obvious difficulty of the Trinitarian doctrine in a logical and philosophical way. His solution to the difficulty is here. I shall briefly discuss it.

His solution rests on a presumed distinction between predication which ascribes real properties that belong to a subject 'of itself', and predication which is merely circumstantial, and which "is not grounded in that which it is for a thing to be". A real property is one which belongs to some thing in respect of that 'which it truly is' (in eo quod ipsa est). A circumstantial property is what no way belongs to a thing itself (minime vero ex sese). Circumstantial predication in no way "augments, diminishes or changes the thing itself of which it is said". He gives the following example of circumstantial predication:

[…] let someone stand. If I approach on his right he will be 'left' in
comparison to me, not because he is himself left (ille ipse sinister sit), but
because I will have approached him on his right. Again, I approach on his left:
he will likewise be to my right. not because he is 'right’ in himself (non quod
ita sit per se dexter), as something might be white or tall, but because he
becomes right by my approaching, and that which he is by me or from me is in no
wise from him himself.

But certain forms of predication, in particularly the category of relation (such as father to son, son to father) are merely circumstantial. He says:

Therefore those things which do not produce a predicate in respect to a property of some thing, in that which it truly is, are able to alter or change nothing and can vary no essence in any way. Thus if 'Father' and 'Son' are predicated in relation, and they differ in no respect but this relation alone, as was stated, and if [this] relation is not predicated of that of which it is predicated as though that relation were also on the side of the thing [secundum rem] of which it is said*, then this predicate does not produce a difference of things in that of which it is spoken, but indeed -if it can be said- it produces something that can scarcely be understood: a difference of persons.

[…] Thus substance holds together unity, while relation brings number to the Trinity: therefore those things which are brought forth in isolation and separately are of relation. For the Father is not the same as the Son, nor is the Holy Ghost the same as either of them. Yet God is the same as the Father, the Son and the Holy Ghost. He is the same as justice, goodness, greatness and all the things which can be predicated of Him Himself.

This is not at all easy to follow! The argument seems to be that the relation of God the father to God the son is circumstantial to God himself, and so is consistent with the identity of the Father and the Son. But where does that leave us with respect to Leibniz principle that things which are truly identical are indiscernible, and that things which are discernible are not identical? Boethius appears to be saying that

(*) father(a, b) and not father(b, a) and b = a.

on the grounds that the relation of fatherhood of a to b is merely circumstantial to a, and circumstantial to b, and so is consistent with the essential, non-circumstantial identity of a and b. This clearly violates Leibniz' principle, which does not make any distinction between the two kinds of predication (if indeed the distinction is intelligible in the first place).

Boethius, if he were around, might argue that the principle fails for certain forms of predication: indeed, that his distinction between real and circumstantial predication is precisely the distinction between predicates for which Leibniz holds, and those for which it doesn't. But that doesn't seem to work. You might argue that the distance between me and some fly buzzing around in China is not real, but merely circumstantial. But it nonetheless holds that if I am now 8,000 miles from that person, and some person X is now 8,001 miles from that fly, then I am not identical with X. Leibniz principle ought to be valid for any form of predication. But in that case, Boethius' argument fails.


* The italicised portion is my my translation as I cannot believe Kenyon is right. I am translating relatio vero non praedicatur ad id de quo praedicatur quasi ipsa sit et secundum rem de qua dicitur. Kenyon has "and if this relation is predicated neither relative to that of which it is predicated, as though it were the same, nor according to the thing itself of which it is said". It may be that Moreschini's edition has a different Latin, but I doubt it.

Individuation in the Logic Museum

Some sizeable and magnificient additions to the Logic Museum today.

• A new page on Individuation.
• It includes a brief history of the question of individuation by Phillips.
• Boethius' essay on the Trinity.
• Some works of Thomas, including the long but unfinished commentary on Boethius on the Trinity.

Thomas commentary includes question 4, a penetrating analysis of numerical difference and identity. See Article 1, Whether Otherness Is the Cause of Plurality, Article 2, Whether Variety of Accidents Produces Diversity According to Number, Article 3, Whether Two Bodies Can Be, or Can Be Conceived of as Being Simultaneously in the Same Place, and Article 4, Whether Variety of Location Has Any Influence in Effecting Numerical Difference.

Why haecceity is not repeatable

The difficulty raised by Paasch is as follows. If haecceity involves a form of relation to an individual, the haecceity cannot be prior to the individual which it individuates, and then the individual must be already an individual. The haecceity arrives 'too late'. But if haecceity is absolute, then it is not contradictory for God to create another, numerically different individual with the same haecceity. I will attempt to answer this question. I am using Spade's translation of the Vatican edition of the Ordinatio, section references are also to that edition.

It is fairly clear that for Scotus, haecceity is not any relation between an individual and something else. This seems clear from his reply to the 'negation' theory of Henry of Ghent discussed in Question 3 (nn 49-56). 'Nothing is absolutely incompatible with any being through a privation in that being, but rather through something positive in it" (n 49). He gives the example (n50) of there being nothing present to sight. This does not produce any incompatibility with the sense of sight. By analogy, if being indivisible were simply a negation like not having anything present to sight, there would be no contradiction or incompatibility in something that is extrinsically indivisible being intrinsically divisible. So individuality is not a form of negation, and by inference not any form of relation. Individuality must be intrinsically a feature of the individual. "It is necessary through something positive intrinsic to this stone … that it be incompatible with the stone for it to be divided into subjective parts. That positive feature will be what will be said to be by itself the cause of individuation. For by 'individuation' I understand that indivisibility - that is, incompatibility with divisibility". (n57)

That leaves the other difficulty raised by Paasch. If haecceity is an absolute, positive, intrinsic feature of this stone, why is not contradictory for God to create another individual with the same haecceity. What specifically about this feature makes it, in Scotus's words 'incompatible with division'?

The answer to this probably lies in the sections of distinction III (nn 48, 76, 165) where he explicitly says what he means by haecceity.

In section 48 he says that we must not ask what it is by which such a division is formally incompatible to an individual (since it is formally incompatible by incompatibility), but rather what it is by which, "as by a proximate and intrinsic foundation", the incompatibility is in it. What is it in this stone by which, as by a proximate and intrinsic foundation, it is absolutely incompatible with it to be divided into (subjective) parts? (See my note on 'subjective parts' here).

In section 76 he says that individuation or numerical unity is not the indeterminate unity by which a species (e.g. man) is said to be one species. A designated unity is a 'this', that which it is inconsistent to divide into subjective parts. The cause is asked not of 'singularity in general' but of this designated singularity, i.e. as it is determinately this.

In section 165 he says that which is a 'this' is such that it is contradictory for it to be divided into several subjective parts, and contradictory for it to be 'not this'. It cannot be divided by anything added to it, for if it is incompatible for it to be divided of itself, it is incompatible with it, of itself, to received anything by which it becomes 'not this'. To say that something can be this and that through something extrinsic that is added is to say contradictory things.

In summary: haecceity for Scotus is an absolute, intrinsic feature of an individual thing. It is the feature whereby we conceive of and signify a thing as this. For any this, anything that does not possess this feature is a not-this, and thus not the same individual. Thus it would be contradictory for God to create another individual from this one with the same haecceity as this one. To have the same haecceity it would have to be this. To be a different individual had would have to be not-this.

Contradiction.

Indivisibility and Unrepeatability: Subjective Parts

Before I attempt an answer to Paasch's question there is a preliminary notion that needs to be clarified, as it is crucial to Scotus' account of individuation, and it is also one of those medieval ideas that are obscure to us schooled in the thought of the modern predicate calculus.

In book II, d3 section 48 (Vatican edition) he says that we must not ask what it is by which such a division is formally incompatible to an individual (since it is formally incompatible by incompatibility), but rather what it is by which, "as by a proximate and intrinsic foundation", the incompatibility is in it. What is it in this stone by which, as by a proximate and intrinsic foundation, it is absolutely incompatible with it to be divided into subjective parts?

A 'subjective part' is a term that would have been familiar to any scholastic logician. Peter of Spain explains it [1], together with the notion of 'integral part', in his Treatise on Logic, a standard textbook of the time. "The [term] 'whole universal', as taken in this way, is anything superior and substantial, taken in respect of its inferior. For example, animal to man, man to Socrates. A 'subjective part' is said of any inferior, taken under the whole universal. […] The 'whole integral' is is a composite of parts having quantity, and its parts are called 'integral parts'. An integral part is what, taken with the other parts, gives the quantity of the whole'.

Walter Burley explains it [2] by definition as well as by example, saying that an individual is a subjective part of a species, because the species is directly predicated of the individual, and for the same reason the species is a subjective part of the genus, because the genus is directly predicated of the species, and this is the difference between an integral part and a subjective part, because the whole is directly predicated of a subjective part, but is not directly predicated of an integral part, but only indirectly. And so 'a hand is a man' is false, or 'a head is a man'.

The distinction probably comes from Porphyry's introduction to Aristotle's Categories, where he says that that individual is a part of the species, and the species by the genus, so that genus is a sort of whole, the individual is a part, and species both whole and a part.

Thus (returning to Scotus) we have the sense in which an Socrates is indivisible or 'individual'. The genus 'animal' can be divided into subjective parts such as man, giraffe, grasshopper and so on. The species 'man' can be divided into subjective parts such as Socrates, Plato and so on. But these cannot be divided in the same way. Socrates is not like a species having some member x of which we can truly say that x is Socrates. This conception of division is fundamentally different from modern logic. We predicate 'animal' or 'man' of some x (e.g. Socrates). But the subject is always an individual. We have man(Socrates) and animal(Socrates). We do not and cannot have animal(man), for as Geach notes, modern predicate logic assumes a fundamental distinction between the relation of class-inclusion (man to animal) and the relation between individual and class (Socrates to man, Socrates to animal). Thus we cannot even understand Scotus' conception of individuation unless we drop an idea that is part of the language of thought for modern analytic philosophers. The idea may be wrong and misguided, even incoherent (as Geach cogently argues). But we cannot even begin to 'get inside the head' of the medieval logician unless

This should also clarify the distinction between the modern notion of individuation as 'unrepeatability' and notion of it as indivisibility. Repeatability is another idea of modern predicate calculus. A predicate is repeatable when it be 'instantiated' more than once. An instance of F is an x such that Fx, another instance is a y such that Fy, and x <> y. Note that the instance must be an individual x or y, not another predicate. We can have man(Socrates) and man(Plato), but not animal(man), animal(giraffe), or at least not when the function-argument notation is understood as in standard predicate logic. But divisibility, as Scotus and other medieval logicians understand it, is fundamentally different. Animal is divisible because it is (as it were) instantiated by man or giraffe. 'Man' is repeatable because it can be instantiated, in exactly the same sense, by Socrates and Plato. But Socrates cannot be further instantiated.

Hence there is not really a problem of individuation for modern logic. The argument to a propositional function is guaranteed to be individual because anything other than a sign for an individual in the argument place (or a variable representing it) will make the expression ill-formed. Scotus, by contrast, has to explain why the Porphyrian tree comes to an abrupt halt with individuals such as Socrates and Plato, because he is assuming that the relation between Socrates and his species is fundamentally the same as that between the species and its genus. If the relation between Socrates and man is essentially like the relation between man and animal, why is it that we can't repeat Socrates into subjective parts, the way that we can repeat animal into subjective parts such as man and giraffe.

So, you can either argue that the problem of individuation is a silly problem that can't even be stated in modern logic. Or you can take it seriously, as I will try to do in a later post. More later.

[1] Totum universale, ut sic sumitur, est quodlibet superius et substantiale, sumptum ad suum inferius, ut animal ad hominem, et homo ad Socratem. Pars subiectiva dicitur quodlibet inferius, sub toto universali sumtum . . .Totum integrale est, quod est compositum ex partibus, quantitatem habentibus, et pars eius dicitur pars integralis. Pars integralis est, quae cum aliis partibus reddit quantitatem totius.

[2] Expositio super librum Porphyrii: De genere quidem et specie. Recapitulans dicit quod intelligendum est quod individuum est pars subiectiva speciei, quia species predicatur de individuo in recto; et propter eandem causam species est pars subieciva generis, quia genus predicatur in recto de specie; et hec est differentia inter partem integralem et partem subiectivam, quia de parte subiectiva vere predicatur suum totum in recto, sed de parte integrali non vere predicatur totum in recto, sed in obliquo. Manus enim et caput sunt partes integrales hominis, quia integrant hominem. Et ita hec est falsa: ‘manus est homo’, vel ‘caput est homo’. Text from here.

Is haecceity repeatable?

I've read through four of Paasch's five posts. Some comments.

In Scotus: haecceities must be some positive entity he introduces Scotus' notion of haecceity: some presumed feature of an object that makes it the individual thing it is, different from any other individual. Paasch notes Scotus' rejection of the theory that individuals are individuated by a unique set of incidental features (a theory which was in some way comparable to the description theory of proper names rejected by Kripke in the 1970's). In What are haecceities? he wonders about the difference between 'haecceity' or thisness, and 'quiddity' or whatness. Thisness is the 'unrepeatability' of a feature. A qualitative or 'what kind of' feature is essentially repeatable. If you can have one man or giraffe, you can have as many men or giraffes as you like. Thisness is not repeatable. He asks "why couldn't God create an identical copy of a haecceity? What makes it so unrepeatable?".

In What makes a haecceity unrepeatable? he argues that God can do anything that does not involve a contradiction [correct - a standard medieval assumption, denied by only a few such as Peter Damian, possibly]. Then he introduces the idea of a reference relation or identity relation, arguing that only by the assumption of such a relation can we explain why the repeating 'thisness' would involve contradiction. Suppose the haecceity, the 'being this person' of Socrates involves the feature 'being identical with Socrates', call this Socrateity. And suppose God tried to clone another individual who also had Socrateity. But any individual with Socrateity has the feature being-identical-with-Socrates. Another individual would (from the definition of 'another') be non-identical. "One might take this example and generalize: the only way that cloning a thisness will result in a contradiction is if the thisness involves some sort of intrinsic reference to the individual in question".

I don't quite see why the generalisation follows. His argument shows that a relation of such a sort guarantees unrepeatability, not that only such a relation will do this. But let's move to his final post. In Are Scotus's haecceities really unrepeatable? he gives two arguments.

1. The identity relation (by which I assume he means the relation between some thisness, e.g. Socrateity, and any individual that instantiates it) is a relation, but Scotus argues that thisnesses are absolute (non-relational) entities. (Actually I'm not sure whether Scotus argues this. He only explicitly mentions relation - relatio, respectivum - twice in distinction III. But I am far from comprehending Scotus). But if haecceity is an absolute entity, why couldn't God clone it, or rather, clone an individual having the same haecceity.

2. Scotus believes that a relation 'supervenes on' the things they relate, and is thus posterior to the things it relates. If haecceity involves a relation between the haecceity and the individual it individuates, then the individual is already individuated. Relationships "cannot do any individuating, for they show up on the scene too late, as it were, to do any individuating". Actually this objection (according to Peter King) derives from Abelard*. The individuality of an individual cannot derive from or be dependent on the individual himself.

In summary: if haecceity is a relation, it involves a relation with the individual, thus is posterior to the individuals existence, thus cannot explain its individuality. If it is an absolute entity, why can't it be repeatable?

I have no answer to this right now (I am merely summarising four long posts by Paasch). I am wondering whether Scotus can be defended at all, or whether he can be defended using his idea that individuation is a sort of indivisibility (for that is what individuum actually means), and that it involves what Scotus calls the 'repugnance' of an individual to further division. Et ita natura speciei specialissimae non est de se haec, sicut nec aliquid divisibile ex natura sua est de se hoc, ita quod repugnet sibi de se dividi in partes, quia tunc non posset recipere aliquid per quod formaliter competeret sibi talis divisio. "And so the nature of the most specific species is not of itself this, just as something divisible is not from its nature of itself this, so that it is of itself repugnant to it to be divided into parts, because then it could not receive something through which formally such division would belong to it".

* Logica Ingredientibus 1.01 n26, cited in Peter King, "The Problem of Individuation in the Middle Ages", Theoria 66 (2000), 159-184, preprint here.

Buridan on Individuation

Here is a splendid passage from the 14C logician John Buridan. The Latin you can find on Peter King's website, here, of which my hasty English translation is below. The passage is interesting because, while logicians like Ockham anticipate Russell's idea of scope distinction (i.e. between ~ the F is G and the F is ~ G), Buridan here also anticipates the idea that proper names are telescoped definite description. (Buridan uses the wonderful Latin word circumlocutio). Note also the examples of 'teacher of Alexander' (magister Alexandri) and 'student of Plato' (discipulus Platonis) as the relevant circumlocutio of 'Aristotle'. These are familiar from Kripke, but he just got them from Frege, who had a good German classical education, and probably got them from some unknown scholastic source.

Another familiar idea is that genuinely singular terms are really demonstrative. Buridan says that a proper name is a circumlocution, but that a truly singular term is used in the presence ('prospect') of something, whose function is not to indicate similarity, but to indicate that it can belong to no other thing.

See also the following pages in the Logic Museum.

Aquinas on the name 'God'.
Ockham's Theory of definite descriptions.

'But if you say, how can I conceive Aristotle in a singular way, when he was never in my prospect? In reply, I say that it is not possible for you, properly speaking, because you do not conceive him differently from other men except according to a sort of circumlocution, such as 'the greatest philosopher', 'the teacher of Alexander', 'the disciple of Plato', who composed the books of philosophy which we read &c. Now although this description does not in truth belong to anyone but him, yet it is not properly a singular term (terminus singularis) - Although it does not belong to anyone except him alone, it is not inconceivable (repugnat – fudge) that in this way of signifying or imposition that it may belong to many and stand (supponat) for many, and if there were another God similar, the name 'God' would belong to him and would stand for him without a new imposition of the word – and so if there were another who were the greatest philosopher and the master of Alexander and the disciple of Plato &c, the said description would belong to him and would stand for him.

'For thus it is not a term that is absolutely and properly singular. Because if this thing in my prospect I call 'Socrates' by a proper name, it is not because he is such and such but because the name 'Socrates' would never belong to those other things insofar as they are similar – unless from another imposition [that name] were imposed to signify that other thing, and thus equivocally'.