Necessary beings

We don’t have to buy everything that Frege says about concepts to agree that using a concept expression F we can say things like ‘There are three Fs’ or ‘the number of Fs is n’. We can also say ‘There is at least one F’ which, according to Frege, is equivalent to ‘Fs exist’ or ‘there are Fs’. That seems uncontroversial.

Therefore ‘girls over the age of 17 at Mallory Towers’ is a concept-expression. For we can say that there are three girls over the age of 17 at Mallory Towers, or that the number of girls over the age of 17 at Mallory Towers is three. And we can say that, since there is at least one girl over the age of 17 at Mallory Towers, that there are girls over the age of 17 at Mallory Towers.

But here’s the problem. If it is true that ‘girls over the age of 17 at Mallory Towers’ is the name for a concept, then such a concept is not a necessary being. For in a possible world where there is no such school as Mallory Towers, we cannot specify the content of the concept. The property of being a girl over the age of 17 at Mallory Towers cannot be specified without reference to the actual Mallory Towers.

But that seems impossible. In such a possible world, there are no girls at Mallory Towers, since the school doesn’t exist, hence there are no such girls over 17. Therefore the non-existence of such girls is the non-instantiation of the concept *girl over the age of 17 at Mallory Towers*, and so that concept, in that possible world, has the property of being non-instantiated. But in order to have that property, it must exist. Since this is any possible world, it follows that the concept must exist in every possible world, and so is a necessary being. Yet we just supposed that it wasn’t a necessary being. Contradiction.

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.

Future identifying reference

Vallicella is agonising here (see also here) about the problem of how (or whether) it is possible to identify individuals who do not exist, but will exist in the future. This requires that there must be a way to individuate all possible individuals that in no way depends upon their actual existence. But that in turn means that 'haecceities' must exist - supposed non-descriptive properties that have no other function than to belong to the very individual they belong to. Or as Vallicella puts it:

A haecceity is a property H of x such that: (i) H is essential to x; (ii) nothing distinct from x exemplifies H in the actual world; (iii) nothing distinct from x exemplifies H in any metaphysically possible world.

Vallicella takes it for granted there cannot be haecceities. They are 'creatures of darkness'. But assuming there aren't, the problem is that if God is omniscient (i.e. knows everything that is, has been and will be) then he must have known which individuals he was going to create when he created the world. (For example, he must have known he was going to create Socrates). This cannot be explained without presuming haecceities (per Vallicella). Since there are no such things, God is not omniscient.

I reply: if we can make an identifying reference for items that exist now ('this baby here'), and items that existed in the past ('Isaiah'), why can't we make identifying references in the future? Isn't the 'he' below such a future identifying reference? Does it require a haecceity existing when Isaiah made the prophesy? Why? Why can't the reference reach over the future centuries in order to identify the yet-to-be-born Jesus?

For to us a child is born,
to us a son is given,
and the government will be on his shoulders.
And he will be called
Wonderful Counselor, 
Mighty God,
Everlasting Father,
Prince of Peace. [Isaiah 9:6]

Intentionality and Proper Names

The Maverick Philosopher has an insightful post on modes of being, haecceity and proper names. Proper names are the real difficulty for a theory of intentionality. We can express the difficulty by means of the following ‘aporetic tetrad’. (I define ‘empty name’ as a proper name that does not signify an existing object).

1. An empty name signifies something
2. Every thing is an existing thing
3. A name does not signify a concept
4. A (significant) term signifies a concept or an object.

Taken together, the four are inconsistent. If (1) an empty term signifies something, and if (2) every thing is an existing thing, then an empty term signifies an existing thing. But (3) that existing thing is not a concept, so (4) an empty name signifies an existing object. But (from the definition of ‘empty name’) an empty does not signify an existing object. Contradiction.

Yet each of the four propositions has a strong claim to our acceptance. (1) Surely the semantics of an empty name are no different from a non-empty one. We can’t tell whether there was such a person as John the Baptist by analysing the meaning of the name as used in the New Testament. (2) There is plenty of evidence for the ‘Brentano thesis’ that I have discussed frequently. (3) There are plausible arguments against proper names signifying concepts – see Maverick’s argument, for example. (4) The distinction between concept and object is practically a given. No contemporary philosopher of language has seriously challenged it, as far as I know.

There are three known resolutions to the tetrad, according as philosophers have denied proposition 1, 2, or 3 respectively. Direct reference theorists deny (1). They hold (implausibly, to my mind) that an empty name does not signify. To the argument that we cannot tell whether a name (e.g. ‘John the Baptist’) is empty from its semantics alone, they reply that this is ‘Cartesianism’. If there is no such person as John the Baptist, direct referentialists claim that we know this, even though we utter things like ‘we do not know whether the name ‘John the Baptist’ signifies or not’. The Maverick and other Meinongians-in-denial deny (2), by driving a wedge between being a thing, and being a thing that exists. And (3) people like Mark Sainsbury, and indeed Edward Ockham himself, argue that proper names signify ‘singular concepts’.

In posts for this month (March 2011), I will put forward some arguments in defence of singular concepts. More later!

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.

Paasch on haecceity

I put J.T. Paasch (Blog: Boring Things - "nothing but fun") on my visiting list some time ago. But then it was not updated for some time and I neglected to visit, and so missed a fine series of posts about Scotus and 'haecceity'. List below.

This is something to return to. I have been struggling with Scotus' account of haecceity for years. The standard place is the six questions in Distinction III of book II of his Ordinatio (Opera omnia, ed. C. Balic and others (Rome, 1950-), vol. 7, p. 458ff). There is a very similar discussion in the earlier questions on the Metaphysics (Quaestiones super libros Metaphysicorum Aristotelis, Libri VI–IX, edited by G. Etzkorn, R. Andrews, G. Gál and others, Opera Philosophica 4 (St. Bonaventure, N.Y.: The Franciscan Institute Press, 1997).

Scotus' argument, as far as I can make it out, is that there exists an identity less than numerical identity (minor unitate numerali). This is the identity of a species, the one of "man is one species, giraffe is another". But a species is essentially repeatable. If you can have one man, you can have another man, another individual of the same species.

But the same is not true of individual identity. We cannot repeat Socrates as we can repeat man. One of Scotus' targets here is the theory of Porphyry, that an individual is defined by a collection of differentia. We start with the most general genus, i.e. being of some kind, then descend to living being, then animal, then rational animal. As we get more specific, the number of features required to define the species increases. Finally we get to the most specific species, namely the individual - descendentibus nobis per divisionem a generalissimus ad specialissima iubet Plato quiescere. Scotus rightly argues against this. Being individualised can't be like being the most highly specified species at the bottom of the tree of being. Being a species is essentially to be divisible into further species. "... 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".

It is not clear what Scotus' haecceity is - he practically defines it as what it is not. Paasch is concerned with the question of whether a haecceity really can be unrepeatable. More later.

Thursday, August 26, 2010. "Are Scotus's haecceities really unrepeatable?"
Friday, August 20, 2010 "What makes a haecceity unrepeatable?"
Saturday, August 14, 2010 "What are haecceities?"
Saturday, August 7, 2010 "Scotus: haecceities must be some positive entity"
Friday, July 30, 2010 "Individuation is a question of the formal cause"

Meanwhile, I see that according to his Facebook page, Paasch is working on a PhD in philosophy and theology at Oxford, when he is not working as a bartender, introducing his favorite customers to excellent vintage cocktails he has dug out of old cocktail books. Well then! Mine's an Old Fashioned please.

Since I went on the wagon I'm
certain drink is a major crime,
For when you lay off the liquor
You feel so much slicker -
Well that is, most of the time.
But there are moments sooner or later,
When it's tough, I've got to say, not to say, "Waiter
Make it another old fashioned please".

My favourite drink. More information on Wikipedia.