A priori

As noted in an earlier post, Phillips says here that the sense of 'a priori' as used by scholastic writers differs from the modern sense. He writes

In order to avoid any misunderstanding it is necessary to notice that the phrase
' a priori proof' is used in quite different senses by the Scholastics and by
many modern writers who have adopted Kant's phraseology. For the Scholastic it
means one which from a cause argues to its effect, while an a posteriori proof
is one which argues from effect to cause. In modern non-Scholastic works an a
priori argument is often identified with a deductive one, an a posteriori
argument with an inductive.

This is a little misleading. 'A' in Latin is 'from', and 'priori' is the ablative of 'prior', meaning 'before' (or 'prior', of course). So 'a priori' is literally reasoning from what is before to what comes after, or knowledge based on such reasoning. Similarly 'a posteriori' is reasoning from what comes after to what comes before. However, I don't think the modern sense is as different from the scholastic one as Phillips suggest, for they practically amount to the same thing. The exemplar of a priori reasoning is mathematical demonstration, for example from the definition of a triangle (three straight lines enclosing a space) to one of its properties (the sum of the angles is that of a straight line). So a priori reasoning is going to be deductive. By contrast, the exemplar of a posteriori reasoning is from effect to cause - Aristotle frequently gives the example of an eclipse, where we observe the effect of the sun going into shadow, and reason that its cause is the moon going in front of it. But in that case we have no direct or immediate knowledge of the cause. All we have to go by is what we observe, the effect. Since there is no logical connection between the effect and the cause, it follows that the reasoning cannot be deductive, and may well be 'inductive'.

That said, there may be an example of reasoning which is a posteriori in the scholastic sense, but a priori in the modern, namely reverse mathematics. Reverse mathematics is the project of determining which axioms are required to prove which theorems of mathematics. It goes in reverse from the theorems to the axioms, thus 'a posteriori', in contrast to the ordinary mathematical practice of deriving theorems from axioms 'a priori'. However, I don't think the project of reverse mathematics would make much sense to Aristotelians. As I understand, it depends on the assumption that we can pick and choose axioms, thus getting stronger and weaker systems of mathematics. This would make no sense to the Peripatetics, from whom an axiom is a proposition whose truth is self-evident.

This reminds me of another curiousity: the Latin term per prius. Logically this means the same as 'a priori'. 'Per' is 'by' or 'by means of', 'prius' is the neuter accusative of 'prior'. So 'a priori' means 'from what is prior', 'per prius' means 'by means of what is prior'. It's hard to see the difference. Yet if we use the excellent Latin site searcher at the Logic Museum to search the excellent Franciscan archive for Bonaventura's use of a priori and of per prius we see that he distinguishes the terms. A further curiousity is that whereas Ockham uses the term 'a priori', he apparently does not use 'per prius'. But a caveat here: the whole of Summa Logicae has yet to reach the web in corrected form - this is a current Logic Museum project.

The Ontological Argument

An addition to the section on the Ontological argument in the Logic Musum. Two chapters from Phillips on that subject. Generally good value, and a characterisation of the argument that would be hard to find anywhere else on the Web.

There is more to say on the argument, though, and perhaps more later.

It's about time I offered a prize for anyone who can identify the artist of the Logic Museum picture:

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.

More in the Logic Museum

1. A new page on the Ars Vetus, or 'old logic' of the scholastics. This includes three of the seven works of the old logic, with the Latin translations of Aristotle's Greek in parallel with English.

2. Some pictures of the 2007 Montreux conference on the square of opposition, retrieved from my original site.

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.

The Logic Museum is back

Here. Now with its own URL (.com no less). This is the first time I have ever paid to have a site hosted. Most of the original material is there, although fixing broken links was a problem. The museum will be for primary material in Latin, providing a source for those who do not have access to university libraries (or where, as is often the case, the library simply does not have the material).

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.

Reverse Straw Man

A Straw Man argument is where your opponent takes you to be arguing for some B instead of A, proceeds to demolish B, and serves not-B up to you as a fait accompli. Reverse Straw Man is an extreme version of this where your opponent takes you to be arguing for not-A, proceeds to demolish not-A and slaps A in your face as complete and irrefutable. Even though you were arguing for A all along (or have pretended to, see below).

For obvious reasons it is difficult to bring off, and requires considerable skill at generating confusion about the initial purpose and objectives of the dispute, and so usually confined to domestic disputes, arguments with teenagers, drunken discussion in bars and so on. But it can be found in serious philosophical dispute, typically when your opponent realises with horror, halfway through, that they are wrong, and need to cover their tracks. Because of its inherently symmetrical nature, you can employ it yourself, i.e. pretend you were actually arguing for A along. When your opponent proudly presents you with irrefutable evidence for A, you reply that you gave that argument half an hour ago.

The tactic is best used in verbal discussion where it is difficult for anyone to remember what anyone said. If on an internet thread it is more difficult, as someone is bound to quote your very words back at you. A simple tactic is to accuse them of quoting you out of context, and perhaps throw in an accusation of bad faith: "It is quite clear I was arguing for A, please do not quote my words out of context". This has the risk of making them angry, but in that case they will either resort to capital letters and ranting, in which case they have lost, or they will present a carefully reasoned and detailed case that you could not have meant that, even in context. Because this requires supplying the original context, as well as a carefully reasoned and detailed argument around it, it will be too long for anyone to read or listen, and so they have also lost.

Straw man (which involves confusion about the aims and conclusion of the argument) is closely related to ground-shifting. Ground-shifting is when you change your argument or evidence half-way through the argument. There is a good characterisation of it here. The author correctly notes that the skillful employment of it requires deliberate and purposeful unclarity about definitions.

'Anybody who knows ...'

One of the comments at the discussion raging at Vallicella's site illustrates perfectly the 'translation problem' that I mentioned in an earlier post. The problem is that any attempt at 'proving' or 'disproving' an ordinary language statement by using the well-defined proof procedure of the modern predicate calculus is highly vulnerable to the process of interpreting the ordinary language statement in the calculus. If the interpretation is not correct, then the proof, though perfectly valid, may be proving the wrong thing.

Suppose we want to prove the validity of an ordinary language consequence having the following form.

(*) If it was the case that A was identical with B then it is the case that A is identical with B

We can try to do this by translating the placeholders A and B (which substitute for grammatically singular OL terms) into the 'a' and 'b' of the predicate calculus (which substitute for logically singular terms), and translating the tensed statements of OL into the 'nec' or 'necessary' of predicate calculus, as follows:

(1) a=b (Assumption for conditional proof)
(2) a=b -> (Fa -> Fb)
(3) Nec(a=a)
(4) a=b -> (Nec(a=a) -> Nec(a=b)) (Substitution Instance of (2))
(5) Nec(a=a) -> Nec(a=b) (Modus Ponens, 1&4)
(6) Nec(a=b) (Modus Ponens, 3&5)
(7) a=b -> Nec(a=b) (Conditional Proof, 1-6)

The problem is that the 'proof', if understood as a proof of the ordinary language consequence, can't possibly be valid. Substitute 'the president of the US' for 'A' and 'John F. Kennedy' for 'B' to give

(*) If it was the case that the president of the US was identical with John F. Kennedy then it is the case the president of the US is identical with John F. Kennedy

But ex vero nunquam sequitur falsum: the false cannot follow from the true. Whenever the antecedent is true and the consequent false, consequentia non valet, the consequence is not valid. But the antecedent is true - the president of the US was (in September 1963) identical with John F. Kennedy, and the consequent false - the president of the US is (in September 2010) not identical with John F. Kennedy. So the consequence is not valid. If the formalised part of the proof is valid (which I am not denying), it follows that the translation of our ordinary language consequence into the formal consequence (i.e. (7) above) is wrong. But that is just the place we forgot to look.

At this point, the formalist will object that the translation "would be accepted by just about anybody who knows how to translate from ordinary language to formal logic". And that is another problem: a cultural problem, not a logical or philosophical one. We were taught as students the 'correct' way to translate awkward and messy ordinary language statements into the clean language of MPC. I too was taught this (using what was only 10 years old then, but has since become a classic text) quite some time ago. Having learnt this, we 'know' how to translate from ordinary language to formal logic. And, proud of this knowledge, we are now 'anybody who knows', and we can put down anyone who does not know.

What a formidable barrier to progress.

The Tibbles Puzzle

It is time to re-tell the famous story of Tibbles. Tibbles is a cat, who has just lost a tiny piece of hair Let T be all the parts of Tibbles - flesh and bones and internal organs and all - plus the now-detached piece of hair. Let T* be all the parts that now constitute Tibbles - namely all the parts that constitute T less the hair. Then (ignoring for now any problems about souls and animated bodies)

(1) Tibbles previously was identical with T.
(2) Tibbles now is identical with T*.
(3) T is not identical with T*
(4) Therefore (by substitutivity) Tibbles is not identical with T. Contradiction with (1) above.

Well, supposedly a contradiction. Tibbles is not now identical with T, but this does not contradict (1), which says that Tibbles was then identical with T. Is there any contradiction in being identical with some A in the past, and yet not being identical with A in the present? Does "A was identical with B" always entail "A is identical with B"? More later

Concerning plurals

A guest post from Tom McKay, who writes:

Concerning plurals, there is no problem about expressing the things you
mention within the system for plurals that I developed. (That by itself doesn't
answer the metaphysical question initially posed. But it provides some
linguistic resources for discussing it. Also note that van Inwagen himself uses
plural language when he asks when some things compose a single thing. The
relation ‘These compose that’ is non-distributively plural in its first argument
place. There is no representation of that in standard (singular) first-order
logic, without the help of set theory or mereological summing or something like
that as a means to introduce a singular representative of some things.)

Naïve set theory ordinarily allows the building of a hierarchy of sets
(some sets are members of other sets), and the plural language does not in
itself introduce anything like that.

Russell spoke of ‘a set as many’ (as well as another conception of ‘a set
as one’). But by calling it ‘a set’ he is already undermining the idea of there
being many. I think that Russell just didn’t follow this idea out in a coherent
way.

The Perils of Analysis

An argument mentioned by Bill Vallicella here neatly illustrates the danger of using modern predicate calculus to penetrate the logic of natural language. He cites an argument of Peter Van Inwagen, as follows.

Suppose that there exists nothing but my big parcel of land and such parts
as it may have. And suppose it has no proper parts but the six small parcels. .
. . Suppose that we have a bunch of sentences containing quantifiers, and that
we want to determine their truth-values: 'ExEyEz(y is a part of x & z is a
part of x & y is not the same size as z)'; that sort of thing. How many
items in our domain of quantification? Seven, right? That is, there are seven
objects, and not six objects or one object, that are possible values of our
variables, and that we must take account of when we are determining the
truth-value of our sentences. ("Composition as Identity," Philosophical
Perspectives 8 (1994), p. 213)

Van Inwagen's argument employs a method that is fundamental to all analytic philosophy. We have two ordinary language statements A and B below, and we want to decide whether B follows from A.

(A) There is a large parcel of land having two smaller parcels as proper parts.
(B) There are three things (the large parcel of land and the two smaller parcels)

If the inference is valid, then there is a third thing 'over and above' the two smaller things, and there is an 'ontological distinction' between the large parcel of land and its parts. Otherwise there are only two things, and the existence of the 'large parcel of land' simply reduces to the existence of the parts. It is not 'ontologically distinct'. This is an important philosophical conclusion, if we can establish it.

The procedure is to translate both statements into the language of predicate calculus, which has a determinate proof procedure, and see whether the inference holds. Thus

(A*) For some x, x is a large parcel of land having proper part x1 and proper part x2 and x1 /= x2.
(B*) For some x, for some y, for some z, x/=y and x/=z and y/=z

Clearly, given the additional premiss that no object x is identical to any of its proper parts (i.e. x /= x1 and x /= x2) we can establish that B* follows from A*. Thus the apparently simple translation from a natural language statement into the language of modern predicate calculus apparently leads to a philosophical conclusion. And a lot of modern analytic philosophy is like that. We are worried about whether the ordinary language statement A implies the ordinary language statement B. For ordinary language has no agreed and determinate proof procedure. So we translate A into a statement A* of the predicate calculus, which does have an agreed and determinate proof procedure, and we translate B into B*. Then we determine whether A* implies B*, which seems to solve the problem. But of course it doesn't, for the real question is whether the translation is correct. If we are unsure whether A implies B, how can we be sure that either of the translations (of A onto A* and B into B*) are correct? If the translation is obvious, how is it we were unsure of the implication in the first place?

The 'method of analysis' is not fundamentally unsound. If we are certain of the 'logical form' of an ordinary language statement - i.e. a form that makes inferences to other statements determinate and certain, then analysis is a useful technique. Otherwise it is not. What is the logical form of 'this big parcel consists of two small parcels'? If it is the same as 'This pair of shoes consists of 2 shoes', then we should proceed with caution.

A perfect difficulty

In an earlier post I suggested that the semantics of a noun or referring phrase does not include time. The sense of time is what a verb brings in. Hence past, present and future tenses, and hence qualifying adverbs like 'now' and 'then'. This avoided the philosophical difficulty about treating the ship composed of the old planks ('the ship as it was then') being any different from the ship composed of the new planks ('the ship as it is now').

But perhaps there is a difficulty, indicated by the distinction between the simple past tense (the ship was composed of the old planks) and the perfect tense (the ship has been composed of the old planks). The distinction (though familiar and its ordinary usage well understood*) is not philosophically clear, and grammar books tend to fudge the explanation. But it seems to be: we use 'has been F' as a predicate to qualify the object 'as it as now', and 'was F' to qualify the object 'as it was then'. Otherwise the grammatical distinction makes no sense. It must distinguish something, and the distinction seems to be the philosophically dangerous one that I said we should avoid.

A similar distinction is evident in the difference between 'in 10 years time people will have a better standard of living' and 'in a 100 years' time, people will live for much longer'. In the first 'people' apparently ranges over people who exist now. In second, it clearly ranges over people who have not been born yet, but will exist in the future. Perhaps there is some notion of tense built into the subject of a proposition. But it's puzzling, and there is not much I can say about it, as things are now.

* The idea for this post came after reading a paper by Braakhuis, who wrote 'In 1940 Grabmann has drawn attention to this collection'. The use of the perfect, rather than the simple past, misleadingly suggests that Grabmann is still alive, which he isn't (he died in 1949).

Bad philosophy

"Bad mathematics is merely boring, whereas bad philosophy is nonsense" - found here.

Eliminativism: the elusiveness of the ordinary

There is a deeper puzzle about eliminativism.

(E) There are no A's. There are only B's.
(R) There are A's but A's are only B's.

Clearly (E) and (R) do not disagree about the basic ontology. They agree that there are only B's. But they fundamentally disagree about the definition of 'A'. The eliminativist (E) claims that an A, as the term 'A' is correctly and properly understood, cannot exist, because its definition would include features inconsistent with being a B. The reductivist (R) is saying that, as the term 'A' is correctly and properly understood, it is entirely consistent that an A can be a B, indeed that every A is a B.

But if it is merely a quarrel over definitions, why is there any disagreement at all? There is no disputing over definitions. Perhaps the answer lies in the difficulty that surrounds all philosophically interesting notions. The SEP says "Like many philosophically interesting notions, existence is at once familiar and rather elusive. Although we have no more trouble with using the verb ‘exists’ than with the two-times table, there is more than a little difficulty in saying just what existence is". That is, there are certain terms which we all understand and have no difficulty using with a standard sense in everyday life, but which we find terribly difficult to define. Hence there may be profound disagreement over which features are essential to the term, and hence profound disagreement between (E) and (R). Both agree that in using the term 'A' they are talking about the same kind of thing, and using the term in the same sense. But they disagree about what are the fundamental features of an A. The eliminativist believes that there is some feature of A's, correctly understood, that makes it inconsistent with an A being B. And since he believes there are only B's, he holds that there are no A's. The reductivist agrees that this feature is inconsistent with being B, but regards it is non-essential, and so it is possible - indeed true - that no A actually has the feature.

Considering the example of truth - which is as philosophically interesting as any - we have

(E) There is no truth. There is only warranted assertibility.
(R) There is truth, but truth is only warranted assertibility.

The disagreement here does not involve equivocation (as I previously thought). Both (E) and (R) both think they are talking unequivocally about the same thing: truth, an idea that we have no more trouble in employing than in using the two-times table. Both agree on the 'ontology': there is warranted assertibility and nothing more. Where they disagree is that (E) thinks that truth involves more than warranted assertibility, and is inconsistent with the ontologyl.(R) by contrast thinks that truth involves no more than that, and so its existence is consistent with the ontology.

So the disagreement is not about ontology or about which entities/features are to be eliminated. Both agree that 'truth involving more than just warranted assertibility' is to be eliminated. But (E) eliminates it by eliminating truth itself. (R) eliminates it by holding onto truth, but eliminating anything more than just warranted assertibility. The disagreement lies in the analysis of the everyday notion of truth, and not 'ontology'.

The deeper puzzle is how people can agree on the meaning of a term, and yet disagree about its definition. How can we agree on the meaning of 'existence' - a term which is no more difficult to use than a times-table, and yet disagree profoundly on how to define it? Why are there similar puzzles and disagreements over the nature of truth, individuation, identity, reference and all the rest? This problem goes back at least to Plato, and we appear to be no closer to solving it.