Le Verrier's Vulcan and Pierre Menard's Quixote

Phoenician Bill objects to my argument yesterday about singular concepts. Why do we need singular concepts? Why can’t we represent “Vulcan does not exist” as “The concept Small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit is not instantiated”, which involves a general, not a singular, concept?

I reply: see my post last year, also replying to some Phoenician quibble, and in particular the point about the Borgesque thought experiment*. Suppose I write an explicitly fictional story about a planet which I call ‘Vulcan’, unaware of the planet whose real existence was postulated by Verrier. And suppose that in my story Vulcan is a small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit. Then I am not talking about the Vulcan of LeVerrier. Reference to my Vulcan requires acquaintance with my text. Reference to LeVerrier’s Vulcan requires acquaintance with his writing, or writing about his writing which ‘borrows’ the Vulcan reference. As I said:

It is this specific connection to items of information, texts etc. that guarantees the acquisition of individual concepts by different people, and their successful use to make individuating reference. What guarantees that we are thinking about Julius Caesar is the right kind of relation to a certain set of texts – not a relation to any existing person, which is irrelevant. What guarantees that we are all thinking about Frodo is exactly the same kind of relation. The existence of the individual referred to, and even their causal relation to the text, is irrelevant.

This is very important.

*I did not mention it in the post, but I was alluding to Borges story “Pierre Menard, Author of the Quixote”, published in 1939.

Something exists

An excellent post by the Phoenician Maverick on the difficulty of translating 'something exists' into Frege-Russell logic, as defended by Londonista David Brightly.

I don't agree with  David 's approach, which is to invent the predicate 'Object(x)', a predicate which is satisfied by everything, and which fails to be satisfied by nothing.  This translates 'something exists' into 'for some x, object(x)'.  Neat - in Frege-Russell 'for all x F(x)' is true even when nothing exists.  But unsatisfying, because there remains the difficulty of negative existential singular sentences.  How do we translate 'Pegasus does not exist'?  If 'Pegasus' is a name at all, then Object(Pegasus), which translates to 'Pegasus exists', which is false.

I prefer a non-standard logic which (as David knows) extends the Frege approach from general existential statements to singular statements.  For Frege, 'serpents exist' means that the concept 'serpent' is instantiated.  If we accept singular concepts, it follows that 'Pegasus exists' means that the concept Pegasus is instantiated, and 'something exists' means that some concept is instantiated.

For more on singular concepts, use this search key.  Maverick has objected to the notion of singular concepts many times, but has failed to address any of my masterful replies.

Vallicella against singular concepts

Vallicella has a good post here about why he rejects individual concepts (aka singular concepts, haecceity concepts, singular meanings etc.).

His argument is that an individual concept, if there is such a thing, is either pure, or not. A pure concept C “involves no specific individual and can be grasped without reference to any specific individual”. If there such a concept C, or not. If there is, it is either pure or not. But every pure concept, no matter how specific, is possibly such as to have two or more instances. So C is not pure. But then it must involve an individual - the very individual of which it is the individual concept, and no individual can be grasped as such, and so C is not pure either. Thus there can be no such C.

I reply: the definition of “pure concept” is ambiguous, for the verb ‘involves’ is ambiguous between being logically transitive and logically intransitive. I discussed this idea back in March. A logically intransitive verb is one which has a grammatical accusative but no ‘logical’ accusative, i.e. such that ‘aRb’ can be true, without ‘Ex x=b’ being true. ‘Refers to’ is such a verb. Thus

(1) ‘Frodo’ refers to Frodo.

is true. And so is

(2) ‘Frodo’ refers to someone.

But

(3) Someone is such that ‘Frodo’ refers to them.

is not. If the verbs ‘involves’ and ‘grasps’ of Vallicella’s definition are logically intransitive, then the minor premiss of his argument – that we cannot grasp an individual – is questionable. For then you can grasp the concept of Frodo without any real relation to any existing individual.

To clarify, I hold that you can only grasp the concept of Frodo if you have read ‘Lord of the Rings’ (or some other book or text or body of information that references Frodo). It is analogous to ‘the former’ and ‘the latter’. These are descriptions which appear to be first-level, and to qualify the individuals referred to, but really, as it were, qualify the text itself (or the information received).

Borgesque thought-experiment: a Chinese author, who has never read Lord of the Rings, writes a very similar or identical work. I say that when people read this work and talk about the characters – say the one corresponding to Frodo – then they are not talking about Frodo. The right kind of causal connection to the work is not available. By contrast, if I read a sequel to LOTR in which Frodo appears as a character, and if I make it explicit the reference to Tolkien’s text, then I am referring to Frodo, and people who talk about my character are referring to him also. Thus, by the right kind of causal connection to a particular text (or mass-produced copies of it) we acquire individual concepts – in this case, individual concepts corresponding to things that do not exist.

The case of real history (e.g. Julius Caesar) is no different. There is no semantic connection between my individual concept of Caesar, and Caesar himself. But there is a connection between this concept and the historical texts I learned at school, or from books I read. It is this specific connection to items of information, texts etc. that guarantees the acquisition of individual concepts by different people, and their successful use to make individuating reference. What guarantees that we are thinking about Julius Caesar is the right kind of relation to a certain set of texts – not a relation to any existing person, which is irrelevant. What guarantees that we are all thinking about Frodo is exactly the same kind of relation. The existence of the individual referred to, and even their causal relation to the text, is irrelevant.

Old wine in new bottles

There is an interesting claim by Tim Crane in his paper "The Singularity of Singular Thought" that bears a marked resemblance to something said by Duns Scotus in his Questions on Aristotle's Perihermenias.  Crane says

What is relevant to generality is not that as a matter of fact the information is true of many things, but the fact that a thinker can make sense of it being true of many things (or of different things in different possible situations). Conversely, what is relevant to singularity is not the fact that the information in one’s file is true of just one thing, but that one cannot make sense of it as being true of many things.

Scotus says

Terminus communis secundum quod habet rationem communis est natura prout concipitur sub ratione ‘dicibilis de pluribus’, et ita suppositum est natura concepta apud intellectum sub ratione ‘indicibilis de pluribus.* “A common term, according as it has the nature of the common, is a nature as conceived under the aspect ‘predicable of many,’ and so a suppositum is a nature conceived in the understanding under the aspect ‘incapable of being predicated of many".

A suppositum is a technical term difficult to translate, and is often left untranslated. Scotus here often uses it to mean any object that falls within the range of a common term (or the 'value' of a variable, if you like). Thus any man is the suppositum of the common term 'man'. 

* Book I Question 6 n43.  As some readers of this blog will know, I am working with Jack Zupko on an English translation of this early work of Scotus. This may even get published this year, who knows.

The roots of direct reference - argument 4

I borrowed this one from Teresa Marques' paper "On an argument of Segal’s against singular object-dependent thoughts" (Disputatio, volume II, no. 21, pp. 19-37) although it owes much to John McDowell and Gareth Evans.

Argument Four. Truth-conditional semantics rests on the assumption that the conditions for the truth of a sentence give the sentence’s meaning or significance. But there is no truth evaluable content when reference failure occurs.  If there are no truth conditions, then there is no thought-content. Hence, if one’s utterance of a sentence has no truth-conditions, then it also has no truth conditions and therefore also no significance or meaning. Likewise, an utterance of such a sentence fails to express a singular thought.

The Singularity of Singular Thought

I just found an excellent paper by Tim Crane - "The Singularity of Singular Thought".  Today I will say some things I like about the paper, tomorrow some things I don't like so much.

Crane begins by picking up a remark by Quine that "a singular term is one that ‘purports to refer to just one object’".  This suggests to Crane that a singular term is one that appears or ‘claims’ to be doing something – referring to just one object, and which still appears to do this even if there is no such object.  Readers of Beyond Necessity will understand that I find this attractive.  Common sense suggests that a proper name, together with many other types of singular terms, has the same semantics whether or not there is an object corresponding to it.  The semantics of proper names, I have argued, is object independent.

The difficulty, as Crane acknowledges, is to explain how this is consistent with the distinction between singular and general thought, which any adequate theory of mind must account for. As I suggested in some earlier posts, there are apparently strong arguments showing that we can only explain the distinction by invoking semantic dependency on objects.  Singular thoughts (according to these arguments) are precisely those which depend for their existence on the existence of the objects they are about.  John McDowell defines a singular thought as ‘a thought that would not be available to be thought or expressed if the relevant object, or objects, did not exist’.

Crane's objective is a theory of singular thought - of which he provides only a brief sketch - which accommodates the distinction between singular and general thought, "but which also takes seriously the idea that a singular thought might merely purport to refer. In other words, a thinker can think about a particular object and yet fail to refer to that object in thought.”

More tomorrow.

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.

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!