Arizona Bill commits the existential fallacy

In a post today, Maverick Bill talks about fictional and incomplete objects again, which reminds me of an idea that originally occurred to me in February 2011, and which I developed in a series of posts on logical intransivity.

The idea was that there are certain verbs – I call them logically intransitive – which take a grammatical but not a logical accusative. Let me explain. In the sentence ‘Tom is looking for a wife’ the verb ‘wants’ is logically intransitive. It clearly has a grammatical accusative (‘a wife’), but there is no object corresponding to that term, i.e. the sentence can be true (Tom really is looking for a wife) without there being any person or wife to whom the term corresponds. Clearly so, for Tom would not be looking for one, if he had already found her. By contrast ‘Tom has found a wife’ is logically transitive. It cannot be true unless there is someone to whom ‘a wife’ corresponds.

I developed the idea as follows. There is a certain species of bad philosophy which proceeds by taking sentences which are not existential with respect to their accusative, because of logically intransitive verbs, and converting them into sentences which are existential with respect to the same accusative. This typically happens in two ways.

(1) By converting a logically intransitive verb phrase into a logically transitive one. For example by translating ‘Tom is thinking of a mermaid’ into ‘Tom stands in the relation ‘thinking of’ to some mermaid’. Clearly the first sentence does not imply the existence of mermaids because of the logically intranstive ‘is thinking of’. But the second does, because of the transitivity of ‘stands in the relation ‘thinking of’ to’. Bill commits this fallacy here when he argues “When Tom thinks about a nonexistent item such as a mermaid, he does indeed stand in a relation to something”.

(2) By converting a sentence from a passive to an active form, so that the object of the logically intransitive verb becomes its subject. Since subject terms (generally, not always) are existential, the sentence when converted implies existence, whereas before converted is does not. Both of these are specific versions of the existential fallacy, i.e. arguing from premisses which are not existential to a conclusion which is existential.

Arizona Bill’s blog is a wonderful and rich mine for instances of the fallacy. In today’s post there are at least three. In the first set of sentences below, the verbs ‘want’ and ‘imagine’ are clearly intransitive, and to not imply the existence of any table.

(A1) I want a table, but there is no existing table that I want
(A2) I want a table with special features that no existing table possesses.
(A3) In the first case I imagine the table as real; in the second as fictional.

In the next three sentences, he converts grammatical object to grammatical subject, in order to imply the existence of the wanted or imagined objects.

(B1) The two tables I am concerned with, however are both nonexistent.
(B2) There is a merely intentional object before my mind.
(B3) The table imagined as real is possible due to its ontic character of being intended .

Of course, this leads to the inconsistency of implying the existence of a non-existent object. In (B1) above, he asserts the existence of the tables by the apparently referring subject term ‘the tables’, then denies it using the predicate ‘non existent’. Bill usually evades this, when he can be bothered to, by claiming there are two sorts of existence.

Appeals to phenomenology

IN his latest post on ‘pure ficta’, Arizona Bill wheels out what looks like an argument from revelation.

If Ed denies that there are merely intentional objects, then he is denying what is phenomenologically evident. I take my stand on the terra firma of phenomenological givenness. So for now, and to get on with it, I simply dismiss Ed's objection. To pursue it further would involve us a in a metaphilosophical discussion of the role of phenomenological appeals in philosophical inquiry.

Well, it probably would involve us in such a discussion, and I wouldn’t want to go there, correct. I don’t recognise the validity of any kind of appeal to revelation in strictly philosophical enquiry.

None of these men [the pre-Socratics], it is to be noted, tried to answer these questions by an appeal to any revelation, to myth, or religious knowledge of any kind; but attempted to extract the answer by using their reason; and they used it almost without reference to sensible observation and experiments. Why was this ? Clearly because they were convinced that the thing they sought lay deeper in the heart of the world than the superficial aspect of things, of which alone the senses could tell them. (Modern Thomistic Philosophy, R.P. Phillips, London 1934)

But is Bill really making such an appeal? I don’t think so. He is actually appealing to premisses which are uncontroversial, such as our ability to create fictional characters, imagine centaurs etc, and then arguing from such uncontroversial premisses to a more controversial conclusion. So it’s a matter of logic, not ‘phenomenological appeal’. The argument looks like this:

(1) You cannot write or understand a story without thinking about various fictional characters. (2) When you create a fictional character, you bring before your mind an intentional object. (3) The existence of such intentional objects is therefore phenomenologically evident.

I can buy the first premiss. The second I can understand only figuratively. What is an intentional object? The third I reject. It is bizarre to make an existence claim about things which purportedly do not exist, and such existence is far from evident. It’s a neat example of the fallacy of logical intransitivity. You start with a premiss containing a logically intransitive verb, such as ‘imagine’, ‘desire’ and so on. A logically transitive verb is one which takes a grammatical accusative but not a logical one. The accusative of the sentence ‘Jake wants to marry a mermaid’ is ‘a mermaid’, but the sentence is consistent with ‘nothing is a mermaid’. A logically transitive verb, by contrast, requires a real object. The truth of ‘Jake married a mermaid’ requires that some person is such that she was married by Jake. The fallacy consists in drawing a conclusion that contains a logically transitive verb, and which for that reason is existential. The fallacy is a specific instance of the more general existential fallacy, in which we erroneously draw an existential conclusion from non-existential premisses.

Over to you Bill.

Existence and quantification

Maverick argues:

Ed thinks that the assumption that the domain of quantification is a domain of existing individuals is a contingent assumption. But I didn't say that, and it is not. It is a necessary assumption if (1) [namely that ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’] and sentences of the same form are to hold. [My emphasis]

But he then says that there is nothing in the nature of logic to stop us from quantifying over nonexistent individuals, which I don't follow at all. We start with the initial logical or definition assumption about the meaning of the verb 'exists'.

(1) 'A golden mountain exists' = 'Some mountain is golden'

If we accept that, we also have to accept the equivalence where the right hand side does not explicitly contain the copula 'is', but has a verb which is logically equivalent to a copula plus participle. That is a standard assumption, namely that 'John runs' is logically equivalent to 'John is running'. Thus

(2a) 'John owns a house' = 'some house is owned by John

and thus, given (1), and given that John owns a house, it follows that:

(2b) John's house exists

A brief qualification here. The equivalence in (2a) only holds when the verb is what I call 'logically transitive. I explain this idea here. Clearly, if John wants a beautiful wife, it does not follow that some beautiful wife is wanted by John.  Given that, it is plain that our Brentano equivalence applies to the following quantifier type sentences:

(3) 'The domain contains islands' = 'some individuals in the domain are islands' = 'there exist individuals in the domain which are islands'

(4) 'The term 'volcano' ranges over volcanos' = 'ranged-over volcanos exist'

and so on. Hence there clearly is something 'in the nature of logic' which prevents us quantifying over non-existent individuals, namely the same thing as what prevents us owning non-existent houses, given the definition of 'exists' above. I can't believe that Bill does not grasp this. I think what he fails to see is that 'logical' verb phrases like 'ranges over', 'contains', 'quantifies over' are subject to the same logical rules as 'owns', 'lives next door to', 'loves' and so on. That any domain contains existing individuals is therefore a logical truth.

Are Meinongian objects incomplete objects?

The Maverick asks whether Meinongian objects are 'incomplete'? According to his definition, these are objects which have all and only the properties specified in their descriptions. For example, The Yellow Brick Road is described (in the story) as being yellow, but is not described as being coloured. So The Yellow Brick Road is yellow, because the property of being yellow is ascribed to it, but does have the property of being coloured. So Meinongian objects are 'incomplete'.

Which makes no sense to me. Every yellow object is coloured. Therefore there are no yellow objects which are not coloured. Therefore there is no 'incomplete object' such as Maverick has described. You object: Bill has described such an object, therefore there is such an object as Bill has described. I reply, the verb 'described' is logically intransitive. It takes a grammatical object, i.e. an accusative, but no logical object. 'S describes A' does not entail 'for some x, S describes x'. I can describe a yellow brick road, and perhaps I can even describe a road that is yellow but not coloured. But it does not follow that there is some yellow non-coloured object described by me, for no object is yellow but not coloured.

Reprise (reference)

A number of new readers have joined since I started the topics on 'reference' more than a year ago. To avoid going over the same ground again, I will link to some earlier posts for background. Of course, this is all work in progress, and anything may change.

For example, Anthony objects that I am attempting "to develop a theory of reference based on fictional stories". Correct, and that is the whole point. As I argued earlier, the semantics of empty proper names do not obviously differ from that of non-empty names, and it seems that the names of historical characters individuate in just the same way as fictional ones. See also this post about the reference of 'God' and 'Allah'.

I have argued further here that there cannot be such a thing as reference failure. To understand a proper name is to understand which person its sentence is about.

This means (I have argued) that reference cannot be relation between a term – a linguistic item - and an item in non-linguistic reality. The verb 'refers to' is therefore logically intransitive. I explain the notion of logical intransitivity here, and its application to reference here. This leads to the "'Frodo'-Frodo" theory of reference.

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.

An interesting net

Bill Vallicella mentions another argument for non-existent objects here. He writes

Imagination of a mermaid is not consciousness of a mental image or other content
of consciousness but precisely consciousness of a mermaid. Consciousness of a
mermaid is just as outer-directed and revelatory of a material item as
consciousness of a dolphin. But mermaids do not exist. Therefore, some objects
do not exist.

Here is the argument expressed in numbered statements. I have added some additional premisses and logical steps

1. (A) Tom is conscious of a mermaid
2. (A) Consciousness of a mermaid is just as outer-directed and revelatory of a material item as consciousness of a dolphin.
3. (interpreting 2) If Tom is conscious of a mermaid then Tom is conscious of some object which is a mermaid.
4. (from 1, 3) Tom is conscious of some object which is a mermaid.
5. (A) 'Is conscious of' is a logically transitive verb.
6. (from 4, 5) some object is a mermaid.
7. (A) Mermaids do not exist.
8. (from 6, 7) Therefore, some objects do not exist.

The questionable assumption is (5). I argued earlier that a 'logically transitive verb' Ø is such that the truth of 'a Ø's an F' is inconsistent with the truth of 'nothing is an F', and so implies 'something is an F'. Bill needs to justify the assumption that 'is conscious of' is logically transitive. This is questionable. 'Bill is conscious of a mermaid' is clearly consistent with 'nothing is a mermaid'.

"A clever man got caught in this net of language! So it must be an interesting net. "

Contemplation and logical transitivity

Some verbs may be logically transitive or intransitive, depending on sense or context. 'Contemplate' has a number of different senses, including

(1) To think about intently
(2) to look at thoughtfully
(3) to have in mind as a possibility.

The first sense is clearly logically intransitive - you can intently think about a mermaid without there being a mermaid. The second sense by contrast is (logically) transitive. You cannot look thoughtfully about a mermaid without there being a mermaid you are looking at. With the third sense, we are back to logically intransitive. God can contemplate creating a mermaid, even though there are no mermaids.

But, pace Vallicella, this doesn't entail there are any 'incomplete beings'. How?

Is reference logically intransitive?

In its strict technical sense (i.e. as used by philosophers of language) the verb phrase ‘refers to’ is logically transitive. If ‘London’ refers to London, then something is the referent of ‘London’ and ‘refers to’ is therefore logically transitive in the sense defined here. Thus the following conjunction is inconsistent when ‘refers to’ is taken in its technical sense.

(*) Tom is referring to a winged horse, but there are no winged horses.

Informally and in ordinary use, however, it seems to be logically intransitive. For example, you might get the following question in a multiple choice exam:

(**) Who is Shakespeare referring to when he says “the power of beauty will sooner transform honesty from what is to a bawd than the force of honesty can translate beauty into his likeness”? (see here for a real example)

Clearly the answer will be right or wrong, and thus true or false. Indeed, the a generally accepted answer is that Shakespeare is referring to Hamlet’s mother Gertrude, and so ‘Shakespeare is referring to Gertrude’ is true. But Gertrude being a fictional character, there is no such person as Gertrude. Thus

(***) Shakespeare is referring to Gertrude, but there is no such person as Gertrude

is not inconsistent. thus, in its ordinary sense (for example in GCSE exam questions about Shakespeare and Dickens), the verb phrase ‘refers to’ is logically intransitive.

In the posts that follow I will be exploring the concept of Story relative reference – reference to an individual within a text (or group of texts) such that the individual is identifiable within that text, but not outside it, and I will demonstrate its connection with the subject I began with, namely the intentionality of singular thoughts.

Logically intransitive verbs

I looked at the posts for January and February and while there are many passing references to the distinction between ‘intentional’ and ‘non intentional’ verbs, there is no specific post about it. So I’m writing one now. I’m going to use a new terminology and distinguish between ‘logically transitive’ and ‘logically intransitive verbs. A logically transitive verb is one which takes a logical as well as a grammatical accusative, such that there must be an object that verifies the accusative. That is, if ‘S V O’ is true, there must be an object corresponding to the accusative noun phrase ‘O’. All the verbs in the following propositions – note the last – are logically transitive.

1. Tom owns a house in the desert
2. Tom is building a house in the desert
3. Tom / has / a thought about a house in the desert

That is, if Tom owns a house in the desert, at least one house (Tom’s) is in the desert. So ‘owns’, in this context, is logically transitive. If he is building a house in the desert, there must be at least one house in the desert that he is building. And if he has a thought about the house, there must be at least one thought that he has, namely the one about a house in the desert. The verb ‘has’ is logically transitive in this context.

A logically intransitive verb is one which may have a grammatical accusative, but does not need a logical accusative to verify it. I.e. ‘S V O’ may be true without there being any object that satisfies 'O'. Thus all the verbs in the following are logically intransitive.

4. Tom wants a house in the desert
5. Tom is looking for a house in the desert
6. Tom / has a thought about / a house in the desert

If Tom wants or is looking for a house in the desert, it does not follow there is any such house. The verbs ‘want’ and ‘looking for’ are logically intransitive. Note well that proposition (3) is the same as proposition (6). But there are two different verb phrases: ‘has’ and ‘has a thought about’. The object of ‘has’ is ‘a thought’, and that must exist in order for there to be a thought. The object of ‘has a thought about’ is ‘a house in the desert’, but no such house has to be in order for there to be such a thought. So ‘has a thought about’ is logically intransitive.

Tomorrow, as we approach the problem of proper names, I will talk about verbs of reference and individuation.

Being, subsistence, existence etc.

Vallicella is still going on about the Intentionality problem. Here is his ‘aporetic triad’ again.

1. We sometimes think about the nonexistent.
2. Intentionality is a relation that ties a thinker to an object of thought.
3. Every relation is such that, if it holds, then all its relata exist.

He wonders (albeit hesitantly) if we can resolve the problem by distinguishing between different ‘modes of being’. He says

Some will be tempted at this point to distinguish between two modes of being,
a strong mode and a weak mode if you will, call them existence and
subsistence. The relations principle could then be reformulated to say
that if a relation R holds, then all of R's relata have being (either exist or
subsist). This seems to allow a solution of our problem. When Tom
thinks about a nonexistent item such as a mermaid, he does indeed stand in a
relation to something, it's just that the item in question subsists rather than
exists. The object of thought has being but does not exist.

But of course we already addressed that problem in a few places, e.g. here. Consider

Tom is thinking about a mermaid, but nothing is a mermaid.

The range of ‘thing’ in ‘nothing’ covers absolutely everything whatsoever – existing objects, objects with being, subsisting objects. ‘Thinking of the nonexistent’ covers even ‘thinking of a non-thing’. A mermaid is not a thing, not any kind of thing, not even a subsisting Meinongian thing, and still Tom can think of a mermaid. Different kinds of existence or being is no good.

Thinking about something

The intentionality thread at Vallicella’s has died down a bit. Except for his note here, where he wonders whether to think is always to think of something. Are we thinking of anything when we think, e.g., that that Tom is tired? Yes, he says. If we are thinking that Tom is tired, then we are thinking about Tom, for we cannot think this without thinking of him. And “If I am thinking that nothing is in the drawer, or nobody is at home, then I am thinking about the drawer and the home, respectively.”

Is that right? If I think that nothing is a unicorn, am I thinking about unicorns? More later: I particularly want to follow up the idea I broached here that we can parse ‘Tom has a thought about a unicorn’ in two ways, as follows.

Tom / has / a thought about a unicorn
Tom /has a thought about/ a unicorn

Both are of subject – verb – accusative form, and the subject is 'Tom' in both, but the verbs and accusatives are different. The first verb is ‘has’, and the accusative is ‘a thought about a unicorn’. This seems no exception to our rule that ‘has’ is always non-intentional. Thus the sentence is inconsistent with there being no thoughts about unicorns. The second verb is ‘has a thought about’ and the accusative is ‘a unicorn’. ‘Has a thought about’ is clearly intentional, for the sentence is consistent with there being no unicorns. This suggests we can analyse some (perhaps all) mental states that appear to involve a direct relation between a person and a ‘weird object’ into a relation between a person and a propositional state whose description involves a ‘weird term’. This could make the problem of intentionality tractable. Perhaps. More later.

Blog traffic has soared after the post by William Connolley here. Welcome scientists! What does intentionality have to do with science? Well, quite a lot. Intentionalists like Vallicella believe that when we think, there must be something we think about: an ‘intentional object’. These objects have a weird ontological status that seems difficult to reconcile with materialist theories of mind. (A materialist theory of mind reduces all thoughts, feelings, emotions and all ‘mental states’ in general to physical brain states).