Monday, January 31, 2011

Some pages the spider forgot

Sunday, January 30, 2011

Reid on intentionality

Bill Vallicella cites here the Scottish enlightenment philosopher Thomas Reid, saying that Reid already understood that when one thinks of a unicorn one is not thinking of a mental image, but of an animal. Perhaps he is referring to passages such as this one.
[The object of conception] is not the image of an animal—it is an animal. I know
what it is to conceive an image of an animal, and what it is to conceive an
animal… The thing I conceive is a body of a certain figure and colour, having
life and spontaneous motion. The philosopher says, that the idea is an image of
the animal; but that it has neither body, nor colour, nor life, nor spontaneous
motion. This I am not able to comprehend. (Essays on the Intellectual powers
of man
, 4.2, 321-2)
Perhaps this is what is driving Bill's argument from the premiss ‘Tom is thinking of something’ to the conclusion ‘Tom’s thinking has an intentional object’? Tom is thinking of unicorn, Tom is thinking of something other than the thought of a unicorn, ergo Tom stands in some 'intentional relation' to some quasi-unicorn, an 'intentional object'.

Sadly for Bill, this will not work. If I am thinking of a unicorn, then I have a thought of a unicorn. Thus the two following propositions are broadly equivalent.

(A) Tom is thinking of a unicorn
(B) Tom has the thought of a unicorn

But this still doesn't get the conclusion that Bill wants, namely

(C) Tom's thinking has an intentional object.

For (B) can be true even though there are no unicorns. The verb phrase 'has the thought of' is intentional. But the verb 'has' on its own is non-intentional. 'Tom's thinking has an intentional object' is inconsistent with 'there are no intentional objects'. As I have argued, we cannot argue without other assumptions from a sentence using an intentional verb, to a sentence using a non-intentional verb.

The confusion probably occurs because of the two grammatical accusatives in sentence (B) above. The first is 'the thought of a unicorn', which is the object of the non-intentional verb 'has'. We cannot have an F without there being an F, and so cannot have the thought of a unicorn without there being a thought of a unicorn. The second is 'a unicorn', which is the object of the verb phrase 'has the thought of'. Seeing that the first accusative has a corresponding logical accusative, we are tempted to assume that the second has also. But the second verb phrase is clearly intentional, and so the existence of its grammatical accusative does not justify the existence of any logical accusative.

The fact that there are two grammatical objects in (B) does not justify the conclusion that there are two logical objects. This only follows if the two corresponding verb phrases are non-intentional. But they are not, and so the conclusion does not follow.

* Essays on the Intellectual Powers of Man, Derek Brookes (ed.), University Park: Pennsylvania State University Press, 1785/2002.

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Friday, January 28, 2011

Carentional objects

Are there intentional objects? Well, are there carentional objects? Let me explain. Suppose we are house hunting, but reject the following houses because

(A) Number 15 lacks a bathroom
(B) Number 18 lacks a kitchen
(C) Number 6 lacks a garden

What is the common property or quiddity or essence of bathrooms at number 15, kitchens at number 18, gardens at number 6? Why, they are ‘things that are lacked’! So let’s define a Latin term ‘carentionality’ to signify the essence or common property of all objects corresponding to the accusative of the verb ‘lacks’! Let’s translate (A) as ‘Number 15’s lacking has a carentional object’ or ‘Number 18 stands in a carentionality relation to some kitchen’.

We could even restate Bill Vallicella's famous aporetic triad as follows:

(1) Some objects lack the nonexistent
(2) Carentionality is a relation between an object, and the object that is lacked
(3) Every R is such that, if R obtains,then all its relata exist

But of course the whole point of the accusative of ‘lacks’ is precisely that there is no object corresponding to it. Otherwise nothing is lacking! The realist will perhaps object that this house is lacking something (a bathroom, a kitchen, a garden). The nominalist agrees, but disagrees that this implies that the house possesses something, or stands in some relation to something, as a result. The logic of ‘is lacking’ is entirely different from, indeed opposite to, the logic of ‘possesses’.

We could even truly say ‘something is lacking in this house – a bathroom’. But that just proves how careful we must be in analysing ordinary English sentences. For we cannot formalise that sentence as ‘for some x, x is in this house and x is lacking’.

Note also the similarity between ‘is lacking’ and ‘is wanting’ as in ‘a single man with a good fortune is in want of a wife’, which is a truth universally acknowledged.

Further thought: there is a whole class of verbs – which in most cases are the same words as the recognised ‘intentional’ verbs, which take an impersonal, non-animate subject. For example

Number 15 lacks a garden
Our bedroom wants a good clean.
That paper deserves an A grade.
This chair is missing a leg.

In all cases, they have the characteristic feature of the properly ‘intentional’ verbs of there not being an object corresponding to their accusative. I.e. there is no garden at no 15, our bedroom has not had a cleaning, the paper didn’t receive an A grade, the chair doesn’t have a leg and so on. In most or all cases we can replace the accusative noun with ‘something’, e.g. if the house lacks a garden, it lacks something, if the chair is missing a leg, it is missing something, and so on. Why is it that these constructions do not tempt us into ‘metaphysical’ theories about the accusative? I’m assuming not, anyway. We aren’t tempted to say that the chair is missing the non-existent. Or to invent a word like ‘carentional’ (from the Latin ‘to lack’) to describe some relation between the chair and some ‘queer’ entity.

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Monday, January 24, 2011

Metaphysical reasoning

I just noticed an argument by Bill Vallicella that is a perfect example of the ‘metaphysical reasoning’ that I commented on earlier. He writes

There is a clear sense in which every intentional mental state 'takes an
accusative,' 'is of or about an object.' That object could be called the
intentional object. Accordingly, whether I want a three-headed dog or a
one-headed dog, my wanting has an intentional object.
In other words, he clearly regards as valid the inference from (A) to (B) below:

(A) Bill wants a three-headed dog
(B) Bill’s wanting has an intentional object

This is the crucial step in the argument for ‘intentional object’, and it is clearly faulty. Look at the verbs of sentences (A) and (B). Sentence (A) contains the verb ‘wants’. Sentence (B) contains the verb ‘has’. These are different types of verb, and of course the whole problem began with important logical differences between ‘intentional’ verbs such as ‘wants’, ‘thinks about’, ‘is looking for’ and so on, and other verbs such as ‘owns’, ‘works in’, ‘is to the left of’ and so on. Both realist and nominalist agree that ‘Bill wants a three-headed dog’ is consistent with ‘no dog is three-headed’, and therefore does not imply ‘some dog is three-headed’. And they also agree that ‘Bill lives in a house in the desert’ is inconsistent with ‘no house is in the desert’, and therefore does imply ‘some house is in the desert’.

With that agreed, it is unreasonable for the realist to argue from (A) to (B). The verb ‘has’, which connects ‘Bill’s wanting’ and ‘an intentional object’ doesn’t look like an intentional verb. It is a verb of posession like ‘owns’. Thus it is inconsistent with ‘no object is intentional’, and therefore does imply ‘some object is intentional’. Similarly for the argument given by Peter Lupu where he says “Bill defines whatever it is that they [intentional states] are about, or are of, or directed towards by the term 'intentional object'. “ But the sentence

(B’) Bill’s wanting is directed towards an object

also contains a verb ‘is directed towards’ which is not obviously an intentional verb. The nominalist will challenge both of these inferences, on the grounds that (A) does not imply the existence of anything at all apart from Bill and his mental states, whereas (B) and (B’) do imply the existence of something apart from Bill’s and his mental states, and on the grounds that ‘whatever is implied by the consequent is implied by the antecedent’.

Note that this nominalist line of reasoning is purely logical. It starts with something that both sides agree on – namely that the logic on ‘intentional verbs’ is different from ‘non-intentional verbs’, and that what the logical properties of ‘wants’ may be different from the logical properties of ‘has’. Then the nominalist simply points out that a crucial step in the realist’s argument depends on the assumptiont that the logical properties of ‘wants’ are not different from the logical properties of ‘has’.

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Sunday, January 23, 2011

Aristotle's Physics (Logic Museum)

Just out. A version of Aristotle' Physics in the Logic Museum. Fully indexed with Bekker numbers and other references so that (unlike other versions on the web) you can take a reference from some other source and locate it exactly. Accompanying it is Thomas Aquinas' commentary, fully linked to Aristotle's text.

The Physics includes many of Aristotle's most famous claims, some of them now discredited, such as that

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Saturday, January 22, 2011

Meaning and Meinong

David Brightly asks whether we can avoid Meinong quite so easily. Meinong draws a distinction between being and existing. Thus some things which have Being may not exist - the golden mountain which I am thinking of, perhaps?

I already engaged with this objection in my second point here. The problem for the Meinongian thesis is that "Vallicella is thinking of a non-existent thing" is perfectly consistent with "no thing is non-existent", where scope of 'no thing' covers every object whatsoever, and is therefore inconsistent with "some non-existent thing has Being". So the Meinongian solution doesn't solve anything.

I suppose the Meinongian could object that the scope of 'no thing' may fail to cover those things that have Being but which are non-existent. But (a) I can still insist that I mean nothing whatsoever, not just nothing that is not a non-existent Being. And (b) as I argued here it would not be possible for the Meinongian and the anti-realist to have an argument at all unless they agreed on the meaning of categorical statements like 'no A is B' or 'some A is not B'. When the anti-realist says that there aren't any non-existent, he is denying exactly what the Meinongian asserts when he asserts that there are such things. The expression 'there are' is completely unambiguous in this argument, and has to be, in order that there can be an argument at all.

David also comments on the curious fact we can reason about apparently non-existent objects. Indeed. The Square of Opposition seems to work for fictional characters. 'All the characters in Lord of the Rings are hobbits' implies 'some of the characters in Lord of the Rings are hobbits', is the contrary of 'none of the characters in Lord of the Rings are hobbits' and is the contradictory of 'some of the characters in Lord of the Rings are not hobbits'. More is needed.

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Thursday, January 20, 2011

Meinong's gambit

In yesterday’s post I argued that not only is the inference

(*) Vallicella is discussing a non-existent thing, therefore something is non-existent

invalid, but that practically everyone will agree it is invalid. Even the most hardened and extreme realist or Meinongian will concede the possibility that nothing is non-existent (even though, as a matter of fact, they believe that some things actually are non-existent). It follows that they cannot use Meinong's gambit to explain intentionality. They can’t explain Bill’s thought as being somehow about a non-existing thing, because they concede that he could have the same thought even if there were no such objects at all.

With this in mind, we can approach the problem which (according to Bill Vallicella here) is central to the phenomenon of intentionality. Bill says that the problem can be expressed in terms of an aporetic triad, saying that while each of these propositions has some claim to plausibility, all three cannot be correct. At least one must be false. Which?

W1. We sometimes think about the nonexistent.
W2. Intentionality is a relation between thinker and object of thought.
W3. Every relation R is such that, if R obtains,then all its relata exist.

I will begin by ‘Ockhamising’ these propositions so that they express the same problem, but in language more acceptable to an Ockhamist. (E.g. I argued here that a term like ‘the nonexistent’ is question-begging).

O1. The proposition ‘Bill is discussing a nonexistent thing’ can be true even when there are no nonexistent things.
O2. The proposition ‘Bill is discussing a nonexistent thing’ expresses a relation between two things.
O3. Every relation is such that if it obtains, all of its relata exist.

With my previous comments in mind, the answer may now be obvious. We can assume that the first proposition is true. The third proposition must also be true. As argued above, the realist cannot plead the ‘nonexistence’ amendment. He can’t argue that the third proposition is false because Bill’s thought may relate him to a nonexistent thing. For the problem remains even when there are no nonexistent things. It is not that we sometimes think of the nonexistent. It is that the predicate "Bill is thinking of ---" may not apply to anything at all, rather than applying to some nonexistent something. Thus, even if there were nonexistent things, this would not explain the problem of intentionality, i.e. the problem that all three propositions above are inconsistent.

It remains that the second proposition must be false. Indeed, isn’t this obvious? The simplest and most economical hypothesis to explain this is that while the proposition ‘Bill is discussing a nonexistent thing’ has grammatically the form of a relation, and is syntactically similar to ‘Bill is meeting his wife’, it does not actually express or signify a relation. What other explanation is there? The second proposition has no claim to plausibility at all.

This explanation involves no recourse to ‘queer objects’ of any kind. The underlying logic of the proposition must be different to the underlying logic of ‘Bill is meeting his wife’. As is manifest and provable, for the latter implies ‘someone is such that Bill is talking to her’. ‘Something is such that Bill is discussing it’.

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Wednesday, January 19, 2011

Distinguishing queer from straight

In my previous post I gave four criteria for distinguishing ‘queer’ from ‘straight’ terms. The most important of these was the last one: a queer term does not refer to or denote anything, and thus does not pick out any category or kind of thing. Bill Vallicella and Peter Lupu are now impatiently challenging me on this. What are the considerations or criteria on the basis of which we decide how to draw the distinction between terms which refer or denote*, and those which do not refer or denote?

There are several techniques used by Ockham throughout Summa Logicae. The one I will use is as follows. Take any proposition p containing a possibly queer occurrence of some term F. Construct a proposition q that uses the term to assert that there are F’s – preferably avoiding the use of ‘exists’ or its cognates, to prevent the realist from driving a wedge between ‘something’ and ‘some existing thing’. Then show, by logical analysis, that p does not entail q, i.e. it is possible that p is true but q false. We can easily do this using an earlier example.

(1) Jake is looking for a gold mine in Surrey, therefore some gold mine is in Surrey.

Even the most hardened realist will agree that the inference is not valid. For it is perfectly possible that the antecedent is true, and that Jake is looking for a gold mine in Surrey, but the consequent false – for there is no gold mine in Surrey, and so ‘some gold mine is in Surrey’ is false. Note my careful use of the categorical sentences ‘some gold mine …’ and ‘no gold mine …’ here, and the avoidance of the word ‘exists’. This is necessary in case the realist argues that there is no existing gold mine in Surrey, i.e. there are gold mines, but they are not ‘existing’ or ‘existent’ ones. We reply: that there is no gold mine in Surrey, not even in this qualified sense. It is not that there is no existent gold mine, as though there could be some non-existent gold mine. That is an abuse of language, and it leads far from the truth. There are no gold mines in Surrey at all.

This reasoning can be confirmed as follows. Consider

(2) Vallicella is discussing a non-existent thing, therefore something is non-existent

The realist cannot explain away the truth of the antecedent, as he might try to do with ‘gold mine in Surrey’, by reference to non-existent things. For he agrees that the inference is invalid, therefore he agrees that the consequent is false, and so nothing is non-existent. It is not merely that the non-existent does not exist (as though there were some things, which happen to exemplify the property of non-existence). It is that nothing - not even a non-existent thing - is non-existent.

Thus I have distinguished a ‘queer’ from a ‘straight’ term by purely logical means. Tomorrow, I shall address Vallicella’s ‘aporetic triad’. We can think of the non-existent; ‘thinking of’ is a relation; a relation must relate existing relata. Does the triad make sense? And if it does, which of the propositions is false?

* I have changed Lupu’s wording from “refers in a way that entails ontological commitments” because I do not understand it. If a term refers, by definition it refers to something, and so there is something to which it refers. By Brentano’s equivalence (i.e. ‘there exists an F’ is convertible with ‘there is an F’), it has existential commitment.

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Tuesday, January 18, 2011

Intentionality: more objections

More objections at Valicella's place. Let's summarise where we are. In the two posts here and here, I gave three criteria for distinguishing 'queer' from 'straight' terms. As follows.

(1) the term is categorial (read ‘noun phrase’). This rules out trivial examples like ‘not’ and ‘the’.
(2) a significant number of people think it does refer or denote. This addresses Bill’s objection about ‘net too wide’. The net is just wide enough to catch the right sort of fish.
(3) the reason these people think it refers is not based on mere empirical considerations. This rules out non-referring/denoting terms like ‘ghost’.
(4) the term, in fact, does not refer or denote.

The next part of the question, which I haven’t answered yet, is what are the sub-criteria by which we address criterion (4)? How do we engage the people picked out by criteria (2) and (3), who will naturally challenge (4)? I will address this shortly. The reason I haven’t addressed it before is so we can be absolutely clear about the form of nominalism I am defending – namely the nominalism defended by Ockham in chapters 49-51 of the Summa Logicae, and throughout the whole section of that book where he discusses Aristotle’s theory of categories. (Ockham argues that the Aristotelian ten categories of being really reduces to two, and that we only really need substance and quality. In chapters 49-51 he is discussing relation, arguing that a relation is nothing absolute and distinct from the terms related, when suitably referred to).

More tomorrow, where I will tie the question back to the thread about 'intentional inexistence'.

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Monday, January 17, 2011

More confusion about intentionality

Vallicella has been picking up on some of the issues discussed here over the last week.

His aim to highlight what he thinks is a fundamental confusion in the Ockhamist characterisation of intentionality. It is characteristic of certain mental states (intentional states) to refer beyond themselves to certain items. For example, states of desire refer beyond themselves to items that are not part of the states. In desire something is desired, and so on. Unfortunately (he says) the word 'something' will cause certain people (that's us here) to stumble, leading them wrongly to suppose that “a concrete episode of desire cannot exist unless there also exists, independently of the desire, something that is desired”.

His point seems to be that the inference

(A) Something is desired, therefore there exists something that is desired.

is not valid, but Ockhamists wrongly think it is valid.

This is wrong. (A) certainly is valid. I have argued, particularly here, that when the word ‘something’ occurs in the subject position of a sentence, then Brentano equivalence applies, so that the categorical sentence ‘Some A is B’ is convertible with the existential ‘Some A-that-is-B exists’. Thus there is fundamentally no difference between the following three sentences.

(A1) Something is desired by Tom
(A2) There is something desired by Tom
(A3) There exists something desired by Tom

Thus (A) is valid. If something is desired, then there is something desired. The move from 'something is desired' to 'there is something desired' is a mere grammatical transformation. C.J.F. Williams says that English inherits from Anglo-Saxon the dislike of the verb ‘is’ at the beginning of a sentence, and so we put the word ‘there’ in front. Thus the logical move from ‘Something is desired by Tom’ to ‘is something desired by Tom’ is followed by the grammatical move to ‘There is something desired by Tom’. This in turn is no different from ‘There exists something desired by Tom’.

Brentano equivalence applies when ‘something’ is the subject. It does not apply, as I have argued, when it is the predicate. It is the following inference which is invalid.

(B) Tom desires some F, therefore some F is desired by Tom.

Indeed, the examples given by Vallicella testify to this. He says that ‘Tom wants a sloop, therefore something is a sloop’ is invalid, because Tom may want a sloop even when nothing is a sloop. And the fact that a woman now wants a baby is perfectly consistent with the fact that there are (now) no babies satisfying her want. It is (B), not (A) above, that is the problem.

The question is, why is this a problem?

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Friday, January 14, 2011

Queer entities and the supernatural

Before I go on to discuss what distinguishes ‘queer’ terms from ‘straight’ ones, I should add a third characteristic of queer terms to the two which I gave in my post yesterday. (The first characteristic was that a queer term does not refer to anything. The second, that it must appear, at least to some people, to refer, even though it doesn’t. This is what makes for its ‘queerness’, that illusory quality that deceives some people into believing it has a reference. Its queerness is the linguistic equivalent of an optical illusion).

A further characteristic is necessary to distinguish queer terms from other non-referring terms like ‘dragon’, ‘goblin’, ‘ghost’ and so on. The reason that some people believe these terms refer is unconnected with the reason that metaphysicians believe that there exist such things as intentional objects, or universals, or haecceities. People believe that ghosts exist because they believe that certain objectively verifiable phenomena are evidence for the existence of ghosts. For example, the photograph on the left undoubtedly exists. It is a real photograph that anyone reading this blog can see. And some people may believe it is evidence for ghosts.

But metaphysicians do not use physical items like photographs, recordings, eye-witness reports or anything which is observable, as evidence for the existence of universals or haecceities or whatever. The only evidence required is an argument or a line of reasoning of some kind. To persuade you of the existence of universals, a metaphysician requires only your time, a modicum of intelligence, the ability to read a text, possibly extending over innumerable volumes, considerable patience with his or her obscurities of expression, and a grain of salt. Nothing else is required. The text can be as old as you like. No specific knowledge of the world is required, other than of language and of technical abstract terms, some of which may be invented by the author. This is the ‘evidence’ of the metaphysician. The only laboratory required is an armchair, the only tool a thick pair of reading glasses.

Thus, the third characteristic of a ‘queer term’ is that the reason for believing that it refers must not consist of observable or empirical evidence. The reason must consist of a text that has no reference to the world except the use of abstract terminology. (I was about to say ‘abstract objects’, but these of course are ‘queer’, and Ockhamists generally avoid using queer terms, although they frequently have to mention them).

In summary, a ‘queer term’ is a categorical term such that

1. It does not refer to or denote anything.
2. Some people (metaphysicians) believe that it does denote or refer
3. Their reason for believing this is not based on empirical observation (or revealed by supernatural agency for that matter).

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Thursday, January 13, 2011

Ockham's nominalism

At this stage, I should discuss Peter Lupu’s objections (mostly in the extended comment on Vallicella’s blog here) to the nominalist program.

I should first explain what I think the nominalist program is. I am taking my lead from a principle that William of Ockham neatly formulates in his Summa Logicae book I, chapter 51, where he accuses 'the moderns' of two errors, and says that the root of the second error is “to multiply entities according to the multiplicity of terms and to suppose that every term has something real (quid rei) corresponding to it”. He says grumpily that this is erroneous and leads far away from the truth. ('Radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei; quod tamen abusivum est et a veritate maxime abducens'). See also an early definition of nominalism here.

What does he mean? Well he says that it is an error. He implies it is a common one, by attributing to the moderns and by the fact he mentions it all. Thus he implies that there exist terms which do not have something real corresponding to them.

If Ockham is correct, the relevant distinction to draw is between queer and straight terms. Straight terms have something real corresponding to them, queer terms don’t. Furthermore, there must at least be some temptation to imagine that queer terms refer to or denote something, otherwise there would be little point in making it.

Which brings me to the main point raised by Peter Lupu, who asks “What are ‘queer-entities’ and how do we determine whether a given entity is “queer” or “straight”? There are two parts to his question. In answer to the first, there are no such things as queer entities, if Ockham is right. There are only ‘queer terms’. These, by definition, are terms that don’t refer to or denote anything, and so by implication there are no ‘queer entities’.

This is what makes any debate with realists difficult. Realists, namely those who think that queer terms refer, will persist in using the queer terms as if they did refer, and so will ask what kinds of thing are referred to, what is their ‘ontological status’ and so on. Ockhamists will naturally refuse to use these terms as if they referred, and refer the names of the terms instead, typically by using real or scare quotes.

There is a similar difficulty in the debate between those who believe in ‘paranormal phenomena’ and those who don’t. Believers talk about ‘the phenomena’ (without scare quotes) as though there were such things as alien abductions, electronic voice phenomena, telepathic radiation and so on. But to use such talk is to presume the existence of such things, as though the only real debate were about their precise nature and properties. Non-believers will rightly refuse to use such terms, and will instead talk about the reports of such things, or of the supposed evidence for them. Reports and evidential phenomena are real enough. The question is whether there exist any things of which they are reports, or evidence.

That deals with Peter's first question. What are queer entities? We can't say, because there are no such things, just as we can't say what kind of things ghosts are. But we can say what 'queer terms' are. These are terms that are categorical, but which (a) have no reference or denotation and (b) appear, or are believed by many, typically on grounds of reason alone, to have a reference or denotation.

Peter’s second point, on how we determine whether given entity is “queer” or “straight”, I will leave for the next post, although clearly the first point applies here also. If the nominalist is right, we cannot ask this question of anything, just as we cannot ask whether a UFO came from Alpha centauri or Betelgeuse. We can only ask whether a given term is queer or straight. More to follow.

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Tuesday, January 11, 2011

Seeking the nonexistent

Yesterday I discussed an apparent problem for the Brentano thesis (that every categorical sentence of the form ‘some A is a B’ is convertible with an existential sentence of the form 'an A-B exists'). The problem is sentences like

(1) Gerald is looking for a gold mine in Surrey

which can be true even though gold mines in Surrey don’t exist.

Such sentences are admittedly a problem, but they are not a problem for the Brentano thesis as such. For (1) above is equally consistent with the following sentence

(2) No gold mine is in Surrey

which is not existential, but categorical. Indeed, Brentano equivalence clearly holds for the conversion of ‘No gold mine is in Surrey’ and ‘no gold mine in Surrey exists’ or ‘a Surrey gold mine does not exist’. The problem is not for Brentano at all, but rather for Aristotle, and the principle of conversion of the particular proposition. According to Aristotle (and according to modern logic, as it happens) ‘Some A is B’ is convertible with ‘Some B is A’. But if ‘Gerald is looking for a gold mine in Surrey’ is true, then by conversion of the particular, the following sentence:

(3) some gold mine in Surrey, is looked for by Gerald,

ought to be true. But surely it isn’t, since it implies that some gold mine (namely the one sought by Gerald) is in Surrey, and we agreed that no gold mine is in Surrey. Is the principle of particular conversion invalid? Or is there something else going on? To me, this is the strongest evidence that there is a deeper logical structure to (1) than the surface grammar suggests. Consider:

(4) Some gold mine, thought by Gerald to be in Surrey, is looked for by him.

which I think is true. And that is roughly equivalent to

(5) Gerald thinks there is some gold mine in Surrey, and he is looking for it.


(6) Gerald is looking for a gold mine which he thinks is in Surrey

Thus the quantifier noun phrase ‘some gold mine’ has to be qualified by ‘is thought by’ or some other intentional construction, before the conversion is valid, and thus it is not an ordinary conversion. None of this (pace Vallicella and Lupu) has to do with metaphysics or weird objects or ‘the nonexistent’, except figuratively, but rather it has to do with a more complex logic that underlies our ordinary discourse, and which we need to make visible, if we can.

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Sunday, January 09, 2011

A problem for the Brentano thesis

As discussed yesterday, a 'Brentano equivalence' holds when we can convert existential sentences of the form 'an A-B exists' and categorical sentences of the form 'Some A is B'. The Brentano thesis is that every such (genuinely) categorical sentence is convertible.

This effectively amounts to the claim that any sentence of the form 'something is such and such' is existential. If anything is such and such, then that thing is an existing thing. The range of our natural language quantifiers 'every' and 'some' covers the entire realm of existence. Every thing is an existing thing.

There are strong arguments for this thesis. But there are strong arguments against, as well, which brings us back to the problem of intentionality. Surely the following inferences are all valid.

  • Jake is looking for a gold mine in Surrey, therefore Jake is looking for something (namely a gold mine in Surrey).
  • Bill wants a cigarette, therefore Bill wants something (a cigarette).
  • Andy is thinking about Pegasus, therefore Andy is thinking about something (Pegasus).

The problem is that any of these antecedents could conceivably be true, the inference seems valid, yet the 'something' in the consequent does not appear to be any existing thing. Clearly Jake can be deludedly looking for a Surrey gold mine, and so looking for a mine, and so looking for something. Yet, as far as we know, there are no gold mines in Surrey. The simple categorical sentence 'Jake is looking for something' can be true, without requiring that the something exists, contra Brentano.

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Saturday, January 08, 2011

The nonexistent

Sadly, Bill finally had enough of my comments on intentionality. I'm not sure exactly what underlies it, but I suspect it is my persistence on the 'Brentano equivalence'. There is more here and very much more here. Briefly, a Brentano equivalence holds when we can convert existential sentences of the form 'an A-B exists' and categorical sentences of the form 'Some A is B'. There is much evidence that such an equivalence holds in ordinary subject-predicate sentences. Thus 'some buttercups are yellow' is convertible with 'yellow buttercups exist' and 'no buttercups are blue' with 'blue buttercups do not exist'. And as I commented here, there seems little difference between 'Tom's worship has an object' and 'there is an object of Tom's worship' or 'there exists an object of Tom's worship'.

Hence my objection to Bill's claim that 'We sometimes think about the nonexistent'. 'The nonexistent' is an abstract noun phrases built out of an adjective, like 'the unemployed', 'the French', 'the damned', which appear to refer to a whole class of things (unemployed people, French people, damned souls). If the same is true of 'the nonexistent', then it refers to a whole class of things - things which do not exist - and we can divide all things in reality into those which do exist (mountains, horses, yellow buttercups) and those which do not (golden mountains, unicorns, blue buttercups, four-leaf clovers and so on). You can see the idea in the picture on the left (from the Logic Now and Then symposium in 2008 - I don't remember who the speaker was).

Clearly, no one who divides reality up in this way can consistently hold the Brentano equivalence, according to which any thing is also an existing thing. If 'the nonexistent' refers at all, it refers to nonexistent things. But a nonexistent thing is a thing which does not exist, and so is a thing such that there is no such thing. But there is no such thing. So 'the nonexistent' does not refer. Accordingly, we cannot think of the nonexistent, if the Brentano equivalence is valid.

Clearly there is a problem, as true sentences like 'the Greeks worshipped Zeus' or 'Tom is thinking of Pegasus' suggest. But I will talk about this in the next post.

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Friday, January 07, 2011

Ockham and the golden mountain

Reading Valicella’s discussion of Twardowski’s ‘solution’ to the paradox of intentionality brought to mind my old translation of Ockham’s commentary on Aristotle’s Perihermenias. The whole thing is worth a read, but section 9 is particularly relevant.

Replying for those who say that an intentional object is a real being, Ockham argues that 'a chimaera exists in reality' has distinct meanings according to whether 'chimaera' denotes personally, or materially or simply. If it denotes personally (i.e. if it is meant to denote a chimaera itself) it is false. But if it denotes ‘materially’ (i.e. if it stands for the word 'chimaera') or ‘simply’ (it stands for the concept of a chimera), it is true, for the word 'chimaera', and the concept chimaera both exist in reality. Similarly the proposition 'a chimaera is understood' is false, if 'chimaera' is meant to stand for a chimaera, but true, if it stands either for the word itself, or for the concept of a chimaera. (An argument he repeats in Summa Logicae II.72). This solution seems close to the one that Twardowski criticises. When I think about the round square or the golden mountain (in whatever psychological mode) the object of my thought is neither a mental content nor an abstract object. And ‘the golden mountain’ refers to the golden mountain, not, as Ockham’s comment suggests, to the concept of a golden mountain.

Note Ockham’s use of the example ‘golden mountain’ (mons aureus). I can find only one earlier example, in Scotus’ questions on the Metaphysics (q.6), written in the late 1290s, but it must surely be older than that.

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Thursday, January 06, 2011

Intentional objects

Given that

(*) Tom worships Zeus is true, which of the following, if any, are true?

(1) Tom’s worship is object-directed
(2) Tom’s worship is directed towards an object
(3) Tom’s worship has an object it is directed to
(4) There is an object that Tom’s worship is directed to
(5) There exists an object that Tom’s worship is directed to
(6) The object that Tom’s worship is directed to exists

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