Maverick repeats his circularity argument, which boils down to this:
(*) If concept F is instantiated, then it is instantiated by an individual that exists.
He has still not replied to my detailed critique of his argument, however. My critique, in brief, was that not every sentence of the form of (*) contains a circularity. For example "If a man is a bachelor then he is a bachelor who is unmarried".
I gave another objection here, which he has also clearly ignored. The objection is that if the word 'exists' on the right hand side of this definition
Some philosopher is American = An American philosopher exists
is merely a copula, then we cannot 'descend to singulars' via 'American philosopher' but only via the subject of the left hand side, namely 'philosopher'. Maverick may object that 'exist' is not a copula, in which case I accept his argument – but that does not appear to be his argument.
Showing posts with label brentano. Show all posts
Showing posts with label brentano. Show all posts
Wednesday, June 13, 2012
Friday, May 18, 2012
Thin existence and circularity
For reasons that Bill the Maverick will understand, I have recently been exercised by his argument that the 'thin' definition of existence is circular. He says here, for example, that "to account for the existence of an individual in terms of the instantiation of some concept or property is blatantly circular: if a first-level property is instantiated,then it is instantiated by something that exists" (my emphasis).
The thin conception, as I understand it, is that the first statement below is broadly equivalent to any of the three statements that follow it.
1. An American philosopher exists
2. The concept 'American philosopher' is instantiated
3. There is an American philosopher
4. Some philosopher is American
Maverick, as I understand him, believes that this equivalence involves a circularity. I.e. The definition of the first statement in terms of the second (and probably the third or the fourth, though he has never said this) is circular. What does he mean?
By way of preliminary, let's talk about what a circular definition actually is. A circular definition is one where the left hand term, the term to be defined, the definiendum, contains a term or a word that is also contained in the defining expression, the definiens. For example, if I say, as some people do, that money is whatever people treat as money, that is a circular definition, because the word 'money' is used to define itself. When we look at the right hand of the definition, we have to ask what 'money' means, and so we ask again by putting it on the left, and if we get the same reply, we go on and on in an endless circle.
Now I emphasised 'term' and 'word', because that is very important. The definition is circular because of the repeated word, not because of a repeated concept. Clearly the concepts corresponding to the left and right hand expressions must be repeated, otherwise it wouldn't be a definition. The whole point of a definition is to explain an expression you don't understand in terms of an expression you do understand. For example, you may not understand the word 'mutton', but you may understand the word 'lamb'. So I tell you that mutton is the same thing as lamb, and you understand. Now it's no good objecting that the definition is circular because the concept of mutton presuppposes the concept of lamb, indeed is identical to it. Of course it does, and that is the whole point. I am explaining that the concept corresponding to 'mutton' is identical to the concept corresponding to 'lamb'. So the fact that the same concept occurs (as it were) on both sides of the definition does not mean the definition is circular. On the contrary, that is what makes the definition work in the first place. It's a repeated word that is the only problem.
With that preliminary out of the way, it seems clear that defining (1) above in terms of any of the following three statements is in no way circular. The word 'exists', which is the one we want to explain or define, does not occur in any of the three defining statements. So why does Maverick there is any circularity?
Now he says 'if a first-level property is instantiated, then it is instantiated by something that exists" (my emphasis). That seems to me like objecting that if something is lamb, then it is lamb which is mutton, and so defining mutton as lamb is circular. Which is absurd. Now he may mean that the adjective 'existing' adds something to the expression 'American philosopher', and so 'American philosopher' and 'existing American philosopher' are not equivalent. If that is true, then the definition certainly would be circular. For the statement 'some philosopher is American' of (4) above would be elliptical for 'some philosopher who exists is American', and the defining right hand expression would thus contain the term 'exists', which was on the left hand side. But that is precisely what the thin theorist is denying, indeed strenuously denying. 'Existing philosopher' and 'philosopher' are, for him, exactly the same, and so 'instantiated by something' and 'instantiated by something that exists' are exactly the same, just as 'instantiated by something' and 'instantiated by something that is something' are the same. Indeed, just as 'cooking lamb' and 'cooking lamb which is mutton' are the same.
Or does he mean that the concept of existence is presupposed in statements (2)-(4) above? Well of course it is, just as the concept of mutton is presupposed by the concept of lamb. To understand the statement 'someone is an American philosopher', you have to understand the concept of existence, for the existence of an American philosopher is exactly what the statement asserts. Similarly, in order to understand 'lamb is on the menu' you have to understand the concept of mutton, for the concept of mutton and the concept of lamb are one and the same. But that doesn't mean that the definition 'mutton is lamb' is circular.
Perhaps Maverick intends something different. But if he does, I am very far from understanding it, and the first duty of a philosopher is enable understanding.
The thin conception, as I understand it, is that the first statement below is broadly equivalent to any of the three statements that follow it.
1. An American philosopher exists
2. The concept 'American philosopher' is instantiated
3. There is an American philosopher
4. Some philosopher is American
Maverick, as I understand him, believes that this equivalence involves a circularity. I.e. The definition of the first statement in terms of the second (and probably the third or the fourth, though he has never said this) is circular. What does he mean?
By way of preliminary, let's talk about what a circular definition actually is. A circular definition is one where the left hand term, the term to be defined, the definiendum, contains a term or a word that is also contained in the defining expression, the definiens. For example, if I say, as some people do, that money is whatever people treat as money, that is a circular definition, because the word 'money' is used to define itself. When we look at the right hand of the definition, we have to ask what 'money' means, and so we ask again by putting it on the left, and if we get the same reply, we go on and on in an endless circle.
Now I emphasised 'term' and 'word', because that is very important. The definition is circular because of the repeated word, not because of a repeated concept. Clearly the concepts corresponding to the left and right hand expressions must be repeated, otherwise it wouldn't be a definition. The whole point of a definition is to explain an expression you don't understand in terms of an expression you do understand. For example, you may not understand the word 'mutton', but you may understand the word 'lamb'. So I tell you that mutton is the same thing as lamb, and you understand. Now it's no good objecting that the definition is circular because the concept of mutton presuppposes the concept of lamb, indeed is identical to it. Of course it does, and that is the whole point. I am explaining that the concept corresponding to 'mutton' is identical to the concept corresponding to 'lamb'. So the fact that the same concept occurs (as it were) on both sides of the definition does not mean the definition is circular. On the contrary, that is what makes the definition work in the first place. It's a repeated word that is the only problem.
With that preliminary out of the way, it seems clear that defining (1) above in terms of any of the following three statements is in no way circular. The word 'exists', which is the one we want to explain or define, does not occur in any of the three defining statements. So why does Maverick there is any circularity?
Now he says 'if a first-level property is instantiated, then it is instantiated by something that exists" (my emphasis). That seems to me like objecting that if something is lamb, then it is lamb which is mutton, and so defining mutton as lamb is circular. Which is absurd. Now he may mean that the adjective 'existing' adds something to the expression 'American philosopher', and so 'American philosopher' and 'existing American philosopher' are not equivalent. If that is true, then the definition certainly would be circular. For the statement 'some philosopher is American' of (4) above would be elliptical for 'some philosopher who exists is American', and the defining right hand expression would thus contain the term 'exists', which was on the left hand side. But that is precisely what the thin theorist is denying, indeed strenuously denying. 'Existing philosopher' and 'philosopher' are, for him, exactly the same, and so 'instantiated by something' and 'instantiated by something that exists' are exactly the same, just as 'instantiated by something' and 'instantiated by something that is something' are the same. Indeed, just as 'cooking lamb' and 'cooking lamb which is mutton' are the same.
Or does he mean that the concept of existence is presupposed in statements (2)-(4) above? Well of course it is, just as the concept of mutton is presupposed by the concept of lamb. To understand the statement 'someone is an American philosopher', you have to understand the concept of existence, for the existence of an American philosopher is exactly what the statement asserts. Similarly, in order to understand 'lamb is on the menu' you have to understand the concept of mutton, for the concept of mutton and the concept of lamb are one and the same. But that doesn't mean that the definition 'mutton is lamb' is circular.
Perhaps Maverick intends something different. But if he does, I am very far from understanding it, and the first duty of a philosopher is enable understanding.
Monday, March 12, 2012
Stromboli and flying horses
I replied to this Maverick post, but will copy it here as well. Maverick says that the following argument is valid but not sound:
Pegasus exists.
Pegasus is a flying horse.
Ergo
A flying horse exists.
And he claims that the first premise [Pegasus exists], though false, is needed for the argument to be valid. Do I agree? Certainly not. On my view, which is not a standard view, 'Pegasus is a flying horse' has two meanings, a literal and a non-literal. The literal meaning is such that its truth implies that something is a flying horse. I also hold the Brentano-Quine view that 'something' is always 'existing something'. Thus the argument is valid with the second premise alone. "Pegasus is a flying horse" is equivalent (literally understood) to "Something is Pegasus and it is a flying horse" which implies "something is a flying horse" without the help of the first existential premise. Literally understood, "A is B" is always existential.
The second meaning, the non-literal one, is 'In Greek mythology, Pegasus is a flying horse', which means the same as 'Greek mythology says that Pegasus is a flying horse'. This is not existential, at least in respect of the that-clause. It can be true that I say that some horses fly, even though it is false that any horse flies (as far as I know). Thus, on this non-literal interpretation, Bill's argument is not valid, for it really reads:
Pegasus exists.
Greek mythology says that Pegasus is a flying horse
Ergo
A flying horse exists.
which is not valid. At most, it would imply 'some [existing] creature is said by Greek mythology to be a flying horse'.
This is not a standard view, of course. The standard view would be that 'Pegasus' is meaningless because it fails to refer. Therefore Bill's argument is invalid anyway.
Pegasus exists.
Pegasus is a flying horse.
Ergo
A flying horse exists.
And he claims that the first premise [Pegasus exists], though false, is needed for the argument to be valid. Do I agree? Certainly not. On my view, which is not a standard view, 'Pegasus is a flying horse' has two meanings, a literal and a non-literal. The literal meaning is such that its truth implies that something is a flying horse. I also hold the Brentano-Quine view that 'something' is always 'existing something'. Thus the argument is valid with the second premise alone. "Pegasus is a flying horse" is equivalent (literally understood) to "Something is Pegasus and it is a flying horse" which implies "something is a flying horse" without the help of the first existential premise. Literally understood, "A is B" is always existential.
The second meaning, the non-literal one, is 'In Greek mythology, Pegasus is a flying horse', which means the same as 'Greek mythology says that Pegasus is a flying horse'. This is not existential, at least in respect of the that-clause. It can be true that I say that some horses fly, even though it is false that any horse flies (as far as I know). Thus, on this non-literal interpretation, Bill's argument is not valid, for it really reads:
Pegasus exists.
Greek mythology says that Pegasus is a flying horse
Ergo
A flying horse exists.
which is not valid. At most, it would imply 'some [existing] creature is said by Greek mythology to be a flying horse'.
This is not a standard view, of course. The standard view would be that 'Pegasus' is meaningless because it fails to refer. Therefore Bill's argument is invalid anyway.
Friday, January 13, 2012
Men and non-men
Anthony rightly raised the problem of my ‘some men are not men’. He suggested (rightly I think) that this is a problem for ‘Brentano equivalence’, the thesis that ‘Some A is B’ is equivalent to ‘An A-B exists’, and that ‘some A is not B’ is equivalent to ‘An A-not-B exists’.
He is right. If Brentano is right, then ‘some men are not men’ is equivalent to ‘men that are not men exist’, which is clearly wrong. So what’s the problem? I suggest that Brentano is wrong. Clearly we can say that some of the men who landed on the moon have now died ( for example, Alan Shepard, the one who played golf on the moon). So, some men such as Shepard are no longer men. If Brentano is right, that implies that men who are non-men exist, which is false. Non valet consequentia, so Brentano is wrong.
The late thirteenth century philosophers of language, such as the early Scotus, were acutely aware of this problem. Many of them distinguished between so-called indefinite negation of the form ‘A is a non-B’, and pure negation ‘A is not B’. Indefinite negation is affirmative. It affirms the existence of an A that is non-B. In this sense ‘some man is a non-man’ is false. By contrast, pure negation denies everything, including the affirmation of existence. In that sense ‘some man is a not a man’ is true, pace Brentano.
The problem is to render this in predicate logic. The formal sentence ‘for some x, Ax and not Bx’ is affirmative in the traditional sense: it asserts that some x is both A and non-B. However, the pure negative for ‘not for some x, Ax and Bx’ is not equivalent to the medieval ‘some A is not B’. The predicate logic version simply denies the existence of anything that is both A and B, whereas the medievals understood it in the sense we understand ‘some men (such as Alan Shepard) are not men (i.e. are men no longer)’.
Brentano’s thesis was the first formulation of one of the key assumptions of the modern predicate calculus. It is wrong for the same reason the calculus is wrong. It does not translate the meaning of a standard English sentence in the way we want to translate it. So what is the meaning of the sentence, and into what formal language can we translate it?
He is right. If Brentano is right, then ‘some men are not men’ is equivalent to ‘men that are not men exist’, which is clearly wrong. So what’s the problem? I suggest that Brentano is wrong. Clearly we can say that some of the men who landed on the moon have now died ( for example, Alan Shepard, the one who played golf on the moon). So, some men such as Shepard are no longer men. If Brentano is right, that implies that men who are non-men exist, which is false. Non valet consequentia, so Brentano is wrong.
The late thirteenth century philosophers of language, such as the early Scotus, were acutely aware of this problem. Many of them distinguished between so-called indefinite negation of the form ‘A is a non-B’, and pure negation ‘A is not B’. Indefinite negation is affirmative. It affirms the existence of an A that is non-B. In this sense ‘some man is a non-man’ is false. By contrast, pure negation denies everything, including the affirmation of existence. In that sense ‘some man is a not a man’ is true, pace Brentano.
The problem is to render this in predicate logic. The formal sentence ‘for some x, Ax and not Bx’ is affirmative in the traditional sense: it asserts that some x is both A and non-B. However, the pure negative for ‘not for some x, Ax and Bx’ is not equivalent to the medieval ‘some A is not B’. The predicate logic version simply denies the existence of anything that is both A and B, whereas the medievals understood it in the sense we understand ‘some men (such as Alan Shepard) are not men (i.e. are men no longer)’.
Brentano’s thesis was the first formulation of one of the key assumptions of the modern predicate calculus. It is wrong for the same reason the calculus is wrong. It does not translate the meaning of a standard English sentence in the way we want to translate it. So what is the meaning of the sentence, and into what formal language can we translate it?
Friday, December 09, 2011
On an existential problem suggested by Anthony
I am beginning to appreciate more the comments provided by Anthony (if only he would think before commenting, and not endlessly comment and delete - bear in mind that any comment whether deleted or not comes through my email box).
I suggested earlier that some things used to exist, but no longer exist. Given my acceptance of Brentano's equivalence - that "some A is B" is equivalent to "Some A that is B exists", Anthony has spotted that this entails that some things are no longer things, and are thus not things (although, to be sure, they were things). And indeed some men (e.g. Caesar) who were a man, are no longer a man. Ergo, some men are not men.
This has the distinct whiff of paradox, which I will investigate later.
I suggested earlier that some things used to exist, but no longer exist. Given my acceptance of Brentano's equivalence - that "some A is B" is equivalent to "Some A that is B exists", Anthony has spotted that this entails that some things are no longer things, and are thus not things (although, to be sure, they were things). And indeed some men (e.g. Caesar) who were a man, are no longer a man. Ergo, some men are not men.
This has the distinct whiff of paradox, which I will investigate later.
Sunday, October 16, 2011
Do false statements exist?
Commenter Anthony questions whether false statements exist, and says
So we need to demonstrate to Anthony's satisfaction that some declarative sentences are false. That is easy. The sentences "The sky is red" is a declarative sentence, and it is false. So, some declarative sentences (i.e. at least one) are false. If Anthony denies that "The sky is red" is false, there is an equally easy reply. If you deny something, you are denying that it is true. But if you are right in denying this, it must be false. So in order to make the objection at all, you have to concede that at least one declarative sentence, in this case "'The sky is red' is false" is false, and thus concede the point. More generally, to affirm "no declarative sentence is false" is to deny "some declarative sentence is false". But if that denial is right, "'some declarative sentence is false' is false" is true, and so at least one declarative sentence is false, namely "no declarative sentence is false". Slightly more formally:
(1) No declarative sentence is false (assumption)
(2) "Some declarative sentence is false" is false (E and I are contradictory opposites)
(3) "Some declarative sentence is false" is a declarative sentence (definition)
(4) Some declarative sentence is false (substitution)
(5) Contradiction (1 and 4)
I doubt this will be the end of the matter.
In order for me to concede that false statements exist, I would need clarification of what is meant by "statements" and what is meant in saying that they "exist". If the answer I receive is "they just do" or "most people accept that they do", you can argue all you want about "burden of proof", but I will not be convinced, any more than I would be convinced by the same "arguments", that "red unicorns exist".OK then. Starting with the definitions. There are various definitions of 'statement' but I will go with 'declarative sentence' for this one. As for 'exists', I will read 'false statements exist' as equivalent to 'some statements are false'. See my earlier remarks about Brentano equivalence.
So we need to demonstrate to Anthony's satisfaction that some declarative sentences are false. That is easy. The sentences "The sky is red" is a declarative sentence, and it is false. So, some declarative sentences (i.e. at least one) are false. If Anthony denies that "The sky is red" is false, there is an equally easy reply. If you deny something, you are denying that it is true. But if you are right in denying this, it must be false. So in order to make the objection at all, you have to concede that at least one declarative sentence, in this case "'The sky is red' is false" is false, and thus concede the point. More generally, to affirm "no declarative sentence is false" is to deny "some declarative sentence is false". But if that denial is right, "'some declarative sentence is false' is false" is true, and so at least one declarative sentence is false, namely "no declarative sentence is false". Slightly more formally:
(1) No declarative sentence is false (assumption)
(2) "Some declarative sentence is false" is false (E and I are contradictory opposites)
(3) "Some declarative sentence is false" is a declarative sentence (definition)
(4) Some declarative sentence is false (substitution)
(5) Contradiction (1 and 4)
I doubt this will be the end of the matter.
Saturday, February 19, 2011
Ockham and Brentano-equivalence
I talked about 'Brentano equivalence' a few times, e.g. here. It is the thesis that "some A-B exists" is convertible with "some A is B", and is closely connected with the thesis that existence is not a predicate. Something very similar can be found in Ockham's Summa Logicae, Book III, part 2, chapter 26. Parallel Latin-English below. Note that the similarity is not exact - Brentano also held that 'every A is B' is equivalent to the negative 'no A is not B', or to 'not: something that is A and not-B exists'. Ockham, by contrast, agreed with Aristotle that 'every A is B' is affirmative, and that it implies the particular 'some A is B'.
On the confusion about the 'existential import' of the universal proposition, I have a piece here.
On the confusion about the 'existential import' of the universal proposition, I have a piece here.
| Latin | English |
|---|---|
| Si autem propositio dubitabilis in qua praedicatur esse exsistere per propositionem de inesse vel de possibili habeat pro subiecto nomen connotativum vel respectivum vel negativum vel unum compositum ex multis nominibus, quandoque potest demonstrari, quandoque non. | Now if there is a dubitable proposition in which existential being is predicated by an assertoric or de possibili proposition, and the proposition has for a subject a connotative, relative, or negative name, or one composed from many names, sometimes it can be demonstrated and sometimes it cannot. |
| Talis enim propositio semper aequivalet uni propositioni in qua praedicatur passio de subiecto, saltem large sumendo passionem. Sicut ista proposito ‘eclipsis est’ aequivalet isti ‘aliquid eclipsatur’; et ista ‘calefactivum est’ aequivalet isti ‘aliquid est calefactivum’; et ista ‘habens tres angulos aequales duobus rectis’ aequivalet isti ‘aliquid est habens tres angulos aequales duobus rectis’. | For such a proposition is always equivalent to a single proposition in which an affection is predicated of a subject, at least when we take "affection" broadly. Thus the proposition, "An eclipse exists" is equivalent to "Something is eclipsed"; and "A heatable thing exists," is equivalent "Something is heatable"; and "Something having three angles equal to two right angles exists," is equivalent to "Something is a thing having three angles equal to two right angles." |
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?
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?
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.
or
(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.
(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.
or
(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.
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.
Thursday, December 23, 2010
Brentano and the convertibility of ‘exists’
Brentano held that a thought must have an object. Did he mean to qualify this by ‘existing object’? According to at least one important thing he said, he would not have drawn any distinction between ‘object’ and ‘existing object’. According to what is now called the Brentano-Venn analysis of propositions, every categorical proposition (one of the form ‘A is B’) is convertible with an existential proposition ‘An A-B exists’. He says, for example
The categorical proposition "Some man is sick", has the same meaning as the
existential proposition "A sick man exists" or "There is a sick man".
It follows from this that 'some hobbit is thought about by some man' is convertible with 'some hobbit thought by some man exists' or 'there is a hobbit thought about by some man'. I have more to say on the history of this here.
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