It's well known that 'queer theorists' successfully reclaimed the term 'queer', which used to be a term of abuse for homosexual, and turned it into a sort of verbal flag for the homosexualist movement.
Can we do the same thing for the term 'prude'? By far the most common statement I see on one side of the porn debate is 'I am not a prude' (the most common statement on the other side is 'I am against any form of censorship'). But I am always puzzled by what a 'prude' is. It seems like a term of abuse, given that so many people are so eager to deny being one. I have never seen anyone admit to being a prude. Is this because prudes are a bit like homosexuals were in the 1950s, and afraid to admit this. Should prudes come out of the closet? It's difficult to say, because whereas it was clear in the 1950s what 'homosexual' meant, it's not clear what 'prude' means.
So we can't reclaim a term if we don't know what it means. Time for some further research.
Thursday, May 31, 2012
A sound bite for circularity
Maverick has just posted a reply to my request for what he calls a ‘sound bite’ on his argument for circularity. Before I comment, a brief aside on my dislike of the term ‘sound bite’. In philosophy, particularly ‘Internet philosophy’, I frequently encounter it when I ask for a clear and concise explanation of or argument for the opponent’s position. “You can’t reduce my argument to a sound bite”. Well in that case I am not interested in the opponent’s argument, for it is not an argument at all. I suspect the underlying reason is a fear that the position really is incoherent, or that the underlying argument is invalid. There should be an informal fallacy ‘The Sound Bite fallacy’ named after it. And in any case I do not want a ‘sound bite’, which is simply a short slogan summarising a position or attitude such as ‘This was their finest hour’, often little more than a cliché. Note also my previous post, where I argued that the ‘circularity objection’ is actually more complex and difficult than Maverick originally implied, and that it is unfair to say I am being disingenuous, when I claim I fail to understand it. I feel he has now conceded that it is somewhat more complicated and less obvious than he originally suggested.
But anyway: Maverick has now given a pretty clear outline of his argument, which I copy verbatim below.
1. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated.'
2. If a first-level concept such as *F* is instantiated, then it is instantiated by an individual.
3. Let the arbitrary constant 'a' denote an individual that instantiates *F.*
4. By LNC, a cannot both exist and not exist.
5. By LEM, a must either exist or not exist.
6. If a does not exist, i.e., if a is a Meinongian nonexistent object, then the link expressed in (1) between existence and instantiation is broken.
Therefore
7. If *F* is instantiated, then *F* is instantiated by an individual that exists.
Therefore
8. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated by an individual that exists.'
9. A definition (analysis, account, theory, explanation) is circular iff the term to be defined occurs in the defining term.
10. 'Exists' occurs both in (8)'s definiendum and its definiens.
Therefore
11. The thin theory is circular.
Is it valid? Well, my first point is that the argument is even more complex than this, by reason of premisses (7) to (10). Consider the following, obviously invalid argument:
(1a) ‘Bachelor’ means the same as ‘unmarried man’.
(2a) (From 1a, definition) Every bachelor is an unmarried man.
(3a) Every bachelor is a bachelor who is an unmarried man.
(4a) ‘Bachelor’ means the same as ‘bachelor who is an unmarried man’.
(5a) ‘Bachelor’ occurs in the definiendum and the definiens of (4a)
(6a) The definition of ‘bachelor’ is circular.
What’s wrong with it? Well, from the fact that a definition occurs somewhere in the argument it doesn’t follow that whatever we derive from the definition can itself be turned into a definition. The universal proposition (3a) above is perfectly true and follows from the original definition, but it doesn’t follow that we can turn any old universal proposition into a definition. So the move to (4a), which turns the universal proposition into a definition, is blatantly fallacious.
Likewise, even if I grant the truth of the universal proposition corresponding to Maverick’s (7) above, i.e. “any F that exists is an F instantiated by an individual that exists”, it doesn’t follow that you can turn this into something that looks like a definition. Quite obviously not. In particular, Bill needs to avoid the charge that he has reintroduced the term ‘exist’ in (7) in much the same way that ‘bachelor’ has been reintroduced in (3a).
But anyway: Maverick has now given a pretty clear outline of his argument, which I copy verbatim below.
1. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated.'
2. If a first-level concept such as *F* is instantiated, then it is instantiated by an individual.
3. Let the arbitrary constant 'a' denote an individual that instantiates *F.*
4. By LNC, a cannot both exist and not exist.
5. By LEM, a must either exist or not exist.
6. If a does not exist, i.e., if a is a Meinongian nonexistent object, then the link expressed in (1) between existence and instantiation is broken.
Therefore
7. If *F* is instantiated, then *F* is instantiated by an individual that exists.
Therefore
8. On the thin theory, 'An F exists' means the same as 'The concept *F* is instantiated by an individual that exists.'
9. A definition (analysis, account, theory, explanation) is circular iff the term to be defined occurs in the defining term.
10. 'Exists' occurs both in (8)'s definiendum and its definiens.
Therefore
11. The thin theory is circular.
Is it valid? Well, my first point is that the argument is even more complex than this, by reason of premisses (7) to (10). Consider the following, obviously invalid argument:
(1a) ‘Bachelor’ means the same as ‘unmarried man’.
(2a) (From 1a, definition) Every bachelor is an unmarried man.
(3a) Every bachelor is a bachelor who is an unmarried man.
(4a) ‘Bachelor’ means the same as ‘bachelor who is an unmarried man’.
(5a) ‘Bachelor’ occurs in the definiendum and the definiens of (4a)
(6a) The definition of ‘bachelor’ is circular.
What’s wrong with it? Well, from the fact that a definition occurs somewhere in the argument it doesn’t follow that whatever we derive from the definition can itself be turned into a definition. The universal proposition (3a) above is perfectly true and follows from the original definition, but it doesn’t follow that we can turn any old universal proposition into a definition. So the move to (4a), which turns the universal proposition into a definition, is blatantly fallacious.
Likewise, even if I grant the truth of the universal proposition corresponding to Maverick’s (7) above, i.e. “any F that exists is an F instantiated by an individual that exists”, it doesn’t follow that you can turn this into something that looks like a definition. Quite obviously not. In particular, Bill needs to avoid the charge that he has reintroduced the term ‘exist’ in (7) in much the same way that ‘bachelor’ has been reintroduced in (3a).
What should we do about Wikipedia’s porn problem?
By Larry Sanger here. The logic of arguments for and against porn is interesting, although I don't have a great deal of time to go into it now. The top level argument, as it were, is that people, i.e. all people, should have the right to see absolutely whatever they like, and that any restriction is an encroachment upon freedom. The objection to this is that not all people, namely young children, should have this right. Then we encounter all sorts of counter-objections and replies to the counter-objections. For example, what exactly is wrong with children seeing such images. If sex good or not? If it is good, why shouldn't children participate in the good, etc etc. Larry (who is a philosopher) covers some of these arguments in his post.
At least Augustine had a clear approach to this. Sex, or rather shame about sex, is the result of original sin. I'll look up the reference some time.
At least Augustine had a clear approach to this. Sex, or rather shame about sex, is the result of original sin. I'll look up the reference some time.
Wednesday, May 30, 2012
It's not obvious what's obvious
"It ain't obvious what's obvious". Thanks to the Maverick for that insight by Hilary Putnam. I suppose everyone knows the mathematician's joke about the lecturer how - discussing some result - says 'That's obvious'. He then pauses, looks down, then goes off for about twenty minutes. Then he comes back and announces 'Yes, it's obvious'.
Judging from the comments, there's been a bit of misunderstanding about my position on the 'thin conception' of existence. I don't necessarily agree with the conception. My question is whether the brief arguments given by Maverick, and which seem as obvious as day to him, really are obvious. Now I think, pace Dr. Putnam, there is a simple test for obviousness. If you can state your position or argument in less than about five sentences, and if the terms are clear or well-defined, or have a common and undisputed meaning, if any assumptions underlying the position are beyond dispute, and if all deductive steps are valid, then it is obvious. Otherwise it isn't.
Now Maverick's argument, as I understand it, is this:
The thin conception of 'exists' is that 'An F exists' means the same as 'The concept *F* is instantiated'
But if *F* is instantiated, then it is instantiated by an individual that exists
Therefore the thin conception of 'exists' is circular
This is deceptively simple, but fails my test for obviousness. Why? The subject of the conclusion is 'the thin conception of exists'. The predicate is 'circular'. The predicate of the conclusion is called the 'major term' and it is an undisputed rule of logic that the major term should appear in the premisses. Which of course it doesn't. This would probably be fine if the idea of a circularity were undisputed and clear, by I have argued elsewhere that it isn't. It is very slippery.
So what is needed is an argument of the following form:
The thin conception of existence is of form X
Any conception of form X is circular
The thin conception of existence is circular.
I would accept any argument of that form as 'obvious'. And I hope that clears me of any charges of being disingenuous.
Judging from the comments, there's been a bit of misunderstanding about my position on the 'thin conception' of existence. I don't necessarily agree with the conception. My question is whether the brief arguments given by Maverick, and which seem as obvious as day to him, really are obvious. Now I think, pace Dr. Putnam, there is a simple test for obviousness. If you can state your position or argument in less than about five sentences, and if the terms are clear or well-defined, or have a common and undisputed meaning, if any assumptions underlying the position are beyond dispute, and if all deductive steps are valid, then it is obvious. Otherwise it isn't.
Now Maverick's argument, as I understand it, is this:
The thin conception of 'exists' is that 'An F exists' means the same as 'The concept *F* is instantiated'
But if *F* is instantiated, then it is instantiated by an individual that exists
Therefore the thin conception of 'exists' is circular
This is deceptively simple, but fails my test for obviousness. Why? The subject of the conclusion is 'the thin conception of exists'. The predicate is 'circular'. The predicate of the conclusion is called the 'major term' and it is an undisputed rule of logic that the major term should appear in the premisses. Which of course it doesn't. This would probably be fine if the idea of a circularity were undisputed and clear, by I have argued elsewhere that it isn't. It is very slippery.
So what is needed is an argument of the following form:
The thin conception of existence is of form X
Any conception of form X is circular
The thin conception of existence is circular.
I would accept any argument of that form as 'obvious'. And I hope that clears me of any charges of being disingenuous.
Tuesday, May 29, 2012
Analytic vs European
There is a further installment from the Maverick in the dispute about the thin conception of existence. Maverick asks whether I think the notion of a non-existent object is self-contradictory. I reply: we need to be shown that it is self-contradictory. The thin conception of existence is first and foremost a definition, and you can't argue against a definition as such. The only way of progressing is to show how the defined term in its ordinary (or perhaps philosophical) use is not consisent with the definition. But I am not seeing that in any of Maverick's arguments, and particularly the 'circularity' argument, which I entirely fail to understand.
One of his arguments, for example, is that there is an inbuilt assumption that the domain of quantification contains only existing things. But in what sense is he using the italicised 'existing' here? If in the sense that the Brentano defines it, then the domain does contain only existing things, but in the most trivial and non-circular way, for the word 'thing', by definition, means 'existing thing' or 'thing which is a thing'. If in some stronger sense, Maverick needs to explain what that sense is. Those of us trained in the analytic method are taught to give examples. Find a use of the verb 'exists' that is not consistent with the definition set out by Brentano. But I am not seeing that.
Maverick ends:
One of his arguments, for example, is that there is an inbuilt assumption that the domain of quantification contains only existing things. But in what sense is he using the italicised 'existing' here? If in the sense that the Brentano defines it, then the domain does contain only existing things, but in the most trivial and non-circular way, for the word 'thing', by definition, means 'existing thing' or 'thing which is a thing'. If in some stronger sense, Maverick needs to explain what that sense is. Those of us trained in the analytic method are taught to give examples. Find a use of the verb 'exists' that is not consistent with the definition set out by Brentano. But I am not seeing that.
Maverick ends:
Ed begs the question against me by simply stipulating that the meaning of the verb 'exists' shall be identical to the meaning of 'Some ___ is a --.' That is what I deny.Not at all. I am questioning his arguments to show that 'exists' has any meaning stronger than that. I would like to see an argument with numbered steps, with assumptions clearly labelled, with any deductive steps clearly identified. All I am seeing is European 'novelistic' gestures at an argument, with laboured repetition of the same point, and without logical justification of that point. Like CJFW, who I mentioned in an earlier post, I don't do Continental.
Appearance and reality
I just noticed the Maverick’s comment on C.J.F. William’s obituary here, and was struck by the fact that his wheelchair-bound existence was news. This reminded me of the contrast between what we know of the thought of a philosopher such as Duns Scotus, which is immense, and what we know of his life, which is almost nothing, and what we do know is mostly guesswork based on other facts, and thus is not even knowledge.
CJF being in a wheelchair was in one way the most striking thing about him. I remember helping carrying it – with him in it – up the steps of the Wills building. The building was designed in the grand neo-Gothic manner (in about 1908) and so the flight of steps was about half a mile long, and I remember entertaining with horror the idea of us letting go the wheelchair and it moving with gathering speed to the bottom where it would crash into the porter’s lodge with horrifying consequences, perhaps carrying off a few undergraduates along the way.
But in another way it was the least important, and once you got to know him, you were hardly ever aware of it. He was teaching philosophy after all.
One story he liked to tell was about his special trousers he had, with a zip at the back going right up from bottom to top. A colleague came to collect him one day, and saw a spare pair of these lying on the floor, fully unzipped and looking like a tiger skin rug, except without the stripes. “Now I understand the difference between appearance and reality”, said the colleague.
There was a constant philosophical war going on between CJF and another philosopher in the department, Edo Pivcevic. Edo was Czech, or from some central European place – he was hired by the late Stefan Korner – and was a ‘phenomenologist’ always talking about Husserl and Heidegger, and saying things like ‘to answer the question about the meaning of being we must analyse the being of Man’. CJF was utterly contemptuous of this European stuff, although he taught Frege and Wittgenstein, who were very European in their own way.
CJF also told a Swinburne story. Once Swinburne offered to drive him from some place to another, probably Bristol to Manchester. However, Swinburne qualified the offer by saying he never drove over 30 miles an hour. Thinking he meant urban zones where a 30 mph limit applies in Britain, and thinking this exemplary practice, he accepted. What Swinburne meant, however, was that he drove at this speed even on motorways, where most people are whizzing along at speeds in excess of 70 mph. I don’t know how long it took to get to Manchester up the M5, although I can picture it.
CJF being in a wheelchair was in one way the most striking thing about him. I remember helping carrying it – with him in it – up the steps of the Wills building. The building was designed in the grand neo-Gothic manner (in about 1908) and so the flight of steps was about half a mile long, and I remember entertaining with horror the idea of us letting go the wheelchair and it moving with gathering speed to the bottom where it would crash into the porter’s lodge with horrifying consequences, perhaps carrying off a few undergraduates along the way.
But in another way it was the least important, and once you got to know him, you were hardly ever aware of it. He was teaching philosophy after all.
One story he liked to tell was about his special trousers he had, with a zip at the back going right up from bottom to top. A colleague came to collect him one day, and saw a spare pair of these lying on the floor, fully unzipped and looking like a tiger skin rug, except without the stripes. “Now I understand the difference between appearance and reality”, said the colleague.
There was a constant philosophical war going on between CJF and another philosopher in the department, Edo Pivcevic. Edo was Czech, or from some central European place – he was hired by the late Stefan Korner – and was a ‘phenomenologist’ always talking about Husserl and Heidegger, and saying things like ‘to answer the question about the meaning of being we must analyse the being of Man’. CJF was utterly contemptuous of this European stuff, although he taught Frege and Wittgenstein, who were very European in their own way.
CJF also told a Swinburne story. Once Swinburne offered to drive him from some place to another, probably Bristol to Manchester. However, Swinburne qualified the offer by saying he never drove over 30 miles an hour. Thinking he meant urban zones where a 30 mph limit applies in Britain, and thinking this exemplary practice, he accepted. What Swinburne meant, however, was that he drove at this speed even on motorways, where most people are whizzing along at speeds in excess of 70 mph. I don’t know how long it took to get to Manchester up the M5, although I can picture it.
Monday, May 28, 2012
Brightly on meagre existence
David Brightly on singular existential statements here. I liked this bit
[...] there is an important asymmetry between singular existential assertions and denials. If the name 'Vulcan' has been properly introduced by a general existential assertion then 'Vulcan exists' tells us nothing new. In contrast, 'Vulcan doesn't exist' amounts to a denial of the general existential statement by which the name was introduced to us. On the other hand, if the name 'Vulcan' has not been properly introduced then 'Vulcan exists' is meaningless to us.Although I'm sure I said the same thing myself somewhere :)
Existence and quantification
Maverick argues:
(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.
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.
Sunday, May 27, 2012
Frege on predication
I mentioned Frege's distinction between concept and object earlier, and said I was taking a feature of that distinction as fundamental, namely that the distinction between predicate and sentential negation only applies to concept words (or rather, quantified concept words), and not to object words ('logical subjects').
David Brightly wasn't so sure it was a feature of that distinction, as opposed to a mere accident. Well, two further reasons. First, it is build into the predicate calculus that simple singular propositions have only one form of negation. We write '~Fa'. The syntax of the calculus is designed so that we cannot even represent the difference between 'Socrates is not running' and 'it is not the case that Socrates is running'.
Second, Frege begins his discourse by saying that a concept is predicative, whereas the name of an object, a proper name, is quite incapable of being used as a grammatical predicate. Now, we can say that someone is Alexander the Great, or is the planet Venus, but this is not predicating the object itself. For the predicate 'is the planet Venus' is predication not of Venus itself but of the concept of being identical with Venus. The verb 'is' is not a mere copula, its content is an essential part of the predicate.
Thus for an object-word to signify, it has to signify an object. It is essential to an object word like 'Venus' that it has to be satisfied, whereas it is essential to a concept word like 'planet' that it can be satisfied, or not. "An equation is reversible; an object's falling under a concept is an irreversible relation.
Thus "‘Venus exists’ is true in virtue of the meaning of the proper name ‘Venus’. Maverick says that this has it precisely backwards. What I should say is that 'Venus' has meaning in virtue of the truth of 'Venus exists'. Not at all. 'Venus' has meaning in virtue of its meaning something, just as you are an employer in virtue of your employing someone.
David Brightly wasn't so sure it was a feature of that distinction, as opposed to a mere accident. Well, two further reasons. First, it is build into the predicate calculus that simple singular propositions have only one form of negation. We write '~Fa'. The syntax of the calculus is designed so that we cannot even represent the difference between 'Socrates is not running' and 'it is not the case that Socrates is running'.
Second, Frege begins his discourse by saying that a concept is predicative, whereas the name of an object, a proper name, is quite incapable of being used as a grammatical predicate. Now, we can say that someone is Alexander the Great, or is the planet Venus, but this is not predicating the object itself. For the predicate 'is the planet Venus' is predication not of Venus itself but of the concept of being identical with Venus. The verb 'is' is not a mere copula, its content is an essential part of the predicate.
Thus for an object-word to signify, it has to signify an object. It is essential to an object word like 'Venus' that it has to be satisfied, whereas it is essential to a concept word like 'planet' that it can be satisfied, or not. "An equation is reversible; an object's falling under a concept is an irreversible relation.
Thus "‘Venus exists’ is true in virtue of the meaning of the proper name ‘Venus’. Maverick says that this has it precisely backwards. What I should say is that 'Venus' has meaning in virtue of the truth of 'Venus exists'. Not at all. 'Venus' has meaning in virtue of its meaning something, just as you are an employer in virtue of your employing someone.
Saturday, May 26, 2012
Circularity of the thin conception: Maverick replies
Maverick finally replies to my circularity objections. I agree with his broad conclusion, as it happens. I just disagree with his way of getting there. He argues (I have numbered his sentences).
1. ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’
Agree, of course.
2. This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals.
Disagree profoundly. The equivalence, being logical, cannot depend on any contingent assumption. From the logical equivalence of (1), it follows that ‘the domain of quantification is a domain of existing individuals’ is equivalent to ‘some individuals are in the domain’. But the equivalence is true whether or not any individuals are in the domain. E.g. suppose that no islands are volcanoes. Then ‘Some volcano is an island’ is false. And so is ‘island volcanos exist’, by reason of the equivalence. But the equivalence stands, because it is a definition. Thus the move from (1) to (2) is a blatant non sequitur.
3. If the domain were populated by Meinongian nonexistent objects, then the equivalence would fail.
This rests on the assumption that it is a contingent matter whether the description ‘Meinongian nonexistent objects’ is satisfied. But if the equivalence is logical, i.e. if ‘some objects are in the domain’ is logically equivalent to ‘some object in the domain exists’, then by definition there cannot be Meinongian nonexistent objects, any more than there can be bachelors who are married. Maverick takes an equivalence which is purportedly true by definition, then turns it into a contingent statement. But if it is contingent, the equivalence cannot be true by definition, he argues, and the rabbit is out of the hat.
4. The attempted reduction of existence to someness is therefore circular.
Wrong. The argument is fallacious, because the move from (1) to (2) is fallacious. We cannot agree that something is true by definition, i.e. subject and predicate are logically equivalent, to making its truth a contingent matter, as in (2).
1. ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’
Agree, of course.
2. This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals.
Disagree profoundly. The equivalence, being logical, cannot depend on any contingent assumption. From the logical equivalence of (1), it follows that ‘the domain of quantification is a domain of existing individuals’ is equivalent to ‘some individuals are in the domain’. But the equivalence is true whether or not any individuals are in the domain. E.g. suppose that no islands are volcanoes. Then ‘Some volcano is an island’ is false. And so is ‘island volcanos exist’, by reason of the equivalence. But the equivalence stands, because it is a definition. Thus the move from (1) to (2) is a blatant non sequitur.
3. If the domain were populated by Meinongian nonexistent objects, then the equivalence would fail.
This rests on the assumption that it is a contingent matter whether the description ‘Meinongian nonexistent objects’ is satisfied. But if the equivalence is logical, i.e. if ‘some objects are in the domain’ is logically equivalent to ‘some object in the domain exists’, then by definition there cannot be Meinongian nonexistent objects, any more than there can be bachelors who are married. Maverick takes an equivalence which is purportedly true by definition, then turns it into a contingent statement. But if it is contingent, the equivalence cannot be true by definition, he argues, and the rabbit is out of the hat.
4. The attempted reduction of existence to someness is therefore circular.
Wrong. The argument is fallacious, because the move from (1) to (2) is fallacious. We cannot agree that something is true by definition, i.e. subject and predicate are logically equivalent, to making its truth a contingent matter, as in (2).
Schools Wikipedia
Jon Davies (Chief Executive of Wikimedia UK) gave me a 'Schools Wikipedia' CD which I gratefully accepted along with a Wikimedia UK coffee mug, which I use for my early morning mug (thank you Jon!).
I didn't look at the disc until today, fearing what horrors there might be, but actually it is quite good. It has clearly been edited to remove the worst of the grammatical abominations. The pictures are a more sensible size so there is none of that ugly white space, and, best of all, no footnotes except where necessary. The links to the very worst article have been removed.
Yet there is one more thing of great significance. When I checked the Age of Enlightenment article, it was much better than the version of the article I criticised here. For example, I criticised the current article (permalink) as stating that the Age of Enlightenment was a movement when, as its name suggests, it is a period. The schools article, by contrast, correctly states that it is a period after all.
Sigh of relief that the corruption of our schoolchildren is not imminent, at least in this case. But why the difference? Had the mistakes been edited out by professionals? Well, probably not. A bit of research shows that the school version dates from around October 2005. Which bears out what I have always said. A lot of reasonably good people were contributing to Wikipedia around that time, then left after a wave of vandalism and trolling hit the project in 2006. The vandalism was like 'drinking water from a firehose'. This was countered by a massive increase in the number of vandal fighters, but at the same time and by that very token the project was turning from building into an encyclopedia, which requires certain skills, to protecting against vandals, as well as running a secret intelligence force that would have made Stalin proud, and this requires different skills.
Very significant that the quality of Wikipedia has got demonstrably worse over 2005-12.
I didn't look at the disc until today, fearing what horrors there might be, but actually it is quite good. It has clearly been edited to remove the worst of the grammatical abominations. The pictures are a more sensible size so there is none of that ugly white space, and, best of all, no footnotes except where necessary. The links to the very worst article have been removed.
Yet there is one more thing of great significance. When I checked the Age of Enlightenment article, it was much better than the version of the article I criticised here. For example, I criticised the current article (permalink) as stating that the Age of Enlightenment was a movement when, as its name suggests, it is a period. The schools article, by contrast, correctly states that it is a period after all.
Sigh of relief that the corruption of our schoolchildren is not imminent, at least in this case. But why the difference? Had the mistakes been edited out by professionals? Well, probably not. A bit of research shows that the school version dates from around October 2005. Which bears out what I have always said. A lot of reasonably good people were contributing to Wikipedia around that time, then left after a wave of vandalism and trolling hit the project in 2006. The vandalism was like 'drinking water from a firehose'. This was countered by a massive increase in the number of vandal fighters, but at the same time and by that very token the project was turning from building into an encyclopedia, which requires certain skills, to protecting against vandals, as well as running a secret intelligence force that would have made Stalin proud, and this requires different skills.
Very significant that the quality of Wikipedia has got demonstrably worse over 2005-12.
Friday, May 25, 2012
Concept and Object
Here I mentioned Frege's distinction between concept and object, and Anthony is rightly asking questions about it. How does direct reference relate to the distinction?
So I go back to Frege, and his famous essay. It's rather hard to get anything out of it, because he never properly defines the distinction. He says that his explanation is not meant as a proper definition. "One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance". What is logically simple cannot have a proper definition (as Aristotle also noticed).
But he does give the famous example of "all mammals are land dwellers", which will do for my purpose. He says that if 'all mammals' were the logical subject of 'are land dwellers', then to negate the whole sentence we should have to negate the predicate, giving "all mammals are not land-dwellers". That is obviously wrong, for this predicate negation gives the contrary of the sentence it negates, not the contradictory. Thus we must put the 'not' in front of the 'all', to give sentence negation. But no such distinction applies to genuinely singular subjects, i.e. object words. Indeed, he proves this by re-writing the original sentence as "the concept mammal is subordinate to the concept land-dweller". By negating the predicate we get "the concept mammal is not subordinate to the concept land-dweller", which is the contradictory of the original sentence. And so a useful criterion for determining whether an expression is a concept expression (a logical predicate) or an object expression (a logical subject) is to determine whether predicate negation is equivalent to sentence negation or not. If it is, then the grammatical subject is a logical subject as well. Otherwise it is a logical predicate.
With that test in mind, and on the assumption that proper names are logical subjects, direct reference immediately follows, as I shall show tomorrow.
So I go back to Frege, and his famous essay. It's rather hard to get anything out of it, because he never properly defines the distinction. He says that his explanation is not meant as a proper definition. "One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance". What is logically simple cannot have a proper definition (as Aristotle also noticed).
But he does give the famous example of "all mammals are land dwellers", which will do for my purpose. He says that if 'all mammals' were the logical subject of 'are land dwellers', then to negate the whole sentence we should have to negate the predicate, giving "all mammals are not land-dwellers". That is obviously wrong, for this predicate negation gives the contrary of the sentence it negates, not the contradictory. Thus we must put the 'not' in front of the 'all', to give sentence negation. But no such distinction applies to genuinely singular subjects, i.e. object words. Indeed, he proves this by re-writing the original sentence as "the concept mammal is subordinate to the concept land-dweller". By negating the predicate we get "the concept mammal is not subordinate to the concept land-dweller", which is the contradictory of the original sentence. And so a useful criterion for determining whether an expression is a concept expression (a logical predicate) or an object expression (a logical subject) is to determine whether predicate negation is equivalent to sentence negation or not. If it is, then the grammatical subject is a logical subject as well. Otherwise it is a logical predicate.
With that test in mind, and on the assumption that proper names are logical subjects, direct reference immediately follows, as I shall show tomorrow.
Thursday, May 24, 2012
Sinn und Bedeutung
Frege famously classified the semantic function of a proper name into sense (Sinn) and reference (Bedeutung). But this conceals a difficulty. The sense of a proper name is clearly part of its meaning, and Frege even says this in a letter to Bertrand Russell written in November 1904. My father would have been alive then, although only eight months old. Frege writes
And if Mont Blanc itself isn't part of the meaning of its name, there is a further difficulty for Frege's theory that I commented on yesterday. If the name retains its sense after the Bedeutung, the referent, is destroyed, then we must suppose the sense of a name is something permanent to which its referent bears an impermanent and external relation. Let's say the sense is 'satisfied' when the referent exists. So, the sense of 'Mont Blanc' was not satisfied before the enormous geological upheaval created its referent, but is satisfied now, although it would once again not be satisfied if Mont Blanc exploded into nothingness. The difficulty is that his theory depends on the concept-object distinction. According to that distinction, concept words or predicates are fundamentally different from object words or singular terms, in that concept words are sensitive to the scope of negation, whereas singular terms are not. Take 'a man is not running' and 'it is not the case that a man is running'. The predicate negation is true when there is at least one man, and he is not running. The sentential negation is true only when no man runs. But there is no such distinction with singular propositions, at least as the object-concept distinction requires it. 'Socrates is not running' and 'It is not the case that Socrates is running' is true only when Socrates exists, and he is not running. There appears to be no room for the possibility of Socrates not existing. Yet if the meaning of a proper name is its sense, and if the sense exists even when the referent does not, 'Socrates is running' is false when Socrates does not exist, yet 'Socrates is not running' is false as well.
Russell replied, a month later in the days before email, that Mont Blanc really is a part of what is asserted by 'Mont Blanc is more than 4,000 metres high'. I think he changed his mind shortly later, but then Russell often changed his mind (which is a good thing).
As I noted in the page linked above, I could not then find where Russell was writing from. He moved there in 1904 in order to work out a theory of denoting that could be used in Principia Mathematica, but which would avoid the Paradox (now known as Russell's paradox) that he had discovered while working on the Principles of Mathematics. He took his first wife Alys there, but this was a disastrous part of a disastrous marriage, and he was probably not very happy there. Nor actually was she, as Russell seems to have been a beast towards her. Thanks to Google maps I think I have located the place. It certainly is secluded, a short distance from Lower Frensham pond in a fairly exclusive part of the Surrey stockbroker belt. I don't like Surrey. Mostly places like that. Small roads in the English countryside, looking as they might have looked two hundred years ago, then suddenly there appears a large, usually Edwardian mansion at the end of a long gated drive. Inside, they still drink gin and tonic. But nothing wrong with that, I suppose.
Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4,000 metres high ... The sense of the word 'Moon' is a component part of the thought that the moon is smaller than the earth. The moon itself (i.e. the Bedeutung of the word 'Moon' is not part of the sense of the word 'Moon'; for then it would also be a component part of a thought. We can nevertheless say: 'The Moon is idential with the heavenly body closest to the earth'. What is identical, however, is not a component part but the Bedeutung of the expression 'the Moon' and 'the heavenly body closest to the earth'. We can say that 3+4 is identical with 8-1; i.e. that the Bedeutung of '3+4' coincides with the Bedeutung of '8-1'. But this Bedeutung, namely the number 7, is not a component part of the sense of '3+4'. The identity is not an identity of sense, nor of part of the sense, but of Bedeutung ...But if so, in what sense is the 'Bedeutung' a meaning at all? Bedeuten: the German for 'mean' or 'signify'. Frege is clearly disturbed by the idea that Mont Blanc, with its massive snowfields, could be part of a thought. But if it isn't, how could it still be part of the meaning? If Mont Blanc is destroyed in an enormous eruption (here Frege's other analogy to Etna would have been more appropriate), does the meaning of 'Mont Blanc', or some part of it, remain?
And if Mont Blanc itself isn't part of the meaning of its name, there is a further difficulty for Frege's theory that I commented on yesterday. If the name retains its sense after the Bedeutung, the referent, is destroyed, then we must suppose the sense of a name is something permanent to which its referent bears an impermanent and external relation. Let's say the sense is 'satisfied' when the referent exists. So, the sense of 'Mont Blanc' was not satisfied before the enormous geological upheaval created its referent, but is satisfied now, although it would once again not be satisfied if Mont Blanc exploded into nothingness. The difficulty is that his theory depends on the concept-object distinction. According to that distinction, concept words or predicates are fundamentally different from object words or singular terms, in that concept words are sensitive to the scope of negation, whereas singular terms are not. Take 'a man is not running' and 'it is not the case that a man is running'. The predicate negation is true when there is at least one man, and he is not running. The sentential negation is true only when no man runs. But there is no such distinction with singular propositions, at least as the object-concept distinction requires it. 'Socrates is not running' and 'It is not the case that Socrates is running' is true only when Socrates exists, and he is not running. There appears to be no room for the possibility of Socrates not existing. Yet if the meaning of a proper name is its sense, and if the sense exists even when the referent does not, 'Socrates is running' is false when Socrates does not exist, yet 'Socrates is not running' is false as well.
Russell replied, a month later in the days before email, that Mont Blanc really is a part of what is asserted by 'Mont Blanc is more than 4,000 metres high'. I think he changed his mind shortly later, but then Russell often changed his mind (which is a good thing).
As I noted in the page linked above, I could not then find where Russell was writing from. He moved there in 1904 in order to work out a theory of denoting that could be used in Principia Mathematica, but which would avoid the Paradox (now known as Russell's paradox) that he had discovered while working on the Principles of Mathematics. He took his first wife Alys there, but this was a disastrous part of a disastrous marriage, and he was probably not very happy there. Nor actually was she, as Russell seems to have been a beast towards her. Thanks to Google maps I think I have located the place. It certainly is secluded, a short distance from Lower Frensham pond in a fairly exclusive part of the Surrey stockbroker belt. I don't like Surrey. Mostly places like that. Small roads in the English countryside, looking as they might have looked two hundred years ago, then suddenly there appears a large, usually Edwardian mansion at the end of a long gated drive. Inside, they still drink gin and tonic. But nothing wrong with that, I suppose.
Wednesday, May 23, 2012
The argument from circularity and singular existential statements
After reading some of Maverick’s other posts on the subject, and reading some material he sent me, it is clear I have misrepresented his argument. Although I am still some way from understanding it, I think it is this.
Suppose there is only one American philosopher, and suppose that it is Vallicella. Then the sentence ‘an American philosopher exists’ is true because Vallicella (qua American philosopher) exists. Now we can translate ‘an American philosopher exists’ into ‘some philosopher is American’, which reduces the verb ‘exists’ to the copula ‘is’. But we can’t translate ‘Vallicella exists’ in the same way. Thus general existential statements presuppose the truth of singular existential statements (or a disjunction or conjunction of singular existential statements). But we cannot analyse away ‘exists’ from singular existential statements. Therefore there is circularity: the same word appears on the right and left hand side of the definition. An American philosopher exists if and only if Vallicella exists.
But there is an obvious route out of this problem. What actually makes ‘some philosopher is American’ true is ‘Vallicella is an American philosopher’, which does not use the word ‘exist’. Vallicella may object that ‘Vallicella exists’ has to be true for that to work. Certainly, but we can reply in two ways. We could suppose that empty proper names are meaningless, and that ‘Vallicella’ is only meaningful because it names something. I.e. if it names something, it must name an existing something. ‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’. Or we could allow that empty proper names are meaningful, and that they have a sense but not a reference. Then we can appeal to the idea of instantiation, as with general concepts. ‘Vallicella exists’ means that the sense of ‘Vallicella’ has a referent or instance. ‘An American philosopher exists’ means that the sense of ‘American philosopher’ has an instance.
That is, either common names and proper names fall into different logical categories, in which case we don’t need to use the word ‘exists’ in singular sentences at all. Or they fall into the same category, in which case we can analyse singular existential statements exactly as we analyse general existential statements. In neither case is the definition of ‘exists’ circular.
Suppose there is only one American philosopher, and suppose that it is Vallicella. Then the sentence ‘an American philosopher exists’ is true because Vallicella (qua American philosopher) exists. Now we can translate ‘an American philosopher exists’ into ‘some philosopher is American’, which reduces the verb ‘exists’ to the copula ‘is’. But we can’t translate ‘Vallicella exists’ in the same way. Thus general existential statements presuppose the truth of singular existential statements (or a disjunction or conjunction of singular existential statements). But we cannot analyse away ‘exists’ from singular existential statements. Therefore there is circularity: the same word appears on the right and left hand side of the definition. An American philosopher exists if and only if Vallicella exists.
But there is an obvious route out of this problem. What actually makes ‘some philosopher is American’ true is ‘Vallicella is an American philosopher’, which does not use the word ‘exist’. Vallicella may object that ‘Vallicella exists’ has to be true for that to work. Certainly, but we can reply in two ways. We could suppose that empty proper names are meaningless, and that ‘Vallicella’ is only meaningful because it names something. I.e. if it names something, it must name an existing something. ‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’. Or we could allow that empty proper names are meaningful, and that they have a sense but not a reference. Then we can appeal to the idea of instantiation, as with general concepts. ‘Vallicella exists’ means that the sense of ‘Vallicella’ has a referent or instance. ‘An American philosopher exists’ means that the sense of ‘American philosopher’ has an instance.
That is, either common names and proper names fall into different logical categories, in which case we don’t need to use the word ‘exists’ in singular sentences at all. Or they fall into the same category, in which case we can analyse singular existential statements exactly as we analyse general existential statements. In neither case is the definition of ‘exists’ circular.
Monday, May 21, 2012
Supposition theory
I have expanded the Logic Museum page on 'supposition' to include more about the various divisions of the subject, plus something on 'simple' supposition. I need to write something about 'personal' supposition to complete it, and notice the red link on 'reference'. Reference is a modern notion, no less vague than supposition, and needs careful treatment.
Sunday, May 20, 2012
Another version of the circularity argument
Jason has questioned which argument of Bill's I am talking about. I did link to one version of the argument (I have been involved with many over the years). But I found another one here, slightly longer. Bill says:
One might as well argue that this meat being lamb cannot boil down to this being mutton, for it is lamb because it is mutton. Therefore the definition 'mutton is lamb' is circular. But that argument is blatantly bad.
Now either x exists or it does not.I follow the first leg of the argument. If there are non-existent objects, then existence obviously cannot boil down to instantiation. That is very clear. It is the second leg which makes no sense. The argument seems to be that some philosopher is blogging, only because a blogging philosopher exists. Therefore the existence of a blogging philosopher cannot boil down to some philosopher being a blogger.
Suppose it does not. Then we have instantiation without existence. If so, then existence cannot be instantiation. For example, let C be the concept winged horse and let x be Pegasus. The latter instantiates the former since Pegasus is a winged horse. But Pegasus does not exist. So existence cannot be the second-level property of instantiation if we allow nonexistent objects to serve as instances of concepts.
Now suppose that x exists. Then the theory is circular: it presupposes and does not eliminate first-level existence. The concept blogging philosopher is instantiated by me, but only because I possess first-level existence. One cannot coherently maintain that my existence consists in my instantiating that concept or any concept for the simple reason that (first-level) existence is what makes it possible for me to instantiate any concept in the first place.
One might as well argue that this meat being lamb cannot boil down to this being mutton, for it is lamb because it is mutton. Therefore the definition 'mutton is lamb' is circular. But that argument is blatantly bad.
Existence and the enlargement principle
In my earlier post I argued that the 'thin conception' of existence does not involve any obvious circularity. We define the verb 'exists' in terms of the following equivalence
"An American philosopher exists" is(def) equivalent to "some philosopher is American"
The verb 'exists' only appears on the left hand side of the definition, and so the definition is not circular, by the definition of circularity. To the objection that the right hand side has an elided adjective 'existing', i.e. that the definition should really be
"An American philosopher exists" is(def) equivalent to "some existing philosopher is American"
I appealed to what I will call the 'enlargement principle'. This is the principle that any adjective or qualifying term must, if it is to be meaningful, enlarge the conception signified by the term that it contracts. Thus 'blue' enlarges the concept signified by 'buttercup' when we attach the terms to form the composite 'blue buttercup'. Thus it is meaningful. But 'existing' does not enlarge the concept signified by 'American philosopher', for the sentence 'some philosopher is American' already states that an American philosopher is existing.
Against. Consider the concept signified by 'character in War and Peace'. There are hundreds of such characters. Some of these, such as Napoleon and the Czar of Russia, and the Russian general whose name I have forgotten, are or were historical characters. So they are existent in some sense (i.e. they used to exist, or exist in the afterlife). Others, such as Prince Bolkonsky or Natasha, never existed at all. So the contracting term 'existing' or 'historical' does enlarge the conception signified by the term it is attached to. And it does diminish the extension of the contracted term. The total number of characters in the book is large, but decreases significantly when we consider only the real historical ones. Thus the term 'existing' or 'historical' or 'real' is meaningful, and a real predicate. Thus the thin conception of existence does involve circularity.
"An American philosopher exists" is(def) equivalent to "some philosopher is American"
The verb 'exists' only appears on the left hand side of the definition, and so the definition is not circular, by the definition of circularity. To the objection that the right hand side has an elided adjective 'existing', i.e. that the definition should really be
"An American philosopher exists" is(def) equivalent to "some existing philosopher is American"
I appealed to what I will call the 'enlargement principle'. This is the principle that any adjective or qualifying term must, if it is to be meaningful, enlarge the conception signified by the term that it contracts. Thus 'blue' enlarges the concept signified by 'buttercup' when we attach the terms to form the composite 'blue buttercup'. Thus it is meaningful. But 'existing' does not enlarge the concept signified by 'American philosopher', for the sentence 'some philosopher is American' already states that an American philosopher is existing.
Against. Consider the concept signified by 'character in War and Peace'. There are hundreds of such characters. Some of these, such as Napoleon and the Czar of Russia, and the Russian general whose name I have forgotten, are or were historical characters. So they are existent in some sense (i.e. they used to exist, or exist in the afterlife). Others, such as Prince Bolkonsky or Natasha, never existed at all. So the contracting term 'existing' or 'historical' does enlarge the conception signified by the term it is attached to. And it does diminish the extension of the contracted term. The total number of characters in the book is large, but decreases significantly when we consider only the real historical ones. Thus the term 'existing' or 'historical' or 'real' is meaningful, and a real predicate. Thus the thin conception of existence does involve circularity.
Saturday, May 19, 2012
A brief history of existence
Yesterday’s post caught a few people by surprise. What is the background to all that? What is the ‘thin’ conception of being? Etc. Of course there is a background to this, and it is large, and it should be part of the baggage of anyone studying modern analytic philosophy. So here is a brief history of the subject.
We start in the fourth century B.C. with Aristotle and his Perihermenias, his treatise on the second operation of the understanding, where two simple concepts are combined to form a proposition. In the tenth chapter he has an obscure paragraph about the verb ‘is’ being predicated as a ‘third elements’. In the scholastic Latin which was used to translate Aristotle’s Greek, this is rendered as tertium adiecens, literally third adjoinment or third adjective. What on earth does that mean? Thomas (in the middle of the thirteenth century) makes a valiant attempt to explain it in his commentary on the work. He says that sometimes the verb ‘is’ is predicated by itself in a proposition, such as in “Socrates is“ i.e. Socrates exists. By this we signify that Socrates really exists. That is predication of ‘is’ as a second element, i.e. existence predicated of itself, existence as a predicate. At other times it is not the main predicate but is joined to the main predicate to connect it to the subject, as in “Socrates is white.” Here we are not asserting that Socrates exists, but rather attributing whiteness to him by the verb ‘is’. Hence, ‘is’ said to be a third element, not because it is a third predicate, but because it is a third element or word in the proposition.
Roll forward to the eleventh century and to Anselm and his so-called ontological argument. This was an argument to prove the existence of God through logic alone, by proving that the concept of God has the concept of existence built into it. He argues as follows
The whole issue was extensively discussed in the late thirteenth century, but this is rarely if ever mentioned in modern philosophy courses because of the assumption that all philosophy began in the early modern era as a byproduct of the glorious enlightenment process. Thus students tend to hear about the ontological argument in the context of Descartes, rather than Anselm or thirteenth century philosophers. Descartes writes in his Meditation V:
Roll forward again to Kant, the glorious eighteenth century philosopher of the high enlightenment, who famously tells us (in The Critique of Pure Reason, A 598/B626) that existence is not a ‘real predicate’. This was a period when all good philosophers wrote in German (Sein* ist offenbar kein reales Praedikat). 'Existence' is not a determining predicate which enlarges the concept of the subject to which it is added, in the way that ‘white’ enlarges the concept ‘man’ by increasing its intension but reducing its extension. When philosophers talk about existence not being a predicate, it is usually Kant’s discussion they have in mind. (Maverick has strong views about this, but I’ll pass over those for now).
Kant had little influence on modern logic, however. The main development of the question whether ‘existence is a predicate’ comes in the middle of the nineteenth century. I have a bit about the history in a discussion of Brentano here, and see also this contemporary paper here. Brentano argued that we can always translate any sentence containing the verb ‘exists’ into one that does not contain it. Thus ‘a sick man exists’ translates to ‘some man is sick’. This idea is the direct ancestor of the modern view, often associates with Quine, that existence is what the existential quantifier expresses. It is uncertain how it got into modern predicate logic, as there are at least three contenders, namely Brentano, Frege and the American Charles Peirce. Probably it was Peirce via the German logician Ernst Schroeder. I wrote a short piece on this for Wikipedia years ago, which is still there (permalink).
So the issue of detail is whether the verb ‘is’ is simply a copula that joins subject to predicate. This is essentially the view embedded into modern predicate calculus and the use of ‘existential’ quantifier. The general and important position that it underlies is whether we can prove the existence of God, or not. If existence is merely ‘someness’, i.e. if ‘existing thing’ is equivalent to ‘something’, the ontological argument does not get off the ground. But if it is something larger or ‘thicker’, the argument at least stands a chance. Thus large things sometimes hang on small things.
One day I should write this history up properly. Every discussion I see has some part of the history, without taking a view of the whole.
*I literally just noticed that Kant is using the German 'sein', which is the infinitive of the German verb 'to be'. English philosophy tends to follow Latin philosophy in using the distinct verbs 'to be' (esse) and 'to exist' (existere). That distinction is a subject in its own right, which I will pass over for now.
We start in the fourth century B.C. with Aristotle and his Perihermenias, his treatise on the second operation of the understanding, where two simple concepts are combined to form a proposition. In the tenth chapter he has an obscure paragraph about the verb ‘is’ being predicated as a ‘third elements’. In the scholastic Latin which was used to translate Aristotle’s Greek, this is rendered as tertium adiecens, literally third adjoinment or third adjective. What on earth does that mean? Thomas (in the middle of the thirteenth century) makes a valiant attempt to explain it in his commentary on the work. He says that sometimes the verb ‘is’ is predicated by itself in a proposition, such as in “Socrates is“ i.e. Socrates exists. By this we signify that Socrates really exists. That is predication of ‘is’ as a second element, i.e. existence predicated of itself, existence as a predicate. At other times it is not the main predicate but is joined to the main predicate to connect it to the subject, as in “Socrates is white.” Here we are not asserting that Socrates exists, but rather attributing whiteness to him by the verb ‘is’. Hence, ‘is’ said to be a third element, not because it is a third predicate, but because it is a third element or word in the proposition.
Roll forward to the eleventh century and to Anselm and his so-called ontological argument. This was an argument to prove the existence of God through logic alone, by proving that the concept of God has the concept of existence built into it. He argues as follows
… it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist;. and this being thou art, O Lord, our God. (Proslogion chapter 3).I won’t go into the tortuous logical details of the argument now, but the argument is generally thought to be invalid, and the reason is generally thought to be treating the verb ‘is’ as a predicate, i.e. as the main predicate in the sentence, rather than as a copula or ‘third element’ which simply joins the real predicate (being wise or being good) to the subject.
The whole issue was extensively discussed in the late thirteenth century, but this is rarely if ever mentioned in modern philosophy courses because of the assumption that all philosophy began in the early modern era as a byproduct of the glorious enlightenment process. Thus students tend to hear about the ontological argument in the context of Descartes, rather than Anselm or thirteenth century philosophers. Descartes writes in his Meditation V:
… the existence can no more be separated from the essence of God, than the idea of a mountain from that of a valley, or the equality of its three angles to two right angles, from the essence of a [rectilinear] triangle; so that it is not less impossible to conceive a God, that is, a being supremely perfect, to whom existence is awanting, or who is devoid of a certain perfection, than to conceive a mountain without a valley.Note that Descartes was writing in Latin, another fact that is sometimes overlooked. This is because we associate the enlightenment process with the modern romance languages rather than Latin, which belongs to the dark ages before the early enlightenment.
Roll forward again to Kant, the glorious eighteenth century philosopher of the high enlightenment, who famously tells us (in The Critique of Pure Reason, A 598/B626) that existence is not a ‘real predicate’. This was a period when all good philosophers wrote in German (Sein* ist offenbar kein reales Praedikat). 'Existence' is not a determining predicate which enlarges the concept of the subject to which it is added, in the way that ‘white’ enlarges the concept ‘man’ by increasing its intension but reducing its extension. When philosophers talk about existence not being a predicate, it is usually Kant’s discussion they have in mind. (Maverick has strong views about this, but I’ll pass over those for now).
Kant had little influence on modern logic, however. The main development of the question whether ‘existence is a predicate’ comes in the middle of the nineteenth century. I have a bit about the history in a discussion of Brentano here, and see also this contemporary paper here. Brentano argued that we can always translate any sentence containing the verb ‘exists’ into one that does not contain it. Thus ‘a sick man exists’ translates to ‘some man is sick’. This idea is the direct ancestor of the modern view, often associates with Quine, that existence is what the existential quantifier expresses. It is uncertain how it got into modern predicate logic, as there are at least three contenders, namely Brentano, Frege and the American Charles Peirce. Probably it was Peirce via the German logician Ernst Schroeder. I wrote a short piece on this for Wikipedia years ago, which is still there (permalink).
So the issue of detail is whether the verb ‘is’ is simply a copula that joins subject to predicate. This is essentially the view embedded into modern predicate calculus and the use of ‘existential’ quantifier. The general and important position that it underlies is whether we can prove the existence of God, or not. If existence is merely ‘someness’, i.e. if ‘existing thing’ is equivalent to ‘something’, the ontological argument does not get off the ground. But if it is something larger or ‘thicker’, the argument at least stands a chance. Thus large things sometimes hang on small things.
One day I should write this history up properly. Every discussion I see has some part of the history, without taking a view of the whole.
*I literally just noticed that Kant is using the German 'sein', which is the infinitive of the German verb 'to be'. English philosophy tends to follow Latin philosophy in using the distinct verbs 'to be' (esse) and 'to exist' (existere). That distinction is a subject in its own right, which I will pass over for now.
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.
Thursday, May 17, 2012
A thought is a proposition with sense
Der Gedanke ist der sinnvolle Satz. Someone made a video of this, and I felt so sorry for it (only 43 views) I felt compelled to link to it.
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