*Thanks to Eric Barbour for this titbit.
Thursday, March 31, 2011
Longest article in Wikipedia
Tuesday, March 29, 2011
Meinongians who aren’t Meinongians
Peter van Inwagen is an example of the first kind of Meinongian, but not the second. He argues* (p. 237 ff) that the correct way, and the only way, to understand the use of variables and quantifiers is to show how they can be translated into expressions of ordinary English that we already understand. He gives a few examples to show how it is clear that the formal predicate calculus is simply a regimentation of the ‘all’ and ‘there are’ of ordinary English. He concludes (p.239) “The existental quantifier therefore expresses the sense of ‘there is’ in ordinary English. (As an opponent of any form of Meinongianism, I would say that the existential quantifier is appopriately named – for the reason that, in expressing the sense of ‘there is’ in English, it thereby expresses the sense of ‘exists’ in English).” To the objection (p.242) that this account of the meaning of a sentence containing quantifiers does not tell us the conditions under which it would be true, he neatly replies that “the conditions under which a sentence would be true, are not the first thing about the meaning of a sentence. The first thing about the meaning of a sentence is what the sentence means” – which is just what his account tells us about sentences containing quantifiers, he says.
This has an important consequence for fictional discourse (meaning not the discourse you find in works of fiction, but rather what is spoken or written about works of fiction, such as found in literary criticism). Such discourse can potentially include complex quantification. Inwagen’s example is
(1) There is a fictional character who, for every novel, either appears in that novel or is a model for a character who does.
This involves apparent existential quantification and a complex quantificational structure, as well as the ability to generate all the inferences licensed by quantifier logic. For example, we can deduce
(2) If no character appears in every novel, then some character is modelled on another character.
If the quantification is real, and given Inwagen’s rejection of the second kind of Meinongianism (i.e. the kind that accepts existential quantification but not existential commitment) then we must accept the reality, indeed the real existence, of fictional characters. If the quantification is not real, we must explain (p.244) how to paraphrase the two sentences above, show whether the second sentence follows from the first, and if not, why it does not. In summary:
*The existential quantifier expresses the sense of ‘there is’ and ‘there exists’ in English.
* ‘For some x, x is a fictional character’ is true.
* There are fictional characters, i.e. fictional characters exist.
Thus Inwagen is a Meinongian in the first sense. He affirms the reality of fictional characters in the most direct way, claiming that they exist. But he is not a Meinongian in the second sense. For he upholds the Brentano thesis - ‘For some x, x is a fictional character’ = ‘There are fictional characters’ = ‘Fictional characters exist’.
Van Inwagen recognises he must explain the apparent truth of sentences like ‘Sherlock Holmes does not exist’. I will discuss his explanation tomorrow.
* "Quantification in fictional discourse", in Empty Names, Fiction and the Puzzles of Non-existence, Stanford 2000, pp. 235-247.
Sunday, March 27, 2011
Quinean and non-Quinean quantification
(a) Something is eating my cheese, probably a mouse.
the occurrence of the quantifier 'something' is Quinean. Clearly 'something which exists' is intended. By contrast, the occurrence of the same quantifier in
(b) Something is keeping me awake at night, namely the monster I dream about.
is non-Quinean. Monsters don't exist, so nothing which exists is keeping me awake at night. Therefore modifying 'something' with 'which exists' would change the truth conditions of the second sentence, therefore the occurrence of the quantifier is non-Quinean.
This is pretty close to the thesis of Peter Lupu's that I was moaning about earlier. The idea is that we can explain the consistency of the conjunction 'Tom is thinking of a mermaid, but nothing is a mermaid' by interpreting the 'nothing' as a Quinean quantifier. That is, the conjunction really means Tom is thinking of a mermaid, but nothing which exists is a mermaid. However, the 'something' in the claim 'there is something Tom is thinking of' is non-Quinean, since it is false that there is something which exists which Tom is thinking of.
I have given enough objections to this sort of thing for now. Enough to say that it can be true that Tom is thinking of a mermaid even if absolutely nothing whatever is a mermaid, i.e. where non-Quinean quantification for 'absolutely nothing' is intended. I have another fundamental objection to this idea, namely the use that Meinongians put it to.
Even if we buy the distinction between Quinean and non-Quinean quantifiers, a further problem is the way Meinongians persistently make inferences from contexts that involve non-Quinean quantification, to contexts that unambiguously require Quinean quantification. I already gave an example here of a move such as this:
Tom is thinking of something, therefore Tom's thinking is directed towards something.
This is illegitimate because (in my terminology) 'is thinking of' is a logically intransitive verb, whereas 'is directed towards' is logically transitive. In Hofweber-speak, even if the first 'something' is non-Quinean, the second is unambiguously Quinean. Nothing can be 'directed towards' something unless it is something which exists. The Meinongian makes these illegitimate moves all the time. Example: he argues (p. 255, my emphasis) that Quinean quantifiers are restricted to things that exist, and so
since non-Quinean quantifiers don't have such a restriction this shows that the domain of quantification really is what the non-Quinean quantifiers range over. Quinean quantifiers range over a subdomain of this domain, namely over all or some of the things in the domain that exist. Thus the true domain of discourse contains non-existent objects ...Note the verb 'contains'. This verb is unambiguously logically transitive, i.e. 'a contains an F' is always inconsistent with 'nothing is an F'. Thus the quantifier 'an F', as it occurs as the accusative of 'contains', is Quinean. Even if we buy the distinction between Quinean and non-Quinean, the quantifier 'everything' in 'everything that the true domain of discourse contains' is Quinean. Thus everything the Meinongian wants to talk about, he cannot talk about. Therefore he should remain silent. Another example of language on holiday tomorrow.
* "Quantification and non-existent objects", in *Empty Names, Fiction and the Puzzles of Non-existence*, Stanford 2000, pp 249-273.
Nothing fails to exist
(*) Tolkien tells us which hobbit carried the ring to Mordor, but nothing (at least, nothing real or existing) is a hobbit,where the bracketed qualification opens the door to something unreal or non-existing being a hobbit. This reminds me of something that Thomas Hofweber says, which I will discuss tomorrow.
Saturday, March 26, 2011
An interesting net
Imagination of a mermaid is not consciousness of a mental image or other contentHere is the argument expressed in numbered statements. I have added some additional premisses and logical steps
of consciousness but precisely consciousness of a mermaid. Consciousness of a
mermaid is just as outer-directed and revelatory of a material item as
consciousness of a dolphin. But mermaids do not exist. Therefore, some objects
do not exist.
1. (A) Tom is conscious of a mermaid
2. (A) Consciousness of a mermaid is just as outer-directed and revelatory of a material item as consciousness of a dolphin.
3. (interpreting 2) If Tom is conscious of a mermaid then Tom is conscious of some object which is a mermaid.
4. (from 1, 3) Tom is conscious of some object which is a mermaid.
5. (A) 'Is conscious of' is a logically transitive verb.
6. (from 4, 5) some object is a mermaid.
7. (A) Mermaids do not exist.
8. (from 6, 7) Therefore, some objects do not exist.
The questionable assumption is (5). I argued earlier that a 'logically transitive verb' Ø is such that the truth of 'a Ø's an F' is inconsistent with the truth of 'nothing is an F', and so implies 'something is an F'. Bill needs to justify the assumption that 'is conscious of' is logically transitive. This is questionable. 'Bill is conscious of a mermaid' is clearly consistent with 'nothing is a mermaid'.
"A clever man got caught in this net of language! So it must be an interesting net. "
Friday, March 25, 2011
Historical names and the Jesus Myth
You will make the natural and reasonable objection that such story-relative reference is a word-word relation. Story-reference is intra-linguistic: it is a semantic relation between different names of the same type within the same narrative. This may be acceptable as an account of fictional semantics, but as an account of history, where there is reference to real people, it is inadequate. Genuine reference is word-world: a relation between language and the world outside the mind.
I reply by asking: what difference does the truth of the narrative make to the semantics of the proper name? The semantics of the following brief history* are no different from a story.
Jesus Christ was born in Israel 2000 years ago. Jesus lived a traditionalThe story is considered to be more or less factual by most historians, yet some have questioned whether Jesus existed at all. If the semantics of non-fictional names were fundamentally different from the semantics of fictional ones, the ‘Jesus Myth’ problem would have been resolved. We could simply work out from the meaning of the name ‘Jesus’ whether there really was such a person. But we cannot, therefore the semantics of non-fictional names are not fundamentally different from the semantics of fictional ones.
Jewish life until his twenties. Then Jesus began his public teaching and display
of recorded miracles, although he never travelled more than 200 miles from his
birthplace. Over a three year period, Jesus' reputation spread nation
wide. Jesus' most controversial act was that he repeatedly claimed to be
God. Because of this, the religious leaders asked the Roman government to
execute Jesus. Jesus was crucified and died, although (according to many
witnesses) Jesus returned from the dead three days later.
Therefore the names of historical characters individuate in just the same way as fictional ones. The meaning of the proper name is simply to tell us which individual – whether in a story or in the historical narrative – is the subject of the proposition, and it can tell us this without there being any such indidividual. A story can tell us which F is G, without anything actually being an F.
* Adapted from here
Wednesday, March 23, 2011
More fiction turns to fact
You chose the wrong example. "In the 12th century, Sharaf al-Din al-Tusi foundWilliam points out that the source for this disputed statement - the Encyclopedia of Ancient Egypt which at first sight looks as reliable as you could get – had itself used Wikipedia as a source. He goes on to say that “the source is therefore clearly worthless as a citation to support statements made in Wikipedia”. Yes, although I question his ‘clearly’: it may have been obvious in this case, but as more secondary sources use Wikipedia as a primary source, the problem will continue, and will be increasingly difficult to spot.
algebraic and numerical solutions to cubic equations and was the first to
discover the derivative of cubic polynomials." is in the Encyclopedia
of Ancient Egypt at Google Books, and it took me just 0 seconds to found it
out. Please DO NOT DELETE contents because of your POV. Please, use inline
templates instead. Cheers. –pjoef 20:10, 18 March 2011 (UTC)
Tuesday, March 22, 2011
The ‘case for the prosecution’ cites another example of this style of editing. The article “List of inventions in medieval Islam” contains the following assertion:
Central heating through underfloor pipes: The hypocaust heating system used byThe claim is cited, but the cited author Hugh N. Kennedy however writes something rather different:
the Romans continued to be in use around the Mediterranean region during late
Antiquity and by the Umayyad caliphate. By the 12th century, Muslim engineers in
Syria introduced an improved central heating system, where heat travelled
through underfloor pipes from the furnace room, rather than through a hypocaust.
This central heating system was widely used in bath-houses throughout the
medieval Islamic world.
In one respect, however, the early Islamic bath had more in common with theOne of the arbitrators expressed surprise at the request, having been under the mistaken impression that Jagged 85 had been banned. “Who could have known that someone could get away with such behaviour on Wikipedia with only a single 24 hr edit-warring block”, he says. Yet there seems little chance that the committee will do something about the problem. Its terms of reference do not include ‘content dispute’. And there seem as many friends and supporters of the disputed editor as there are people who are concerned about the situation. On Wikipedia, which sources material from the crowd, anyone’s view counts the same as any other. Wikipedia: the encyclopedia that anyone with an agenda can edit.
classical one than with the later Islamic. Late antique and Umayyad bath
builders continued to use the hypocaust, though on a reduced scale, for
heating the hot chamber, whereas later Muslim baths used a simpler
system of underfloor pipes from the furnace room.
Saturday, March 19, 2011
The snows have scattered
There is another (very non-literal) translation here. Another set of translations here.
|1 Diffugere nives, redeunt iam gramina campis|
Mutat terra vices et decrescentia ripas
|The snows have scattered, and back comes grass to fields|
And leaves to trees.
Earth changes seasons, and declining [between their] banks
|5 Gratia cum Nymphis geminisque sororibus audet|
Ducere nuda choros.
Immortalia ne speres, monet annus et almum
Quae rapit hora diem.
|The Grace with the Nymphs and her twin sisters dares|
To lead, naked, the dance.
Lest you hope for immortal things, the year warns you, and the hour,
That hurries away the kindly day.
|Frigora mitescunt Zephyris, ver proterit aestas|
10 Interitura, simul
Pomifer autumnus fruges effuderit, et mox
Bruma recurrit iners.
|Frosts grow mild in the western winds; Summer tramples Spring,|
Who will herself perish once
Fruitful Autumn has poured out fruit; and soon
Fruitless Winter returns.
|Damna tamen celeres reparant caelestia lunae ;|
Nos ubi decidimus,
15 Quo pater Aeneas, quo dives Tullus et Ancus,
Pulvis et umbra sumus.
|Yet the moons are fast to make good their heavenly losses;|
We, when we have fallen to
Where good Aeneas and wealthy Tullus, and Ancus [have]
Are dust and shadow.
|Quis scit an adiciant hodiernae crastina summae|
Tempora di superi ?
Cuncta manus avidas fugient heredis, amico
20 Quae dederis animo.
|Who knows whether [they] will add to the sum of to-day,to-morrow's|
Time - the gods above?
All will escape the greedy hands of your heir,
Which you gave to your dear soul.
|Cum semel occideris et de te splendida Minos|
Non, Torquate, genus, non te facundia, non te
|But when once you have fallen, and on you Minos|
Has made majestic judgment,
Neither, Torquatus, shall family or eloquence
Or loyalty restore you.
|25 Infernis neque enim tenebris Diana pudicum|
Nec Lethaea valet Theseus abrumpere caro
|For neither from the shadows below does Diana virtuous|
Hippolytus set free;
Nor can Theseus break Lethe's
Chains from [his dear] Pirithous
On the revival of Latin
His main theme is the need for a common language. "The necessity of some common language is seen in the fantastic attempts to create one artificially. You will find enthusiasts for stuff like Esperanto, which is about as much like a human language as a jig-saw puzzle is like a living face." He was writing just before the internationalisation of English. He does not mention at all the importance of Latin to philosophers, namely that the philosophical language of thought - its vocabulary and to a large extent its syntax - is essentially Latin.
His characterisation of what we now call The West is interesting. "There is one unmistakable thing which, in spite of a badly diseased and divided social state, is still in the main the common descendant of the old Christian culture. Its dress, its manner of living, its main social ideas are the same".
Thursday, March 17, 2011
The encyclopedia that anyone can be paid to edit
What is unethical about it? Wikipedia is branded as the ‘encyclopedia that anyone can edit’, and it permits this because of the theory of ‘crowdsourcing’. Just as the crowd at the country fair guessed the weight of the bull better than any expert, so (supposedly) a crowd of people editing Wikipedia will arrive at the truth better than any expert. So why can’t employees of Koch Industries edit? Logic suggests that the range of ‘anyone’ covers them too.
The paid editing merely exposes the fallacy of crowdsourcing. No one edits Wikipedia for free. As I pointed out here, everyone has an interest of some sort. Pedophiles write on Wikipedia to get the pedophile point of view across. Proponents of the fraudulent ‘Neurolinguistic programming’ edit to promote their view on NLP. Brahma Kumaris edit to promote Brahma Kumarism or whatever. Because they don’t get paid for it doesn’t mean they are not being rewarded in some way. So what’s the problem with a financial reward? Presumably if Charles Koch had the time to edit the article about him, he would do that. Being a busy man, and a rich one, naturally he pays someone to do it.
In summary: if you believe in crowdsourcing, you have no problem with paid editing.
Consequens autem falsum, ergo antecedens.
Monday, March 14, 2011
Indiscernibility of Identicals
Fa and a=b implies Fb
Is this always true? A slightly different way of expressing the law is that if Fa, and if 'a' denotes exactly what 'b' denotes then Fb. But in this form the law is clearly not valid. Suppose there is a shortage of red paint, and that only Ferraris are red. Then it follows that if Ferraris are fast, then red cars are fast, and conversely. But it does not follow that if John thinks Ferraris are fast, then he thinks that red cars are fast – perhaps he is imagining a red reliant Robin that he once saw. I.e. F = ‘John thinks that every – is fast’ and a = ‘Ferrari’ and b = ‘red car’. Then Fa and the fact that ‘a’ denotes everything that ‘b’ denotes does not entail Fb.
You will object that indiscernibility of identicals applies only when a and b are proper names. Proper names are referring terms, not common terms like ‘Ferrari’ or ‘red car’. I reply: what is a referring term? If it is defined as something to which indiscernibility of identicals necessarily applies, then the ‘Shakespeare’ arguments in the previous posts suggest that indiscernibility of identicals does not apply to ordinary proper names at all.
Saturday, March 12, 2011
On discovering what we already knew
I will discuss these objections later. Meanwhile, another puzzle. If Leibniz II is correct, we can substitute any two proper names so long as they are names for the same person, salva veritate. Thus, if Shakespeare and Edward de Vere (another contender for the identity) were the same person, it follows that
- We have always known that Shakespeare was De Vere, since we have always known that Shakespeare was Shakespeare, a logical truth.
- We could never discover that Shakespeare was De Vere, since you cannot discover what you already know.
And so on.
Thursday, March 10, 2011
Story relative reference
In a chronicle of remote date, we might conceivably identify the unknownI'm not sure about the horse part, and I shall argue this is true only for the first occurrence of a proper name or singular term, but this is roughly right. By 'particular judgment' Bosanquet means the judgment opposed to the universal judgment - a general existential judgment 'Some A is B'. In respect of the first occurrence of a name in a fictional narrative, where we have no means of identifying or individuating the character except through the story, he is right. When you first encounter the name - say 'Aeneas groaned', which is the first time we meet him in the Aeneid, the sense of the proposition is no more than "someone called Aeneas groaned".
possessor of some name as figuring in several scences or incidents without being
sure what he, she or it might be; whether man or a woman, or a favourite
horse. In this sense the judgment that deals with a proper name is merely
For subsequent occurrrences, as I argued here, the proper name has a stronger sense. Later on we learn that Aeneas was shipwrecked off Carthage. But the conjunction 'Someone groaned and someone was shipwrecked off Carthage' does not tell us that someone who groaned was subsequently shipwrecked, for it could be true of different people. Repeating the proper name (in the right context) tells us that the person who was shipwrecked was the same person as the one who groaned. And so for the following sequence of propositions:
Aeneas fled his home
Aeneas was shipwrecked
Aeneas came ashore at Carthage
Dido was the queen of Carthage
Aeneas met Dido
Dido died of grief
Aeneas sailed to Italy
These tell us that for some x and some y, x fled his home, was shipwrecked off Carthage, y was queen of Carthage, x met y, y died of grief, x sailed to Italy, and so on. Overall, the sense is perfectly general. We cannot locate x or y in history, i.e. in the narratives we call 'history'. But we can locate them in the story, and this is how the proper name individuates. The name 'Aeneas' signifies the subject of the proposition as being the same as x, without signifying it to be the same as y. The name 'Dido' signifies the subject to be the same as y, without signifying it to be the same as x.
Is this the entire sense of a fictional name? Is it the entire sense of any proper name?
* Logic, Bk I ch. 5, Oxford 1888 p. 208
Wednesday, March 09, 2011
Textual analysis using pure logic
The big question was whether, besides the alephs, there are also other powers of
sets; for two years now I have been in possession of a proof that there are no
others; so that, for example, the arithmetic linear continuum (the totality of
all real numbers) has a determinate aleph as its cardinal number.
The Bacon-Shakespeare question, on the other hand, is for me completely
finished; it cost me a great deal of time and money; to pursue it further I
should have to make much greater sacrifices, travel to England, study the
archives there, etc. With warm greetings to you and your sister [etc.]
It's interesting because Cantor made one of the greatest contributions to mathematicians and logic in the whole history of the subject (e.g Godel's proof and much else ultimately depends on the insights of Cantor's elegant diagonal argument), and yet here he is spending 'much time and money' on something generally regarded as, well, a bit cranky.
But enough of that. The aim of this post to is show 'Nishadani' and his like that we can prove the falsity of Baconian, Oxfordian Marlovian theories etc. etc., without any tedious recourse to textual analysis, biography or any other such un-philosophical considerations. We can prove it by pure logic. Let ‘Shakespeare’ denote whoever it was that wrote the plays attributed to the man of that name.
1. Shakespeare and Bacon were one and the same person.
2. There is no doubt as to whether Shakespeare wrote The Tempest
3. There is some doubt as to whether Bacon wrote The Tempest
4. If a=b and Fa then Fb (Indiscernibility of identicals)
Since the four propositions are aporetic, i.e. jointly yield a contradiction, one of the premisses must be false. The first is a mere assumption. Clearly the second is true: obviously the man who wrote the 'Shakespeare' plays called himself 'Shakespeare', just as 'Nishadani' calls himself 'Nishadani'. That is pure logic. The third is true - there wouldn't be so much arguing and gnashing of teeth on Wikipedia if there were no doubt at all. And the fourth (from Leibniz) is beyond all doubt. If Shakespeare and De Vere (or Marlow or whoever) were one and the same person, and De Vere was accused of pederasty, then so was Shakespeare. If De Vere died in 1604 (or whenever) then so did Shakespeare, assuming the identity.
But all four imply a contradiction. By substitution of 'Bacon' for 'Shakespeare' in proposition (2), and by indiscernibility of identicals (4), we have
(*) There is no doubt as to whether Bacon wrote The Tempest
But this proposition contradicts (3) above. It cannot be true that there is some doubt that Bacon wrote the Tempest (even a tiny bit of doubt) and that there is no doubt. Contradiction. Therefore the weakest of the four propositions above must be rejected, namely that Bacon and Shakespeare were the same person.
So forget the historical and textual crap. By purely logical and philosophical methods we can clarify all manner of difficult questions like this.
Tuesday, March 08, 2011
Your understanding of Kaplan is excellent. But for him propositions areOn the Russell-Kaplan view (although Russell himself probably never consistently held such a view), the semantics of singular thought is ‘object dependent’. A thought about Mont Blanc actually contains Mont Blanc – with all its snow fields. That seems absurd for a number of reasons. How can a thought contain a physical object? How can a thought even be internally related to an object when the thought remains the same whether or not the object exists? Does the proposition ‘Etna is a volcano’ cease to be meaningful even if Etna is completely destroyed in an eruption? Surely not. Is the proposition ‘Caesar was a man’ meaningful even though Caesar does not exist? Surely it is.
Russellian, not Fregean. If 'Mt Blanc is snow-covered' expresses a Russellian
proposition, then Mt Blanc itself, that massive physical object, together with
its snow fields and subterranean gopher tunnels, etc. etc. is a constituent of
the proposition. But I can't swallow the Russellian view; how could a finite
mind wrap itself around such a monstrous object?
The problem is to explain individuation. The name ‘Mont Blanc’ individuates. It tells us which large object is the subject of the proposition 'Mt Blanc is snow-covered'. It distinguishes that object from other similar objects such as Ben Nevis, Kilimanjaro, Everest and the rest. How do we give an object-independent account of the semantics of individuation?
The key, as I shall argue, is to explain the semantics of fictional names. The name ‘Aeneas’ distinguishes a character in Virgil’s epic from all the other characters mentioned in the Aeneid. If we can explain how that is possible, it will be possible to explain individuation in general, I believe.
Sunday, March 06, 2011
You will be Marcellus
Marcellus was one of those future Romans whom Aeneas sees in the underworld in Book VI of the Aeneid. The passage from 865-885 recounts Marcellus's life and laments his early death. The line at 882 'tu Marcellus eris', 'you will be Marcellus' supposedly caused Octavia to faint with grief when it was read to her and Augustus, and inspired many bad paintings.
Why does Abelard mention this here? The context is a discussion of Boethius' account of individuation, that individuation comes about by a set of properties that are unique to each individual. Socrates is individuated because the collection of properties ‘bald’, ‘snub-nosed’, ‘old’, ‘son of Sophroniscus’ is found in no other person except Socrates. (Saul Kripke famously criticised a very similar theory in Naming and Necessity).
Abelard says that the reply was ‘Marcellus’ not because of the substance which he was seeing, but because of the unknown quality which could not be perceived by sense - which Boethius seems to agree with when he gives the made up name of 'Platonity' (platonitatem) to the whatever property it is that individuates Plato (Non propter substantiam quam videbat, responsum est 'Marcellus' sed propter ignoratam qualitatem quam sensu percipere non poterat. Cui etiam Boethius consentire videtur in editione secunda super Perihermeneias, ubi proprietatem Platonis ficto nomine platonitatem appellat).
Perhaps Abelard also has in mind how the future Romans are those whose souls are owed a second body. It is Mind that sets all matter in motion, by infusing the material bodies with spirit. When some people die, their spirit is not wholly freed from the ills and miseries of the body. Some of these souls are stretched out to dry in the winds, or are sent over the plains of Elysium until the days remove the ingrained corruption of the body and leaves them pure ethereal sense. They are drenched by God in the river of Lethe, which removes all their memories so that they go back for a second bodily life. In that case, their identity cannot consist in any perceptible property. Perhaps Abelard is alluding to this.
What is individuation?
The concept (as with so many philosophical concepts) goes back to the medieval period. It is clearly articulated by Henry of Ghent (Quodlib. 5. quest. 8) as being a 'double negation', and by Scotus (Ordinatio II. iii. q2) as 'privatio divisionis in se et privatio identitatis ad aliud' - the privation of division, and the privation of identity with another.
Taking the first of these negations (I will discuss the second elsewhere), what does 'a privation of division' mean? It is where we get the word 'individual' - literally, the undivided or undividable. What is meant is that the division of genus into species, the division of the species into sub-species, and so on, comes to a halt when we reach the individual. We can divide a genus (e.g. animal) into different species of the same genus, such as giraffe, koala, swan, man, and so on. A species such as man can be divided into individuals of the same type, such as Socrates, Plato, Aristotle and so on. But there it ends. You cannot divide Plato into different things of the type Plato.
This is all rather medieval, but it has a simple logical consequence. It means that the inference
A man is white and a man argues, therefore something that argues is white
is invalid, for Socrates might be the only person who is white, and Plato the only person who is arguing, and so no one individual is both arguing and white. The inference fails because there can be always be different things of the same kind, for anything above the 'most specific species' (i.e. the individual). But on the other hand
Socrates is white and Socrates argues, therefore something that argues is white
is valid, for there cannot be one Socrates who is white, and another different Socrates who is arguing (at least when 'Socrates' is understood in the same sense). A name, taken in the same sense, cannot be verified of different individuals. Or rather, what we mean by 'individual term' is such that inferences of the type above are valid. If 'A is B and A is C' implies that some B is C, i.e. if it cannot be true that A is B and A is C, without it also being true that some B is C, then 'A' must be a singular or individual term. The semantics of the singular term is defined - I will argue wholly defined - by this feature.
Saturday, March 05, 2011
Contemplation and logical transitivity
(1) To think about intently
(2) to look at thoughtfully
(3) to have in mind as a possibility.
The first sense is clearly logically intransitive - you can intently think about a mermaid without there being a mermaid. The second sense by contrast is (logically) transitive. You cannot look thoughtfully about a mermaid without there being a mermaid you are looking at. With the third sense, we are back to logically intransitive. God can contemplate creating a mermaid, even though there are no mermaids.
But, pace Vallicella, this doesn't entail there are any 'incomplete beings'. How?
Friday, March 04, 2011
Is reference logically intransitive?
(*) Tom is referring to a winged horse, but there are no winged horses.
Informally and in ordinary use, however, it seems to be logically intransitive. For example, you might get the following question in a multiple choice exam:
(**) Who is Shakespeare referring to when he says “the power of beauty will sooner transform honesty from what is to a bawd than the force of honesty can translate beauty into his likeness”? (see here for a real example)
Clearly the answer will be right or wrong, and thus true or false. Indeed, the a generally accepted answer is that Shakespeare is referring to Hamlet’s mother Gertrude, and so ‘Shakespeare is referring to Gertrude’ is true. But Gertrude being a fictional character, there is no such person as Gertrude. Thus
(***) Shakespeare is referring to Gertrude, but there is no such person as Gertrude
is not inconsistent. thus, in its ordinary sense (for example in GCSE exam questions about Shakespeare and Dickens), the verb phrase ‘refers to’ is logically intransitive.
In the posts that follow I will be exploring the concept of Story relative reference – reference to an individual within a text (or group of texts) such that the individual is identifiable within that text, but not outside it, and I will demonstrate its connection with the subject I began with, namely the intentionality of singular thoughts.
Wikipedia: fiction becomes fact
The ensuing discussion is on the Wikipedia Astronomy project page.
Thursday, March 03, 2011
Logically intransitive verbs
1. Tom owns a house in the desert
2. Tom is building a house in the desert
3. Tom / has / a thought about a house in the desert
That is, if Tom owns a house in the desert, at least one house (Tom’s) is in the desert. So ‘owns’, in this context, is logically transitive. If he is building a house in the desert, there must be at least one house in the desert that he is building. And if he has a thought about the house, there must be at least one thought that he has, namely the one about a house in the desert. The verb ‘has’ is logically transitive in this context.
A logically intransitive verb is one which may have a grammatical accusative, but does not need a logical accusative to verify it. I.e. ‘S V O’ may be true without there being any object that satisfies 'O'. Thus all the verbs in the following are logically intransitive.
4. Tom wants a house in the desert
5. Tom is looking for a house in the desert
6. Tom / has a thought about / a house in the desert
If Tom wants or is looking for a house in the desert, it does not follow there is any such house. The verbs ‘want’ and ‘looking for’ are logically intransitive. Note well that proposition (3) is the same as proposition (6). But there are two different verb phrases: ‘has’ and ‘has a thought about’. The object of ‘has’ is ‘a thought’, and that must exist in order for there to be a thought. The object of ‘has a thought about’ is ‘a house in the desert’, but no such house has to be in order for there to be such a thought. So ‘has a thought about’ is logically intransitive.
Tomorrow, as we approach the problem of proper names, I will talk about verbs of reference and individuation.
Wednesday, March 02, 2011
Intentionality and Proper Names
1. An empty name signifies something
2. Every thing is an existing thing
3. A name does not signify a concept
4. A (significant) term signifies a concept or an object.
Taken together, the four are inconsistent. If (1) an empty term signifies something, and if (2) every thing is an existing thing, then an empty term signifies an existing thing. But (3) that existing thing is not a concept, so (4) an empty name signifies an existing object. But (from the definition of ‘empty name’) an empty does not signify an existing object. Contradiction.
Yet each of the four propositions has a strong claim to our acceptance. (1) Surely the semantics of an empty name are no different from a non-empty one. We can’t tell whether there was such a person as John the Baptist by analysing the meaning of the name as used in the New Testament. (2) There is plenty of evidence for the ‘Brentano thesis’ that I have discussed frequently. (3) There are plausible arguments against proper names signifying concepts – see Maverick’s argument, for example. (4) The distinction between concept and object is practically a given. No contemporary philosopher of language has seriously challenged it, as far as I know.
There are three known resolutions to the tetrad, according as philosophers have denied proposition 1, 2, or 3 respectively. Direct reference theorists deny (1). They hold (implausibly, to my mind) that an empty name does not signify. To the argument that we cannot tell whether a name (e.g. ‘John the Baptist’) is empty from its semantics alone, they reply that this is ‘Cartesianism’. If there is no such person as John the Baptist, direct referentialists claim that we know this, even though we utter things like ‘we do not know whether the name ‘John the Baptist’ signifies or not’. The Maverick and other Meinongians-in-denial deny (2), by driving a wedge between being a thing, and being a thing that exists. And (3) people like Mark Sainsbury, and indeed Edward Ockham himself, argue that proper names signify ‘singular concepts’.
In posts for this month (March 2011), I will put forward some arguments in defence of singular concepts. More later!