Thursday, December 07, 2006

Buridan on Individuation

Here is a splendid passage from the 14C logician John Buridan. The Latin you can find on Peter King's website, here, of which my hasty English translation is below. The passage is interesting because, while logicians like Ockham anticipate Russell's idea of scope distinction (i.e. between ~ the F is G and the F is ~ G), Buridan here also anticipates the idea that proper names are telescoped definite description. (Buridan uses the wonderful Latin word circumlocutio). Note also the examples of 'teacher of Alexander' (magister Alexandri) and 'student of Plato' (discipulus Platonis) as the relevant circumlocutio of 'Aristotle'. These are familiar from Kripke, but he just got them from Frege, who had a good German classical education, and probably got them from some unknown scholastic source.

Another familiar idea is that genuinely singular terms are really demonstrative. Buridan says that a proper name is a circumlocution, but that a truly singular term is used in the presence ('prospect') of something, whose function is not to indicate similarity, but to indicate that it can belong to no other thing.

See also the following pages in the Logic Museum.

Aquinas on the name 'God'.
Ockham's Theory of definite descriptions.

'But if you say, how can I conceive Aristotle in a singular way, when he was never in my prospect? In reply, I say that it is not possible for you, properly speaking, because you do not conceive him differently from other men except according to a sort of circumlocution, such as 'the greatest philosopher', 'the teacher of Alexander', 'the disciple of Plato', who composed the books of philosophy which we read &c. Now although this description does not in truth belong to anyone but him, yet it is not properly a singular term (terminus singularis) - Although it does not belong to anyone except him alone, it is not inconceivable (repugnat – fudge) that in this way of signifying or imposition that it may belong to many and stand (supponat) for many, and if there were another God similar, the name 'God' would belong to him and would stand for him without a new imposition of the word – and so if there were another who were the greatest philosopher and the master of Alexander and the disciple of Plato &c, the said description would belong to him and would stand for him.
'For thus it is not a term that is absolutely and properly singular. Because if this thing in my prospect I call 'Socrates' by a proper name, it is not because he is such and such but because the name 'Socrates' would never belong to those other things insofar as they are similar – unless from another imposition [that name] were imposed to signify that other thing, and thus equivocally'.

Sunday, October 15, 2006

The Frozen Past

Most scholastic philosophers, with the exception of St Peter Damian, say that God cannot change the past.

St Thomas includes it on his list in Summa Contra Gentiles (II. 25) of what God cannot do (Deus non potest facere quod praeteritum non fuerit). In
On Eternity
he says that the proposition that the past did not exist contains in itself a contradiction. For which reason Augustine says in the book against Faustus [xxvi c.5] 'Anyone who says "If God is omnipotent, let him bring it about that those things which happened, did not happen", does not see that he says 'If God is omnipotent, let him bring it about that those things which are true, are false in that very thing by which they are true' [PL 42, 481.].

The problem with this is that it is a logical argument, and for that reason it applies to the future as well as the past. Paraphrasing Augustine, 'The Future' means 'those things which will happen', and God cannot bring it about that the Future will not happen they way it will, otherwise we have the contradiction that those very things which will happen, are not those very things.
Yet we are more tempted to say that God could change the future. The future is not frozen in the way the past seems to be. But if this being frozen is not a logical being, what is it?

Tuesday, July 18, 2006

That was the same cat as this

Brandon argues here, that if 'this cat' has no tail, but 'that cat' did not have a tail, then the title sentence is false.

Let's assume that 'this' is a true demonstrative, made in the physical presence of the object we are pointing to. But for the same reason, 'that' cannot be, for Tibbles-of-yesterday is not present – literally not present – for us to point to. So the 'that' must be some sort of referring description, perhaps 'the cat we saw sitting on the front doormat of the Jones's house yesterday'.

But why would we ask whether that was the same cat as this? Perhaps we are wondering whether the Jones have two cats or not. Brandon argues that the cat we saw yesterday had a tail, but this cat (here) does not. Thus 'That was not the same cat as this is'. Ocham agrees. Of course, the cat here is not the same, in the sense of *qualitatively* the same, as the one we saw yesterday.

But Ocham happens to have seen the accident when a car ran over this cat's tail, and it fell off. Thus, argues Ocham, the Jones really have just one cat. The cat we saw yesterday, and the cat we see here now, are one and the same cat. They are 'numerically the same'. Ocham agrees that this cat is not qualitatively the same as that cat, but they are numerically the same (and so of course are not really 'they' at all).

And I wonder, would we say 'the car ran over this cat's tail' (pointing to this cat here), or 'the car ran over that cat's tail' (meaning the cat we saw yesterday).

Wednesday, June 28, 2006

The Logic Museum

The Logic Museum is a collection of source material, much of it Latin and medieval, on logic and metaphysical writing, and particular on the "big questions" like, does existence exist, for how long, and, is it open on Sundays sort of thing. Links below.

Logic Museum Home

The latest set of pages (July 2006) is on connotation.

Some other of the big subjects:

Time and Eternity
Traditional Logic

Plus lots of other stuff, which you can access easily from the main page.

In June 2006 I will be working on a translation of the commentaries of Abelard, Boethius and Aquinas of the De Interpretatione.

Wednesday, June 07, 2006

On Miracles

Alan Rhoda has found a link to a fascinating debate here, on whether there is "Historical Evidence for the Resurrection of Jesus?" between William Lane Craig and Bart D. Ehrman.

All these have more of the theatrical and gladiatorial than the logical and rational. One feels that a hatchet or a knife or even a gun should be issued at a suitable point in the proceedings so they can get down to the real business. And what is always so fascinating, is the irrationality of the argument increases with the obvious intelligence of the participants. But interesting all the same.

Both sides misrepresented Hume. Hume's point, in the essay On Miracles, is that in considering the evidence for an extremely implausible event (which is what the word 'miracle' really implies, namely something amazing or to be wondered at, something which is scarcely believable), we must always consider which is more implausible, the miraculous event itself, or the possibility that the evidence for it is flawed in some way, however small.

Also no one mentioned the possibility that the evidence is flawed is greatly increased, is when the person producing the evidence have some interest in what it is evidence for. I don't know much about what motivated the authors of the gospels to write them. If the motive for writing the gospels were in any way correlated (think of official histories) with the need to prove them correct, we might deservedly be suspicious.

Some of the sillier quotes.

"Hume had an excuse for his abject failure: the probability calculus hadn’t yet been developed in his day.".

"everybody’s read The DaVinci Code" (false - I haven't).

"In order to show that that hypothesis is improbable, you’d have to show that God’s existence is improbable. But Dr. Ehrman says that the historian cannot say anything about God. Therefore, he cannot say that God’s existence is improbable."

Saturday, March 18, 2006

Overheard in a bar

'I worked with him a few years ago and he was always trying to convert me to Islam. It would drive me mad. Finally, I said "So you believe that when I die, I will go to hell and suffer eternal punishment, and so will my wife, and so will my two beautiful daughters". He thought about this for a bit then said "Yeah. But let's not let that get between us as mates"'.

A similar thought, isn't it, to this "The Roman Catholicks are certainly the most zealous of any sect in the Christian world; and yet you will find few among the more sensible people of that communion who do not blame the Gunpowder-treason, and the massacre of St. Bartholomew, as cruel and barbarous, though projected or executed against those very people, whom without any scruple they condemn to eternal and infinite punishments. All we can say in excuse for this inconsistency is, that they really do not believe what they affirm concerning a future state; nor is there any better proof of it than the very inconsistency." (Hume, Treatise of Human Nature, I. iii. 9).

Thursday, March 02, 2006

Being and Nothingness

Too good to keep off the internet. A companion piece to Dens of Robbers.

"The reflective nihilation, however, is pushed further than that of the pure for-itself as a simple self-consciousness. In self-consciousness, in fact, the two terms of the dyad 'reflected-reflecting' were so incapable of presenting themselves separately that the duality remained perpetually evanescent and each term while positing itself for the other became the other. But with reflection the case is different since the 'reflection-reflecting' which is reflected-on exists for a 'reflection-reflecting' which is reflective. Reflected-on and reflective, therefore, each tend toward independence, and the nothing which separates them tends to divide them more profoundly than the nothingness which the For-itself has to be separates the reflection from the reflecting. Yet neither the reflective not the reflected-on can secrete this separating nothingness, for in that case reflection would be an autonomous for-itself coming to direct itself on the reflected-on, which would be to suppose an external negation as the preliminary condition of an internal negation. There can be no reflection if it is not entirely a being, a being which has to be its own nothingness. (Sartre, Being and Nothingess, Pt III c1. , 4)

Hobbes and Ockham on ordinary language

There are two approaches to ordinary language philosophy, one represented by Hobbes, the other by Ockham. According to the first, there is no problem at all with ordinary language. The apparent difficulties are the result of meaningless technical language (in Hobbes' day, the Latin of the schoolmen), designed for the defence of what is really absurd and untrue. According to the second, the problem is ordinary language itself, which is systematically misleading. Thus, Ockham argues our propensity to believe every name is the name of something is the source of all philosophical error (Summa Logicae 1.51)

Wittgenstein represents both views. In his polemics against mathematical logic and set theory, to be found in his mathematical writings of the early 1930's and in the Remarks on the Foundation of Mathematics, he takes the Hobbesian line. '"Mathematical logic" has completely deformed the thinking of mathematicians and of philosophers, by setting up a superficial interpretation of the forms of our everyday language as an analysis of the structures of facts. Of course in this it has only continued to build on the Aristotelian logic'.

At other times, he takes an Ockhamist approach. 'A clever man got caught in this net of language! So it must be an interesting net. ' ' Human beings are entangled all unknowing in the net of language.' ' In philosophy it's always a matter of the application of a series of utterly simple basic principles that any child knows, and the – enormous – difficulty is only one of applying these in the confusion our language generates.'

See here for all the Wittgenstein quotes.

Dens of robbers

Here is a passage from Locke, in a similar spirit to Hobbes, and with the same ingredients. The gibberish of metaphysicians, contrasted with the solid good sense of the statesman, the businessman and the 'contemned mechanic'.

"For, notwithstanding these learned disputants, these all-knowing doctors, it was to the unscholastic statesman that the governments of the world owed their peace, defence, and liberties; and from the illiterate and contemned mechanic (a name of disgrace) that they received the improvements of useful arts. Nevertheless, this artificial ignorance, and learned gibberish, prevailed mightily in these last ages, by the interest and artifice of those who found no easier way to that pitch of authority and dominion they have attained, than by amusing the men of business, and ignorant, with hard words, or employing the ingenious and idle in intricate disputes about unintelligible terms, and holding them perpetually entangled in that endless labyrinth. Besides, there is no such way to gain admittance, or give defence to strange and absurd doctrines, as to guard them round about with legions of obscure, doubtful, and undefined words. Which yet make these retreats more like the dens of robbers, or holes of foxes, than the fortresses of fair warriors: which, if it be hard to get them out of, it is not for the strength that is in them, but the briars and thorns, and the obscurity of the thickets they are beset with. For untruth being unacceptable to the mind of man, there is no other defence left for absurdity but obscurity."

Wednesday, March 01, 2006

Hobbes: Ordinary Language Philosopher

"There is yet another fault in the discourses of some men; which may also be numbered amongst the sorts of madness; namely, that abuse of words, whereof I have spoken before in the fifth chapter, by the name of absurdity. And that is, when men speak such words, as put together, have in them no signification at all; but are fallen upon by some, through misunderstanding of the words they have received, and repeat by rote; by others from intention to deceive by obscurity. And this is incident to none but those, that converse in questions of matters incomprehensible, as the schoolmen, or in questions of abstruse philosophy. The common sort of men seldom speak insignificantly, and are therefore by those other egregious persons are counted idiots. But to be assured, their words are without anything correspondent to them in the mind, there would need some examples; which if any man require, let him take a schoolman in his hands and see if he can translate any one chapter concerning any difficult point, as the Trinity; the Deity; the nature of Christ; transubstantiation; free-will, &c., into any of the modern tongues, so as to make the same intelligible; or into any tolerable Latin, such as they were acquainted withal, that lived when the Latin tongue was vulgar. What is the meaning of these words, "The first cause does not necessarily inflow anything into the second, by force of the essential subordination of the second causes, by which it may help to work?" They are the translation of the title of the sixth chapter of Suarez' first book, "Of the concourse, motion, and help of God." When men write whole volumes of such stuff, are they not mad, or intend to make others so? " (From the Leviathan)

Saturday, February 25, 2006

Ockham on Past and Future

The latest exhibit in the Logic Museum is a parallel Latin English translation of Ockham's theory of past and future tenses, in chapter 7 of book II of his Summa Logicae. Find it here. It is connected with the discussion going on below concerning the problem of supplying truth conditions for past and future tense propositions.

Wednesday, February 22, 2006

Rain tomorrow

"There is some actual state of affairs which constitutes its now being the case that it’s possible that it rain tomorrow"

But is this actual state of affairs is the same state of affairs as the state of affairs which will obtain when it rains tomorrow? This seems to be the argument.

1. A statement must be true or false, and so there must be conditions under which it is true.

2. To state the conditions when a given proposition is true, is to say what IS the case, if it IS true. Merely to state the truth conditions is to specify something that exists now.

3. Thus statements about the future can be reduced to statements in the present tense. For if the truth condition obtains, the statement that it obtains, is true now. If it does not obtain, the statement that it does not obtain, is true now.

But why should the truth conditions be in the present tense? I agree that a proposition like 'Tom thinks it will rain tomorrow' says something about the present. It says that Tom has a certain thought, right now, in the present. Similarly 'the weather forecaster says it will rain tomorrow' says something about what the person on the TV says, now. Likewise 'It is causally determined that it will rain tomorrow'. Similarly also for 'it is possible that it will rain tomorrow', which says something about the speaker's present state of knowledge.

But 'it will rain tomorrow' doesn't say anything about the present. 'It will rain tomorrow' is true if and only if it WILL rain tomorrow.

Saturday, February 18, 2006

Locke on Truths of Reason

And here is Locke on the distinction between truths of reason and truths of fact, from Bk 4 ch xi, 13 ' Of our Knowledge of the Existence of Other Things'

13. Only particular propositions concerning concrete existences are knowable. By which it appears that there are two sorts of propositions:—(1) There is one sort of propositions concerning the existence of anything answerable to such an idea: as having the idea of an elephant, phoenix, motion, or an angel, in my mind, the first and natural inquiry is, Whether such a thing does anywhere exist? And this knowledge is only of particulars. No existence of anything without us, but only of God, can certainly be known further than our senses inform us. (2) There is another sort of propositions, wherein is expressed the agreement or disagreement of our abstract ideas, and their dependence on one another. Such propositions may be universal and certain. So, having the idea of God and myself, of fear and obedience, I cannot but be sure that God is to be feared and obeyed by me: and this proposition will be certain, concerning man in general, if I have made an abstract idea of such a species, whereof I am one particular. But yet this proposition, how certain soever, that “men ought to fear and obey God” proves not to me the existence of men in the world; but will be true of all such creatures, whenever they do exist: which certainty of such general propositions depends on the agreement or disagreement to be discovered in those abstract ideas.

The distinctions that Locke makes (see previous post) are therefore as follows:

1. propositions which are truths of reason, but merely trifling or verbal;

2. propositions which are truths of reason, but where the predicate is not actually contained in the subject, but is a necessary consequence of it;

3. propositions which are simply matters of fact, not deducible by reason alone.

Locke on Analytic vs Synthetic

Here is a passage from the Essay (Bk IV, c. viii, 8) that is suggestive of the Analytic / Synthetic distinction.

8. … We can know then the truth of two sorts of propositions with perfect certainty. The one is, of those trifling propositions which have a certainty in them, but it is only a verbal certainty, but not instructive. And, secondly, we can know the truth, and so may be certain in propositions, which affirm something of another, which is a necessary consequence of its precise complex idea, but not contained in it: as that the external angle of all triangles is bigger than either of the opposite internal angles. Which relation of the outward angle to either of the opposite internal angles, making no part of the complex idea signified by the name triangle, this is a real truth, and conveys with it instructive real knowledge.

Friday, February 17, 2006

Hume's Fork

Spur writes here

Leibniz and Hume have the same basic distinction in mind, between those truths which are necessary and can be known a priori, and those which are contingent and can only be known a posteriori. The two philosophers use slightly different terminology, and Leibniz would balk at Hume's use of 'relations between ideas' in connection with truths of reason only, but the basic distinction seems to me to be the same.

But the question is more difficult, and is related to a change in logic that happened at the very beginning of the early modern era. The scholastic logicians said that in a proposition (which for them meant a sentence) the predicate is affirmed or denied of the subject. 'Subject' and 'predicate' here are objectively existing things.

Influenced by Descartes, Antoine Arnauld argued that it is not one THING that is predicated of another thing, but one IDEA that is predicated of another idea. Locke (who studied Arnauld's logic carefully) introduced this to the English world (Book IV of the essay is the locus classicus). For example, he sets its down as a principle, that all our knowledge consists in perceiving certain agreements and disagreements between our ideas.

There you have Hume's fork. Before, there was the difference between accidental and essential propositions. An essential proposition is where the predicate belongs in the subject by right, as it were. An accidental proposition is whether the predicate belongs in the subject, but possibly may not. It is not relevant whether this can be known or not. There are (as Aquinas notes) essential propositions which cannot be known because mere humans cannot understand the true meaning of the word which signifies the subject. But the notion of a proposition true in itself but unknowable because the 'subject' is unknowable, is impossible where the proposition consists of ideas stuck together.

In summary: Hume's fork is a consequence of the early modern view of the proposition. The scholastic view was that the proposition connects things. The early modern view is that it connects ideas. The distinction between truths of reason and truths of fact only makes sense on the latter view.

There a number of passages which support this argument & I will make a posting in due course.

Wednesday, February 15, 2006

Praedicatum inesse subjecto verae propositionis

'The predicate is included in the subject of a true proposition'. Leibniz says this (in a letter to Arnauld) but of course his use of Latin signals that he is quoting an orthodox principle of the schools.

And the principle has nothing to do with the analytic/synthetic distinction. It has to do with the true/false distinction. If Socrates is the subject, and the subject is bald, and if the proposition states that the predicate 'is bald' is included in the subject (Socrates) then the proposition is true. Otherwise it is false.

What, then, is the analytic/synthetic distinction?

Tuesday, February 14, 2006

Truth in Hell

What on earth is going on here? and particularly here? Fr. Alexis Bugnolo, a Franciscan who is developing an internet library of Scholastic Theology and Philosophy (and good luck to him, I say – this material has lain buried and neglected for too long) is incensed by what he calls a sodomitic slur against St. Anselm in an article in the internet encyclopedia, Wikipedia. The original article, now locked down, is here, and the talk page, which gives a full background to the dispute is here.

Bognolo stirs up a number of demons, which I won't discuss here. It is what he says about truth that interests me. He says 'Wikipedia is not much different that the real lower regions, where demons wittle the hours of their impending ultimate damnation on the Day of Judgement, idling wailing and complaining and arguing among themselves against the pittible [sic], little truth that their darkened intellects can still behold. … Suffice it to say, that at Wikipedia, they are obsessed with a false definition of truth. For them truth is something neutral, between the medium of two personal opinions. They wrongly believe that falsehood does not exist. Now of course such a definition of truth only prevails in Hell, and that is why those who accept the Wikipedia system end up with the sensibilities of devils, who cannot endure anything at all being said that is true, lest someone arrive at the truth.'

Now there are some real problems at Wikipedia - mainly because professional researchers and academics have no incentive to contribute to it, whereas cranks have every incentive. But I don’t think they have a 'false definition of the truth'. Truth is not something neutral. Of two contrary opinions, at least one must be false, and of two contradictory opinions at least one must be true. Wikipedians would not claim otherwise.

But, when the truth is difficult to determine, Wikipedians say that different opinions about the truth must be given, and (in controversial cases like this) the opinions supported by evidence (or references to that evidence). What is wrong with that?

Monday, February 13, 2006

Mesmerized by science

Any philosopher who mentions my work in their Ph.D. thesis is to be recommended, in my view. One such is Oxford philosopher Edward Kanterian. But what Kanterian says here transcends mere self-interest. Here he is, defending the currently unfashionable view that the methods of philosophy are altogether unlike the methods of the sciences. Even more interesting, he says this fashionable view has a transatlantic source.

'American culture is mesmerized by science. It seems to me that all too many American philosophers think that all real problems can be resolved and answered by scientific methods and that philosophy is either continuous with science or at any rate ought to emulate the methods of the sciences. I have the impression that such a view is widespread in America. It is certainly a view that was encouraged by Quine. And most American philosophers seem to think that Quine showed that the analytic/synthetic, a priori/a posteriori, conceptual/empirical distinctions are obsolete, invalid and to be rejected.'

But read for yourself.

Saturday, February 11, 2006

Aquinas on the names of God

Brandon here has pointed out that it is not inconsistent to hold that there are three persons in the Trinity, but only one God. For the following statements are consistent:

Jack has an F
John has an F
Jack /= John
There is only one F

However, this is true so long as we do not read 'is God' in 'the Father is God' as an identity statement, but as something like ' has the divine nature'. If, on the other hand, we read 'God' as a logically proper name, and 'the Father is God' as an identity statement, it is clearly inconsistent to hold that three things (the Father, the Son and the Holy Ghost) are identical with a fourth thing (God).

Is that right? It is certainly consistent with what Aquinas says here, that no name signifying any individual thing is 'properly communicable to many', except by way of similitude; as a person can be called "Achilles". Thus the name 'God', can only be communicated by way of similitude. 'But if any name were given to signify God not as to His nature but as to His "suppositum," accordingly as He is considered as "this something," (hoc aliquid) that name would be absolutely incommunicable; as, for instance, perhaps the Tetragrammaton among the Hebrew; and this is like giving a name to the sun as signifying this individual thing.'

It suggests that our ordinary words for God only signify by description (as philosophers now say) not 'by reference'. But is that right?

Friday, February 10, 2006

Alarm clock dreams

These are discussed in Freud's great work, The Interpretation of Dreams, which I dusted off after a discussion at Bill Vallicella's place here.

These dreams are apparently caused by a stimulus (such as an alarm clock) which the sleeper interprets as an event in the dream (church bells, sleigh bells).

The puzzle of these dreams is that the interpreted event cannot occur any earlier than the stimulus. Yet there is often a complicated chain of events in the dream that leads up to the interpreted event: how can the dreamer aparently compress such a large quantity of material into the short space between the time that the stimulus occurs, and the beginning of the dream events which conclude with the interpreted event?

A famous example is a dream of Maury, which was about the French Revolution. He witnesses frightful scenes of murder, is brought before a revolutionary tribunal, is questioned by Robespierre, Marat and other revolutionary heroes. After some other incidents which he did not remember clearly, he was condemned, and led to the guillotine in front of an immense crowd. He was bound to the plank by the executioner, the blade of the guillotine fell. He felt his head separated from his body, woke up – and found the top of his bed had fallen and had struck his head in the same place as the blade of the guillotine in the dream.

The puzzle is that the story leading up to the dream was long, and presumably must have begun long before the bed head collapsed. But it seems an extraordinary coincidence that an event in the outside world that so resembled a guillotine, should happen at that time.

Another dream, related by Hildebrandt, is of strolling through green fields until the dreamer came to a village. He saw the villagers strolling through the fields with hymn books. It is Sunday! He went to the churchyard to cool down, read some of the tombstones and then watched the bell ringer climb the tower, and watched the bell first stand motionless, then slowly swing, and finally ring so piercingly that he woke up – to his alarm clock.

The puzzle is to explain how a chance event like the alarm clock could so neatly fit into a dream plot that must have begun some time before the event.

Here is a third example: the dreamer is waiting for a long time for a sleigh to arrive. The sleigh finally comes to the door, there were detailed preparations such as the fur rug, the foot muff, until finally the sleigh started off, with such violence that the sleigh bells ring wildly – his alarm clock.

In all of these cases, the interpreted event is the denoument of what appears to be a complex plot, which happens exactly at the right time and place in the dream. Yet the dreamer (we suppose) has no knowledge or foresight of the actual event which is so interpreted.

Possible solutions are 1. That the dream is made up on waking 2. that the dreamer does have fore-knowledge of the external event (though this hardly explains Maury's dream) 3. The person who told the dream was inventing it.

Wednesday, February 01, 2006

Existential Import

'Existential Import' is a term so frequently bandied around (e.g. here and here) that it is worth explaining its correct meaning, and historical context. I have a complete discussion of it here, but it broadly amounts to this: In traditional logic, the sentence or categorial proposition consists of three parts: the predicate which is 'affirmed' or 'denied', the subject of the affirmation or denial, and the copula which signifies whether the predicate is affirmed or denied. The copula was thought to be signified by the verb 'is', (Latin: est). For example, in the proposition 'man is mortal', the verb 'is' signifies that the predicate 'mortal' is affirmed of the subject 'man'. Thus Mill writes

  • Every proposition consists of three parts: the Subject, the Predicate, and the Copula. The predicate is the name [sic] denoting that which is affirmed or denied. The subject is the name denoting the person or thing which something is affirmed or denied of. The copula is the sign denoting that there an affirmation or denial (Mill, System of Logic).

What is now called a general existential proposition, such as 'some men are mortal' was then called a 'particular' proposition. It was not called 'existential', because it was not thought to be existential. A proposition of the form 'A exists' combines the subject 'A' with the verb 'exists'. Since (according to the traditional theory) every proposition consists of subject, predicate and copula, it follows that 'exists' must be a grammatical abbrevation of copula and predicate, and that it really stands for 'is existent' or something similar. If so, it is not the copula 'is' that signifies existence, but the adjective 'existent'.

The question of 'existential import' was traditionally whether a 'particular' proposition such as 'some mountains are golden' implies the corresponding 'existential' proposition 'golden mountains exist'. Mill argued that it does not.

  • That the employment of [the word 'is'] as a copula does not necessarily include the affirmation of existence, appears from such a proposition as this: A centaur is a fiction of the poets; where it cannot be possibly implied that a centaur exists, since the proposition itself expressly asserts that the thing has no real existence. (System of Logic I.iv.1)

Note that this section is called 'Of the Import of Propositions', from which, perhaps, the term 'existential import' derives. There is another discussion of the question in Joyce's manual of traditional logic here.

Note also that the distinction between particular (Some A is B) and existential (Some A-B exists) also corresponds to the distinction made by Alexius Meinong in Chapter III of his master work 'On Assumptions', between being so or 'Sosein', and being or 'Sein'. This is not to be confused with his distinction between 'subsistence' and 'existence'.

Monday, January 30, 2006

The Default Position

To me, the following three sentences seem identical

No mountains are golden
There are no golden mountains
Golden mountains do not exist

Brandon writes here:

> On what principles do you make the equivalence of the three the 'default' position?

I reply: on the principle that I don't understand what the other position might be. The default position is simply that I don’t understand the supposed difference between any of the sentences. There is a tendency to to assume that there is a clearly understood and definable difference between so-called 'existential' and 'quantifier' uses. I don’t understand it. Someone please explain it. (See my related posting on Alan Rhoda's attempt to explain it).

Indeed, it is difficult to have the argument unless we assume these formulations say the same thing. Brandon says 'There is a way of looking at the problem such that it's false to say that 'of course' there are no nonexistent objects'. I take him to be asserting the existence of a certain way of looking at the problem. He says 'There is a way …', and I deny the existence of such a way. I could not deny this without the default position that 'such a way does not exist' contradicts his assertion 'there is a way'.

He says that 'nothing about a quantifier requires that it import existence'. But this is itself a quantifier sentence denying the existence of anything about a quantifier that signifies existence. His point seems self-refuting, for to understand it at all is to understand it – a quantifier sentence - as denying existence.

In summary The default position is that the sentence 'there is a default position' asserts the existence of a default position. If you deny this, you have accepted the default position.

Quidquid latine dictum sit, altum videtur

I argued (commenting in Alan Rhoda's weblog here) that

(1) It is possible that there are unicorns.

does not imply

(2) There are unicorns

Alan disputes this, arguing that (1) can be formalised

(3) (∃w)(Ww & (∃x)(xEw & Ux))

But how do we translate this formalisation? If it translates 'it is possible that there are unicorns' we still can't infer that there are unicorns. The 'that' clause acts, as it is designed to, to protect us from any inference as to the truth of the statement embedded in the clause (just as it protects us from inferring 'there are unicorns' from 'Jack thinks that there are unicorns'. If, on the other hand, we translate it as

(3') There is a possible-world, and there are unicorns, such that the unicorns are in that world

then this does logically imply there are unicorns. But that is because the translation strips out the 'that' clause. Which begs the question. If we are allowed to translate 'it is possible there are unicorns', which does not imply there are unicorns, by a sentence that contains 'there are unicorns' as a logical component, and which does for that reason imply there are unicorns, then Alan has pulled off the trick. But are we allowed to?

Whatever is said in formal logic, seems deep.

Sunday, January 29, 2006

Meinongian Objects

Brandon writes here:
  • For the Meinongian solution to negative existentials -- i.e., that there are nonexistent objects independent of thought -- is a very elegant one. It's usually accused of 'ontological extravagance', but I don't think most people have much of an idea what they mean by phrases like that.

I would accuse it of ontological extravagance for the following reason: it claims that "there are" nonexistent objects. But of course there aren't.

An 'ontological claim' is just a fancy expression that there are (or there aren't) things of a certain kind. There are no non-existent things, because to say that unicorns are non-existent is just another, clearly confusing to some, way of saying that there are no unicorns.

Tuesday, January 24, 2006

On the spelling of Ocham

Someone queried this but, yes, that spelling is fine. At least, that is how the Latin texts do it. (Indeed, a good way to locate Latin commentaries on Ocham is to Google it like that).
'Ockham' is of course better known (as is 'Occam'). But who can say which is right. 'Ockham' is the spelling of the picturesque Surrey village where the man is supposed to come from. Yet even that is uncertain. He may have come from 'Oak Ham' or Woking, which is not picturesque at all, being one of those many old English towns that somehow got annihilated in the twentieth century when the councils improved them with monstrous brown brick shopping malls and ring roads & dreaded pedestrian precincts filled with litter and other undesirable things.

Things such that there are no such things

Alan Rhoda argues as follows:

'In one sense of the word, to say something "exists" is to say that it is actual or real. But that can't be the sense implied when we say that something "is" possible but non-actual or that something "is" impossible because both of those categories exclude actuality. So we have to recognize at least one additional sense of "exists" besides "is actual"'.

Do we have to? I'm sceptical. Here's Alan's argument in a nutshell.

(A) Things such as unicorns are possible, though there aren't such things
(B) There are some things which are possible, though there aren't such things

I suppose we have to admit (A) for the same reason we have to admit 'Some of Jane Austen's characters are working class'. But (B) seems to imply

(C) There are such things, such that there are no such things.
I'm not sure I want to admit that. Certainly Meinong said 'Those who like paradoxical modes of expression could very well say "There are objects of which it is true to say there are no such objects'. But then he would, wouldn't he? And it is paradoxical.

Saturday, January 21, 2006

London Calling!!

I thought I would never start a 'blog', for a number of reasons. (i) The name is off-putting (blob, glob, bog, gob). (ii) It is probably an American invention. (iii) It is really a sort of electronic diary, and so belongs in the same box with holiday pictures, amateur novels, school rock bands, drunken confessions, children's poetry, buskers &c. (iv) I have no political opinions, apart from a dislike of George Bush's accent, and a suspicion of high taxes.

Where to start? The most interesting thing that happened today was a whale got beached on the river by Battersea bridge, so the whole town trooped down to have a look. But we missed even that, being forced to spend a afternoon of stultifying boredom at the bathroom shop looking at different sorts of taps. And what was wrong with the old bathroom I ask? Apart from the fact the ceiling fell in, it was fine.

Anyway, more to come. A bit of bathroom news, certainly. I hope to attract an international audience with this, many of whom will be unaware of the London plumbing crisis. You will learn many interesting things. For example, the lady having clinched the deal on the overpriced goods, we learn the assorted hardware will be arriving on the 30 March on a 'tailgate service'. For the uninitiated, this means the lorry driver dumps it all on the pavement and refuses to carry it up the steps or anywhere the place it is meant to go, i.e. the bathroom. Apparently the plumber deals with it from the doorstep onwards. But this being London, the plumber will not be there.

In parallel with this, there is the sewage crisis in our road. This is apparently unconnected with the bathroom problem, a part of the main sewer having fallen in, and so blocking the drains of all the houses from 2-10. So the stuff you send down the pipes all comes back, just like the Amityville horror. But more on that later.
Other bits and pieces to watch out for: philosophy, a dash of malt whisky and a bar or two of Louis Armstrong.

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