Briefly offline

I will be avoiding the internet for a week, possibly two, in order to concentrate on writing the new book.  I wish all my readers a happy and fulfilling summer break.

The Afterlife

Maverick posts about The Afterlife.  Giles Fraser used to go on in this vein, saying how the perfect life would become boring after a long while.  All pleasure is cloying*, eventually we will long for the 'true death' of total annihilation, assuming true annihilation is logically possible. 

I disagree. Giles would always use golf as an example. Of course, how could even a week of golf not induce disgust and nausea.  But I could easily endure an infinity of the life that I find good.  Namely, rising at an early hour with the chirping of the birds, in the crisp purity of the morning.  A fine breakfast served by pleasant staff - strong coffee and orange juice.  Repair to a table in the verandah of a magnificient house fronting onto a lake filled with all kinds of wildlife (not of the dangerous kind).  Four of five hours of concentrated philosophical and logical speculation, enough to fill a chapter or two of an infinitely long work. 

A walk in the afternoon to admire the beauties of nature, then return to the verandah to enjoy the finest single malt (or two) while watching the sunset over the lake. An evening with wife and friends, and a fine cigar (there are no carcinogens in heaven).  Repeat endlessly, with infinite variations on that theme.  This is of course a form of the 'spiritual materialism' that the Maverick (and Giles) abhor in their different ways, but I don't altogether see the problem with it.

*producing distaste or disgust after too much of something originally pleasant

Argument by analogy and copyright infringement

There's an interesting argument on Jimmy Wales Wikipedia talk page, that deserves the attention of logicians. Jimmy has organised a petition against the extradition of Richard O'Dwyer, the Sheffield student who ran a website linking to and (apparently) streaming copyrighted material. Some called 'Incu Master' argues

If someone facilitates credit card fraud, using the credit card numbers of US citizens, helping US citizens commit fraud against other US citizens, and taking a cut of the "profits", while running a website served out of Sweden from his/her home in the UK, and gets extradited to the US, would you be writing a petition to stop the extradition? It seems you are saying there is something special about copyright law in this regard, and I don't understand it because you seem to agree that copyright infringement is, and should be, illegal. Incu Master (talk) 14:10, 26 June 2012 (UTC)

Jimmy replies

I think one question that has been raised repeatedly in this thread is one that makes no sense. No, I would not launch a petition to save someone from extradition for credit card fraud. But you can't conclude from that anything about my position on credit card fraud or how bad it is relative to copyright infringement nor how I privately think credit card fraud should be dealt with legally, etc. For a variety of reasons, demands on my time among them, I don't take a personal interest in every issue on earth. I am not particularly knowledgeable about the laws surrounding credit card fraud, nor do I have any particular reason to become interested. I am not interested enough in the issue to get involved at all. Nor would the general public be particularly interested in my views on the matter, as I am not known in that field.--Jimbo Wales (talk) 12:18, 28 June 2012 (UTC)

I don't follow his reply. Incu's argument is a version of 'argument from analogy'. Here are two similar cases X and Y. Why is your judgment about X so different from your judgment about Y, given the formal similarity between them? Facilitating credit card theft is illegal in both countries, and merits extradition. Facilitating copyright theft is illegal in both countries, and merits extradition. If you don't organise petitions against one, then logically you don't organise petitions against the other. Jimbo's reply is that there is a difference, namely he doesn't have an interest in credit card fraud, and that he is not particularly knowledgeable about it. So, logically, and given that he does regard facilitating copyright theft as illegal, it is OK to organise petitions against extradition for illegal activities, so long as you have an interest in it, and you are particularly knowledgeable about it?

Technological determinism and the naturalistic fallacy

Sorry for the long title.  'Technological determinism' is the view that the Internet is an unstoppable force (for good) and that trying to close down piracy sites such as Pirate Bay and TVShack will just lead to them being reopened elsewhere.  Implicit (often explicit) in this view is that this force is on the side of good, and right and so on.  A victory of the People against the Man.  The naturalistic fallacy is the fallacy that because something is the case, it ought to be the case.   Though it does not invoke the fallacy, this very nice site here explains it very well in the context of the 'free culture' or 'piracy' movement.

Yes. It is technologically easy to:

• Drive 120 miles an hour.
• Use someone else’s credit card to purchase goods online.
• Log into someone else’s bank account and transfer money to yourself.
• Shoot someone with a gun.

This does not imply that it is right to do so.

Free culture looters

The stupid Internet is buzzing about the case of Richard O'Dwyer, a 24 year old British student at Sheffield University in the UK, who is facing extradition to the USA and up to ten years in prison, for creating a website – TVShack.net – which linked to places to watch TV and movies online. The pro-piracy chief of Wikipedia, Jimmy Wales, writes in the Guardian. Phrases like "encroachments on our civil liberties in the interests of the moguls of Hollywood" are chock-full of power words like 'moguls', 'civil liberties', 'interests' and so on. But as I commented here, the piracy dispute is essentially between the hugely powerful advertising industry and the hugely powerful entertainment industry. Obviously content creators have their civil liberties too. This writer put it well*.

What the corporate backed Free Culture movement is asking us to do is analogous to changing our morality and principles to allow the equivalent of looting. Say there is a neighborhood in your local big city. Let’s call it The ‘Net. In this neighborhood there are record stores. Because of some antiquated laws, The ‘Net was never assigned a police force. So in this neighborhood people simply loot all the products from the shelves of the record store. People know it’s wrong, but they do it because they know they will rarely be punished for doing so. What the commercial Free Culture movement (see the “hybrid economy”) is saying is that instead of putting a police force in this neighborhood we should simply change our values and morality to accept this behavior. We should change our morality and ethics to accept looting because it is simply possible to get away with it. And nothing says freedom like getting away with it, right?

By analogy, what O'Dywer was doing (as someone has already pointed out in a comment on Jimmy's post), was running a site where people could post up the location of the shops where the owners were absent, and had poor security locks, or open windows, so that the looters could go there as well. So I am not impressed with the claim that "I wasn't a looter myself".

Jimmy also discusses it on Wikipedia, where he objects to a mischievous claim that the Wikipedia's pro-piracy and looting-support vote back in January was by IPs or newly-registered accounts. ("Spirits from the vasty deeps"). As I commented in January, there certainly was a significant amount of voting of this kind.

*Link fixed.

Getting the Londoners' goat

A post yesterday by the Maverick which is 'guaranteed to get London Ed's goat'. The argument he alludes to can be summarised as follows:

Brian Wilson's song says that there is a girl called Rhonda
The song does not say how tall she was
Therefore there is someone (Rhonda) who is indeterminate with respect to the property of being tall

He ends "The record will show that I myself eschew Meinongianism". It's a mystery to us Londoners.

Web 2ology

Web 2.0 prophet Cory Doctorow has been awarded an honorary doctorate in computer science from the Open University. He writes

Networks -- by which I mean the Internet, which is like some ancient god with a thousand faces and guises, but which is actually a single, sprawling network that appears to different people and societies in different garb -- are the most significant means of changing our social circumstances. The UK Champion for Digital Inclusion, Martha Lane Fox, commissioned a PriceWaterhouseCooper study on the impact of Internet access on the poorest and most vulnerable families in the UK. The study concluded that families with network access have better outcomes on every social axis, from nutrition to employment, from education and social mobility to civil engagement and political awareness. Simply put, the Internet is a single wire that delivers freedom of speech, freedom of assembly, freedom of the press, and access to nutrition, education, employment, politics, and community.

This may be tongue in cheek or some kind of joke, but I suspect not. He is serious. I'm sure there is a correlation between quality of housing and income and access to the Internet. But he seems to be saying that the one is the cause of the other. See fallacy of false cause.

It's time we sceptics added another item to our list of 'ologies'. We already have scientology, astrology, reflexology, cosmobiology. What is the 'ology' for the belief in and the study of weird magical properties of the internet?

Are logical truths empirical?

Anthony mentions in his comments here that he holds that logic itself is empirical, whereas I holds (he believes) that knowledge of logic is innate.

Well, I wouldn't exactly describe my position the way he does. I lean towards the Wittgensteinian position that there are no 'logical truths' as such, but rather principles like the Contradiction and Excluded Middle are built into the 'scaffolding' of our language, so that we can't describe them using language, but only show them, as it were. On the idea that 'logic itself is empirical' – by which I assume he means that logical truths are empirical – I don't know what to say. What does 'empirical' mean? If the idea is absurd, how would we demonstrate its absurdity?

Aristotle discussed the problem in book 4 of the Metaphysics. Aquinas' commentary on it is in the Logic Museum here. It includes links to Aristotle's original text.

Time travel and sleep

Some of the commenters on my last post pointed out that time travel itself is not problematic - after all we travel through it, day by day, all the time.  The problem is the discontinuity.  Can one and the same thing 'jump' from one point in time to some future point in time without existing in the time in between?  If so, then since it does not exist at the point just after which it has jumped, and begins to exist again after it has landed.  This seems to violate Locke's maxim.

Some further points to consider.  Dr Who's time actually isn't discontinuous.  He steps into the Tardis, fiddles about with the dashboard and that glass thing that goes up and down, and waits.  Then he opens the door onto a different time, far in the future perhaps.  From his point of view, there is no discontinuity, which only exists from the point of view of someone outside the Tardis.

It's the same with sleep (by which I mean deep sleep).  My consciousness does not exist during sleep. But there is no apparent discontinuity on my side.  I turn out the light, think of sheep, and then the next thing I know there is light underneath the curtains.  Consciousness in its very nature is continuous, and (as I argued in a series of posts around here) it is finite. 

A further problem.  In what sense am 'I' asleep, or unconscious?  If I am my consciousness, and if my consciousness ceases to exist when I am unconscious, how can I be said to be asleep, or unconscious?

Is time travel possible?

Maverick quotes John Locke (great English philosopher and father of the American constitution) on the impossibility of two beginnings of existence, as follows.

When therefore we demand whether anything be the same or no, it refers always to something that existed such a time in such a place, which it was certain, at that instant, was the same with itself, and no other. From whence it follows, that one thing cannot have two beginnings of existence, nor two things one beginning; it being impossible for two things of the same kind to be or exist in the same instant, in the very same place; or one and the same thing in different places.

He infers from this the impossibility of a soul not existing from the death of its body in 1890 (say) to its rebirth in a different body in 1990 (say). Does this also refute the possibility of time travel? Dr Who gets into his trusty police box in 1999 and travels to the year 2101. He lives out the rest of his life in the 22nd century and never travels to the 21st century. Therefore, Dr Who never existed in the 21st century. But he exists at the end of the 20th, and exists again at the beginning of the 22nd. Is this inconsistent with Locke's maxim about the impossibility of two beginnings? It's odd. The maxim seems correct, and it seems impossible that the same thing cannot have two beginnings. It seems almost a logical truth. Yet the impossibility of time travel does not seem a logical truth at all.

Maverick on circularity again

Maverick repeats his circularity argument, which boils down to this:

(*) If concept F is instantiated, then it is instantiated by an individual that exists.

He has still not replied to my detailed critique of his argument, however. My critique, in brief, was that not every sentence of the form of (*) contains a circularity. For example "If a man is a bachelor then he is a bachelor who is unmarried".

I gave another objection here, which he has also clearly ignored. The objection is that if the word 'exists' on the right hand side of this definition

Some philosopher is American = An American philosopher exists

is merely a copula, then we cannot 'descend to singulars' via 'American philosopher' but only via the subject of the left hand side, namely 'philosopher'. Maverick may object that 'exist' is not a copula, in which case I accept his argument – but that does not appear to be his argument.

Maverick discusses my reincarnation post

Maverick discusses my reincarnation post. He has spotted the obvious problem with my hypothesis that an ego can exist for a certain period, then cease to exist, then exist again, citing an 'authority' in his defence.  It is probably easier to read his (elegant and clear) discussion of the problem rather than for me to attempt a garbled summary.

I am looking for scholastic discussion on what happens to souls while they are waiting for the judgment day, so more later. Meanwhile, here is Scotus' discussion in the Ordinatio II distinction 2 on the question of whether an angel (read: soul) can be in two places at one, and here is the same question discussed in the (probably earlier) Lectura.  Maverick defends a similar idea.

[edit] The first argument is that if an angel (or soul) could be in different places, then it would be distant from itself, just as one place is different from another. This is because two things which are together in respect of some third thing, have to be together themselves, and conversely if they are not together, the third thing they are together with would be distant from itself.  He replies, that the third thing to which the first two are compared is not limited in the respect in which the two things are compared to it, as is clear in the case of the soul in the right hand, and the soul in the left hand. The hands are distant from each other, but the soul is not distant from itself. Likewise, God is not distant from himself, and yet those things which are with God here (i.e. in Oxford), and those things which are with God in Rome, are distant from one another.

I'm not clear about the sense in which my soul is 'in' my hand, nor in the sense that God is 'with' someone in Oxford as well as someone in Rome.  Is it the same as the sense in which this blog post is 'with' Bill in Phoenix, as well as with me here?  And with Anthony, David and the other places where my readers are?

On the logical possibility of reincarnation

Anthony asked what logical possibility is.  I'm not sure, but I think a proposition is logically possible if it does not involve or imply a contradiction.  In that sense, is the proposition "I have been reincarnated" logically possible?  Does it fail to involve or imply any contradiction?

I think it is logically possible. The key assumption is that the term 'I' does not refer to my body alone. For being reincarnated means having once had a body that is numerically different from the one I have now.  I say 'numerically different' because obviously my body was qualitatively different from how it is now.  It used to weigh somewhat less, for example.  So, having a body that was numerically different from the one I have now, means not identical to the body I had in 1980, or 1970.  I don't think there is anything in the reference or meaning of 'I' that entails such an identity.

That's not to countenance disembodied egos or anything like that.  The possibility of reincarnation does not require there to be a disembodied referent for 'I'.  But if there are no disembodied egos, and if reincarnation takes place some time after the death of the previous body, there has to be a time when the 'I' does not exist. E.g. suppose my body used to be Napoleon's body. He died in (er, looks in Wikipedia) 1821.  I was born in 19xx. So if that were the case, my ego would have temporarily ceased to exist in 1821, then was recreated in 19xx.

Does that mean I am the same person as Napoleon, if that were true?  On the assumption that two egos cannot own the same body, then yes. Does reincarnation violate any basic non-logical principles, such as the principle of sufficient reason, or Ockham's principle?  More later.

Too schlocky?

Not even the Maverick had the gumption to post a link to a song by Fabian Forte. Nothing too schlocky for this place, however, so here is Gonna Make You Mine.  (Filed under 'kitsch').

Logic and censorship

Can logic help us with arguments about sexual morality, censorship and so on? Only so far it can expose contradictions and fallacies. At some point in any such argument, someone will invoke a principle or universal proposition, and the problem with principles or universal propositions is that they do not allow exceptions. The proposition 'all swans are white' is false so long as there exists one black swan. It's quite binary. So anyone who asserts such a principle cannot allow any exception to it, without modifying it in such a way that it is still a principle, i.e. such that it contains no arbitrary exceptions or modifications or special pleading. For example, the guy arguing here is dangerously close to a principle:

That's how repressive regimes begin. First you start with the sexual content that offends people, then you move on to the religious content, and finally, the political content. Funny how it's always the people screaming "freedom" and "liberty" the loudest who are always trying to curtail it.

This is called the 'slippery slope' argument. As soon as you are on the slope, you will always slide to the bottom, therefore you must not get onto the slope in the first place. In this person's case, being on the slope means having an image filter on Wikipedia, and the universal principle being "You must not filter out content that offends people". But such a principle allows no exception. Would this person not want to 'filter out' content such as child pornography or torture pornography or snuff pornography?

Philosophical passwords

I've been amusing myself on this site finding out what passwords people used to access the compromised site LinkedIn. Type in a password of choice, such as 'moonshine', and the page computes a 'hash' for that password, then sends the hash to the server database to see if it is there. Hashing is a very clever algorithm which converts a string of letters, i.e. your password, into a long alphanumeric code – the hash. The clever thing is that even if an attacker knows the hash code, and knows the hashing algorithm, they cannot in theory reverse engineer the hash and discover the original password. The algorithm is a so-called 'trapdoor function' that lets you go one way, but not the other. That is, you cannot compute the inverse of the function, even when you know the function.

In theory, that is, because if you choose a simple dictionary word or even a combination of simple dictionary words, it is easy to run a 'brute force' program that hashes every single simple dictionary word, or combination, until it finds a hash that matches. E.g. the SHA1 hash for the word 'moonshine' is befa39749509fd9ab56743e14f9d68d843ea4038, which if you Google it returns any number of sites that managed to crack it.

Testing for philosopher names I see that 'Aristotle' and 'Wittgenstein' and even 'BertrandRussell' were chosen passwords for LinkedIn members. Even, gasp, 'Animaxander'. However 'WilliamOckham' and 'DunsScotus' were not, although a Google search for their hashes shows that one clever site managed to crack them.

The hash for 'consciousness' is e02c4a06f389ccdd0f5682e257af382928ce3110

Do I use philosophical passwords? No.

Consciousness and reincarnation

Anthony objects that where one was born is a matter of biology and circumstance. Well, if it is a necessary or logical truth that the referent of 'I' or 'myself' is identical with my body, then of course. But suppose it isn't – and I can't see any reason why it should be. Suppose, for example, that reincarnation is possible. That means that I, me, myself could be re-born after my bodily death into a different body, and some indeterminate future point in time. Then biology could not explain why I was reborn with that particular body, in that particular place, at that particular time. Obviously biology would explain why that body had the parents it happened to have, and why it had the particular DNA it had. But biology could not explain why I, the person I am referring to now by the personal pronoun 'I', was reborn in that body.

Contra: perhaps it isn't logically possible, on account of the principle of sufficient reason. The principle says that there must always be a reason why something happens one way rather than another. But there is no conceivable reason why I should be reborn in one body rather than another. To be sure, there are religious views about karma that attempt to give reasons for a particular kind of rebirth. But these are hardly scientific, i.e. as far as I know they are not based in unassailable principles known per se and aided by logic.

Reply: But then we are back to the original question: if there is no reason to explain why anyone should be reborn - i.e. born again – in one body rather than another, there is no reason to explain why anyone is born – i.e. born the first time – in one body rather than another. The principle of sufficient reason does not, on its own, establish that reincarnation is logically impossible.

Is slavery harmful?

Larry Sanger's recent post brought out the usual idiotic comments. But some thoughtful and clever comments too, in particular from someone called 'Carl Gombrich' who I suspect is the grandson of E.H. Gombrich. Some asked for evidence which supports Larry's implicit assumption that pornography is harmful to children. Gombrich replies, asking whether there is any evidence that slavery is harmful.

[…] as far as I know there is nothing we could really call evidence to show that slavery is bad, either collectively or for individuals kept as slaves. Are those refusing to move on restricting the access of children to pornography therefore in favour of legalising slavery until we have ‘evidence’ (presumably a longitudinal study over many years involving several hundred people, control groups etc) to show that slavery is harmful? Specifically that it is so harmful to individuals that it should therefore be outlawed? If they do not advocate such a move, why don’t they? That is the logic of the position: no evidence, no move.

But the important point is that slavery is bad, and the argument that it is bad was successfully made on moral grounds by previous generations in the West. That is why it is outlawed in many countries.

Now ask: is it better or worse for children to come across hardcore pornography? We are talking children, not adolescents searching out of curiosity or for arousal, but children, for whom sexuality is a very different thing. I would like to know the libertarian answer to this question. If you think it is better that children do not see hardcore pornography, then we should something about the fact that, increasingly, many of them do.

Conscious and the existence of consciousness

I'm beginning to think that my earlier idea that the entire universe had been created this morning was somewhat fanciful and implausible. It was immediately rejected by some commenters, by one of them on the grounds that there has to be a sufficient reason why the world was created this morning (together with a lot of stuff that makes it appear to be much older than one day old, such as dinosaur bones).

OK, but that's a different supposition from the idea that the world always existed, but that my consciousness came into existence this morning.  Here's my puzzle. The world has existed for billions of years, and if consciousness exists at all, there must have been millions or billions of conscious beings.  If my consciousness began to exist in 1955, why then?  Why not in Victorian times?  Why in England?  Why not in the future?  It's completely bizarre, and against the principle of sufficient reason.  And if that principle cannot disprove my consciousness coming to exist in 1955, why should it disprove my coming to exist on 6 June 2012?

Why can't we suppose that my consciousness before this morning was embedded in President Obama, but that all my memories as Obama were wiped out and replaced by 'my' memories?  Perhaps 'my' memories were really Obama's, but they were wiped out and replaced Obama memories when he moved to Obama's body.

This arose out of a conversation with my wife, who was wondering whether reincarnation was a good idea, given that you might be reincarnated as someone who had a tattoo, or a body piercing. I replied that in that case, you would be born with a mindset that liked a tattoo, or a body piercing.  She said that was even worse. I wonder if Maverick has an answer to this, as he usually does.

Direct reference and existence

Maverick asked me the other day what connection could possibly be between the theory of direct reference and existence. Well, there is certainly a connection between direct reference and the verb 'exists'. If the direct reference theory is correct, then this verb cannot take a singular term as a subject. So we can say 'An American philosopher exists', meaning that 'philosopher' is truly predicated of at least one singular term referring to an American, (e.g. 'William Lane Craig'). But we can't say 'William Lane Craig exists', because it is ill-formed. We can predicate 'exists' of general terms only. See the argument I gave here.

The direct reference theory is not to be confused with 'linguistic idealism' – whatever that is. The theory does not deny there is any 'extra linguistic reality'. It simply denies that 'William Lane Craig exists' is meaningful, in the strictest sense of 'meaningful'. If it means anything, the sentence means that the proper name 'William Lane Craig' refers to something. But if it referred to nothing, it would not be a proper name – for the direct reference theory says that whatever counts as a proper name must be meaningful (as opposed to a string of letters or an utterance), and that its meaning is what it refers to. Therefore if the utterance refers to nothing, it means nothing, and so cannot be a proper name. And the fact it refers to something guarantees that it refers to something in 'extra linguistic reality'.

As far 'existence', which is an abstract noun formed from the verb 'exists' – well, 'The existence of William Lane Craig' presumably alludes to the fact that 'William Lane Craig' refers to something. Simple.

Consciousness and existence

Sometimes I ponder on the possibility of being born again into a different existence, without any memory (if materialism is correct) of my previous existence in this life here and now.

Then it occurred to me, on waking up this morning, that perhaps this had already happened, and that today was the first day of my conscious existence.  To be sure, I have the recollection of a previous existence in this body, and there is a whole list of posts on this blog that I have been maintaining since 2006.  But that could just be an implanted set of memories.

Perhaps the whole world was created today?  Does anyone here have any evidence otherwise?

Success

So we drove down the A3, whizzing past the village of Ockham, where the real Ockham (reputedly) once lived, and aimed for the wilds.  We reached Tilford, which is itself in a pretty rural part, and made enquiries with neighbours.  There was a full-blown cricket match taking place on the green, and a ball landed a few feet away from where we were parked.

Then down a minor road for a few miles, ask some more neighbours, and we head down a dirt track for a while.  And - right at the end of the track, just before you head into a dark pine wood with goblins - there it was.  The house where Bertrand Russell wrote the early parts of Principia Mathematica.  It is the place where he wrote this letter to Frege.

Russell moved there early in 1904 for the seclusion and have the freedom to think.  He was still with his first wife Alys, who he treated pretty badly.  He moved back to London (Ralston St, Chelsea) at the end of the year, so the letter to Frege (dated December 1904) must have been the last time he stayed in Tilford.

Neither the present occupier, who kindly showed me around, nor the neighbours knew of the Russell connection. However, the Hindhead area seems to have been a sort of writers' colony in the early twentieth century. Shaw lived there, as did the somewhat different writers J.M. Barrie and Conan Doyle.  Harold Joachim, who wrote The Nature of Truth, and who coined the term 'Correspondence Theory' lived in High Pitfold just down the road, as did Russell's uncle Rollo.

I will ask the current owner if I can publish photos of the house itself - he was intrigued by the connection - but meanwhile there is a picture of the garden above, nicely set in splendid 4 acre grounds.  Just the thing to look at while you are working on the theory of types.

Quidam philosophus Americanus est

Yesterday we looked at the argument from descent to singulars.  There are two ways of descent, depending on whether we take the right hand or the left hand side of the definition below:

Some American philosopher exists = Some philosopher is American

If we take the right hand, we range over every philosopher and test whether they are American.  E.g., we ask whether Quine is American.  This test does not explicitly test for 'existence'.  But if we take the left hand, we range over every American philosopher, and test for existence.  This test explicitly invokes the  concept of existence.  E.g. we have to ask whether Quine exists.  Therefore the definition above is circular.  Even though 'exist' isn't explicitly invoked on the right hand side, it is implicitly and irreducibly part of the sentence.

Against, consider the Latin translation of the definition above.

Quidam philosophus Americanus est = Quidam philosophus est Americanus

The only difference is word order. Latin is flexible about word order, as its semantics are given by inflection, unlike in English.  So we can either put the copula 'est' at the end of the sentence, as on the left, or we can interpose it between 'philosophus' and 'Americanus', as on the right.  The semantics, indeed the syntax of the two sentences is identical. What becomes of our argument?  Well, it is invalid because it involves a mistake about logical form. We can only descend via the subject of a subject-predicate sentence, if all such sentences really have the logical form subject-copula-predicate. We obviously can't pretend that the subject and predicate are really a single subject, and that the copula 'is' is really a predicate.  That was the whole point of Aristotle's remark about 'is' being used as a 'second element', which I discussed here.  Therefore we cannot descend to singulars by ranging over individuals which satisfy subject and predicate together, and the 'descent' argument is invalid.

Against that.  In reply, the Phoenician may object that a sentence like 'Quine exists' (or 'Quine is', if you like) is certainly meaningful. Then either (a) the proper name 'Quine' embeds a hidden subject and predicate Qa-Qb, just like 'American philosopher', and so 'Quine exists' really means 'Qa is Qb'.  But that seems implausible.  Or (b) the verb 'is' is genuinely a predicate, in which case the descent to singulars argument is valid.

PS today I drive to Rushmoor in Surrey, hoping to locate the place where Russell began work on Principia Mathematica, and where he wrote the letter to Frege that I discuss here.   If this is successful, I may return with photographs.

Circularity and descent to singulars

Here’s a different argument for the circularity of the ‘thin conception’ of existence. First, some preliminaries. In scholastic logic (and in modern logic, for that matter) there is an explication of the truth conditions of general statements in terms of singular statements. The universal proposition ‘every man is running’ is explicated as a conjunction of singular statements ‘Socrates is running and Plato is running and .. etc’, where every man who exists is the referent of exactly one proposition in the conjunction. Likewise, the existential proposition ‘some man is running’ is explicated as a disjunction of singular statements thus ‘Socrates is running or Plato is running or .. etc’. This is called ‘descending to singulars’.

With that in mind, let’s consider the thin definition of the term ‘exists’:

(def) ‘Some American philosopher exists’ = ‘Some philosopher is American’

It’s evident that we can descend to singulars in either of two ways. We can take the defininiens statement on the right, and descend to all the singulars falling under ‘philosopher’. For example, suppose the only three living philosophers are Plato, Socrates and Quine. Then the statement on the right explicates to ‘Plato is American or Socrates is American or Quine is American’. Obviously the first two are Greek, so they won’t do, but Quine is American so the disjunction is true.

However, the statement on the left, the statement to be defined, the definiendum is more difficult. We have to take all the singulars falling under ‘American philosopher’, and form a disjunction of the form ‘a exists or …’. Since the only American philosopher in our domain is Quine, that gives ‘Quine exists’. But we can’t define ‘Quine exists’ in terms of any non-existential statement. The problem is that the thin definition of ‘exists’ only works for general existential statements. The defining propositions must have the form ‘some F is G’, which is general. There is no equivalent explication for singular existentials. Therefore the ‘descent to singulars’ proves that we cannot eliminate the term ‘exists’ from our discourse, and the thin conception is therefore circular.

Will that do? Well no, but more tomorrow.