On set construction

Belette asks about rules for ‘constructing’ Ockham sets (osets). It should be noted that there is no sense in which osets are, or need to be ‘constructed’, and in this way osets are fundamentally different from their mathematical counterparts, as should be clear from the following example. Zermelo (1908) says

(A) If a and b are any two objects of the domain, there always exists a set {a, b} containing as elements a and b but no object x distinct from them both

This is a rule (the ‘axiom of pairs’) that tells us that we can ‘construct’ a set {a, b} given the existence of its members a and b. We need this rule because we cannot infer the existence of a mathematical set, an individual object different from either of its two members, from the existence of its members alone. The consequent does not logically follow from the antecedent. In this, by contrast -

(B) If Peter preached in Jerusalem and Paul preached in Jerusalem, then Peter and Paul preached in Jerusalem.

we are not giving a rule for constructing any non-linguistic entity, nor are we making any existence assumptions beyond what is given in the antecedent. (B) simply gives a rule for constructing expressions: it tells us that the consequent means the same thing as the antecedent. Given the propositions ‘Is_F(a) and Is_F(b) and Is_F(c) and …’ the rule allows us to construct the proposition ‘are_F(a and b and c and …)’.

So my question remains. We assume the following

(1) At least one element exists
(2) One element is finite
(3) Any finite x’s and a single element are finite
(4) Any finite x’s are such that there is some y such that y is not one of the x’s.

This does not ‘construct’ anything. Rather, it asserts the existence of certain things. The only things it explicitly asserts are the existence of finite things. For example, it asserts the existence of one thing (the ‘first’ thing). It asserts (by inference) the existence of two things (the first thing plus some y which is not that thing), the existence of three things (the first two things and some other y), all of which are finite. The question is whether from statements 1-4 we can also implicitly infer the existence of infinite things (an infinite oset) in exactly the way that we can infer the existence of Peter and Paul from a statement about Peter and a statement about Paul. Can we construct an expression that refers to all of the elements of the domain? For if we can, it follows that all the elements of the domain exist – whether or not we actually constructed the expression. Peter and Paul exist whether or not we have an expression such as ‘Peter and Paul’. Do all the infinite elements of the domain exist, whether or not we construct the expression ‘all the elements of the domain’?
I hope this makes the problem clearer.

The price and the value of knowledge

Following my earlier comments about the availability of Latin philosophical texts, I found that a version of Wadding’s 1639 edition is available from a Tokyo bookseller.

Here is all you need to know about this edition. It was originally published in 1639. It was reprinted in 1895 by Vives (with minor changes). The Vives was reprinted by Gregg International in 1969, and that is the one for sale here. That’s right, $12,421.83 for a reprint of a reprint. How wrong. There are two values to a material book. One is the value of the knowledge contained in it, and that – in financial terms – should be free. That’s because, to employ a cliché, knowledge – or rather the means of acquiring it - should be free. The other value is the rarity or commodity value of the material book. I don’t mind paying for the latter – the most recent addition to my collection is a 1555 edition of the works of Horace, all of which are available in digital form off the net, but not in a beautiful way that you can look at and touch, and which I am willing to pay for. But paying a large sum for a recent reprint of no real material value, is absurd.

Oddly enough, the Heythrop actually does have the original Wadding 1639, which must be priceless. It is mouldering away in a basement, which flooded a few years ago, causing damage to not a few books. Parts of the Vatican edition are there, also in a bad state, with loose leaves all over the place. Ironically some parts have never been read, still in their uncut state. It is truly absurd that in the information age, this valuable commodity is still being held in material form that cannot be indexed, and which can be easily damaged, lost or stolen. But we have no better system, yet.

What’s up at the Logic Museum

The Logic Museum is now a wiki, although a closed one, meaning not everyone can edit.

It’s still in the experimental stage. It uses Semantic Mediawiki which means pages can be tagged and sorted in the database. This page shows the kinds of queries that can be run. And it includes a text editor that deals with tables better than a standard wiki – parallel non-English vs English texts are a key feature

The principles of the project are set out here, but essentially it is all about bringing key texts to a wider audience. In two ways.

(1) Specialists in medieval philosophy recognise the difficulty of obtaining sources even in Latin editions. Critical edition projects like Bonaventura and Vatican have a limited print run, and not all libraries purchase these. I have access to the finest libraries in London, including the Warburg, which specialises in medieval and renaissance texts, and the Heythrop, which has a separate theology and philosophy library. Even these are missing some of the texts I would like to read, including Mazzarella’s edition of Simon of Faversham, and Scotus’ Quodlibeta. (The British Museum would certainly have copies, but I have so far avoided this institution as a result of previous experience). So a project that brings Latin texts to the Internet would be useful even to specialists.

(2) The second way involves translating these texts into English thus bringing them to a much wider audience.

The technical problems of the Logic Museum are now pretty much solved. The problem of getting it to work as a collaborative project are only starting. Wikipedia proved that crowdsourcing worked to a certain extent – although many of my posts here have been critical of the project, I still strongly believe it achieved something worthwhile and important. However, Wikipedia relies mostly on unskilled volunteers. By contrast, apart from document scanning, most of the skills involved in putting the Logic Museum together involve some sort of specialist skill. There is still no digitiser that understands Latin spelling and grammar. Thus a typical raw output looks like this. Correcting these texts means human spell-checking. Translating the texts into English requires a higher level of expertise. It’s not the grammar which is difficult. Rather, philosophical Latin employs a number of technical terms which are unintelligible even to a specialist in classical Latin. E.g. ‘dicuntur de quolibet’, which means nothing to someone brought up on the Latin of Cicero and Vergil.

Of course there is a large pool of specialist expertise in philosophy and theology departments across the world. But here you have the problem that crowdsourcing is a volunteer activity, whereas academic specialists depend for their career on publications in recognised sources. Actually they volunteer for that also – no one is paid for their contributions to journals, or for published books. The key is ‘recognised source’. Until someone can put on their CV that they have had a Logic Museum translation accepted, it is unlikely that the project will attract much interest from specialists. There is no reason in principle why this should not happen – think of the Logic Museum as potentially a sort of publishing house which has a review and acceptance process identifying which individual made which important contribution to the project.  But setting this up in the right way requires more thought, and more work.

Intuitions about infinity

I must confess my intuition, which rarely lets me down, fails me in the present case.  The question is whether the 'Ockham set' axiom of infinity is possible or not:

(Ockinf) For any x's, there is some y such that y is not one of the x's.

Against: if we can speak of 'any x' in an infinite domain, then surely we can speak of 'all the x's'.  But if the axiom above is true, it follows that we cannot speak of all x's.

For: there is no logical impossibility here. Indeed, if we take x's as being an ordinary mathematical set, the statement corresponds to a version of standard set theory (being part of ZF-inf).  Why should a different in the interpretation of the terms lead to a difference in truth value?

So I shall leave this one for now (but any comments or ideas gratefully accepted).  It's connected with a wider question of whether there could be a nominalist version of set theory, and whether it would differ in any way from standard set theory.

Sentences as names

I regularly visit Vallicella’s place although no longer comment there due to the sometimes alarming responses. Today’s one caught my eye. I stopped right at the first leg of his aporetic triad, and went no further.

1. 'Al is fat' is the name of the fact of Al's being fat.

Come off it. The expression ‘the name of the fact of Al's being fat’ is the name of the fact of Al's being fat. As for 'Al is fat', it names nothing. Although it does express the proposition that Al is fat.

Malezieu and infinite sets

A commenter wondered whether Malezieu's principle (that a number of things - say 20 - exist because the first exists, the second exists,  and so on) applies because there are a finite number of things, and a finite time is all we have to count anything.

I don't think so. First of all, the fact that the first thing exists, the second thing exists, etc., is independent of anyone counting the things.  You object that nominating one of the things as 'first' is arbitrary, and therefore involves human choice.  I reply: take any of the things you like.  Then the fact that this thing exists, and the fact that any other one of the things exist, and the fact that any other one apart from those two exists, etc., ensures that all of them exist, and this fact is independent of any human counting going on.

Moreover, Malezieu's principle, as applied to an infinite universe, is a logical one.  We start with the nominalist assumption that only individual things exist.  We then assume that there are two possible worlds in which every individual in one is identical with some individual in the other.  Malezieu's principle then tells us that any oset of individuals that exists in one world, also exists in the other.  This is a logical consequence of the fact that existence claims relate to individual existence only.

More about Malezieu’s principle

As I have defined an Ockham set or oset, an oset is nothing different from its elements. A term referring to an oset (‘that dozen of eggs’) is referring to all its elements in just the way that a grammatically plural term (‘those 12 eggs’) is referring to them. It just happens to be grammatically singular, and should not be confused with a genuine singular term referring to a thing. It is not a thing, but a number of things (except in the limiting case of the singleton oset, perhaps, which is identical with its only member).

Malezieu’s principle is that if the things exist, then the oset exists. If a exists (singular) and b exists (singular), then a and b exist (plural) , and the oset O (i.e. a and b) exists also. If some or all of the elements do not exist, or cease to exist then the oset does not exist, or ceases to exist, also. The reference of ‘that dozen eggs’ fails as soon as even one egg is broken. This contrasts with set theory, where we have to postulate the existence of a set containing the members.

Thus there cannot be two possible worlds, each of which contains a and b, such that the oset of a and b exists in one possible world, but not the other. This has the following corollary

(M) If an oset exists in one possible world but not another, it follows that at least one of its elements is in the first world, that is not in the other.

This leads to the problem of the infinite universe where there is no oset corresponding to the infinitely many elements. If we allow the possibility at all, it follows from (M) above that there cannot be two possible worlds where any element one is identical with some element in the other, but where the oset of all of them exists in one, but not the other. Either such a world is impossible, or every infinite world is like this. If it is impossible, then Oxinf is not independent – if every finite oset excludes at least one thing, unlike set theory this guarantees the existence of infinite oset. But if it is possible, this rules out infinite osets.

Can any music be really bad?

I have a broad musical taste and there is no music that I entirely dislike.  Often I have wondered whether there is any really bad, irredeemably bad music. Particularly when I found myself watching Last Night of the Proms yesterday evening.  But even there, is it irredeemable?

Remember that music exists to create certain thoughts and emotions in us, thoughts and emotions that would not necessarily be there without it.  Just as sexual desire is in some way beyond our control, in the way that Augustine complained about, so is the emotion created by music.  I cannot listen to this, for example, without emotion.  Yet what is it saying?  That God once visited England, and that we should fight both mentally and physically, with a sword, to establish some weird vision of England in this country? The thoughts are strange, but the music conspires with the words to make them temporarily acceptable.  (Also disturbing is the sight of Victoria Beckham struggling with the words, but that is something else).  If we have a problem with this, we have a problem with all music.  And since we don't have a problem with all music, clearly not, we don't have a problem with this.  Ergo, no music is totally problematic.

Last week I was wondering whether Mickey Gilley's version of "It wasn't God who made honky tonk angels" had finally got us there.  It is exceptionally bad, in fact so bad that there is no version of it on YouTube (ponder that for a moment).  But then the original version by Kitty Wells is tolerable, and the version by Patsy Cline brings us close to the sublime.

So forget the words - songs are just bad poetry redeemed by music.  Is there any music that is simply too bad to be saved?

Independence of the axiom of infinity

In my last post, I introduced the 'Ockham' version of the axiom of infinity

(Ockinf) For any X's, there is some y such that y is not one of the X's.

which, for a suitable definition of infinity, gives us an infinitely large universe, but no infinitely large Ockham set to correspond to it.  Every Ockham set is finite, yet the universe is infinite.  As 'Belette' has spotted, this may be no surprise, for it is well known that the axiom of infinity cannot be derived from the rest of the axioms of Zermelo Fraenkel set theory, and we can even construct a model of the axioms where the axiom of infinity is replaced by its negation (called ZF-INF).

But it is not so simple as that, and I will complete my argument by returning to the point I made in my first post on this subject, about the difference between Ockham sets and mathematical ones.  The key difference is that, given the existence of the elements corresponding to an Ockham set, the set itself has to exist, for the set is identical with its members.  This is Malezieu's principle: if twenty men exist, it is because the first, the second, the third man etc., exist.  If a exists and b exists, then the Ockham set a and b exists also.  By contrast, in set theory we have to posit this using an axiom such as the axiom of pairs.

Thus, given a universe with an infinite number of elements but no oset corresponding to them, can we wave a magic wand and bring that corresponding oset into existence, as we can easily do in ordinary set theory?  I suggest we can't.  For an oset simply is its members.  If we bring an oset into existence, we must bring at least one of its elements into existence. But we can't do that here. By hypothesis, every member of the infinitely large universe exists already. What is lacking is the oset of all of them. If we now create the oset, what exactly are we creating?  Nothing.  There are no things to create, for they are already there.  Nor can we suppose that there is any other possible universe corresponding to this possible one, containing identical elements, but also containing the oset itself.  So, if a universe consisting of these elements is possible, it is necessarily the case that there is no oset containing all its elements.  And in general, there can be no universe containing an infinite number of elements, together with the oset of all of them.  If every possible world is such that p, then necessarily p.

This is a surprising result.  The alternative is to reject (Ockinf) above, and thus reject the possibility of an infinite universe without a corresponding oset. But that is equally surprising, for it would amount to rejecting the independence of the axiom of infinity.  We could merely define 'finite oset' as we did before, assert that to every finite oset there is an (equally finite) oset containing one extra element, and then deduce the existence of an infinite oset, based on the logical impossibility of (Ockinf) above.

Comments welcome.

Ockham sets: preliminaries

Judging by the comments from 'Belette', we need some preliminary remarks about Ockham sets. Let's begin with plural reference. In English (and Latin, and probably most natural languages) we have plural terms as well as singular terms. We can form plurals either by concatenating singular terms together, as in 'Peter and Paul'. Or we can use an ordinary plural referring term, as in 'those [two] apostles'. Both of these take verbs in the plural form. Thus "Peter and Paul are apostles", "those apostles are preachers". Finally, we can form a collective noun of the form 'an X [of] Ys'. Thus 'a dozen apostles', 'a pair of shoes' and so on. These nouns are grammatically singular, and usually take verbs in the singular. Thus "a pair of shoes is in the cupboard", "one dozen eggs is a good thing to buy". (Although intuitions differ. Do we say that a number of people are in the room? Or is in the room? But this is merely grammatical accident, and has no relevance to logic, I think).

It is a fundamental assumption of Ockham set theory that the singular form of the collective noun is a grammatical feature only, not a logical one, and that we can assert identities using all three forms of plural noun. Thus

1. Peter and Paul are these apostles.
2. These apostles are a couple of apostles
3. This couple of apostles is [or are] Peter and Paul.

The equivalent to a mathematical set containing more than one member, say {Peter, Paul}, is the reference of the expression formed by concatenating the two proper names with 'and'. Thus 'Peter and Paul'. The equivalent to a set defined by comprehension, e.g {x: apostle(x)}, would be the reference of the plural referring term '[all] the apostles'.

There is no real equivalent to the singleton set {Peter}, because the comma in set notation corresponds to the 'and' in Ockham notation, and once we remove the 'and' from 'Peter and Paul', we are left with 'Peter'. Thus in Ockham set theory, {Peter} = Peter, if that makes any sense. Remember that the curly brace is set theoretical notation, and has no equivalent in natural language. Ockham set theory is meant to capture our logical intuitions about the behaviour of plural and collective nouns in ordinary language, not some invented language like set theoretical notation with modern predicate logic.

There cannot be an empty set in Ockham. Once we remove the name 'Peter' from the expression " 'Peter' ", we are left with nothing at all. An Ockham set is identical with its members, and it is impossible that something is identical with nothing.

Set membership is signified in Ockham by the relational term 'one of'. This can be defined in terms of the primitive 'and' mentioned above, as follows.

a is one of Xs if (def) for some Ys, Xs = a and Ys

For example, let the Xs be Peter and Paul and John. Then there are clearly Ys, namely Paul and John, such that

Xs = Peter and Ys.

I.e. Peter is one of those three persons, Peter and Paul and John.

Belette also asked for a definition of 'infinity'. Let's try starting with 'finity' first, by the recursive definition.

1. Any one thing is finite in number
2. If any Xs are finite in number, then those Xs and any one y are also finite in number.

Thus Peter is finite in number, hence Peter and Paul are finite in number, hence Peter and Paul and John are finite in number, and so on.

Then I say that there are 'finitely many things' when there exists an oset O such that O is finite in number, and such that every thing is one of O. And finally, there are 'infinitely many things' when it is not the case that there are finitely many things. This could happen in two ways. In the first, as I have defined it in the previous post. If every oset is such that at least one thing is not one of it, there cannot be an oset O such that every thing is one of O, and so our condition for finitude fails. Or there can be an oset such that it is not finite, and no finite oset contains everything, and so our condition for finitude fails again. I shall argue that of these two ways in which there could be infinitely many things, only the first is possible.

Ockham sets and infinity

In my previous post about infinity, I distinguished 'Ockham sets' or osets from ordinary mathematical sets.  An Ockham set is like a pair or a dozen.  It is not a thing, but rather a set of things, just as a dozen things is not a thirteenth thing separate from the twelve things it is a dozen of.

Now I shall ask whether it is possible that there could be infinitely many things, without there being an oset of those things.  My aim is to show that while it is possible that there are infinitely many things, it is impossible that there should be an Ockham set of those infinitely many things.  And my first step will be to ask whether it even could be possible that there were infinitely many things, without there being an Ockham set of them.

Assume that at least one thing exists.  Then ask whether the following could be true:

(Ockinf) For any X's, there is some y such that y is not one of the X's.

If it is true, then clearly there are infinitely many things.  For if there were finitely many, we could count through all the things there were, and come to a halt at some point.  Then all the things we had counted would fall within the range of the 'for any X's' above, and there would be at least one y that was not one of the things we had counted, which contradicts the assumption that we had counted all the things.  So there are not finitely many things, if Ockinf is true.  Therefore, if it is true, there are infinitely many things.

But is that even possible?  It is possible in standard set theory. Indeed, there is even a version of set theory where the axiom of infinity is denied.  But is possible in Ockham world?  I believe it is, but it runs counter to our natural assumption that we can talk about or refer to 'all the things there are'. For if the assumption above is possible we can't refer to 'all things'.  Suppose we can.  But the statement above says that for any X's, i.e. for any things whatsoever, there is at least one thing that is not one of them.  Hence there would be at least one thing that was not one of all the things, which is contradictory, for 'all things' includes absolutely everything, leaving no thing out.

You might argue that Ockinf above is impossible, because it is self-evident that, how many things there are, we can always refer to all of them.  But can we?  The statement above denies precisely that.  Is it false in virtue of its meaning?  I don't think so (although I'm not sure either).  Clearly 'any x' must be satisfiable by any x in the domain.  The lasso of a singular variable must be far reaching enough to get its singular loop round any object.  There can't be some x that isn't any x.  But any X's?  The plural variable lasso loops around numbers of objects in the domain.  There can't be some X's that aren't any x's.  But the statement above doesn't claim this.  It says that there are not some plural X's such that they include every singular x.

The lasso of plural quantification is flexible enough to rope around any number of finite things.  But it is not big enough to capture all of infinitely many things.  It will always fall at least one short.  And if we pull it a bit to get that one thing, we find to our frustration that there is yet another one that we missed!

In conclusion, it seems possible that there are infinitely many things, without there being an Ockham set that includes all those things.  Or at least the obvious arguments that would suggest it wasn't possible, are invalid.  In the next post, I shall argue that if this is possible in some domain, then it is so in every domain, i.e. there cannot possibly be any Ockham set that includes infinitely many things.

The Soft Machine

I will post some more about the intriguing thought experiment suggested by Michael Heap. Meanwhile, some music by the Soft Machine from 1967. The group were named after the book by the American writer William Burroughs.  The name itself refers to the human body.  (Michael's thought experiment involves recording the brain states of a person on a computer, thus copying the form of experience encoded in a soft machine made of DNA, onto a hard machine like a computer.

Are there infinite sets?

I shall argue that there are there no infinite sets. Which I shall immediately qualify by distinguishing between mathematical sets, and Ockham sets. A mathematical set is a thing that can contain things. The set {a, b} contains two things – the elements a and b – and is itself a third thing separate from them both. Since I hold that there are no such things as mathematical sets (which I will not argue here, let’s assume that for now), it immediately follows that there are no such things as infinite mathematical sets, but do not worry about that.

An Ockham set, by contrast, is a set of things that is not itself a thing. Let me explain. We speak of ‘a dozen’ or ‘one dozen’ things. If they are dozen, then they are 12. The ‘one’ dozen is not one thing in addition to those 12 things, but rather ‘a dozen’ is a collective noun for twelve things (and nothing else). I claim that there are no infinite Ockham sets.

This may take a few posts, so I will begin with a feature of Ockham sets that does not apply to ordinary (mathematical sets), and which will be essential to my argument. Since an Ockham set is its elements (i.e. the dozen things is or are those twelve things), it follows that if each element exists. I.e. if a exists and b exists, then a and b exist, i.e. the plural expression ‘a and b’ refers to some things. Therefore the Ockham set – the reference of ‘a and b’ or ‘those two things’ or ‘that pair of things’ also exists. If twelve eggs exist, then a dozen eggs exist, and so on. I shall call this Malezieu’s principle, after the French geometer about whom we know almost nothing except what Hume says about him:

I may subjoin another argument proposed by a noted author [Mons. MALEZIEU], which seems to me very strong and beautiful. It is evident, that existence in itself belongs only to unity, and is never applicable to number, but on account of the unites, of which the number is composed. Twenty men may be said to exist; but it is only because one, two, three, four, &c. are existent, and if you deny the existence of the latter, that of the former falls of course. [link]

I.e. if the elements exist, the Ockham set exists. And if the Ockham set does not exist, at least one of its members fails to exist. This principle is not true of ordinary sets. If a is in the domain, and b is also, we need an assumption – the axiom of pairs – that allows us to assume the exist of the ordinary set {a, b} containing as elements a and b, and nothing else.

More tomorrow.

Thought experiment about consciousness

Michael Heap (forensic psychologist and chairman of the Association for Skeptical Enquiry) has sent me the following thought experiment.

You are at the moment taking part in an experiment in which all the activity of your nervous system associated with your conscious experience is being recorded in real time and uploaded onto a computer.  This computer is thus having identical conscious experiences as you - perceptions, thoughts, images, memories, feelings, emotions, pain and so on.   At some point the scientists announce that the experiment is over and they are about turn off the computer.  Do you let them? 

Answers please!

Two senses of ‘formal’

There are two interesting posts by Catarina here and here about the problem of ‘system imprisonment’. This is what happens, she says, when the process of formalising arguments or observations leads to the replacement of real issues by system-generated ones, which are really issues emerging from the formalism being used, and not the underlying or real issue. She says her favorite example here is the issue of 'free variables' in de re modal sentences, which then became seen as a real, deep metaphysical issue.

This is close to some concerns I have aired here over the past year, and I will take this up again in subsequent posts. To begin with, it should be noted that there are at least two senses of the term ‘formalise’.

Formalisation in the strict sense means representing sentences or arguments in any language (usually a natural language like English or, in the case of the medievals, Latin) with schematic letters in place of expressions, in order to display the logical form of the sentence or argument. Thus “every B is C, every A is B, therefore every A is B” represents the form of the ‘Barbara’ syllogism. Every instance of that argument form, i.e. every instance obtained by replacing ‘A’, ‘B’, ‘C’ etc., with common nouns like ‘man’, ‘animal’ and so on, is valid – the premisses cannot be true and the conclusion false. In this sense Aristotle, who seems to have been the first to use such schematic representations, was the originator of formal logic

In another sense, formalisation means the translation of ordinary language sentences into a formal language, usually a calculus with a syntax and vocabulary that does not resemble natural language much at all. Thus, we translate ‘every man is an animal’ into the formal language as (for example) ‘Ax [ man(x) -> animal(x) ]’.

I believe that Catarina means ‘formalisation’ in the second sense. Without formalisation in the first sense, i.e. representing different arguments as having a common ‘valid’ form, it is not clear we could do logic at all. But with formalisation in the second sense, i.e. using a non-natural ‘formal’ language into which metaphysical statements or arguments are translated, we run the risk of being trapped inside that language in the way that Catarina is worried about.

More later.

Was all Wikipedia written before 2008?

Here is an example of the charts I mentioned in my last post. Most of the growth in the article about The Book of Laughter and Forgetting (Milan Kundera) was before February 2008.   And the majority of edits (around February 2008) were by a single account.  Lest we be seduced by the argument that the article has reached some sort of perfect or equilibrium state, note part seven: “The Border” has the tag “This section is empty. You can help by adding to it”, added in January 2011, and not addressed since.

Consider further that the article is only 10kb, which is small compared to a Wikipedia article of any substance, and is fantastically minute compared to the extraordinary List of My Little Pony characters, weighing in at 180k.  At least 'My Little Pony' has bucked the trend.  Editing picked up considerably in 2011.

Who writes Wikipedia?

I hacked together a tool to determine the size and date of each past version of any Wikipedia article, and to chart size against date to determine the growth of the article through time. Then I looked at a sample of articles from the Time ‘100 best English language novels’to determine how these grew through time. The study would need to be formalised and extended if continued to publication, but the initial results are surprising.

I wanted to test the idea discussed here. The official ‘crowdsourcing’ doctrine of Wikipedia is that editors are easily replaceable units of work, each of whose contributions are equally valuable. Supposedly, large numbers of small edits will, over time, make an article 'drift' towards quality and accuracy, even if each individual edit only improves the article imperceptibly. This philosophy has determined the way Wikipedia is administered. Those who perform purely administrative work – categorising, formatting and (mostly) vandal fighting – are rewarded by promotion within the hierarchy. Those who produce content, by contrast, receive no formal recognition, on the crowdsourcing assumption that no one person can be identified with any single article, and that content producers are replaceable anyway.

My study flatly contradicts this official doctrine. Growth in a genuinely crowdsourced article would look like Brownian motion with upward drift, as thousands of minor edits gradually ‘stick’ in a Darwinian competition for survival. This is by no means the case.  In the majority of articles sampled, there is a pronounced ‘staircase’ appearance to the growth of the article. The size increases rapidly, often within a day and a handful of edits. Then it flattens as the changes stabilize, with minor growth for months of years. Then another editor (or often the same one) adds more content and the size grows rapidly, to be followed by another flat period and so on. It is not unusual for an article that has had thousands of edits to have reach its current size through only a handful of real edits. The majority of the other edits are vandalism followed by reversion of vandalism, or minor formatting changes or adding of categories. Many articles have effectively only one editor.

Another observation is that most of the growth occurred in the period from 2004 until 2007-8. What explains this? It is well known that the overall number of Wikipedia editors has been decreasing since then. One theory is that Wikipedia is ‘full up’. Most of the ‘useful knowledge’ has already been captured. So is it that each of the articles about the ‘100 greatest novels’ reached its optimum or ideal length in 2007, and no further work is needed? No. Most of the articles in this series are short – about 10k bytes. But some are longer, and a handful are as large as 80k (which is the longest length an article should be, for practical purposes). So most of the articles are well below the length they could be: Wikipedia articles on great novels are not ‘full up’.

Then could it be that articles about novels have an optimum size, determined by their notability? Well, no. One of the longer articles (60k) is about Hemingway’s classic The Sun Also Rises. This is indisputably a great work, possibly Hemingway’s greatest work. But is it any more notable than the article on Great Expectations, which weighs in at a mere 40k? Or Pride and Prejudice, universally acknowledged to be one of the great classics of English literature (a paltry 36k)? Of course not. The article on Hemingway’s book was written by a single Wikipedia editor, and was a mere stub before he or she got to work on it. Given the small number of editors who work on these articles, a large article reflects an interest by some editor who put in a lot of work to make it that way, rather than genuine notability. A small article is the result of mere chance.

I shall publish some of these charts in subsequent posts.

Augustine on the guilt of babies

‘Belette’ cites the Wikipedia article on original sin, which claims that according to Catholic theology, human beings do not bear any "original guilt" from Adam and Eve's particular sin.

What Catholic theology actually is, is a nice question. But there is no doubt what Augustine says. He argues here (in a polemic against Pelagius) that Adam was created with the intellectual faculties of an adult. After the Fall, by contrast, humans are created in a ‘cloud of ignorance’, i.e. the baby state. This cloud of ignorance lasts far longer than any cloud of drunkenness. If this ignorance is contracted as soon as we are born, “where, when, how, have they by the perpetration of some great iniquity become suddenly implicated in such darkness”, he asks. A new-born child is already guilty of offence.

Seeing now that the soul of an infant fresh from its mother's womb is still the soul of a human being—nay, the soul of a rational creature—not only untaught, but even incapable of instruction, I ask why, or when, or whence, it was plunged into that thick darkness of ignorance in which it lies? If it is man's nature thus to begin, and that nature is not already corrupt, then why was not Adam created thus? Why was he capable of receiving a commandment? And able to give names to his wife, and to all the animal creation? For of her he said, She shall be called Woman; Genesis 2:23 and in respect of the rest we read: Whatsoever Adam called every living creature, that was the name thereof. Genesis 2:19 Whereas this one, although he is ignorant where he is, what he is, by whom created, of what parents born, is already guilty of offense, incapable as yet of receiving a commandment, and so completely involved and overwhelmed in a thick cloud of ignorance, that he cannot be aroused out of his sleep, so as to recognize even these facts; but a time must be patiently awaited, until he can shake off this strange intoxication, as it were, (not indeed in a single night, as even the heaviest drunkenness usually can be, but) little by little, through many months, and even years; and until this be accomplished, we have to bear in little children so many things which we punish in older persons, that we cannot enumerate them. Now, as touching this enormous evil of ignorance and weakness, if in this present life infants have contracted it as soon as they were born, where, when, how, have they by the perpetration of some great iniquity become suddenly implicated in such darkness? On Merit and the Forgiveness of Sins, and the Baptism of Infants Book I, Chapter 67 On the Ignorance of Infants, and Whence It Arises.

Does evolutionary biology refute the doctine of original sin?

Maverick philosopher asks here whether the doctrine of Original Sin is empirically refutable by evolutionary biology. He argues not, because it is absurd to suppose that the doctrine of the Fall 'stands or falls' with the truth of a passage in Genesis literally interpreted. I think he is right if it is the literal interpretation – of original biologically human parents – that is the intended target. But, as I argued earlier, evolutionary biology addresses the ‘spiritual’ interpretation of the Fall also. The doctrine of Original Sin is roughly this:

1. We are beset by a host of evils (e.g. crime, illness, sexual desire) that make our existence in this life wretched.
2. This present wretched state is a punishment.
3. The punishment is for an act committed by distant ancestors.

Interpreting ‘evil’ as a threat to our survival, evolutionary biology explains this as the result of life having evolved by competition for survival. Since competition for survival always involves the danger of extinction, it is only natural that our life should be ‘wretched’ in this sense. (That sexual desire is an evil is a view of Augustine’s that we should leave for later).

The second assumption – that this state is a kind of punishment – is in no way consistent with evolutionary biology. In evolutionary biology, there is no one to mete out punishment. And the third assumption, that we are being punished for something that others did, makes no sense for the same reason. And even if others committed a crime, it violates natural justice to suppose that we should be punished for what they did, without participation or choice in their act.

Augustine’s argument is that since God allows young infants to suffer, original sin must exist. An all-powerful god would not allow innocent beings to suffer, therefore even children cannot be innocent. And since they have done nothing in their own life to merit punishment, it follows that they are being punished for the sins of their distant ancestors. Evolutionary biology entirely rejects this argument, of course.

In summary, evolutionary biology rejects a spiritual, as well as a literal, interpretation of the theological doctrine of original sin.

Ambiguous proper names

Earlier, I suggested that the problem of when a person is thinking about X – which involves the difficult question of empirically unobservable entities such as ‘thoughts’, can be reduced to the apparently simpler problem of when two occurrences of a proper name have the same sense or meaning. Specifically

(*) Tom has a thought about Sherlock Holmes

is true if and only if Tom has a thought which, if expressed, would contain a term synonymous with the name ‘Sherlock Holmes’ as it occurs in the sentence above (*). The problem is now to explain when any occurrence of the name ‘Sherlock Holmes’, has the same meaning as used above. This would be simple question to resolve if proper names always had the same meaning. Clearly in the ‘Sherlock Holmes’ stories it does. Conan Doyle uses it only to refer to the same fictional detective. But as I noted here, there is a living person called 'Sherlock Holmes' (a minister of the church in Massachusetts, America). If Tom is having a thought about the fictional detective, and if by 'Sherlock Holmes' above (*) I mean that person living in Massachusetts, then (*) is false. So how do we determine when proper names are not being used ambiguously? What do we mean by ‘having the same sense’? Isn’t this almost as difficult as explaining when two thoughts are the same?

Genetics and the fall

Maverick philosopher posts here on the fall, arguing that there need be no inconsistency between the Biblical account of man’s fall (which has the world beginning with two human beings, who are then punished by God for an act of sinful pride), and the genetic account, which has human beings beginning with about 10,000 individuals, who in turn were descended from apes.

Genetics may not contradict the Biblical account (assuming a ‘spiritual’ rather than a ‘literal’ account), but it seems to contradict Augustine. As I commented a year ago, Augustine aims to prove that original sin exists, citing the ‘host of cruel ills’ which the world is filled with. These can be restrained by laws and punishments, but law and punishment is itself a means of restraining the evil desires that we are born with. Even great innocence is not a sufficient protection against the evil of this world, for God permits even young infants to be tormented in this life, teaching us ‘to bewail the calamities of this life, and to desire the felicity of the life to come’ (City of God XXII).

But genetics suggests the explanation of this host of cruel ills is not original sin at all. Pain is explained as a self-defence mechanism, teaching us which dangers to avoid. Fear is an awareness and an anticipation of danger – felt as unpleasant because it is the anticipation of something unpleasant (pain or death). That danger exists at all is explained partly by the competition for survival, partly by the fragility of DNA. Likewise death. Genetics and science tell us that no one was responsible for this predicament, in the way that Augustine (and the Bible) tell us that our ancestors (Adam and Eve) were responsible. Now Maverick writes:

But in the encounter with the divine self which first triggered man's personhood or spiritual selfhood, there arose man's freedom and his sense of being a separate self, an ego distinct from God and from other egos. Thus was born pride and self-assertion and egotism. Sensing his quasi-divine status, man asserted himself against the One who had revealed himself, the One who simultaneously called him to a Higher Life but also imposed restrictions and made demands. Man in his pride then made a fateful choice, drunk with the sense of his own power: he decided to go it alone.

But does self-consciousness explain pride and selfishness? Against: if the essence of self-consciousness involves pride and selfishness, and if pride and selfishness are bad, how can self-consciousness be good? Yet surely self-consciousness is good. Moreover, does self-consciousness explain pride and selfishness anyway? Many animals, who are not supposed to be self-conscious, also exhibit pride and selfishness. Indeed, according to Richard Dawkins, a gene is selfishness itself. Its sole aim is to replicate itself. Thus, bacteria and wild yeast and giraffes are selfish.

Masks at the masked ball

There is an interesting discussion here between some of Wikipedia’s dwindling number of competent editors. The complaint is the usual one about the Wikimedia foundation's obsession with the overall number of editors, rather than the quality of work that editors produce. “Certain people associated with the Foundation have been saying for years that it doesn't matter who makes the edits; we are all just masks at the masked ball, and what matters is numbers alone. I suspect they'll start to see the folly of that position, though it may take a few years".

I suspect the Foundation will not see the folly of that position, because of its deep-rooted faith in crowdsourcing. The official teaching of the church of Wikipedia is that editors are easily replaceable units of work, each of whose contributions are equally valuable. Supposedly, large numbers of small edits will, over time, make an article 'drift' towards quality and accuracy, even if each individual edit only improves the article imperceptibly.

But as one of the editors comments (and I am certain she is right) “when the history of Wikipedia is written, we're going to be astonished by the small number of people who created and maintained it”. Another agrees that “crowd-sourcing is largely irrelevant, as most articles are edited by very few editors, often only two or three, which is hardly a crowd, and almost all of the content often comes from only one or two editors”.

This is almost certainly true. Good articles are written by a handful of good editors. The same is true of bad articles, which are nearly always the result of a single spectularly incompetent and inept author writing a personal essay about a favourite subject. See e..g Intellectual history (“The concept of the intellectual is relatively recent”) almost entirely written by this chap. Or how about the really awful History of Europe, quite an important subject, you would think, and deserving of thoughtful treatment, but contains such gems as “During this time many Lords and Nobles ruled the church. The Monks of Cluny worked hard to establish a church where there were no Lords or Nobles ruling it. They succeeded”.

Nor does the crowd always pick up even the easily correctable mistakes. In May 2005, someone claimed that Belgian businessman Georges Jacobs (born in the late 1940s) was a commander of the Waffen SS's 28th SS Volunteer Grenadier Division Wallonien (presumably disbanded in 1945). The claim was removed only recently (August 2010), and so had been there 6 years without any of the ‘crowd’ noticing.

But then why are the masks complaining, while they continue to edit Wikipedia?  The whole experiment only appears to work while these poorly rewarded individuals fight a losing battle against a tidal wave of vandalism and illiteracy.  They need to stop fighting, get a life, and watch Wikipedia work out a solution for itself.  (And if Connolley is reading this, that means him too).

More on predicate logic and direct reference

David Brightly asks here whether modern predicate logic (MPL) in fact rests on ‘weak’ (relativistic) reference, not strong (direct) reference. He appeals to the way that singular sentences in MPL seem to have a meaning even when the singular term is empty.

There are a number of connected reasons why this won’t work. Here are the main characteristics of the relativistic logic (RL) I have defended here.

• In RL there are two forms of negation for singular sentences. There is a narrow form ‘nonF(a)’, which is true when a exists and it is not the case that Fa, i.e. a is a nonF; and a wide form, which is true when either nonF(a), or when a does not exist. Excluded middle applies only to the wide form, naturally. By contrast, MPL has no such feature.
• In RL, a sentence of the form ‘An S is P’ has a narrow existential sense: it is convertible with ‘An S-P exists’. There is no distinction between a wide sense conveyed by ‘some’, and the narrow sense conveyed by ‘exist’. RL is not Meinongian. By contrast, it is open to MPL to invent an existence predicate ‘E()’, which may satisfied by some members of the domain, but not by others.
• As a direct consequence, in RL, the wide negation ‘it is not the case that Fa’ never implies the existential form ‘some x is non-F’. By contrast, in MPL a singular sentence is existential, at least in the wide sense: ‘~Fa’ implies ‘Ex ~Fx’.
• A further difference, though probably not relevant here, is that some relational statements in RL are not existential. ‘aRb’ does not always imply ‘Ex aRx’, namely in the case where ‘R’ is not logically transitive. This is how RL avoids the problem of intentionality without invoking Meinongian non-existent objects.

The net result is that if a singular sentence in MPL cannot be empty in the sense required by RL. Let ‘v’ be a term that purports to denote Vulcan (a non-existent planet). Then either Vulcan lies within the orbit of Mercury - OM(v), or not - ~OM(v). The problem is the negation. If ~OM(v), standard predicate logic implies Ex ~Fx. But that leads to Meinongianism, i.e. positing objects that do not exist, and this, as I have argued, is a form of direct reference. Direct reference is the thesis that if ‘Fa’ is meaningful, then ‘a’ refers to something - possibly a non-existent something.

Another argument: how can we even say in MPL that Vulcan does not exist? The sentence ‘~Ex x=v’ will not do, for it asserts of something in the domain that it is not in the domain; ‘~E(v)’ will do, where ‘E’ means ‘exists’, but this comes at the price of Meinong’s junkyard. For ‘~E(v)’ implies ‘Ex ~E(x)’, which is precisely Meinongianism. Or it can be denied that ‘OM(v)’ means anything at all, which is strong Direct Reference of the familiar variety. There is no escape. Either we adopt a radically different semantics and inference schemata, on the lines of RL above, or we are left with Direct Reference.

Google takes up Latin

I was excited when I saw that the Google translator now includes Latin, and immediately gave it an untranslated section of the Logic Museum to look at.  Results below.  Not promising, sadly, so I am stuck with the tedious manual method for the moment.

Logic Museum	Google
Fit autem fallacia consequentis vel arguendo ex propositionibus quarum una sequitur ad aliam et non e converso; vel arguendo ex una condicionali ad aliam condicionalem in qua oppositum antecedentis primae condicionalis ponitur antecedens et oppositum consequentis primae condicionalis ponitur loco consequentis.	Or by arguing the fallacy of the consequent becomes one of which follows from propositions to another and not vice versa, or by arguing on the one in which the opposite of the antecedent of the first conditional to another conditional is placed opposite of the consequent of the first antecedent and the consequent CONDITIONAL place is placed.

Is God fair to scientists?

Is God fair? We have to assume that God will punish, harshly, those who do not believe his word. In which case, why did God design the universe in such a way that those of an intelligent and inquisitive disposition would conclude that the universe was not designed by God in the way he said he designed it?

Take the case of epicycles, of which ‘Belette’ comments.

“The massive difference, now, over say Copernican days is that the observations and calculating ability we have are so much better than before. It is no longer possible tlo believe in epicycles, because observations demonstrate clearly that they don't work, except in the trivial sense that any path can be fit by enough epicycles to an arbitrary degree of precision.”

I agree. One of Galileo’s motivations for his heliocentric theory was his observation of the phases of Venus. These cannot be observed properly without a telescope. Venus is lit by the sun from angles that are not consistent with the Ptolemaic system. There is a good explanation of this in the Wikipedia article on the Ptolemaic system. Why did God design the geocentric system in such a complex way that those of an inquisitive disposition, after inventing telescopes, would observe such apparent inconsistencies? In 1838, Friedrich Wilhelm Bessel successfully measured the parallax of the star 61 Cygni, which is also difficult to explain in the geocentric system. Why did God go to the trouble of designing the geocentric universe in such a complicated way that an detailed observations such those of Bessel appeared to contradict the way God said (in the Bible) that he had in fact designed things?

Note, I am not arguing that the geocentric model is wrong. What I mean is that, if God says it is correct, and if, as seems to be the case, detailed observation and deduction (such as by Galileo and Bessel) suggests that it is not correct, and if God punishes harshly those who disbelieve what he says, then it seems as though God is not being fair. He has designed the universe in such a way that the way it appears to be designed is not the way he has said it was designed, and thus designed it in a way that invites punishment of the inquisitive and intelligent.

What reply can we make to this? Well, we could avoid fundamentalism by distinguish between literal and analogical truths. When it says in Psalm 93 that “the world also is established, that it cannot be moved”, perhaps it does not mean that the earth is literally immoveable. Perhaps it is immoveable in a spiritual sense. Or that it cannot be moved from its orbit around the sun, all things being equal. Perhaps it is a statement about the constancy of physical constants, such as gravitational acceleration etc. Yes, that is a reasonable objection, but then we can turn the whole question around. Why did God make statements that are so easily open to a literalist misinterpretation? If so, then it seems God is discriminating against fundamentalists. Is that fair? Surely not.

Or it could be argued that the inquisitive and intelligent are simply wrong. A careful examination of the matter (see the websites linked to in earlier posts) shows that the geocentric theory is the correct one. I reply: whichever theory is correct, it remains that God’s design has misled an extraordinary large number of people. Either he is being unfair to astronomers and scientists, or he is being unfair to fundamentalists. We have to choose, and either way it seems that he is not being entirely fair.

Or it could be argued that the inquisitive and intelligent have violated a version of the charity principle. They have followed a line of observation and reasoning that leads them to conclude that God has not told the truth. But logic, as well as the principle, should tell them that God would not have designed the universe in such a way as to contradict what he says. If any theory or reasoning of yours leads to a contradiction with sacred scripture or the teaching of the church, there is something wrong with your reasoning. Indeed, as Ockham argues – as discussed in my last post), we should even make exceptions to the laws of logic when this happens*.

So, is God not being fair to someone?  And is that not inconsistent with an essence into which goodness, justice, fairness etc. are built into as though by definition?


* Yes, I realise that Ockham’s point is more subtle than that. But this is internet land, where we lay things on with trowels.

Ockham’s solution to the Trinity problem

In the fifth chapter of the third book of his monumental Summa Logicae, Ockham presents an interesting solution to the problem of the Trinity. He says that the following syllogism is not valid:

Every divine essence is the Father
The Son is a divine essence
Therefore, the Son is the Father

Why not? Surely it is valid by the rule of dici de omni that Ockham frequently applies to arguments. According to this rule, a universal proposition denotes that the predicate is truly affirmed or denied of anything of which the subject is predicated. Thus “every divine essence is the Father” denotes that of whatever ‘divine essence’ is predicated, so also ‘the Father’ is predicated. Since the minor premisses states that ‘divine essence’ is predicated of the son, it follows (by this rule) that ‘the Father’ is also predicated of the Son. So the conclusion “the Son is the Father” apparently follows. Why, then, does he now say that it does not follow?

Ockham answers that the proposition “every divine essence is the Father” does not denote that the predicate is truly affirmed or denied of anything of which the subject is predicated. And so the argument above is not governed by dici de omni, and so it does not have to be valid.

We can only know when such an argument holds, or when not, from sacred scripture, or from the determination of the church. If scripture, or the church, states that the premisses of such an argument are true and the conclusion false, we can be sure that the argument is not governed by ordinary logical laws. He notes also that such an argument is always valid in the physical or ‘created’ world. For “in the world of created things it is impossible that something one in number, simple and singular, really be several things, really distinct” (inter creaturas impossibile est quod una res numero, simplex et singularis, sit realiter plures res distinctae realiter).

More fixed earth

There is more information about the geocentric theory here. This suggests a problem. The original motivation for the geocentric theory was its apparent simplicity, given that the heliocentric theory requires an extra assumption – a tilted earth – to explain the seasons. But it turns out the geocentric theory also needs an extra assumption to explain the seasons, and the apparent motion of the sun that corresponds to this.

A good way to imagine this is to look at a potters wheel as it turns . . . it turns once every 24 hours . . . at the center is the Earth . . . place your finger in the clay, you make a circle, this is the sun . . . now slowly move your finger out 3% of the radius of your first circle . . . now move your finger inward 3% . . . that is the motion of the sun albeit the sun would also move in a spiral helix up and down while it is moving out and in by 3% of the radius . . . there are two motions here, one is up then down the other is in then out again. So there is the spiral up and down motion to account for the seasons but the size of the spiral is constantly changing to account for changes in the distance over the course of a year.

Yes but why does the sun move that way? The assumption of a tilted earth plus gravity seems a simpler explanation and thus (pace Dr Connolley) should be preferred. Obviously the underlying rationale for neo-geocentricism (‘neo-geo’) is the Bible and God, but that raises another question: is God fair? It seems unfair to create a universe whose nature seems almost designed to be misunderstood, once observed carefully. Observations by Galileo and other astronomers, phenomena like Foucault’s pendulum, and many other observable phenomena, suggest a reality that is quite different from the literal truth of the Bible. Geological observations suggest the Earth is much older than 6,000 years. Why did God create the Earth in a way that seems almost designed to mislead? Why did God create dinosaur bones, without mentioned dinosaurs in the Bible? Was that fair of God?

It could be replied that, correctly understood (where correct understanding means theories like ‘neo-geo’), these phenomena do not contradict the literal truth of the Bible. But then, clearly, many millions or billions of people, including all eminent scientists since Galileo’s time, have not correctly understood the evidence. Was it fair of God to create a world whose true nature misled so many brilliant people?

Thinking about Frodo

Dr Vallicella has a post about intentionality here which reminds me I haven’t addressed the question of when two people are having thoughts about the same individual.

I characterised intentionality in this series of posts and particularly this. I have argued that it is merely a semantic phenomenon: certain verbs are ‘logically intransitive’ – they have a grammatical accusative, but no logical one. ‘Tom wants a cigarette’ has the grammatical subject ‘Tom’ and the grammatical accusative ‘a cigarette’. But, unlike ‘Tom is smoking a cigarette’, the sentence is consistent with ‘nothing is a cigarette’. Thus the verb ‘wants’ is logically intransitive. I also argued that we can parse a sentence like ‘Tom has a thought about a hobbit’ in two ways. First, as

Tom / has a thought about / a hobbit

where the verb phrase ‘has a thought about’ is logically intransitive (it appears to relate two objects: Tom and a hobbit, but clearly it can’t, as there are no hobbits). The other way of parsing it is

Tom / has / a thought about / a hobbit

where the verb ‘has’ relates Tom and a thought. This is logically transitive, given that there are such things as thoughts, and given that Tom can be related to his thoughts by thinking them. That suggests we can analyse any sentence containing a logically intransitive verb phrase into a sentence containing a logically transitive one. If possible, that would explain intentionality completely. But what about

(*) Tom has a thought about Frodo ?

It seems easy to explain a thought ‘about hobbits’. It is a thought we would express using the word ‘hobbit’, or which would involve the attributes we commonly attribute to hobbits (being short, having furry feet, being prone to finding magic rings etc). But Frodo? How do we explain the possibility of two different people having a thought about the same individual fictional character, without being drawn into Meinong’s junkyard of non-existing objects?

To resolve this, I shall invoke two principles. The first is the ancient view that thought is a form of silent speech which, if expressed, would signify to the thought to another. Since signification is in some sense public – many people can grasp the meaning of speech, which is indeed the whole point of language - this resolves the apparent problem of thoughts being unobservable or inaccessible. The second is that the term ‘thought of X’ is true of any thought which, if expressed, would contain a term synonymous with ‘X’. I.e. ‘Tom has a thought about Frodo’ is true iff Tom has a thought which, if expressed, would contain a term synonymous with the name ‘Frodo’ as it occurs in ‘Tom has a thought about Frodo’.

Thus the apparently intractable problem of explaining when two thoughts – scientifically unobservable events – can be reduced to the simpler problem of explaining when two proper names have the same meaning. More tomorrow.

How the left conquered Wikipedia

Here. Correct in all the main points (except for its faint suggestion that we might even begin to take Conservapedia seriously).

When I worked on Wikipedia, I was continually irritated by the politically correct view that, when it comes to philosophy, all cultures and all traditions had to be treated absolutely equally. So that, for instance, ‘Eastern philosophy’ had to receive equal coverage. There were two problems with this. First, the average Wikipedia editor knows even less about Eastern philosophy than about ‘Western’ philosophy (which is not very much). Second, there is no way that these subjects can be given the same sort of treatment. Eastern philosophy is so absolutely different to the Western variety that they are effectively different subjects, which happen to have the same name.

Wittgenstein on relativity

William has given us an interesting link here.

Meeting a friend in the corridor, Ludwig Wittgenstein (1889-1951) said: "Tell me, why do people always say that it was natural for men to assume that the sun went around the earth rather than the earth was rotating?"

His friend said: "Well, obviously, because it just looks as if the sun is going around the earth."

To which the philosopher replied: "Well, what would it look like if it had looked as if the earth were rotating?"

How clever of Wittgenstein. He is not asking what it would have looked like if the earth were rotating, but what it would have looked like if it had looked as if the earth were rotating. Implying that to look as though the observer is moving with respect to their environment is the same as looking as though the environment is moving with respect to the observer.

But is that true? As a postgraduate I house-shared with a research assistant who was working on the neurophysiology of perception. Some of his work showed that the world actually looks different dependent on whether the observer is moving with respect to a stationary environment, or the other way round. There are a number of kinaesthetic sensors in the body which respond to bodily motion or rotation, and these interact with the visual sense in various ways. You can fool these sensors in all sorts of ways – for example you can create the illusion of acceleration by tilting their seat backwards, which is how flight simulators like this work. The answer to Wittgenstein’s question could well be “well, it would look exactly like that” – namely, looking as if the earth were moving, rather than the sun.

Translating ordinary language into predicate logic.

Vallicella has now apparently accepted my arguments against grammatically proper names being translatable into the ‘logical constants’ of modern predicate logic (MPL). But this leaves him with the problem that there are also strong arguments against translating them into the predicates of MPL.  I summarised these arguments earlier in June, as follows.

Argument 1 was that a proper name does not signify something that is repeatable, therefore does not signify a property. Therefore it signifies an object. A reply is here.

Argument 2 was that a name cannot be significant or intelligible to another unless the idea of what the name applies to is in the other person’s mind. But we can only have the idea of a particular thing by being acquainted with that thing, which is only possible if that thing actually exists. A reply is here.

Argument 3 was that definition proceeds by genus and specific difference. Therefore a proper name cannot be defined, for they name individuals, and individuals are not species. They have no specific difference, and can only be distinguished by the proper name itself.  A reply is here.

Argument 4 was that truth-conditional semantics rests on the assumption that the conditions for the truth of a sentence give the sentence’s meaning or significance. But there is no truth evaluable content when reference failure occurs. If there are no truth conditions, then there is no meaning or significance. I have not replied to this argument yet.

If Vallicella accepts these arguments as well as those he summarises in his post, he is apparently left with the problem that ordinary language cannot be translated into MPL at all. Is that a problem?

Does the earth actually rotate?

Perhaps not.  Listen to these curious and entertaining broadcasts, particularly these two sessions, about the 'nine assumptions' of Copernican science. The argument is broadly this: if you start with the first assumption that the earth rotates (as opposed to what your senses tell you, namely that the earth is fixed, and that the sun and moon revolve around it), then you need eight further assumptions in order to make the first one consistent with what we observe.  This, as the broadcasters say, is not science.  And they have a point, no?  We tend to reject any theory whose basic assumption we have to save by a series of further assumptions. Isn't the simplest theory of the solar system the Aristotelian and biblical one, which is evidently supported by our senses?

Ant

About half the hits to Beyond Necessity come from Google. The keywords are mostly self-explanatory, e.g. "existential import", "Augustine", and so on.  But one of the most frequent is "ant".  I have no explanation for this, unless it has something to do with my post about ants here.

Augustine on lust

Someone said to me recently that Augustine had some very strange views on sex.  So I had a look at what he says.  And yes, some of it does seems strange to us moderns.  For example:

Although, therefore, lust may have many objects, yet when no object is specified, the word lust usually suggests to the mind the lustful excitement of the organs of generation. And this lust not only takes possession of the whole body and outward members, but also makes itself felt within, and moves the whole man with a passion in which mental emotion is mingled with bodily appetite, so that the pleasure which results is the greatest of all bodily pleasures. So possessing indeed is this pleasure, that at the moment of time in which it is consummated, all mental activity is suspended. What friend of wisdom and holy joys, who, being married, but knowing, as the apostle says, "how to possess his vessel in santification and honor, not in the disease of desire, as the Gentiles who know not God," would not prefer, if this were possi ble, to beget children without this lust, so that in this function of begetting offspring the members created for this purpose should not be stimulated by the heat of lust, but should be actuated by his volition, in the same way as his other members serve him for their respective ends? But even those who delight in this pleasure are not moved to it at their own will, whether they confine themselves to lawful or transgress to unlawful pleasures; but sometimes this lust importunes them in spite of themselves, and sometimes fails them when they desire to feel it, so that though lust rages in the mind, it stirs not in the body. Thus, strangely enough, this emotion not only fails to obey the legitimate desire to beget offspring, but also refuses to serve lascivious lust; and though it often opposes its whole combined energy to the soul that resists it, sometimes also it is divided against itself, and while it moves the soul, leaves the body unmoved. (City of God, Book 14 c. 16)

On the other hand, the logic is clear.  Lust is beyond our volition, out of our control.  So there is something wrong with it.  (But then so is hunger, of course).

How often does the moon rotate around the earth?

Connolley makes a curious objection here to my claim that the moon rotates around the earth once a day. What is wrong with that? Doesn’t it? From the beach on holiday this effect was clearly visible. I concede that it does not do this exactly once a day. But simplification is a virtue, as Connolley himself shows when he refers to ‘two tides a day’ (actually there are two tides every 24h and 50 minutes).  So what, broadly speaking, is wrong with my claim?

Referential and attributive use of descriptions

Vallicella mentions Keith Donnellan’s distinction between the ‘attributive’ and ‘referential’ use of definite descriptions. This prompted me to look at Donnellan’s paper again after some years*. 

According to Donnellan, a speaker who uses the description 'the F' attributively means to state something about whoever or whatever is F.  A speaker who uses the description 'the F' referentially uses it to pick out who or what he is talking about. By implication, then, the attributive use does not pick out who or what we are talking.  Probably the most well-known claim of the paper is that we can use a description referentially even when nothing fits the description.  Donnellan gives the example of 'the man with the Martini', which could be used to successfully pick out someone who (in fact) is drinking water, not Martini, and to say something (according to Donnellan) which is true.  For example, we could truly say 'the man with the Martini has glasses' in the event that the man drinking water has glasses.  I noted with interest that Donnellan attributes this idea to Leonard Linsky - we can say of a spinster that 'her husband is kind to her', referring to her lodger.

I don't understand the distinction between referential and attributive at all.  In the sense that 'referential' means that the semantics of the referring term is dependent on the existence of an object referred to, I hold that no terms are referential. Meaning is independent of external reality.  In the sense that 'referential' means picking out or signifying which individual we are talking about, all meaningful singular terms do this, as I argued here and particularly here.  Even 'the King of France' - Donnellan's favourite example of an attributive use - tells us which king we are talking about.  Not the King of England, nor of Ireland, nor of Spain, but the one who rules France.  Of course, there is no such person as the King of France, but even as I say this, I have just told you which king there is no such king as.

So Donnellan's distinction is artificial.  And certainly it cannot be invoked to explain why the following argument is valid in one sense, invalid in another.

The prime minister of the UK is a man
The prime minister of the UK used to be a woman
Some man used to be a woman

Vallicella means (I think) that the argument is valid if the description 'the prime minister of the UK' is used referentially, i.e. to refer to Cameron, invalid if not.  By contrast, I say that the argument is valid when the description has the same sense in both premisses (meaning 'the UK Prime Minister in 2011') but invalid when it has different senses.  If it means 'the UK Prime Minister in 2011' in the first premiss, but 'the UK Prime Minister from 1979-1990' in the second, then it is invalid, just as any argument is invalid when the middle term is used equivocally.

*”Reference and Definite Descriptions”, Philosophical Review, 75 (1966), pp. 281-304.

Rigid designation

Is the following argument valid?

The UK Prime Minister is a man
The UK Prime Minister used to be a woman
Some man used to be a woman

You will probably say not.  The first is true because David Cameron (who at the time of writing is Prime Minister) is a man.  The second is true because Margaret Thatcher (who used to be the Prime Minister until the 1990s) is a woman, and always has been.  But the implication is clearly invalid, since the premisses could be true and the conclusion false if no man had ever undergone a sex change.  

Kripke's take on this is famous: definite descriptions such as 'The UK Prime Minister' are not rigid. They have different referents in different possible worlds, and so the inference is not valid, because of the non-ridigity of reference.  By contrast, proper names are rigid designators.  Understood in the same sense, they always refer to the same individual.  Thus, if you substitute 'David Cameron' into the inference above, you get something that is valid (although not sound, of course, for the second premiss is false - as far as we know, David Cameron never used to be a woman).

But how about this?

The leader of Cambridge City Council is a woman
The leader of Cambridge City Council used to be a man
Some woman used to be a man

As it happens, the (current) leader of Cambridge City Council is Jenny Bailey, who underwent a sex change operation to become a woman. So Jenny Bailey is now a woman, but used to be a man, and so some woman used to be a man.  The premisses can't be true (assuming "The leader of Cambridge City Council" has the same referent in both premisses) and the conclusion false, so the inference is valid.

How do we explain this?  Are definite descriptions rigid or not?

Ockham has a quite different take on this, distinguishing between 'sense of composition' and 'sense of division'.  He explains it in Book III of his great Summa Logicae here.  In the sense of composition it is signified that a mode (such as 'is possible' or 'was the case that') is predicated of the whole proposition. In the sense of division it is denoted that the predicate is predicated of the subject by a verb determined by such a mode. Thus we must distinguish between 'it was the case that the (then) PM was a woman' and 'it is the case that the (current) PM was a woman'.  Clearly, read in the sense of composition, the subject term may have a different sense in the different premisses.  In 'The UK Prime Minister used to be a woman', the subject term means Margaret Thatcher. In 'The UK Prime Minister is a man' it means David Cameron.  Hence (read in the sense of composition) the inference is not valid because of equivocation, just as any syllogism is invalid because of equivocation.  But read in the sense of division it is valid.  If by 'The UK Prime Minister used to be a woman' I mean that David Cameron used to be a woman, the first inference is valid, just as the second is (where 'The leader of Cambridge City Council' refers in both premisses to Jenny Bailey).

Hence we do not have to accept any fundamental distinction between definite descriptions and proper names.  Rather, it is easier to read definite descriptions in an ambiguous way.  When we say 'The UK Prime Minister used to be a woman', we can read it either as saying that the present PM used to be a woman, or that some former PM used to be a woman.  And this ambiguity is not fundamentally different from the one we find here.

William Pitt was the youngest Prime Minister
William Pitt was not the youngest Prime Minister
the youngest Prime Minister was not the youngest Prime Minister

For there was more than one person called 'William Pitt', just as there was more than one person called 'Prime Minister of the UK'.

Sentence negation, predicate negation and direct reference

There is a good post here by Vallicella, about a comment I made to an earlier post of his. My claim, in essence, is that if we cannot distinguish between sentence negation and predicate negation of a singular sentence, then we have to accept ‘direct reference’. Let me explain. Predicate negation – e.g. ‘a is non-F’ is such that its truth requires that the object denoted by ‘a’ exist, and that this object is not F. Sentence negation, by contrast, is when we simply deny whatever is asserted by ‘a is F’.

In modern predicate logic, we do not distinguish between these two forms of negation, at least for singular sentences. The negation ‘~Fa’ is true whenever some thing is referred to by the singular term ‘a’, and when that thing is not F. Thus it is predicate negation. But it is also the contradictory of ‘Fa’. If it is not true that ~Fa, then it is true that Fa, and conversely. Thus it is sentence negation.

By contrast, in traditional logic (or at least in standard forms of it) we do distinguish between these forms of negation. ‘Socrates is a non-runner’ is true when there is some such person as Socrates, and that person is not running. Thus ‘Socrates runs’ and ‘Socrates is a non-runner’ are contraries. Both can be false when Socrates does not exist.  This is predicate negation (or ‘indefinite negation’ as the scholastics called it). This was considered distinct from propositional or ‘extinctive’ or ‘destructive’ negation, where everything asserted by ‘Socrates runs’ is denied, and which can be true even when there is no such person as Socrates.  Thus ‘Socrates runs’ and the destructive negation ‘It is not the case that Socrates runs’ are contradictories. Both cannot be false, for one denies everything the other asserts.

Now I claim that in systems where there is no distinction between predicate and sentence negation, we have ‘direct reference’. This is easily shown. Direct reference in a singular sentence is when the sentence is meaningless when the singular subject fails to refer. Assume that ‘a is F’ is not meaningless. If it is true, then there is a referent for ‘a’. If it is not true, the sentential negation ‘It is not the case that a is F’ is true. If sentential negation is equivalent to predicate negation, it follows that ‘a is non-F’ is true, and so a exists, and so, there is a referent for ‘a’. But (by excluded middle) either ‘a is F’ is true, or its contradictory (the sentential negation) is true. In either case, ‘a’ has a referent. Thus if ‘a is F’ is not meaningless, ‘a’ has a referent. Conversely if ‘a’ does not have a referent, ‘a is F’ is meaningless. But that is Direct Reference, as I have defined it.

In systems where we can make a distinction between the two forms of negation, we do not have to accept Direct Reference. If ‘a is F’ is meaningful but false, this could either be because the predicate negation is true, or because there is no referent for ‘a’.

Both Peter Lupu and David Brightly challenged this idea in their comments to the post.

Peter argued that we do not have to accept Direct Reference if we accept the distinction between meaning and reference (or ‘sense’ and reference or whatever you call it). I reply: in accepting this distinction we have (tacitly) accepted the distinction between the two forms of negation. If we are happy that ‘a is F’ may not be true in the case that ‘a’ has a sense but not a reference, and assuming that (in this system) we can say that this is so, i.e. state that a does not exist, then we can state the disjunction ‘a does not exist or a exists but is non-F’. But that disjunction is equivalent to the sentential negation of ‘a is F’, and is therefore distinct from the predicate negation ‘a does exist and is non-F’.

David argued that we can suppose a singular term has a referent, and prove a contradiction in order to show that it does not have a referent. For example, let ‘a’ denote the largest ordinal number. That supposition leads to a contradiction, therefore ‘a’ cannot denote that. Yet (according to David) it is meaningful to make assertions using the singular term ‘a’. I reply: what is meant by ‘denotes’ here? If it means ‘signifies’ or ‘means’, then the supposition that it has a meaning leads to a contradiction, and so it does not have a meaning. This is Direct Reference. On the other hand, if it does not mean ‘signifies’, but rather that a exists, then my reply is the same as to Peter. To accept the possibility that ‘a’ is meaningful but fails to correspond to any existing number, is tacitly to accept the distinction between the two forms of negation.

On simple explanations

Clever Connolley caught me out with a comment here on simple explanations. Mencken says that the reason for the 'inferior man' hating knowledge is because it is complex. All superstition is a short cut to make the unintelligible simple. Connolley, apparently agreeing with Mencken, chides me for wanting a simple explanation for global warming.

But is Mencken right? The appeal of true scientific explanation generally does lie in its simplicity. There are obvious exceptions - the proof of the four colour theorem for example. But consider the explanation of an eclipse. That is pretty simple. The moon goes round the earth, the earth goes round the sun. The sun lights up the earth. Occasionally the moon gets in the way and casts a shadow. How simpler could it get? The theory that the eclipse is caused by a dragon crossing the sun, by contrast, requires a theory of dragons, and no theory of dragons - at least not one that gives a comprehensive treatment of them, including their metabolism, genetic structure etc - could be simple at all.
 
Or consider Augustine's explanation of why evil exists:

That the whole human race has been condemned in its first origin, this life itself, if life it is to be called, bears witness by the host of cruel ills with which it is filled. Is not this proved by the profound and dreadful ignorance which produces all the errors that enfold the children of Adam, and from which no man can be delivered without toil, pain, and fear? Is it not proved by his love of so many vain and hurtful things, which produces gnawing cares, disquiet, griefs, fears, wild joys, quarrels, lawsuits, wars, treasons, angers, hatreds, deceit, flattery, fraud, theft, robbery, perfidy, pride, ambition, envy, murders, parricides, cruelty, ferocity, wickedness, luxury, insolence, impudence, shamelessness, fornications, adulteries, incests, and the numberless uncleannesses and unnatural acts of both sexes, which it is shameful so much as to mention; sacrileges, heresies, blasphemies, perjuries, oppression of the innocent, calumnies, plots, falsehoods, false witnessings, unrighteous judgments, violent deeds, plunderings, and whatever similar wickedness has found its way into the lives of men, though it cannot find its way into the conception of pure minds? (City of God, Book 22 chapter 22)

The explanation - that Adam and Eve offended God, and that these evils are a punishment - appears simple at first sight, just like the dragon explanation.  But it is not, for it requires a theory of God, and also a theory of Paradise, which is problematic.  Sociobiology could probably provide a simpler one (although I'm not sure it has, yet).

Superstition is not necessarily a simpler theory. So, what distinguishes superstition from science?

Hello again

Apologies for the absence of posts recently.  The manuscript of the Scotus translation (plus extensive commentary) is to be submitted to the publishers soon and work on that takes precedence.  I shall be posting sporadically, however.

The Lindy Hop

The Wikipedia article on the history of Lindy Hop (which is not materially different from the article on Lindy Hop itself) says that the dance was "replaced by Rock and Roll dancing". Not entirely true. Compare this from the 1941 movie Hellzapoppin (featuring Whitey's Lindy Hoppers) with this by Bill Haley, from no earlier than 1956, and particularly compare these moves with these.  The only difference is the colour of the dancers.

More hoppin' from Whitey's hoppers here, some other dancing from the movie Swing Fever here, and see also a reconstruction, wonderfully done, from the film Malcolm X.  Note the same type of move here.  The tune 'Flying Home' was by Lionel Hampton, with a storming solo on saxophone by Illinois Jacquet.

Sadly, arguments over copyright mean that there is no sound for 'Lady be good' by Artie Shaw, where the dancing starts here, but there is a sound version without the pictures.  Don't miss Buddy Rich at 2m10s.