Logic and male status

Pamela Gerloff has commented on my earlier post with some remarks that deserve to be taken seriously.  Her main points are as follows (I hope I have summarised them correctly).

1.  That the discussion on this site is  male-dominated.
2. That research (such as by sociolinguist Deborah Tannen) shows that male conversation typically serves a different purpose than female, leading to misunderstanding.
3. Male discussion is characterised by jockeying for position and establishment of status, which is different from how women tend to approach discussion.
4.  Likewise, discussion on this site is about commenters asserting their own status as superior thinkers and logicians and not about fruitful intellectual inquiry.

How do we answer this?  In one sense, it is easy. Logicians are concerned about the validity of arguments alone, and the complaints by the commenters here were about exactly that.  Pamela's arguments simply weren't valid.  Now even if it is correct that the men's comments were motivated by positioning and status, in order to establish themselves as 'superior thinkers and logicians', that hardly invalidates their position.  If an argument is invalid, it is invalid, whatever my motivation in affirming its invalidity.  The reply to Pamela seems clear: her first argument was invalid, and so was her reply to critics, which was a form of ad hominem (addressing the person, not the reasoning).

In another sense it is more difficult.  I am sure Pamela will reply that my objection remains stuck on the rails of 'male logic'.  Calling ad hominem is just another move in the game of patriarchal domination. Why, after all, is it called 'ad hominem' (to the man)?  There is a nice observation by Robin Turner along this line.

If women reject logic and rely solely on feelings, they are left in the weak position of having to argue with feelings. Feeling that something is true does not make it true, and it will not convince anyone else that it is true either. You can say, "I feel X", but the person you are arguing with can just as well reply, "Well I don't." The result is that the argument usually goes nowhere. This is particularly damaging in arguments between men and women, since both sides are likely to go away with their prejudices strengthened; the men think women are subjective, emotional and illogical, and the women think men are impersonal, cold and over-intellectual.

To justify their feelings of hurt at being "beaten" in an argument, the women concerned may go further and dismiss the whole thing as "male logic", as though there were two types of logic, on for men and another for women. This then places the men in an impossible position, since if they attempt to be reasonable, they are accused again of using "male logic", in the same way that if a woman gets upset in an argument, it is taken as proof that she is overly emotional, and hence irrational. This does not only lead to a lack of communication between the sexes, it leads to a lack of communication in which women come off worse, since policy is generally made as the result of argument, not sharing feelings. [link]

Bad music: unreasonable music

As it's been a bit of a New Age week here at Beyond Necessity, and because it's Friday, when we venture into the world of strange and bad music, here is some music people were simply too wasted to get anything right*. We'll start with the 13th Floor Elevators, 60s psychedelic band and stoner heroes.

Ex-bandsman Tommy Hall is on the right, a 66 year old who has spent most of his life dropping acid. "We were trying to get into the results of acid," he says, "to get into the results of the universe." So he made it a rule to drop acid every time someone picked up an instrument. As the  interview says, "it's challenging to comprehend everything he's saying". Why would that be. Hall wrote the sleeve notes for The Psychedelic Sounds of the 13th Floor Elevators, their 1966 album, urging everyone to get away from that boring and narrow old Aristotelian logic.

Actually some of their music does anticipate the music of the 1970s, but not Don't Fall Down, which sounds terrible even if you are very stoned.  This is proof that 'psychedelic drugs' damage the rational parts of the mind.

Moving, on here is Journey by Gentle People, which actually managed 21,000 views.  The original is actually 15 minutes long but that wouldn't fit onto YouTube, which is just as well.  I already pointed out that marijuana destroys the short-term memory, which has a bad effect on logic, but also music, where you get stuck at the repeat bar :|| for ages, similar to driving round Swindon.

Finally something more modern and rappy.  "5 weed songs", of which I only got past the first, and Cypress Hill performing Stoned Is The Way Of The Walk.  Note the endless repetition of the initial motif, supposedly sampled from Grant Green's Down on the Ground, which is also very bad.

*Yes there is something wrong with that sentence.

Objective reality revisited

The proprietor of Maverick Philosopher, who we will call 'Bill', has just posted about my comments on objective reality. Definitely worth reading, but makes me realise my comments (that there is such a thing as 'objective reality') were not entirely consistent with what I have been strenuously maintaining both here and over there,  namely that there is no such thing as objective reality after all.  For example, way back here, or here.

I have argued that there are no truthmakers, otherwise the truth of 'it will be sunny tomorrow' would depend on the existence of a present truthmaker.  But if that truthmaker does exist, then a few seconds later it did exist. But we can't change the past, so we can't change the truthmaker, and since the truthmaker makes the future true, it follows that we can't change the future.  But we can change the future: it is not determinate.  Therefore there are no truthmakers.  Therefore there is no 'objective reality'.

Fortunately Bill failed to spot this irregularity.

Logic: a guy thing?

One of the commenters yesterday apparently suggested that all this obsession with logic is ‘a guy thing’. Hmm. I strenuously try to avoid any form of political correctness, but what if I had asked whether sewing was ‘a girl thing’. Public flogging? Roasting? Actually I know a lot of female logicians, e.g. Catarina Dutilh-Novaes who blogs here, who is not only a logician but a specialist in medieval logic, nothing better than that. The late Elizabeth Anscombe was famous for her rigorous argumentation, so much so that C.S. Lewis (supposedly) abandoned his career as a philosopher theologian for Narnia, after being soundly defeated by her.

In logic and reasoning, there is no male and female, for logic involves thought, and assuming we are thinking (and not spewing out a meaningless word salad), we cannot think illogically.

Thought can never be of anything illogical, since, if it were, we should have to think illogically. . . . It used to be said that God could create anything except what would be contrary to the laws of logic. —The truth is that we could not say what an ‘illogical’ world would look like. . . . It is as impossible to represent in language anything that ‘contradicts logic’ as it is in geometry to represent by its coordinates a figure that contradicts the laws of space or to give the coordinates of a point that does not exist [Wittgenstein, Tractatus 3.03]

Perhaps there are male/female differences when it comes to the art of persuading. Men persuade in various, often unsubtle ways. Females, and in particularly my wife, persuade by asking questions a bit like those computer dialogue boxes with radio buttons: “Shall we leave at 6:30 or 7:00 tonight, Yes/No”. With the difference that the computer dialogue box has a default marked so that if you hit return, you get the default, and I think there is no female equivalent of this.

Non-Aristotelian states of consciousness

I have been following up Dr. Pamela Gerloff’s post about the ‘Possiblity Paradigm’ with a few comments of my own, most of them on this page. I pointed out a number of logical flaws in her argument, and she has finally replied exactly as I thought she eventually would, by saying “From within your paradigm it appears to be gobbledlygook, and full of logical inconsistences. That's correct, when perceived from within your paradigm,” and “You are trying to understand what I'm saying from within your philosopher/logician's thought framework/paradigm.”

This is the ultimate get-out-of-jail-free card for the purveyor of New Age mumbo-jumbo. If you try to point out any flaw in their reasoning whatsoever, they will simply reply that the flaw is from your ‘logical’ standpoint or ‘paradigm’. It is a limitation of your mind constrained by ordinary logic. And of course there is no reply to that. If your opponent in argumentation refuses to abide by the rules of logic, the argument is over. Except to note that New Ageists nearly always use ‘ordinary’ logic to put forward their arguments. In her original post, Gerloff claims that Lester Levenson exists, and backs up her claim by saying she knows former students of his, which is an obvious appeal to standard scientific reasoning (give evidence). She cites evidence that Lester recovered from apparently incurable cancer as reason for believing the more extraordinary claims, such as being able to withstand nuclear blasts by the power of thought. So she is trying to persuade us using ordinary logic as a first step. Yet as soon as we question her second step, she explains that ‘ordinary’ logic fails. But if that were true, the first step would fail. This is inconsistent.

This reminds me so much of the 1960s and 70s. The 13th Floor Elevators were a 60s band who advocated chemical agents (such as acid and weed) as a gateway to a higher, 'non-Aristotelian' state of consciousness, which would transcend ordinary ‘Aristotelian logic’. I remember many conversations, or what passed for conversations with the smokers of weed and the herb where this very same argument was propounded. Not really arguments, of course. Any substantial logical point was met with that irritating condescending smile of the weeder who is already at the ‘higher state of consciousness’. “You simply don’t understand, man”. The fact being, of course, that marijuana blocks all short-term memory so effectively that any movement from premisses to conclusion – which requires remembering what the premisses were – is impossible.

Objective reality

Some of the more serious minded are getting irritated by this.  Someone called Dr. Pamela Gerloff, who claims to hold a "doctorate in Human Development" from Harvard University tells us that it is possible to cure yourself of cancer, heal other people, fix broken TVs simply by the power of the human mind (or awareness), by "seeing them as perfect".  She quotes, with apparent approval, one practitioner saying "If a nuclear bomb were to go off right now next to you, you wouldn't have to be affected by it."

The comments, both from the ones who find it a little unconvincing, and from others who are more sympathetic, are worth reading.  Philosopher Stephen Law writes "Are you actually suggesting that if we really, really believe we can fly by flapping our arms, and jump of the roof, then we will fly? Surely this takes the "power of positive thinking" too far?!".  Gerloff's reply included this gem:

From my point of view, and in my ongoing experience of life, I do not make the kind of judgments, decisions, and conclusions that you do about what is "objectively real" and what is not. When I say "anything is possible" I mean that in my operative framework of reality, I find it useful to approach the world *as if* anything is possible. It is possible/potentially not possible all at once.

I generally recommend people not to get upset about this sort of thing,  because in nearly all cases, and I think in this one, the problem is a simple logical confusion.  Clearly Gerloff does make the same judgments about what is 'objectively real' as we all do. I am sure she looks carefully when she crosses a busy street, and turns the gas burner off after she finishes cooking, and all those things.

Also, it's clear that even to disagree that there is such a thing as objective reality requires the existence of an objective.  Suppose Gerloff says "there is no objective reality".  Perhaps she means by that, that all reality is personal, or subjective, or constitutes her "operative framework of reality", or something like that.

But then she is saying that it is true that there is no objective reality.  And if I disagree with her (as I do), I have to say that this is false.  And to do that, I have to deny what she is saying.  I.e. whatever it was that she is saying is true, I am saying is false.  So that same thing - the thing she is asserting, and the thing I am denying - has to be common to both of  us.  We both have to get hold of the same proposition or thought or statement in order for her to assert it, and for me to deny it.

So, in order for me to disagree with Gerloff, there has to be an objective reality.   And I do disagree with her. Hence there is an objective reality.

A neutral point of view?

The 'The Neutral Point of View' rule is the second best known rule on Wikipedia. (The first is ‘verifiability, not truth', which I will talk about later). I have been doing some research on how this rule became a part of Wikipedia. An early version was completed by Larry Sanger for Nupedia in November 2000, as part of his editorial policy guidelines. Section D of part III on General Nupedia Policies (‘Lack of Bias’) contains the core idea of the neutrality principle.

Sanger’s test for lack of bias is whether it is difficult or impossible for the reader to determine what view the author holds. This in turn means that “for each controversial view discussed, the author of an article (at a bare minimum) mention various opposing views that are taken seriously by any significant minority of experts (or concerned parties) on the subject”. He adds that, in a final version of an article, “every party to the controversy in question must be able to judge that its views have been fairly presented, or as fairly as is possible in a context in which other, opposing views must also be presented as fairly as possible” (my emphasis).

In a second attempt at such a guideline, the ‘Neutral point of view’ policy drafted in December 2001, he writes “The neutral point of view attempts to present ideas and facts in such a fashion that both supporters and opponents can agree.” And “you should write articles without bias, representing all views fairly”. And “to write without bias (from a neutral point of view) is to write so that articles do not advocate any specific points of view; instead, the different viewpoints in a controversy are all described fairly.” (my emphasis, again).

The principle, as stated, is fundamentally flawed. If one view that p is contrary to another q (meaning that p and q cannot both be true), then it is very easy to determine which view the author holds, on the assumption that he or she is rational, and wants to avoid inconsistency (i.e. avoid asserting two things that cannot both be true). And of course it would be absurd to suppose that an encyclopedia, a source of knowledge, true propositions, should be asserting inconsistent statements.  Thus, the view that the author holds to be true is the one that the article states as true, and all other contrary views must be represented as false, or as mere beliefs.    Sanger's criterion that it should be difficult or impossible for the reader to determine what view the author holds is  impossible to apply.

His use of the term ‘mention’, and ‘fairly’ suggests a way out. We can state what the view is, i.e. truly say what its adherents hold, without saying anything true or false ourselves. For example, the statement ‘Flat earthers hold that the earth is flat’ is true (that’s what they say, after all), even though ‘the earth is flat’ is false, as far as we know.

 But that is no good either, at least not in an encyclopedia. For example, the article on the World Geodetic System opens

The World Geodetic System is a standard for use in cartography, geodesy, and navigation. It comprises a standard coordinate frame for the Earth, a standard spheroidal reference surface (the datum or reference ellipsoid) for raw altitude data, and a gravitational equipotential surface (the geoid) that defines the nominal sea level.

It does not assert that this is what round-earthers say or believe, nor does it mention the views of Flat Earthers at all. Wikipedia, and other encyclopedias, represents mainstream scientific opinion as true, and only represents other significant views by way of true statements about what its adherents believe.

There is exactly the same difficulty with Sanger’s December 2001 version.

If we're going to represent the sum total of "human knowledge"--of what we believe we know, essentially--then we must concede that we will be describing views repugnant to us without asserting that they are false. [my emphasis]

Another way round the difficulty is the idea of including only ‘significant’ views on a subject. Thus, in the Nupedia 2000 policy, Sanger refers to views hold by a ‘significant minority of experts’. In the later Wikipedia 2001 policy he refers to “all different (significant, published) theories on all different topics”. This is better, but still weak, for two reasons. First, the ‘published’ criterion includes all sorts of nonsense. Second, whether a view is significant or not is a value judgment, and thus difficult to verify.

In summary, none of these ways of ensuring neutrality – or rather, getting a bunch of internet amateurs to agree on matters on which there is considerable disagreement, such as Neurolinguistic programming, Pedophilia, The Palestine question or even the name of the British Isles* - were likely to work, and the only solution in past disputes has been simply to ban the disputing parties. It is impossible to assert any proposition without asserting that it is true. Simply mentioning it as a belief of certain people is inappropriate in a reference work. And deferring to mainstream scientific opinion makes it simply a copy of mainstream scientific opinion (which is what an encyclopedia should be anyway).

The 'verifiablity' principle came a bit later.  More tomorrow, or next week.

* A notable and long-running dispute in Wikipedia. The talk page of the British Isles article runs to a whopping 39 archives. Among the protagonists was user ‘Sarah777’, accustomed to saying things like “I'm staggered (not) at how ill-informed some British Nationalist editors are in relation to the history and symbolism of the Union Jack. It is akin to Germans still using the Swastika to represent Germany”. was banned in May 2012 for “total failure to adhere to the most basic principles of editing in a collaborative environment”.

Bad music: so boot if at all

Not that bad, actually, but a necessarily preliminary if we are to tackle the difficult subject of jazz rock.  Here is Kahimi Karie singing Good Morning World.  I first heard this in 1995 somewhere over the Atlantic, and was intrigued by the sampling from 1960s Soft Machine.

Move to Sweden?

Stephen Law has a post here about the Swedish economic model. His argument could be expressed in syllogistic form as follows.

Sweden has not suffered badly in the economic crisis
Sweden is a high taxing, high public spending, highly redistributive, bank-and-finance-regulating country
Not all high taxing, high public spending, highly redistributive, bank-and-finance-regulating countries have suffered badly in the economic crisis

Reading the proper name ‘Sweden’ as a universal term, this is a valid syllogism of the form EAO, Felapton. Thus disproving the proposition “All high taxing, high public spending, highly redistributive, bank-and-finance-regulating countries have suffered badly in the economic crisis”, which was what Stephen wanted to prove.

I don’t dispute the second premiss, but it is misleading, as it mixes together a number of different and logically independent subjects.

The first is ‘redistribution’. Redistribution and public spending are not the same, as a simple thought experiment proves.Calculate an average national gross income then substract all earnings above that and pay it proportionally to those earning under the average. This need involve no public sector, and no public debt. Think of Robin Hood. There was a survey years ago* asking economists whether this was a good model, and the consensus that it was not, because lower gross earners would not spend the surplus on worthy things like education and theatre and art but rather on cigarettes and beer and cars and TV’s etc. (Actually high-cost things like opera and ballet and art would be completely impossible on this model, but that's a different subject).

Then there is ‘public sector’. This is where people are forced to pay a certain amount in return for state-provided services. This need not have to involve redistribution – there could be the same flat fee paid by everyone. (Although it would be hard to provide high-cost services, as noted above). It certainly would not have to involve public debt.

Finally there is public debt. This is the state issuing debt, either to its citizens or (more usually in the case of the Western countries) to people and corporate or state entities outside the country. The current mess is complex, but essentially due to over-borrowing. On Sweden, this had a massive, and famous, debt crisis in the 1990s, caused by an out of control property boom and much over-borrowing. There is something about this here. (Yes, a Wikipedia article).

* Brittan, S. Is there an economic consensus?: an attitude survey. London: Macmillan, 1973.

Collective wisdom

There was a huge burst of traffic yesterday from Crooked Timber discussing the wisdom of crowds.  Someone linked to my Wikipedia posts here, so I return the favour.  As well as the posts on this blog, there is an article I wrote for the Skeptical Adversaria, of which a copy is on the web here. I have argued many times that crowdsourcing can work well for items of 'hard' knowledge - easily verifiable facts of the sort you would find in an almanac, scientific constants, domains subject to clear proof, such as mathematics.  For the humanities, and in general for any abstract subject that requires thoughtful summarisation, it is a disaster.  Enough said.

There is an entertaining discussion of relativism about truth on Stephen Law’s blog, with a fascinating and irritating quotation about ’truth’ taken from a ‘psychic’ website, as follows.

I was told that there is no absolute truth. I was told that ‘truth’ is a very personal, subjective thing. Something that is ‘true’ = a perception or a belief that serves us personally.

My guides then explained this, using the law of attraction to illustrate it. They said:
“You know that your beliefs create your reality and that you can create any reality you want by changing your beliefs. If you focus your attention on something and hold it as a belief, whether you like it or not, you will begin to see evidence of it being true, all around you. Therefore, you must only believe things which feel good to you. Truth is that which feels good to you; that which serves you.”
So, according to my guides:
Truth = something you have focused on, something you decided you want to experience = it shows up in your reality.
Untruth = something you reject, something you don’t want to experience = it doesn’t show up in your reality. – from Psychic but Sane.

This is an extreme example of the kind of things you come across in teaching beginners in philosophy, which I mentioned earlier here. The standard reply is that in claiming that truth is relative, or that truth can differ from person to person, you yourself are making a statement which can be denied by others. You say that we can both be right about contradictory propositions. I say that we cannot both be right. According to you, we are both right. Therefore I am right, ergo we cannot both be right.

The argument from beauty

I just discovered the ‘argument from beauty’. There is a brief description in Wikipedia, and a more detailed one here. The argument may be summarised as follows:

Beauty exists in a way that transcends its material manifestations
According to materialism, nothing exists in a way that transcends its material manifestations
Therefore, materialism is false

I wonder if there is a fallacy here similar to the one about trees being made high enough so that giraffes did not have to lean down, or the sun moving the way it does in order for crops to be harvested at the right time.

Perhaps objects are beautiful in the way that food tastes good. It would be obviously fallacious to argue that God made food taste that way in order that we would enjoy it, would want to eat it, and so would not starve. Clearly, our nervous system has adapted that way. Are there similar reasons for things looking beautiful to us?

Adamson on Anaxgoras

I just listened again to Peter Adamson's podcast about Anaxagoras.  Entertaining and improving, and an interesting characterisation of the argument from design.

There is a grand tradition, in both philosophy and religion, of invoking God, or the gods, to explain the fact that the world looks so well designed. Think about how the sun moves in just the right way to give us the seasons, so that we can plant and harvest food to keep ourselves alive.  Think of the giraffe with its long neck - just the thing for reaching those tasty leaves in the trees.  Think even of how much it hurts when you step on something sharp. Sure, you don't feel grateful when it happens, but if not for the pain, you would be a lot less careful in the future, and you would probably wind up with cuts all over your feet and then where would you be? So, even the bad things in life seem designed to make things better. Socrates assumed that is was roughly where Anaxagoras was heading when he put mind in charge of the cosmos.

The argument about the sun moving in just the right way is not exactly parallel to the argument about giraffes.  For them to be parallel, it would have to be argued that God created trees at just the right height so that giraffes, with their long necks, would not have to be constantly be leaning over and getting backache, or toppling over.

There is more to be said about arguments from design generally.  What are they?  What do they argue from?  What are they arguing for?

Wikipedian logic

An interesting syllogism on Jimbo Wales' talk page here.

Wikipedia is not intended to be an academic encyclopedia, mainly because the stated goal is to provide a free encyclopedia to every human being. Most human beings are not academics, so it follows this is not an academic encyclopedia.

Anachronism and infinity

William Connolley (aka our commenter 'Belette') is discussing the problems of characterising early scientific thinking - in this case, Galileo's thinking about infinity. Everyone who has tried this is familiar with the problem of anachronism: mistakenly characterising the thoughts and ideas of early thinkers in a way that they would not have recognised or understood. This is particularly difficult when, as usually happens you are translating their work from another language. Clearly you cannot use exactly the terms  they would have used, since they were writing a different language. So you have to use terms with the same meaning, while avoiding meanings they may not have understood. For example 'one to one correspondence' or 'set'.

A further wrinkle is terms in modern mathematical and scientific and philosophical language that are directly inherited from early writers. Most scientific language before the twentieth century was imported from Latin or Greek. Thus, we have the word 'continuum'. In Latin this just means 'the continuous'. Do you translate it as 'continuum' - running the risk of connoting ideas probably alien to medieval and early modern writers on mathematics? Or 'the continuous', which may wrongly imply that the Latin word had no technical meaning. Similarly 'vacuum', which would be wrongly translated as the modern 'vacuum', i.e. airless, when the Latin writers didn't just mean without air, but without anything at all, 'the void'. On other hand, it is clearly correct to ascribe concepts like 'concentric', which simply means 'having the same centre', and is derived from 'concentricus' which entered the Latin language in about 1260.

Concerning Galileo's problem, of explaining how the points of a circle can be put into 'one to one correspondence' with a smaller concentric circle, here is a chapter from Ockham I am working on, which addresses a similar issue.  He writes (my translation)

Likewise, it is of the thinking of Aristotle (as is clear in Physics IV) that air can be condensed without all or some of its qualities, changing. Hence, when air is condensed, it does not have to lose any quality, or at least it does not have to lose every quality which it had before. From which I argue that when air is condensed, either the whole preceding quantity remains, and precisely that which [was there] before, or not. If so, then the same quantity is now less than before only because the parts of quantity lie closer now than before. Therefore since the parts of the substance are in the same way lying closer now than before, and quantity is not supposed to exist for any other reason, it seems quantity is superfluous. But if the whole quantity which was there before does not remain, therefore some part is lost, and since from the corruption of the immediate subject there some accident of it is corrupted, it follows that not every quality remains, which is against Aristotle.

This clearly has an affinity with Galileo's problem of "a small ball of gold expanded into a very large space without the introduction of a finite number of empty spaces, always provided the gold is made up of an infinite number of indivisible parts".

The definition of philosophy

A new page in the Logic Museum today: the first chapter of the oxymoronically titled Modern Thomistic Philosophy (R.P. Phillips, 1934), concerning the definition of philosophy.  Phillips rightly draws on the history of philosophy, taking us through all the early Greek philosophers as Thales, Heracleitus, Pythagoras, the Sophists, ending with Plato and Aristotle.  He concludes by saying

None of these men, it is to be noted, tried to answer these questions [about the nature of the universe] by an appeal to any revelation, to myth, or religious knowledge of any kind; but attempted to extract the answer by using their reason; and they used it almost without reference to sensible observation and experiments. Why was this ? Clearly because they were convinced that the thing they sought lay deeper in the heart of the world than the superficial aspect of things, of which alone the senses could tell them. They were seeking the underlying causes of things, and this is the special point of view from which philosophy discusses its multifarious objects, which are dealt with from another aspect, by special sciences, such as chemistry, biology, zoology, and so on.  It intends to go further into their nature than these do, and not to rest content until it has uncovered the absolutely fundamental reasons of them all [my emphasis].

Thus we define philosophy: the attempt to uncover the fundamental reason of everything, without (like religion) appealing to revelation, myth or other forms of authority, but without (like natural science) the use of observation of experiment.  Approaching the world by pure unaided reason.

Also just out in the Logic Museum, the commentary on Aristotle's Metaphysics by Albertus Magnus.  I have corrected the scan up to book I tract 3, the rest is a bit of a mess.  And of course it is only in Latin.  Tract 3 is Aristotle's own account of the history of philosophy before him.

Henry of Ghent on dying without baptism

While uploading some texts by Henry of Ghent I noticed three questions that are pertinent to the current discussion (see e.g. here) on our fallen state, and original sin.  So I had a go at translating them. First, Henry asks whether a child who dies before baptism is damned.  Against: in Matthew 9, Jesus heals a man brought to him on account of the faith of others.  For: John 3 says that unless we are born again through baptism, we cannot enter the kingdom of God.  Henry upholds John - without baptism, we cannot be saved.  In reply to the argument he distinguishes between 'first grace' and 'second grace'. (I do not understand this distinction, perhaps a theologian can help me out here).  Through the faith of others, a man can deserve first grace.  But he could not receive second grace unless, through being aroused to action by the first, he elects to receive second grace by his own free will.  Since a child cannot choose to do this, he or she cannot be cleansed of original sin.  So the cases of the man healed by Jesus through the faith of others, and that of the child dying without baptism, are not the same.  Although Henry adds that perhaps this could happen by 'special grace'.

In the next question, Henry asks whether the punishment for original sin will be the same for that child, as for the child of a 'Saracen' (i.e. a muslim).  He replies that it will be the same, because original sin is the same in all humans, and so the punishment will be the same.  He qualifies this by saying that this punishment is simply being deprived of the vision of God, and is a sort of nothingness.  By implication, it will not be the sort of horrific, eternal torment described here.

In the final question, he asks whether such a child should be buried in a cemetery.  He argues that it should not.  A cemetery is simply a resting place for the children of the church until the final judgment.  But, just as the excommunicated cannot be buried there because separated from the church, so a child dying before baptism cannot, because in the absence of baptism it never was a member of the church.

Bad philosophy of mathematics

Maverick has a nice post here about dubious philosophy of mathematics.  Numbers are not physical objects, therefore they are in the mind, goes the argument. Valid or not?  Read his post.

Anyone who has taught first year undergraduate students has a box of arguments ready for the common arguments that all beginners in philosophy seem to make.  For example, the confusion between epistemological questions (how can we ever know the truth?) and semantic ones (what exactly is truth).

My favourite is the one I mentioned in the comments section somewhat earlier.  It is argued that fictional names (or names for numbers or abstract objects), since they cannot name anything real, must name ideas in our mind.  Thus, 'Pegasus' is a name for my idea of Pegasus.   For this, we reach in our box and reply "But the phrase 'my idea of Pegasus' names my idea of Pegasus, surely?".  They think for a bit and then see the point.  The reply is mentioned in Quine's *Methods of Logic*, but is much older than that.

Brandon (at Siris) had a nice post a year or so back about the difficulties philosophers encounter in arguing with non-philosophers.  I can't find it, however.

Friday night is bad music night

Following the unexpected success of my last music post, I investigated the attic and found enough vinyl and shellac to justify a regular weekly slot.  That is, bad music.  Maverick has a slot for good music.  Why discriminate?

Some ground rules.  We should try and avoid the obvious, for too much has been written about that.  E.g. one commenter wrote last week "in my personal view there is no aspect of this song which is not bad", and he (or she) is absolutely right.  But a little too obvious.  Likewise, practically anything from the Eurovision song contest.  Or this, which is infamously bad, but not in a way that is news to anyone.

No.  We must explore music which has seeds of badness, or which is clearly bad, but whose toxic characterisation eludes us.  We must explore the world of Youtube of 200 views or less, or (better) the world of music that has not even reached Youtube. 

We must explore even the fantastically popular, and I want to start with the other one our commenter suggested was much better, namely this. 65 million people watched it.

Is it bad?  If it is bad, why?  I don't know. It is manifest that something is badly wrong with it.  I had forgotten, or never noticed, it was the Black Eyed Peas who made it, and now I think of them differently.  In the way that, when someone years ago suggested that all wine tastes faintly of vinegar, I realised that all wine really does taste faintly of vinegar.

For more vinegar, here is Alanis' version which gets us closer to why it is horrible, but without any precise, definitive answer that would be philosophically satisfying.

Cantor's proof

As we are close to the subject, and because it is beautiful and remarkable, here is Cantor's proof of the uncountability of the reals*.

1. For all s, for some n, s = f(n).
2. f(n) = {m: x not in f(m)} (from 1).
3. If n in f(n) then n not in f(n), and if n not in f(n) then n in f(n) (from 2).
4. Contradiction.

It is beautiful because it is short, and all short things are beautiful.  It is remarkable because the scholastic philosophers never produced anything close to it.  In nearly all matters of logic, the culture of the renaissance and early modern period never approached the heights that logic attained in the early 14th century.  But not this.
 
It needs a little explanation, of course.  The first statement follows from the claim that sets of natural numbers are 'countable', i.e. to do this, to any set s of natural numbers, there must correspond some natural number n.
 
The second follows from the first.  There must be some natural number corresponding to the set of natural numbers that are not in the set corresponding to them.  The third draws a simple conclusion from that.  The fourth states that the third is a contradiction.  We can therefore infer that one of the first two statements is false.
 
To forestall impudent hairsplitters, I should add that (as far as I know) Cantor never gave a proof in precisely that form.  His actual proof is in the Logic Museum, with my English translation. 
 
To any other quibblers, I reply that I am not a mathematician.

*Modified this evening o/a of Belette's complaint of sloppiness.

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).