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.