I wish the name of Gordon Brown didn’t always take the lead in these promotions but I don’t know of any more effective way of promoting the cause of women’s education around the world – and I do think that cause is perhaps the most important one in the air right now.
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My previous post refers to some aspects of Godel’s famous theorems about incompleteness in mathematics. But since the context which brought them to mind was a posting on an atheist blog it’s ironic that Godel believed he had a proof of the existence of God.
The irony is compounded by the fact that he was allegedly reluctant to publish the proof because he was worried that people might think that he actually did believe in God – but in fact he apparently did! Of course he also went essentially mad, but his wife claimed that he read the bible regularly and he once described himself as “baptized Lutheran (but not member of any religious congregation). My belief is theistic, not pantheistic, following Leibniz rather than Spinoza.”
And among his papers at death was a page entitled ‘My Philosophical Viewpoint’ which lists fourteen points including:
1. The world is rational
10. Materialism is false
14. Religions are, for the most part, bad – but religion is not.
In the light of the way he expressed the undecidability results in his 1951 Gibbs lecture (“Either . . . the human mind . . . infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems”), perhaps the result of his God proof should be expressed as “Either God exists or Modal Logic is fundamentally flawed”. As for me, not having either the will or the capacity to get into modal logic, it could go either way – or perhaps I could say that, within the powers of *my* human mind, both questions are undecidable.
In the discussions following Landon’s Guest Post @» Butterflies and Wheels (on the value in philosophical training) there is an exchange between Landon and Harald Hanche-Olsen on the question of whether Logic is a branch of Philosophy or Mathematics. I make no claim on logic per se, but the Boolean Algebra which models its basics is a branch of mathematics and that relatively trivial bit is all that has relevance to computers – which is what Landon was on about, but that is not what I want to look at here.
Further down in that exchange the question of Godel’s proofs came up (though that definitely has nothing to do with real computers!) and Landon made some claims that I had to dispute. (In particular he denied the relevance of the well known restriction to systems which include a model for the natural numbers). This led me to revisit the little book by Nagel and Newman – and actually there is still a gap in my understanding. On page 78 N&N show how the statement that formula x is a leading part of formula y corresponds to the Godel number for x being a factor in that for y. So far so good, but on page 79 they assert that there is a similar but more complicated arithmetic characterization of the statement that number z is the Godel number for a proof of the statement with Godel number x. This seems quite plausible but I have never checked it. It could be considered an ‘exercise’ but it might be a hard one to actually carry out in detail. But that’s not the issue I want to address here either.
In order to point out the silliness of claiming that the restriction to systems which include the natural numbers is irrelevant it is of course necessary to identify a mathematical system which does not include them. Simple Boolean Algebra is one – whose consistency is in fact provable. But given Landon’s position, that might not be an effective example. Other algebraic structures naturally come to mind – except for the awkwardness that they are often (though probably not essentially so) set up in terms of a “set” of objects and so it might look at least superficially as if the axioms therefore presuppose those of ZF set theory which does include a model of the natural numbers (and on to just about everything else). Then I thought “aha the existence of Finite Geometries must show that the Euclidean axioms don’t imply the ability to construct a full model of the Natural numbers”. But fortunately I checked before posting and noted that only the incidence axioms were listed – which is fine for my purposes but raises the question of whether the standard Euclidean geometry could have been used as an example. If I had thrown out my first thought there, it would not have taken an expert to see that I was wrong (or at least hadn’t thought carefully enough about which of the often not clearly itemized axioms I was referring to). Anyone with even the slightest familiarity with high school Euclidean Geometry could have said “But Euclidean geometry allows you to construct the mid-point between any two points, and if you then construct the mid-point between that and one of the first two, and so on then don’t you get an infinite sequence of distinct points which could be identified with the ordinal numbers?” and I would have had to stop and think about what goes into that mid-point construction which has been left out of the axioms in terms of which finite models do exist.
In mathematics, and actually I suspect in other disciplines as well, it is often newcomers who make the major advances because those new to the field are less encumbered by either repeatedly reinforced preconceptions or masses of irrelevant detail. If I can be excused a bit of a play on words: they may be expert but they are not yet experts.
Ophelia Benson’s post on Patricia Churchland’s 2011 book ‘braintrust’ points out that, in contrast to the efforts of Sam Harris and Michael Shermer, Churchland makes a much more modest claim for what she is doing. Indeed Churchland’s claim “is not that science will wade in and tell us for every dilemma what is right or wrong. Rather, the point is that a deeper understanding of what it is that makes humans and other animals social, and what it is that disposes us to care about others, may lead to greater understanding of how to cope with social problems.” Harris on the other hand, and to a lesser extent Shermer, does seem to be claiming the goal of determining what is right or wrong rather than just how people in a certain context might judge it. I was happy to see this point made in a relatively high profile setting as it seems very much in line with my own earlier criticisms of Harris
But a parenthetical comment in Ophelia’s first paragraph has prompted a discussion orthogonal to that of whether science answers moral questions – namely (but putting it a bit crudely) does philosophy do so either?
And I think an exploration and continuation of that discussion may be relevant to concerns some Philosophers seem to have about public perception of their discipline – perhaps including the recent “Physics vs Philosophy” wars. …more »
I do NOT want my cable fees used to pay for biased propaganda that undermines the caring culture that I have chosen to live in (and which, with bad luck, I may one day have to depend on).
Those who want this garbage are not prevented from buying it but please do NOT force me to join them!Sign the AVAAZ petition.
Our experience always involves a lot of complexity which we typically manage by isolating just a few quantities of interest which are related by compactly expressible relationships. I am curious to see whether “complexity theory” really proposes general methods for dealing with cases where this is not possible – or whether it just consists of introducing some particular new ways of extracting simplified models from more complex ones.
And at the Atlantic Alexis Madrigal responds to Jack Dorsey on the role of luck (in addition to hard work and genius) in the making of a great success story.
Something similar came to mind when I read Ta-Nehisi Coates (also at the Atlantic) discussing the challenges faced by daily newspaper columnists, and frankly wondering whether he could meet them himself. But my response is that actually no-one can, and the annointing by newspaper editors of a precious few with the gift of that platform is an insult to those who pay for the papers. (Though I have to admit that if people continue to pay for it then it’s not surprising that that’s what the papers will continue to dish out.)
Whether it’s access to audience via a media pulpit, to political power, or to money, the fact is that there’s an instability in the sense that once you have a certain amount it becomes easier to get more – or as the Bible says “Unto him that hath shall be given, and from him that hath not shall be taken away – even that which he hath”.
According to G. Michael Maddock and Raphael Louis Vitón, “Conscious Capitalism” Will Be The Framework For Your Next Decade Of Innovation, but I’m more inclined to Mr Garth’s skeptical position on this,
This idea of “doing well by doing good” is fine up to a point, but ultimately it amounts to a denial rather than an affirmation of any non-monetary values.
If doing the right thing leads to increased profits that’s all well and good and deserves pointing out, but since seekers of profit will always find it, such pointing out is not really necessary. The challenging situations are those where the claim that doing the right thing will lead to increased profit are either false or hard to prove. In such cases, the only way to get the profit motive to drive business in the right direction is to ensure that it does so by adding costs to doing the wrong thing. This means regulations with enforced penalties of a serious magnitude.
End of story.
ThinkProgress reports that Lomborg Urges Climate Inaction With Misleading Stats In Murdoch's Wall Street Journal.
This is the same guy who first threw up a wall of phoney statistical arguments against the reality of Anthropogenic Global Warming and then when they had all been refuted said effectively “Well ok it is happening but we don’t need to do anything about it”. This would have been ok (in a moral sense) if he had really believed the first position, but he is too smart for that and I am sure that he presented his anti-AGW argument in the full knowledge that it was bogus.
The most important point to note about this guy is that he is prepared to adopt any argument in support of his goal of inaction but will drop it as soon as its capacity for creating further delay becomes weakened. The fact that he adopts positions that he probably knows are untenable just to create delay is what is most offensive, but may also eventually come to be recognized if the point is made often enough.
Sadly he is not unique. There are people on both sides who adopt positions with regard to climate change (and the choice of optimal response to it) who do so with less regard to the validity of their arguments than to whether or not they support some ulterior motive.
William M. Briggs claims that Women In Combat Results In A Suboptimal Military but his argument belies his supposed expertise in statistics.
I am taller and stronger than the average woman, but only around the 80th percentile. So 20% of women are physically stronger than me. I could probably dominate half of those by virtue of a more highly testosterone-fuelled aggressive nature, but that leaves about one woman in ten who could probably have whupped my ass in my prime if properly trained to. If I had been in the right age cohort and location I could easily have passed muster to enter combat-ready military service, but one of those “nasty” women would have been a better protector for my country. It only makes sense to pre-select on the basis of population averages when the variable(s) of interest are hard to assess directly.
Perhaps Mr Briggs needs to (re?)learn some statistics.
Of course this is not to say that there is a case for demanding “equity” in the form of equal representation of genders or for any lesser reduction in the qualities required of a female as opposed to a male soldier, but the fact is that when much of modern combat is enacted from what is essentially the console of a video game it is less physical strength than various mental capacities which should control the selection.
One of the most intriguing points was that even a placebo identified as such to the patient can have a beneficial effect. So perhaps whatever benefit people derive from religious rituals does not require insistence on actual belief from the participants.
On the other hand, the subjective relief from the placebo (even when not identified as such) is apparently usually not matched by any objective improvement in the actual pathological condition. (The mental effects may have objective manifestations in brain chemistry or whatever of course, but the underlying illness and physical damage continues to progress.)
Masking pain, or feeling good about life, can be a valuable goal but should not be allowed to divert attention from effective treatment of a curable illness – or from giving effective attention to the ills of the world around us.
Using the click2play option, a page needing JAVA (or any other plugin) requests permission to run it (which I can ignore if I don’t both trust the source and need the service).
This is the only sensible option anyhow when other plugins also have occasional security issues and always take up resources which are best left available to other applications until the plugin is actually needed.
So why has James Fallows joined the latest anti-JAVA panic which has the effect of having people shut themselves off completely from useful tools on trusted sites?
…because I have freely decided to do it!
Those who claim to have evidence that “you probably don’t have free will” or who assert that complex chaotic systems’ unpredictability “is what gives you free will” are both either unprincipled or naive in accepting that the idea of “free will” has any absolute meaning.
I have yet to see a coherent definition of what it would mean to have, as opposed to not have, free will. But I cannot follow along with the game of debunking the concept by refuting a definition that was proposed in order to debunk the concept.
On the other hand, if Dennett is right in his claim that “Philosophers have done some real work that the scientists jolly well should know” then I’d like to see a brief sample of what he considers the best (just in case there’s a chance that looking further wouldn’t be wasting my time).
One has to wonder why anyone would rework a song like R.E.M.’s “Losing My Religion” from Minor to Major Scale, though I suppose at least it serves someone’s political purpose. But to do the same with the Doors ‘Riders of the Storm’ really does just convert a great song to Muzak
Actually I prefer to go the other way, especially with national anthems (for which the American one becomes quite beautiful and particularly appropriate for anyone disappointed at the apparent failure of an enterprise of great promise)
Spanish Runner, Ivan Fernandez Anaya, gave up the opportunity to take advantage of a misunderstanding by his opponent and then was sincerely frank about why he did so.
This doesn’t change my opinion as to the silliness of high-stakes athletic competition but it can’t help but raise the spirit with regard to how decent people can be when the stakes may be high but are not cranked up to ridiculous levels.
It is clear from the video that Abel Mutai was confused by a change of track colour rather than experiencing a failure of strength or will, so I suppose Anaya had good reason to think that it would be unfair to win (if one thinks of the race as a purely physical contest). But what I particularly like is his frankness about his own motives.
At the end of the El Pais report he is quoted as saying “Of course it would be another thing if there was a world or European medal at stake. Then, I think that, yes, I would have exploited it to win… But I also think that I have earned more of a name having done what I did than if I had won. And that is very important, because today, with the way things are in all circles, in soccer, in society, in politics, where it seems anything goes, a gesture of honesty goes down well”
William M. Briggslaments the abuse of statistics in many of its applications. But I really think that he undermines his case when he attacks “classical statistics” itself rather than its abuse. Such abuse is definitely all too common in many fields but it is just not true that “*Every* analysis begins by assuming more than is warranted”(emphasis added). And on the other side of the argument the “superior” alternate (Bayesian/predictive) methods he advocates are just as susceptible to abuse as the old – perhaps more so as they are arguably harder to explain than the classical theory and so people are more inclined to take the word of an “expert” on faith rather than really understand the assumptions that it comes from.
I have always thought that if anyone had a brain the financial world should have collapsed when the US “debt ceiling” was first enacted, since it amounts to a declaration of total financial irresponsibility by the largest participant in that world.
I wish that I could have got away with the same thing myself – but who would have given me a mortgage or credit card if I had loudly announced that once my debts exceeded a certain amount I would stop paying them off?.
In this sports roundtable at The Atlantic, Patrick Hruby, Jake Simpson, and Hampton Stevens discuss their reactions to the prospect of Lance Armstrong’s upcoming interview with Oprah Winfrey, and I must say I’m most closely aligned with Hruby.
The best outcome would be for this to open a real debate about the whole idea of “fair competition” in any arena, and the essential silliness of organized sport of any kind.
Back in the day, it would have been considered ungentlemanly in some circles for a real amateur to even practice his sport before the event, and now we have some individuals selected at a young age and intensively trained with healthy stipends from advertising sponsors so as to enable total devotion to the sport and access to the best available equipment. The silly “rules” about what equipment is “fair” and what is not (eg ruling out certain “unfair” fabrics for swimsuits) only level the playing field among those who can afford the best of what is “legal” and still leave those who can’t at a significant disadvantage.
When it comes to drugs and doping, the “rule” really is simply “don’t get caught”. There is no pretense that the use of substances not yet declared out of bounds is “cheating”; it is considered perfectly acceptable to take drugs which enhance performance by combating a particular medical condition so long as they don’t produce the same test results at performance time as drugs which improve the performance of everyone. There is at present no censure of drugs and doping outside of some arbitrary time frame and the definition of an excluded substance is essentially that it shows up in whatever tests are being applied (even if those tests show positive because of something that would normally be considered a necessary medical intervention).
According to present rules, it would be “fair” to feed a child hormones to enhance future athletic ability so long as there would be no detectable evidence of that treatment at the time of actual performance.
Is it “fair” to subject some children to a distorted life of single-minded pursuit of an athletic (or academic or artistic) objective? or is it unfair to permit the child to choose such a life? even for Mozart, if the lack of such experience would have held him back from reaching his full potential? (But what about one who has the same motivation and apparent early talent but turns out to never reach the same level of mature brilliance?)
So what should Lance Armstrong say? It depends on whether or not he actually lied about what he did and/or about the contents of various test samples he supplied.
If he did lie then he is a liar. But if he did not and if he either had positive results or failed to attend required test sessions (perhaps out of fear that they would show against him) then the worst he is guilty of is a miscalculation. If the rules require attendance which he missed or if he attended and showed positive then it doesn’t matter whether he took a banned substance or something else which produces the same test results. If he broke the rules he loses the trophy but is no more blameworthy than a player who gets a goal disallowed for being offside. There may have once been a world where the player who had scored the offside goal would halt the game and forego the goal on his own initiative if the linesman failed to call it. And if so that would have been a better world than this one. But in the disgusting world of modern organized sport such nobility would only be considered a weakness.
update:Apparently a bunch of slimy hypocritical baseball sportswriters who all looked the other way when it was happening have decided to punish the drug enhanced players of the 90s (but didn’t have the gumption to actually award any of those they claim did not partake!)
And here’s another comment on the hypocrisy of it all.
Here he discusses the fact that (contra Django) the sentiment of ex-slaves appears to have been significantly less vengeful than that of those who now feel on their behalf, and this leads me to wonder if there is a general pattern. (This thought may also be motivated to some extent by observing some of my own reaction to the recent Indian bus rape case.)
The righteous indignation that many of us so easily bring up on behalf of wrongs done to others (and the joy we feel in bringing or imagining horrible punishment down on those who have not harmed us directly) may be just the masterbatory exercise of an important component of the brain chemistry that underlies our capacity for altruism, but I wonder how much it shows up in other species which are also on the evolutionary path towards non-selfish morality. Do the monkeys which show anger when shortchanged in the sharing of treats also react on behalf of third parties? and to what extent might a tendency toward such reactions (even at a cost to the individual who has them) serve as an evolutionary advantage to the gene complex which drives it?
It’s no insult to Obama to say that TIME’s “Runner-Up”, Malala Yousafzai would have been a better choice than the boring predictability of giving a second nod to a re-elected president.
Actually if Obama has a second year to own it may be one of the next two if he can actually complete some of his program, and especially if that leads to control of congress in 2014.
But Malala’s introduction as a focus for a moement that could really change the world may well turn out to be the most important individual-related event for a long time.