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Blackheath

April 18th, 2013 24 comments

This Saturday, I’ll be at the Blackheath Philosophy Forum in the Blue Mountains, talking about the economic feasibility of social democracy.

Categories: Philosophy Tags:

Out of the Crooked Timber of Humanity, no Straight Thing was ever Formed

September 6th, 2011 18 comments

That’s the tagline of Crooked Timber, the group blog of which I’ve been a member for quite a few years. I knew that it was quoted by Isaiah Berlin as a translation of something written by Kant, but I’ve never, until yesterday, seen it in a more complete context. That’s when I finally stumbled across Berlin’s, The Crooked Timber of Humanity, Chapter 1 of which ‘The Decline of Utopian Ideas in the West’ ends as follows

a liberal sermon which recommends machinery designed to prevent people from doing each other too much harm, giving each human group sufficient room to realise its own idiosyncratic, unique, particular ends without too much interference with the ends of others, is not a passionate battle-cry to inspire men to sacrifice and martyrdom and heroic feats. Yet if it were adopted,it might yet prevent mutual destruction, and, in the end, preserve the world. Immanuel Kant[1], a man very remote from irrationalism, once observed that ‘Out of the crooked timber of humanity no straight thing was ever made.’ And for that reason, no perfect solution is, not merely in practice, but in principle, possible in human affairs, and any determined attempt to produce it is likely to lead to suffering, disillusionment and failure.

Broadly speaking, I’m sympathetic to what Berlin is saying here. Revolutionary utopianism has been a disaster, particularly for the left. But, we still need a feasible version of utopia to oppose to the appeal of irrationalist tribalism and the naked self-interest of the top 1 per cent. And, whatever Berlin may have intended by it, “prevent people from doing each other too much harm” should not mean leaving the rich to enjoy the fruits of a system constructed in their own interests, and letting the devil take the hindmost.

A social democratic and feasible utopia should giving all human beings (individually and as a member of various groups) sufficient room and resources to pursue their own idiosyncratic, unique, particular ends with a reasonably equal capability of achieving ends that are feasible given the resources available to society as a whole.

It’s hard to spell out what that means, but I think easy enough to see that developed societies were moving in that direction, broadly speaking, until the 1970s, and are mostly moving away from it today (with some exceptions in areas like gay rights). The failure of the market liberal model to deliver on its promises, evident in the global financial crisis, along with the current struggle over austerity provides an opportunity to recover some of the ground lost in the last thirty years while, hopefully preserving the gains.

fn1. As in many such cases, our blog’s name and tagline owe at least as much to Berlin’s translation as to Kant’s original.

Categories: Philosophy, Politics (general) Tags:

Moral philosophy, casuistry and the ethics of organ donation (crosspost from CT)

January 30th, 2010 22 comments

As Harry Brighouse mentioned at CT, I’m sceptical of the value of artificial “thought experiments” in moral philosophy, without having a fully coherent basis for this scepticism. One thing I don’t like about the term “thought experiment” is the implication that the results of such thought experiments constitute data, and therefore that an ethical theory is more satisfactory if it fits such data than if it does not. The way I’d prefer to approach such problems involves an iterative loop, with repeated stages of (i) consider reasonable general principles (ii) compare to intuitions about specific cases (iii) where appropriate, adjust judgements on specific cases (iv) revise general principles to give a better fit to adjusted intuitions. That is, I don’t think either general principles or specific intuitions are trumps.

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Categories: Philosophy Tags:

Consequentialism and confidence

November 23rd, 2009 21 comments

I’m finally collecting my thoughts in response to Chris Bertram’s CT post on Consequentialism and Communism, particularly this remark imputing to consequentialists in general

the very same disregard for, or scepticism about, the rights of individuals, the same willingness to sacrifice individual lives for valuable goals

that characterized the Bolsheviks and their successors.

As regards willingness to sacrifice individual lives for valuable goals, I think this is an unfair criticism of consequentialists. Look at any of the standard anti-consequentialist philosophical examples – trolley car, organ bank, survival lottery, violinist and so on. It’s always the hard-nosed consequentialist who is supposed to want to save as many lives as possible, and the noble anti-consequentialist who proposes to sacrifice individual lives for “valuable goals” such as clean hands, natural rights and bodily integrity.
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Categories: Philosophy Tags:

Moral arbitrage

January 10th, 2009 32 comments
.!.

I posted this in response to some discussion at Crooked Timber on the Iraq war, Gaza and so on.

Looking at the discussion, it seems as if nearly everyone is concerned about the (foreseeable) consequences of their actions, but there are a lot of claims that some consequences should be treated differently from others (intended vs unintended, direct vs intermediated by the predictable reactions of others, and so on).

To an economist, what this naturally suggests is the possibility of moral arbitrage.

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Categories: Philosophy Tags:

A bit more on the economics of happiness

November 10th, 2008 32 comments

I was discussing the economics of happiness with my son, and in particular the Easterlin paradox. Within a given country, people with higher incomes are more likely to report being happy. However, in international comparisons, the average reported level of happiness does not vary much with national income per person, at least for countries with income sufficient to meet basic needs. The same is true over time – average happiness levels don’t change much even as incomes rise.

This is often taken to mean that it’s relative rather than absolute income that determines happiness, so an increase in everyone’s income won’t make anyone happier. Hence, we shouldn’t worry so much about increasing income, but should focus more on factors likely to contribute to happiness. The point that struck me was that, given Easterlin’s data, the paradox is almost certain to apply whatever potential source of happiness we consider, in one form or another.

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Categories: Economics - General, Philosophy Tags:

The dormitive quality of rational choice

October 10th, 2007 8 comments

This Matt Yglesias post has already made it on to my colleague Andy McLennan’s door. It’s short enough to quote in full

I’m not sure I understand why Greg Mankiw thinks economists “don’t understand tipping.” When I was learning economics, I learned that people are utility-maximers and that whenever you see some behavior that doesn’t seem explicable in purely financial terms that must be because people are deriving utility from the foregone financial advantage. Thus, as any economist could tell you, people tip because of the utility they derive from the tipping in much the way that economists can explain all aspects of human life.

Have I ever mentioned that philosophers tend to think that economics is vacuous? Which isn’t to say that you shouldn’t listen to economists. These days, they tend to know a lot of math, and math is a very useful thing.

Matt omitted the irony alerts, but I tried to spell out the same point here.

Given any data on any observed set of problems involving the selection of one or more choices from a set of alternatives, the observed choices can be represented as the maximisation of an appropriately specified function.

Playing straight man to Matt, that doesn’t mean utility functions are useless – the functional representation lets you do lots of math that is much harder if you try to work directly with preferences. But any competent economist knows that utility isn’t an explanation of observed choices, it’s a way of representing them. The representation is simpler if choices satisfy some minimal consistency requirements, like transitivity (if you prefer A to B and B to C then you should prefer A to C).
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Categories: Economics - General, Philosophy Tags:

Rationality and utility

September 17th, 2007 20 comments

Over at Cosmic Variance, physicist Sean Carroll offers some admittedly uninformed speculation about utility theory and economics, saying

Anyone who actually knows something about economics is welcome to chime in to explain why all this is crazy (very possible), or perfectly well-known to all working economists (more likely), or good stuff that they will steal for their next paper (least likely). The freedom to speculate is what blogs are all about.

I didn’t notice anything crazy but there’s a fair bit that’s well-known. For example, Carroll observes that utility is generally not additive across commodities, and that some goods are likely to be more closely related than others. That’s textbook stuff, covered by the basic concepts of complementarity and substitutability.

This is a more interesting and significant point

But I’d like to argue something a bit different — not simply that people don’t behave rationally, but that “rational� and “irrational� aren’t necessarily useful terms in which to think about behavior. After all, any kind of deterministic* behavior — faced with equivalent circumstances, a certain person will always act the same way — can be modeled as the maximization of some function. But it might not be helpful to think of that function as utility, or as the act of maximizing it as the manifestation of rationality.

I can only agree. But economists and (even more, I think) political scientists in the “rational choice” tradition regularly get themselves tied up in all sorts of knots about this, switching between the trivial notion of maximising a function and substantive claims in which rationality is frequently equated with egoism. Joseph Butler demolished this kind of reasoning nearly 300 years ago, but it keeps on popping up.

* This qualification isn’t necessary, and Carroll notes later on that choices are often stochastic. The resulting probability distributions still maximise an appropriately defined function.

Categories: Economics - General, Philosophy, Science Tags:

Conserva-bible

May 13th, 2007 12 comments

I can’t resist following Conservapedia, the Tlön version of Wikipedia, in which the liberal, anti-American bias of the Earth version is replaced with virtue and apple pie. But where did this bias come from, and how is it so deeply rooted in our culture? The answer, it turns out is the Bible, not of course the true version held in the vaults of Uqbar, but the liberal Earth Bible known by such as names as the King James and Revised Versions.

In the Uqbar version, as explained at Conservapedia, all sorts of politically correct liberalism is eliminated or glossed out of existence. Uqbar scholars have discovered that the soft-on-crime John 8:7 ‘”If any one of you is without sin, let him be the first to throw a stone” was inserted by time-travelling liberals some time around the 4th century. Naturally, Conservapedia says, Wikipedia sticks to the Earth version, though a check of the actual site suggests that the annoying liberal habit of looking at all the evidence is at work here as well.

Conservapedia has able assistance from other conservative sources. All that class warfare stuff about the rich not getting into heaven (Matthew 19:21-24) turns out to mean that if you want money, you should cut God (or his earthly representatives) a good share in advance. Other kinds of warfare are fine with the Prince of Peace, though. As for turning the other cheek ((Luke 6:27-31), it’s No More Christian Nice Guy.

Categories: Philosophy Tags:

In praise of libertarianism

March 17th, 2007 10 comments

I got a great response from libertarian readers to the Great Shave Appeal, and so the final instalment in my ‘In Praise of ..’ series is addressed to them.

Although they are often at loggerheads, libertarians and social democrats share plenty of ideas, derived in large measure from common sources. Both draw heavily on the 19th century liberalism of John Stuart Mill, who managed to write effectively in support of both classical free-market economics and, later in life, a rather abstract form of socialism.

It’s not surprising then, that I broadly agree with libertarians on the classic civil liberties issues – freedom of speech, freedom from arbitrary arrest and detention, opposition to government intervention in private decisions such as sexual activity and drug use and so on.

The attacks on civil liberties since the Iraq war have made many of these issues more vitally relevant and led me and others to stress our areas of agreement with libertarian defenders of freedom such as blogger Jim Henley. They have helped to distinguish genuine libertarians from otherwise orthodox authoritarians (typically US Republicans), who happen to take a relaxed view on sex and drugs.

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Categories: Philosophy, Politics (general) Tags:

I refuse to use that word, but …

October 18th, 2006 22 comments

I’m using my blog to beg for help on a minor point.

The Wikipedia article on pscyhological egoism, which draws on the e Stanford Encyclopedia of Philosophy includes

Finally, psychological egoism has also been accused of using [[circular logic]]: “If a person willingly performs an act, that means he derives personal enjoyment from it; therefore, people only perform acts that give them personal enjoyment”. In particular, seemingly altruistic acts must be performed because people derive enjoyment from them, and are therefore, in reality, egoistic.. This statement is circular because its conclusion is identical to its hypothesis (it assumes that people only perform acts that give them personal enjoyment, and concludes that people only perform acts that give them personal enjoyment).

I’ve added the claim, based on memory that “This objection was made by William Hazlitt in the 19th century, and has been restated many times since then”, but Google only produces reference to a previous occasion on which I made the same claim. Can anyone point to a good citation of Hazlitt on this, or to any other versions of this argument from the 19th and 20th centuries?

Categories: Books and culture, Philosophy Tags:

Pessimism

August 31st, 2006 10 comments

This NYT piece by Adam Cohen starts with the observation that Americans are feeling pessimistic about the war in Iraq, Hurricane Katrina and so on, then jumps to a recent work on philosophical pessimism by Joshua Dienstag, whose basic argument is summarised in this sample chapter. As Cohen says, pessimism in this sense is not a gloomy disposition, but a worldview that “simply doubts the most basic liberal principle: that applying human reasoning to the world’s problems will have a positive effect.’ Cohen concludes “Part of Mr. Bush’s legacy may well be that he robbed America of its optimism “.

But if optimism holds that applying reasoned analysis will have a positive effect, the experience of the Bush Administration merely illustrates the point that the converse is also true.
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Categories: Philosophy Tags:

The apparent deceptiveness of the world

August 29th, 2006 9 comments

Googling around in connection with my review of Unspeak, I came across an old LanguageLog post on The apparent deceptiveness of the world, which cites the paradoxical statement

Appearances are not deceptive; it only seems as if they are.

and invites Brian Weatherson (who’s now one of the crew at Crooked Timber) to analyse it, saying

Clearly, if this is true, then it has to be false, and if false, it must be true. Yet it is not a standard liar-paradox sentence like as in classic liar sentences like This statement is false, or Everything I tell you is a lie, including this. It does not mention truth or falsity, or refer to itself. It is a metaphysical claim, as far as I can see. It speaks not about language or truth but about the nature of reality. It says (contrary to the old proverb) that reality does not present itself in a way that deceives our senses, and any perception we may have to the contrary is incorrect.

I think we can extract a coherent claim with the aid of Hamlet’s observation “For there is nothing either good or bad, but thinking makes it so”. I’d read the statement as saying something like “First appearances are not deceptive; it’s thinking about them that leads you astray”. While this is obviously false as a general statement, I think direct perceptions are usually closer to the mark than the results of the kinds of analysis (Freudianism, large parts of Marxism, a lot of public choice theory) that purports to strip away surface appearances and reveal the underlying truth.

Categories: Philosophy Tags:

BrisScience and BrisReligion

August 13th, 2006 14 comments

The next in the BrisScience lecture series is on tomorrow (Monday) night, at City Hall, 6pm for 6:30. Continuing to diversify the range of topics, the speaker is Margaret Wertheim, on the topic ” Space and Spirit: Why Science and Religion Together are Driving us Crazy”. As the extract over the page suggests, Wertheim thinks that we have a fundamental pyschological need for a reconcilation of science and religion.

I’m not so sure about this. One of the most striking features of the late 20th century was the collapse of active religious belief in most of the developed world, with the glaring exception of the United States. This didn’t result in any direct sense from scientific discoveries about the universe. And, surprisingly, it didn’t seem to produce any big changes in behavior (there have been changes in sexual mores, but these have been just as noticeable in the US as elsewhere) or any obvious rise in cosmic angst. You can find some statistical differences between believers and non-believers, and between those who regularly attend religious services and those who don’t, but they are a lot smaller than much of the discussion of this topic would suggest.

Unfortunately, I won’t be able to make it, as I’ll be presenting at the IAAE Conference in the Gold Coast so maybe some Brisbane-based reader would like to put in a brief report on proceedings.
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Categories: Philosophy, Science Tags:

Conservatism invented in 1953:NYT

August 2nd, 2006 33 comments

The term “conservative” gets bandied about a lot these days, and readers may wonder where it comes from. Jason DeParle in the NYT has the answer. It was invented by one Russell Kirk in 1953. DeParle’s opening para (“lede” in US newsspeak) introduces us to

Russell Kirk, the celebrated writer who a half-century ago gave the conservative movement its name

and elaborates later on

Kirk, who died in 1994, wrote 32 books, the most famous being “The Conservative Mind,� which was published in 1953. It championed 150 years of conservative thought, and offered “conservative� as a unifying label for the right’s disparate camps.

I must say, it’s a great term, offering a neat contrast with “progressive”. Surprising nobody came up with it earlier, really.

Categories: Philosophy Tags:

Repost on organ banks

May 5th, 2006 5 comments

Over at CT, I’ve reposted this piece from 2003 on thought experiments in ethics.
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Categories: Philosophy Tags:

In praise of speciesism (crossposted at CT)

August 13th, 2005 17 comments

Nicholas Gruen at Troppo Armadillo is unimpressed by Peter Singer’s Animal Liberation. Nicholas argues that the whole idea is an unnecessary and unhelpful, since we can justify concerns about animals suffering from the simple observation (the basis of Jeremy Bentham’s argument for laws against cruelty to animals) that animals suffer. He says

What does the term ‘speciesism’ add to this? If Oscar Wilde had nothing to declare but his genius, Peter Singer’s book and its central concept of speciesism had nothing to declare but its circumlocution.

I haven’t got a fully consistent position on all this, but I think that, however ugly it is as a word, speciesism is a meaningful concept, and I’m in favour of it. That is, in opposition to Singer’s views on the subject, I’m in favour of treating all human beings, from birth to brain-death as having specifically human rights, simply by virtue of the fact they are humans, and whether or not they are self-aware and capable of perceiving themselves as individuals. I’d argue for this on rule-utilitarian grounds, which I understand to be Singer’s general viewpoint, though the same conclusion could be reached in other ways.
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Categories: Philosophy Tags:

Opportunity costs redux (crosspost from CT)

July 21st, 2005 19 comments

Harry Brighouse has a question about my post on consequentialism and opportunity costs, as applied to the Iraq war, which raises a couple of important points about consequentialism, and also leads me to suggest a specific correction to my post on this topic.
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Categories: Philosophy, World Events Tags:

War and its consequences (cross-posted at CT)

July 18th, 2005 66 comments

Chris Bertram’s recent post on responsibility got me started on what I plan to be the final instalment of my attempts to analyse the ethical justification for war. Comments much appreciated.
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Categories: Philosophy, World Events Tags:

Heidegger and the Nazis, again

June 4th, 2005 40 comments

Continuing on a European theme, and on recycled debates, the hardy perennial issue of Heidegger and the Nazis has re-emerged.

Back in the Pleistocene era of Australian blogging (2002), there were some interesting discussions of how we should react to the political mistakes and crimes of philosophers. Examples included Heidegger’s involvement in Nazism, Hayek’s support for Pinochet and Sartre’s adherence to the Stalinist French Communist Party . Don Arthur (site long gone, alas), Tim Dunlop (can’t find a link, but maybe still in the archives), Jason Soon and Ken Parish all had some interesting things to say.

Most contributors to the debate were more willing than I was to separate thought and action. I don’t think the idea that the arguments of a political theorist or philosopher can be treated in isolation from their life and work as a whole is, in general, sustainable. There are exceptions to this: a philosopher might collaborate with a dictatorial regime out of fear or ambition, even though this was the opposite of the course of action implied by their philosophical views. But that doesn’t appear to be the situation in any of the cases I’ve mentioned.

Much closer to the centre of the action, controversy over Heidegger has been reignited by the publication of Emmanuel Faye’s Heidegger, l’introduction du nazisme dans la philosophie, which also includes an attack on Carl Schmitt, another thinker associated with the Nazis but now popular on the left (Mark Bahnisch gives some background here). Not surprisingly, Faye’s book has produced a reaction, in the classic form of a manifesto (in 13 languages!). The manifesto announces this site, with many contributions (all in French), , with lots of references to to rprevious contributions to the debate, but without a systematic organisation, which makes it all a bit hard to follow. Some of the arguments focus on the details of the historical evidence, and others on the more general question of whether this kind of attack is legitimate.

I haven’t read Faye, and it sounds as if he pushes his case too far, but I’m not ready to acquit Heidegger of collaboration with the Nazis or to conclude that his philosophical views are untainted by his own apparent interpretation of them as a guide to action. Comments appreciated.

Categories: Philosophy Tags:

All bloggers are liars?

March 11th, 2005 9 comments

Slate runs a good debunking of romantic popular misinterpetations of Godel’s theorem. Key quote

The precise mathematical formulation that is Gödel’s theorem doesn’t really say “there are true things which cannot be proved” any more than Einstein’s theory means “everything is relative, dude, it just depends on your point of view.”

I’ve lost count of the number of times I’ve seen dubious appeals to intuition or claims about chaos theory and the like supported with reference to Godel’s theorem, but I have derived the following proposition:

Quiggin’s metatheorem: Any interesting conclusion derived with reference to Godel’s theorem is unfounded.

Feel free to evaluate with reference to the post title.

Categories: Philosophy Tags:

Hayek and Pinochet: One more time

February 25th, 2005 35 comments

Thanks to Bruce Littleboy for pointing me to this complete translation of Hayek’s 1981 interview with the (pro-Pinochet Chilean) newspaper El Mercurio in which he stated

Personally I prefer a liberal dictator to democratic
government lacking liberalism.

As the interview makes clear, Hayek supports the Pinochet dictatorship, on the assumption (correct in the end) that it would eventually give way to a more liberal regime. Of course, many supporters of dictators make this assumption and all dictatorships, like all governments, pass away sooner or later.

Plenty of people have made worse political mistakes than backing Pinochet, most obviously those sections of the left who supported Stalin, Mao and their lesser accomplices. Still, the fact that both the Mont Pelerin society and leaders of the free-market right like Thatcher and Reagan gave their enthusiastic support to this mass murderer should be remembered when they, and their followers, try to claim the moral high ground as against the moderate left.

Categories: Philosophy, Politics (general) Tags:

The bleeding edge

December 23rd, 2004 Comments off

There’s a new version of the MT Blacklist program out, fixing a critical error in which deleting one weblog could cause you to lose another. Users of MT & Blacklist will be pleased to know that, in the process of fighting off comment spammers and abusive morons, your intrepid host discovered this critical error the hard way. Jason Hoffman at Textdrive not only saved my bacon with a near-perfect backup file, but reported the bug which Jay Allen has now fixed. I think the grip of the law is gradually tightening on comment spammers, but no doubt they’ll be with us for some time, and morons will be with us always.

Categories: Philosophy Tags:

A real life ticking bomb problem

December 23rd, 2004 13 comments

A while ago, I looked at the ticking bomb problem and concluded that, whatever the morality of using torture to extract life-saving information in emergencies, anyone who did this was morally obliged to turn themselves in and accept the resulting legal punishment. Reader Karl Heinz Ranitzsch has pointed me to a real-life case, reported by Mrs Tilton at Fistful of Euros. The case involved a threat of torture, rather than actual torture, and the deputy police commissioner involved was convicted and fined. Without detailed knowledge of the circumstances, I tend to agree with Mrs T that this was about the right outcome.

Categories: Philosophy Tags:

Revolution and Revelations

September 30th, 2004 14 comments

While we’re on the interface between religion and politics, here are a couple of questions I’ve been wondering about for a while.

The first one relates to my memories of the late 1960s, when most people of my acquaintance gave at least some credence to the belief that there would be a revolution of some kind, sometime soon. At about the same time, I encountered the Revelation-based eschatology of people like Hal Lindsey. Thirty years later, there’s been no revolution, and I don’t know of anyone who seriously expects one. As I recollect, belief in the possibility of a revolution had pretty much disappeared by 1980.

Revelation-based prophecies have similarly failed time after time, but they seem to be more popular than ever. What is about apocalyptic Christianity as a belief system that protects it from empirical refutation? I assume there’s heaps of research on this kind of thing, but I hope to get readers to point me to the good stuff.

The second point is that, as can be seen from Lindsey’s site, he and other apocalyptic Christians have strong political views, which could broadly be summarised as favouring a vigorous military response to Antichrist (variously identified with the Soviet Union, the UN and so on). How does this work? Do they think that another six armoured divisions could turn the tide at Armageddon? If so, wouldn’t this prevent the arrival of the Millennium and the Day of Judgement[1]?

And how does all this affect believers in rapture? Do they install automatic watering systems for their gardens and arrange for unsaved neighbours to feed the cat? Or do they just pay into their IRAs as if they expect the world to last forever?

fn1. There’s a genre of horror movies (The Omen, The Final Conflict and so on) that takes pretty much this premise.

Categories: Philosophy, Politics (general) Tags:

Care of strangers

August 30th, 2004 19 comments

Here’s a guest post from regular commenter Brian Bahnisch, on the philosophy behind our stance on asylum seekers. It raises some important (though not entirely new) questions about the adequacy of utilitarianism in contexts like this.
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Categories: Oz Politics, Philosophy Tags:

Riemann hypothesis proved ?

June 11th, 2004 9 comments

According to this report, Louis De Branges claims to have proved the Riemann Hypothesis. If correct, it’s very significant – much more so than the proof of Fermat’s Last Theorem by Wiles.

It is also, I think, the last of the big and well-known unsolved problems in mathematics, and its nice to see the search ending in success. Some of the other big problems have been closed, rather than solved. The classic problems of the Greeks such as squaring the circle were shown to be insoluble in the 19th century, and the Hilbert program of formalisation was shown by Godel to be infeasible. And the four-colour problem (not a really important problem, but a big one because it was easily described, interesting and very tough) was dealt with by a brute-force computer enumeration.

Almost instant update Commenter Eric points to Mathworld which says “Much ado about nothing”. On the other hand, the same page reports a proof of the infinitude of twin primes which has been an open question for a long time, though not a problem in the same league as those mentioned above.

Categories: Philosophy Tags:

Paradoxes and infinity

June 1st, 2004 6 comments

Following up my three-way classification of paradoxes,[1] I want to argue that paradoxes involving infinity are always of type-3, that is, the result of ill-posed problems or inappropriate ways of taking limits. (Much the same position is defended in the comments thread by Bill Carone). In fact, I’d argue for the following general principle, applicable to all models relevant to human decisionmakers.

Whenever a result, true for all finite n, is strictly[2] reversed for the infinite case, the problem in question has been posed incorrectly

To defend this, I rely on the premise that we are finite creatures in a finite universe. If a mathematical representation of a decision problem involves an infinite set, such as the integers or the real line, it is only because this is more convenient than employing finite, but very large bounds, such as those derived from the number of particles in the universe. Any property that depends inherently on infinite sets and limits, such as the continuity of a function, can never be verified or falsified by empirical data. Since we are finite, any result that is true for all finite n is true for us.
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Categories: Philosophy Tags:

The point of paradox

May 26th, 2004 5 comments

Suppose you have encountered Zeno’s Achilles paradoxfor the first time. Zeno offers a rigorous (looking) proof that, having once given the tortoise a head start, Achilles can never overtake it. Would you regard this as[1]

# A startling new discovery in athletics;

# A demonstration of the transcendent capacity of the human spirit – although the laws of logic forbid it, Achilles does in fact catch and overtake the tortoise; or

# A warning about how not to take limits?
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Categories: Philosophy Tags:

Two envelopes

May 19th, 2004 7 comments

Via Juan at Philosophy617 (who doesn’t think much of the proffered solutions, and probably won’t like this one) I came back to this version of the two-envelope problem put forward by Brian over at Crooked Timber last year.

In this case, once you observe that Brian’s angel is giving you faulty theology, it’s easy to show that you should reject his[1] mathematics, and his offer. At the end of the problem, the angel says “It’s purgatory,” says the angel, “take all the time you want.” But the whole point of Purgatory is that it’s finite – you purge off your sins one at a time until they’re all paid off. Since we now have a finite problem, the solution is straightforward.
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Categories: Philosophy Tags: