Tuesday, August 31, 2004

Logic and Possibility

The Maverick Philosopher responds to my charge of question-begging:
Rethinking this, my argument strikes me as logically impeccable. Am I assuming what I need to prove? Not that I can see. What I am arguing, very simply, is that LNC cannot be an empirical generalization since if it were, it would be logically contingent, i.e., logically possible false. But this is absurd since LNC is the criterion of logical possibility. LNC defines what it is to be a logically possible world. Hence a logically possible world in which LNC fails to be true is a world in which a contradiction is true. Hence, by RAA, (1) is false.

To make things clearer, I have emphasised in bold the exact stage which strikes me as question-begging.

I could be mistaken here, but as I understand it, to question the necessity of the laws of logic is to question their metaphysical necessity. Surely no-one would doubt that the laws of logic are logically necessary. That's as absurd as doubting that the laws of nature are 'naturally necessary' (by the definition given in my previous post). It's just an empty tautology - as Bill himself noted, "LNC is the criterion of logical possibility". So long as we remain within the framework of classical logic, it is trivially true that the laws of logic could not possibly be false. They are true by definition - by mere stipulation.

And that is why I consider it question-begging to defend the necessity of logic by merely pointing out that it is "logically necessary". For that (I take it) is not in question. Instead, we are asking whether we must be bound by the limits of classical logic. We are asking whether this system itself is necessary (in the broadest sense, which I take to be metaphysical necessity). One cannot answer this, as the Maverick Philosopher seeks to, by remaining within the system and saying that from this position, the system is necessary. That is question-begging. You could make that move of any system whatsoever. From within the framework of natural laws, the laws of physics are necessary and not merely contingent. But of course, that doesn't really say anything much at all.

So, to repeat the central point of my previous post, modal notions must be assessed against some background framework of limitations. Something might be necessary within one framework, but merely contingent within another. Perhaps this is the case with classical logic? (I take it that the Maverick Philosopher considers the metaphysically possible to be a subset of the logically possible, whereas I would consider the relation to be reversed. Indeed, as discussed in the previous post, I have trouble seeing how we could justifiably rule out anything as being impossible in the broadest sense - which is how I understand metaphysical possibility.)

Having said all that, I don't actually think the laws of logic are mere "empirical generalisations" either. I think it more likely that our brains are hardwired to think in that way, in much the same way that we are hardwired to perceive the world in terms of absolute space and absolute time. But just as our intuitions about the latter are mistaken, and just as Euclidean geometry turned out to be but one possible system among many, so do I think that classical logic might suffer from similar imperfections.

So I'm actually defending a position slightly different from that which the Maverick Philosopher was attacking. Nevertheless, I still think his 'reductio' begged the question against the empiricist. For I take it that the empiricist claims not that the laws of logic are logically contingent, but rather, that they are metaphysically contingent. Logic, he suggests, is generalised from our experience of reality, but that reality could have been different, and so our logical systems could have been different. Of course, that new logic would be 'impossible' according to the constraints of classical logic ("logical possibility"). But that is to be expected, given that it is precisely those constraints that are in question here. To appeal to those constraints (i.e. logical possibility) in their own defense is indeed to beg the question.

Update: more here.

So Many Possibilities...

What's really possible? I'm deeply confused by modality - though whether that's due to the subject's intrinsic incoherence, or simply my ignorance, I'm not sure. So I'll ramble about it a bit here to try to sort my thoughts out, and hopefully someone a bit more knowledgable can leave a comment and help me out.

Here's my current position: modal notions (i.e. possibility versus necessity) cannot be applied simpliciter. Instead, they need to be assessed against some background framework of stipulated limitations. Some examples would be:
  • Epistemic possibility - Whether a state of affairs is consistent with our current state of knowledge.

  • Physical possibility - Whether something contradicts our actual (practical) physical capabilities and such. E.g. it is physically impossible for a human to run a mile in ten seconds.

  • Natural possibility - Whether something contradicts the 'natural laws' (or laws of physics) that govern our universe. E.g. travelling faster than light is impossible in this sense.

  • Logical possibility - Whether something is logically consistent. E.g. it is logically impossible for my cat to be both alive and not alive (at the same time).

One might also extend this template to interpret deontic possibility (or rather, permissibility) in terms of what is consistent with (or allowed by) some particular set of rules - e.g. a moral or legal code.

But what about metaphysical possibility? What's really possible? What could have existed? I don't think we can answer this question. I'm not even sure if it's asking anything meaningful.

Some might equate metaphysical possibility with what people can imagine or conceive of. But conceivability merely tells us about the limits of human cognition, and doesn't necessarily imply anything deeper about the possible nature of reality. I have difficulty conceiving that time and simultaneity could be relative, not absolute. Yet this is not only possible, but indeed true!

Others might simply equate metaphysical with logical possibility. But I'm not sure that this is justified either. After all, what reason is there to think that logical impossibilities are metaphysically impossible? We cannot conceive of them, sure, they seem "absurd". But, as suggested above, this cannot be reason enough.

Besides, it might (this is an epistemic 'might') be the case that some logical contradictions are in fact true. [Update: I reconsider and indeed retract this claim, here.] Quantum physics is the most serious contender here (did the photon go through the left slot or the right? Is Schrodinger's cat dead or alive?). Some also argue that the Liar's Paradox is best understood as being both true and false. If we adopt a paraconsistent (rather than classical) logic, then this is not a disastrous result.

And this then brings up another reason for doubt: namely, that there are many different logics! "Logical possibility" is (I think?) bound by classical logic. But there's no reason to think that reality is, when there are so many alternatives to choose from. For those who think it "obvious", and the alternatives "absurd", the fall of Euclidean geometry provides a handy precedent. For centuries, mathematicians and philosophers thought that Euclidean geometry was "absolute truth". But in actual fact, it merely applies to flat planar surfaces, and if we instead consider curved surfaces, then non-Euclidean geometries (complete with different laws and a priori 'truths') result. So although people in the past took it as a necessary truth that exactly one line can be drawn through a point, such that this new line is parallel to some other given line, in actual fact this axiom isn't even always contingently true!

Don't get me wrong, I think the idea of "possible worlds" can be a useful heuristic. But if they're merely defined by logical possibility, rather than metaphysical possibility, then we should be clear on that. For example, the usually-sharp Maverick Philosopher attempted to refute the idea that laws of logic are empirical generalisations (and hence only contingently true), by equating contingency with logical contingency. But of course this is quite blatantly question-begging. Of course if you assume that metaphysical possibility simply is (or implies) logical possibility, then the laws of logic are necessary and not merely contingent. He reached the conclusion by (implicitly) assuming it as a premise, which is a rather cheap (and unconvincing) move. [Update: see here and here for more detail.]

To change tack slightly, I was also struck by the problem of (categorical) possibility when writing my essay on Van Inwagen & Free Will. For if determinism is true, then given the current state of affairs and the laws of nature, there is only one categorically possible future. And that seems to be an awfully limited understanding of possibility! Indeed, even if we ignore determinism, the fatalist's "argument from truth" would seem to establish this categorical uniqueness.

The Fatalist's Argument From Truth:
1) Let E be any event that occurs in the future
2) Then, the proposition that E will occur is true.
3) So, nobody can bring it about that E does not occur.
4) That is, E is inevitable.

In my essay above, I argued that adopting a categorical notion of 'could' (i.e. possibility) commits one to the soundness of this absurd fatalist argument. After all, one presumably could not (categorically) bring about a logically inconsistent state of affairs.

I conclude, then, that categorical possibility is so empty as to be effectively meaningless - we are better off adopting a hypothetical understanding of choice and modality.

Modal notions seem to arise from a certain sort of counter-factual thinking. We establish some particular limitations, and then we consider what states of affairs are allowed within our chosen framework. But divorced of any such framework, modal notions strike me as meaningless. If you take away the limitations, then we're stuck with the empty truism: "anything is possible".

Am I missing something here?

Carnival Update

With the generous help of Matthew Mullins, I've updated the Philosophers' Carnival homepage so that people can now easily submit links for the carnival, using a form right there on the page itself. No more email, no more hassle. It's great.

The 'Post Link' is the only really crucial part of the form - we need to know the URL of the post if we are to link to it! The rest is optional, though it would be helpful to fill it in anyway - especially the "Post Description", which the carnival host can then use as their quoted excerpt. Note that "Your Email" address will simply be used to send an automatic confirmation email.

So now all we need is some submissions...

If you have a philosophy blog of your own, you should:
  • Link to the carnival homepage from your own site, encouraging your readers to get involved
  • Submit a post yourself!

  • (Also, we need volunteers for future hosts. This requires a little bit more work - not very much though, and my site got about a thousand hits from the first carnival, so it's well worth your while. Send me an email if you're interested.)

    I should emphasise that this is a community project, and relies upon your participation. We need your help. If you read a post you like, then submit it. If you have a philosophy blog of your own, you should definitely submit something.

    Remember, carnival #2 is coming soon, and hosted by Brandon of Siris. If a post of yours is selected, be sure to link to the new carnival once it's up and running!

    Monday, August 30, 2004

    Parableman on Affirmative Action

    Jeremy Pierce has kicked off a series where he will examine 12 arguments for and against affirmative action. His analysis looks to be balanced and very well thought out. Go read.

    Update: It appears that Jeremy is continually updating the linked-to post with further links to each new post in the series. So I've removed the extra links from this post. You can find them all over there instead.

    Sunday, August 29, 2004

    Longer than it is

    Two guys wander down to the pier, and one of them says in surprise, "I thought your boat was longer than it is". The other guy raises an eyebrow and replies: "No, my boat is not longer than it is". (This example came up in our semantics class a while back. I think it originates from Bertrand Russell.)

    I found it quite amusing, but what's really fun is trying to puzzle out exactly what each person is trying to say. The key seems to be the distinction between de dicto (about the words) versus de re (about reality) readings of the boat's "length". To represent these alternatives formally (using 'i' to refer to the first speaker, and 'b' as the boat), we have:

    1) [The x: LENGTH(x,b)] THINK(i,[The y: LENGTH(y,b)] LONGER(y,x) )
    i.e. "Call the actual (de re) length of your boat 'x'. I thought that the (de dicto) length of your boat was greater than that value x".

    Compare that to the following (absurd) version:
    2) [The x: LENGTH(x,b)] THINK(i, LONGER(x,x) )
    i.e. "Call the actual length of your boat 'x'. I thought that this value x is greater than itself."

    3) THINK(i, [The y: LENGTH(y,b)] LONGER (y,y) )
    i.e. "I thought the length of your boat (whatever it may be) was longer than itself".

    The first guy obviously intended to mean (1). The others are both absurd. I'm not sure which of (2) or (3) the second guy mistook him as saying - probably (3) fits best?

    Anyway, that struck me as an interesting sort of case. It sorta reminds me of scopal ambiguity. I take it that in general, the de re reading is achieved by having the quantification occur outside of the intensional predicate (so the predicate then refers to this external reality). By contrast, quantifying inside the predicate creates the de dicto reading, as the variable is cut off from anything external, and instead merely represents the concept (or 'words') it is defined by.

    What about similar cases that don't involve quantifiers?

    Suppose Lois thinks Superman is in danger. Then suppose you say to Clark Kent's parents, "Lois thinks Clark is in danger". Is what you say true? (Recall that Clark is Superman, though Lois does not know this.) There seems to be an ambiguity between de re and de dicto readings here too.

    I'm not sure how to represent these formally, however, as there only seems to be one option (with 'l' = Lois, and 'c' = Clark):
    THINK(l, IN DANGER(c) )

    This is the de dicto reading, and it falsely claims that Lois thinks the proposition "Clark is in danger". But how can we get the de re reading? I wonder if perhaps we need to indirectly refer to Clark by way of a restricted quantifier:

    1) [The x: x=c] THINK(l, IN DANGER(x) )
    i.e. Regarding the person who is Clark, Lois thinks that person is in danger. (This is the de re reading, and it is true.)

    2) THINK(l, [The x: x=c] IN DANGER(x) )
    i.e. Lois thinks that "the person who is Clark is in danger".
    (This is the quantified version of the de dicto reading. It's still false, of course.)

    Is that a legitimate formalisation? Is there any other way to capture the two possible readings?

    Saturday, August 28, 2004

    Useful Links

    Here are some free internet resources that I very much appreciate:
  • Create your own blog with Blogger. You'll be amazed at how quick and easy the whole process is.

  • If you read many blogs (or online newspapers, magazines, etc), you can save yourself hours of wasted time by getting an RSS/XML aggregator. These services automatically check for updates from your favourite sites, and collect them all together for you. I use Bloglines, and am very happy with it.

  • If you have a blog of your own, visit Technorati regularly to see who has linked to you recently

  • Wikipedia is the greatest encyclopedia in the world.

  • Mozilla Firefox is a better browser than Internet Explorer

  • Gmail - Joining is by invite only, but I've a few to spare if anyone wants one.

  • Feel free to add your own suggestions...

    Blog Changes

    I've gone and introduced Blogger comments after all. The biggest advantage is that there is no size limit. Also, old Haloscan comments disappear after four months, which is really annoying.

    I've copied across any conversations I thought were particularly worth saving (so you'll see a few posts with "1 comment" which is actually several old ones put together).

    In other news, the template saw some minor tweaking (hopefully the links look a bit better now - that grey hover background was awfully ugly).

    I've also introduced Blogger's new "email this post" feature - that's the little envelope you should see next to the permalink at the bottom of each post. If you click on it, you can quickly and easily email the link of that post to a friend (e.g. if you think it might be of interest to them).

    Lastly, you can use the search bar at the top of the page to search this site for key words.

    Update: You may notice that some of my older posts do not have Blogger comments enabled on them. Unfortunately, there is no way for me to fix them all at once. However, I can introduce the comments feature to the posts one at a time. So if there is an old post you wish to comment on, simply send me an email with the link of the post, and the request "please enable comments on this post", and I will do so. You may find the new "email this post" feature to be convenient for this purpose. My email address is described on the sidebar.

    Wednesday, August 25, 2004

    Law & Morality

    There seems to be quite a strong connection between law and morality. Although people sometimes say "you shouldn't legislate morality", they presumably don't really mean this - why would we outlaw rape and murder if they weren't wrong? Instead, I suppose they mean that people shouldn't impose their personal moral views (especially regarding sexuality) upon others. I would agree with that sentiment, though my reason is precisely because I think legislation should be morally informed, and the "moral views" in question are entirely misled.

    As a quick aside: it is unfortunate that the word "morality" has become associated with conservative values, because the obvious invalidity of those values to many people tarnishes their attitude towards morality as a whole. And that is a damn shame. When conservative groups advocate bigotry masquerading as "family values", we need to recognise the injustice of this, and instead stand up for what is right. But I digress - this isn't intended as a post about how liberals need to reclaim the moral high ground.

    So we accept that there is a connection between law and morality, but what sort of connection is it? Their domains are clearly not entirely identical - for example, it may be wrong to lie to your parents, but it certainly is no business of the law. Perhaps the best way to explain this is to acknowledge that the law is an extremely blunt tool, and so will be of no help when dealing with minor or subtle moral issues.

    But even if some morality is outside the scope of Law, could Law's domain be a subset of the Moral? That is, should we only ever outlaw immoral acts, and never morally permissible ones?

    I would like to say 'yes', as it does seem like a good principle. But I can't, because it contradicts my position on some other issues. That is, I think morality is purely 'other-regarding' in nature, and merely harming yourself (e.g. smoking in private) is not immoral. On the other hand, I previously suggested that state paternalism could be acceptable even in cases where Mill's harm principle would forbid it.

    So I'm stuck with the following inconsistent triad:
    1) X should be illegal only if X is immoral (and sometimes not even then)
    2) Purely self-harming actions are not immoral
    3) Sometimes, purely self-harming actions should be illegal

    Those claims cannot all be true. Each strikes me as plausible, though I am not certain of any of them. I'm sympathetic towards utilitarianism as a moral theory, which implies the falsity of (2). But I also think of morality as a purely social phenomenon, so (2) should be true. So that's another conflict I'll need to sort out someday. For now though, I'm most inclined to doubt (1).

    To approach this topic from a slightly different angle now, I owe to Alonzo Fyfe the intriguing suggestion that we understand law and morality in terms of belief-desire psychological theory. That theory claims that any human action can be explained solely in terms of the beliefs and desires of the agent. For example, if I turn on a heater, this may be because I desire to be warm, and I believe that turning on the heater will achieve this end. To apply this to our current topic, consider how society can influence the actions of its members. According to belief-desire psychology, there are two broad options: change someone's beliefs, or change their desires.

    Morality, by this understanding, corresponds to the latter option. That is, morality is a system of socialisation whereby society instills in its members the desire to act in certain ways. (I discuss some of the implications of this view in more detail here.)

    The other method of influence is to alter people's beliefs about how best to fulfill their desires. This is where Law comes in. Its role (according to this interpretation) is to serve as a deterrent for those who, for whatever reason, fail to be bound by morality. It achieves this through the threat of punishment, i.e. by instilling in citizens the belief that breaking the law is not in their own best interests - they could get caught and sent to jail, which would surely thwart many of their other desires.

    So by this view, law and morality are just two sides of the same coin - namely, that of socialisation. Morality seeks to influence our behaviour by way of our desires, whereas law is the 'back-up' option, and targets our beliefs.

    Do you think that sounds plausible? Comments welcome, as always.

    Monday, August 23, 2004

    Philosophers' Carnival #1

    Welcome to the first ever Philosophers' Carnival - a showcase of quality posts from a wide range of philosophy blogs. If I could just pull you away from the candyfloss stand for a moment, you'll notice the many other attractions vying for your attention further down the page. Some were chosen and submitted by their authors - either voluntarily or with a little gentle prodding - whereas others I picked myself because they're just too good to ignore.

    First up, we have John of Fake Barn Country with You Can't Get Away With Murder That Easily:
    In his article, "How Satisficers Get Away with Murder," Tim Mulgan argues that satisficing consequentialism cannot make good on its promise to avoid the demandingness objection, while at the same time avoid a devastating counterexample.

    I disagree.

    While at FBC, be sure to also read Allan's Once more unto the breach, a puzzle which inspired several follow-ups (as readers of this blog might recall):
    Premise 1: Either we will win the battle, or we will lose the battle.
    Premise 2: If we will win the battle, then we ought to attack with a small force.
    Premise 3: If we will lose the battle, then we ought to attack with a small force.
    Conclusion: We ought to attack with a small force.

    Getting back to the topic of murder, there was a gem at Orange Philosophy a while back - Help Me Choose a Murder Victim - which sparked many interesting comments:
    Suppose I'm deciding whom to kill, and I want to inflict the most harmful death possible. How old should my victim be?

    From Michael Cholbi at PEA Soup, we have Competence and the Condemned:
    One moral issue surrounding punishment that has not received enough attention from moral philosophers is the somewhat perverse insistence that those on death row can only be executed if they are competent to be executed.

    Shieva Kleinschmidt of Emiratio raises some questions about Conditional Desires:
    In Reasons and Persons, Derek Parfit presents us with the category of conditional desires. These are desires that "are implicitly conditional on their own persistence" (p. 151). Parfit uses as an example his desire to swim when the moon rises, which he desires to occur only if, at the time that the moon rises, he still desires to swim. [...] But how should we cash out the notion of a conditional desire?

    At Certain Doubts, we have Paradox vs Surprise:
    A paradox is different from a result that is merely surprising, but what is the difference? This question touches on matters beyond epistemology, but it is applicable to the major epistemic paradoxes, including preface, lottery, surprise quiz, and knowability. It is the latter that prompts my question.

    At The Eye in the Door, Robert Skipper (of Philosophy of Biology fame) discusses Stem Cells and Alzheimer's:
    It's been three years since President George W. Bush issued his decision to ban federal funding for stem cell research requiring the destruction of human embryos intentionally created for new lines. But when former President Ronald Reagan died in June of this year of pneumonia related to his struggle with Alzheimer's, the politics of stem cell research became a campaign issue.

    Wo's Weblog posts on Harmless Zombies:
    A zombie world is a world physically just like our world but in which there is no consciousness. Must a type-A materialist deny the conceivability of zombie worlds? No, not quite.

    The Garden of Forking Paths has an active discussion going on in Deny or Deflate:
    My friend has heard of a philosophical approach according to which, to determine what, say, responsibility is, we collect the truisms about responsibility and then find the item in the world that best fits them (provided, of course, that something fits well enough). In this way, he's been told, we sometimes learn that things aren't what, in our armchair theorizing, we thought they were.

    Maverick Philosopher tackles The God-Man Identity Theory:
    Christianity tries to combine transcendence and immanence: God the Father remains radically transcendent, while God the Son enters into history.

    Both of the Christian doctrines pose serious logical problems which threaten their coherence.

    Jeremy at Prosblogion discusses Open Theism and Evil:
    I've gotten the sense that the problem of evil is the primary motivation for many who subscribe to what's commonly called open theism, i.e. the view that God does not know the future, takes risks, and changes his mind due to learning new information.

    In a more light-hearted post, Michael of Phluaria argues that God is Made of Gluten:
    And so the only reasonable conclusion to draw is: God is made of gluten. (A weaker, and slightly less exciting, implication might be simply that wheat is a divine substance. But why not bite the wafer - I mean, the bullet?)

    From Philosophy of Art we have an intriguing suggestion for Bad works, ironic performances:
    [T]he Dworkinian method seems to make the work better than it is. The ironic performance builds a critique of the work into a performance of it — it performs the work against its own grain.

    Tom of Legalistic Fingerpointing suggests that we Don't throw out our philosophy just yet:
    What hijinks! What could I, a soon-to-be-philosophy student, and committed atheist (a- without, -theism religious belief) and skeptic possibly say to answer Fraser's charge that philosophy is a refuge for wooly-thinking theism-collaborators? Well, first, it's imperative that I point out the flaws in his argument.

    Experimental Philosophy discusses D.P.P. v. Smith--A New Study:
    In this landmark case, jurors in England had to determine the guilt of a man named Smith who had driven a car containing stolen goods in a zigzag course in order to shake off a policeman who had been clinging to the side of the car. When the policeman was finally shaken off, he rolled into oncoming traffic and sustained fatal injuries. I wanted to see whether moral considerations affect people's judgments concerning a) whether Smith knowingly brought about the officer's death, and b) whether Smith intentionally brought about the officer's death. So, I developed two cases--one involving a thief and an officer and another involving a driver and a car-jacker.

    Brian Weatherson of Thoughts Arguments and Rants offers the most technically challenging post here, with Exists and Type Raising:
    Names, they said, were disguised descriptions, so it’s possible that they can make meaningful contributions to propositions without actually denoting. Nowadays orthodoxy is that that’s wrong, and names are directly referential.

    I want to revive a version of the quantificational view.

    Uriah of Desert Landscapes posts Against Saving Physicalism by Appeal to a Concept/Property Distinction:
    The most popular approach to the explanatory gap, the Knowledge Argument, and the like challenges to physicalism is one developed in the late 80s by Brian Loar and Michael Tye. On this approach, these challenges are premised on a confusion between concepts and the properties for which they are the concepts. Thus, the *concept* of pain and the *concept* of C-fiber firing are so different as to bring up the specter of the explanatory gap; but the property picked out by these concepts is the concept is in fact one and the same. So there is no ontological gap even though there’s an explanatory gap.

    Though a committed physicalist, I don’t think this approach works. It misses the force of the explanatory gap.

    Update: We also have a last-minute entry from Lindsay Beyerstein of Majikthise, with The Epistemology of Rape:
    Lithwick argues that rape shield laws are unacceptable because they deprive the defendant of potentially exculpatory evidence. If sexual history were more illuminating or less prejudicial, I would agree.

    Lastly, Brandon of Siris offers On an Argument for the Existence of Bodies:
    My own view on this point is that Malebranche has the stronger argument. In a Cartesian framework, "God is not a deceiver" is a good reliability-ensuring principle at a very general level of the design. That is, if God is not a deceiver, the cognitive faculties he gave us must be able to come to the truth. But there is nothing in the principle to tell us how easy or difficult coming to the truth might be, nor does it seem to give us any certainty about particular beliefs.

    Brandon has kindly volunteered to host the next Philosophers' Carnival, which will be held (approximately) a fortnight from now. Remember, we rely on your participation, so don't forget to send in a link to your favourite new post. Emailed submissions for the next carnival should contain the words "Philosophers' Carnival" somewhere in the subject line (for easy identification), and be sent to Brandon at the following email address (spam-proofed: please remove all spaces and replace 'AT' with '@', and 'DOT' with '.'):

    bwatson AT chass DOT utoronto DOT ca

    We also need more volunteers for future hosts. If you're interested, please send me an email:
    r DOT chappell AT gmail DOT com

    Enjoy your reading!

    Sunday, August 22, 2004

    Liberty & Independence

    A while ago I posted about J.S. Mill's arguments in favour of liberty, which I generally agree with. I'm not a full-blooded libertarian, however. For example, I think it is entirely appropriate that wearing seatbelts in cars is legally required, despite that being a pretty clear breach of the 'harm principle'. There are two major reasons behind my position here.

    Firstly, I - like Mill - consider the value of liberty to derive from its utility, rather than any absolute right. As a general rule, we are best off when given freedom to do as we please (so long as we harm or endanger no-one else). This is not always the case however, and so - in theory - liberty should be suspended whenever doing so would maximise wellbeing. In practice, of course, people's judgements here will often be mistaken, so we should be very wary of giving them such power over us. Nevertheless, there will be times when the evidence is so strong that their intervention could be well justified.

    Secondly, mere civil liberty is insufficient to secure personal independence. It would be naive to think that the government is the only (or even the major) threat to our freedom. We are far more influenced by - and dependent upon - other individuals, both economically and psychologically. The question of whether (or to what extent) such dependencies can be relieved or avoided, was one of the driving forces behind Rousseau's political philosophy, and a major focus of the essay I wrote about him earlier this year.

    The economic problem is especially obvious. Anyone who truly values individual freedom and independence is committed to the necessity of some degree of wealth redistribution. Without this, less fortunate citizens could find themselves forced to submit to the will of (richer) others in order to satisfy their material needs. Rousseau's answer was that "no citizen should be so opulent as to be able to buy another, and none so poor as to be constrained to sell himself".

    The psychological problem is more subtle. Rousseau was particularly concerned by how dependent we are on the opinions of others for our self-esteem. Not only does resting our happiness on such a shaky foundation leave us very vulnerable, but it can also erode our independence as we mould ourselves to please others: peer pressure being a clear example of this phenomenon. Rousseau hoped (perhaps unrealistically) that a well-structured society could help alleviate the worst of this personal dependency, by allowing the state itself to become a source of self-esteem for its citizens. (See my essay for more details.)

    I'm not that utopian. I don't think the state can free us from our psychological dependencies, that just isn't realistic (and perhaps not even desirable). However, it does open up another possible justification for state coercion: namely, in those instances where our independence has already been eroded by society/culture.

    I think it might be possible to have a law justified in virtue of its effect on societal norms. For example, imagine a society where cyclists generally don't wear helmets (say it's considered too 'uncool' or whatever). Suppose individuals face significant pressure from this societal norm, and so tend to go along with it against their better judgement (just do an intro course on social psychology if you doubt for a moment the plausibility of this). Then I think it would be entirely justified to introduce a law making cycle helmets compulsory (assuming that this has a significant beneficial effect, e.g. it saves lives, etc). In such a case, the introduction of a seemingly coercive law could actually have the effect of increasing an individual's freedom - i.e. by giving them an excuse to break the (previously) prevalent norms. (I say 'previously' because the hope would be that the legislation eventually helps change what behaviour is accepted as normal in the society.)

    Such a scenario at least seems possible. Perhaps it isn't very likely, I'm not sure. Social norms probably aren't so easy to shape as that. It would be overly simplistic to think that one could create a perfect culture simply by passing laws. But you might be able to have some positive effect, at least.

    What I'm trying to suggest here is that state intervention might at times actually be justified for the sake of freedom, strange though that sounds. But just as people shouldn't be able to forfeit their future freedom by selling themselves into slavery, so (perhaps) they shouldn't be able to take significantly harmful drugs, or needlessly endanger themselves (say by failing to wear a seatbelt). A more obvious example would be compulsory education - though we usually don't treat children as fully free agents anyway.

    Paternalism is a slippery slope, though, and one that we should always be careful of. There is no simple rule that will always provide the right answer. Mill's 'harm principle' is a useful heuristic, but there will be times when our evidence is strong enough to justify breaking it on utilitarian grounds. Sometimes government interference might even help individuals attain a greater degree of personal freedom. Sometimes.

    Update: See also my posts on The New Freedom and Freedom & Autonomy.

    Saturday, August 21, 2004

    Category: Science & Metaphysics


    • Ontological Commitment - Looks at Quine's formulation of ontological commitment, and how it allows us to talk of (e.g.) Pegasus without implying there is some existing thing (Pegasus) that we are talking about.

    • Gappy Objects - is the fusion/sum of {apple + Mars} any less a single metaphysical object than the fusion of atoms that constitute the apple by itself? If so, what sets common-sense objects apart?

    • Universals Overview - surveys the various positions in the 'universals debate'.

    • Identity, Properties & Reduction - something I found puzzling

    • Conceptual Nominalism - includes a basic overview of the universals debate in metaphysics, before I outline my own ideas on the matter.

    • An introduction and defence of trope theory

    • Lewis and im/possible worlds nominalism - discusses possible worlds nominalism, a problem with it, and a possible solution involving impossible worlds.

    • An introduction to the particulars debate, with an emphasis on Bundle Theory, including the "identity of indiscernibles" objection.

    • Mixed Metaphysics - Arguing that we can have reality (scientifically-informed metaphysics), or common-sense ('folk' metaphysics), but they shouldn't be confused.


    Related Topics: For posts on free will, philosophy of mind, cognitive science, and related technology, see the Mind / CogSci category.

    The topics of truth, modality, and fiction, can be found under Logic & Semantics.

    Thursday, August 19, 2004

    Whose Freedom?

    Suppose Bob tortures and murders Sue. Could an omnipotent, omnibenevolent being allow such an event to take place? Seemingly not, yet such atrocities occur in our world all the time. So, the argument goes, God must not exist. Theists sometimes try to rebutt this "problem of evil" by suggesting that God allows such evils for the sake of free will. But why should Bob's will count for more than Sue's in this case? How, exactly, is God preserving free will by allowing Bob to impose his will upon Sue? Wouldn't it be better - maximising not just utility, but also freedom - to prevent Bob's actions, and uphold Sue's desire not to be harmed? The imposition on Bob's freedom is fairly trivial when compared to that which would otherwise have befallen Sue. So it seems that despite conventional wisdom, considerations of free will might actually exacerbate the problem of evil.

    There's something quite counterintuitive about the above reasoning (to me, at least - I assume others' intuitions are similar). That doesn't necessarily mean it's wrong - instead I think our intuition is. But it just seems strange to talk about Sue's will in such a case. We see the victim in a passive light, whereas 'will' seems to be an intrinsically active phenomenon. (Isn't "passive exercise of will" a contradiction in terms?) But I think the ascription of passivity was probably where our intuitions go awry. Anyone being tortured would surely 'will' (very strongly and actively) that the torture cease.

    So why do we think divine interference would be an assault on free will? Perhaps this laissez-faire approach rests on a deontological rather than consequentialist view of divine morality: that is, it would be wrong for God to obstruct any person's free will, even for the sake of others' freedom. I don't know, maybe that could work, but it doesn't seem very plausible to me. In fact, preventing people from doing evil strikes me as an entirely good thing. It is in no way bad that you are obstructing their will. If their will is to do evil, then it ought to be obstructed. They can still choose to be evil (in character), and attempt evil deeds, but any omnibenevolent being would surely do all in his power to ensure that those attempts did not succeed in harming anyone else.

    But in case you disagree on the above points, there is an even more compelling example of God-withheld freedom: addiction. What possible justification could there be for making human brains predisposed towards addiction of any sort? It only impedes our freedom, restricting our ability to make rational decisions and exercise our 'free will'. Similarly for mental illness. Our brains are far from optimal when it comes to freedom and rationality. If God existed, he could free us from the bondage of addiction and other serious mental defects. So I think the importance of free will actually counts against the theist when considering the problem of evil.

    Some other aspects of the problem of evil were discussed elsewhere a few months ago: See, for example, Chris' objection to the "God works in mysterious ways" response. Also, Jonathan Ichikawa and Brian Weatherson describe some clever (possible, if perhaps not entirely plausible) solutions from possible worlds.

    The best (most interesting) solution I've ever come across is undoubtedly Mark Steen's (scroll to April 27) Lagadonian extension of Ken Gemes' response:
    "God did not create this world, he merely thought of it. Our world then is a merely possible world, one God thought of but chose not to create. Presumably it was his knowledge of the evil in this world which led him to decide that it was beneath creation..." (Gemes)

    [...]The major problem, of course, is dealing with incredulous stares and people pounding their Moorean fists. How to reply? The answer is that God speaks and thinks in Lagadonian, and, while ‘speaking’ the actual world in Lagadonian, he merely thought of our world in Lagadonian. But what, pray tell, is Lagadonianism? Well, I’m glad you asked.

    A 'Lagadonian' language [...] is a (or 'the') language where every object is a name of itself (and, similarly, every event is it's own name/description, every property is a name for itself, every state of affairs is its own description, and so on). Just as we can represent the state of a affairs of 'the apple is red' by 'le pomme est rouge', 'la manzana es rojo', by morse code [etc...] so is, or possibly can be, the state of affairs of the apple being red represented in the apple's being red.
    Now, assuming God exists, we'd like to suppose that he would think in the most perfect language possible. There's a prima facie case, if a Lagadonian language is possible, that God would think in Lagadonian.

    The idea being that all the physical objects in our world are merely the Lagadonian "words" God has thought of, but not actually said. That makes our world non-actual, so the evils in it don't matter, so the empirical facts are consistent with an omnimax God after all. You've gotta love philosophy.

    Monday, August 16, 2004

    Category: Favourite Posts

  • Dreams & Sensations - do the latter really occur in the former?

  • Sensation & Subjectivity - Are sensations purely subjective things? How about beliefs? Could you have one without realising it? Could you think you have one, when really you don't?

  • Inclination vs Duty - Is it better to act morally because you want to, or because you feel obliged to?

  • Artificial Empatelligence - When computers get personal.

  • Interactive Fictions - a.k.a. The Philosophy of Video Games.

  • Truth & Relativism - On the absurdity of extreme relativism, but the usefulness of a more limited sort, which can help us to understand value-claims objectively.

  • Skepticism & the Matrix - outlines the problem of skepticism, and a possible response from Alethic Contextualism.

  • 2-envelopes paradox - an interesting puzzle about probability.

  • Brash on Crime - What role should prisons play in society?

  • Affirmative Aristocracy - why Maori shouldn't get preferential treatment based solely on race

  • All New Zealanders - Rejects both extremes of assimilation vs biculturalism, in favour of reciprocal integration

  • Personality Tests - The best one I know of. Take it yourself!
  • Petal Puzzle

    Petals Around the Rose is a fun little puzzle I just came across on Matt Carter's activation page.

    See if you can figure it out. It took me several minutes - which is quite a long time when it's nearing midnight and you really want to go to sleep but you know you won't be able to unless you first solve that darned puzzle...

    Sunday, August 15, 2004

    Interactive Fictions

    Last Tuesday, Grant Tavinor of Lincoln University presented a very interesting seminar to us Cantabrians on (I kid you not) the philosophy of video games.

    By understanding video games as interactive fictions, we can take advantage of the framework provided by more general philosophy of fiction (about which there are some good posts at Fake Barn Country). The core idea, I take it, is that we understand fictional narratives generally as an invitation to pretense (i.e. engage in a game of make-believe).

    In the case of a novel, the author creates a static "work world" - as described in the book - which we are invited to imagine. Our own involvement (including beliefs and desires about the fiction) give rise to a new fictional world, let's call it the "game world", deviating from the author's pure work. Note the one-way influence here: our game-world is derived from the author's work-world, but nothing we do (or pretend) in our game-world can change what's true of the work itself. The work-world is fixed by the printed pages of the book.

    Video games, by contrast, are interactive. That is, not only does the system created by the programmer (i.e. the "work world") influence our imagined game-world, but our involvement in the game actually alters what's true of the fictional work. One might even say that there is no longer any distinction at all to be made between the 'work' and 'game' worlds. (I don't think I would go so far, however, as a gamer might enhance his experience by imagining things that still aren't, strictly speaking, part of the fiction. In such cases, the distinction would seem to retain significance.)

    Interactive fictions place the audience/players inside the work itself, and so grant them the power to influence it. Here's a thought: does this shift of position (so to speak) lead to a change in our cognitive relations to the fiction? Hmm, I don't think I expressed that very clearly. Let's try an example. Jonathan Ichikawa has convincingly argued that our desires about (traditional) fictions are often imagined rather than real ones:

    Suppose that I watch an episode of Buffy: the Vampire Slayer and think, I hope Buffy survives. This is a perfectly natural thing to think. But how do we make sense of it? ... I could cache out my desire for her not to die in terms of a desire for the fiction to turn out a certain way, but this also seems wrong...

    I don't really believe that Buffy exists, but I imagine that she does, and this imagining plays a parallel role to belief in my thinking about Buffy. I imagine in a belief-like way. Let belief-I refer to such a state, and belief-R refer to an actual ('real') belief. So the apparent paradox here is easily resolved: I believe-R that Buffy does not exist, and neither do vampires, and I believe-I that they do exist, and Buffy's job is to slay the vampires.

    It is perfectly natural to make this distinction about beliefs, and I believe that we should do the same for desires. Rather than attribute contradictory desires to me, I prefer to say that I desire-I that Buffy live, and that I desire-R that the season end with her death. My desire-I is responsive to my beliefs-I in just the same way that desires-R are responsive to beliefs-R – I believe-I (and do not believe-R) that Buffy is a noble hero. This causally interacts with my desire-I (and not my desire-R) that Buffy survive.

    But I wonder if games might be slightly different in this respect? Suppose you're playing a war game: you don't just pretend-want ('desire-I') to win the battle, you really (desire-R) want to win it. You still realise it's just "in the fiction", of course. But you nevertheless really want the game to result in a victory for you. So whereas a passive film audience might primarily have pretend-desires about events in the fictional world, I think that an interactive gamer relates to the fiction with a different kind of cognitive attitude: he is more likely to have real desires about the unfolding of fictional events.

    Interactive fictions also seem to be more influenced by features of the real world - specifically, the objects used as interactive props. For example, if a child playfully 'wrestles' with a tree-stumped-turned-"grizzly bear", the size of the bear may be determined by the size of the tree stump. When playing video games, we interact with various physical props [computer, keyboard, etc] which in turn influence the fiction. (I wonder if we could say that the fictional world supervenes upon the props, in some sense?) This seems different from traditional (non-interactive) fictions. In books, at least, the representations are linguistic rather than physical. Though perhaps films, plays, etc are more similar to games in this respect.

    Tavinor's fundamental distinction was between passive and interactive fictions. But I think there is an alternative way of dividing up the fictional space: between closed vs open-ended fictions.

    A closed fiction is (roughly) one where all the possibilities are fixed in advance. Most traditional fictions (like books and films) fit into this category. Not all passive fictions are closed, however - consider an improvised theatre or comedy performance. Also, not all interactive fictions are open. Consider a pick-a-path book, where readers can 'choose' (from various options) which page to turn to next. Despite our interaction with it, the fiction is undeniably closed in this sense - all possible 'paths' are laid out in advance, black ink on white pages.

    Now, one might complain that computer games are actually closed too. The structure of the program will determine what options are open to the gamer at each stage of the game. He can choose between them, sure, but that alone is not enough to make the fiction truly open-ended.

    I think that is a mistaken view, however. For one could say a similar thing about real life: "We are constrained by the laws of physics, which allow us various options. We can choose between them, but that is not enough to make reality truly open-ended." That seems absurd, though.

    I'm not at all sure of this, but I think the best way to understand open-endedness is in terms of predictability. A fiction is open-ended iff it has the potential to unfold in a way unimagined by the author. (That's just a very rough definition, but I hope you get the idea.) By tying the concept to human cognitive abilities in this way, we can obtain open-endedness simply by expanding a closed system so that it is so large and complex that the author can no longer comprehend it all.

    This approach implies that tic-tac-toe is a closed game, yet chess is open-ended. [I've heard that even if you restrict the game to 40 moves or less, there's still about as many possible chess results as there are particles in the universe. Something like that, anyway. Gotta love those combinatorial explosions!] These classifications fit my intuitions, though I'd be curious to hear what others think, and also any suggested 'borderline cases'.

    Open-endedness remains a fairly vague concept, though, and could vary a lot depending on how detailed we require the author's predictions to be. For example, we can imagine a video game with a very strict plot which constrains the player overall (perhaps there is only one possible ending), yet the player has much more freedom at the micro-level, with far more possible action-combinations than any human mind could comprehend. We might want to say, then, that such a game is closed at the macro-level, yet open-ended at the micro-level. Indeed, the open-closed distinction is probably best understood not as a strict dichotomy, but rather a continuum.

    (A simpler alternative would simply be to define an open-ended system as one with infinite possibile outcomes. However, I would rather include large finite numbers - a fiction with trillions of possible endings is open enough for me!)

    Anyway, I think this is a useful alternative way of categorising fictions. For it seems to me that there is an important respect in which pick-a-path books (or unusually strict & limited computer games) have more in common with traditional fictions than with other interactives such as role-playing games, children's pretenses, and (more open-ended) computer games. I guess this is all depends on the intuition that it matters whether our contribution really helps shape the fiction, or if we're merely picking one pre-created work from a list. I want to say that in open-ended fictions we contribute to the authorship, whereas in closed fictions - even if interactive - we do not.

    Saturday, August 14, 2004

    Philosophers' Carnival?

    In light of the Tangled Bank science blog 'carnival', I've been thinking that philosophers really need a similar carnival of their own.

    The basic idea is that each week - or however often it is held - philosophy bloggers can email the carnival 'host' with a link to their best recent post. The host then collates all of those links together, and posts them (each with a brief excerpt) in one convenient location.

    I think something like this could prove very beneficial to the booming philosophical blogosphere. It would provide many relatively unknown blogs with the opportunity to gain some exposure and attract a wider audience. It would also be extremely convenient for busy readers, to see the best that a wide range of philosophy blogs have to offer, without having to go to the bother of searching through them all individually.

    I'm currently thinking that the best and easiest way to organise it would be to model the carnival on Tangled Bank, and have a central website, but a new host each week. Such shared hosting could encourage a wider group of bloggers to participate and become involved in the project.

    I'd be happy to organise this myself - though any help or advice would be very much appreciated. To get this project started, we'll need two things in particular:
    • A name for the carnival
    • Some influential bloggers to spread the word and generally help promote it.
    Please leave a comment, or email me, if you think you can help in any way here.

    Update: I've created a homepage for the Philosophers' Carnival (I'm still waiting to hear suggestions for a better name). So check it out, and email me with any suggestions, feedback, or submissions!

    Friday, August 13, 2004

    GoMemes as Extended Hat-tips

    I've been following Nova Spivak's posts explaining GoMemes and their potential benefits. It's interesting stuff, for sure, but perhaps not quite as revolutionary as you might think.

    There already exists a natural precursor to GoMemes within the blogging culture: the practice of hat-tipping. Suppose you find an interesting article from reading Joe's blog. If you then link to that same article, you might acknowledge Joe as your source, by appending something like "Hat-tip: Joe" or "(via Joe's bloggs)" to your post. [But with real links, of course.]

    The only significant difference with GoMemes is that they (ideally) include a full path-list of all previous sources. That is, you don't just link to Joe, but also whoever Joe found the link from, and so forth. To achieve this functionality, Spivak's experimental memes required tedious instructions (see this example) to be appended to the meme-post.

    This is the unavoidable result of introducing new practices - people don't know how to perform them unless instructed. But such tedium could perhaps be avoided if, rather than portraying GoMemes as a completely new idea, we instead expanded upon an existing practice: namely, hat-tipping.

    The process of extended hat-tipping is conceptually very simple. If the post you wish to acknowledge offers no acknowledgements itself, then you simply hat-tip it as usual. However, if it does offer another source, then you instead copy that source-list and append a link to the current site to the end. For example, if Joe's post says "via Bob", then in my post I would write something like "via Bob to Joe". And so on.

    The crucial point is that although I've explained the process here in some detail, it would not be necessary to do so in practice. Once the custom caught on, and bloggers saw each other offering extended hat-tips in this fashion, others would pick up the practice quite naturally: imitating it without any need for formal instructions. It would just become a part of blogging 'culture'. And that, for the sorts of reasons Spivak explicates, could prove beneficial to us all.

    Update: For some explicit go-memes, see my personality and politics survey, Academic Blog Survey, and the Metapolitics Go-meme.

    Wednesday, August 11, 2004

    Tangled Bank

    This week's Tangled Bank is now up at Pharyngula:
    This time around, the Tangled Bank is populated with an even dozen members — some repeat members, some new people, and one prodigal returning after a long hiatus. We've got everything from dinosaurs to ulcers, and birth control to the nature of time, so be prepared to settle down and read for a while.

    There are some really interesting posts on offer there (and I'm not just saying that because one of them is mine)... go see for yourself.


    ... is in the ear of the beholder, apparently:
    Whether people find you “hot or not” could depend on the sound of your name, suggests a new study.

    Linguist Amy Perfors of the Massachusetts Institute of Technology in Boston, US, placed photos with fake names on a website called “Hot or Not”, which allows viewers to rank strangers’ photos for attractiveness.

    She found that men labelled with names including “front vowels,” such as the “aaa” sound in Matt were rated as more attractive by website viewers than photos labelled with “back vowel” names, such as the “aw” sound in Paul. The opposite was true for women’s names.

    Bizarre. My favourite line:
    “An attractive person with a bad vowel name is still more attractive than an unattractive person with a good vowel name,” says Perfors.

    You don't say.

    Monday, August 09, 2004

    Scopal Ambiguity

    Scopal ambiguity arises when a sentence contains different types of quantifiers, but is unclear as to their correct order. For example, the sentence "some students heard both concerts" could be interpreted as saying either:
    (i) There exist some students such that each of them heard both concerts.
    or (ii) Both concerts were such that each, individually, got heard by some students (but not necessarily the same ones).

    The ambiguity becomes clearer if we try to formalise the sentence, as each option can find the alternative merely by swapping the order of the quantifiers:
    (i) [Some x: STUDENT(x)][Both y: CONCERT(y)] HEAR(x,y)
    or (ii) [Both y: CONCERT(y)][Some x: STUDENT(x)] HEAR(x,y)

    Now, what I found interesting is that the ambiguity seems to disappear when the sentence is extended in a certain way. Consider: "Some students who heard both concerts were interviewed by Holmes" (new bits in italics). There is only one plausible reading of this sentence - the ambiguity seems to have disappeared entirely. Why is this?

    Here is a formal representation of the sentence:
    [Some x: STUDENT(x) & [Both y: CONCERT(y)] HEAR(x,y)] INTERVIEW(h,x)

    A key difference here is that the 'both' quantifier is embedded within the 'some' quantifier, so they can no longer easily be swapped. But let's try to construct a (ii)-style interpretation of this sentence:

    [Both y: CONCERT(y) & [Some x: STUDENT(x) & HEAR(x,y)]] INTERVIEW(h,x)
    But note that this cannot work, because the 'some x' quantifier is embedded within the 'both y' one, and so the variable 'x' actually expires before we get to the INTERVIEW predicate. That is, the second argument of the predicate doesn't actually refer to anything!

    We can, however, construct an un-embedded version as follows:
    [Both y: CONCERT(y)][Some x: STUDENT(x) & HEAR(x,y)] INTERVIEW(h,x)
    This says that for both concerts (taken individually), Holmes interviewed some students who heard that (one) concert.

    So what's wrong with this? Could this, in theory, be a reasonable interpretation of the sentence "some students who heard both concerts were interviewed by Holmes"? Well, I'm not entirely sure. It certainly doesn't come naturally to us, but that is a practical, not theoretical, matter. However, I think there might be an underlying theoretical problem with it too. That is because it seems to me that to achieve the natural reading, the 'both' quantifier must be embedded within the 'some' - there is no way to make an un-embedded version which means the same thing.

    Suppose we tried to simply swap the quantifiers used in the un-embedded (ii)-type attempt above:
    [Some x: STUDENT(x) & HEAR(x,y)][Both y: CONCERT(y)] INTERVIEW(h,x)
    This doesn't work because the variable 'y', when first used, is as yet undefined. Instead we'd need to shift the 'HEAR' predicate across to the latter quantifier:

    [Some x: STUDENT(x)][Both y: CONCERT(y) & HEAR(x,y)] INTERVIEW(h,x)

    But now this sentence has a different meaning. The 'some' quantifier is far less restricted than it used to be. That is, it merely restricts x to "some students". But what we really want is for x to be restricted to "some students who heard both concerts". So this unembedded version is unfaithful to the original sentence.

    My (tentative) conclusion is that the ambiguity disappeared because - in the extended version of the sentence - one quantifier was embedded within the other, and this prevents the sort of 'swapping' which gives rise to ambiguities. I'm not sure how generally this applies though. Are all such embedded quantifiers non-ambiguous? Can some be reformulated into an un-embedded equivalent (which would then, presumably, be open to ambiguous readings)?

    Sunday, August 08, 2004

    Better Battle Tactics

    Some further thoughts on my previous battle tactics post... I want to look at the problem in a slightly different way from before.

    In the FBC comments, Jamie offers the following consequentialist version of the argument:
    C1: Either we will win the battle or we will lose the battle.
    C2: If we will win the battle, then it is better to attack with a small force.
    C3: If we will lose the battle, then it is better to attack with a small force.
    CC: It is better to attack with a small force.

    It is the same general form as before: a 'proof by cases', we could call it. The first premise lists all possible cases, and the remaining premises assert that in each of those cases, it is better to attack with a small force. Thus, we conclude absurdly, it is always better to attack with a small force.

    So here's the problem: the argument doesn't actually cover all of the cases. I don't mean that there is any fault with the first premise. (Some at FBC objected that it could be a draw, but that is rather besides the point.) Rather, the 2nd and 3rd premises fail to capture the full range of cases that they purport to cover.

    There is more than one way each that we could win or lose the battle. And it simply isn't true that in every case where we will win the battle, it is (or would have been) better to attack with a small force. An obvious counterexample is that discussed previously, where we will win the battle with a large force, but would have lost it with a smaller one. In such a case, although we will win the battle (because we will take a large force), if - contrary to fact - we had taken a small force, we would instead have lost. And that, of course, would not be "better" at all. So the conditional expressed in premise 2 fails to hold in this particular case.

    Now, there is a reading of premises 2 & 3 which makes them look more plausible. That is if we read C3 (for example) as saying something like "of all those close possible worlds where we will lose the battle, those where we attack with a small force are better than the others". That could well be true. But the problem is that it's only making comparisons to other losing worlds. It never considers whether in that world itself it would have been better to attack with a large force (and perhaps win instead of lose).

    So, by that limited reading of the conditionals, we can no longer conclude that it is in all cases better to attack with a small force. Why not? Because, simply enough, our premises no longer cover all the cases. They are ignoring cases like the counterexample discussed above. And that means that the 'proof by cases' logical form is not being used validly. The premises, by this understanding of them, though all true, are insufficient to ensure the conclusion.

    Again, the argument looks valid because it looks as though it covers all cases (given that we either win the battle or lose it). But premises 2 & 3 are only true if we interpret their conditionals in a weak sense whereby they no longer cover the entire set of cases that we might expect from them. The logic requires that they be true in the strong sense, e.g. that C2 asserts something like "In every case [possible world] where we will win the battle, it is better to attack with a small force in that case". But this strong version is quite definitely false - as the counterexamples demonstrate.

    So what can we conclude from the weaker premises? We're given that (1) we either win the battle or lose it; (2) The best winning worlds are those where we attack with a small force; and (3) the best losing worlds are those where we attack with a small force. So from here we can validly conclude that the best worlds are those where we attack with a small force.

    Is that the same thing as saying that "it is better to attack with a small force"? Well, no. It would only be "better" if we ended up in one of those 'best' worlds. But there's no guarantee that fulfilling that one criteria would achieve that end (in fact it's extremely unlikely that it would). After all, there are also a lot of really crappy worlds where we attack with a small force (e.g. the counterexample worlds). Chances are we'd end up in one of them, which would not be a "better" result for us at all!

    (As an analogy: So far as my finances are concerned, the best possible world might be one where I win the lottery. That is, a world where I buy a lottery ticket. But in most worlds where I buy a lottery ticket, I lose, and so have wasted my money. So it would be a mistake to say categorically that it is 'better' for me to buy a ticket. The mere fact that I do so in the 'best' world is insufficient to reach that conclusion.)

    Conclusion: the apparent 'paradox' arises from conflating two possible interpretations of the conditional premises. According to the strong interpretation, the argument is a logically valid "proof by cases", but the conditional premises are demonstrably false. Alternatively, the weak interpretation allows us to accept the premises as true, but at the cost of rendering the logic invalid. Instead we should be concluding that "the best worlds are those where we attack with a small force". But this does not mean that it is better to attack with a small force. So, either way, we avoid the absurd conclusion.

    Saturday, August 07, 2004

    Now and Forever

    I'm currently reading Brian Greene's wonderfully mind-boggling book The Fabric of the Cosmos. An excellent example of my first 'ideal' approach to metaphysics is his discussion of how special relativity affects our understanding of time's existence.

    Background: There are two broad understandings of time's existence - presentism and eternalism. Presentism suggests that only the present (the 'moving now') truly exists. Eternalism, by contrast, puts all times/moments on an equal metaphysical footing, saying that they all exist in exactly the same way. We basically just conceive of time as being another dimension, complementing the 3 spatial dimensions we are more used to. The result: a 4-dimensional space-time loaf.

    The eternalist picture fits nicely with Einstein's special relativity. To extend the 'loaf' metaphor, we can understand a moment of time as being a 'slice' of the loaf, which contains all the events occuring throughout all of space at that moment. However, observers in relative motion will cut the loaf at different angles, resulting in a different set of events. That is, different events will appear to occur simultaneously to you, depending on your frame of reference. Moreover, there is no basis for judging that any frame of reference is more "right" than any other. We are left with the amazing conclusion that time is not absolute: the proposition that events E1 and E2 occur simultaneously, is not absolutely true or false. The answer will vary relative to the frame of reference.

    The problem for Presentism: Presentism seems like the more 'common-sense' approach. It's the way we all intuitively understand the world. However, if special relativity is true, then presentism effectively collapses into eternalism (or at least a far more expansive conception of time's existence than it originally aimed for). In what follows, I will try to outline Greene's explanation of why this is...

    First of all, let's introduce the concept of a now-list. A 'now-list', as the name suggests, is simply a list of all the events that are occuring right now. It's a sort of mental freeze-frame image of the entire universe at any given moment. This then lets us understand presentism as the claim that all and only things on the now-list currently exist.

    Before we go on, there is one clarification that needs to be made to this account. (All quotes are from Greene, pp.133-139, original italics):
    Nothing you see right now belongs on your now-list, because it takes time for light to reach your eyes... If you know how far away something is, you can determine when it emitted the light you see now and so you can determine on which of your time slices it belongs - on which already past now-list it should be recorded.

    Here's the problem: As mentioned earlier, two observers in relative motion have different judgements of what events occur simultaneously. That is, they experience different nows, and so have different now-lists. As Greene puts it, "Observers moving relative to each other have different conceptions of what exists at a given moment, and hence have different conceptions of reality".

    We never notice this in everyday life because the discrepancies are tiny. We cut the space-time loaf in almost identical slices to each other. But the differences can be amplified in two ways: either travel near light-speed (so increasing the angle of the cut), or separate the observers through a huge gulf of space (so even a tiny angle makes for a large end result).

    Greene asks us to imagine a simplified scenario (ignoring motions of the planets, etc) where Chewie is sitting 10 billion light-years from Earth, and that we are at rest relative to each other. This means that we would slice up spacetime in an identical way, resulting in identical now-lists. But suppose Chewie stands up and starts to walk away from us.
    This change in Chewie's state of motion means that his conception of now, his slicing up of spacetime, will rotate slightly. This tiny angular change has no noticable effect in Chewie's vicinity: the difference between his new now and that of anyone still sitting in his living room is miniscule. But over the enormous distince of 10 billion light-years, this tiny shift in Chewie's notion of now is amplified. His now and your now, which were one and the same while he was sitting still, jump apart because of his modest motion.

    So which now-list provides the list of existing things? We presumably have to say "both". But then we have to conclude that a very wide range of times can all exist together. For if Chewie were to move away from us at 1000 mph, his now-list would suddenly include events on Earth that from our perspective took place 15,000 years ago! If Chewie's twin brother Dewey moved towards us at that speed, his now-list would instead include earthly events 15,000 years into our future. Chewie and Dewey exist at the same time, yet they disagree (by 30,000 years!) on what earthly events are also occuring at that moment. Both view-points are equally valid. The presentist must take both now-lists as listing existing events. Too bad that we're now stuck with the existence of events which occur thousands of years into our past and future.

    [Just remember that none of the observers discussed would be able to know any of this at the time. What we really mean is that 10 billion years later, when Chewie's descendents calculate his now-lists, they will find that a bunch of cavemen belong on the same now-list as when he was zooming away from us, whereas just a moment earlier (when he was sitting still) Chewie's now-list included your reading this blog-post.]

    The reasoning in the Chewie scenario can then be extended much further. If we collate all of the overlapping possible now-lists, we will end up with a substantial chunk of spacetime (all of it, in fact, if space is infinite).
    So: if you buy the notion that reality consists of the things in your freeze-frame mental image right now, and if you agree that your now is no more valid that the now of someone located far away in space who can move freely, then reality encompasses all of the events in spacetime... Just as we envision all of space as really being out there, as really existing, we should also envision all of time as really being out there, as really existing, too.

    Crazy stuff, physics. It's incredibly cool - and perhaps kind of surprising - how it can help to shed light on metaphysical questions such as the nature of time's existence. But there you go.

    Thursday, August 05, 2004

    Battle Tactics / Future Truths

    Allan at FBC asks what's wrong with the following argument:
    Premise 1: Either we will win the battle, or we will lose the battle.
    Premise 2: If we will win the battle, then we ought to attack with a small force.
    Premise 3: If we will lose the battle, then we ought to attack with a small force.
    Conclusion: We ought to attack with a small force.

    As The Ethical Werewolf put it:
    I recommend that you reject premise 3: "If we will lose the battle, then we ought to attack with a small force."
    Suppose the antecedent is true: We're going to lose the battle. There are many reasons why this might be the case. One of them is that we aren't going to bring a large enough force. Then it's the case that we ought to bring a large force including many werewolves and some hippogriffs. In this case, the ought-claim that is the consequent of the conditional -- "we ought to attack with a small force" is false. Since the antecedent is true and the consequent is false, the conditional is false.

    I think he's exactly right there. Though I think that we should also reject premise 2: "If we will win the battle, then we ought to attack with a small force". For suppose it is true that we will win the battle with a large force - so the antecedent is true - but that with a lesser force we would have been defeated. (This is a plausible enough scenario, and indeed it is due to cases like this that we know the conclusion is false. So it is worth seeing how this case affects the premises.) Is the consequent also true? Ought we attack with a small force? Quite simply: no. If we were to attack with a small force, then we would lose. So we ought not attack with a small force.

    "But we cannot lose," you object, "because we've already stipulated that we will win!". Okay [but see section on 'future truths' below]. So by attacking with a small force, we would bring about a logically inconsistent state of affairs. This is impossible. So we cannot attack with a small force. And since ought implies can, it is not the case that we ought to attack with a small force (in the given scenario).

    Before anyone gets worried that I've just argued us out of free will, note that the claim "we cannot attack with a small force" is conditional on the supposition that we will win. And the truth of that claim is one that will be affected by our choices (i.e. whether to attack with a small or large force). That is, I'm merely pointing out that in this scenario, the following material conditional holds: "If we will win the battle, then we will not attack with a small force". That shouldn't be controversial, given how I described the scenario (i.e. both the antecedent and consequent are true). Now take the contrapositive: "If we will attack with a small force, then we will not win the battle". This is confusing because the consequent contradicts our assumption. Nevertheless, it is clear enough that we ought not attack with a small force. So in the above scenario, premise (2) would be false.

    Future Truths:
    Consider the following, analogous, argument (based on the assumption that I really enjoy free-fall):
    (1) Either I will die tomorrow, or I will not
    (2) If I will not die tomorrow, then I should jump off a cliff (fun and safe! Let's assume I either won't get injured, or don't care if I do.)
    (3) If I will die tomorrow, then I should jump off a cliff (so I at least have some fun before I die).
    (4) Therefore, I should jump off a cliff (tomorrow).

    Premises (2) & (3), here as in the battle argument, seem to be based on an assumption of fatalism. That is, future truths exist in the present, and we cannot possibly make them false (they are, after all, truths.)

    A better way to understand future truths might be to say that as a matter of convention, we will call a statement about the future 'true' if (in retrospect) it turns out to be accurate. The truth itself is in no way embedded in the present, however.

    This is why it is not true that "If we will win the battle, then we ought to attack with a small force". The truth value of our winning the battle, is not decided until after we have made our attack. Once this has been done, we can look back and say "in retrospect, it was true all along that 'we will win the battle'". But I think talking of truth in this way is just a matter of convention, and not actually saying anything much about reality.

    So here's the problem in a nutshell: the truth of "we will win the battle" (W) may well be dependent upon the falsity of "we will attack with a small force" (S). If S is true, then W is false. So it just doesn't make any sense to argue from the truth of W to the claim that we ought to make S true. That combination is inconsistent (in the particular scenario being discussed). You can't just stipulate the truth of W and then fiddle with other propositions on the assumption that W will stay true. It won't. And that's why we ended up with all those contradictions in the previous section.

    Update: see my Better Battle Tactics post.

    Wednesday, August 04, 2004

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