Friday, October 29, 2004

Universals Overview

What follows is another short essay I wrote for my Epistemology & Metaphysics exam several months ago. This one provides an overview of the 'universals debate' in metaphysics.

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Metaphysical realists posit the existence of universals - multiply-exemplifiable properties that are shared by various particular objects. Their existence is posited primarily to explain three phenomena: attribute agreement, predication, and abstract reference.

When two objects agree in attribute (e.g. both are red), the realist suggests that this is because they both exemplify the same universal (e.g. that of redness). As for predication: to say that an object "is red", is just to say that it has the universal in question (redness). Abstract reference is the realist's strongest support. It seems that we are able to meaningfully refer using abstract nouns such as "redness" and "wisdom". The realist's explanation is that we are simply referring to the appropriate universal.

There are problems with realism, however. These abstract objects seem very odd; it is difficult to see precisely how - or where - they are supposed to exist. Presumably they exist outside of space and time (at least, so says the Platonist, who allows for the existence of unexemplified universals, contrary to the Aristotelian), but then how do we interact with them? This seems to raise serious epistemic difficulties.

Furthermore, it could be argued that the very notion of unrestricted properties (universals) is inherently inconsistent. For consider the apparently meaningful property of Being Non-Self-Exemplifying (BNSE) - the property which is held by all and only those properties that do not exemplify themselves. We can ask: is this property itself self-exemplifying?

Suppose it is. It thus has the property of BNSE, so it is not (by the definition of that property). Conversely, suppose it is not self-exemplifying. It thus has the property of being non-self-exemplifying - which is of course precisely the property required for us to say that it is self-exemplifying! So either way, there is a contradiction.

The realist must therefore deny that there is any such property as BNSE. Perhaps exemplification is merely a 'tie', not a relation. But such responses seem implausibly ad hoc.

For these reasons, and Ockham's Razor, nominalists suggest that we had best not posit such entities (i.e. universals) unless absolutely necessary. They tend to recommend we take predication and attribute agreement as basic, unanalysible facts about particulars. The difficulty is in explaining abstract reference. To deal with this, several different variants of nominalism have arisen.

According to austere nominalism, talk about universals is really just disguised talk about particular, concrete objects. For example, to say "John prefers red to blue" is translated to "John prefers red objects to blue objects". A problem is that such translations are not always accurate - John could like the colour red whilst hating the objects which happen to be that colour. So the austere nominalist must appeal to ceteris paribus clauses, and other such complications, all of which are deemed to be unanalysible.

It is also unfortunate that we cannot achieve any genuine abstract reference with this theory. For suppose we took the set of F-objects as being the referent of F-ness. Then we would get the unacceptable result that the properties of being human and being a featherless biped were one and the same, as they apply to identical sets of particulars.

This last problem can be overcome if we extend the sets to cover all possible worlds. Then, because there is a possible world where chickens have no feathers, those properties would be appropriately defined as distinct. Possible-worlds nominalism is thus quite a powerful option. But there is still the problem of sets which are necessarily co-referential, e.g. the set of 3-angled objects and that of 3-sided objects. We would not want to say that triangularity and trilaterality are one and the same property.

An intriguing solution to this problem would be to extend our ontology to include impossible worlds. That impossible particular which has three sides but four angles would differentiate the two properties for us.

Alternatively, one might say these properties are built out of distinct component parts, for example "being sided" + "being 3 of ___", as opposed to "being angled" + "being 3 of ___".

For an entirely different nominalist approach, one might appeal to tropes: unrepeatable attributes. This approach fits nicely with our perceptions - we can see the redness of a particular object, existing in space and time right there with it. We might also see an exactly resembling redness on another object, but it is nevertheless numerically distinct - just like two jerseys off a factory line might be made of exactly resembling material, yet of course the particular threads composing each are numerically distinct.

A possible objection to tropes is again a problem with sets. Trope theory takes abstract reference to point to sets of tropes (not objects). Though this avoids the previously discussed set problems, there is still the matter of unexemplified tropes, all of which point to the same set: the empty set. The simplest response is just to join the Aristotelian in denying that unexemplified properties exist. Alternatively, one could plot a parallel course to that discussed above, where we extend our sets to cover all possible worlds (or even impossible ones, if we wish to distinguish between impossible tropes).

Another popular form of nominalism is metalinguistic, translating talk about universals into talk about language. Two immediate problems with this are achieving universality across languages (i.e. making properties multi-lingual), and dealing with only tokens of words, not types (which would be a form of universal).

Both objections are met by Sellars' dot notation. Just as quotes around a word refer to that word in English, so dot-quotes refer to that word and all its functional equivalents, in any language. As for the type/token problem, Sellars suggests his dot-quoted words function as common nouns - singular distributive terms that refer to multiple tokens simulaneously.

So just like "the lion is tawny" refers to many particular lions (according to his analysis of singular distributive terms), so "the *courageous* is a virtue predicate" refers to many particular tokens of "courageous" (and its functional equivalents in other languages).

It is worth noting that Sellars' "functional rules" or "linguistic roles" sound suspiciously like universals - though Sellars insists that they need not be understood as such. Another possible objection is that it just seems counterintuitive that our talk about abstract concepts is merely talk about words.

This raises the interesting possibility of a concept-based nominalism (which I understand was more popular with medieval philosophers than modern ones). A realist's universals are mind- and language-independent. Concepts are in many ways similar, except that they are entirely mind-dependent: they exist only in people's minds, not out there in the external world. This strikes me as an intriguing and intuitive possibility, though there are probably difficulties inherent in the notion of a concept. Concepts may, for example, share a similar type/token problem to that the meta-linguistic nominalist faces with words.

Of all the alternatives on offer here, trope theory would seem to be the least problematic. Realists are stuck with a bloated and implausible "two-worlds" ontology, and have difficulty explaining away the paradox of self-exemplification. Austere nominalists have the opposite problems: though ontologically simple, they must appeal to much theoretical complexity to justify their various translations. Metalinguistic nominalism has difficulty escaping universal notions, and the same may be true of concept-based nominalism. Possible-worlds nominalism has a lot of potential, but the expansion to impossible worlds (which may be required on technical grounds) might strike many philosophers as overly implausible. I think it is an interesting (im)possibility, though!

Monday, October 25, 2004

Philosophers' Carnival #4

The 4th Philosophers' Carnival is now up at Doing Things With Words.

Enjoy!

(And do let me know if you'd be willing to host a future carnival...)

Saturday, October 23, 2004

Skepticism Overview

Note: I wrote the following essay in my Epistemology and Metaphysics exam earlier this year. So it lacks footnotes/references and may be a bit scruffy in places (we were only given an hour per essay, after all). But I quite like it still, so thought I'd type it up here - with some minor editing, including the addition of hyperlinks. I don't recall the exact question, but it was something along the lines of "What is skepticism, and what rational responses can be made to it?"

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Skepticism is the thesis that we cannot obtain genuine knowledge - that even our most basic beliefs about the world are epistemically unjustified. The basis for such an extreme claim is found in the apparent impossibility of ruling out various skeptical scenarios or hypotheses which are inconsistent with our everyday beliefs. For example, it seems possible that we could be brains in vats (BIVs), being 'fed' experiences by a mad scientist electrically stimulating our brains in such a way as to give rise to the exact same phenomenal experiences that we usually assume are caused by reality. The skeptic argues that because we are unable to distinguish the BIV scenario from Realism, we are not justified in assuming either one to be the case. Instead, the skeptic argues, the rational thing to do is suspend belief.

In everyday life, this strikes us as a rather implausible suggestion. As the Humean response goes, we are 'natural-born believers'. No matter the philosophical force of skepticism, it is of little practical import. Many philosophers, however, have thought that we can actually beat skepticism on its own terms. Various rational responses have been made to try to refute the skeptic's argument.

As the skeptic's argument is based on the empirical indiscernibility of Realism from Anti-Realism, the most obvious response would be to try to find an a priori reason for preferring the former. Most of these attempts fail - for example, we cannot assign probabilities to these cases. Nor can we say Realism is necessarily any simpler or more parsimonious.

Some have suggested a semantic response, however. Hilary Putnam argues that when an envatted person says "there is a tree", they speak the truth - given what they mean by 'there' and 'tree' (something like "a tree in-the-image").

Putnam advocates a form of anti-Realism here, but we need not follow him in that respect. David Chalmers has a similar response which sees the "matrix" (the world the envatted people think they occupy) as a genuinely real world in itself. He offers a complete metaphysical analysis of it, arguing that it is a world whereby:
(1) It is computational at the most fundamental level of reality;
(2) Inhabitants' minds exist outside of physical space-time, but interact with physical processes;
(3) Physical reality was created by beings outside of (the matrix's) space-time.
This nullifies the skeptical power of the BIV hypothesis, for we can say that envatted people still have largely true beliefs about their world.

Alternatively, if one is dissatisfied by the a priori responses, one must look elsewhere than foundationalist internalism for epistemic justification.

One possible alternative is coherentism. Here, a belief is said to be justified to the extent that it coheres with our other beliefs. Since we are 'natural born believers', and perception causes (though does not itself justify) us to have beliefs about the natural world, it follows that Realism - as a general framework - coheres better with our existing beliefs, than does anti-Realism. We are thus justified in rejecting the BIV hypothesis, due to the incoherence it would bring to our wider belief system.

However, coherentism cannot judge between equally-coherent alternative systems. So the BIV-believer could always insist that his own beliefs are perfectly coherent (and thus justified) - even though they may clash with ours. Coherentism forces a sort of neutrality, then. If we want to go on the offensive, and argue that common-sense / Realist beliefs are not merely justified, but epistemically obligatory, then we will require the philosophical power of epistemic externalism.

According to externalism, justification arises in part from conditions external to the agent. That is, a belief could be justified without the agent subjectively realising that this was so. This instantly overcomes the skeptic's arguments, for the indiscernibility problem becomes irrelevant.

Reliabilism, for example, merely requires that a justified belief be one which was formed by a reliable process. Now, we may not be aware of whether perception is reliable. But, nevertheless, there is some fact of the matter. If it is reliable, then my beliefs about the world will (according to Reliabilism) be justified.

Contextualism is another popular response to skepticism. It suggests that the standards required for knowledge vary according to context - so although we may not know we are not BIVs according to 'high standards' contexts, we can, contextualists claim, know our everyday beliefs based on the 'lower standards' appropriate in those contexts.

The problem with such a response is that if we are foundationalist internalists, then there is no possible evidence to recommend common-sense Realism over the BIV hypothesis. This means that no matter how low the standards are set, we can still never have justification for our everyday beliefs. For contextualism to be any use at all, it must work in tandem with one of the previously discussed solutions - most usually, externalism. (A common answr is the 'relevant alternatives' view, whereby we only need to rule out alternatives that are relevant to the present context. This is at heart an externalist theory though, since 'relevance' is an appeal to factors external to the agent.)

Perhaps the most impressive such fusion is Keith DeRose's mix of contextualism and possible-worlds externalism. The core idea is that S's belief that P is justified to the extent to which it satisfies the condition S believes that P iff P is true in close possible worlds. The justification is stronger, the more close possible worlds there are where this condition holds; that is, where S's belief "tracks the truth" (as Nozick put it) through those worlds.

DeRose's contextualist twist is that the 'strength' of justification required for knowledge will vary according to context. Our belief that we are not BIVs is very strong, for it is accurate in all nearby possible worlds. The closest world in which we are mistaken (i.e. the BIV world) is a very distant one indeed!

So there are several different rational responses one could make to the skeptic. Skepticism demonstrates that an a posteriori, foundationalist, internalist view of knowledge about reality is untenable. We can thus overcome the objection by denying any one of the three conditions. We need a response which is either a priori, coherentist, or externalist in nature.

Thursday, October 21, 2004

New Zealand Day

This sounds like a good idea:
Waitangi Day would be renamed New Zealand Day and celebrated with a three-day weekend every February under a law change proposed by United Future leader Peter Dunne.
...
Only National - who voted for the 2000 bill - signalled support this time around. Leader Don Brash said he believed the proposal should at least get past its first reading.

"Waitangi Day, unfortunately, has gained a reputation for being divisive, and not a day of national unification, so this is worth considering.

"I intend to ask the National caucus to support the bill going to a select committee so New Zealanders can have a say on the proposal."
...
Commemorations at Waitangi would remain an integral part of the day, but not the sole focus.

I'm a little uncomfortable with the political company I seem to be keeping here (United Future? National? Ick). But it does fit nicely with my previous suggestion that we start focussing on integration over divisiveness. If the right-wingers are the only ones offering that, then so much the worse for my partisan loyalty to the Left.

Wednesday, October 20, 2004

Third-Person Wellbeing

Is it better to be mistakenly happy or mistakenly sad? Or, to put it another way, which matters more: subjective desire-satisfaction or objective desire-fulfillment? In a previous post, I argued for the latter, appealing to the following thought experiment:
Imagine a mad scientist kidnaps you and your family, and offers you the following two options:

(1) He will let your family live in a pleasant but secluded captivity, but you will be made to believe (eg through hypnosis, or whatever) that they were all tortured and killed.

(2) He will torture and kill your family, but you will be made to believe that they are safe and well in a pleasant but secluded captivity.

After making the choice, all recollection of the bargain will be erased from your memory. Which option would you choose? Most people say #1 - the desire fulfillment option. We want our families to be well in fact, and this is more important to us than whether we merely believe that all is well.

I still agree that the first option seems preferable, from a first-person perspective (i.e. if you consider making the decision yourself). But what about the equivalent 'third-person' choice?

Suppose instead that it is Bob's family that is kidnapped, and Bob - rather than you - who has to make the decision. Now, I ask you, which result do you think would be better for Bob?

My intuitions here are far less clear. But I think that (probably) option #2 is better for Bob. Yet I know that if I was in Bob's position, I would choose #1, even for selfish rather than moral reasons - I really would prefer my family to be safe in fact. So judging from the third-person perspective, I have a different idea of Bob's wellbeing, than I do from the first-person perspective. Is that odd?

I'm quite confused by this case, and would very much appreciate hearing some other people's intuitions here. (I don't get a huge number of visitors to this site, so please do leave a quick comment if you can spare the time!)

Which result do you think is better for Bob?

Light Blogging

You may have noticed the pace of this blog slacking off a bit over the last couple of weeks. I've been a bit busy with assessments and such. [Damn real life, always getting in the way! ;) ]

There are a few million things I'd like to write about, but with exams fast approaching, that might have to wait a couple more weeks yet.

Things should be back to normal come November.

P.S. Would you believe that my stupid university is making me pay $15 for my exam script from a class I took earlier this year? I really liked a couple of essays I wrote for that exam, and I want to type them up on here. But they're making me pay for it... for my own writing. That so sucks.

Sunday, October 17, 2004

Upcoming Carnival

A quick reminder that the 4th Philosophers' Carnival (hosted by Doing Things With Words) is just a week away now. If you have a philosophy blog, it's time to start thinking about choosing a post to submit.

(Also, be sure to sign up to the carnival newsletter, so that you don't miss out on any future updates!)

Saturday, October 16, 2004

Doubting Disbelief

Why is it that some religious people refuse to accept that atheists really don't believe in God? A common strategy for intellectually dishonest Creationists (and is there any other kind?) is to misrepresent various eminent evolutionists (e.g. Gould or Dennett) and try to claim them for their own side. Anthony Daniels (though not a Creationist, so far as I know) employs similar tactics in an otherwise decent review of Richard Dawkins' new book.

Consider the following extract:
Dawkins's obsession with proving that God does not exist makes me suspect that he cannot altogether disbelieve.

Why? Wouldn't it be more reasonable to instead 'suspect' that Dawkins believes that religious falsehoods are largely harmful to humanity? In fact, rather than relying on suspicions, wouldn't one do better to just ask Dawkins himself? (Quote: "I care about what's true, I care about evidence, I care about evidence as the reason for knowing what is true. It is true that I come across rather passionate sometimes - and that's because I am passionate about the truth.") But Daniels entirely disregards Dawkins' own stated motives, prefering to second-guess him through psychoanalysis, thereby getting to invent whatever nonsense he likes.

To highlight the invalid (indeed, bizarre) logic behind Daniels' claim, consider this analogous statement: "Martin Luther King's obsession with proving that blacks deserve the same civil rights as whites makes me suspect that he cannot altogether disbelieve the opposite." Isn't it absurd? Wouldn't you think that anyone saying such a thing must be a raving idiot? Yet Daniels is far from the only one to reason in such a manner about outspoken atheists.

Or consider the following:
When [Dawkins] writes at the end of his book, "My objection to supernatural beliefs is precisely that they miserably fail to do justice to the sublime grandeur of the real world", he sounds not so very far removed from religion after all. Indeed, I half-expect a deathbed conversion in his case.

I'm astounded by Daniels' logic. Dawkins says that religion is too superficial to capture the genuine wonders of reality. He clearly feels awe. Hence he must be religious!

It's a bit scary to think that this guy is "a practising doctor". Just imagine him at work one day: "Disease X cannot explain symptoms Y. This patient has symptoms Y. So he must have disease X!"

To be fair, I expect that he is actually relying on a hidden/implied premise, a particularly nasty stereotype about atheists. Something along the lines of: "Atheists are all unimaginative, uncaring, cold and dull people; religion is the source of all awe and wonder in the world". So that would improve the logic at least, though at the cost of importing a blatantly false premise. It sure does expose Daniels' prejudices.

Lastly:
Like most evolutionists, Dawkins overestimates the human significance of the theory of evolution. Explaining how we have come to be what we are is not the same as telling us how we should live from now on - which is a question of some importance.

This section is extremely misleading. Dawkins has explicitly insisted that evolutionary processes should not be seen as the foundation for morality:
I am not advocating a morality based on evolution. I am saying how things have evolved. I am not saying how we humans morally ought to behave... My own feeling is that a human society based simply on the gene’s law of universal ruthless selfishness would be a very nasty society in which to live. (The Selfish Gene, p. 2-3).

So in this review Daniels misrepresents Dawkins, attempts to psychoanalyse him (with bizarre results), and assumes that because the awe of ignorance is often religiously inspired, so too must be the awe of knowledge.

Yet this is not an unusual article. The prejudices Daniels expresses are (un)reasonably commonplace - indeed, he might be more atheist-friendly than most. It's a worrying thought.

Tuesday, October 12, 2004

Placebo Prayers

There's an interesting NYT article which discusses the scientific study of whether prayer has healing effects.

It quotes a Harvard psychologist as complaining that such effects are "by definition beyond the reach of science" - a foolish statement which Jonathan Ichikawa rightly calls him on.

As a naturalist myself, I look forward to rigorous research being done on this topic, to help convince the gullible that prayer really doesn't make a fig of difference. The current lack of hard evidence either way merely gives them an excuse to indulge their wishful thinking. So I don't understand why skeptics would be opposed to such research in principle. (In practice, of course, it's a bit of a waste of money - 2.3 million federal dollars could surely be better spent elsewhere.) It sounds like the kind of issue which CSICOP might have more info on.

There are a variety of variables which I'd like to see tested. For example:
A) Content of prayer: (1) to help or (2) to harm the patient.
B) Target of prayer: (1) Christian God, (2) Allah, (3) Hindu gods [etc.]
C) Sincerity of prayer: i.e. (1) prayed by a true believer or (2) prayed by a non-believer (of the targeted religion).

+ of course the control group, which doesn't get prayed for at all.

You could mix and match various combinations, taking one option from each row. Then you could do it all over again, except this time the new combination is not what gets done in fact, but instead is what you tell the patient. [Though this would square the total number of groups involved, so this 'ideal' experiment is fast becoming impractical. It would no doubt require a huge sample size to get enough people in each group to allow any statistically significant results to be inferred. So a simpler version may be preferable.]

For example, a patient might be told he is being prayed for (positively, by a Christian, to their God), when in fact an atheist is praying to Allah to strike him dead. Or vice versa. (Say, do you think an experiment like this would have trouble getting ethics approval?)

It would be interesting to see how the different combinations played out, so we could learn just what factors actually have a influence.

I'd be willing to bet that the fact of the matter makes no difference whatsoever. But what the patient believes (and his expectations regarding the results of this) might well influence things, as a form of placebo effect.

Incidentally, I think the genuinely religious should be embarrassed by the 'Santa Claus' conception of God implied by the 'believers' behind these experiments.

Chris Mooney suggests that "[t]he real reason intercessory prayer research is absurd is that[...] it not only assumes supernatural forces, but assumes that those forces will be benevolent". Not at all. A benevolent God wouldn't wait for people to ask him to help improve the world. He'd improve it right away.

Jason at Evolutionblog sums it up nicely:
It's hard to see how such studies could actually end up benefitting religion. If they are unsuccessful, that would be evidence that prayer is ineffective. But if they are successful, you are left with a fickle God who makes life and death decisions based on who asks him nicely for intervention.

Lastly, go read Positive Liberty's take on "what happens when you pray to the wrong god". Only semi-related to all this, but very funny.

Monday, October 11, 2004

Psychic Powers

Brain-Machine Interface sounds like an incredibly exciting new field:
A 25-year-old quadriplegic sits in a wheelchair with wires coming out of a bottle-cap-size connector stuck in his skull.

The wires run from 100 tiny sensors implanted in his brain and out to a computer. Using just his thoughts, this former high school football player is playing the computer game Pong. [...]

Further out, some experts believe, the technology could be built into a helmet or other device that could read neural signals from outside the skull, non-invasively. [...] DARPA envisions a day when a fighter pilot, for instance, might operate some controls just by thinking.

I want one of those helmets!

Say, I wonder if they could ever come up with something which works in the opposite direction? That is, transferring information from computers into the human brain. Instant learning, Matrix style. That would be cool. Probably not very realistic, but fun to imagine, at least.

Update: More here and here. Ethical issues discussed here and here. Monkey trials here. Mobile brain implant discussed at NewScientist

Sunday, October 10, 2004

Carnival Newsletter

I've added a new subscribe to newsletter feature to the Philosophers' Carnival homepage. If you fill out your email address, you will be added to the mailing list.

What this means is that you will receive automatic email notification:
1) A few days before an upcoming carnival, as a reminder in case you wish to submit a post to it.
2) Immediately upon the publication of each new carnival.

You can unsubscribe at any time.

Many thanks to Jeremy Pierce for the idea of setting up a mailing list. If enough people sign up to it, this should solve the publicity problem quite nicely.

Thursday, October 07, 2004

Fiction & Emotion

Why do we respond emotionally to fictions? Is it irrational of us to feel joy or sadness about characters and events that we know aren't real?

In a recent seminar given us, Justine Kingsbury of Waikato University suggested that evolutionary psychology - and particularly the positing of informationally encapsulated 'mental modules' - could shed some light on our seemingly odd behaviour here. The core of her explanation is that although we know the fiction isn't real, this information might not be accessible to the emotion 'modules' of the brain. This view suggests that emotions are rather like automatic reflexes (and so a-rational, rather than irrational). If you see a monster on the movie screen, this stimulus may activate your 'fear module', which does not have access to the information that the threat is not real. (A similar explanation may be given of irrational phobias, which must be overcome through training - mere cognition is insufficient.)

I'm not entirely convinced, however. Our emotional response to fiction seems deeper than that. We need to be engrossed in the fiction; mere perception of the superficial stimuli is insufficient to elicit most emotional responses (there are some exceptions, e.g. disgust). I won't feel sad at a character's loss unless I reflect on their situation, and empathise. This suggests that our responses are more cognitive and less automatic than the modularity account would seem to grant. (Unless I'm missing something here?)

I think a better explanation would focus on the role of fiction as a sort of simulation. In reading a novel, we create an internal simulation of the events it portrays. This provides us with surrogate experiences, as of engaging unfamiliar environments or situations, but without any real-life risk. I think it makes sense for us to react emotionally to the simulation, for it would otherwise be incomplete. How we feel about a situation is a crucial aspect of it; to leave this out of the simulation would be to omit something of great importance to us.

So I think it appropriate for us to react emotionally to fictions. Whether it is, strictly speaking, rational cannot be meaningfully answered until we clarify what is meant by that word in this context. Some suggestions from a TLS article:
An emotion is “cognitively rational” if it is based on a well-supported belief (I clearly saw that it was you and not Susan who knocked over my glass of red wine), and “strategically rational” if it leads to actions that will achieve a desirable goal (the urgency of my anxiety encourages me to rush across the room and immediately throw salt on the stain).

I guess what I described above suggests an indirect form of strategic rationality: emotions about fictions are useful in that they help us attain our goal (loosely understood) of learning more about life. Arguing that they are cognitively rational is more difficult, given that these emotions are based on imagined (or simulated) beliefs, rather than real ones.

A neat solution would be to say that the emotions too are merely simulated rather than real. Jonathan Ichikawa has previously argued for something along these lines (at least for some cases). There is some independent evidence to support this claim: Compared to real life, we seem to have an unusual degree of control over our emotional responses to fiction. Also, the resulting emotions are often more transitory, and less likely to influence our behaviour than other emotions. Counter-evidence would include the phenomenological similarities (it seems that we really do feel happy/sad, not that we're merely simulating it), and physiological ones too.

Any suggestions?

Monday, October 04, 2004

Philosophers' Carnival #3

The third Philosophers' Carnival is now up at Philosophical Poetry. Andrew has presented it delightfully, introducing the submissions through a humourous dialogue.

I submitted my post on Observing Morality, and also nominated the posts from PEA Soup and Garden of Forking Paths. Of the others, my favourite is probably Essentialist Intuitions from Mixing Memory.

There are thirteen entries in all, which is a pretty good turnout I think. The overall quality might be higher than in the previous carnivals too (though I guess that's a pretty subjective judgement). So a good result all round! Now all we need is a host for the next one...

Sunday, October 03, 2004

Blargh

I'm too tired to write anything substantial right now. But that's okay, cos there are plenty of other blogs you can read instead. For example, Blargh Blog, where I've just noticed some interesting posts on moral inconsistency and slippery pinnacles (as opposed to slopes). Enjoy!

Saturday, October 02, 2004

Purpose of the Carnival

Mixing Memory (which is, incidentally, my favourite new blog since I came across Positive Liberty) has a post about the Philosophers' Carnival.

The question was raised as to what the purpose of the carnival is, so I added a comment hoping to clarify my own views on that matter. If you're interested, go read it. And be sure to have a look around the rest of the site while you're there.

Comment Hacks

Ah, man, this is so awesome... via Russell Arben Fox I came across a wonderful site called Blogger Hacks, that tells you how to update your Blogger template so that:
1) You can now post comments directly from the post page itself (and commenters don't need to register with Blogger any more either).
2) A list of "Recent Comments" is displayed on the sidebar.

(I understand that his next hack is going to automatically convert old Haloscan comments into Blogger ones. I wish I'd had such a resource available to me when I switched comment systems a month or so ago!)

This really is a huge improvement. I whole-heartedly recommend other Blogger users go update their own templates similarly! :)

Friday, October 01, 2004

Logic Trees and Modal Indexicals

In logic class the other day, we were learning how to do "semantic trees" for the modal system KTS5, and I suggested that indexing modal statements to particular worlds (as we were told must be done) was redundant. My professor wasn't convinced, however, so I'll use this post to set out and clarify my argument.

Notation:
I'll use 'A' to refer to an arbitrary proposition; '~' as the negation operator; 'Nec' as the necessity (box) operator; 'Pos' as the possibility (diamond) operator; '->' as material implication; and '/i' as the index denoting which possible world the entire preceeding statement is true of.

(For example, "PosA -> NecPosA /w" means that the proposition "If A is possible then A is necessarily possible" is true in the possible world w.)

Let 'Gen' be used as a generic modal operator (i.e. it could be filled in by either 'Pos' or 'Nec', or the negation of either).

Also, I will use '=>' to represent a tree rule. Indexing does not extend across the arrow. So "X => Y /w" means that given 'X' in some branch, you can extend that branch by one level and write 'Y /w'.

Overview:
To motivate my view, note that modal statements don't say anything about the specific world they are indexed to. Rather, they make claims about the entire collection of possible worlds. ('NecA' means A is true in all possible worlds; 'PosA' means A is true in some possible world.) So the truth value of "GenA /i" should be constant across all possible indices i.

More formally, we can see that this ties in with axioms S4 and S5. Recall that S4 says: "NecA -> NecNecA"; and S5 says "PosA -> NecPosA". The combined effect of these axioms is to claim that if GenA is true, then GenA is necessarily true. That is, if GenA is true in the actual world, then GenA is true in all possible worlds.

My Proposal:
It simply doesn't matter what world we index a modal statement GenA to. It's either true of all of them, or false of all of them. So why bother indexing modal statements at all?

I propose that we stop indexing modal statements to possible worlds. (Though of course we must retain indexing for all non-modal propositions in the proof!) This move would have both conceptual and formal benefits. Conceptually, it encourages us to recognise the nature of modal statements as being about the entire collection of possible worlds, rather than any one specific world. Formally, it can save us a few tedious steps when constructing a tree-based proof, since we could close a branch the moment it contains both GenA and ~GenA (for the same modal operator 'Gen', of course!), whereas at present this contradiction might be (momentarily) hidden due to different indices being assigned to the respective modal statements.

The Formalities:
Converting the rules is really quite a simple process. The usual (non-modal) rules are left untouched; and of the modal rules, we simply drop the index from all modal statements, and add one new 'de-indexifying' rule.

Recall that the original modal rules are:
  • PosA /w => A /i (for some new i)
  • NecA /w => A /i (for any i) [Do not check off original statement]
  • ~PosA /w => Nec~A /w
  • ~NecA /w => Pos~A /w

My new rules would instead be:
  • PosA => A /i (for some new i)
  • NecA => A /i (for any i) [Do not check off original statement]
  • ~PosA => Nec~A
  • ~NecA => Pos~A
  • GenA /w => GenA

That last rule (or some equivalent) needs to be added so that we can de-index any modal statements derived from the first two rules. See the sample proof below.

Either set of rules (if correctly applied) will give identical results when testing statements for logical consistency within the KTS5 modal system. But the latter set is tidier, faster, and conceptually clearer. So why not use it instead?

Sample Proof: Proving the S5 axiom

The Old Way:
[check] ~(PosA -> NecPosA) /w
|
[check] PosA /w
[check] ~NecPosA /w
|
[check] Pos~PosA /w
|
[check] ~PosA /i
|
Nec~A /i
|
A /k (from 2)
~A /k (from 6)
X

The New Way:
[check] ~(PosA -> NecPosA)
|
PosA
[check] ~NecPosA
|
[check] Pos~PosA
|
[check] ~PosA /i
|
~PosA
X

Quicker, tidier... better.