Monday, March 31, 2008

The value of life and zero utility

My general question is whether there is such a thing as negative value. Perhaps especially relevant in 2008 when the world is just waking up from a collective delusion of limitless borrowing.
It is clearly possible to talk of negative holdings. We do so all the time. How much do you have for example? I give even odds that the answer will be negative. You have a current account balance of minus £800, or, if you are affluent, a mortgage of minus some much larger figure. But have you really got less than nothing? You seem to be clothed and fed, able to navigate around the capital, I've even seen you buying drinks.
Bernoullie counts the exhange value of our earning power and any other exchangeable goods as a part of our holdings, which seems to me to be eminently sensible and easily explains the above paradox. The reader with the overdraft is expected to be able to repay on future earnings. The reader with the mortgage likewise, but failing that can make up the debt by selling her house. So neither really has less than nothing.
We could work out the worth of a man as follows: [resale value of all goods + (expected earnings - minimum living expenses) multiplied by life expectancy] . Call this number L, then we could think of any citizen whose total debts exceeded L as being in possession of negative value. However this is not entirely realistic, since any person whose debts exceeded L could no longer be considered as a debtor, since they could be under no obligation to pay back their debts. They would flip over into being more a thief, beggar or charity case. Perhaps in earlier times it might have been thought possible to extract such debts through torture or other punishment. The logic of this, although eminently human, is, thank evolution, no longer considered rational.
So here's a thought: Perhaps at the moment of suicide we could conjecture that a person has completely nothing.
Now imagine this. We find a large sample of people on the point of suicide. (shouldn't be too difficult, its fast becoming one of the biggest killers, especially if they succesfully reclassify traffic accidents). We then offer them goods to see if we can tempt them to desist from suicide. The quantity of goods necessary to prevent suicide could then be consider equivalent to the negative utility of their holdings at the point of death. Their fate could be considered worse than death by a measurable amount, not just in utility, but in actual money. Since the moment of self slaughter must surely be counted as zero, then this would be a negative value.
Some may think this unromantic, but I think it opens up as yet unseen romantic vistas of great poetic power. Comparisons of value are the very constituents of romance and poetry. Fie on those who say that the most valuable thing in their lives is a two bedroom flat in Dulwich village. Surely the most valuable thing in most peoples lives is their union with their beloved. The greatest negative value at the point of suicide must have been that of Romeo when he thought his beloved Juliet dead. Had one of our hypothetical research team approached Romeo in his last soliloquy and offered him goods to prevent his suicide, what would have stayed his hand? Nothing but the sight of his Juliet alive. As it happens, quite an easy thing to acheive. But what else, had this been impossible? Nothing, (we romantics hope), not the wealth of kingdoms, nor the power of empererors, nor mastery of the seven seas. So now we have a measure of the negative utility of Romeo's holdings, and by comparison the positive utility of Juliet's life. The number we achieve is a kind of de facto infinity. For any sum of money, or office of power, there is something of higher value, and that is Juliet's life. And for any debt, however large, there is a greater possible debt, and that is the debt of someone who owed Romeo his life once Juliete was no more.
As a kind of punch line for affecionados of probability, if we offered Romeo the St Petersburg Game, then we could suppose that he was prepared to pay the ultimate price. But how many consecutive heads would Romeo have to toss before the casino would be obliged to ressurect his Juliet?

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Wednesday, March 26, 2008

Fitch's argument. Where I have gone wrong?

Any metaphysical modal wizards out there that can help me? Here's a line of reasoning that I think is true:
1. In order to wonder whether p is the case, one must be able, at least partially, to understand the content of p.
2. To understand the content of p is to able, at least in some cases, to know that p when it is clearly evident that p.
3. If one didn't know that p when p was clearly evident, then one would not understand that p.

4. Therefore if S understands the content of p, it must be possible for it to be clearly evident that p.
5. If S wonders whether or not "p" where p is a proposition expressible by a declarative sentence, then it must be possible to for S to know that p.
6. If S wonders whether or not p, then (at least in some cases) it is possible that p is true and it is possible that p is false.
7. Therefore it is possible to know a proposition that is false.

Conclusion: Knowledge is not necessarily factive.


It is possible to know that (p and nobody knows that p).
There are many instances of contingently necessary propositions, for example
Jack doesn't know that (there is extra terrestial plant life and Jack doesn't know that there is extra terrestial plant life).

I'm not interested in hearing people disagreeing with the conclusion, I expect that most people do. But it is possible that most people are wrong. What I want to know is which bit of the argument is wrong. I expect there is a scope fallacy going on, or perhaps an illicit blurring of epistemic and metaphysical necessity.


Friday, March 21, 2008

Not necessarily possible

William Bynoe’s most excellent talk provided a argument against two axioms which I find a priori absurd in any case. One is that anything that is possible is necessarily possible. The other is that anything actual is possible. Will gave these principles in terms of accessibility relations between possible worlds. So we can call them:

1. Equivalence: For any worlds A and B, if A is accessible from B, then B is accessible from A.

2. Reflexivity: Every world is accessible from itself.

This fevered adding of axioms renders accessibility redundant and meaningless, since all possible worlds become equally accessible from all others. Will’s argument comes from two premises:
1. (Roughly, there was no hand out): Truths about what is possible are grounded in the actual world.
2. It is possible that there could be nothing at all.

The argument then is, call the actual world WA: it seems possible grounded in the actual world that there could have been nothing. Let us call this possibility WN. WN is accessible from WA. But WA is not accessible from WN, since if WN was the actual world, then there would be nothing in WN that would ground the truth of the possibility of facts in WA. Further more, it might also be claimed that WN is not accessible from itself. So WN provides a counterexample to equivalence and reflexivity.

A lot of the discussion focussed on the nature of N. People found reflexivity and equivalence to be so “intuitively plausible” that the argument just showed that N was impossible. But this kind of thing I found weak for this reason: the intuitive nature of the two dodgy axioms rests on a few examples. But all this shows is that reflexivity holds in some central cases, as does equivalence. To jump from this to the claim that it necessarily holds in all cases requires more than considering a few tailor made examples. It involves a proof, or at very least a confrontation with ordinary usage which in fact throws up many counterexamples. I’ve never seen anything like a proof, and when ever I have offered counterexamples I usually meet with hostile verbal evasion of this kind “You are confusing metaphysical modality with epistemic modality”.

Will began with the intuitive case for the two axioms by giving an example of something possible but not actual. He was actually standing, but he could have been sitting. Reflexivity and equivalence clearly hold in this case. Had he been sitting then it would have been possible that he was standing, and given that he was standing, it is clearly possible that he was standing. So far all we have got is a generalisation based on a single case. 1 is prime, 3 is prime, 5 is prime, 7 is prime, therefore all odd numbers without exception are prime.

Later, for contrast something impossible was considered. Tim is Portugal was the example. This is supposed to be clearly impossible. Why? Because it is nonsense, because it is impossible to imagine. But I thought we were talking about metaphysical possibility, not conceivability or semantics. A state can be defined in terms of its citizens and its territory and perhaps it constitution and economy. It is possible for a state to lose all its territory and all its citizens but one and that one could be Tim. The remaining citizen would then embody the whole of the state. If the state was democratic, and Tim was the last citizen, then the constitution of Portugal would be identical with Tim’s will, its territory identical with Tim’s property and body. Tim would be Portugal in this case. “I am the state of Portugal.” He could say with uncharacteristic grandeur. Is this scenario possible? What relevance does it have to the accessibility relationship?

Perhaps this is not possible because “Tim” and “Portugal” are rigid designators, and this scenario just changes Portugal too much for us to have a hold on what the possibility is supposed to consist in. With this in mind lets go back to the central example. It is possible that William Bynoe (rigidly designated) is sitting down at time t, when actually he was standing at that time. This is clearly not epistemic, since we know he was actually standing. So the accessibility relationship holds symmetrically between WA ( the actual world) and W1 (where William Bynoe was sitting not standing at time t). Now let us consider a second possibility: It is possible that William Bynoe (rigidly designated) does not exist. This is clearly not epistemic since in order to rigidly designate William Bynoe he must exist. The reference fixing must be grounded in the actual world. So the accessibility relationship holds between:
WA (the actual World) and W2 (a world in which William Bynoe does not exist). But is it symmetric? Well no, because in W2, William Bynoe doesn’t exist, so the possibility that William Bynoe is standing is not grounded in W2 and therefore can’t be a possibility. Complicated? Baroque? A misunderstanding of some kind? I don’t think so. Here are two propositions that, realist as you like about possibility, are straightforwardly true:

If William Bynoe did not exist then it would be impossible that he is now standing.

It is possible that William Bynoe did not exist.

There for it is possible that it is impossible that he is now standing.

This is a counterexample to the equivalence relation. It is also a counterexample to the axiom that whatever is actual is necessarily possible, since if William Bynoe is in fact now standing, then it is still possible that it is impossible that he is now standing.


Sunday, March 16, 2008

bernoulli and I on necessity

Necessary and Contingent.

I share these concepts with Bernoulli it turns out. “A proposition is called necessary, relative to our knowledge, when its contrary is incompatible with what we know.” Is how Hacking 19975 explains Bernoulli's use of necessary and contingent propositions. Suppose we are wondering whether H is certain given evidence E. There are 4 possibilities:

1. E is known, H given E is uncertain. Argument contingent, H contingent
2. E is uncertain, H given E is uncertain. Argument contingent, H contingent
3. E is known, H given E is certain Argument necessary, H necessary
4. E is uncertain, H given E is certain. Argument necessary, H contingent

Whether or not E is known would be to an empiricist and empirical matter. This is as much as to say that there are no foundational singular statements of fact. There could be some doubt to this, but this need not worry us here.

What is confusing and equivocal is what is means for H given E to be certain. A straight forward interpretation is that p (H given E) = 1. Now we must wonder what kind of interpretation of probability is at play here. To a rationalist, we might think that H given E is certain if it is a priori. This would be as much as to say that only logical and mathematical inferences are certain and therefore only mathematical and logical truths are necessary. But why can’t we be certain of H given E on the basis of experience? Well, because of the problem of induction. But that is circular, since the problem of induction is only a problem if we accept that we can only be certain of conditionals through pure reason.
Here are some certain conditionals that would count as being learned through experience:
If it is a Blue Whale then it is a Mammal.
If an act is motivated purely by cruelty, then it is wrong.
If a piece of Music is written by Mozart, then it is Classical.
If Jones intentionally fired the gunshot that killed Smith, then Jones killed Smith.
If Smith fell into a meat mincing machine and was turned into mince meat, then Smith is dead.
If x thinks, then x exists.
I guess that many contemporary post graduate students of philosophy would say that the above conditionals are contingent. Would you? I for one am certain of all of them, though I could imagine a different conceptual scheme where they weren’t certain. If Mozart had written some Baroque music, for example, or if “intentionally” included cases of hypnosis, or if Smith was some kind of super being who could regenerate himself, or if “Blue Whales” referred to something ostensibly similar to Blue Whales, but for hidden “scientific” reasons to do with molecules weren’t actually Mammals. I could imagine a society of sadists and masochists where only cruel acts were just. I can imagine a character who thinks, but yet does not exist. Hamlet, for example. But what do all these flights of fantasy have to do with necessity and contingency? Nothing useful, I say. A distinction monger might want to talk of what is necessary in the actual world and what is necessary in every possible world. So Blue Whales are only necessarily mammals here, whereas other worlds they are only contingently mammals. But then we have lost possible world modal semantics. To focus on the one example. Suppose we are certain of proposition E x is a Blue Whale where the reference of x is fixed by clear spatio temporal co ordinates. Now I count it as common knowledge that in general if x is a Blue whale then x is a mammal. Let H be the hypothesis that x is a mammal. Is H necessary or contingent?

Thursday, March 13, 2008

Attributive and referential use of definite descriptions, not a semantic distinction. Tim Pritchard

Tim’s talk last night was very good as most people seemed to agree. The central two claims were that
1. There is no linguistic mechanism that differentiates between referential and attributive uses of definite descriptions . (Although the distinction can be made.)
2. We think what it is we want to communicate, and we then find the best words with which to express it. (In other words there is no such thing as intending to mean by a sentence whatever it is that the sentence means).

To prove Tim’s 1st claim is difficult since no single example will suffice. My thought is that if we give an epistemological informational account of the distinction then we can show that there cannot be a linguistic mechanism that would work. The account would be that the attributive use is one where the speaker is informing the audience that the description is true. The referential use is where the speaker presupposes that the audience presuppose that the description is true. Since in both cases the speaker is intending the description to be taken as true, there can be no semantic difference.
For example, the utterance type
SD: Smith’s murderer is the one who stole the diamonds.
Now we have two definite descriptions. The speaker cannot presuppose that the audience presupposes both descriptions to be true of the same person, since otherwise his utterance would be redundant. But equally clearly the speaker can’t presuppose that both utterances are descriptions that refer to different people, or the utterance is plainly false. So in making utterances of this kind, the speaker must be using at least one attributively. Yet both definite descriptions have the same structure.
This might be clearer if we think in terms of investigations:

Investigation 1. Who murdered Smith?
Background knowledge: John stole the Diamonds.
New Evidence: Smith’s murderer is the one who stole the diamonds
Result: John murdered Smith

Investigation 2. Who stole the Diamonds?
Background knowledge: John Murdered Smith
New evidence: Smith’s murderer is the one who stole the diamonds
Result: John stole the diamonds.

Investigation 3. Who murdered Smith and who stole the diamonds?
Background Knowledge. Someone stole the diamonds and someone murdered Smith.
New evidence: Smith’s murderer is the one who stole the diamonds.
Result: Someone murdered Smith and stole the diamonds.

From these examples it is clear that there is an important epistemological difference between the uses of the new evidence in reaching conclusions. But it should be equally clear that there is no difference in meaning across the three cases. The new evidence in each case expresses the same proposition. The attributive/ referential distinction is purely epistemological.

Just for completeness:

Investigation 4.

Background knowledge. John murdered Smith and Jill stole the diamonds.
New evidence. Smith’s murderer is the one who stole the diamonds.
Result: ERROR!!!! Reject evidence or accept that Smith’s murderer is not Smith’s murderer or the one who stole the diamonds did not steal the diamonds or that John is Jill.

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Friday, March 07, 2008

On Hugh on Two Envelopes, by David Papineau.

On Wednesday Hugh McCormack’s excellent discussion of the two-envelope paradox laid out Sonia’s reasoning as below (if I remember it right).

(For those new to this paradox, Sonia is shown two envelopes, told one contains twice as much money as the other, and is then given one of the envelopes at random, and asked if she wants to swap it for the other. She then reasons . . . )

(1) Let x be the amount in my envelope.

(2) There’s a 50% chance that I’ll lose by swapping and a 50% chance that I’ll win.

(3) If I lose, the other envelope will give me 0.5x. If I win, the other envelope will give me 2x.

(4) The expected result of swapping will thus be 1.25x (50% x 0.5x + 50% x 2x) which is more than x.

(5) So I should swap.

But of course this is a silly conclusion. (If Jim were given the other envelope, he could reason just the same, but there couldn’t be reason for them both to swap.)

Hugh said that Sonia’s calculation must be misapplied because it implies, absurdly, that swapping can lead to an increase in the total money in the envelopes.

That is true enough, but I still hankered to know exactly where the reasoning laid out above goes astray.

I think it’s helpful (as suggested by Hugh in later correspondence) to compare Sonia with Fred. We give Fred an envelope containing a certain amount of money, and then then spin a coin (or something equivalent) to determine whether we put twice or half in the other.

Now Fred can do Sonia’s calculation as above (it’s 50%-50% whether swapping will win or lose, winning yields 2x, losing yields 0.5x . . . so I should swap). But note that in Fred’s case this is a GOOD conclusion. Fred should indeed swap.

So why exactly does Sonia get a bad answer when she does the calculation? After all, it’s equally true of her (since it was random which of the two envelopes she was given) that it’s 50%-50% that swapping will win or lose.

Here's what I would say about the flaw in Sonia's calculation.

(1) Suppose first we understand 'x' as referring fixedly to the actual amount that is in the envelope Sonia (or Fred) is now holding. Then it is NOT automatically true for Sonia (as it is for Fred) that there is a 50-50 chance that she will double or halve THAT amount. (That depends on the probabilistic pattern governing the placing of the amounts in the two envelopes initially presented to Sonia. So, for instance, if the envelope she’s given actually contains a very large amount, towards the upper end of the range of possible amounts, then it's more likely she has 'big' and will lose by swapping--and conversely if her envelope contains an amount towards the bottom end of the range of possible sums.)

(2) What about the TRUTH that Sonia has a 50-50 chance of winning or losing? Well, that's true enough, but we can't plug those 50-50 odds into her calculation. Think of it like this. Her calculation says there are two 50-50 possibilities--she has the big envelope OR she has the small envelope. And the calculation tries to say that in the first possibility swapping will lose 0.5x and in the second swapping will gain x. But 'x' doesn't refer to the SAME number in each of these possibilities. In the first it refers to the amount in the big envelope, in the second it refers to the amount in the small envelope. No wonder this spurious calculation makes swapping seem attractive—it implicitly supposes that the sum in your envelope when you lose will be the SAME as when you win, when in truth it will be twice as big. (Note that for Fred it IS the same amount in his envelope in the two possibilities that he has 'big' and he has 'small'--that's why it is OK for him to do Sonia's calculation using the 50-50 odds.)

(There’s nothing original in the above—the literature says all this and lots more.)

David Papineau

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