@Eisegates
Yes, I was operating on the implicit convention, that true statements must be meaningfull, so I could also say there is no k, so that I have exactly k quobbelwocks.
The nonexistence of a -operator (and of a +-operator) is actually the point. I don’t think preferences of different persons can be meaningfully combined, and that includes, that {possible world-states} or {possible actions} don’t, in your formulation, contain the sort of objects to which our everyday understanding of multiplication normally applies. Now if you insist on an intuitively defined -operator every bounded utility function is an example. For example my utility for the amount c of chocolate available for consumption in some given timeframe could well be approximately 1- exp(1-(min(c/1kg,1)), so 100g<1kg but there is no k to make k*100g>1kg. That is, of course, nothing new even in this discussion. Also more directly to the point, me doing evil is something I should avoid more then other people doing evil. So when I do the choosing “I kill 1 innocent person” < “someone else kills 1 innocent person”, but there is no k so that “I kill 1 innocent person”> “someone else kills k innocent persons”. In fact, if a kidnapper plausibly threatened to kill his k hostages unless I kill a random passerby almost nobody would think me justified in doing so for an imaginable value of k. That people may think different for unimaginably large values of k is a much more plausible candidate for failure to be rational whit large numbers then not adding speckles up to torture.
But basically I wasn’t making a claim, just trying to give an understandable (or so I thought) formulation for denying Thombs’ non-technically stated claim that existence of an order implies the Archimedian axiom.
@Bob
If it’s true, and you seem to agree, that our intuition focuses on actions over outcomes, don’t you think that’s a problem? Perhaps you’re not convinced that our intuition reflects a bias? That we’d make better decisions if we shifted a little bit of our attention to outcomes?
You nailed it. Not only am I not convinced, that our intuition on this point reflects a bias, I’m actually convinced, that it doesn’t. Utility is irrelevant, rights are relevant. And while I may sacrifice a lesser right for a greater right I can’t sacrifice a person for another person. So in the torture example I may not flip the (50a,1 person/49a, 2 persons)switch either way.
@Doug S.
I disagree. An objective U doesn’t exist and individual Us can’t be meaningfully aggregated. Moreover, if the individual Us are meant to be von-Neumann-Morgenstern-functions they don’t exist either.
Can they use quill and parchent?
If so, the usual public key algorithms could be encoded into something like a tax form, i.e. something like ”...51. Subtract the number on line 50 from the number on line 49 and write the result in here:__ …500. The warden should also have calculated the number on line 499. Burn this parchent.”
Of course there would have to be lots of error checks. (“If line 60 doesn’t match line 50 you screwed up. If so, redo everything from line 50 on.”)
To make it practical, each warden/non-prisoner-pair would do a Diffie-Hellman exchange only once. That part would take a day or two. After establishing a shared secret the daily authentication would be done by a hash, which probably could be done in half an hour or less.
Of course most people would have no clue why those forms work, they would just blindly follow the instructions, which for each line would be doable with primary school math.
The wardens would probably spend large parts of their shifts precalculating hashes for prisoners still asleep, so that several prisoners could do their get-out work at the same time. Or maybe they would do the crypto only once a month or so and normally just tell the non-prisoners their passwords for the next day every time they come in.