@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.
@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.