Apologies if this is not the discussion you wanted, but it’s hard to engage with comparability classes without a framework for how their boundaries are even minimally plausible.
Would you say that all types of discomfort are comparable with higher quantities of themselves? Is there always a marginally worse type of discomfort for any given negative experience? So long as both of these are true (and I struggle to deny them) then transitivity seems to connect the entire spectrum of negative experience. Do you think there is a way to remove the transitivity of comparability and still have a coherent system? This, to me, would be the core requirement for making dust specks and torture incomparable.
I agree that delineating the precise boundaries of comparability classes is a uniquely challenging task. Nonetheless, it does not mean they don’t exist—to me your claim feels along the same lines as classical induction “paradoxes” involving classifying sand heaps. While it’s difficult to define exactly what a sand heap is, we can look at many objects and say with certainty whether or not they are sand heaps, and that’s what matters for living in the world and making empirical claims (or building sandcastles anyway).
I suspect it’s quite likely that experiences you may be referring to as “higher quantities of themselves” within a single person are in fact qualitatively different and no longer comparable utilities in many cases. Consider the dust specks: they are assumed to be minimally annoying and almost indetectable to the bespeckèd. However, if we even slightly upgrade them so as to cause a noticeable sting in their targeted eye, they appear to reach a whole different level. I’d rather spend my life plagued by barely noticeable specks (assuming they have no interactions) than have one slightly burn my eyeball.
Theron Pummer has written about this precise thing in his paper on Spectrum Arguments, where he touches on this argument for “transitivity=>comparability” (here notably used as an argument against transitivity rather than an argument for comparability) and its relation to ‘Sorites arguments’ such as the one about sand heaps.
Personally I think the spectrum arguments are fairly convincing for making me believe in comparability, but I think there’s a wide range of possible positions here and it’s not entirely obvious which are actually inconsistent. Pummer even seemed to think rejecting transitivity and comparability could be a plausible position and that the math could work out in nice ways still.
Surreals have multiples and are ordered, yet they contain multiple different archimedian fields. You can have for all r in reals and all s in surreals that r*s exists and that there is another surreal that is greater than all of r*s. Arbitrarily large finite is a different thing than an infinitely large value. You can’t “inch” your way to infinity. If you have a single bad experience and “inch” around it you will only reach one archimedian field but how do you know that you have covered the whole space of bad experience?
Apologies if this is not the discussion you wanted, but it’s hard to engage with comparability classes without a framework for how their boundaries are even minimally plausible.
Would you say that all types of discomfort are comparable with higher quantities of themselves? Is there always a marginally worse type of discomfort for any given negative experience? So long as both of these are true (and I struggle to deny them) then transitivity seems to connect the entire spectrum of negative experience. Do you think there is a way to remove the transitivity of comparability and still have a coherent system? This, to me, would be the core requirement for making dust specks and torture incomparable.
I agree that delineating the precise boundaries of comparability classes is a uniquely challenging task. Nonetheless, it does not mean they don’t exist—to me your claim feels along the same lines as classical induction “paradoxes” involving classifying sand heaps. While it’s difficult to define exactly what a sand heap is, we can look at many objects and say with certainty whether or not they are sand heaps, and that’s what matters for living in the world and making empirical claims (or building sandcastles anyway).
I suspect it’s quite likely that experiences you may be referring to as “higher quantities of themselves” within a single person are in fact qualitatively different and no longer comparable utilities in many cases. Consider the dust specks: they are assumed to be minimally annoying and almost indetectable to the bespeckèd. However, if we even slightly upgrade them so as to cause a noticeable sting in their targeted eye, they appear to reach a whole different level. I’d rather spend my life plagued by barely noticeable specks (assuming they have no interactions) than have one slightly burn my eyeball.
Theron Pummer has written about this precise thing in his paper on Spectrum Arguments, where he touches on this argument for “transitivity=>comparability” (here notably used as an argument against transitivity rather than an argument for comparability) and its relation to ‘Sorites arguments’ such as the one about sand heaps.
Personally I think the spectrum arguments are fairly convincing for making me believe in comparability, but I think there’s a wide range of possible positions here and it’s not entirely obvious which are actually inconsistent. Pummer even seemed to think rejecting transitivity and comparability could be a plausible position and that the math could work out in nice ways still.
Surreals have multiples and are ordered, yet they contain multiple different archimedian fields. You can have for all r in reals and all s in surreals that r*s exists and that there is another surreal that is greater than all of r*s. Arbitrarily large finite is a different thing than an infinitely large value. You can’t “inch” your way to infinity. If you have a single bad experience and “inch” around it you will only reach one archimedian field but how do you know that you have covered the whole space of bad experience?