Abstractions on Inconsistent Data

[I’m not sure this makes any sense – it is mostly bab­ble, as an at­tempt to ex­press some­thing that doesn’t want to be ex­pressed. The ideas here may them­selves be an ab­strac­tion on in­con­sis­tent data. Post­ing any­way be­cause maybe some­body else will prune it into some­thing use­ful.]

i. Abterpretations

Ab­strac­tions are (or at least are very closely re­lated to) pat­terns, com­pres­sion, and Shan­non en­tropy. We take some­thing that isn’t en­tirely ran­dom, and we use that pre­dictabil­ity (lack of ran­dom­ness) to find a smaller rep­re­sen­ta­tion which we can rea­son about, and pre­dict. Ab­strac­tions fre­quently lose in­for­ma­tion – the map does not cap­ture ev­ery de­tail of the ter­ri­tory – but are still gen­er­ally use­ful. There is a sense in which some things can­not be ab­stracted with­out loss – purely ran­dom data can­not be com­pressed by defi­ni­tion. There is an­other sense in which ev­ery­thing can be ab­stracted with­out loss, since even purely ran­dom data can be rep­re­sented as the bit-string of it­self. Pure ran­dom­ness is in this sense some­how analo­gous to prime­ness – there is only one satis­fac­tory func­tion, and it is the iden­tity.

A sep­a­rate idea, head­ing in the same di­rec­tion: Data can­not, in it­self, be in­con­sis­tent – it can only be in­con­sis­tent with (or within) a given in­ter­pre­ta­tion. Data alone is a string of bits with no in­ter­pre­ta­tion what­so­ever. The bit­string 01000001
is com­monly in­ter­preted both as the num­ber 65, and as the char­ac­ter ‘A’, but that in­ter­pre­ta­tion is not in­her­ent to the bits; I could just as eas­ily in­ter­pret it as the num­ber 190, or as any­thing else. Sense data that I in­ter­pret as “my to­tal life so far, and then an ap­ple fal­ling up­wards”, is in­con­sis­tent with the laws of grav­ity. But the ap­ple fal­ling up is not in­con­sis­tent with my to­tal life so far – it’s only in­con­sis­tent with grav­ity, as my in­ter­pre­ta­tion of that data.

There is a sense in which some data can­not be con­sis­tently in­ter­preted – purely ran­dom data can­not be con­sis­tently mapped onto any­thing use­ful. There is an­other sense in which ev­ery­thing can be con­sis­tently in­ter­preted, since even purely ran­dom data can be con­sis­tently mapped onto it­self: the ter­ri­tory is the ter­ri­tory. Prime­ness as an analogue, again.

Ab­strac­tion and in­ter­pre­ta­tion are both func­tions, map­ping data onto other data. There is a sense in which they are the same func­tion. There is an­other sense in which they are in­verses. Both senses are true.

ii. Errplanations

As­sum­ing no er­rors, then one piece of in­con­sis­tent data is enough to in­val­i­date an en­tire in­ter­pre­ta­tion. In prac­tice, er­rors abound. We don’t throw out all of physics ev­ery time a grad stu­dent does too much LSD.

Some­times lo­cat­ing the er­ror is easy. The ap­ple fal­ling up is a hal­lu­ci­na­tion, be­cause you did LSD.

Some­times lo­cat­ing the er­ror is harder. I feel re­pul­sion at the naive util­i­tar­ian idea of kil­ling one healthy pa­tient to save five. Is that an er­ror in my feel­ings, and I should bite the bul­let? Is that a true in­con­sis­tency, and I should throw out util­i­tar­i­anism? Or is that an er­ror in the fram­ing of the ques­tion, and No True Utili­tar­ian en­dorses that ac­tion?

Lo­cat­ing the er­ror is mean­ingless with­out ex­plain­ing the er­ror. You hal­lu­ci­nated the ap­ple be­cause LSD does things to your brain. Your model of the world now in­cludes the er­ror. The er­ror is pre­dictable.

Lo­cat­ing the er­ror with­out ex­plain­ing it is at­tribut­ing the er­ror to phlo­gis­ton, or epicy­cles. There may be an er­ror in my feel­ings about the trans­plant case, but it is not yet pre­dictable. I can­not dis­t­in­guish be­tween a miss­ing er­rpla­na­tion and a true in­con­sis­tency.

iii. Intuitions

If eth­i­cal frame­works are abter­pre­ta­tions of our moral in­tu­itions, then there is a sense in which no eth­i­cal frame­work can be gen­er­ally true – our moral in­tu­itions do not always satisfy the ax­ioms of prefer­ence, and can­not be con­sis­tently in­ter­preted.

There is an­other sense in which there is a gen­er­ally true eth­i­cal frame­work for any pos­si­ble set of moral in­tu­itions: there is always one satis­fac­tory func­tion, and it is the iden­tity.

Prime­ness as an analogue.

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