Abstractions on Inconsistent Data

by eapache2 min read29th Jun 2020No comments

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[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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