Sunday 21 February 2010

Subjectivity

I hate racism, sexism, ageism and basically all forms of discrimination. This is not because I'm a morally reputable, virtuous person; I'm not. It's because these discriminations fly in the face of science, logic and that which is correct.

I care a lot about the right answer - be that to a scientific problem, an artistic ideal (the resolution to a suspended chord; the phrasing of a sentence) or even a societal interaction. There is always such an answer.

Here's why.

Proposition 1 - All is Matter
Every single thing in existence is made up of quanta. I refer not only to physical objects, but also to abstract notions and concepts. The word 'concept', for example, physically exists in a multitude of places: my brain; yours; paper and digital publications - to name a few.

Proposition 2 - Reality is Stateful
Every single thing in existence has a state space. Quantum Field Theory (and specifically, Quantum Mechanics) tells us that the eigenstate of an observable is fixed only at the moment of observation. However, a correct answer requires full knowledge of all variables. This paradox may be resolved once one considers that as the decision involves processing these variables, they must first be observed in order to be utilised, and therefore have a fixed state at the point of decision.

Lemma I - Objectivity Exists
Objective: adj; Of or relating to a material object, actual existence or reality; Not influenced by the emotions or prejudices; Based on observed facts.

Given that all is matter (proposition 1) and that all matter has a defined eigenstate at the point of observation (proposition 2), any problem may have an objectively correct solution, given a means of reaching such a solution and full knowledge of all variables at the point of decision.

Proposition 3 - Context is Everything
All problems exist only within the scope of their context. The most basic, seemingly clear problem - "What is 2+2?" only exists within the implied context "according to classical mathematics and assuming no unstated interference". Likewise, "can I trust this man?" is a question only valid in further implied context - the answer may be "yes" for medical advice and "no" for mechanical.

Conclusion
All problems have a correct answer. Given that problems exist only in their context (proposition 3) and that this context is entirely made up of observable matter (lemma I), all that is lacking is a means to process these observed states. Formal Logic provides a true conclusion given true propositions (et al.).

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The above, whilst interesting, is of little utility in the majority of scenarios. If nothing else, the Uncertainty Principle states it is physically impossible to measure all required variables in a problem in unity.

This brings us to the area of subjective logic, for which I can only recommend the Wikipedia article (written nearly entirely by Jøsang, who defined the field).

Subjective logic offers a means for obtaining the correct answer to a problem with uncertain or unknown inputs. It also allows for the representation of belief - however, if a problem is fully defined within its context this is already taken into consideration, so this aspect of subjective logic is of little interest to this thesis (though obviously may be used in formally defining a context).

The answer to a problem with uncertain inputs is no longer a scalar, but a probability distribution. This distribution may be arbitrarily skewed, and of any dimensionality. The maximum value of the distribution, or the entire distribution itself, may then be used in taking a decision (cf. decision theory) but a correct answer has been ascertained.

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We may now answer any question - from "what is 2x2?" to "is this art?" or "what brushstroke/chord/word should I use next?" correctly. Subjectivity does not imply an answer may not be found, just as objectivity does not imply that there is only one correct answer to any given problem. The objective reality of the full context of the problem both defines, and answers that problem.

I'm still not going to iron my own shirts though.

Xx

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Finally, of potential interest, a lovely (if not quite so scientific) rant on subjectivity in art criticism.

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