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Old 04-13-2007, 05:56 PM   #1
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Revisiting Moral Objectivism with Mathematical Notation

Once upon a time I said
Originally Posted by tk102
With no objective way to measure morality, the argument of what is the most moral course of action is word-play for politicians. You cannot pretend that it is anything like a mathematical equation. It does not hold the same "truth".
Well that statement has bothered me for a couple months and I wanted to explore further the idea of moral objectivity with the help of mathematical notation. I hope others can provide insights into these definitions. I admit having to consult Wiki's Naive Set Theory to remember how to syntax set notation.

* * * *

If x is an action in the set of all possible actions that you can perform, A:
x ∈ A

And m(x) is the morality of action x, then set of all possible moral outcomes, M, is:
M := { m(x) : x ∈ A}

And the moral person seeks to perform the most moral act:
Mmax = max { m(x) : x ∈ A}

So how do we measure the morality of an action? It is inversely proporational to the amount of distress, D, the particular act, x, causes.
m(x) ∝ 1/D(x)

For the sake of clarity, let's define our D function such that we can write this as an equality.
m(x) = 1/D(x)

So our goal to maximize morality could be rephrased to say we seek to minimize distress.
Mmax = Dmin = min{ D(x) : x ∈ A}

So how do we measure D(x)? It should be the summation of all distress felt by all organisms for the given action. To arrive at that formula we must define its elements.

Given an organism capable of feeling distress, y, in the population of all organisms capable of feeling distress, P:
y ∈ P

Then relative distresses, δ, for all organisms for all actions is the set:
δ := { δxy : (x ∈ A) and (y ∈ P) }

But how do we compare distresses of one organism to another? We don't weigh distresses of one organism the same as the distresses of another organism. Most would consider it morally right to kill a mosquito that landed on a friend's neck, for example. In order to define D(x), we will need to translate these relative distresses into an absolute scale that can be summed. Let us propose a conversion factor K where:

For a given action x, in a given organism y, Ky is the proportion of universal distress, Dx, to relative distress, δxy
Ky = Dxxy

A mosquito's relative distress at being smashed would be much greater than the discomfort a mosquito bite would cause in a person, but because Kperson>>Kmosquito, Ddon't smash > Dsmash.

We can now define D(x) as:
D(x) := ∑ δxyKy : (y ∈ P)

(Pardon the notation -- I'm limited by bbcode... read the above as a summation of δ*K for each member of y in P for a given action, x.)

And the most moral act is therefore
Mmax = Dmin = min { D(x) : x ∈ A} = min { (∑ δxyKy : (y ∈ P) ) : x ∈ A }

* * * *

Okay, so what do we see here? Mmax is a function of δxy and Ky. It remains up to us to use our faculties to best interpret δxy and Ky as well as recognizing the full sets of A and P. Let's assume A and P are well-defined. δxy could estimated using faculties of reason, heuristics, and the understanding of organism y. Ky is more difficult to define in an objective manner. Does the size organism matter? Do its mental faculties matter? Or maybe its own ability and desire to act morally? Have I oversimplified something?
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