Category: Epistemology and Method

“Q: WHY DO YOU DEFINE ALL TERMS IN A SERIES?”
(ordinal mathematics)

Do you remember in geometry class, the teacher explained how three points test a line? And the more points you test that appear on that line the more valid the formula for the line?

A line constitutes a dimension of measurement. Points on that line are definitions that are consistent with that dimension. In other words, we are certain that those points, all of which are on a line, share the same properties: the same properties of that dimension.

So, that’s why we use ‘disambiguation by enumeration (listing), serialization (putting them on a line in an order), and operationalization (describing them as actions, and actions as common properties), where those common properties define the dimension(s) we’re measuring.

So, in our canonical example:
|Moral|: Evil – Immoral – Unethical – Amoral – Ethical – Moral – Virtuous.
Given moral value refers to deviation from reciprocity.
Therefore we define the dimension of morality using four properties: Limits(Evil-to-Virtuous), Directness-Indirectness, Severity, and Intention(evil requires intent)

So instead of ‘cardinal mathematics’ (numbers) we call this ‘ordinal mathematics’. Meaning that we can use triangulation of terms to determine the order, producing an unambiguous series of measurements, and the properties we are measuring, so that we prevent ourselves and other from ignorance, error, bias, and deceit by denial, evasion, inflation and conflation.

So just as you decide 4 of something is greater than 3 and less than 5 of it, you decide by this same ‘triangulation’ (Sesame street game) that morality is more indirect(anonymous) than ethics, but less so than virtue.

So, while numbers are names of positions, and our terms are names of positions, in this sense, our terms like numbers, represent only an order in a measurement. Unlike numbers they do not necessarily require the same scale between them. And again unlike numbers, or more correctly, unlike numbers on the same scale, they are not commensurable any more than time (minutes) and space (miles) are commensurable: the second or third position on a given ordinal sequence does not reflect the second or third position on a different ordinal sequence. This is because we are measuring different *dimensions* and dimensions represent one or more causes.

I hope this helps
Curt Doolittle
The Natural Law Institute