WORTH REPEATING : ARBITRARY PRECISION AND INFORMATION LOSS In mathematics, (intu

WORTH REPEATING : ARBITRARY PRECISION AND INFORMATION LOSS

In mathematics, (intuitionist mathematics), the requirement that we demonstrate all operations eliminates the possibility of the excluded middle – which is an unnecessary constraint upon mathematics. (This constraint is equivalent somewhat to computability in computer science.)

However, in order to create mathematical statements in the form of general rules independent of scale, we divorce the statements from scale, maintaining only the relations themselves (ratios).

By doing so – loss of context – we lose the information necessary to determine contextual precision. In other words, we no longer know that 1/64 of an inch is the maximum precision necessary for the given calculation. But in any application of the general statement to a given context we then regain the information necessary to make decisions.

As such general mathematical statements are constructed with arbitrary precision that requires choice independent of context, or contextual application to supply the missing information.

This problem of creating general statements independent of context is why it was necessary to transition number theory from geometry (infinite precision) to sets (binary precision). Thus reducing all mathematics to truth tables. And binary precision (set membership) is the reason why binary mathematics is so crucial to computation: we are always in a true or false state: a truth table that is universally decidable regardless of contextual precision.

These discussions evolved in math as a war against mathematical platonism. And by applying the same principle to ethics the problem changes significantly since we never encounter the problem of arbitrary precision.

In ethics, we do not have the luxury that physics does, in that information cannot be lost and all relations are constant. We are stuck with bounded but relatively inconstant relations.

But we always can test the rationality of any economic statement that is reduced to a sequence of actions. ***And so we never encounter the problem of arbitrary scale and the insufficiency of information.***

So when I speak of empiricism ( observation), operationalism (actions in time), and instrumentalism (reducing the imperceptible to the perceptible) it is in the context of ethics not mathematics and as such is not subject to the failure if operationalism and intuitionism to satisfy the needs of mathematicians.

This is a revolutionary idea.