Life Is Non-Boolean

George Boole (1815-1864) invented what we now call Boolean logic, which effectively assumes that all propositions are classifiable as either “true” or “false”, with no gradations of evidence or undecided cases. This provided the basis for formally defining logical operators in terms of how they transform what are called truth values, which are just the Boolean values of “true” and “false”. The use of so-called truth tables to define logical operators by cases is characteristic of what is today called “classical” logic.

Though it certainly has its uses in technical contexts, this kind of approach has been criticized as tacitly presupposing what has been called logical omniscience or the assumption of a closed world. For example, in computer science Boolean data types are used to represent things that are stipulated to have one of exactly two values. Then if we can rule out one, we can simply assume the other. This creates a closed world. “Omniscience” is implied by this kind of assumption.

The great developer of mathematical logic Gottlob Frege (1848-1925), at least at one point in his career, went so far as to argue that there are really only two distinct logical propositions: “true” and “false”. Depending one’s point of view, what I call real-world meanings are either reduced to nothing by this or are irrelevant to it.

From the point of view of “constructive” logic, on the other hand, there are infinitely many distinct propositions, distinguishable by the combination of what they presuppose and what they imply. It begins to be possible to reconstruct real-world meanings within logic instead of only outside of it.

In real life there are countless distinctions that are relevant and meaningful, and countless things that we simply don’t know. (See also Logic for People.)

Echoes of the Deed

“The kinds of doings [Hegel] is principally interested in are processes rather than events: writing a book, building a house, learning a trade, diagnosing or treating a disease” (A Spirit of Trust, p. 733). Not only that, such doings implicitly include future consequences that are not yet determined. Because of this, their evaluation and place in a normative synthesis may change over time. (The “echo” metaphor of this post’s title should not be taken too literally. I mean something related but relatively independent that happens later, may not have been expected, and possibly could not have been expected.)

Unlike mathematical provability or statically definable structures, what not only looks but (as a result of an enormous process of mutual recognition) genuinely is normatively correct or incorrect or good or bad as of one moment is not guaranteed to remain so as further consequences play out. In this sense, as long as there is a future, no deed and no story will ever be complete, or even necessarily have a predictable ending.

The future may move us to reinterpret the past, and this is as it should be. It gives cause for hope that situations beyond our control can always be better, and that we can play a role in making them so — that how we respond to them matters.