Abuse of Notation - writings on math, logic, philosophy and art - The case against boolean logic

Aβu∑e

∅f

ℕotλtion

--><br>writings on math, logic, philosophy and art

The case against boolean logic

In my last post about generality, I tried to show how our ambition to discover ideas that are all-encompassing and eternal makes our worldview crumble, leaving us unable to think clearly even about simple issues with obvious solutions. Today, I want to discuss another instance of the same problem, in a simpler and more direct way. You can think of this essay as a prequel to “When Universality Breaks.”

What is boolean thinking

Every time someone asks you a yes/no question, you are being coerced into accepting a pattern of thought that we’ll call boolean thinking. The word “boolean” here is used in the sense of the Boolean logic, and the Boolean datatype in logic and programming — a type that admits only two values: true and false. By “boolean thinking,” I am referring to the precondition that every statement should necessarily be categorized as either true or false. This is a law in Boolean logic, known as the “law of excluded middle”).

“But every statement is either true or false,” some might object. This principle might not be entirely false, but it is also not entirely true (ba-dum-tss).

Context is key. By “context”, I mean the set of premises/postulates/axioms, which we presume in order to think. Depending on the context, a statement can be:

Unknown or unknowable (if the context is incomplete)

Senseless (if the question is meaningless)

Both true and false (if the context varies)

You are probably aware of such situations, but you might still not see them as contradicting the Boolean doctrine (boolean thinking, as we shall see, is precisely that—a doctrine). It’s a mode of thought that, although not universally valid, is often useful. For instance, you can’t make plans with someone who says there’s a 40% chance they’ll go out tonight, or that the question doesn’t make sense. Thus, you might be tempted to treat all imperfections of the Boolean model as imperfections of the world — or of thinking agents themselves:

No statement is unknowable — somewhere out there, there must be an answer.

No statement is senseless — given enough effort, every statement can be interpreted.

A statement is both true and false only because we lack sufficient information.

People who think this way, I would say, suffer from a serious case of Boolean thinking. Fortunately, the condition is curable, provided that we understand its cause. As I mentioned, Boolean thinking always has to do with context. Generally speaking:

Each statement can be true in one context and false in another.

Every statement is senseless when presented without context.

Every statement is unknown when the context is incomplete.

The case against boolean logic

We’ve established that the truth or falsity of a statement depends on its context — that is, on the assumptions we take as true or false in order to justify it. Boolean thinking, boolean logic is applicable only if we agree on some universal context — a universal set of true statements on which every evaluation can rest.

Note that aside from being universal (valid for all statements) the context for boolean logic has to also be all-encompassing (relevant for every statement) i.e. the set of logical statements that form it should never, under no interpretation tell something invalid, and at the same time would let us deduce all that is valid. As I argue later, such context resembles what political philosophers call an authoritarian doctrine (although the phrase “authoritarian doctrines” is somewhat deceiving, because it isn’t the doctrines themselves that are authoritarian, but the role they play in people’s thinking patterns).

So, while boolean logic may be splendid when viewed by itself, when viewed in relation to the “real world” there is a huge issue with it, the namely that no logical context, no logical framework is strong enough to capture the things that we usually want to dissect, (the real world, if you must). Proving the claim above is a subject of a different text, for now it suffices to say that although it may not look logical or scientific, it is, however, very backed up by both logic and science. Rather than asking why this is the case, it is more appropriate to ask what makes us think the reverse, what makes us think that the real world may be captured by a boolean logical framework — I’d argue that the thought that it can be is an instance of the so called “is-ought fallacy” — the idea that something is true just because it will be good for us that it is true. But that’s a separate topic as well (see “When Universality Breaks”.

Now, we are ready to make the case against boolean logic:

Because boolean logic overlooks the importance of context (that each proposition can be true in one context, false in another, and also neither true nor false) it inspires dichotomous...