Being and Logic

900 words, 4 minute read

“Thank God for arithmetic!” Now there’s a sentence my 8 year old self never expected to write. But arithmetic enables global commerce and its first cousin, the calculus, powers space travel. Nevertheless, when numericity becomes a fetish, our vision of reality can be obscured.

 It’s not hard to believe in arithmetic:

X + 0 = X

X * 1 = X

X + 1 > X

X*Y = Y*X

X (Y + Z) = XY + XZ.

The fundamental concepts are identity and order. Things are what they are; they don’t become something else unless something (e.g. an operation) makes them something else. You are not Alice and this is not Wonderland! We are empiricists, not magicians.

If X > Y and Y > Z, then X > Z. For an 8 (or 80) year old such relations are crucial. They are the basis of ‘distributive justice’ and they outline an algorithm for determining fairness on the playground (or in the boardroom).

But contrary to philosophers from Pythagoras and Parmenides through Kant and Hegel to Frege and Penrose, logic is not being. The rules of arithmetic don’t always match up with real world phenomena. For example, according to arithmetic, Olympic gold medalist Achilles cannot catch up to a lazy tortoise in a road race. (Zeno)

According to arithmetic, X + (-X) = 0; this is where arithmetic fails us! X + (-X) ≠ 0. Nothing is not the inverse of something; something is and nothing is not. The father of Western philosophy, Parmenides, understood this 2500 years ago:

“You cannot know what is not…because the same thing is there for thinking and for being… (and) it must be that what is there for speaking and thinking, is…whereas nothing is not… Being and not-being have been thought both the same and not the same… (but) never shall it be that things that are not, are.” (On Nature, Fragments 2, 3, 6, 7)

English: Thinking, speaking, and being refer to a common universe of discourse. Therefore, it is impossible to think or speak (meaningfully) of what is not. Not being has been mistakenly viewed as the inverse of being; in fact, being and not being have nothing in common. What is, is, and what is not, simply is not.

Incomprehensibly, we have assumed ‘nothing’, of which we have no experience, to be substructural, while ‘something’, which constitutes all of our experience, is considered ‘emergent’, an exception, an anomaly, a special (degenerate) case of nothingness: the negation of nothing is somehow something. Magical thinking if ever! No wonder we are prone to nihilism (disillusioned magic).

Accepting ‘nothing’ as our baseline, we ask, “How/why is there is something…and not just nothing?” What a weird sentence: “How is there…nothing?” How indeed? Wouldn’t a more appropriate question be, “Since there is obviously something (Descartes), does the concept of ‘nothing’ have any meaning?”

Here, Jean-Paul Sartre comes to our rescue! He redefined ‘nothing’, not as a null state of being but rather as a process -  the process of negation. In Sartre’s syntax, ‘being’ (Etre en soi) functions as a noun while ‘nothing’ (Neant) functions as a verb (negation). ‘To be’ is a transitive, middle voice verb with Being as both its subject and its object.

Being is not just being-in-itself; thanks to ‘Neant‘ it is also being-for-itself, i.e. being concerned with itself.

Middle voice verbs (Sartre’s Etre) are inherently recursive. The subject acts on itself, often through the medium of another: “Do unto others as you would have done unto you.” Recursion is negation and negation recursion. In the course of ‘acting/being’ the subject is changed. All actions negate some aspect(s) of the subject’s base state. In its struggle to change its environment, the subject changes itself. Sounds a lot like real life, doesn’t it?

Neant is only meaningful in the context of Etre (being-in-itself). We have no independent knowledge, no direct experience of ‘nothing’ because, by definition, nothing doesn’t exist and we cannot even think or speak meaningfully of ‘what is not’. (Wittgenstein) Neant is not the meaningless inverse of Etre; it is a process embedded in Etre.

Everything we know, we know about ‘something’; every experience is something. And yet we base our cosmology on a “misplaced concreteness” (Whitehead), i.e. the misapprehension that ‘nothing’ is ‘something’. We are secular idolators - we mistake the ground for the figure – we worship a void, and yet we dare to call ourselves empiricists.

So All Hail to grade school arithmetic (logic); it’s a wonderful tool and I wouldn’t leave home without it, except perhaps to visit the Piraha tribe in the Amazon…but that’s another story for another day. In the meantime, Hail to arithmetic and logic but… if we want to thrive IRL, we’ll need something much stronger. We’ll need recursion!

We will not discover or invent a new mathematics in this space. Suffice to say, IRL numerical values are notinert; they are influenced by context, and so the order of operations does matter. In fact, as a general rule:

X + 0 ≠ X

X + (-X) ≠ 0

X * 1 ≠ X

X*Y ≠ Y*X

X (Y + Z) ≠ XY + XZ

So Being and Logic are related after all…just not in the way we imagined!