The Ground of Logic And The Empty Class

 

Logic, as the ancient Philosophers [before Aristotle] knew and warned, begins in Ontology. If your ontological assumptions aren’t transparent and verified, the Logic will sooner or later buckle.

Logician’s, like Prophets and Politicians, have long cherished the idea of a mystical, divine origin for their calling. But the rules of Logic are not on stone-tablets nor have they fallen from the sky. They are rooted in a set of rarely reviewed, implicit and unstated ontological assumptions. 

The paradigmatic, foundational syllogism: ‘All Men are Mortal; Socrates is a Man; Socrates is Mortal’, begins with the unstated assumption that there ‘is’ an identifiable, stable entity called ‘Socrates’.

The rest of the inference is inevitable.

You can’t spot a Man holding the same pose twice in a lifetime. Take a snapshot of every moment of a Man’s life: no two will be identical.

The atoms in a Man’s body are in constant motion, continuous replenishment, day and night. His skin gets replaced about once every 30 days; his bones about every 6 months. Look in a mirror. Is this the same mug you saw last night? Of course it is: note the fine forehead, the graceful neckline.

Stability, you said? Oh, you mean something inside Socrates…


Logic fondly referred to by Logicians as the ‘Laws of Thought’ [the title to an early text], deals exclusively with abstract things.

But first it needs to lay down some ground rules. And the Classes of Logic are part of the ground rules. If you want to apply the rules of Logic, you must agree to abide by the ground rules.

Logic begins with naming three classes: the Universe Class, the Unit Class and the Null [or Empty ] Class.

This roughly corresponds to what the rest of us call: ‘Everything, One, and Nothing’, or : ‘ Infinity, One, and Zero’.

So where did these Classes come from? We’ll were not too sure. They are sort of like the ‘Conservation Principles’ of Physics that are not themselves derivations from Physics but then get to arbiter what falls under ‘Physics’.

Unlike the Universe or Unit Classes, the Null Class of Logic is a very special class. All absurd expressions, words and phrases that don’t make any sense get to see the inside of the Null Class of Logic.

The Empty [‘Null’] Class of Classical Logic is the sole depository, the designated dumping-ground for all things absurd. It is the ugly-duckling, the black-sheep, the squint-eyed baby Mama tries to hide from the neighbors.

For the Logician such absurd expressions do not apply to the ‘Real World’. The abstracted, doubled, referential world where logical operators are designed to function. There really are no such things.

If you say ‘Round Squares’, it gets put in the Null Class. If you say ‘All Words are Meaningless’, it gets put in the Null Class. And if you say, ‘I don’t exist!’ it gets put in the Null Class. And a Doctor is called to the house to check your mental stability.


Aristotle [384-322 B.C.] National Museum, Athens.

The Bhagavad-Gita exhorts the man to: ‘Active-Inaction’: ‘He who sees Action in Inaction, he is a Yogin.’

In China, Lao-Tzu advised that one live a life based on Wie Wu Wei: ‘Doing Not-Doing’, the central injunction of Taoism.

[Less famously but far more recently, Jiddu Krishnamurthy advised a stance of ‘Alert Passivity’. Aldous Huxley suggested a rephrase to ‘Active Resignation’. And so on.] 

Aristotle is the pioneering formulator of precise, cogent, hugely influential models of reality [they lasted well past Copernicus].

But oddly enough, Aristotle installed a very strange fellow, an indecipherable creature in-fact, in the sanctum-sanctorum of his scrupulous, logically precise modeled world.

From Aristotle’s Metaphysics:

There is therefore also an Unmoved-Mover, being eternal, primary and in act..the first mover is a necessary Being..and is thus a first principle, for there is always a mover of things moved, and the first mover is itself unmoved.’

The ‘Unmoved-Mover‘ of Aristotelian Model is a resident in the Null Class of Classical Logic.

The irony is rich and to be savored slowly. For the great philosopher is the founding father of Classical Logic as we know it. He would have chuckled.


No, no, you are not thinking, you are just being logical famously quipped Neils Bohr, a founder of Modern Physics, How wonderful that we have [finally] met with a paradox. Now we have some [real] hope of making progress.’

This must be one of the oldest Posts in my dog-eared file box. I need to update it with some of the new non-linear loopy logic that’s making the rounds. I’ll get around to it at some point.

Also See: Shūnyathā: ‘Emptiness And Form’