The two most deceptively simple words in the English Language are the midgets: ‘Is’ and ‘Not’. Existence and Absence. [Sanskrit, from the roots: as and na.]
We shall get to the ‘Is’ later. For now, the ‘Not’.
Not; Nothing; Nonsense; Never; Neither; Neutral. They all come from the same gene. One big mischievous joint-family. [I know of no word that more annoys a trained Logician than the word ‘Not’.]
And here is how the mischief begins:
North America and South America together make up the Americas. But North America and Not-North America?
We are not quite sure what exactly is: ‘North America and Not-North America’.
‘Not quite sure?’ That’s right. Not quite sure.
And not quite sure what exactly: ‘Not quite sure’ means.
Nor the above sentence.
Nor the above. Nor the previous…
This is the Self-Negating Expression rolled-out and in full display. The ‘Backward Step’ is simply the unravelling of this sequence, an ‘Infinite Regress’, without winking or blinking, all the way back to ‘True Nothing’.
This is just one example. You can construct one that connects to you, that has you annoyed and cornered. All properly constructed and honestly unwound Self-Negating Expressions will converge at the same terminus.
Try your hand at: ‘All words are meaningless’-itself an expression in words. Or: ‘I don’t exist!’. The Symbol ‘0’ is the fecund founding father of this deranged progeny.
A ‘Point’ is a beginning unit of measure. It is the place where we decided to stop and mark the location with a name [‘Here Ye! Henceforth this shall be called a ‘Point’].
A Line is defined as a ‘Series of Points’ [what Euclid called a ‘breadth-less length’].
We are not sure what a ‘Point’ is; it is formally undefined. But a ‘Line’ is something your little girl understands. No limit of abstraction business here. And away we go with crayon and color. Crayon and color that make up ‘Self’ and ‘World’.
‘Individual’: from the Latin, In-dividuus: that which is ‘Indivisible-Further’, as in a-tomous for ‘atom’.
Any wedge of cheese that I can cut once, I can cut twice. Or thrice. In fact I can cut it as fine as I want. I just need sharper and stronger knives.
I can if I am in the mood, cut it a trillion times. Then anther trillion. And just keep going. But this can get tedious. And what I am cutting no longer tastes like cheese. So where should I stop?
[Make sure to do all this in broad daylight. And do not nick the Higgs-Boson, a.k.a. the ‘God-Particle’, else the scientists at CERN will get very upset.]
What applies for cheese, applies for carrots and broccoli. At some point they get tossed into the salad.
The Atom in Physics, the Element in Chemistry, the Axiom in Logic, the Point in Mathematics, the Word in Language, the Morpheme in Linguistics..
Do you remember where you stopped before climbing into your salad?