What underlying semantic notions connect 'less' to 'not'? [closed]

Question

What underlying notions explain this same semantic shift from 'less' to 'not' (ie: negation)? It appears in all 4 languages below, as evidenced by the Spanish and Portuguese synonymy.

I know that in English, 'less than' can euphemise 'not'. E.g, from Hamlet, Act 1, Scene 2, Page 3, Scene 5, Line 65:, in uttering (as an aside) that Claudius is 'less than kind', Hamlet really means Claudius is NOT 'generous' (and that Hamlet is not really Claudius's child, because Shakespeare was punning bilingually with English and German). But are there any other explanations?

The etymology for 'unless' reveals the etymon of 'un' as 'on', which then suggests 'un ← on' to mean the same as à and a.

unless (conj.)
mid-15c., earlier onlesse, from (not) on lesse (than) "(not) on a less compelling condition (than);" see less. The first syllable originally on, but the negative connotation and the lack of stress changed it to un-. "

à moins que = sauf si.

a menos que, a synonym of which is respectively:
a no ser que (in Spanish)   and   a não ser que (in Portuguese).

Answer 1

Semantically, unless is usually parsed as If Not, introducing a negated conditional clause; i.e, unless he forgets means if he doesn't forget. Logically, it's the ¬P of a proposition ¬P ⊃ Q.

Lexically, less is the diminutive (negative) comparative, contrasting with the augmentative more. (Note that the diminutive less has no alternative suffix like more/-er ; it's completely periphrastic)

Morphologically, -less is an idiomatic privative (and therefore negative) suffix denoting absence:

• formless, gormless, shiftless, childless, reckless, timeless,
  worthless, valueless, priceless

With all the negativity around, it's not surprising that a prepositional prefix gets interpreted as a negative prefix. Negation always has a focus and therefore has a field, like a magnetic pole. Anything in an utterance falling inside that negative field (called a negative's 'scope' in the trade) can pick up secondary negation, or "negation by association". Like pas in French ne ... pas, which is now a negative all by itself,
although it originally meant 'step'.