How to motivate ‘unless’ = ‘if not’, with etymology?

[scherz0]

My students still reckon Lande’s 2 motivations for ‘unless’ = ‘if not’ (below) too abstract, formalistic! Thus I need a 3rd simpler, motivation with merely etymology. But I never studied linguistics! How do I

1. use these etymology quotations, to motivate ‘unless’ = ‘if not’?

2. teach why “less than” means 'if not'?

We turn now to unless. The construction developed toward the end of the Middle English period, in the early fifteenth century. At this stage it is a comparative, lesse than, or in/on/of lesse than.

Traugott E.C. (1987) “UNLESS and BUT conditionals: a historical perspective.” In A. Athanasiadou and R. Dirven (eds.), On Conditionals Again. Amsterdam/Philadelphia: John Benjamins, page 145.

By late ME the construction must have become opaque, because we begin to find the forms unless/onless without than. This is presumably in part a folk etymology relating the connective to a negative derivative un- (it can be assumed that the negative inference from the protasis has been lexicalized into, that is, has taken on a morphological form of, the prefix of the conjunction).

Idem, page 156.

As we have seen, unless derives from less than, and un- has no historical origin in a negative.

Id. 157. See also Etymonline.

mid-15c., earlier onlesse, from (not) on lesse (than) "(not) on a less compelling condition (than);" see less.

The first syllable originally was on, but the quality of negation in the word and the lack of stress changed it to un-.

Lande N.P. Classical logic and its rabbit-holes: A first course (2013), pages 55-7.

In most statements, the word “unless” means if not.

Baronett S. Logic (5th edn 2022), 236

“Unless” is also equivalent to “if not”; so we also could use “(∼B ⊃ D)” (“If you don’t breathe, then you’ll die”).

Gensler H. Introduction to Logic (3 edn 2017), 132.

The word “unless” means “if not”.

[Mentor Note: Obnoxious fonts and colors removed from this post]

 

[Dale]

Why would you waste any time in class with motivating that with etymology? Just tell them “unless” is defined as “if not” in the context of proofs. Then move on.

You have limited time and lots of important concepts to cover. Not all definitions make sense, even with the etymology. In the end, the definition stands on its own, whether it is well motivated or not.

 

[PeroK]

Compare $x < 0$ unless $x \ge 0$, with $x <0$ if $x$ not $\ge 0$.

 

[scherz0]

Why would you waste any time in class with motivating that with etymology?

Why didn't you peruse https://matheducators.stackexchange.com/q/26405 linked in my post, on why etymology assists learning vocabulary ?

 

[Dale]

Why didn't you peruse https://matheducators.stackexchange.com/q/26405 linked in my post, on why etymology assists learning vocabulary ?

Did you peruse it? The only answer, with several upvotes, said “I think etymology is not useful in the way proposed by the OP”. And the OP cited no studies supporting the usefulness of etymology in learning or teaching.

I might provide one very brief dissection of an important word. Not two, and certainly not three.

In my opinion you are wasting precious class time, and you should move on.

 

[PeroK]

Why didn't you peruse https://matheducators.stackexchange.com/q/26405 linked in my post, on why etymology assists learning vocabulary ?

In my experience, as far as mathematics and physics is concerned, it's quite the contrary. Many students suffer from preconceived ideas about concepts because of the words that have been adopted. In fact, we have a lot of threads on here where the battle is to get the layperson or student to accept that just because a word means something in everyday life, this does not affect its meaning as defined within physics.

 

[pbuk]

This post must be in the wrong forum - etymology is nothing to do with mathematics, in mathematics we use definitions. What a word may have meant to anyone before we defined it is at best irrelevant and at worst the source of misunderstanding and confusion.

“When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
Lewis Carrol: Through the Looking Glass

 

[Agent Smith]

Perhaps we could say ...

"John, Jack won't come with you unless you give him $100

We can see here that if not ($100 to Jack) then (John is coming alone). Any amount < $100 implies John is coming alone.