# Which of these 4 conditional statements are the ones using "at least" and "unless"?

The original Reddit question did not number the conditional statements.

Which of the 4 statements did the author intend by "at least"? Is sentence 2 the referent of "unless"?

If you rewrite the sentences it becomes clearer what is actually going on here.

1. The game will start, if there are 10+ participants.

2. The game will not start, unless there are 10+ participants.

When someone says "unless there are 10 participants" it means "if there aren't 10+ participants":

1. IF ≥ 10 participants THEN game start

2. IF NOT ≥ 10 participants THEN NOT game start

The statements in which "at least" and "unless" are used [bold mine] are contrapositive, thus logically equivalent. But by extension, this means that "at least" (≥) and "unless" (NOT ≥) have opposite meanings, despite having similar etymological origins. But when you go look at the etymology it makes sense:

onlesse, from (not) on lesse (than)

• See your previous post : how to intuit "unless". Mar 29, 2018 at 9:41
• The "at least" is embedded into 10+: "are 1+ partecipants" means "at least 10 partecipants" (i.e. greater-or-equal to 10). Mar 29, 2018 at 10:57

1) "The game will start, if there are 10+ participants"

is: "q, if p".

2) "The game will not start, unless there are 10+ participants"

is "not-q, unless p".

We have that "q, if p", is :

"if p, then q",

while "not-q, unless p" is :

"if not-p, then not-q".

They are not in contraposition each other (and they are not logically equivalent).

Regarding the title of the question, only statement 2) contains "unless" and both 1) and 2) contain "at least".

We may re-phrase them as follows:

1) "The game will start, if partecipants are at least 10"

and :

2) "The game will not start, unless the partecipants are at least 10".

When someone says "unless" in a conditional statement that is usually translated as "it is not the case" And That Language Goes In The Antecedant section before the THEN . So if I say " I will not attend your party unless there are two party clowns (with big red noses and all)." This means if it is not the case two party clowns are present I will not attend your party.

When I say "I will attend your party if there are two party clowns" expresses that on the condition party clowns will be there I will attend. NOW if condition one does not hold I will feel you deceived me. That is i attend your party and no clowns ever show up. Thus the phrase might be ambiguous and really expresses a biconditional. I now expect two things instead of only one. That i will See clowns if I go to the party and if I do decide to to the party there better be clowns present. The clowns are neccessary.

The way you wrote your propositions are not in the contrapositive relationship. The way you wrote the propositions express the INVERSE relationship. Q IF P is translated as if P, then Q. The proposition with UNLESS is translated as If ~P, then ~ Q. The tilde (~) expresses NOT.

The original Reddit question that this quoted post attempted to answer was How did 'less than' shift semantically to mean 'not'?

The user Ivxferre posted the original examples showing a transition from the use of "at least" to "unless". I placed them in italics and highlighted the words in question although that is not how the original was formatted:

A possible key might be on expressions like "at least". See the following example:

The game will start when there are at least 10 participants.

This can be rephrased as

The game will not start unless (on less) there are 10 participants.

So there's a rough equivalency between "when at least" and "not on less". The negative meaning would then come from this "not".

Note that the first sentence uses "at least" and the second uses "unless".

Reddit user alpharabbit paraphrased these two sentences first in this manner as posted by the OP:

If you rewrite the sentences it becomes clearer what is actually going on here.

The game will start, if there are 10+ participants.

The game will not start, unless there are 10+ participants.

Note that one loses the "at least" in the first sentence although "unless" is still present in this paraphrasing.

Then the same user offered another paraphrase quoted by the OP:

When someone says "unless there are 10 participants" it means "if there aren't 10+ participants":

IF >= 10 participants THEN game start

IF NOT >=10 participants THEN NOT game start

Note that in these two sentences both the "at least" and the "unless" have disappeared although one can assume that the paraphase intended the first sentence to associate with Ivxferre's first sentence which used "at least" and the second sentence to associate with Ivxferre's second sentence.

Now let's consider the question:

Which of the 4 statements did the author intend by "at least"? Is sentence 2 the referent of "unless"?

Based on the previous discussion the author intended "at least" to associate with the 1st and 3rd sentences, that is, the first of each pair of sentences the author considered. The 2nd and 4th sentences, that is, the second of each pair of sentences, was intended to refer to the original sentence using "unless".

Reference

Reddit Question, "How did 'less than' shift semantically to mean 'not'?" https://www.reddit.com/r/linguistics/comments/5f2jsg/how_did_less_than_shift_semantically_to_mean_not/?sort=new