# How does 'if not' mean 'perhaps even'?

if not = Perhaps even (used to introduce a more extreme term than one first mentioned)

How does (the juxtaposition of) if + not combine to mean the above,
which neither word alone means?

This is where logic or mathematics operates differently from human language (aka natural language). Strictly speaking and mathematically speaking,

1. "N is Y, if not Z" would be read as
2. "if N is not Z, then N is Y".

However, in many human languages, English included, saying 1 doesn't mean just 2. To understand this, we should think a little about the motive of a speaker who said 1.
Quite likely, the speaker's intention was

3. "If N is not so great as Z (or any quantity > Y), it is = Y".

But to say 3 exactly in those words would be clumsy,
and thus the speaker would naturally rephrase 3 as:

4. "N = Y if N ≠ Z",
or in plain English: 5. "N is Y, if not Z".

We can try another approach to show that if not can be used to mean perhaps even.

Let N is the number of people who has an attribute Q.
Consider these two following propositions:

(a) N is Y, if not Z.
(b) N is Y, perhaps even Z.

Let Na is the set of all possible values of N for proposition (a).
It is easy to see that Na = {Y, Y+1, Y+2, Y+3, ..., Z}.

Let Nb is the set of all possible values of N for proposition (b).
It is also easy to see that Nb = {Y, Y+1, Y+2, Y+3, ..., Z}.

Now, it is clear that Na and Nb are equal. Hence, (a) and (b) are equivalent.
Thus, if not can be used to mean perhaps even.
Q.E.D.

• Where you say "it is easy to see that", it seems like you're glossing over the original question that was asked. Commented Nov 2, 2014 at 22:05
• @DanGetz But let's not forget the fact that the OP knows the meaning of "if", "not", "perhaps", and "even". Commented Nov 3, 2014 at 2:06
• ...and is asking how "if not" gets its meaning. You take as given the fact that it means the same as "perhaps even", and show that the logical conclusion of that is...it means the same as "perhaps even". Commented Nov 3, 2014 at 11:38
• I think your notes at the end are what answer the question, shouldn't be presented as optional, and should come before your analysis of the logic. Commented Nov 3, 2014 at 11:39
• @DanGetz Actually, I'm quite glad that, finally, someone spotted the fallacy I inserted into my proof. As I mentioned in our chat room, "I answered the question because I want to make a point that usage in language is not always logical." So I inserted something that makes "[my answer look] right, but it's not, but to say it's not right, it could result in a weird conclusion, which is dictionaries are wrong." Thanks for the noticing! Commented Nov 3, 2014 at 11:53

Consider: X if not Y.

if not is used when you want to say that Y is false,
NOT because Y overstates the extremity of the situation, but because Y understates it.
if not is usually used with numerical values.

There are millions, if not billions, of bacteria on every inch of our skin.

This means: There are millions of bacteria on every inch of our skin,
and if there are not, then there are billions (rather than thousands.)

If not effectively shortens the phrase if there are not, then there are.

I hope that's what you were looking for.

• If not shortens if there are not.
– user6951
Commented Nov 2, 2014 at 1:50
• +!. Thanks. I edited your post minorly and apologise for any offense. Please feel free to refine or revert.
– user8712
Commented Apr 20, 2015 at 19:14

I gather you're talking about phrases like JasonPatterson's example: "There are millions, if not billions, of ..." It doesn't have to be numerical. "John is a smart guy, if not a genius." Etc.

The meaning would be plain if we reversed the order of the clauses and added some qualifiers: "If there are not billions, there are certainly millions ..." "If John is not a genius, he is at least a very smart guy."

That is, it's probably the "big" thing, but if it isn't, it must at least be the "little" thing.

But sometimes we want to give the little thing first, so that we build up to the big thing. I don't want to start out by saying that it's probably the big thing, and then have a let-down where I say, well, okay, maybe it's the little thing. So we turn the word order around and put the little thing first, then say, "if not ...", and then the big thing.

It's just a matter of re-arranging the words to achieve the desired effect. You don't want to give the punch line before you've told the joke.

• I don't think the issue is one of giving away the punchline, so much as it is a means of indicating level of certainty about the size of the numbers. Saying "There are thousands" indicates that the speaker believes that the number is at least 2,000 but tends to suggest the speaker believes that the number is probably less than 30,000 [or else the speaker would have said "tens of thousands". Saying "There are thousands, if not millions" means the speaker knows there are at least 2,000 but may have no idea how much bigger the number might be. Commented May 22, 2015 at 16:40
• If one thought it likely that there were more than 2,000,000 of something, but the number might only be 1,937,183, a good phraseology would be "There are millions, or close to it". If there are probably more than 2,000,000 but there might only be 4,271, then "There are probably millions, but possibly only thousands" would be appropriate. What would be strange would be "There might be millions, but I know there are at least thousands". If one has no particular reason to believe there are millions, one shouldn't lead off with that quantity. Commented May 22, 2015 at 16:43
• @supercat It seems quite plausible to me for someone to say, "I am absolutely certain that there are at least several thousand, and I suspect, but cannot prove, that there are tens of thousands."
– Jay
Commented May 22, 2015 at 20:28
• I see no problem with that, though "There are several thousand, if not tens of thousands" would be more concise. My point is that one would start off with the more certain statement unless one had specific reason to use the other value [e.g. "Can you supply two million? I'm not sure we could do two million, if not we could certainly supply at least 1.8 million." Commented May 22, 2015 at 20:35
• And all I'm saying is that if you want to make a point that something is at least X but is probably mega-X, you may want to structure the sentence to put the lesser thing first, so that you are building up from the little thing to the big thing, rather than working down from the big thing to the little thing. "You're going to die! Well, or at least get very sick" ends on a less dramatic note, while "You're going to get very sick, maybe even die!" builds up to the most dramatic note. In many cases the second would be more effective. The first sounds like you're making a bold claim and then ...
– Jay
Commented May 22, 2015 at 20:39