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The English connective "unless" is commonly considered a conditional or a disjunction (which are really the same thing with some slight re-arrangements and "not"s). Here is an example. Quoting that website:

Given statement: Unless you bribe the minister(#1), you will not get the 2G license.(#2)
Unless = if…..not.
So, I can re-write the given statement as
(new) Given statement: If you don’t bribe the minister(#1), you’ll not get the 2G license.(#2)

To me, that seems wrong. It says that if you DO bribe the minister, then we don't know whether or not you'll get the license. Looking at the original, I feel that it's implied that if you bribe the minister, you DO get your license. Isn't that how "unless" is interpreted in our daily lives?

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  • You may have misinterpreted the last sentence (the one marked as "new"), though I'm not sure, but here goes... Let A be "you don't bribe the minister" and B be "you won't get the 2G license." Then the sentence is equivalent to A->B, which is equivalent to ~B->~A, which may be translated as "If you got the 2G license, then you bribed the minister." This means bribing the minister is a necessary condition for getting your 2G license, which is the result we wanted. – leibnewtz Jul 12 '14 at 2:46
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    @leibnewtz I understand what they are saying, but I disagree that the original sentence means JUST that. I feel that they are making the relationship weaker and tossing away some implication that exists in the original (namely, that bribing the minister does get you a license). – Egor Jul 14 '14 at 16:26
  • This may be a better fit for english.stackexchange.com . English language is not logic. There's the question how good your case for getting the license is, and how much the minister expects a bribe. Both sentences as sentences in the English language give subtly different meanings. – gnasher729 Oct 13 '15 at 20:06
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There are two senses of Unless.

It's possible that "unless" may indicate the strong sense of the word, in which case it takes a different form and you'd be correct, but this implication is contextual. This context can be implied by the sentence's content, or even from the way the sentence is constructed. For instance:

u1. Unless you study, you won't graduate.
u2. You won't graduate unless you study.


The denial of u1's antecedent, "if you study, you will graduate" is certainly not implied. However, using u2's construction in english often (not always) indicates that the exact same word to be taken in a stronger sense. Rather than "if not", we read this stronger sense as "if and only if not". To illustrate, rewriting both examples to use the more familiar logical indicators results in the following clauses:

u1*. If you do not study, then you will not graduate.
u2*. You won't graduate if and only if you don't study.

Note that u1* only guarantees that if you graduate, you studied, allowing you to fail even if you study. However, u2* to use the correct form illustrates why you may feel the example you were reading "feels" wrong. If you're using the stronger sense of unless, then if you don't graduate, you must not have studied— which fits your intuitions.

Incidentally, P <—> ~Q will result in the same truth table as the exclusive disjunction, "xor":

+---+---+----------+--------------------+
| P | Q | P <—> ~Q | (P v Q) & ~(P & Q) |
+---+---+----------+--------------------+
| T | T |    F     |         F          |
+---+---+----------+--------------------+
| T | F |    T     |         T          |
+---+---+----------+--------------------+
| F | T |    T     |         T          |
+---+---+----------+--------------------+
| F | F |    F     |         F          |
+---+---+----------+--------------------+

For a full description of these two uses of "unless", see sections 16 and 17 of this course reader.

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  • Thank you for the link. Unfortunately, my course material never mentioned the two meanings of "unless" while acknowledging that 'or' can be exclusive but should not be taken so in the context of assignments and tests. I just feel that the "strong" sense is more commonly used in every-day language, just like 'or' is (IMO) more commonly exclusive. The fact that others agree that "unless" can mean equivalence is all I really wanted to know. – Egor Jul 14 '14 at 16:21
  • @Egor Glad to help. If it's for a course, ask your instructor about the correct interpretation first. The strong sense may be commonly used, but no offense: that's your personal judgment. If your judgment is more accurate than your instructor's, you could have a problem debating the point. Ask first, and keep an obedient mind... if your goal is marks, anyway. – Ryder Jul 14 '14 at 22:12
  • Oh, I agree entirely that it's my opinion only, and "fighting the man" is rarely good for your grades. I have no problem doing it the way my instructor wants, I just wanted to find out if my interpretation makes sense or is totally out to lunch. For my own knowledge and understanding, that's all. – Egor Jul 15 '14 at 14:46
  • I think this is really iffy. The second construction is used to emphasize that the condition will contribute to the likelihood of the outcome, but it is by no means equivalent to any form of if-and-only-if. The strength does not come from some second meaning of unless, either, it just comes from the lack of the subordinate clause -- basically more indirection implies less urgency. The difference is not nearly as great as is presented here. – user9166 Oct 14 '14 at 21:31
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Egor, Suppose you've got to bribe the minister AND fill out the forms in order to get your 2G license. I.e., unless you bribe the minister AND fill out the forms, you won't get your 2G license. It's still true that unless you bribe the minister, you won't get your 2G license, but it's certainly not true that bribing the minister is sufficient for getting the license. The bribing is a necessary, but not a sufficient, condition. And I think that's generally true, not just in certain nonstandard contexts. 'Unless' generally leaves open the possibility for other conditions being necessary. I do strongly agree with Ryder that how we read the English is up to us, the English speakers, and not up to logic teachers or logic text writers, but I think that we do in fact mean what the logicians say we mean when we use 'unless'.

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  • First off, welcome to philosophy.se. Is there any chance you could use paragraphs / formatting? Right now, the answer seems pretty good to me but kind of text-wallish. – virmaior Oct 14 '14 at 23:06
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I'd like to weigh in to say I agree with Leibnewtz and disagree with Ryder. There are not two senses of unless but one. "A unless B" is the same as "A if not B" which has the truth table T T T F, and hence is the same as "A (inclusive) or B". In your example, "you won't get the license unless you bribe the minister" is the same as "you won't get the licence if you don't bribe the minister". In neither case it is implied that if you do make the bribe it will certainly secure you the license.

Sometimes when you hear "A if B" you interpret it as "A if-and-only-if B" because the context suggests it. In other words, it is what Grice called a conversational implicature. This is distinct from the actual meaning, because an implicature is cancellable. For example, if Alice says to Bob, "If you don't hand over your wallet I'll shoot you", the implicature is clearly that if Bob does hand over his wallet, Alice won't shoot him. Alice didn't actually say she wouldn't shoot him anyway, but this is clearly an implicature because the very reason for saying "If you don't hand over your wallet I'll shoot you" is to provide Bob with a motivation for handing over the wallet. If Bob believed that Alice was going to shoot anyway, he would have no reason to comply.

Now in the case of "unless" it is even more common to interpret "A unless B" as "A unless-and-only-unless B" which has the truth table F T T F - the same as exclusive or. But as with the "if" case above, this is only a conversational implicature - it is not part of the meaning of "unless".

As a footnote, studies of the ability of people to comprehend sentences with various conditionals in them show that people are significantly more likely to misunderstand sentences that contain "unless" compared with sentences that only contain "if". So a good rule of thumb is simply to avoid the whole problem by never using "unless".

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According to the suggested translation of Stephen Cole Kleene, Mathematical Logic (1967 - Dover reprint), regarding a list of natural language expressions (pag.64) :

"A or B" is "A unless B" [usually] and is "A except when B" [usually].

This can be compared with Fitelson's proposal in the above answer, according to which :

"A unless B" is equivalent to : "if not B, then A" [ which in turn is equivalent to : "B or A" ].

Try with the following exercise from J.Barkley Rosser, Logic for Mathematicians (1953 - Dover reprint), Ch.2, Sect.1, page 17 :

Exercise 4. If “P” and “Q” are the translations of “(n−1)!+1 is divisible by n” and “n is prime” then write a translation for “(n−1)!+1 is not divisible by n , unless n is prime”.

Thus, we have to translate : "not P, unless Q".

If we consider the correct mathematical proposition :

if ( (n-1)!+1 is divisible by n ), then (n is prime)

which is :

not ( (n-1)!+1 is divisible by n ) or (n is prime),

we can check that the translation of :

"not P, unless Q"

is : "if P, then Q" and equivalently : "not P or Q".

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    I can also write "If Q then P", as in "If n is prime, then (n-1)!+1 is divisible by n". This shows that a better translation would be "P is equivalent to Q", which is a stronger relationship than "If P then Q". In fact, Wilson's Theorem uses the wording "if and only if", which always means equivalence, and further reinforces my point that "unless" should be considered equivalence/exclusive or (same thing). – Egor Jul 14 '14 at 16:00
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I commented earlier but I think I can provide a full answer. There is nothing about "Unless you bribe the minister you won't get your 2G license" that implies the sentence "If you bribe the minister you will get your 2G license." Let A be "you don't bribe the minister" and B be "you won't get the 2G license." Then the sentence is equivalent to A->B, which is equivalent to ~B->~A, which may be translated as "If you got the 2G license, then you bribed the minister." This means bribing the minister is a necessary condition for getting your 2G license, but not a sufficient condition for getting your 2G license. In other words, the sentence leaves open the possibility that the minister may reject your bribe while asserting that it is nevertheless the only way to obtain the license.

By the way, why A->B implies ~B->~A may be shown using truth-tables.

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  • I understand the logic, but disagree with your assertion that "There is nothing about "Unless you bribe the minister you won't get your 2G license" that implies the sentence "If you bribe the minister you will get your 2G license." To me that assertion is indeed there, I feel a strong implication that successfully bribing the minister will get you your license. – Egor Jul 14 '14 at 15:48
  • There are two senses of implication that are being used here: logical implication and conversational implication. Logically, the sentence does not imply that if you bribe the minister you will get your 2G license, but conversationally it may. That is to say, there is nothing about the structure (which is what logic is concerned with) of the sentence that requires it to be true, but the speaker may have wanted to suggest that most people who bribed the minister got their 2G license. Again, though, logically there is nothing that says you will definitely get the license with your bribe. – leibnewtz Jul 15 '14 at 0:04
  • For further reading check out the wikipedia page: en.wikipedia.org/wiki/Logical_consequence – leibnewtz Jul 15 '14 at 0:07
  • Right, but that's exactly my point. If conversationally the implication is there, but logically it is not, then wouldn't that indicate that the logical structure we've formed does not accurately represent the original sentence? What use is a logical structure that does not convey the meaning we want? – Egor Jul 15 '14 at 15:16
  • For an extreme example consider this: why don't we represent the original sentence as (A & B)? That's a logical structure that has certain implications. It has a totally different meaning than the original sentence, but if we aren't concerned with what the speaker was actually saying then who cares? – Egor Jul 15 '14 at 15:26
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You may have misinterpreted the last sentence (the one marked as "new"), though I'm not sure, but here goes... Let A be "you don't bribe the minister" and B be "you won't get the 2G license." Then the sentence is equivalent to A->B, which is equivalent to ~B->~A, which may be translated as "If you got the 2G license, then you bribed the minister." This means bribing the minister is a necessary condition for getting your 2G license, which is the result we wanted.

Answer by IAS PaperTeam

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It's possible that "unless" may indicate the strong sense of the word, in which case it takes a different form and you'd be correct, but this implication is contextual. This context can be implied by the sentence's content, or even from the way the sentence is constructed.

Answer by IAS Paper Team

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