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Apologies if this question is answered elsewhere. I didn't know how to refer to the following phenomenon and consequently I didn't know what to search for. I'm happy for more expert users to add/remove tags or suggest other amendments to the question.

Take as an example the following sentence:

(S1) Women are not permitted to become priests.

My understanding, and I am a native English (UK) speaker educated to PhD level in philosophy, is that when someone says this, unless they add further clauses cancelling the implication, they imply the following:

(S2) Men are permitted to become priests.

The implication can be cancelled, if the speaker adds, for example, "But nor are men, the state forbids anyone to become a priest" (Perhaps non-binary-gendered people or robots could still become priests in this case).

Is my understanding here correct? If so, is there a name for this kind of implication? Where could I read more about it or direct someone to, to learn more?

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    This is entirely correct: unless creates a conditional sentence. There are other forms (see the link). Note that adding "and even then" simply adds a further condition: "If you have looked both ways and have waited for the green man, you may then..."
    – Andrew Leach
    Apr 1 at 11:48
  • Having said that, I'm really not sure what is being asked in the question.
    – Andrew Leach
    Apr 1 at 11:49
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    You might look at implicit rules of conversation or communication such as Grice's Maxims lancaster.ac.uk/fass/projects/stylistics/topic12/14cp1.htm (Also, looking both ways and then crossing is only safe if no traffic is coming.)
    – Stuart F
    Apr 1 at 14:15
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    Does this answer your question? "I love you." ... "As do I." << If interpreted literally, it would mean ... [the example is irrelevant ] Luckily, the meaning of sentences does not always depend on a literal interpretation of the words spoken. This is called implicature in linguistics and refers to what is suggested in an utterance, even though neither expressed nor strictly implied (that is, entailed) by the utterance. This is part of the wider field of pragmatics. >> Apr 1 at 17:07
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    Precisely, what do you call an implication? What do you mean exactly by "cancellation"? This is not a grammatical term; you find it in mathematics but not in linguistics nor in logic.
    – LPH
    Apr 1 at 18:56
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The entirely correct conclusion drawn in the question is a result of a phenomenon detailed first by the philosopher Paul Grice. The rules he formulated for what he called "Cooperative Communication" are known in linguistic pragmatics as Grice's Maxims.

One of them says we should make cooperative communications true, as far as we know. Another says we should make them as complete as possible. The upshot is that, when one says something less than what is logically possible, one possible reason is always that that's as far as one can go and stay completely truthful.

This is known as a "conversational implicature" (a name picked by Grice so as not to be the same as "implication", which is a different logical animal). There are many words and constructions that have special Gricean meanings, like the difference between try doing it and try to do it.

In the example sentence, if it were the case that no one could become priests (or be made priest, or however one phrased it), then one could say so. And in that case it would certainly be trivially true that no woman (and no man) could become a priest. But if less than that is said, the extra unsaid racist, sexist, etc proposition (this is the way that stuff works, folks -- subliminally), Men may become priests is conversationally implicated. (note: not "implied" -- "implicated", like a politician)

And if you only say

  • Men may become priests.

without hanging a Gricean impicature on it by negation, you leave open the logical possibility that others (e.g, women, children, dogs, oysters) may also become priests.

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    You beat me to it. There is no strict logical entailment from 'women are not permitted to become priests' to 'men are permitted to become priests'. I suspect that even your application of Gricean 'implicature' does not work perfectly without some qualification like 'in the Greek Orthodox church women are not permitted to become priests'. There are many religions in the past (priestesses of Aphrodite, of whom Sappho the poet was perhaps one, or vestal virgins in Rome), and for all I know there may be some today. Continued
    – Tuffy
    Apr 1 at 21:44
  • The original premiss does not exclude children or animals (of these latter, I am afraid, alleged instances can be found on the internet. So I think that, in so far as it is a legitimate conclusion is is not a matter of strict logic, even if it is a kind of common sense.
    – Tuffy
    Apr 1 at 21:49
  • Nothing in philosophy works perfectly. That's the point, if there is one. Apr 1 at 22:26
  • Not in philosophy, perhaps, but in strict logic presuppositions have to be accounted for. Grice gives a very good account of how we go about common sense reasoning. And even dictionaries differ in how they go about defining 'priest'. Cambridge online specifically specifies "persons" in it definition, whereas Merriam Webster does not. But in moving to "men are permitted..." you are making tacit assumptions (such as that children are not permitted...). This may seem obviously true, but it is an empirical truth not embedded in the original premiss.
    – Tuffy
    Apr 1 at 22:38
  • Presuppositions aren't logical (i.e, semantic). They're pragmatic; logic has little to say about them. Most premises are not stated; they're part of the structure of the culture. One needs to distinguish logic from language, just as one needs to distinguish mathematics from physics - one is strictly cognitive, whereas the other has data in the real world that don't proceed from premises and must be accounted for. Apr 2 at 14:44

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