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In Logic: The Laws of Truth, Smith divides the informational content of an utterance into three categories:

  1. What is said - the underlying claim/proposition being expressed.
  2. What is implied - the logical consequences of the proposition being expressed by what is said.
  3. What is implicated - the things that follow from the assumtion that the utterance conforms to the maxims of the Cooperative Principle.

The difference beteween what is implied and what is implicated is then further elaborated in note (3) on page 477 (emphasis added):

  1. In contrast, what is implied are those things that follow from the assumption that what is said is true. As we saw above [see pages 99-100], one can say something true but still not speak correctly. In general, therefore, one will implicate things that one does not imply: things will follow from the assumption that one speaks correctly that do not follow from the assumption that one speaks the truth. Conversely, one may imply things that one does not implicate. The Maxim of Quality says that one should try to make one’s contribution one that is true: one should not say what one believes to be false; one should not say something for which one lacks adequate evidence. So, if we assume someone is speaking correctly—and, in particular, conforming to the Maxim of Quality—it follows that she believes that what she says is true. It does not, however, follow that what she says is true (she may be mistaken). Hence, things may follow from the assumption that what one says is true that do not follow from the assumption that one speaks correctly.

So, a speaker may implicate things he does not imply. Conversely, he may imply things he does not implicate. But I'm not sure I understand how this is possible and was wondering if someone would be able to provide some examples to elucidate the difference between the two scenarios.

I tried coming up with an example for the first scenario. E.g. someone asks me, "What did you do this weekend?" I reply with "I played guitar and I woke up at 9 o'clock". Assuming my account is in fact true, then I am implying that the conjunction of "I played guitar" and "I woke up at 9 o'clock" is true. However, my utterance is not correct in that it does not observe the Maxim of Manner (it is not orderly in presentation and it is ambiguous - did I mean 9am or 9pm?). If we assume that I have spoken correctly, then it follows that, not only did I play guitar and wake up at 9, but that I did these things in some particular order (namely, playing guitar first and then waking up at 9 (am or pm depending on how we disambiguate "9 o'clock").

But what does this discrepancy between what is implied and what is implicated have to do with me speaking incorrectly? Even if I had spoken correctly and said "I woke up at 9 and then played guitar", I would still be implying some sort of ordering that cannot be captured by the conjunction that I am implying, so I'm not sure what Smith means when he says "As we saw above, one can say something true but still not speak correctly. In general, therefore, one will implicate things that one does not imply." (By "above", I think he's referring to the examples on pages 99-100.)

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    Re your above "one can say something true but still not speak correctly. In general, therefore, one will implicate things that one does not imply.", rhetoric speech is important since one can easily say something true discursively while not relevant to one's implicature which is actually quite common. Beware our common classic logic satisfying weakening rule doesn't require all antecedents to be relevant to its implied consequent... Jan 16, 2023 at 4:17

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Usually, conversational implicature is a way of understanding how it is that when someone utters a sentence, they convey more than the literal conventional meaning of the sentence. So, for example, the utterance, "John drove home and drank a beer" carries a different implicature from, "John drank a beer and drove home". In Smith's terminology, both sentences imply the two facts that John drove and John drank, while each implicates that the events happened in the order specified. This is because one of the maxims of the cooperative principle is: Be orderly.

There are plenty of examples like this where someone implicates something without implying it. But Smith makes the further point that one can imply something without implicating it. The point is a little obscure, and I'm not surprised that you find it odd. In Smith's terms, a person speaks correctly if what they is in accordance with the cooperative principle, even if what they say is not true. I find this terminology odd, but there it is.

Suppose, for example, that Mary says, "Jack is at the office", and Mary is following the cooperative principle in that she sincerely believes this to be true and has evidence that it is true. But suppose also that in fact she is mistaken. In Smith's terms, what Mary says is not true, but she has spoken correctly, because she has followed the cooperative principle. What follows from the assumption that what Mary says is true is that Jack is at the office. What follows from the assumption that Mary speaks correctly is that Mary sincerely believes what she says and has evidence for it. The two are clearly different and so things follow from the first assumption that do not follow from the second.

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  • Thank you for getting back so quickly @Bumble, I've been stuck on this for some time, so truly appreciate your help. I've upvoted your answer, however, I'm still unclear about this bit of the quote: "As we saw above [see link to pages 99-100 in my post], one can say something true but still not speak correctly. In general, therefore, one will implicate things that one does not imply." I read this to mean that the risk of implicating something that we do not imply arises only if we speak incorrectly (i.e. violate Grice’s maxims).
    – user51462
    Jan 16, 2023 at 2:18
  • However, as your first example illustrates, this risk is also present if we speak correctly. E.g. say John first goes home and then drinks a beer. Then the utterance “John went home and drank a beer” is both true and correct, but it still contains a temporal implicature (i.e. we are hinting that the two events took place in some specific order) that does not follow from what is implied. So, I’m confused as to what Smith means when he says “one can say something true but still not speak correctly. In general, therefore, one will implicate things that one does not imply.”
    – user51462
    Jan 16, 2023 at 2:18
  • If John first drove home and then drank a beer, it would be true, but misleading, to say, "John drank a beer and drove home." So, what is implied is true, but the implicature is false and the speaker has spoken incorrectly. Hence the speaker has implicated something that is not implied.
    – Bumble
    Jan 16, 2023 at 12:31
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You should read the Wikipedia page on the topic. Quite informative.

As far as I can tell, going by what's on Wikipedia, given a proposition, if the implication is false then so is the proposition itself (strong logical connection), but the implicature being false doesn't render the proposition false (weak logical connection).

B = There's a bar at the next stop.

Implication: They sell alcohol (if this is false, B is false).

Implicature: You'll get beer. (this can be false - the bar's run out of beer, the bar sells only hard drinks, the bar's closed for renovation, etc. - without the proposition being false)

In a very general sense, implications are necessities/certainties, implicatures are contingencies/possibilities. In the example above, alcohol is a certainty in a bar, but beer is only a possibility.

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    That's an interesting characterization. Formal logical consequence is a metaphysical necessity. Implicature is necessarily ambiguous and therefore metaphysically contingent upon context. It would seem defeasible entailment would seem to occupy some middle ground, like presumptuously certain, but necessarily contingent upon unknown defeaters.
    – J D
    Jan 16, 2023 at 4:45
  • @JD, yep, that's how it looks to me. I suppose implicature consists of possibilities the implication generates. Jan 16, 2023 at 5:44
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But I'm not sure I understand how this is possible and was wondering if someone would be able to provide some example to elucidate the difference between the two scenarios.

Context: Medieval prison guard greets the family of a prisoner. The family would like to speak with the imprisoned. The King doesn't care much one way or another, so the guards expect a bribe.
Family: We're here to see Alfred son of Edward the miller.
Guard: (hefting a leather purse) Well, my purse sure is light.
Family: We have no coin, but here's a sack of ground wheat.
Guard: That will do. Right down the tunnel to the right.

What is said: Well, my purse sure is light.
What is implied: There aren't a lot of coins in this purse.
What is implicated: If you're going to see the imprisoned, you'll be needing to provide me something of value.

Pragmatics is the study of how language actually works, as opposed to the details like phonology (studies sound), syntax (patterns of utterances or graphemes), or semantics (conceptual relations). Philosophers have for a long time conceived of words as bearers of meaning. 'Dog', for instance, somehow conveys meaning from one person to another. With the rise of the linguistic turn (Frege, Russell), what has come is scrutiny about the relationship between utterances and meaning in much detail. It turns out, it's quite a complicated affair with context being the central focus in more recent analysis; Richard Montague who was involved in the formalization of context, for instance, rightly helped extend the initial investigations by Frege and Russell, into something more sophisticated by characterizing what are now known as indexicals with n-tuples, possible world semantics, etc. Today, the term in philosophy of language that are relevant for understanding context more technically are indexicality and deixis.

The TLDR is that given a sentence, logicians have been historically interested in logical implication. For instance, take two premises:

P1: Socrates is in the kitchen.
P2: The kitchen is in the house.

The premises are stated: plain English and easy to understand. The logical consequence of these two premises follows from the meaning of the words as well as a certain amount of experience (see the infamous analytic-synthetic distinction):

C: Socrates is in the house.

But, let's add one more premise:

P3: (conveyed with a smirk) Xanthippe is searching for him at the agora. Socrates sure loves his wife.

Now, we've entered implicature-space. If one knows that Xanthippe was a shrew, and that Socrates on occasion may have had the ability to hide from her, we can draw conclusions that go far beyond the logical consequences of the premises. Now, let's finish by addressing the author's use of correct and incorrect.

Remember that Gricean maxims are utilitarian assumptions that are eusocial and the basis of shared intentionality. But, people aren't always competent and altruistic. They make mistakes. They lie by omission and commission (occurence), and much more frequently they palter (disposition). Thus, the author is using correct/incorrect as a normative endorsement of adhering or violating the maxims. In a US court of law, for instance, one cannot perjure themselves (not without consequences in the ideal), but there have been decisions that have found misleading implicature is not perjury. It's not the truth, but it's not a lie, either. So, we have intention, explicit truths and falsity, logical consequence, and a broader contextual consequence all happening. Let's do one final example.

Defendant (at deposition): I didn't abet the homicide because I locked the pistol in the box after cleaning it.
Expert Witness: (at trial) After searching the lockbox containing the pistol, I determined the locking mechanism was broken. I also conducted a residue test on the pistol, and contrary to the witnesses claims, the pistol was dirty.

What is stated: I locked the pistol in the box.
What is implied: The pistol couldn't have been used in some homicide.
What is implicated: I didn't knowingly help the murderer because I didn't intend for him to have access to the pistol.

Now, the analysis. What the defendant has said is incorrect by way of the testimony of the expert witness. If the defendant accused of aiding and abetting genuinely believed the pistol to be locked and secure, then there's no perjury because there is no mens rea (in the context of perjury), no intention to commit a lie. The statement was a falsity, but that may have been unknown to the defendant. If the statement was a falsity, the implication is also false. Obviously, if the box wasn't really locked, then it could have been used for the crime. And yet, the implicature itself may be true if aiding and abetting requires mens rea (in the context of being complicit in the commission of a crime). Now, in US civil procedure, other factors can come into play. What is the character of the defendant? Is he a priest or a drug dealer? Was the box stolen or was it left out negligently, etc. These other facts applied to the argument by the defense are allowable because informal reason, like that used in criminal law, is defeasible (SEP).

Truth of statements, truth of implications, and the truth of implicature are distinct things.

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  • I'm not sure I quite know where your confusion lies, so if I missed the mark, let me know.
    – J D
    Jan 16, 2023 at 4:42
  • Thank you for your answer @JD. Re your first example, I noticed that “what is implied” (“There aren’t a lot of coins in this purse”) is not a logical consequence of “what is said” (“Well, my purse sure is light”) – does this matter? Smith defines "what is said" as the proposition underlying the utterance, and "what is implied" as the logical consequence of that proposition, i.e. where α is what is said by a certain utterance, then every proposition β such that α /∴ β is a valid argument, is implied by that utterance.
    – user51462
    Jan 16, 2023 at 10:41
  • @user51462 I'd say that it is a logical consequence if by context one presumes that there's an unspoken premise, mainly: Coins, which are kept in purses, add heft to the purse. Such a premise is not only true, but if uttered would violate the quantity maxim because it's common knowledge.
    – J D
    Jan 16, 2023 at 16:59
  • Thus, as per the form you describe: P1. My purse is light. P2. Adding coins would add heft. C. Since there isn't heft, there aren't enough coins. Something along those lines. Coming from a place of pragmatic analysis, I would suggest that the exact logical implication isn't important, and more than an analogy need to be exact to have figurative force. The distinction to observe is that WHATEVER logical implication can be drawn from the conversation, it does not lay bare the implicature which is a distinct dimension of communication. For all the nickel words, it's just what's between the lines
    – J D
    Jan 16, 2023 at 17:01

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