"Finite"

In conversation last week, I said to my father that my laptop battery has a “finite number of charge cycles”.

Now, if someone said to me that a battery had fewer than a billion charge cycles, I’d take the speaker to be implicating that it has quite a lot of them, probably between half a billion and a billion. And even besides that implicature, if all my information were that the battery has fewer than a billion charge cycles, then it would seem natural to take a uniform distribution from 0 to 999,999,999 and think that it is extremely likely that it has at least a million charge cycles.

One might think something similar would be the case with saying that the battery has a finite number of charge cycles. After all, that statement is logically equivalent to the statement that it has fewer than ℵ₀ charge cycles, which by analogy should implicate that it has quite a lot of them, or at least give rise to a uniform distribution between 0, inclusive, and ℵ₀, exclusive. But no! To say that it has a finite number of charge cycles seems to implicate something quite different: it implicates that the number is sufficiently limited that running into the limit is a serious possibility.

Actually, this may go beyond implicature. Perhaps outside of specialized domains like mathematics and philosophy, “finite” typically means something like not practically infinite, where “practically infinite” means beyond all practical limitations (e.g., the amount of energy in the sun is practically infinite). Thus, the finite is what has practical limits. (But see also this aberrant usage.)

"Ręka" and "hand"

I've been thinking about a curious issue in translation, which is not that uncommon. In most ordinary contexts, the Polish "ręka" and the English "hand" would be interchangeable in the sense that where a speaker of one language would use the one, the speaker of the other would use the other. Where the English-speaker talks of having something in his hand, the Polish-speaker talks of having it in his ręka, and so on. But the two terms are not synonymous. In non-medical Polish, "ręka" refers to the whole of the upper limb (though in medical Polish, it refers just to the hand), while the English "hand" refers only to the area from the wrist to the fingertips. The Polish term referring to the exact same part of the body as the English "hand" does is "dłoń", but the word is significantly less used than "ręka" (as per Google hits in .pl sites, say), and in many ordinary contexts using "dłoń" for "hand" would make for awkward translation. Conversely, to translate the Polish "ręka" as "arm", which would refer to the same part of the body (I am assuming that the arm includes the hand), would in most cases lead to awkwardness as well. It sounds funny to talk of picking up one's phone with one's arm, and so on.

Thus, it seems that these are cases where the natural translation from one language to the other does not in fact preserve the truth conditions. One can pick up one's phone with one's ręka without picking it up with one's hand (say, use the crook of the elbow), even though in the context of picking up a phone one would translate "ręka" as "hand", unless it was obvious from the context that the hand wasn't the part of the arm that was being used.

Maybe what is happening here is that when a sentence asserts a proposition p and implicates a stronger proposition q, we feel no qualms about using a translation that asserts q, or vice versa. To say in Polish that one picked up one's phone with one's ręka implicates the stronger proposition that one did this with one's hand, since if one had picked it up in the unusual way with the crook of the elbow, say, we would have expected the speaker to mention this. (This is a case where the usual Gricean presumption that one will use an equally brief but more precise term in place of a less precise one is defeated by the fact that the more precise and equally brief term "dłoń" is also less commonly used.) So one translates the implicature rather than the assertion.

I wonder, though. Maybe cases like this are evidence that the distinction between implicature and assertion is artificial. This would have the important consequence that the wrongness of implicating contrary to one's mind, or at least intentionally doing so, is the same sort of thing as lying. I don't want to embrace that consequence in general. I think false implicature is qualitatively less morally problematic than lying.

"God agrees with me" and "I have the truth"

Suppose I am convinced that God exists. Then if p is true, God believes p. So it seems that whenever I have the right to assert p, then as long I should also be willing to say: "And God agrees with me." But to say that God agrees with me sounds awfully arrogant!

I suppose some of the apparent arrogance comes from the implicature that I have independent evidence that God agrees with me—a special line to God. But of course in the typical case, my evidence that God agrees with me about p just is my evidence for p (plus my evidence that God exists and that I believe p).

Or maybe it's that one implicates certainty. (Why? Is it because there is a stereotype that when people make claims about God they are certain of them?)

There is a similar impression of arrogance one conveys when one says: "I have the truth about p." Yet, of course, if one is justified in believing p, one is typically justified in believing that p is true, and hence that one has the truth about p. Again, maybe the issue is that saying one has the truth implicates certainty?

There is, indeed, something odd about claiming that God agrees with one or that one has the truth on a subject where one has only a weak opinion. I am about to have random.org choose a number between 1 and 10, both inclusive. I think that the number will be smaller than 10. But it would be odd to say: "God agrees with me" or "I have the truth on that." Yet, my evidence that I have the truth on the number being smaller than 10 is almost as good as my evidenec that the number will be less than 10, and my evidence that God agrees with me is very good, given that I have very good evidence that God exists. (Oh, and I was right. The number turned out to be 1.)

Do not read, nitpickers only

My son pointed out this odd sign at the zoo today.  We all know what they meant, but if we try to parse it literally, it becomes weird.  We can read it as an exhortation to employees only, not to enter.  We can read it as a pair of exhortations, one not to enter, and the other that only employees should enter.  On this reading, if an employee enters, she violates the first exhortation but not the second, while when a non-employee enters, she violates both exhortations, and is doing doubly wrong.

But of course what is meant is: "Do not enter, unless you are an employee."  What is odd is that on this reading, the sign violates Grice's Maxim of Manner, since that point could be more briefly and less ambiguously expressed by "Employees only."

A Gricean theory of indicative conditionals

The theory consists of two theses and two definitions. I will use → for indicative conditionals. And all my disjunctions will be inclusive.

1. MatCond: "p→q" expresses the same proposition as "~p or q".
2. NonTriv: A use of "p→q" normally implicates that "~p or q" is an evidentially non-trivial disjunction for the speaker.
3. Definition: "a or b" is an evidentially non-trivial disjunction for an agent x if and only if x has non-negligible evidence for the disjunction that goes over and beyond evidence for ~p and evidence for q.

I don't here commit to any particular view of evidence, and if there are non-evidential justifications, one can probably easily modify the theory.

Here is an interesting consequence of the theory which I think is just right. When my evidence that at least one of ~p and q is true is simply the evidence for ~p (or for q), I don't get to say "If p, then q." But if I tell you that at least one of ~p and q is true, then normally you get to say "If p, then q". For when I tell you that at least one of ~p and q is true, then "~p or q" comes to be an evidentially non-trivial disjunction for you: my testimony is evidence for the disjunction and this evidence does not derive for you from evidence for the one or the other disjunct.

Notice that "has non-negligible evidence for the disjunction" has some vagueness to it. Moreover, negligibility is contextual, and that is how it should be. If I tell you that at least one of the following is true: snow is not purple and 2+2=4, then "If snow is purple, then 2+2=4" does not generally become assertible for you. For while you do gain additional testimonial evidence for the disjunction that snow is not purple or 2+2=4 from my speaking to you, the gain is normally negligible over and beyond your earlier evidence that 2+2=4. But if you respond to my assertion with "So, if snow is purple, then 2+2=4", you are speaking quite correctly, since the use of "So" and the conversational context makes the evidence I just gave you salient and hence non-negligible. (Perhaps "salient" or "relevant" could be used in place of "non-negligible" in (3).)

The theory explains why it is that paradoxes of material implication can almost always be made to cease to be paradoxes of material implication as soon as one fills out the evidential backstory in a creative enough way. Take, for instance, the paradox of material implication:

4. If the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

The antecedent is false, so the material conditional is true, but (4) sure sounds bad (it sounds bad to assert and seems to be saying something bad about my manners). Yes, but now suppose that an epistemic authority has just handed me two numbered and folded pieces of paper, with a sentence written on each and folded in half, and told me that either at least the first paper contains a falsehood or they both contain truths. I puzzle out what she says, and I conclude, very reasonably:

5. If the sentence on the first piece of paper is true, the sentence on the second piece of paper is true.

I then unfold the pieces of paper, and notice that the first piece contains the sentence "The president will invite me for dinner tonight" and the second contains "I will have dinner with the president in my pajamas." And so I reasonably infer from (5):

6. So, if the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

(And, moreover, I now gain a new piece of evidence that the president won't invite me for dinner tonight—for it would be absurd to suppose I'd have dinner with him in my pajamas.) With this epistemic backstory, the paradoxical conditional is quite unparadoxical. That's because with this epistemic backstory, the corresponding disjunction

7. The president won't invite me for dinner tonight or I will have dinner with the president in my pajamas (or both)

is epistemically non-trivial. But in normal circumstances, (7) is epistemically trivial, since my only evidence for (7) is evidence for the first disjunct.

A similar kind of epistemic backstory can be given for any of the standard paradoxes of material implication, thereby turning paradoxical sentences into non-paradoxical ones (cf. this post). Our Gricean theory (1)-(3) explains this phenomenon neatly. So do theories on which indicatives are non-cognitive and ones on which they are subjective. But the Gricean theory is, I think, simpler.

Notice that in this Gricean theory we haven't brought in non-material conditionals through any back door, because we have explained the implicated content entirely in terms of disjunctions. Furthermore, (2) is basically a consequence of (1) plus the very plausible claim that disjunctive sentences normally implicate the epistemic non-triviality of the disjunction.

Implicature and lying

Philosophers say things like: "Asserting 'There is no conclusive proof that Smith is a plagiarist' implicates that there is a genuine possibility of Smith's being a plagiarist." (And yet taken literally "There is no conclusive proof that Smith is a plagiarist" is true even if no one ever suspected Smith of plagiarism.) However what one implicates not only has propositional content, but also illocutionary force, and both both the content and the force are implicated. So if we want to be more explicit, we should say something like: "Asserting 'There is no conclusive proof that Smith is a plagiarist' implicates the suggestion (or insinuation or even assertion) that there is a genuine possibility of Smith's being a plagiarist." Which of the forces--suggestion, insinuation or assertion--is the right one to choose is going to be a hard question to determine. Maybe there is vagueness (ugh!) here. In any case, we don't just implicate propositions--we implicate whole speech acts. A question can implicate an assertion and an assertion a question ("It would be really nice if you would tell me whether...").

I used to wonder whether the moral rules governing lying (which I think are very simple, namely that it is always wrong to lie, but I won't be assuming that) extend to false implicature. I now realize that the question is somewhat ill-formed. The moral rules governing lying are tied specifically to assertions, not to requests or commands. One can implicate an assertion, but one can also implicate other kinds of speech acts, and it only makes sense to ask whether the moral rules governing lying extend to false implicature when what is implicated is an assertion or assertion-like.

And I now think there is a very simple answer to the question. The moral rules governing lying do directly extend to implicated assertions. But just as these moral rules do not directly extend to other assertion-like explicit speech acts, such as musing, so too they do not directly extend to other assertion-like implicated speech acts, such as suggesting. The rules governing an implicated suggestion are different from the rules governing an explicit assertion not because the implicated suggestion is implicated, but because the implicate suggestion is a suggestion. If it were an explicit suggestion, it would be governed by the same rules.

That said, there are certain speech acts which are more commonly implicated than made explicitly--suggestion is an example--and there may even be speech acts, like insinuation (Jon Kvanvig has impressed on me the problematic nature of "I insinuate that...") that don't get to be performed explicitly (though I don't know that they can't be; even "I insinuate that..." might turn out to be a very subtle kind of insinuation in some weird context).

I think the distinction between the explicit speech act and the implicated speech act does not mark a real joint in nature. The real joint in nature is not between, say, explicit and implicated assertion, but between, say, assertion and suggestion (regardless of which, if any, is explicit or implicated). Fundamental philosophy of communication does not, I think, need the distinction between the explicit speech act and the implicated speech act. That distinction is for the linguists--it concerns the mechanics of communication (just as the distinction between written and spoken English, or between French and German) rather than its fundamental nature.

Use and mention

I was editing a paper I'm writing with a colleague, and I came on this phrase:

we will draw out the details of the Specific Analogy Thesis (SAT).

It turns out that the acronym "SAT" never gets used anywhere else in the paper. Question: Was it used in the displayed phrase, or was it merely mentioned? I am inclined to think that either it was only mentioned, or it was both used and mentioned. In any case, we have a nice case here where grammar allows mention without either quotation marks or switch of typeface. It looks like apposition is another marker for mentioning, especially where capital letters are used.

Now, consider this sentence as we might find it in a paper on Spinoza: "Spinoza's Independence Thesis is the controversial claim that substances are completely independent beings." Suppose that this sentence contains the first use or mention of "Independence Thesis." The sentence introduces the term "Spinoza's Independence Thesis" into the language of the paper. But the sentence is also an assertion--among other things, the writer is asserting about Spinoza's Independence Thesis that it is controversial. In the sentence qua assertion, "Spinoza's Independence Thesis" is being used. But in addition to the writer's making an assertion, the writer is performing another speech act, the speech act of stipulating a term. Maybe the way to look at it is this: one asserts of Spinoza's Independence Thesis that it is the controversial claim that substances are completely independent beings, while implicating the stipulation that "Spinoza's Independence Thesis" denotes the claim that substances are completely independent beings (note that "controversial" is present in the assertion but not the definition). Or perhaps we should say that both the assertion and stipulation are there in the sentence with equal rights.

Aquinas on the senses of Scripture

The Tradition holds that Scripture has many senses. I found really striking what St Thomas does with this: "The author of Holy Writ is God, in whose power it is to signify His meaning, not by words only (as man also can do), but also by things themselves." In other words, it seems that the Angelic Doctor thinks that the words of Scripture directly only have a literal meaning (which of course isn't the "literalistic meaning"; the literal meaning of an assertoric text is that proposition which is asserted in the text; as Aquinas says, "When Scripture speaks of God's arm, the literal sense is not that God has such a member"). The non-literal meaning is not a meaning of the words of Scripture, but it is a meaning of the realities signified with the words understood in their literal meaning. Thus, the description of the Israelites' crossing of the sea in the Book of Exodus has as its meaning that the Israelites cross the sea. This text signifies a historical event—the Israelites' crossing of the sea. And the further meanings, such as a future baptism in Christ, are had not by the text, but by the historical event itself. The events of salvation history are thus a text, and the non-literal meaning of Scripture is thus not a meaning of the text of Scripture, but a meaning of salvation history itself.

I really like this. If the non-literal meanings of the text were really meanings of the text as such, it is hard to see what would distinguish them from the literal meaning. One alternative is to say that the non-literal meanings are intended by God but not by the human author. But if so, then that makes the human author less fully the author of the text, and it makes God an embedder of secret messages in the text. On Aquinas' view, the human author gets to be fully the author of the text, even if the human author does not grasp any of the non-literal meanings. For the non-literal meanings aren't really meanings of the text. (And there is nothing unusual about the events described by a historian having a meaning going far beyond that which the historian sees in them. But these meanings are of the events, not of the history book.) Moreover, this shifts us from being unduly book-centered. Those who experienced the Sinai event were not in principle worse off than the readers reading about the event. But if the additional meanings were meanings of the text and not of the event itself, then those who experienced the Sinai event were in principle worse off than those who read about it.

All this gives a strong sense to the idea that the non-literal meanings of Scripture depend on the literal meaning. For if the Israelites did not in fact cross the sea, then there is no historical event of the crossing of the sea to bear any of the non-literal meanings. The words of Scripture don't signify a future baptism—they signify a crossing of the sea. The crossing of the sea would signify a future baptism, but since the crossing didn't take place on this hypothesis, that is irrelevant.

Moreover, if Aquinas' idea is right—and I think it is right as the notion that God writes not just in words but in historical events is deeply embedded in the Christian tradition—then the theologian who denies the various miracle stories but hopes to save a non-literal meaning is in even greater trouble. For while we assert by speech and not by silence (unless we set up a special convention—"If I say nothing, assume I agree"), we implicate both by speech and by silence. If the Israelites did not in fact cross the sea, not only is the crossing of the sea not there to bear a non-literal meaning, but the non-existence of the crossing of the sea—i.e., God's refraining from causing a crossing of the sea—carries an implicature that we should be cognizant of. But the implicature carried by refraining from an utterance s is typically (though not always, but a special case would need to be made out that the present case is such an exception) opposed to the meaning that s would have had. So the theologian who reads the miracle stories ahistorically, if Aquinas is right, may well make God out to be implicating something opposed to the non-literal meaning that the theologian hopes to find there.