[hist-analytic] Two´s Company

jlsperanza at aol.com jlsperanza at aol.com
Sun Jan 10 13:33:19 EST 2010

-----Original Message-----
From: Baynesr at comcast.net
To: hist-analytic at simplelists.co.uk
Sent: Sun, Jan 10, 2010 12:30 pm
Subject: The Logic of Reciprocity:  David Lewis etc.

S. R. Bayne quotes my:

>"Reciprocity" should be easy enough to formulate."
and comments, wittily:

>It's like the weather: we should be able to do something about
>it (but what?).
Exactly. Recall that the first five things any student of logic (that 
endures long enough in the semester to be instilled the rudiments of 
Russell´s logic of relations) learns about symmetry, transitivity, 
commutativity, and reciprocity, and reflexivity.

>Reciprocity is fraught with difficulties at all levels.

Indeed. By which we should restrict, perhaps on a first shot, to 
"syntactic", "semantic", and "pragmatic", to echo Morris (on 

>To take one
>example: Bill loves Mary and Mary loves Bill.

In symbols

A(a, b) & A(b, a)

>At first it is easy
>to believe that they love each other.

Indeed. I think "marry" is just as tricky. As in the title of a song 
cited by Horn, as I recall, in his "History of Negation". ¨We were 
happily married (but not to each other)".

>That seems clear enough,
>so reciprocity may be reduced to a form of conjunction.

Indeed, the "&" of the formula above. And note that when I wrote, as 
you quoted me, "formulate", I meant, "formalise", but I see you saw 
what I meant.


That ´conjunction´ is sufficient

>not so obvious.

Indeed, I wouldn´t think it´s obvious in the first place!
>In my idiolect Mary can love Bill and Bill Mary but this is 
>to make the claim that they are "in love" precisely because there
>is a missing sense of reciprocity, even in the binary case.

Exactly. What we need here is a notion of "requited love". Horn once 
shared with me a piece from the New Yorker, I think, where this 
journalist or writer uses all the odd expressions involving negatives 
("she´s not my cup of tea") in the affirmative versions, bringing odd 
pragmatic results: every sung hero needs requited love, and some such. 
I think the title of the piece is "How I met my wife", which may relate 
to reciprocal love.

>It is what is superadded to the conjunctive analysis that conceals the
>sense of ''reciprocity'; relevant to the political discussion.
I see. And amatory discussion, too, I hope. I love Ovid, and his Ars 
Amatoria. He was very much a Gricean or paleo-Gricean, as Scruton has 
revealed to us, or disvealed to us, to use the Rawlsian idiom. For much 
of what happens in sexual relationships, I learn from Grice´s tutee, 
Thomas Nagel, in his "Sexual perversions", in Journal of Philosophy, is 
this lack of reciprocity.

One cannot love (in the sexual sense) a minor (or underconsent human) 
because they are not able to hold reciprocal relations. Only adults can 
do that. Sex which involves non-adults, in the Gricean sense (meaning 
´rational´) is perverted. Scruton examines, for example, Parsiphae´s 
love for a _bull_! in Greek mythology. The mather of this monster, the 
Minotaur. A bull cannot hold sexual feelings for a human as a human may 
hold sexual feelings for a bull. So zoophilia is doomed to fail, 
Griceanly. Scruton also considers sexual implements (like vulgarly 
called ´dill-does´). These are objectifications of sex. I believe one 
list-member here thinks talk of objectification is silly, but let them 

In sum, we need, reciprocal actions or intentions which involve 
something like a ´speculatory´ effect, alla Daellenbach. I called this 
the effect of facing mirrors. And it´s the level usually discussed in 
terms of mutuality. Recal that Grice was invited to deliver this 
lecture at a symposium on "Mutual Knowledge", ed. by N. Smith for 
Academic Press. When everybody was waiting that Grice would have his 
say on such overmentalistic psychologically unreal notions, he gave us 
a myth, rather! (his Meaning Revisited). He manages to poke fun at 
"pseudo-Schifferian" regresses, as he calls them, alluding to 
Strawson´s tutee at Oxford, S. R. Schiffer.

>The notion, also, eludes David

(Kellog), I love that middle name.

>Lewis. For example, he says that
>2) A indicates to both of us that you and I have reason to believe that
>A holds
>applied to
>4). A indicates to both of us that each of us has reason to believe 
that you will return
>5) A indicates to both of us that each of us has reason to believe 
that the
>other has reason to berlieve that you will return.

Indeed. Oddly misapplication of all that´s good about Grice! This sort 
of Strawson-type counterexamples to Gricean intentional analyses of 
things were first presented indeed by Strawson in his 1964 Theoria 
article (I think Theoria, or JP), "Intention and Convention in Speech 
Acts", repr. in his Logico-Linguistic Papers, Methuen, 1971. Kemmerling 
warns us in his P.G.R.I.C.E. contribution: do not disgrice (or 
strawson) if you can grice.

Indeed, R. Grandy (in, if I recall aright, his review of Schiffer in JP 
or elsewhere) adopts something which I did adopt in my PhD: and which 
is inspired by Grice´s manoeuver in WoW. What Grice later called the 
anti-sneaky, or anti-deception clause.

For Lewis is saying that there is a regressus ad infinitum in the 
clause involving this mutuality of perspectives. What Grice and Grandy 
and I show is that a self-reflexive clause:

     (p) Let all claims be open, including this one. I.e. overtly known 
by participants.

---- In the case of your example from Lewis:

    (p) and let Bill and Mary know that they love each other and that p.

By having

     (p) Bill and Mary know they love each other and they both also know 
that p.

you get rid of the regressus ad infinitum. True, you get a 
self-referential, paradoxical alla Liar claim, but hey, I´m honest 
enough not be seduced by liars!

Bayne continues:

>Not only do I not see this, I think it's wrong.

Correct. First, there´s no way to stop. Rachel Kempson, who I have 
corresponded with, in his "Presupposition" book for CUP has it stop at 
level 4, but there´s no rationale for that. It could go on and on for 
ever, and that gives Grice a headache with pseudo-Schifferian 
regresses. Second, you stop the regress by not having it gotten started 
in the first place, by disallowing "covert" intentions.

If Bill loves Mary but there IS an intention on the part of Bill 
regarding his love for Mary that HE intends to be hidden from Mary 
(e.g. that she is the heir to this stately home in Finland) I cannot 
think I can say that they mutually love each other, or that Mary, sweet 
Mary´s, love is requited. I would go as far as to say that Bill is a 
_cad_ -- or as Grice would prefer, a ´sneak´, a ´cheat´.

>Later, he gives one example
>where he may have the connection right (op cit p. 55); but in this 
>I see no warrant for believing that this is equivalent to
>A gives reason to believe of each other that he believes A will return.
>Each has reason to believe of the other that he believes that A will 
 >These last two are authentic reciprocals, not (5).
I see what you mean. Will revise Lewis´s analysis in context and get 
back to you, hopefully.

I think then the context is whether A and B can be said to mutually 
know (if you excuse me the split infinitive) that, say, Jesus will 
return. (I love my variables fixed!). First, ´mutual´ knowledge should 
be distinguished from "common knowledge". I am Gricean enough to go as 
far as to allow talk of "common ground". If it is common ground that 
Jesus will return, we may safely assume that each relevant agent knows 
that the other knows it. This is what comes out in discussions of 
topicality: if it´s common ground (Queen Anne is dead) don´t even 
bother (to introduce it as a topic of conversation). It´s given, or a 
given. We want new.

Second, terms like ´knowledge´ are confusing here, since it´s 
assumptions, mainly. Even perceptions. Schiffer´s example in "Meaning" 
is that the candle standing between us is lit.

But you are also very right when you add "reciprocals" as an excellent 
grammatical (i.e. syntactic, or morphosyntactic), or 
"semantico-syntactic", alla predicate logic, category. The oddity of 
things like "each other" appeals a few. Think of the convoluted ways in 
_Spanish_ to say things like "We love each other" (I can think of "Nos 
amamos a nosotros mismos", which is triply ambiguous: it may mean that 
each of us loves each of us, but not mutually: the narcissistic 


>This is just a logical or grammatical observation; it is debatable but
>recirocity is tied essentiall to "each other" and this eludes Lewis.

Very good. Oddly, Grice is pretty much or remains pretty much a 
"telementional" Cartesian solipsist (in the words of McGinn, who didn´t 
know him but he has the bad taste to report that "he had only one 
tooth" -- Memoirs of a Philosopher). (This in McGinn´s contribution to 
Andrew Woodfield, Thought and Object, Oxford)

Grice on "Meaning" remains pretty solipsistic and it´s only in his 
foundation of things like the "conversational maxims" that he takes 
this "social" (or ´benevolent´ as he would prefer) level into account. 
The each-otherness indeed.


>He (Lewis)
>picks up on this without realizing it is a problem.

Indeed. The blame may be Quine. Recall this is a PhD, Conventions on 
Language, supervised by Quine. And you cannot write a PhD about 


>By the way, in ol' style government and binding theory reciprocals
>have an instructive lesson for political theorist interested in
>distinguishing convention and a contracts. In 'They love each other"
>you have reciprocity that yields obligation.

Exactly. As in the title of this country song, then, "We were happily 
married -- but not to each other", as cited by Horn. I should have the 
full lyrics for that. It seems my kind of defeasibility conversational 
implicature song, for the pragmatic analysis of contradictory negation 
in Russell & Whitehead, Principia.


>I don' think this is the
>case with the merely conjunctive interpretation of binary reciprocity.

You are right. But one has to be VERY careful when cashing in 
"obligation", or deontic operators, as it were. Judith Baker recalls 
how Grice would speak, alla Prichard (edited by Urmson, for Oxford, 
Morality and Interest), of obligation or morality cashing in in desire. 
For Baker is playing (in her contribution to PGRICE, Do one´s motives 
have to be PURE?) on Grice´s analysis of "obligation" or morality or 
duty, exactly, out of interest or motivation:

   Agent wills that p
   Agent wills that he wills that p
   Agent wills that he wills that he wills that p.
   and so on eis apeiron.

If there is no blockage for this sort of iteration, the content of "p" 
may be thought to have been morally justified. It becomes a duty for 
Agent A, or at least, not a crime if he does pursue actions towards the 
fulfilment of p.

>1. Each of them loves the other
>2. They love each other
>3. Each of them loves the others
>The thing to notice is that in a world of two individuals (1) and
>(2) are synonomous.

Very good. Two same-level pirots, as I prefer. For pirots come in 
different levels. To use Baker´s example (in her intro to Grice, 
Conception of Value). A sheepdog is a pirot for a shepherd. It´s a 
pirot to which the shepherd has instilled value. He is obliged to the 
dog, and the dog holds some obligations towards his owner. He must keep 
an eye on the shepherd´s sheep, then. So this is a world with two 
individuals, too.

In truth, I think that conversational maxims for Grice just work for a 
world of TWO individuals, at the same level of pirotic evolution or 
adaptation. He playfully refers that his account is meant to accomodate 
things like one writing an entry in one´s journal (a world of two 
individuals?). Also recall that his reason for not being too appealed 
to quasi-contractualism is that many communicative exchanges do not fit 
the mould that his intentional framework can be adapted to serve: 
letter writing, entries in one´s journal, etc.

Let´s also recall that Grice also found the notion of "Personal 
Identity" difficult enough to dedicate to it a full-length article in 
Mind in 1941, and he comes out with a mnemic account of personality 
that Rawls cites in his essay in "Public Affairs". The idea of personal 
identities, thus in plural, recalls quite some extra material -- are we 
talking of criss-crossed mnemonic experiences here?


>But notice that in a world of ten individuals
>(2) and (3) are not equivalent: (2) doesn't imply all possible
>pairwise hittings. In (3) all possible pariwise hittings are
>fulfilled. Compare here H.. Lasnik's terrific but a little dated
>paper "The Logical Structure of Reciprocal Sentences in
>English" in Essays on Anaphora, Klewer, 1989, p. 38.

Excellent reference, and one that Grice would have loved as he was into 
"formal linguistics" of the generative semanticist school.


>Now don't take this all too seriously in the political context BUT
>note that insofar as reciprocity is obligation creating we cannot
>derive reciprocity like (3) from (1); we would expect this
>on a simple conjunctive analysis. I don't care to expand much
>more at this point, except to say reciprocity is a very deep
>notion and the grammatical features suffuse our understanding
>of the case where obligation is at issue.
Exactly, and thanks for your good thoughts.

I would like to expand on how obligation is created by reciprocals, 
though. It seems that SOME reciprocals are, or seem, to involve, not 
level of obligation. Consider gaze in a bar, or something. Mutual gaze.

There is another field where obligation does not seem to play a role 
but it is NECESSARY for "dry-martini" sort of counterexamples. "The man 
drinking the martini is my father". "Let´s go to the cinema to see that 
movie. It seems extraordinarily interesting". In Joshi et al, "Elements 
of Discourse Understanding", I think the Clarks (Herb and Eve) expand 
on how much of reciprocity is necessary to even _fix_ the referent for 
this sort of cases. "That movie" refers to what the utterer thinks that 
the addressee thinks that the utterer thinks that the addressee thinks 
is the movie being played. Their scenario consists of changes to that 
context, where they both miss the point of the remark.

In the case of obligation, I think it´s because the predicate, rather 
than "gaze" or "refer", mentions a "moral" action, involving the 
well-being of the other. And indeed, it should be neutral or general 
enough to allow for an indefinite range of individuals: and not for a 
simplified universe of discourse of just two, for which we may get a 
pretty good semantics or modelling which proves totally false, as you 
note, when extended to "more than one". But two is a good number, too. 
Recall Humpty Dumpty:

   Alice: I would stop growing if I could. But one can´t.
   Humpty: One can´t, but two may.

Plus, isn´t binary or two-ness involved in "each other"? I don´t think 
so, but it may in Greek. Apparently, the Greeks did have this dual 
number, which is evident when Homer says, "The horses were running", 
meaning just two of them. "Both" is necessarily dual. "We both love 
each other". "Both went to the party". "Both Russell and Whitehead 
wrote the Principia". The Spanish, "ambos", derives strictly from the 
Latin of "ambi-" as in "ambiguity". So while the two-ness may be 
suffused by the grammar, it may not be two irrelevant, either. In the 
effect of opposing mirrors, indeed, it´s just two: the I and the Thou 
of Buber, creating the We, dual. We both. To add a third person seems 
to be Suzanne Sommer´s doom: two´s company, three´s a ...


J. L. Speranza
   for the Grice Circle

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