[hist-analytic] "If" and "If ..., Then ..."

Jlsperanza at aol.com Jlsperanza at aol.com
Fri Oct 16 22:23:33 EDT 2009

I do not want to intrude in the interesting Bayne/Aune commentary, but it  
may do to express my reaction upon reading Grice, "Indicative Conditionals", 
 WoW. Way of Words.

He says, rather stipulatively, that
     "if p, q"
gets the horseshoe.
The addition of the 'inferrability' particle, "then", notably does NOT get  
the horseshoe.
I would think the point may do in the Romance Languages. The 'if' particle  
if just the 'si' of Latin, 'se' of Italian, 'si' of French and Spanish.
"si p, q"
the addition of 'then' may be a trick. In some Spanish-language logic  
textbooks, it gets translated as "entonces",
   "si p, entonces q"
--- but it's never a phrase I heard a neighbour say!
I would think the French equivalent may be the 'donc', but you bet.
Now, as R. Grandy knows -- see his contribution to "Legacy of Grice" for  
the Berkeley Linguistics Society, it was Strawson who mainly Grice is 
thinking  of. Strawson held that there is a parallel between ASSERTED inferences
    therefore, q
unasserted inferences
    if p, q
    if p, then q
Now, for some reason, the 'therefore' gets translated in Spanish-language  
textbooks as "por consiguiente", o "luego", which is NOT again something I 
ever  heard any of my neighbours utter. In Latin it would be 'ergo', but  
Russell/Whitehead POSTdates Latin!
So the best way is indeed to deal, as Bayne does, with Philonian (versus  
Chrysippan?) implication, and consider the horseshoe (whatever its linguistic 
 realisation) as purely truth-functional.
Grice seems to be saying that the addition of the "then" makes for MORE  
than a truth-functional operator. 
Uttering "if" clauses without the 'then' re-inforcer is to Grice no breach  
to the 'paradoxes' of material implication, which are all true.
Oddly, this PHILO is NOT the Philo, apparently, that occupies a few volumes 
 in my beloved Loeb Classical Library. It is, as it were, a minor Philo.
When I was reviewing articles for Margarita Costa for the Bulletin of the  
Institute of Philosophy (in that wonderful building of the University of 
Bueos  Aires in 25 de mayo Street in downtown Buenos Aires) I recall coming 
across what  I then (and still now) thought a jewel:
    J. F. Thomson, "In defense of the material  conditional"
--- this was a posthumous lecture by Thomson, dated 1966 (I think) and  
poshumously published by Mrs. Thompson (Judith Jarvies). Thompson, who  
collaborated with Grice on this and that, holds very similar tenets.
Strawson's reply on the other hand had been doing the rounds since 1968,  
and was finally published by Grandy/Warner, in the PGRICE festschrift. 
(Strawson  has also reprinted it in his Entity and Identity, for the Clarendon  
In this paper, Strawson 'recollects' Grice's distinction between
          conventionally  implies
          non-conventionally  implies
This, _NOT_ in the sense referred to by Bayne in the segment below. Rather, 
 in terms of 'implicature'. For Grice (and recall he is basically 
criticising  Strawson's vademecum, Introduction to logical theory, 1952), 
      by uttering "if p, q", the utterer  NON-CONVENTIONALLY (i.e. 
conversationally) implies (or 'implicates' as he  prefers) that
              there is an inferrability link between p and q.  This is 
cancellable, for  example, in the paradoxes of material implication.
For Strawson, rather, and this seems to be Grandy's point in the Legacy of  
Grice symposium
     by uttering "if p, q", the utterer CONVENTIONALLY  implies such 
inferrability link.
I recall a class on conditionals (held on Saturday mornings no less) by D.  
S. M. Edgington. She, oddly, had never seen the Strawson paper till I 
showed it  to her (The meetings were in a rather derelict, if that's the word, 
section of  Buenos Aires, where the Argentine Society for Philosophical 
Analysis was holding  those seminars). Edgington had come fresh from Oxford to 
teach the natives that  neither Grice nor Strawson nor Russell nor C. I. Lewis 
were RIGHT. "If p, q" has  NO truth-conditions!
If anything, her seminar served me to systematise all the theories  
involved, and with the help of some Jackson and D. K. Lewis, to arrive at a  
neo-Griceanism of sort which still holds the 'identity' thesis between, yes, the  
'if p, q' and the horseshoe.
But a horse says nay.
J. L. Speranza"
In a message dated 10/16/2009 1:48:59 P.M. Eastern Daylight Time,  
Baynesr at comcast.net writes:

he says  that ‘if…then’ is indicated with a horseshoe. This is sometimes 
the case, but  if I’m not mistaken ‘if…then..’ is generally distinguished 
from ‘implies’ and  it is ‘implies’ that gets the horseshoe. If there is a 
doubt take a look at  Russell’s Principles of Mathematics 1903 "Implication 
and Formal Implication."  It’s an old book, but I can’t recall a case where 
‘if…then…’ gets the  horseshoe, but maybe. Any examples? Reichenbach did 
do this occasionally. It  Is not uncommon to think of entailment is just a 
bracketed expression where  the primary operator is material implication, but 
where outside the left  bracket we have a necessity operator. Here there is 
no need to make a  distinction.

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