JLS
for the GC
TALKING, with J, of omissions to "Logic and Conversation", Grice forgot one that did merit a mention later in the William James (lecture 4), viz, the stroke:
p|q
which reads, 'not both'.
----
He listed seven formal devices
1. ~
2. /\
3. \/
4. )
5. (x)
6. (Ex)
7. (ix).
--- As J noted, there's also 'iff' (")("), which should fall after ")", and there's the Sheffer stroke which should fall after ")(". Logical students usually are treated to a more complete list than the one Grice gives. I guess he was trying to make a general point.
My inspiration here has been Gazdar. Using Lukasiewicz's notation, he actually lists ALL the truth-functors (dyadic), and imagines why some are good and some are bad -- by "good" and "bad" he means, 'from a Gricean point of view'.
Grice tries as much in lecture 4. He notes that the Sheffer stroke is clumsy. It relates to Plato's problem of negation, and stuff. It is a very convoluted operator, the Sheffer stroke, whatever HE (i.e. Sheffer) thought about it back in the day, 1913.
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well, you see something similar to Sheffer strokes in computing-related logic, don't you?? NAND, or NOR--ie not both A & B, and NOR= neither A NOR B . I would think a Gricesterian would approve of expressive completeness.
ReplyDeleteWell, yes. I do like 'nand'. I even like 'nall', which apparently WAS used in Anglo-Saxon England. It was, of course, a negation of 'ne' + 'alle'. Somewhere around 1400, etc., Englismen stopped using it: the result: the Square of Opposition is not really symmetrical implicaturally speaking. I have tried to re-introduce "nall" into the language. But I need a Poet Laureate to write a limerick about it. It's only via poetry, Heideggster claims, that language is instituted.
ReplyDeleteOK--in terms of ordinary lang., they may be fugly. But the Sheffer strokes (ie NAND and NOR) certainly have truth values. Jeffrey uses 'em (and Jeffrey was a fairly ..charitable logician, not anal.logic)
ReplyDeleteThe very first time I looked at the circuit diagram for a computer (and possibly the only time I looked at a complete diagram at the gate level), was one that was one entirely in one or other of the scheffer strokes (can't remember which one). There was at one time the advantage that you can just get large numbers of the same kind of gate and build whatever digital combinatory logic you liked from them.
ReplyDeleteOf course they don't do it that way any more.
RBJ
Yes. As a student of logic one is sometimes nicely surprised: "So -- if the Sheffer stroke does for all -- why bother with the multiplicity?"
ReplyDeleteIt´s a bit like logical diversity, biological diversity. You like parrots (truth-functors). Why have such a bunch of them, where they all can be reduced to one parrot (or truth-functor)?
I suppose that must be the idea behind Sheffer when he published his thing in 1913.