Message-Id: <199602052159.XAA01299@xiron.pc.helsinki.fi>
Date:         Mon, 5 Feb 1996 18:55:41 -0300
Reply-To: "Jorge J. Llambias" <jorge@INTERMEDIA.COM.AR>
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: "Jorge J. Llambias" <jorge@INTERMEDIA.COM.AR>
Subject:      Re: tech:logic matters
To: Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 2316
Lines: 53

pc:
>Although I do not really think I am being obscure and I know I am
>trying not to be, a number of people, whom I have every reason to
>believe as intelligent, well-educated and well-intentioned as I am,
>claim not to understand my point and illustrate this claim by citing
>things I have said as saying things I did not mean them to say (and
>cannot now read them as saying).

I don't know if that means me, but I apologize if I said that you
said something that you didn't. It certainly wasn't on purpose.

>                Affirmative                     Negative
>Universal       SaP/(Ax:Sx)xPx          Sep/(0xSx)xPx
>                Every S is P                    No S is P
>
>Particular      SiP/(Ex:Sx)xPx          SoP/(OxSx)xPx
>                Some S is P                     Some S isn't P
>
[...]
>  Although there are 16 ways of
>interpreting the square in terms of which sentences require that there
>are Ss (or Ps for that matter), only a few have been seriously
>considered and two regularly appear as the norms. One of these is to
>take the particulars as having existential import and deny that to the
>universals. [...] The other takes the affirmatives to
>have existential import and the negatives not. [...]

Up to here, I don't think there is disagreement. The disagreement is
with the actual choice:

>On
>technical grounds, the second form is preferable, [...]
>because it is functionally complete: all the various ways of
>interpreting the four basic expressions are definable within this
>system, using either the given forms or their obverses.  For example,
>an importless universal affirmative is just SeP', just as an importing
>universal negative is SaP'.

This choice makes SoP have no import, which means that "Some S isn't P"
is true in the absence of S's.

To me, the fact that, with that choice, SaP is not equivalent to SeP'
is a drawback, not a plus. It means that it becomes very difficult to
pass negations through quantifiers in order to obtain easier to
understand expressions.

But I agree that in the end it is a matter of taste. There is no
pre-defined right answer. You may think that one choice is preferable
on technical grounds, but there is no logical requirement for that
choice. Before, I had understood you to say that we didn't really have
the choice.

Jorge