Thanks Ben, I think that you have got it better than me.
What is meant is certainly as you put it: "to say that all men are
mortal is the same as to say that for every man, for every character, if
said man possesses said character, then there is a mortal who possesses
said character". This expresses that the comprehension of mortal is
included into the comprehension of man while the converse holds only for
the respective extensions (and it is precisely such an inclusive view of
implication that B. Russell will reproach to Peirce). I was used to make
the point that in order to read correctly Peirce we have to throw out of
our heads what we learned before, but I was not obeying my own maxim
here :-).
Thanks Ben and thanks to Thomas Riese too for opening this thread
Bernard
Benjamin Udell a ¨crit :
Bernard, list,
> I returned to the sources and fell short with the following:
------------------------------CP 3.175----------------------------
175. The forms A -< B, or A implies B, and A ~-< B, or A does not
imply B †3, embrace both hypothetical and categorical propositions.
Thus, /*to say that all men are mortal is the same as to say that if
any man possesses any character whatever then a mortal possesses that
character*/. To say, 'if A, then B ' is obviously the same as to say
that from A, B follows, logically or extralogically. By thus
identifying the relation expressed by the copula with that of
illation, we identify the proposition with the inference, and the term
with the proposition. This identification, by means of which all that
is found true of term, proposition, or inference is at once known to
be true of all three, is a most important engine of reasoning, which
we have gained by beginning with a consideration of the genesis of logic
---------------------------------------------------------------------
>The assertion I have underlined in bold strikes me: I would say
exactly the converse. Am I wrong? or did the editors make a mistake or
did Peirce makes it? (there seems to be a conflict here between
extension and comprehension) [The remainder works well for me]
"Is the same as" sounds like an equivalence relation. If Peirce meant
an equivalence, then the converse is the same.
But the equivalence claim doesn't seem _/prima facie/_ true, so I
think that we're talking about the same issue. One might have expected
Peirce to say something like *"/to say that all men are mortal is the
same as to say that for every man there's a mortal such that, for
every character, if said man possesses it then said mortal possesses
it."/* (I'm assuming that there won't be considered to exist two
distinct things such that one's characters comprise a strict subset of
the other.) The point there is that the choice of man & mortal is
fixed before one starts speaking of all characters. But instead Peirce
let the choice of mortal vary dependently on the choice of man &
character. I.e., Peirce's assertion amounted to this: */to say that
all men are mortal is the same as to say that for every man, for every
character, if said man possesses said character, then there's a mortal
who possesses said character./* That all men are mortal seems to imply
its asserted equivalent, but doesn't automatically seem implied _/by/_
it. Instead one wonders, can there be a man whose every character is
possessed by one or another mortal without there being some same
single mortal who possesses all of the said man's characters? So now
the truth of the equivalence depends on what a "character" is, among
other things, and /whether any given thing must have at least one
unique character/ (in which case I think that the equivalence claim
would be true) and one starts to wonder whether the whole issue will
get into infinities in some sensitive way. I remember Peirce's
defining "character" somewhere but I can't find it.
Best, Ben
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