Curious. The formula "S is P" or "S is not P" do not seem to carry enough
information to decide the question.
On the other hand, if "John" lacks reference, the statements "John is blue "
and John is not blue" are consistent. (trivial empty) Further, one may tempted
to treat these as Universals; (or singleton classes). But then, the existent
singleton class inclusive of "every John" doesn't seem to obey the rule of
contrary, namely, "may both be false," unless there are two Johns. Aristotle's
definition of a contradiction seems to me to exclude this. The square of
opposition is always fun to play with. I sometimes like to consider that
"everything exists" so it works alright. BTW, waiting to see how you use the
"rules of passage" in terms of graphs.
Jim W
Date: Sat, 17 Jan 2015 16:07:03 -0500
From: bud...@nyc.rr.com
To: peirce-l@list.iupui.edu
Subject: Contradictories, contraries, etc. WAS Re: [PEIRCE-L] Natural
Propositions : Chapter 8 - On the philosophical nature of semiosis?
Jerry,
The examples that you use from the Aristotelian Square of
Opposition are standard examples of contradictories, contraries,
subcontraries, and subalterns. The examples are not definitive
of them, however. Every pair of propositions (aside from
self-referring propositions and that sort of thing) is one of
the following:
A pair of contradictories consists of two propositions
such as 'John is blue' and 'John is not blue', such that each
proposition is equivalent to the other's negation. That's
to say, that they can't be both of them true and they can't be
both of them false.
A pair of contraries consists of two propositions such
as 'John is blue' and 'John is quiet and not blue', such that each
proposition implies, without being implied by, the other's
negation. That's to say, that they can't be both of them
true, but they can be both of them false. Another example is 'We
have exactly five dogs' and 'We have exactly four dogs'.
A pair of subcontraries consists of two propositions
such as 'John is not blue' and 'John is blue or not quiet', such
that each proposition is implied by, without implying, the
other's negation. That's to say, that they can both of
them true, but they can't be both of them false.
A pair of subalterns consists of two propositions such
as 'John is blue' and 'John is blue or quiet', such that each
proposition neither implies, nor is implied, by the other's
negation. That's to say, that they can both of them be
true, and they can both of them be false. Any contingent
proposition is subaltern with itself, that is, 'John is blue'
and 'John is blue' are equivalents and subalterns of each other.
Formally true propositions are equivalent and subcontrary to
each other. Formally false propositions are equivalent and
contrary to each other. No propositions are each the other's
equivalent and contradictory.
In the Boolean Square of Opposition, A & E are each other's
subalterns. Likewise I & O.
Subalterns used to be distinguished from superalterns but
that's in the old terminology.
I won't provide references, look at 20th-Century logic text
books.
Best, Ben
On 1/17/2015 3:10 PM, Jerry LR Chandler wrote:
List, Ben:
On Jan 17, 2015, at 12:16 PM, Benjamin Udell wrote:
Jerry,
But your 'S is P' & 'S is not P' are
contradictories, not contraries; they can't both be
true and can't both be false.
'The dogs are four' and 'the dogs are five' are
contraries: they can't both be true but can both be
false.
No idea about what your meaning is intended to confer, either
to pragmatism or logic.
First, let me make clear for I was using the term
"contrary".
The distinction between contraries and contradictories are
clearly and distinctly presented in the Sanford Encyclopedia
of Philosophy:
http://plato.stanford.edu/entries/square/
from which one reads:
A
Every S is P
Universal
Affirmative
E
No S is P
Universal
Negative
I
Some S is P
Particular
Affirmative
O
Some S is not P
Particular
Negative
and :
‘Every S is P’ and ‘Some S is not P’ are contradictories.
‘No S is P’ and ‘Some S is P’ are contradictories.
‘Every S is P’ and ‘No S is P’ are contraries.
‘Some S is P’ and ‘Some S is not P’ are subcontraries.
‘Some S is P’ is a subaltern of
‘Every S is P’.
‘Some S is not P’ is a subaltern of
‘No S is P’.
and which shows a clear diagram
illustrating the difference between contraries and
contradictories.
'The dogs are four' and 'the dogs are five' are
contraries: they can't both be true but can both
be false.
This sentence, from either a logical or
mathematical sense, does not mean to me.
Are you certain you intended to use the word
"the" in this context?
The two phrases as in quotation marks which
suggests that you may intend to independent
concepts.
Your two phrases are contrary if and only if
the phrases refer to the same sign for the set of
dogs you have in mind.
Your response illustrates very nicely the point
of my original post. :-)
Cheers
Jerry
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