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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