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- Sep 22, 2007In a message dated 21/09/07 6:40:57 AM Mountain Daylight Time, pluviosilla@... writes:
KEVIN (asked):
JOHN (replied): Right. I recognize that mathematicians and logicians probably never talk about the “degree” of completeness. But as a practical matter in everyday speech we make all kinds of compromises w.r.t. consistency in order to increase the descriptive power of our utterances. Think of the classic paradoxes that so exercised Bertrand Russell, et al, such as:> Is "completeness" a matter of "degree"?
“This sentence is false.”
The sentence can’t be true, because if it is, then it must be false. But neither can it be false, because if it is, then it must be true. But you simply cannot avoid this kind of paradox the minute you allow the sentence to refer to itself, and I don’t *want* to be restricted in that way.
For instance, these are perfectly good & meaningful sentences:
“This sentence has a subject and a predicate.”
“This sentence parses easily and has an intransitive verb.”
We cannot even purify philosophical language, much less everyday language of self-reference
REPLY:
I have no idea what the above has to do with Akrasia, consent or concupiscence. I recall asking 3 questions, in order to get an idea of what your debate on "akrasia" was about, after reading a recommmended article on freedom and will. My questions were, let me recall:-
1) What is the relationship between "self reference" consistency and completeness?
(2) Why must you "sacrifice consistency" to obtain a "degree" of "completeness"?
(3) Is "completeness" a matter of "degree"?
Your answer was "RIGHT!" to either those 3 questions or, more likely, the 3rd question:- (3) Is completeness a matter of "degree"?
My point was arguably that things are either complete or incomplete which is a substantial difference, rather than a matter of degree, as in good, better, best or their contraries bad, worse and worst (the worst possible). So "Right" seems to be an arguably ambiguous answer. ie. "Right! Completeness is a matter of degree." or did you mean "Right! Completeness is NOT a matter of degree.", which seems to be derivable from your following sentence, requote:
JOHN:
I recognize that mathematicians and logicians probably never talk about the “degree” of completeness.
ANALYSIS:
...which may imply:- Right! Logicians and mathematicians don't talk about a "degree" of completeness, because "completeness" is NOT a matter of "degree" (at least to mathematicians and logicians).
MAYBE? Then again, MAYBE NOT?
Whatever! At any rate, I learned what you meant by "self-reference", which doesn't seem to mean a reference to yourself or "oneself" in general, but rather it appears to be about sentences which refer to "themselves". I told you that the post-Kantian generation likes to talk about attributes which are independent of substances. Any sentence which refers to itself is a good example of such Kantian stuff. In sum, and rhetorically:- Do sentences utter sentences about themselves?
However, I do like any reference to "Uncle Bertie Russell", as I think of him. He is one of the few mathematical philosophers who makes jokes about philosophy and he could get anybody "to think" about philosophy. A very amusing guy. But he had a weakness. He once thought that the Ontological Argument was "sound". I don't know when or if he actually changed his mind. He probably did; perhaps because of the "paradox" you mention above. I know almost nothing of the paradoxes for which he was "philosophically famous". I have merely heard that he was famous for them.
JOHN:
But as a practical matter in everyday speech we make all kinds of compromises w.r.t. consistency in order to increase the descriptive power of our utterances. Think of the classic paradoxes that so exercised Bertrand Russell, et al, such as:
“This sentence is false.”
REPLY:
I have thought about such sentences, but not for very long. They are simply "paradoxes" of "true falsehoods", or "false truths", or as the movie mentioned [Arnold Schwarzenegger (spelling) and my favorite comedienne Eddie Fisher's daughter; can't remember her name; One of her first movies was the horror film about "Michael" in a hockey mask? Friday The 13th?] "True Lies" or something to that effect.
The reason that such sentences "exercized" Uncle Bertie's thought was, arguably, because he didn't make the distinctions between what the medievals and Aristotle called (1) material supposition, (2) real supposition and (3) logical supposition.
I think that Uncle Bertie may have been trying to give the "Coherence Theory of Truth" (Consistency Theory of Truth?) gang a hard time, with his paradoxes. But I'm never sure with him because I doubt everything he says --- on principle. Truth and falsehood belong to the intellect and, hence, concern LOGICAL SUPPOSITION.
But grammatical propositions can deal with the materials out of which grammar is constructed, or real things, or logical things. So in your example we have a shift from either (1) grammatical/material supposition or, alternatively, (2) real supposition to (3) logical supposition in one proposition. This sentence, as a grammatical subject appears to be in real supposition. Its predicate, "...is false." is in logical supposition. Anyone who ever, even once, thought that the Ontological Argument is sound, missed the distinction between logical supposition and real supposition. Whether or not he, in this case Bertrand Russell, eventually learned the distinction is an open question.
Aristotle talks about the descriptor (quantifier?) "this" being a source of fallacious arguments in his logical work Sophistical Refutations (ie. the bogus "refutations" of sophists), although I fail to recall exactly what fallacies occur in "this" propositions. Admittedly it is difficult to think of a single proposition constituting a fallacious argument. But consider other similar propositions such as "This sentence is green." or "This sentence is 3 feet long." or "This sentence is 4 years old."
If the first sentence was typed in green letters, it could be considered both green and a true proposition. If the second sentence was written in large letters and accurately spaced across a bill board, it could, then, be truly described as "3 feet long". And on Sept. 22nd, 2011, I suppose it might be true to say that the 3rd parallel example to your or Russell's paradox ("This sentence is false.") could be considered true in 4 years, but false until Sept. 22nd, 2011.
Aristotle certainly knew more about fallacies than most moderns, as did Aquinas. Aristotle's logical teaching was that only propositions have truth or falsity in them, and propositions symbolize truth or falsity in men's souls, or minds, according to modern teachers. He further taught that every simple proposition has one simple contradictory proposition as its logical opposite. So the contradictory proposition to your "paradox" should be "This sentence is not false." vs. "This sentence is false."
Aristotle teaches that if you choose one of a pair of contradictory propositions to be true or false (your choice) then its contradictory proposition has the opposite truth (or falshood) value. Simple enough. And he finally teaches that propositions have no power to admit contrary qualities (eg. truth vs. falsehood) because propositions have neither the power nor the potential to change. Quote
ARISTOTLE:
If, then, a man should make this exception and contend that statements and opinions are capable of admitting contrary qualities, his contention is unsound. For statements and opinions are said to have this capacity, not because they themselves undergo modification, but because this modification occurs in the case of something else (than the sentence KB). "The truth or falsity of a statement depends on facts and not on any power on the part of the statement itself of admitting contrary qualities. In short there is nothing which can alter the nature of statements and opinions. As, then, no change takes place in themselves, these cannot be said to be capable of admitting contrary qualities."(Aristotle The Categories; Ch. 5.)
The sentence can’t be true, because if it is, then it must be false. But neither can it be false, because if it is, then it must be true. But you simply cannot avoid this kind of paradox the minute you allow the sentence to refer to itself, and I don’t *want* to be restricted in that way.
Aquinas makes the same point, citing this section of Aristotle's Categories, when discussing Truth at Summa I, Q. 16., Article 1, Reply Obj. 3. Below we have you, John, thinking your way through the proposition,"This sentence is false.", and considering what "follows" from the above proposition admitting contrary qualities (truth vs. falsehood) in itself, or "self referentially", to use your terms, quote
JOHN:
REPLY:
There you go, thinking about the opposite consequences of 1 sentence admitting contrary qualities (truth vs. falsehood) in itself. Neither Aristotle nor Aquinas want you to be "restricted" by unsound contentions, either, which is why Aristotle wrote LOGIC treatises and Aquinas quoted Aristotle.
JOHN:
For instance, these are perfectly good & meaningful sentences:
“This sentence has a subject and a predicate.”
“This sentence parses easily and has an intransitive verb.”
[N.B. Now you seem to be arguing the opposite case. KB]
JOHN:
We cannot even purify philosophical language, much less everyday language of self-reference.
REPLY:
"Philosophical language", which is always annexed closely to the art of sophistry, isn't all that "pure". Everyday language was fine for Socrates and should be for most actual philosophers, for, as Plato says, philosophy is not "high and mighty". As to the mention of "self reference" with respect to sentences, the terms "contentious and unsound" were mentioned by Aristotle, who was an excellent logician. Hence it is reasonably arguable that "self reference" in propositions should be avoided, if we want to "purify" ouselves of contentious and unsound arguments.
"Self referential" propositions, as you have now explained them, John, are not very common at all, in everyday speech. And your perfectly good "self referential" sentences, above, could be phrased more objectively with the same meanings.
Kevin