The principle of non-contradiction.: Philosophy Forums

Philosophy Forums » Logic and Philosophy of Math » The principle of non-contradiction. » The principle of non-contradiction.

The principle of non-contradiction.
What if (P & ~P) is true?

Page: 1 2 3 4

The principle of non-contradiction.

Banno
Old goat

Usergroup: Sponsors
Joined: Aug 15, 2004
Location: Oz

Total Topics: 111
Total Posts: 6303

Posted 07/29/09 - 02:54 PM:	#11
Can you construct a useful language without the principle? What would you put in place of coherence? i must admit, I have not read your links...
Davidson: We make maximum sense of the words and thoughts of others when we interpret in a way that optimizes agreement. Russel Morris: There's a meaning there, but the meaning there doesn't really mean a thing... Ned: Such is life

xzJoel
Bio-clump

Usergroup: Sponsors
Joined: Aug 30, 2005
Location: New Jersey

Total Topics: 32
Total Posts: 843

Posted 07/29/09 - 03:19 PM:	#12
Construct in what way? I can certainly use a language without it, but I doubt a linguist or logician would be a fan of it. Take any assertion about a state of being (rather than existence) such as "Aflak is a coward." On occasion 1, I observe Aflak displaying cowardice. On occasion 2, I observe Aflak displaying bravery. (Take brave to be not a coward.) Now you ask me about, "Hey J, is Aflak a coward?" I respond, "He both is and is not a coward." You say, "Huh?" I explain my observations to you. Was my statement, "He both is and is not a coward" false? ___________ Consider your grey rock. When the lights are on, it is grey. When off, it is not. Now what color is the rock? Is it fair to say, "The rock is both grey and not grey?" Suppose I allege that "color" is a qualia (for whatever that is) and that a blind man does not experience the greyness of the rock. Does that complicate the question? It is grey to you but not grey to him. Linguistically we can try to work around this by trying to be ever more precise in our language, but we end up having to freeze time or specify and be able to speak of discrete moments in order to avoid the problem of the law of contradiction not permitting "the same thing to be both true and not true in the same way at the same time." Don't we end up running ourselves into situations that are fundamentally at odds with how we relate to reality? Don't we end up contorting language to fit our logical structures rather than having our logical structures make sense of our language? While these are quick and seemingly detached thoughts, can’t you envision examples in your own life where it would be perfectly sensible to assert both P & ~P? I am full, but I am still hungry. I hate you, but I love you. The test was hard and not hard. Edited by xzJoel on 08/28/09 - 04:52 AM
Make a joyous noise onto the lord... Not a good one, just a joyous one.

Cadrache
Tenured Poster

Usergroup: Members
Joined: Dec 09, 2006
Location: AB, Canada

Total Topics: 104
Total Posts: 2644

Posted 07/29/09 - 03:24 PM:	#13
I normally forget to look at the "to do" list. Soo much lazier then remembering everything... Quick question; is it possible that some contradictions lie on different um... paths(?) Sort of like Reinmann's system; but you have two membranes. PQ therefore R as an example; with PQ on one membrane and R on the other. To get to PQ therefore R, you must follow a specific function. The contradiction of said function however may not use a form that is equivalently an inverse ratio.
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

brainpharte
Huh?

Usergroup: Members
Joined: Jan 07, 2009

Total Topics: 7
Total Posts: 968

Posted 07/29/09 - 05:01 PM:	#14
xzJoel wrote: Take any assertion about a state of being (rather than existence) such as "Aflak is a coward." On occasion 1, you observe Aflak displaying cowardice. On occasion 2, you observe Aflak displaying bravery. (Take brave to be not a coward.) Now you ask me about, "Hey J, is Aflak a coward?" I respond, "He both is and is not a coward." You say, "Huh?" I explain my observations to you. Was my statement, "He both is and is not a coward" false? But this does not violate LNC because LNC stipulates that the statement refer to the same time (and same sense). A given predicate applies to the referent at one time but not at another, or applies in one sense but not in another. Attributes need not be permanent or "essential" or even defining properties of the referent. Consider your grey rock. When the lights are on, it is grey. When off, it is not. Now what color is the rock? Is it fair to say, "The rock is both grey and not grey?" Again this violates the "at the same time and sense" stipulation. The rock appears grey at one time and under one set of conditions, but not-grey at a different time and under different conditions. Linguistically we can try to work around this by trying to be ever more precise in our language, but we end up having to freeze time or specify and be able to speak of discrete moments in order to avoid the problem of the law of contradiction not permitting "the same thing to be both true and not true in the same way at the same time." Yes, we can resolve much of our self-confusions by being more precise and clarifying ambiguities caused by sloppy conflation of different times (and referents and senses.) While these are quick and seemingly detached thoughts, can’t you envision examples in your own life where it would be perfectly sensible to assert both P & ~P? I am full, but I am still hungry. I hate you, but I love you. The test was hard and not hard. Full does not necessarily mean not-hungry, so this does not violate LNC. (It takes the metabolic processes several minutes to inform the brain that it can turn off the hunger neurons, while the more tactile feeling of a full stomach is more quickly sensed.) "I hate you" here is not an exhaustive judgment. A clearer statement is probably something such as "I hate some things about you but I love many other things about you." This does not violate LNC. The test was hard in some ways or on some questions, but not hard in other ways or on some questions. This does not violate LNC. When LNC seems to be violated, it's usually because the time or sense stipulations haven't been met. SOmetimes LNC seems to be violated when there actuallly are ambivalent referents.
"I don't see much sense in that," said Rabbit. "No," said Pooh humbly, "there isn't. But there was going to be when I began it. It's just that something happened to it along the way."

Banno
Old goat

Usergroup: Sponsors
Joined: Aug 15, 2004
Location: Oz

Total Topics: 111
Total Posts: 6303

Posted 07/29/09 - 05:25 PM:	#15
I read somewhere ( )that we can have either completeness or consistence but not both. Give me consistency before completeness. Contradictions are markers telling you that you have not got the story right yet. Keep working on it.
Davidson: We make maximum sense of the words and thoughts of others when we interpret in a way that optimizes agreement. Russel Morris: There's a meaning there, but the meaning there doesn't really mean a thing... Ned: Such is life

xzJoel
Bio-clump

Usergroup: Sponsors
Joined: Aug 30, 2005
Location: New Jersey

Total Topics: 32
Total Posts: 843

Posted 07/29/09 - 06:38 PM:	#16
brainpharte wrote: But this does not violate LNC because LNC stipulates that the statement refer to the same time (and same sense). A given predicate applies to the referent at one time but not at another, or applies in one sense but not in another. Attributes need not be permanent or "essential" or even defining properties of the referent. Again this violates the "at the same time and sense" stipulation. The rock appears grey at one time and under one set of conditions, but not-grey at a different time and under different conditions. Yes, we can resolve much of our self-confusions by being more precise and clarifying ambiguities caused by sloppy conflation of different times (and referents and senses.) Full does not necessarily mean not-hungry, so this does not violate LNC. (It takes the metabolic processes several minutes to inform the brain that it can turn off the hunger neurons, while the more tactile feeling of a full stomach is more quickly sensed.) "I hate you" here is not an exhaustive judgment. A clearer statement is probably something such as "I hate some things about you but I love many other things about you." This does not violate LNC. The test was hard in some ways or on some questions, but not hard in other ways or on some questions. This does not violate LNC. When LNC seems to be violated, it's usually because the time or sense stipulations haven't been met. SOmetimes LNC seems to be violated when there actuallly are ambivalent referents. These were such somewhat intuitive examples of when linguistically we would find it useful, efficient, and accurate to assert something that violates the LNC. You can, as I said, attempt to be increasingly specific in your descriptions so as to satisfy the LNC, but that doesn't mean the proper description is any more useful than the violating description. Frankly, the LNC is violated by the liar's paradox pretty unequivocally. To say that a statement that asserts both itself and its opposite is false does not pass intellectual muster. If need be, you can resort to the strengthened liar's paradox in order to more firmly convince yourself that the LNC is inadequate. A: This statement is false. B: A is false or neither true nor false. The strengthened liar's paradox is to address a person who is willing to say that the law of bivalance does not hold. The only question is, are there dialethia that are useful beyond frustrating classical logic? The reason that I posted the links was to avoid reexplaining that which Stanford did a pretty good job at explaining. There are several modern justifications for the desire to abandon the absolute application of the LNC. To the extent that you are concerned with the phenomena of explosion (anything follows from a contradiction), there are paraconsistent logics to deal with this problem.
Make a joyous noise onto the lord... Not a good one, just a joyous one.

Incision
Professor

Usergroup: Administrators
Joined: Jan 04, 2008
Location: Utah

Total Topics: 23
Total Posts: 906

Posted 07/29/09 - 09:07 PM:	#17
xzJoel wrote: Was my statement, "He both is and is not a coward" false? Yes, even without qualifying the statement or the LNC. Notice that English statements in the simple present tense usually express permanent, general truths. So if you say "he is a coward," I'd take you to mean "he consistently shows cowardice," which his behavior on occasion 2 falsifies. We should describe him therefore neither as cowardly nor as courageous, but as vacillating. Is it fair to say, "The rock is both grey and not grey?" Again, I don't think so. You'd normally say that a rock is gray if it looks gray to normally-sighted people on normal occasions. The test was hard and not hard. Surely this can't be defended on grounds of perspicuity. Even if true, it would take no more time and would be clearer and more informative to say, "Question 3 was hard, but 14 wasn't." So embracing contradiction here will not facilitate communication.

xzJoel
Bio-clump

Usergroup: Sponsors
Joined: Aug 30, 2005
Location: New Jersey

Total Topics: 32
Total Posts: 843

Posted 07/31/09 - 10:29 AM:	#18
Cadrache wrote: I normally forget to look at the "to do" list. Soo much lazier then remembering everything... Quick question; is it possible that some contradictions lie on different um... paths(?) Sort of like Reinmann's system; but you have two membranes. PQ therefore R as an example; with PQ on one membrane and R on the other. To get to PQ therefore R, you must follow a specific function. The contradiction of said function however may not use a form that is equivalently an inverse ratio. I tried to find out what you are talking about, but I think it has something to do with Bernhard Reimann and Reimann surfaces, but I don't know enough about it to comfortably discuss it. Maybe if you point me in the right direction, I can read up on it and see if I can learn enough to form an opinion. http://en.wikipedia.org/wiki/Bernhard_Riemann http://en.wikipedia.org/wiki/Riemann_surface
Make a joyous noise onto the lord... Not a good one, just a joyous one.

xzJoel
Bio-clump

Usergroup: Sponsors
Joined: Aug 30, 2005
Location: New Jersey

Total Topics: 32
Total Posts: 843

Posted 07/31/09 - 11:00 AM:	#19
Incision wrote: Yes, even without qualifying the statement or the LNC. Notice that English statements in the simple present tense usually express permanent, general truths. So if you say "he is a coward," I'd take you to mean "he consistently shows cowardice," which his behavior on occasion 2 falsifies. We should describe him therefore neither as cowardly nor as courageous, but as vacillating. Again, I don't think so. You'd normally say that a rock is gray if it looks gray to normally-sighted people on normal occasions. Surely this can't be defended on grounds of perspicuity. Even if true, it would take no more time and would be clearer and more informative to say, "Question 3 was hard, but 14 wasn't." So embracing contradiction here will not facilitate communication. The first sentence is a matter of interpretation. Cowardice is enduring. If you are a coward once, you are a coward always. To say someone is a coward is not say what they will do, but to make a statement about their essence. In the same way, if you are not a coward, you are not a coward always. It is something essential. Now we get to a problem, two different enduring states are displayed by two discrete acts. You want to say that acting one way one time and another way another time indicates that a person is neither a coward nor a non-coward. You have just abandoned the rule of bivalence. Are you comfortable giving up the rule of bivalence? Perhaps what you are suggesting is that people do not have an essential nature? In more concrete terms, we have equal evidence for contradictory positions. Does the presence of evidence that someone is P negate evidence that he is ~P? If we have sufficient evidence to reasonably believe that a person is P, does that negate our equally sufficient evidence that he is ~P? Which belief becomes unreasonable? The belief for or against? I think you commit the same sort of error with the grey rock. To say the rock is grey is to comment on the nature of the rock. Nature is not relative, it is absolute. Rather than deal with the problem of essential nature, you sidestep the issue and speak of the subjective nature of the rock’s essence. Again, assuming that we can trust the report of the sited man and the blind man, we have equal evidence for the rock’s greyness and non-greyness. Why should we be afraid to assert that it is both grey and not grey? These issues highlight two different aspects of the LNC – the ontic nature and the epistemic. I think, perhaps, we should address the epistemic nature of the LNC prior to attacking the ontic nature if only because people are less willing to accept that something can both be and not be simultaneously. A random example comes to mind – blame it on process philosophy and non-referential indexicals. Let’s say that it is raining here. Let’s say that it is not raining over there. What do you make of the sentence, “It is and is not raining?” As to the hardness issue, I know you don’t intend to simplify for the purpose of being right, but come on, is that really how you took my sentence? That two discrete problems were of different difficulty? Pretend for a moment that a test had 200 questions, each question with various steps. Each problem was of mixed difficulty and each section of the test was of mixed difficulty. Now your mother asks you how the test was? You: “It was and wasn’t hard.” Mother: Dear, that violates the LNC, that statement is false. Do you mean some of the sections of the test were hard and some weren’t? Y: No. That isn’t quite what I mean. Each of the sections were both hard and not hard. M: You are making no sense, how can a section be hard and not hard? It is only one or the other, not both. Perhaps you mean each of the sections had some hard questions and some not hard questions? Y: No, that isn’t it either. While there were sections, the questions themselves were both hard and not hard. M: Dear, I’ve already reminded you twice about the LNC, you are trying my patience. Surely the questions themselves must have been hard or not, but not both! Y: I wish it were so mother, but that isn’t true either. I am trying to be direct, but even the questions were composed of steps and each of the steps were both hard and not hard! M: Perhaps we should start from the beginning. I asked you how the test was, isn’t there a generalized description that uses the word “hard” and that is true or false, but not both? Y: No. M: Boy, didn’t I ever teach to generalize? Y: You both did and didn’t! M: I’ll tell you, son, I rue the day I taught you the word "ambivalent." Tell me, where in that story do you think you actually added something useful to the conversation by being more specific? Do you honestly believe that your mother wouldn't have understood you when you said that the test was both hard and not hard?
Make a joyous noise onto the lord... Not a good one, just a joyous one.

Incision
Professor

Usergroup: Administrators
Joined: Jan 04, 2008
Location: Utah

Total Topics: 23
Total Posts: 906

Posted 07/31/09 - 02:10 PM:	#20
It may just come down to competing intuitions, but I'll try to defend myself. First, your account of cowardice doesn't seem to match your own usage. You said, "If you are a coward once, you are a coward always." And your remark You want to say that acting one way one time and another way another time indicates that a person is neither a coward nor a non-coward. suggests you view "cowardly" and "courageous" as exhaustive. But if that's true, then someone must be courageous just in case they've never committed a cowardly act. And then there's no reason to find Aflak courageous. After all, we only specified that he committed one noncowardly act, not a lifetime. To explain what I think cowardice is, notice that some things are enduring (being a murderer), but some things aren't (being a liar). I think being a liar is not enduring because almost everyone has lied once, so, if it were enduring, calling people liars would be unhelpful. Likewise, I think being a coward is not enduring because almost everyone has behaved cowardly once, so, if it were enduring, calling people cowards would be unhelpful. Also, Aristotle says that a vice is a habit of choosing the mean between two extremes, and cowardice is a vice. Consequently, I think that someone is courageous if they habitually show courage, and vice versa. Courage and cowardice form contraries but not contradictories: you can be indifferent, if, like me, you never have much opportunity to show either, or vacillating, if you show them both. As for the rock, I think I've been misinterpreted. On my account, we don't have equal evidence for grayness and nongrayness. The rock is gray if normally-sighted people under normal conditions perceive it as gray; this is not a relativistic definition, since it's an absolute truth that normally-sighted people under normal conditions perceive it as gray. If the blind man doesn't see it as gray, that doesn't matter. He's not normally sighted. And yes, I actually did assume you were imagining a test with different questions of different difficulty. Honestly, I wasn't sure at first what to make of "hard and not hard"; brainpharte's interpretation didn't meet with protest so I assumed it was accurate. Now I frankly have no idea what you mean -- perhaps I have an unusual fetish for consistency, as I myself would never describe a test as hard and not hard. However, maybe that isn't true of everything. If I remember, Priest in Doubt Truth to be a Liar suggests that our perceptions of some optical illusions might best be described in contradictory terms. What about this one? Edited by Incision on 07/31/09 - 05:52 PM

Page: 1 2 3 4

Sorry, you don't have permission to post. Log in, or register if you haven't yet.