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

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The principle of non-contradiction.
Doug Shaver
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Posted 08/03/09 - 05:54 AM:
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#21
xzJoel wrote:
Was my statement, "He both is and is not a coward" false?


Without LNC, I don't have the foggiest notion what that question even means.
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Posted 08/03/09 - 12:01 PM:
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#22
Well, with truth tables, it is easy to see that the truth and falsity of a statement depends on the number of variables taken into account. Thus, whence we tackle one variable, true is true; and once we tackle two variables, what had formerly been true has been been split- leaving another tautology of 'true' and a new proposition.

Curiously, the adding of variables can be extended for quite some time, leaving me only able to argue or agree, but never set my thoughts in stone.

And thus, the principle of non-contradiction only holds within a framework; As I cast off the framework, its use notes that all frameworks have contradictions- and nothing leads one closer to the unutterable truth than the recognition of these contradictions- for they form a pattern.

One might say "he is courageous" and another might say "he is fool-hearty", but these are mere names. He is known by what he does; he is known by his works. And he might come to know himself that way, too.

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realistcat
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Posted 08/26/09 - 09:20 PM:
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#23
in the case of Aflak and his cowardice on certain occasions and courageousness on others, you'll notice that the issue seems to come down to whether these are contraries that exclude each other. It's true that courageousness and cowardice are usually interpreted in some sort of dispositional sense. I don't want to take a position on whether "He is cowardly and he is courageous" is inconsistent. As I say, it depends on whether you think of them as contraries.

But, in that case, notice a very pervasive feature of our world. Properties tend to be organized into contraries that exclude each other. So, this is true of weights, colors, lengths, pitch of a sound, age.

And if we think of simple subject/predicate sentences of the form

F(A) or "A Fs"

the predicate often tracks some property that falls into a range that has contraries. We might even use this idea to hold that "not" can be interpreted as a kind of disjunction:

A is not F iff A is either G or H or I or J...
where we have a list of the contraries that would exclude F.

Thus we might say that the LNC is so entrenched because of this pervasive feature of our world. It's hard for us to think of things being otherwise.

But if this is the real basis of the LNC, then it's not clear that it is some sort of apriori necessity, but more like an extremely well entrenched hypothesis.
\
xzJoel
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Posted 08/27/09 - 05:54 AM:
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#24
realistcat wrote:
in the case of Aflak and his cowardice on certain occasions and courageousness on others, you'll notice that the issue seems to come down to whether these are contraries that exclude each other. It's true that courageousness and cowardice are usually interpreted in some sort of dispositional sense. I don't want to take a position on whether "He is cowardly and he is courageous" is inconsistent. As I say, it depends on whether you think of them as contraries.

But, in that case, notice a very pervasive feature of our world. Properties tend to be organized into contraries that exclude each other. So, this is true of weights, colors, lengths, pitch of a sound, age.

And if we think of simple subject/predicate sentences of the form

F(A) or "A Fs"

the predicate often tracks some property that falls into a range that has contraries. We might even use this idea to hold that "not" can be interpreted as a kind of disjunction:

A is not F iff A is either G or H or I or J...
where we have a list of the contraries that would exclude F.

Thus we might say that the LNC is so entrenched because of this pervasive feature of our world. It's hard for us to think of things being otherwise.

But if this is the real basis of the LNC, then it's not clear that it is some sort of apriori necessity, but more like an extremely well entrenched hypothesis.
\


I am not dwelling too long on the Aflak story for all of the reasons that people have mentioned. My general point of the story is that there are reasons to utter dialethia with the assertion that they are true. Even if on further analysis the “is” and the “is not” of the dialethia can be shown to refer to different things, the structure of the sentence as expressed is contradictory. I argued that sometimes it is useful to make contradictory statements, especially when people are asking you to summarize a variety of feelings/impressions/descriptions into one predicate.

This is only tangentially to your point, but it reminds me of one of the examples from the Stanford article.

"He both is and is not a bachelor." In as much as something true is said, the argument will be leveled that "bachelor" is relational and that the "is" refers to one sense of the word and "is not" refers to another. Any non-physical description is subject to the same sorts of objections, i.e. that the words are not precise enough to exclude a variety of meanings such that there isn't some sense in which any particular category both is and is not true.

I mention this because you speak in terms of contraries of properties. Properties are, to my imagination, mere mental constructs that have no relationship to what is actually happening. On a fundamental level (and yes, I'm going atomistic here) we have particles and spatiotemporal relationships. The way in which a particle both is and is not in a place at the same time is of great moment to me, but whether our language/conceptions is/are sufficiently precise such that the use of a word successfully excludes all contraries is of less importance.

I do agree with you that the LNC is a well entrenched hypothesis. People are wholly committed to logic as consistency. Since people want so desperately for the world to be logical, they can't concede the point that the world is illogical/inconsitent. I think it would be more profitable to recognize a logic that more accurately reflects the world than it does our preference.

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Posted 08/27/09 - 10:02 AM:
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#25
"I mention this because you speak in terms of contraries of properties. Properties are, to my imagination, mere mental constructs that have no relationship to what is actually happening. On a fundamental level (and yes, I'm going atomistic here) we have particles and spatiotemporal relationships."

If predicates don't track properties, what do they do, what is their function? You also mention "spatiotemporal relationships" -- relations are properties.

Language is a biological function of humans. It's likely that it has an evolutionary explanation. What is it about it that makes it adaptive for humans? If we think of hunter-gatherer bands and someone coming back and telling them about an area where there is a food source, or warning of a dangerous large predator, we can see here how description of states of affairs in the world would be highly useful for survival. This means that the facts they conveyed had to be accessible to them...they didn't know about particles and all that.

Why do all human languages have a subject/predicate structure to the descriptive sentences? Again, if we assume that the predidates track properties in the world, then we have an acount of what the function of a sentence is...it is to convey that something A has some property P. So "truth" means it serves its function, "false" means it fails to serve the function of a descriptive sentence, it is defective that way.

Properties can't be "reduced" to particular entities. If there were only particular entities there'd be no facts, no states of affairs that obtain, and nothing for sentences to convey.
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Posted 08/27/09 - 11:28 AM:
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#26
realistcat wrote:
"I mention this because you speak in terms of contraries of properties. Properties are, to my imagination, mere mental constructs that have no relationship to what is actually happening. On a fundamental level (and yes, I'm going atomistic here) we have particles and spatiotemporal relationships."

If predicates don't track properties, what do they do, what is their function? You also mention "spatiotemporal relationships" -- relations are properties.

Language is a biological function of humans. It's likely that it has an evolutionary explanation. What is it about it that makes it adaptive for humans? If we think of hunter-gatherer bands and someone coming back and telling them about an area where there is a food source, or warning of a dangerous large predator, we can see here how description of states of affairs in the world would be highly useful for survival. This means that the facts they conveyed had to be accessible to them...they didn't know about particles and all that.

Why do all human languages have a subject/predicate structure to the descriptive sentences? Again, if we assume that the predidates track properties in the world, then we have an acount of what the function of a sentence is...it is to convey that something A has some property P. So "truth" means it serves its function, "false" means it fails to serve the function of a descriptive sentence, it is defective that way.

Properties can't be "reduced" to particular entities. If there were only particular entities there'd be no facts, no states of affairs that obtain, and nothing for sentences to convey.



I can't respond to the idea of what a particle is and what a property is without going vastly off topic and doing a lot more typing. I will try to focus on the relationship of language to facts.


I think facts are limited to no more than particles and their location in space and time. Language is artifice - that is to say that language conveys only mental constructs that we impose upon facts. There are no actual facts that language reports on, rather language is a convenient way of generalizing massive amounts of information about individual, unknowable particles. "A cat jumps" is something useful, certainly, but is wholly outside of the realm of reporting what is factual.


Let me try to put it in a specific way, if I write, "I am typing.", I communicate nothing about existence. The subject "I" is indeterminate and the verbal phrase "am typing" refers to a whole class of actions, no particular one of which is specified. You may have an idea about what is going on conceptually, but you know nothing about what actually exists - you know nothing about an individual particle. I may have communicated effectively, but it isn't because I told you anything specific about a fact of the world.


I would argue that language is pragmatic; that it does what works - for whatever that means.


In this context, I allow for people to wiggle out of apparent contradictions by arguing that when a sentence asserts both P and ~P, that to the extent the sentence is true, it is only because there are different senses of P intended in its assertion and in its denial. This type of linguistic avoidance of contradictions is warranted for, after all, language is something that can be construed any way the participants like.


When we are discussing existence (that is, is it possible for something to both exist and not exist in the same way at the same time?), games of language will not resolve the underlying question. We must directly compare our logic to our world and see if the rules match the reality.


In my mind, the idea of motion is precisely this problem. As to any moment, t1, what is the state of a particle? Does it exist at a specifiable location? If there is no moment at which you can specify its location, does it exist at all? If you can specify its location at t1, how can it have momentum/velocity? Cf. Heisenberg Uncertainty Principal and Zeno’s paradox of the arrow.


I realize that our concepts exist as features of language, so it is impossible to talk about existence as if we are free of the constraints of our language, but pretend as if we can. Putting language aside, is it ontically the case that a particle both exists and not exists at the same time?


If ontologically it appears necessary to conceive of something both being and not being, shouldn’t we have a logic that permits us to work with the world as it appears? Shouldn’t we have a logic that permits at least some dialethia, even if it is only a dialethia related to an ontic claim? Don’t the ontic facts call for a logic that does not rigidly apply the LNC?


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Posted 08/27/09 - 11:57 AM:
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#27
quote:
"When we are discussing existence (that is, is it possible for something to both exist and not exist in the same way at the same time?), games of language will not resolve the underlying question. We must directly compare our logic to our world and see if the rules match the reality."

How do you compare "logic" (whatever that is) to "our world" (whatever that is)? What is a "match" with "reality"?

If I say "there are two cats on the sofa," it's clear from the context which sofa i'm referring to. You can observe that sofa and see if you detect two cats on it.

This is not difficult. In this case if I see the cats curled up on the sofa, i'm observing them, their fur, their shape on the sofa and their spatial relationship to the sofa, and the their twoness, that is, that there are two of them.

Now these are all properties I observe in the situation.

Elementary particles are not something we observe directly. What physicists do observe are their apparatuses in various experimental situations and so on...they are thus doing exactly what I'm doing when I observe the cats on the sofa. If I'm not observing facts, then neither are they. But their positing of particles occurs in the context of complex set of hypotheses whose function is to explain countless observations of the sorts I've just described.

If these observations do not observe properties of things, various facts about things, then there is no evidential base for the hypotheses of the physicists, and there would then be no reason to believe them.

YOU:
"In my mind, the idea of motion is precisely this problem. As to any moment, t1, what is the state of a particle? Does it exist at a specifiable location? If there is no moment at which you can specify its location, does it exist at all? If you can specify its location at t1, how can it have momentum/velocity? Cf. Heisenberg Uncertainty Principal and Zeno’s paradox of the arrow."

Motions and other states of particles are properties. There is no reason to believe these properties exist while colors and weights and meows of cats do not. One type of property is not "more real" than the other. Since the evidential force for the hypothesis that there are these particles is entirely based on observation of macro-level properties that humans are capable of observing, if the latter are not real neither are the former.

If you're talking about the collapse of the wave function, this has been one reason some people have questioned LNC. There are also interpretations that can get away from having to deny LNC. But if LNC is just an entrenched hypothesis, then this is consistent with saying that in certain spheres...such as at the very smallest micro level...it doesn't apply.

YOU:
"I realize that our concepts exist as features of language, so it is impossible to talk about existence as if we are free of the constraints of our language, but pretend as if we can. Putting language aside, is it ontically the case that a particle both exists and not exists at the same time?"

I don't think this is a question of our language but of our hypothesis about properties. The LNC may not hold in this case. But th LNC isn't about our language but about properties and things, and thus about obtaining of states of affairs. LNC says that S can't both obtain and not obtain. This is speaking in the ontological mode, that is, about what corresponds to sentences rather than talking about sentences.

YOU
"If ontologically it appears necessary to conceive of something both being and not being, shouldn’t we have a logic that permits us to work with the world as it appears? Shouldn’t we have a logic that permits at least some dialethia, even if it is only a dialethia related to an ontic claim? Don’t the ontic facts call for a logic that does not rigidly apply the LNC?"

I don't know what you mean by "ontic realm." Ontology refers to what there is. A person's ontology is said to be whatever they think there is. When we think that things exist and have properties, they are by that fact part of our ontology.
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Posted 08/27/09 - 12:45 PM:
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#28
realistcat wrote:
quote:
"When we are discussing existence (that is, is it possible for something to both exist and not exist in the same way at the same time?), games of language will not resolve the underlying question. We must directly compare our logic to our world and see if the rules match the reality."

How do you compare "logic" (whatever that is) to "our world" (whatever that is)? What is a "match" with "reality"?

If I say "there are two cats on the sofa," it's clear from the context which sofa i'm referring to. You can observe that sofa and see if you detect two cats on it.

This is not difficult. In this case if I see the cats curled up on the sofa, i'm observing them, their fur, their shape on the sofa and their spatial relationship to the sofa, and the their twoness, that is, that there are two of them.

Now these are all properties I observe in the situation.

Elementary particles are not something we observe directly. What physicists do observe are their apparatuses in various experimental situations and so on...they are thus doing exactly what I'm doing when I observe the cats on the sofa. If I'm not observing facts, then neither are they. But their positing of particles occurs in the context of complex set of hypotheses whose function is to explain countless observations of the sorts I've just described.

If these observations do not observe properties of things, various facts about things, then there is no evidential base for the hypotheses of the physicists, and there would then be no reason to believe them.

YOU:
"In my mind, the idea of motion is precisely this problem. As to any moment, t1, what is the state of a particle? Does it exist at a specifiable location? If there is no moment at which you can specify its location, does it exist at all? If you can specify its location at t1, how can it have momentum/velocity? Cf. Heisenberg Uncertainty Principal and Zeno’s paradox of the arrow."

Motions and other states of particles are properties. There is no reason to believe these properties exist while colors and weights and meows of cats do not. One type of property is not "more real" than the other. Since the evidential force for the hypothesis that there are these particles is entirely based on observation of macro-level properties that humans are capable of observing, if the latter are not real neither are the former.

If you're talking about the collapse of the wave function, this has been one reason some people have questioned LNC. There are also interpretations that can get away from having to deny LNC. But if LNC is just an entrenched hypothesis, then this is consistent with saying that in certain spheres...such as at the very smallest micro level...it doesn't apply.

YOU:
"I realize that our concepts exist as features of language, so it is impossible to talk about existence as if we are free of the constraints of our language, but pretend as if we can. Putting language aside, is it ontically the case that a particle both exists and not exists at the same time?"

I don't think this is a question of our language but of our hypothesis about properties. The LNC may not hold in this case. But th LNC isn't about our language but about properties and things, and thus about obtaining of states of affairs. LNC says that S can't both obtain and not obtain. This is speaking in the ontological mode, that is, about what corresponds to sentences rather than talking about sentences.

YOU
"If ontologically it appears necessary to conceive of something both being and not being, shouldn’t we have a logic that permits us to work with the world as it appears? Shouldn’t we have a logic that permits at least some dialethia, even if it is only a dialethia related to an ontic claim? Don’t the ontic facts call for a logic that does not rigidly apply the LNC?"

I don't know what you mean by "ontic realm." Ontology refers to what there is. A person's ontology is said to be whatever they think there is. When we think that things exist and have properties, they are by that fact part of our ontology.



You make many good points, many of which I agree with.


The reason I invoke Zeno is, in part, to deal with your macro/micro level points. Granted, particle physics is all indirect observation/inference compounded upon itself many times. I have no qualms with saying that that the genesis of our knowledge must be through something capable of effecting the human mind (that is something that we can perceive directly.) Everything outside of direct observation is conjecture.


When dealing with the arrow, we have the ability to speak of the situation logically and then compare our logic with our observations. In the case of the arrow, it seems logically/mathematically impossible for the arrow to move because, from Zeno’s perspective, an infinite series of “instants” wherein an arrow is at “rest” cannot be combined to create the phenomenon of motion. It follows that our rules of logic would not permit the observation of motion even though we actually observe motion, thereby being a paradox. Zeno’s problem is rooted, I think, in his implicit adoption of the LNC and the requirement that in a 0s instant, the arrow must only be where it is, it may not both be and not be where it is.


This sort of direct observation combined with logical theory is what I consider to be “matching”.



I will borrow from Stanford in the dialetheism article:


“Stanford” wrote:

An alternative, dialetheic account of motion, which takes at face value the aforementioned Hegelian idea that “Something moves, not because at one moment it is here and another there, but because at one and the same moment it is here and not here, because in this ‘here’, it at once is and is not”, is exposed in Priest, 1987, Ch. 12.



Granted, we can never observe an “instant” because we are in time, so a discussion of what *is* at time t1 is fundamentally unobservable, but theoretically, which logic provides a more satisfactory match to our observations? That the arrow never moves or that motion is a property of an object such that even when frozen in time, it is moving? That the arrow both is and is not located at a particular place in single instant?


I think our usage of ontology is a bit confused (which is most likely my fault.) When I want to speak of what is, I speak of the “ontic case”. This “is” is not a feature of ontology (what you suppose what “is” to be), but rather what it actually is. When I speak of “ontology”, I am speaking of our theories of what is. My conclusion was intended to focus on what our observations require of our ontology. If we “know” what the ontic case is, does it make sense to have an ontology that would force us to try and explain away our observations? (It isn’t really moving, rather motion is what we name a series of discrete moments wherein an identifiable object is in two different places in consecutive “frames” of reality.)


Please tell me if I am confusing the issue or clarifying it. If I am making no progress in making myself understood, I’d rather try a different approach instead of throwing more words at the problem.

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Posted 08/27/09 - 06:36 PM:
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#29
i still don't understand what you're trying to say. If it's a question of what "really exists", then it seems to me a criterion of this is anything that does anything or is needed to explain something or anything that actually occurs or has any causal powers.

We don't perceive an instant, which is infinitesimally small, but we do perceive things as occurring "now." We can take "now", at time of use, to designate a finite duration. In particular, to designate the time when we say or think "now". Thus the "interpretation" for "now", as an indexical, requires its referent to be determined by the time of use of the word.

Of course it is a true that a thing may be changing during that finite time designated by "now." In practice "A is F" is taken to be true if A has property F at some time during that duration or througout that duration, depending on how reference to time is interpreted in that case. In a number of non-Indo-European languages (such as Chinese) verbs do not pack in a reference to time. You need a separate temporal adverb for this purpose.

Thus if it's a question of something's location "now", and that thing is moving, we could interpret the reference to location as incorporating the entire area occupied by it throughout that time. So if it's moving from P1 to P2 during the finite time designated by "now", we can take that P1-to-P2 trajectory as the location designated by "there" in "It's there now".

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Posted 08/28/09 - 12:40 AM:
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#30
Referring to Stanford:

If the thesis of at least one version of Dialetheism is true, then it's not true; and if it's not true, then it's not true. So it's not true.

I have a marvellous proof of that claim, but unfortunately the margin of this thread is too exiguous to contain it.
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