Freethought & Rationalism Archive

tk · 02-25-2003, 08:27 AM

This is getting me confused...

Quote:

A dialetheia is a true contradiction, a statement, A, such that both it and its negation, ~A, are true. Hence, dialeth(e)ism is the view that there are true contradictions. Dialetheism opposes the so-called Law of Non-Contradiction (LNC) (sometimes also called the Law of Contradiction): for any A, it is impossible for both A and ~A to be true. ...

Dialetheism appears to be a much more common and recurrent view in Eastern Philosophy than in the West. In ancient Indian logic/metaphysics, there were standardly four possibilities to be considered on any statement at issue: that it is true (only), false (only), neither true nor false, or both. Early Buddhist logic added a fifth possibility: none of these. ... Contradictory utterances are a commonplace in Taoism. For example, the Chuang Tsu says: `That which makes things has no boundaries with things, but for things to have boundaries is what we mean by saying "the boundaries between things". The boundaryless boundary is the boundary without a boundary' (Mair, 1994, p. 218). When Buddhism and Taoism fused to form Chan (or Zen, to give it its Japanese name), a philosophy arose in which contradiction plays a central role. ...

The only sustained defense of the LNC in the history of philosophy is ... that given by Aristotle in Chapter 4 of Metaphysics, Gamma. Given the influence this chapter has had, the arguments are surprisingly poor. ...

Whilst the question of the conditions under which it is rational to accept something is a moot one, it is commonly agreed that, as Hume put it, the wise person `proportions his beliefs to the evidence' (1955, p. 118). Hence, if a sufficient case can be made out for a contradiction, it will be rational to believe it. And cases there are. For example, the case for the truth of the liar sentence, `this sentence is not true', was gestured at in the previous section.

John Page · 02-25-2003, 08:12 PM

Yes, things are not always what they seem - even truths!

Brain X applies logic to proposition P and arrives at the determination A.
Brain Y applies logic to proposition P and arrives at the determination ~A.

Proposition: Brains always tell the truth. Answer = FALSE (given the evidence above).

Thus, if brains do not always tell the truth, then some truths are false.

Have fun! What I think the above demonstrates is that truths are not universals. i.e. When someone talks about "The Truth" they're misrepresenting the knowability of truth.

Cheers, John

02-25-2003, 09:03 PM

Quote:

Originally posted by tk

For example, the Chuang Tsu says: �That which makes things has no boundaries with things, but for things to have boundaries is what we mean by saying "the boundaries between things". The boundaryless boundary is the boundary without a boundary� (Mair, 1994, p. 218). When Buddhism and Taoism fused to form Chan (or Zen, to give it its Japanese name), a philosophy arose in which contradiction plays a central role. The very process for reaching enlightenment (Prajna) is a process, according to Suzuki (1969, p. 55), "which is at once above and in the process of reasoning. This is a contradiction, formally considered, but in truth, this contradiction is itself made possible because of Prajna."

No, the contradiction is possible because of our limited human understanding wherefore transcendence is possible.

jpbrooks · 02-25-2003, 10:51 PM

Hi tk! Nice topic.

In my view, this paragraph in the essay is important:

"A more persuasive worry about dialetheism, relating to rationality, is the claim that if a person could legitimately accept a contradiction, then no one could be forced, rationally, to abandon a view held. For if a person accepts A then, when an argument for A is put up, they could simply accept both A and A. But this is too fast. The fact that some contradictions are rationally acceptable does not entail that all are. There is certainly a case that the liar sentence is both true and false, but this in no way provides a case that Brisbane is and is not in Australia. (Of course, if one subscribes to the claim that entailment is explosive, a case for one contradiction is a case for all; but if entailment is paraconsistent, this argument is of no use.) ...".

Concerns about Paraconsistent Logics aside, Dialetheism (as stated above) undercuts its own retionality. If it is assumed to be true, then the whole idea of defending/refuting any view (including Dialetheism) becomes meaningless. Adopting Dialetheism would thus bring about the end of rational discourse in all subject areas, since the most fundamental assumptions of each subject are philosophical.

None of this means, however, that contradiction can't serve some purpose outside of rational discourse, such as (perhaps) in Psychology, or in belief systems such as Taoism.

John Page · 02-26-2003, 06:09 PM

Quote:

Originally posted by jpbrooks
.......Dialetheism (as stated above) undercuts its own retionality.

Isn't reality very similar to dialethism, lots of people saying "Its true because I believe it to be true", when in fact they are mistaken? Here's the proposition for you to analyze:

"When people are not rational they are dialethic." So, are you using dialethic to define rationality or the other way round?

Quote:

Originally posted by jpbrooks
If it is assumed to be true, then the whole idea of defending/refuting any view (including Dialetheism) becomes meaningless.

Why does dialethism have to be "true"? Or "false" come to that matter? Dialethism exists, whether you judge it true or not.

I suggest that a dialethic approach is consistent with skepticism and, furthermore, it can be considered as a model of brain operation where the contradicting positions are both (literally) assumed valid until they are played out.

Am I deliberately pushing the envelope here - absolutely dialethically!

Cheers, John

tk · 02-27-2003, 08:00 AM

Thanks for all the interesting replies. I just composed an apologetic in favour of LNC, based on an empirical (rather than metaphysical) argument. I welcome comments on it.

Quote:

"When people are not rational they are dialethic." So, are you using dialethic to define rationality or the other way round?

This is an interesting question I think. Priest suggests other measures of rationality, however I have issues with some of them:

1. Rejecting theories which are unduly complex. This isn't definitive. For example, does a proof of Fermat's Last Theorem become invalid because it's hundreds of pages long?

2. Rejecting a theory which has observable consequences that are not observed. But does this not assume the principle of non-contradiction once more? Something is supposed to be observed, and it was not observed; ergo, false.

Quote:

Brain X applies logic to proposition P and arrives at the determination A.
Brain Y applies logic to proposition P and arrives at the determination ~A.

Proposition: Brains always tell the truth. Answer = FALSE (given the evidence above).

I'm under the impression though that logic is something that can be applied by machines, and doesn't depend on an `intelligent' being...

Quote:

None of this means, however, that contradiction can't serve some purpose outside of rational discourse, such as (perhaps) in Psychology, or in belief systems such as Taoism.

I sort of agree. Irrationality is fine if one only wishes to describe what Taoism is. But when one needs to explore how Taoism is relevant to the real world, some notion of rationality will be needed.

John Page · 02-27-2003, 08:23 AM

Quote:

Quote from link by tk
I show that the paradoxes proposed so far are merely the products of our invention.

I don't see where you showed this. If paradoxes exist in our mind, are you saying we invented our minds?

Quote:

Quote from link by tk
There is currently no reason to believe that truth is naturally contradictory.

I think this is an invention of your mind.

What do you mean by "naturally contradictory"? Do you think there are natural and unnatural truths? How would I tell?

Cheers, John

Big Spoon · 02-28-2003, 03:15 AM

In the field of propositional logic it's possible to construct and evaluate statements whose truth value is either both true and false or neither true or false- I think the statement "this statement is a lie" is an example of one of those, which is kind of similar to Russell's paradox. Is it problems of self reference that cause these inconsistencies?

John Page · 02-28-2003, 04:36 AM

Quote:

Originally posted by Big Spoon
....it's possible to construct and evaluate statements whose truth value is either both true and false or neither true or false....

You got me thinking. Here's one.

"This sentence is neither true nor false"

If what you said in your post was True then the above sentence, at first reading, is literally a statement of that and therefore neither True nor False. On the other hand, in accordance with the rules of some logicians, the above sentence is bound to be True.

Thoughts?

Cheers, John

tk · 02-28-2003, 06:00 AM

Quote:

If paradoxes exist in our mind, are you saying we invented our minds?

I'd say we invented our beliefs. One can hold any set of beliefs, much like one can enter any string of zeros and ones into a PC. But just as the zeros and ones don't need to describe reality in any way, our beliefs don't need to be synchronized with reality.

Quote:

What do you mean by "naturally contradictory"? Do you think there are natural and unnatural truths? How would I tell?

I think the best way to put it is (as I have done) this: the world is naturally contradictory if any accurate model of the world is bound to contain true-and-false statements.

Admittedly, this is somewhat contorted. But it's likely necessary, because if Godel is any guide, any model of the world will have to contain some concepts which don't naturally exist in the world.

I agree, this is disgusting... :boohoo:

Quote:

Is it problems of self reference that cause these inconsistencies?

An interesting thing is that literal self-reference isn't needed to produce such a inconsistency. Suppose I define a function on a functor which yields a truth value, thusly:

F(P) = ~P(P)

Then I can try to ask, "what is F(F)"? There are no obvious self-references here; one can argue that the self-reference occurs in the typing of the function, but still one'll need to dig deeper to find it...

Symbolic logic deals with this by defining different orders of logic: in propositional logic, predicates may take no argument, while in first-order predicate logic, predicates may not take as argument anything involving truth values (so e.g. predicates can't describe other predicates). Both logical systems have been (intuitively) proven to be sound and complete. At the same time though, neither system can describe itself.

02-25-2003, 08:12 PM	#2
John Page Veteran Member Join Date: May 2001 Location: US Posts: 5,495	Law of Contradiction Yes, things are not always what they seem - even truths! Brain X applies logic to proposition P and arrives at the determination A. Brain Y applies logic to proposition P and arrives at the determination ~A. Proposition: Brains always tell the truth. Answer = FALSE (given the evidence above). Thus, if brains do not always tell the truth, then some truths are false. Have fun! What I think the above demonstrates is that truths are not universals. i.e. When someone talks about "The Truth" they're misrepresenting the knowability of truth. Cheers, John

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02-25-2003, 10:51 PM	#4
jpbrooks Senior Member Join Date: Aug 2000 Location: Chicago Posts: 774	Hi tk! Nice topic. In my view, this paragraph in the essay is important: "A more persuasive worry about dialetheism, relating to rationality, is the claim that if a person could legitimately accept a contradiction, then no one could be forced, rationally, to abandon a view held. For if a person accepts A then, when an argument for A is put up, they could simply accept both A and A. But this is too fast. The fact that some contradictions are rationally acceptable does not entail that all are. There is certainly a case that the liar sentence is both true and false, but this in no way provides a case that Brisbane is and is not in Australia. (Of course, if one subscribes to the claim that entailment is explosive, a case for one contradiction is a case for all; but if entailment is paraconsistent, this argument is of no use.) ...". Concerns about Paraconsistent Logics aside, Dialetheism (as stated above) undercuts its own retionality. If it is assumed to be true, then the whole idea of defending/refuting any view (including Dialetheism) becomes meaningless. Adopting Dialetheism would thus bring about the end of rational discourse in all subject areas, since the most fundamental assumptions of each subject are philosophical. None of this means, however, that contradiction can't serve some purpose outside of rational discourse, such as (perhaps) in Psychology, or in belief systems such as Taoism.

02-28-2003, 03:15 AM	#8
Big Spoon Junior Member Join Date: Feb 2003 Location: UK Posts: 74	In the field of propositional logic it's possible to construct and evaluate statements whose truth value is either both true and false or neither true or false- I think the statement "this statement is a lie" is an example of one of those, which is kind of similar to Russell's paradox. Is it problems of self reference that cause these inconsistencies?

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