1. This sentence is false.

So what do we make of this? If it is true then it is false. This seems to violate the law of noncontradiction, the basis of logic. The sentence cannot be both true and false at the same time, but this one certainly seems to be.

Paradox can only exist in words. In a three dimensional world, reality is logical. The fact that paradox is even possible in language is just a sign that verbal/linear/one-dimensional reasoning is inferior to spatial reasoning. :)

Darn you, why must you torture me with this statement....

I lean towards the notion that paradox is a product of how things are set out with language, and that they indicate pushing the limit at times also. I would not call reality logical though, even if the universe seems to consistently obey laws.



Why would verbal/linguistic reasoning be one-dimensional? All reasoning is mental, yes?

The standard refutation of the liar's paradox is to call it meaningless due to it's being self-referencing. Meaning/identity requires distinction. None is made here.

This sentance, identity not withstanding, is false.


There you go, I fixed it.

Dialetheism

That link expounds an entire logical system(paraconsistent logic) which does away with the law of noncontradiction, based on one manner by which we can make 'sense' of paradoxes like the OP.

Did you read it Di?

Escher has three charcoal drawings or etchings, I don't know which; three graphics that show impossible three-dimensional events. Spacial paradoces. "Waterfall", "Belvedere" and "Up and Down".

I don't know how to copy visuals onto here.

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A one-word paradox is "omnipotence".

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Paradox, if it exists only in words, does not necessarily prove the inferiority of lingual representation or the inaccuracy of lingual representation of reality vis-a-vis spacial representation. It's just in spacial representation there is no "truth" and "falsehoods" whereas every affirmation in a lingual representation is either "true" or "false". If a statement is both true and false, it is a paradox. Without an assignment of truth value, paradoxes can't exist.

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The existence of paradox in language is a sign of superiority of lingual representation of reality, compared to visual representation of reality. Language is superior to spacial representation, in many ways, it being more complex, more expressive, having a larger domain, and much more many different distinct domains, than spacial representation. It is also superior in its ability to create paradoxes, which is a complex concept, and not a false concept. It is, in our mental worlds, no more than a mental toy, and an intellectual curios. In some technical issues, in master-slave switch chip technology, for instance, the issue of paradox rears its head, and it is not at all a concept of a mind, but a paradox that can potentially exist even if man and his mind is not in existence. In other words, paradoxes can be found to freely occur in nature, in physical reality.

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A larger number of known paradoxes exist in spacial representation than in language.

Aside from the Escher drawings, there is always the fact that continuous lines are said to comprise points, and points only can make a continuous straight line, yet it can be shown that in a straight line no two points are ever placed side-by-side.


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Daniel, welcome to the forums.

M.C. Escher

Wux,

Do you have a good understanding of dialetheism?

This is the most famous of Escher's drawings, but it is NOT a visual paradox. It is just playing with gravity, but it has no paradox. It is pitting three-dimensionality against gravity. There is simple falshood here, it is not flip-flopping from falsehood to truth.

Try "up and down".



No, I never had ever heard or seen this word before. Before this thread, it was mentioned earlier as well.

What is "dialetheism"? A new drink at Starbucks, or a teflon-coated pocket-puuuuussy?

Seriously, and honestly, I don't know what it even is. Theism is a belief in god or a set of concerns or study that focus on the belief in god. Dial is what you used to crank on telephones back twenty years ago. I just can't interpret "e" that's in there. What does "e" mean in English?

Thanks for the link, I read parts of the article.

It fails in its claim. I'll examine two: Hegel's moving object and "the manifold opinion of men must all be true, though some of the opinions being contradictory."

Hegel"s moving object explanation fails to nullify the Law of Non-contradiction, by removing the "in the same respect" part. The law of non-contradiction states "nothing can both be and not be at the same time and at the same respect." Hegel said "the ball is HERE now and THERE a moment later, but from there, the ball is THERE and now, a moment later, it is HERE."

Clearly, Hegel used two reference points, that were non-identical and he violated the following of the rule, the definition; it is not that the definition is false. Hegel omitted to observe the part of "in the same respect." My respective view here is different from that respective view from there. No dialetheism there, only false logic.

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Many men have different opinions, and some are contradictory, but then it is false to assume that each opinion is right , true, correct . Some are correct, some are not, and the correct ones are negations of the incorrect ones. Here there was an invalid assumption, that all opinions must be true, correct. That is not the case.

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Pre-socratic philosophers were judged to be on hallucinogenic drugs when they said "you can not step in the river twice" or something like that, and the likes of it . These statements can be easily explained by pointing out that they simply make no sense.

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ON EASTERN PHILOSOPHIES REGARDING DIALETHEISM, VIA EXAMINING THE WORKING FUNCITONALITY OF EASTERN SCHOOLS OF PHILOSOPHY, IN CLOSE COMPARISON TO WESTERN SCHOOLS

Eastern philosophies do not concern themselves with explanations and rigorous proofs. They are more spiritual. Eastern philosophers therefore tended to write short aphorisms, that either made sense or not, but they made the reader or listener think. In western philosophy, the game is to rob the listener from the joy of thinking, by presenting each step of a logical explanation in such a way, that the explanation is air-tight. Therefore Western philosophy texts are long and boring and tedious.

It is therefore the job of the western philosophers to disprove the works as presented by their peer, and it is therefore the job of the eastern philosophers to provide evidence to support the works as presented by their peer.

Seeing the above, Eastern philosophies can be blown to pieces by western thinkers, by simply saying "t his does not make sense, and it is not well explained", and Western philosophies are easily supported by Eastern-type thinking, by saying, "yep. This is true. For instance, ..." and an example is given.

Jesus and the Buddha were compared by many soft-headed thinkers. These people failed to see the inherent equivocation of "Jesus" when these thinkers could not bother to, or were unable to, separate the philosophy of Christianity from the spiritual element (religiosity) of Christianity, and these thinkers were also unable to see that the Buddha presented many falsehoods in his philosophies but the falsehoods were never challenged, but were supported, because they were always treated in the tradition of Eastern philosophical schools.

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P.S. I did not copy the above; I just wrote it now. It could be derived by any clear-thinking individual, one does not need to study and "be familiar" with dialetheism to see or figure out what I wrote above. This is actually child's play in thinking. I am not proud of it, I just wish to avoid the challenge that I knew this from studies. No studies are needed to get to the above conclusions.

That was going to be my response, self referential, circular. Without a real subject/object relationship.

All truth statements have either a subject or object that they reference, not themselves.

The paper is white.

The grass is green.

There are no gods.

Where is the subject, or object in.

This statement is false.

The statement itself is what is being called false, I would just as soon claim this statement is not really a statement becuase it has no object or subject that it is setting out a state of affairs for/against.

Statements are not things, but descriptions of things. A description of a description? What is that? How can a description of a description be true or false if it does not reference some object or subject?

I tend to find these kinds of things to be trivial, and tend to not spend much time thinking on them.