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Can the above words be used interchangeably?

The phrase "circular reasoning" is mentioned under "paradox" in wikipedia, which led me to think about "tautology". I understand "dialectical" to mean (a relationship) characterised by opposites, which, is synonymous with contradictory and therefore similar to "paradox"?

What are the demarcation lines of usage between them?

Thanks very much if you can help me demystify these three words.

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Goodness, no. Don't ever rely on Wikipedia for accurate philosophy-related information. That said, I think everyone here would recommend plato.stanford.edu as a resource, but your current question's easy enough to answer.

Firstly, they are all different, but you're right in picking out the relationship between circular reasoning, tautologies, and (some) paradoxes. They are all similar in that they refer to themselves in some way.

However, What makes them clearly different from one another is the nature of this reference.

Tautologies have the simplest relation. They are statements which must be true by virtue of what they say, such as "all unmarried men are bachelors", or "mortal creatures die." If you know the definition of the terms unmarried, men, and bachelors, or mortality and 'to die', then there is no further assessment you can make, and the statement is "trivially" true. We ought use the word "trivial" here because these statements contribute no new information.To assess the truth of these statements, I must must first consult the meanings of the terms used, but by acquiring the definition of the terms to evaluate the truth of the statement, I've already answered the question- so "that the statement is true" isn't itself even new information.

Circular reasoning, on the other hand, occurs when someone wants to prove that a thing is true, but assumes that it's true as a condition for their argument. It results in the nasty problem of having the truth of an argument's conclusions resting on only the results of the conclusions, instead of separate premises that can be independently verified. The classic example is Descartes, who claims

1) He has "clear and distinct" ideas, and when ideas are clear and distinct, it means they cannot be doubted. 2) Because he has a clear and distinct idea of God, thus God cannot be doubted. 3) Why does he know that clear and distinct ideas are true? Because they must be given by God, and God wouldn't lie. 4) Therefore, *clear and distinct ideas cannot be doubted.

And so the circle goes on...

Paradox, on the other hand, comes in different flavors. The word is used in a looser sense to indicate that there is a state of affairs other than we would expect, but this sense is not the one which is similar to the others. Self-referential paradoxes are the wicked creatures here. These kinds of paradoxes exist when an argument contradicts itself. Contradiction is simply one statement which makes another false. "All ravens are black" is contradicted by evidence of a white raven. So a paradox is similar to circular reasonin in that the result of an argument has an impact on the truth of one of the premises, but this impact is negative instead of affirmative. Typical examples of this are "I am a Creatn, and all Cretans always lie." If the statement is true, then it must be that the person saying it is lying. If it is the case that the statement is a lie, and false, then the speaker is telling the truth.

"Dialectical" is in a different category altogether. It's not a descriptive term about an argument's validity, but instead is a method for argumentation- one that involves a back-and-forth conversation of challenges and counterchallenges to a claim or statement, with the goal of arriving at or approaching the truth of or refinement of the claim being made. Just read anything by Plato to see how it's done, but I would specifically endorse reading Meno for an xplicit use of the method in teaching and learning.

For more information on how to separate these things, try Baggini's "The Philosopher's Toolkit", or Schaum's Outlines - the one on Elementary Logic (workbook). All of these terms are defined in fill and far more clearly than I can hope to on SE. I hope I've made their differences a little clearer, though.

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Not only do you cite Randal Monroe's game incorrectly (it's the first link not in paranetheses or otherwise not about the content per se), there is an instructive counterexample to your statement. If you start from "Mathematics" and follow the second link in each article that has to do with the content, you take a rather interesting tour of several pages which returns ultimately to Mathematics (if you take the second link of the Mathematics section of the 'collection' disambiguation page, where one is sent to from 'set'). But this does not indicate that Wikipedia is a bad resource for math. –  Niel de Beaudrap Nov 11 '12 at 15:01
    
I should've re-read that one, thanks for the correction. Also, apologies for the rant in general- I've edited out that little bit of nonsense. Chalk it up to inebriation- and a lesson learned about leaving answers at night ... –  Ryder Dain Nov 11 '12 at 21:59
    
@NieldeBeaudrap, was that really the only criticism? I'm becoming a little proud of myself. ...I don't like the feeling much, it makes my head feel fat. –  Ryder Dain Nov 12 '12 at 23:05
    
I didn't really have substantive comments on anything but the prologue, which seemed to be more editorial than informative, and also formally an invalid argument. –  Niel de Beaudrap Nov 13 '12 at 0:05
    
Excellent. And thank you, too. –  Ryder Dain Nov 13 '12 at 23:44
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I'd like to add a shorter version of distinguishing "paradox" from "tautology". In short, they are closer to being opposites than synonyms.

A Paradox is a situation that cannot exist sensibly, eg: "This statement is false". Attempting to evaluate the truth of that statement is impossible, as truth forces it to be false, and falsehood forces it to be true. Time-travel stories love paradox. The important aspect of a paradox is that it cannot be meaningfuly evaluated, not that it proves itself false. Also, paradoxes are almost always self-referential, in order to have that quality.

Tautology is a statement that proves its own truth. The examples given above (eg "All unmarried men are bachelors") are perfectly good ones. In general use, a tautology is a repetitive statement of the same fact (as opposed to a redundancy, which is stating a fact, and one that can be implied by it). eg "The black cat is black" is a tautology. "The black cat is not white" is technically a redundancy, although one that trivial feels like a tautology. (Note, that definition is more about language than logic, included here for completeness)

x->x is a tautology. x->~x is not a paradox, it is just false.

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