Wednesday, October 12, 2011

Paradox and contradiction

Remind me never to contribute to an internet discussion forum on any subject save the most uncontroversial or simple (say, gardening). "No, it is not a paradox. Contradictions do not exist." There are two mistakes here.

(1) Mistake one is that the existence of a paradox implies the existence of a contradiction. Not so. A paradox involves an apparent contradiction, i.e. two statements that appear to contradict. Thus a paradox does not imply a contradiction any more than any statement of the form 'it appears that p' implies a statement of the form 'p'. For the antecedent can be true with the consequent false. It can appear that the sun is going round the earth, without the sun going round the earth.

(2) Mistake two is that contradictions do not exist. Not so.  A contradiction is two statements, one of which denies the other.  Since such pairs of statements exist, it follows that contradictions exist.  For example, the statements 'the earth is flat' and 'the earth is not flat' are a contradiction. The statements exist, ergo etc.  Probably the claimant meant that no state of affairs expressed by a contradiction exists, which is true, if you believe the Principle of Contradiction.

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37 Comments:

Blogger David Brightly said...

Agree entirely with what you say in (2). Not sure about (1) though. What do you mean by 'appear to contradict'? Surely it's syntactically obvious whether two statements contradict---you explain it very well in (2). Rather, a paradox is a pair of arguments from the same premisses P (and background assumptions B) whose conclusions contradict. If we believe the Principle of Contradiction we expect that one or more of the arguments is invalid or that P,B are inconsistent.

3:42 pm  
Blogger Edward Ockham said...

>>What do you mean by 'appear to contradict'?

Just that. As I spelled it out, it is obvious, but the statements may be rendered more or less vaguely, so that they appear to contradict, but when resolved properly, do not.

The example discussed was of Ayn Rand's views on altruism, and the contradictory statements were 'altruism is immoral' and 'altruism is not immoral'. The former is Rand's view, but it is not clear whether she was using it in the ordinary sense of 'altruistic' (whatever that is).

In the interests of brevity, I didn't include the other condition of paradox, which is that the paradoxical statements have a strong claim to our acceptance.

Thus we can resolve the paradox either by showing the apparent contradiction is not real (e.g. because of equivocation) or that one or both of the statements do not have any claim on our acceptance.

5:14 pm  
Blogger Edward Ockham said...

Another example of apparent contradiction

"Spinach tastes disgusting"
"Spinach does not taste disgusting"

Uttered by different people, these could both be true without any real contradiction.

6:25 pm  
Blogger David Brightly said...

Hmmm. 'Altruism is immoral' and 'altruism is not immoral' make a 100%, 22 carat, copper-bottomed contradiction. We can explain this by showing how one or other of these conclusions arises from fallacious argument (eg, equivocation) or from inconsistent or unacceptable premisses. Talk of 'apparent' versus 'real' contradictions just adds more confusion in my view.

10:08 am  
Blogger Edward Ockham said...

>>Hmmm. 'Altruism is immoral' and 'altruism is not immoral' make a 100%, 22 carat, copper-bottomed contradiction.

If 'altruism' has the same meaning in both sentences, then I agree. But it's one of those terms that is slippery. On one theory of action, no action at all is altruistic, e.g.

Another kind of equivocation is if there is an implicit 'for me' in the statement, as in the spinach example. Spinach tastes good (to my wife), but it does not taste good (to me).

10:55 am  
Blogger Anthony said...

If 'altruism' has the same meaning to whom? At what time?

A paradox contains an apparent contradiction, but it very well may contain two statements that really do contradict (but one or both of which are false).

In any case, a pair of contradictory statements is only a paradox if both statements seem to be true. "1+1=2. 1+1=3. Therefore 2=3." is not a paradox, because 1+1=3 is obviously false.

Finally, "No, it is not a paradox. Contradictions do not exist." is not equivalent to "No, it is not a paradox because contradictions do not exist."

11:48 am  
Blogger Anthony said...

Oh, one other thing. The word "contradiction" has more than one meaning.

11:59 am  
Blogger David Brightly said...

Sure. I think we agree that in all these cases some kind of 'mistake' is being made. But the fallacies are only revealed by an examination of the arguments leading up the the contradictory conclusions. Perhaps it's the cases where the fallacy is close to the surface, as perhaps in your spinach example, that you describe as 'apparent' rather than 'real'. Is this a distinction worth maintaining?

12:53 pm  
Blogger Edward Ockham said...

>>If 'altruism' has the same meaning to whom? At what time?

A term can have the same meaning without having the same meaning to any one, or having it at any time. A dictionary gives you the meaning of words, without giving dates.

>>A paradox contains an apparent contradiction, but it very well may contain two statements that really do contradict (but one or both of which are false). In any case, a pair of contradictory statements is only a paradox if both statements seem to be true. "1+1=2. 1+1=3. Therefore 2=3." is not a paradox, because 1+1=3 is obviously false.

Yes, the two conditions for paradox are that the paradoxical statements should (a) have a strong claim to our acceptance and (b) be contradictory, or appear so.

>>Finally, "No, it is not a paradox. Contradictions do not exist." is not equivalent to "No, it is not a paradox because contradictions do not exist."

That is the natural way of reading it.

2:26 pm  
Blogger Edward Ockham said...

>>Oh, one other thing. The word "contradiction" has more than one meaning.

Properly used, it means always a linguistic item. How otherwise could we say 'that is a contradiction'. If a contradiction were some impossible state of affairs, there would be nothing for 'that' to refer to.

2:28 pm  
Blogger Edward Ockham said...

>>Perhaps it's the cases where the fallacy is close to the surface, as perhaps in your spinach example, that you describe as 'apparent' rather than 'real'. Is this a distinction worth maintaining?

The same applies to ethical paradoxes, I think. If ethical statements are really implicit declarations of taste, as Hume claimed (I think), then the spinach case applies.

Ethical statements may also be concealed imperatives, in which case they are cannot be proper contradictions. A contradiction properly so-called involves assertions, not commands.

2:32 pm  
Blogger Anthony said...

The statement we are talking about is "Contradictions don't exist.", not "That is a contradiction." Something obviously doesn't need to be possible in order to correctly say that it doesn't exist. :)

As for the natural way of reading it, personally I think it is most natural to read it in a way that makes sense :).

11:58 pm  
Blogger Edward Ockham said...

>>The statement we are talking about is "Contradictions don't exist.", not "That is a contradiction."

Regular readers will smile at this point.

The connection between the two propositions is that if 'that is x' is to make sense at all, there must be a referent for the demonstrative 'that'. But to say "there is a referent" is one and the same as saying "a referent exists". Hence, if 'that is a contradiction' is true, there must be (i.e. there must exist) a referent for 'that', and this must be a contradiction, ergo 'contradictions don't exist' is false.

In summary "that is a contradiction" implies "contradictions exist".

:)

7:36 am  
Blogger Anthony said...

This comment has been removed by the author.

11:46 am  
Blogger Anthony said...

I never said "That is a contradiction."

12:17 pm  
Blogger Edward Ockham said...

>>I never said "That is a contradiction."

Very well, but you said

>>A paradox contains an apparent contradiction, but it very well may contain two statements that really do contradict (but one or both of which are false).

"Two statements that really do contradict" is another term for a contradiction. But if a paradox (as you concede) contains a contradiction, it contains an existing contradiction. So you concede that contradictions exist.

1:09 pm  
Blogger Anthony said...

This comment has been removed by the author.

2:11 pm  
Blogger Anthony said...

Actually after considering your argument, I do not concede that contradictions exist. Rather, I believe I made a mistake in conceding (implicitly) that false statements exist.

2:12 pm  
Blogger David Brightly said...

Anthony, look at what Ed says in his (2). A contradiction is just a language thing---a pair of sentences that deny one another, like '2 is even' and '2 is odd'. We can produce them at the drop of a hat. They aren't so terrible!

3:17 pm  
Blogger Edward Ockham said...

>> I believe I made a mistake in conceding (implicitly) that false statements exist.

Wow. That statement is false.

4:26 pm  
Blogger Anthony said...

We can't produce existents at the drop of a hat. To exist is to exist independent of our consciousness.

>> Wow. That statement is false.

I don't believe I made a mistake?

5:12 pm  
Blogger Anthony said...

I think it goes without saying, but when I say that A exists or B does not exist, I'm talking about existence in reality, not "existence in the imagination".

5:15 pm  
Blogger Edward Ockham said...

>>We can't produce existents at the drop of a hat. To exist is to exist independent of our consciousness.

So emotions, thoughts, don't exist?

>>I don't believe I made a mistake?

Let me spell this one out. You made the statement that false statements don't exist. I said that your statement was false.

>>I think it goes without saying, but when I say that A exists or B does not exist, I'm talking about existence in reality, not "existence in the imagination".
<<

So do you mean that nothing exists in the imagination? Surely my idea of Mickey Mouse exists in my imagination. In any case, statements (as linguistic items) generally exist in reality, not in our imagination. Or did I imagine your statement above? Did you not really make it?

Anthony, we're are going through philosophy of language 101 here. There are a lot of mistakes that first year students make in tutorials, and you are going steadily through all of them. Forgive me for saying this.

6:02 pm  
Blogger Anthony said...

This comment has been removed by the author.

6:31 pm  
Blogger Anthony said...

Again, when I say that A exists, or B does not exist, I'm talking about existence in reality, not "existence in the imagination".

If I say that "contradictions do not exist", it is in the same sense that I would say that "Mickey Mouse does not exist" or "unicorns do not exist". One may say that "Mickey Mouse/unicorns exist in the imagination", but that would be equivocating.

As for your first year students making the same "mistakes", maybe some of them aren't actually making mistakes at all. You certainly haven't proven any of your points, merely stated that I am wrong ("I said that your statement was false.") and/or responded with a nonsequitur ("So emotions, thoughts, don't exist?").

Emotions and thoughts exist.

7:34 pm  
Blogger shane said...

"The sky is red."

There, I just made a false statement. Or do you (Anthony) deny that "the sky is red" is a false statement? If it is, then there is at least one false statement that exists.

What's your basis for saying that only false statements are the ones that don't exist? Why would the statement "the sky is blue" exist while the statement "the sky is red," say, doesn't?

8:07 pm  
Blogger Anthony said...

I did not say any of those things, shane.

If you want to try to convince me that false statements exist, feel free. Be sure to define "statement" and what it means to "exist".

8:27 pm  
Blogger Edward Ockham said...

>>I did not say any of those things, shane.

Nor did Shane claim that you said them. He's simply giving examples of false statements, and asking whether you agree. If you disagree, you have to say whether it is because they don't exist, or whether because they are not false. It's a procedure often used in philosophical analysis. It doesn't require defining the words 'statement' or 'exist'. Rather, to find out what you mean by such terms.

On where the burden of proof lies: given most people agree that there are such things as false statements, it's up to you to explain why you think that is not so.

Note also that your claim that no statements are false logically implies that all statements are true. This implies that my statement that your statement is false is true. But if is true, at least one statement is false, namely your statement. Therefore the claim that no statements are false is false.

8:49 am  
Blogger Anthony said...

1) I cannot respond to shane's "questions" because he was both presenting a false dichotomy and asking loaded questions.

2) A claim that false statements do not exist does not imply that true statements exist, just as a claim that red unicorns do not exist does not imply that non-red unicorns exist.

3) As for "burden of proof", I will not believe something exists simply because most people believe so. I need evidence in order to believe that something exists. If you reread what I said, I did not say that I can prove that false statements do not exist. Rather I said "I believe I made a mistake in conceding (implicitly) that false statements exist."

In order for me to concede that false statements exist, I would need clarification of what is meant by "statements" and what is meant in saying that they "exist". If the answer I receive is "they just do" or "most people accept that they do", you can argue all you want about "burden of proof", but I will not be convinced, any more than I would be convinced by the same "arguments", that "red unicorns exist".

12:13 pm  
Blogger Anthony said...

Please note that comment moderation has been enabled on this post.

12:14 pm  
Blogger Edward Ockham said...

>>Please note that comment moderation has been enabled on this post.

Posts older than 3 days are moderated. It is not specific to this post (except in that it is older than 3 days).

7:35 pm  
Blogger Anthony said...

>> You made the statement that false statements don't exist.

Is "False statements don't exist" even a statement? Isn't it only a statement if false statements actually do exist? Otherwise, it is no more of a statement than "Red unicorns don't exist." or "The King of France is wise."

Right?

9:49 pm  
Blogger Edward Ockham said...

>>Is "False statements don't exist" even a statement? Isn't it only a statement if false statements actually do exist? Otherwise, it is no more of a statement than "Red unicorns don't exist." or "The King of France is wise."
<<

See my post today. Both "Red unicorns don't exist." (=no unicorns are red) and "The King of France is wise." are statements. Obviously so.

2:07 pm  
Blogger Anthony said...

It is not obvious, as the definition of "statement" is not obvious.

2:13 pm  
Blogger Edward Ockham said...

>>the definition of "statement" is not obvious.

Standard term in logic and philosophy of language, with a well-understood usage.

8:41 am  
Blogger Anthony said...

You should have no problem pointing me to the definition, then.

1:15 am  
Blogger Unknown said...

The statements can exist. Sure. But, the object referenced by contradictory statements can not. It is either one, or the other, or neither, but never both. Thus the object described using contradictory properties to define the thing is non-existent. You've completely failed to understand the essential meaning of the law of non-contradiction.

11:27 am  

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