How do you solve a contradiction?
Literally typed this into Google and no coherent answer?
Is the question ill-posed, or does it mean anything, as it seemingly does to me, at least?
Is the question ill-posed, or does it mean anything, as it seemingly does to me, at least?
Comments (34)
Contradictions inform of what isn't the case.
The word 'solve' is maybe not the best word there, and the question is a bit general as the answer will differ depending on the subject matter.
We allways use a language, be it maths or a regular language, to speak about anything. One way you can get a contradiction is if you made a mistake in the logical steps leading up to the contradictory conclusions. That is generally true for all subject matters.
Another way you can get contradictions, even if you made no logical mistake, is because of the premisses. Here it will depend on the subject matter what a contradiction means.
In maths and the exact sciences for instance it can only mean that your premisses are wrong if no logical mistakes where made. Wrong premisses can be the result of wrong assumptions or bad data. It is assumed here that if you talk about the 'world' then there shouldn't be any contradictions, so a solution should be possible in principle… by examining your logic or your premisses.
If we are talking about something man-made however, like values, morals or law for instance, contradictions need not necessarily imply a logical mistake or faulty premisses, because we aren't describing the world, but we create values and morals etc... and those could be contradictory. The way to deal with those is not necessarily by 'solving them', but could be to just accept it and make amends for values that are necessarily contradictory.
Yes, if not a contradiction, then what exactly is it, then?
Very interesting stuff hereabouts.
It is still a contradiction, but you can't really say it's because of bad logic or because the premises are not true. Truth doesn't really apply there.
To give a simplified example, you get raised with two values, to be ambitious and to enjoy life. If you start to reason from those values to be able to decide on concrete actions in your life, often enough you will come to the conclusion that they lead to opposite courses of action. This isn't because one of the values is wrong per se, you can't 'correct' a mistake to solve the contradiction (like you can in maths or the exact sciences). You then could decide to choose between values and abandon one of them, or maybe if you can't, you need to figure out when you will favour one over the other etc...
This is often why in political discussions people tend to talk past eachother. People simply have different values that aren't compatible. and then the discussion cannot really be resolved... other than someone abandoning their values in favour of the other.
Is it necessary that one abandon ones belief posing as the solution here?
No maybe not, maybe that's to strong of a claim. Your could also accept that you have different values, and look for a solution that is a compromise between the two.
Gödel proved that true sentences of self-reference can be unresolved contradictions in his incompleteness theory.
Plato: What Socrates is about to say is false.
Socrates: Plato has just spoken truly.
In light of that what then should guide a person to formulate his or her own values, if you don't mind me badgering you?
Yes, in formal systems; but, akin to what @ChatteringMonkey is mentioning, they can also arise in informal languages?
...you mean like 'intuition'? He discussed that also........
What made you say that, as I'm off base.
This is a very difficult question, and I'm not sure if I can adequately answer that...
But the way I see it, is that we do not start in a vacuum. We get raised by our parents and in a society that promotes certain values. And we also find ourselves in certain positions relative to that society. By the time we are sufficiently self-reflective and can start thinking about these things we already have a good amount of baggage that we can't merely make abstraction of. You start from somewhere...
The other important factor is your temperament. A good part of it is probably biologically determined, and so formulating your values (which goes to the core of your being) is not so much a matter of choice, but of discovering what those are.
And you find out what those are by trying different things in the first place, and then reflecting on your experiences afterwards. What did you agree with, and what didn't sit well, what choices did you make and why etc... If you manage to abstract that into more general values, you can then again go the other way by drawing the ramifications of those values by comparing them against certain concrete possible scenarios... and tease out contradiction along the way. And ultimately, like I said in earlier post, try to figure out how you want to deal with those. It might mean abandoning certain inherited values altogether, or sometimes that is not possible, and you'll have to try to reconcile conflicting values.
Needless to say maybe, but this isn't done overnight... it might take a while.
What does that even mean?
I wrote it as clear as I could, but if you say the moon is made out of cheese and I say it is not made out of cheese we have a contradiction. In order to “solve” the contradiction we need to determine which of the statements is accurate.
But, what of differing or clashing values that don't correspond with any particular state of affairs in the world, necessarily?
The problem with values and value systems is that they are often internally contradictory. I think some form or other of compromise suffices. Perhaps politics is the result.
How so?
“if its values contradict each other, and its exceptions are highly situational and inconsistently applied.”
https://socialsci.libretexts.org/Bookshelves/Sociology/Book%3A_Sociology_(Boundless)/3%3A_Culture/3.5%3A_Culture_and_the_Dominant_Ideology_in_the_U.S./3.5C%3A_Value_Contradictions
With regards to what?
Do facts factor in here?
For some reason the correspondence theory of truth deserves a mention of it's 'bout facts.
But what about values?
Well, if I'm in contradiction then it matters if it's about something factual (hence correspondence with respect to the world) or it may be about something that's truth is more malleable or subject to change, like values?
It appears to me that there are two types of contradictions:
1. The obvious one that goes (p & ~p) in which the two statements of the conjunction have opposite truth values: if one is true then the other has to be false. This type of contradiction is used in reductio ad absurdum proofs which is the application of the law of noncontradiction ~(p & ~p).
2 A contradiction is a statement that is always false. Type 1 contradiction seems to be subcategory of this type of contradiction because (p & ~p) is always false.
How type 2 contradiction differs from type 1 contradiction requires a discussion of inconsistency. A group of statements is inconsistent if and only if the truth table of the group doesn't have a single line where all the statements are true.
You'll notice that if all the statements of a group of inconsistent statements are put under a conjunction i.e. joined together with the & connective, we will get a contradiction. After all for a conjunction to be true all conjuncts have to be true and that isn't possible with a group of inconsistent statements.
Where type 2 contradictions differ from type 1 contradictions is that it's possible for all statements in a group of inconsistent statements to be false while in type 1 contradictions the component statements have to be of opposite truth value.
How do we "solve" a contradiction?
1. Type 1 contradictions require you to negate the assumption that led to the contradiction.
2. Type 2 contradiction literally means whatever belief system you're operating from is logically flawed because it's impossible for all the statements that constitute it to be true at the same time. For instance imagine a belief system X composed of statements A, B, and C. If A, B and C are inconsistent with each other the conjunction A & B & C always evaluates to false, is a contradiction of type 2, which means X on the whole is a false belief system. Naturally, we have to discard X.
Banno, how would you propose correcting the misspoken-ness?
Yep!
Sorry Wallows, I was confusing incompleteness with indeterministic phenomenon (i.e.; secret game of 20-questions- Wheeler's Cloud- from Paul Davies Book, The Mind of God).
Then, how do you correct a faulty belief system, or how do you create one where these contradictions don't arise?
Yes, you solve paradoxes (apparent contradictions) not contradictions.
Values are subjective, not objective. Opposing objective facts would be a contradiction. Opposing values are not a contradiction because they arent about the same thing. Values exist only in our heads, so it is a category error to make them objective and therefore contradictory. We have goals that come into conflict, which is why it seems that our values are contradictory, but our values are based on our goals as individuals.
Saying that some thing is good while another says it is bad is not a contradiction because they are both talking about two different things - their own values, not the actual thing that they claim is good or bad.