Saturday, January 12, 2008

Are Contradictions So Bad?

Granting the law of non-contradiction, do we necessarily have reason to avoid holding inconsistent beliefs (as such)? If so, then our pre-existing beliefs, no matter how absurd, would 'bootstrap' reasons into existence. But that seems dubious: just because one believes that the world is 6000 years old, it does not follow that one has any reason whatsoever to refrain from believing that the world is over a billion years old. (One ought to revise the former belief instead!)

In 'The Myth of Instrumental Rationality', pp.20-1, Raz addresses the grounds of our lingering hostility to contradictions:
When we learn that there is a contradiction among our beliefs we learn (1) that some of our beliefs are false, and (2) that we hold some beliefs that if used together as premises in an argument may lead us astray in a special way [i.e. logical 'explosion']. Big deal! We hope that we all know that some of our beliefs are false anyway. And the risk that we will actually be led astray not by the logical implications of our false beliefs, but by their contradictory features, is, for all practical purposes, negligible...

To conclude: There is nothing wrong with holding contradictory beliefs as such, and the fact that one does is no reason to change one's beliefs. At most we could say that we should abandon our false beliefs. But that is so not because of the contradiction. Knowing that a set of propositions is contradictory has epistemic relevance: It tells us that the contradictory set contains a falsehood. It may be part of a case for believing that one particular proposition is false. But it is no such case by itself. Without such a case we have no reason to abandon any of them. For all we know, we may then abandon a true belief and remain with false ones. Nor do we have reason to suspend belief in all the propositions in the contradictory set. The cost, epistemic and otherwise, of doing so may be too great. That is why the logical paradoxes are rightly not generally taken as a reason to suspend our acceptance of the principles that generate them.

What do you think?


  1. How does the bootstrapping work? That is, why does it follow from that one has reason not believe that p and not-p, and that one believes that p, that one has reason not believe that not-p?

  2. There's an underlying assumption that we have reason to bring ourselves into conformity with the other reasons that we have. To refrain from believing that not-p, is one way to avoid contradiction. So if we have reason to avoid contradictions as such, then this is a reason to refrain from believing that not-p. (By so refraining, we will succeed in conforming to the alleged requirement.) See also my discussion of wide-scope 'oughts' here.

  3. But there are also two other ways of bringing oneself into conformity - (i) to not believe p & believe not-p, and (ii) to believe neither. Why does it follow from merely having the prior belief that p that the believe p & not believe not-p option is the one one has reason for?

  4. We have reason to do either. Insofar as an option will bring us into conformity with our reasons, that's something to be said in favour of that option. (It may equally be said of some alternatives, though.) It's not necessarily a conclusive reason. But many philosophers would claim that there should not be any reason here at all.

  5. While I'm unconvinced of the 'lawfulness' of the principle of non-contradiction, I can grant it for the sake of argument. Even so, it seems like Raz is just equivocating on something here...

    "There is nothing wrong with holding contradictory beliefs as such, and the fact that one does is no reason to change one's beliefs."

    Okay, the fact that my beliefs in P and ~P are contradictory is itself neither a reason to reject my belief that P nor a reason to reject my belief that ~P. But surely this much is apparent. However, granting the assumption of LNC, and hence the implication that a contradictory set of beliefs contains a false belief, the fact that my beliefs are contradictory is a reason to seek evidence which will settle which of my beliefs is false, so that I may reject that one. At least, this follows if it is a norm of belief that we ought to accept what is true and reject what is false. Anyone want to challenge this norm?

  6. Right, Raz agrees with that: we have reason to reject false beliefs. But contradictions are no further problem. For example, supposing P is false, it is not necessarily worse to believe the inconsistent {P, -P} than to just believe the false {P}. Being in the former state gives us no reason to shift to the latter.

  7. We don't have to "bootstrap" reasons into exist. They exist. Holding some contradictory beliefs is a good way to see that they exist. Because believing P & -P is a reason to believe we hold at least one false belief. If holding contradictory beliefs is not a reason to think one or the other is false, then there are no reasons.

    Richard says: "[S]upposing P is false, it is not necessarily worse to believe the inconsistent {P, -P} than to just believe the false {P}. Being in the former state gives us no reason to shift to the latter."

    But this seems - like Railton's article in those two 'graphs (haven't read the article) - to me a complicated way of missing the point. Is it worse to believe two inconsistant things or just one false thing? I don't know. What does that have to with anything? What the heck does "worse" mean? For all I can see it may be better - in terms of getting elected - for politicans to hold lots of different, contradictory beliefs. So, what if we stimpulate is it epistemically better of worse? Again, you can't answer this without knowing lots of facts about the particular dispute, without getting a lot further into epistemology than logic. But here's one thing you need to know: it ain't gonna be P & -P. How do you know that? Because believing P & -P gives you a reason to believe you are wrong on one or the other. Which is why his second sentance is just plain false. Of course, beliefing in contradictory things gives you a reason to simply believe one or the other. It may not always trump all other considerations, but (again) if that doesn't count as a reason, what could? We don't need, as Richard says, "an underlying assumption that we have reason to bring ourselves into conformity with the other reasons that we have;" we just need to believe that two contradictory facts cannot both be right; and, voila!, we magically have a reason to bring our beliefs into conformity - namely, they can't both be right.

    To me this is very unintersting Rorty-style mucking about. Of course, logical reasons, or the axioms instrumental practical reasoning, are not the only reasons we have for regulating belief change in certain ways, and so they may not always prevail (espcially in the short term). But, yes, Virgina, contradictions are bad and lead to false beliefs.

  8. I think it all depends on the type of belief and the necessity of knowing the truth. About the age of the earth, something factual but difficult to ascertain, it seems reasonable to drop one belief even if it could later be found to be the correct one.

    But I sometimes think we're all spiritually connected by some thread of something or other, yet at other times I say bullocks, we're all in this alone. Each belief works for periods of time for me, yet I see the contradiction clearly. Knowing which is most accurate just isn't necessary to my well-being.


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