For those who don't know, the "preface paradox" is an epistemic paradox wherein an author painstakingly researches every single fact he asserts in a new book he's releasing. As a result, he believes each assertion made in the book with a high degree of certainty. However, he also takes care to write in the book's preface that, being cognizant of his own fallibility and of the unlikelihood that he's released a perfect work, he's likely to have made a mistake somewhere, and pre-emptively apologizes for doing so. Thus the paradox arises as it seems he rationally believes two beliefs that cannot be true at the same time, yet is aware of this inconsistency.

Generally, this has been framed as a question of whether one can rationally hold jointly inconsistent beliefs. My question is what ramifications this has on whether one can consciously hold inconsistent beliefs, period. If its psychologically possible to consciously hold inconsistent beliefs, is it also possible to hold contradictory beliefs as well?

(more info on the paradox) http://plato.stanford.edu/entries/epistemic-paradoxes/#PrePar

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    Human mind never operates in perfect extremes. That's why it can function in states of doubt and wonder. – user2411 Oct 11 '12 at 5:54

It is certainly possible to consciously hold contradictory beliefs, at least in the case in which one does not notice them to be contradictory. For example, many believe the truth of Goldbach's conjecture, but if the conjecture is false it is necessarily false, and contradicts the content of many other true beliefs about mathematics that those same people surely have.

A more interesting question is whether one can consciously believe that p-and-not-p. Probably we should only care whether such an outright contradiction can be believed rationally: it is likely that all sorts of crazy stuff can be believed, if the believer is allowed to be irrational -- as you say, that question is best left to psychology.

But, apparently, some outright contradictions can be believed rationally: dialetheists hold that some sentences are both true and false. For example, some of them claim that the liar sentence,

This sentence is false

is both true and false. Of course, if you are to say such a thing you need to tweak logic to avoid ex falso quodlibet, the feature of classical logic in virtue of which one is allowed to derive anything from p-and-not-p. Such logics without explosion, paraconsistent logics, do exist, though, and the dialetheists that have formulated them (at least the ones I know) are highly intelligent, highly rational folk :)

By the way, one nice way to go about the preface paradox is the following: positive doxastic attitudes towards a proposition come in degrees, from full acceptance (1) to full rejection (0). Suppose that belief in a proposition requires placing a creedence of 0.99 in the truth of the proposition. If the book in question expresses more than 458 propositions (that can be true or false independently), then the writer can assert, without contradiction that:

  • She believes every proposition expressed in her book (places a .99 creedence in each of them)
  • She believes that not all of them are true (the creedence she places in all of them being true is 0.99^459 < 0.01)
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  • That's a huge help. Thanks so much. What about when one knows that their beliefs are contradictory? What is there to prevent us from actually doing that, if anything? And if so, can it be discussed philosophically, or is it purely a matter of psychology or neurology? – Gnostic Agnostic Jun 29 '12 at 4:40
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    Hi, @GnosticAgnostic, I have tried to elaborate on your comment in my reply. Let me know if that is any clearer now! – Schiphol Jun 29 '12 at 15:05
  • I'm not sure if one can truly say that it is impossible to consciously believe p and not p. I do believe it is impossible to do so consistently within the realm of logic, but to presume that extends to all of consciousness is a tricky issue. As a real life example, there are plenty of people who believe all results from science are statistical, and yet simultaneously violently defend the ascertain "evolution is true." I have found many that are willing to admit to holding these beliefs, even when they recognize them as contradictory. – Cort Ammon Dec 12 '15 at 19:31

I do not think the possibility of holding contradictory beliefs is controversial. For instance, a simultaneous belief in a god and a causal universe is commonplace. Claiming to know both are true is controversial..

In the preface paradox I claim I both know every statement I wrote is accurate, and I know I made a mistake somewhere.

In the lottery paradox I say to a friend who is buying a ticket, "I know you won't win, and I know someone will win." Say a lottery is held which guarantees a winner while maintaining the ridiculously long odds of typical lotteries. I know, with a probability greater than .99 that my friend will lose, so I confidently claim I know he will lose. I cannot claim that each participant will lose, though, because I also know someone will win.

The challenge is to define criteria of knowledge which exclude contradictory knowledge claims and yet justify some knowledge claims. Gettier argues successfully that we do not know how to do this. I do not know who argues successfully that we do know how.

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  • And why should belief in a deity contradict belief in a causal universe (it's not clear what you mean by causal universe in the first place mind you)? – danielm Oct 13 '12 at 8:20
  • It is rational to hold a belief without proof. I might believe in a god because there is no better explanation of x y and z. I might believe in a god because I was inculcated with the belief. I may not be versed in science but believe scientists are reliable, and so trust its assertions. I may know that my beliefs in science and religion overlap and contradict, but have a need for both. So far no irrationality. – ataraxic Oct 13 '12 at 15:11
  • It is irrational is to say I have proof of and know two contradicting positions. The preface paradox is meant to exemplify the assertion of two contradictory knowledge claims. I know the facts are accurate and I know there is a mistake among them. – ataraxic Oct 13 '12 at 15:12

I'm not certain the preface paradox, as stated, holds water. Why? Because we ignore that our psychological constitutions do not dwell in some eternal world. Indeed, we think and perceive in time. Take, for instance, the phenomenon of cognitive dissonance. Now when an author writes his book, he may in fact experience certainty about the quality of his work. He may, when writing the preface, either out of institutionalized modesty or a genuine onset of doubt, come to experience a reduced certainty of the quality of his work. In fact, Ɓukasiewicz, in his book on the principle of contradiction, points out that Aristotle suggests three such principles in his work, one of then psychological, one which amounts to the assertion that one cannot hold two contradictory beliefs simultaneously. If that is the case, then one must ask whether what appears to be a contradiction to an observer is reconciled in some "hidden" way.

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I am not sure how this is a philosophy question, but as a psychology question the answer seems obvious. Cognitive dissonance is a real thing. Different parts or layers of a personality can believe opposite sides of a dichotomy, and action or analysis can give one of these influence over the other.

As the original Cognitive Dissonance experiments show, one can be made to believe something superficially for social reward that one does not hold at a deeper level. If you are distracted from thinking about it explicitly, acting on the superficial beliefs will cause your internal beliefs to shift toward them. The movement itself proves that both beliefs are in some sense real, and that the underlying mental processes are seeking harmony between them.

In fact it is quite common for unconsidered action to be motivated by the wish that one did not believe what one really believes, and attempting to disprove it through reality testing, to the point that it is a stereotype of trite psychology in bad writing -- I am a wimp, so I bluster, but the things I am saying are not false.

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Yes. One can consciously hold contradictory beliefs. Because of faith - an inner sense/belief that another principle is at work which is bigger than the immediate/apparent one.

Here are some statements from some theoretical authors upon being confronted with their preface paradox:

Author #1:

I know that my argument is contradictory. But I have faith based on a feeling or experience that I have missed something in my argument. While I can't pinpoint the specific reason any one of my arguments is wrong - I find it likely that at least 1 of the 100 elements involved in all the evidence, presuppositions, historical references, and the total logic chain, is wrong. I might have gotten a lot of "As" in school, but most of them were 95%-99%, 100%'s are a rare thing!

Author #2:

I researched everything in the book and fully believe my research was complete. But in the past I have believed it was complete and discovered I was wrong. Especially in a particular case where I did the final edit to a term paper in a marathon all-nighter kind of like the last 3 weeks of this book to meet my publisher's schedule...

So, I have a feeling, a gut feeling - a semi-logical argument in the back of my mind, based on a host of experiences, thoughts, discussions that I've had over the years - many of which I don't even explicitly remember any more, but have become a part of my psyche, that there is a decent chance I have missed something out of the entire work which involved 2 whole years of my life!

Granted, not formed as a strict proof or in elegant philosophical terms - but I hope I've conveyed the basic argument well enough!

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