PHILOSOPHY - Epistemology: The Preface Paradox [HD]

my name is Jonathan Weisberg I teach philosophy at the University of Toronto in this video I'm going to tell you about the preface paradox in 1965 David Macon s'en posed the following puzzle imagine an author writing a book of nonfiction maybe it's a history textbook in the books preface the author thanks everyone who helped them catch mistakes before it went to print then they graciously accept responsibility for the errors that inevitably remain understandably the author believes that the book still contains some errors after all is several hundred pages long so a few mistakes are inevitable maybe one of the dates is wrong or maybe the book says King Nick X decreed something that was actually decreed by Queen Nick why historical records are never perfect still the author of the book does believe each of the things they wrote otherwise they wouldn't have written them but that means the author's beliefs are contradictory they believe each of the historical statements they wrote in the book but they also believe that some of those statements are false so here's the puzzle where did the author go wrong which of their beliefs should they change usually when we realize that our beliefs contradict one another we change them Lois Lane starts out thinking Superman can fly but not Clark Kent when she learns that Clark Kent and Superman are the same person though she changes her beliefs she stops thinking Clark Kent is incapable of flight and starts thinking he is very much capable of flight so what should the author of our history book change to make their beliefs consistent should they retract the part of the preface where they admit the book contains errors that seems wrong nobody's ever written an error free history book certainly not one of that length maybe they should retract one of the historical claims in the book instead but if so which one as far as the author can tell they're all true they researched every statement in the book carefully after thinking about this a while you might start to feel like the author is stuck their beliefs are contradictory which seems bad but they don't have any good way of changing their beliefs to remove the contradiction even if they go back and triple-check every statement in their book they'll still have to admit that some errors are to remain makin sense puzzle isn't really about history books or historians it's about everyone we all have numerous beliefs about the world I believe that I was born in October that Gandhi was born in India that Andromeda is the galaxy closest to the Milky Way and so on but we also know that we make mistakes sometimes I've been wrong in the past I used to think Helsinki was the capital of Iceland now I know it's the capital of Finland and I'm sure some of my beliefs are still false that means everyone has contradictory beliefs including you imagine everything you believe written down in a book would that book contain any falsehoods of course it would nobody is infallible so at the beginning of your belief book we should include the following statement some of the statements in this book are false so your belief book contradicts itself one reason this paradox is troubling is that it calls the basic rules of logic into question we often point out internal contradictions in people's beliefs as a way of getting them to change their minds for example some atheists argue that people who believe in God have contradictory beliefs on the one hand they believe that God is perfect on the other hand they realize that the world is imperfect for example innocent people sometimes suffer often it seems unnecessarily that's contradictory say the atheists if a perfect God existed there would be no suffering in the world of course believers in God usually respond that there is no contradiction here despite appearances maybe the suffering is ultimately for the best for example so the world actually is perfect or at least as perfect as it's possible to be if you're interested in that particular debate check out Sally Hass langurs Wi-Fi video on the logical problem of evil but whichever side of that debate you think is right the point to realize here is nobody in that debate on either side is happy to just accept a contradiction believers in God try to explain why their beliefs are not contradictory after all in general when a belief leads to a contradiction we conclude that it must be false in fact that rule of logic is one of the oldest and most widely used in mathematics so the preface paradox creates a mystery everybody's beliefs are contour victory apparently everybody's belief book contains some mistakes and we all know that about ourselves at some level so are we all breaking a fundamental rule of logic all the time here's another simple law of logical reasoning that the paradox calls into question I believe that Omkara is in turkey call that belief eh I also believe the Bosporus is in turkey call that belief B so I should believe that Ankara and the Bosporus are both in Turkey in other words I should believe the combined statement a and B this simple rule of logical reasoning is so simple you probably don't even ordinarily notice it if a is true and B is true then the combined statement a and B is true so if you believe a and you believe B then you should believe the combined statement a and B but thanks to the preface paradox we know what happens if we apply that rule too many times imagine I collect together all my beliefs about Turkey into one long statement a and B and C and D and so on as I keep adding beliefs the chance of adding a false belief gets larger and larger if the big long combined statement is long enough the chance of an error somewhere in there is really high so I shouldn't believe that the statement as a whole is true that means at some point I have to break a simple rule of logical reasoning there comes a point where I have to say well I believe the combined statement a and B and C and D and so on I also believe some further statement call it X but I don't believe the combined statement a and B and C and D and so on and X so what should we make of this paradox some philosophers think it shows that belief and logic are really probabilistic I don't simply believe that on crows and turkey they say what I really think is that it's almost certain that it's in Turkey and you can't just conclude that a combined statement a and B is true because you believe a and you believe B you have to consider how probable the combined statement is and that depends on how certain you are about a on its own and how certain you are that B is true too so belief is fundamentally a matter of degree according to these philosophers we never really accept anything completely at least not if we're being reasonable instead we believe some things with a very high degree of certainty so high that we talk as if it were certain nevertheless we always acknowledge some chance of error deep down but other philosophers think that's unrealistic sometimes we do close the book on a question no reasonable person doubts that the earth is round not even the most humble scientifically minded geologists would say well we should keep an open mind maybe the earth is flat in fact as the philosopher Jennifer Nagel points out there's a large body of psychological research on this topic psychologists Aria Koga Lansky and Donna Webster have extensively studied when and how people treat a question as closed many philosophers also think it would be way beyond our abilities to reason in terms of probability all the time if we always had to calculate the chance that a and B are both true based on the chance that a is true and the chance that B is also true we'd never get up in the morning we have to think in terms of simple yes/no answers at least sometimes there's a big debate going on right now about how to reconcile the two sides of this argument on the one hand it seems right that nothing we believe is 100% perfectly certain if we step back and think about it carefully there's always some way we could be wrong on the other hand it seems right that we have to ignore the possibility of errors at least sometimes that way we can use simple laws of logic to get through the day maybe there's a way to combine these two approaches probabilistic reasoning which always admits uncertainty and simple logical reasoning which doesn't account for uncertainty but it's really not obvious how to fit these two ways of thinking together let me leave you with one last puzzle to chew on we said that pretty much nothing is a hundred percent perfectly certain there's always a chance of error however small but knowledge seems to require certainty if you know something is true you've ruled out all possible alternatives if you know the earth is round then it can't be flat or square or anything like that so if nothing is really perfectly certain then we don't really know anything it's hard to imagine how we could be wrong about the earth being round but you can imagine a way if you get creative enough maybe we're part of an experiment being conducted by an alien race like rats in a maze and whenever we get to the edge of the earth or fly up into the sky they move things around so it looks as if the earth is really round like moving the walls in the maze so the rat keeps running in circles it's absurdly improbable but it's a possibility however remote so here's the thing if some of our beliefs are bound to be wrong if there's always a chance of error then we don't really know anything any belief we have could be one of the false ones and we have no way of knowing which ones they are so the question I'll leave you with is this how can we reconcile the certainty of knowledge with the uncertainty created by our own phal ability you

Channel: Wireless Philosophy

Views: 83,147

Rating: 4.4567165 out of 5

Keywords: Khan Academy, Philosophy, Wireless Philosophy, Wiphi, video, lecture, course, epistemology, logic, belief, reason, paradox, Preface Paradox, University of Toronto, Jonathan Weisberg, Jennifer Nagel, brain in a vat, contradiction

Id: 7fwQJu9ywT4

Length: 9min 50sec (590 seconds)

Published: Mon May 23 2016

Reddit Comments

[u/draaroncox]

We are given the following premises: 1.) Author believes everything he wrote to be true. 2.) Author believes that he may have written at at least one false statement.

However, the first premise could be more accurately worded to say "the author believes what he wrote to be generally true". The problem is not a logical error. The problem is that the knowledge that exists outside of ourselves has a chance of being false because we do not know it for certain to be true. However, in order for us to operate in a manner outside our minds, we must hold our outside experiences to be generally true, while accounting for the small possibility that they are not. Nevertheless, we are able to come to certain truths that do not come from experience. These are things such as basic logic and math, and because we are able to come to these truths without outside experience, we do not need to account the the possibility that they may be false.

Given this, I would change the premises of this problem to the following: 1.) The author believes what he wrote to be generally true. 2.) The author believes that there is a possibility one or more statements he wrote may be false.

I would also propose that the problem could be solved by separating knowledge gained from outside of us from knowledge "from within us" such as logic. Doing this, we would operate on probability-based knowledge in regard to knowledge gained from outside experience and certainty-based knowledge in regard to that knowledge we are able to figure out independent of experience.

[u/Glayden]

"If you know something is true, you've ruled out all possible alternatives"

Yeah, no. That's an absurd claim. Absolute certainty isn't required for knowledge. The epistemic closure principle is not accepted as a requirement for knowledge in any reasonable definition of knowledge and is only given by some skeptics to create an idealized version of knowledge which has virtually no relation to how the word is used in any real world context. The term "knowledge" becomes useless in practical settings if you require absolute (warranted) certainty since no one can ever be said to know anything with such a definition (brain-in-vat, evil demon, faulty memory, etc. would make ruling out all other possibilities with absolute certainty impossible). Let's not conflate "knowledge" in some pure/unattainable sense posed as an ideal by epistemic skepticism with the word as we use it in every other context.

There's no paradox here. People are not perfectly precise rational beings and do not have the capacity to be perfectly rational in determining the exact degree of confidence that should be associated with each belief. We use loose approximations and we inevitably believe some things which are false and contradictory as our beliefs become composed of many approximations. The probabilistic model is about how we would want to rationally work with our beliefs to maintain self-consistent degrees of confidence for beliefs, not about our actual capacity to do so perfectly.

[u/inom3]

1) first he should notice the distinction between specific beliefs about facts and a meta-belief about the possibility that one of these beliefs (or more) may turn out to be false. It is NOT the situation that someone believes P and not P. It is rather that one has carefully accounted a large set of beliefs, making up the book, and it is in fact true that one believes all of them, but that when one thinks of the book as a whole, one recognizes that it is likely that one is incorrect about something in the book. There is something to be reconciled here, but it is not the P not P paradox he presents. 2) he then mentions the earth is flat belief, AS IF this was a good example for all the beliefs in a book. In fact, in pretty much any book, there will be large numbers of assertions that are not at the level of certainty involved in believing the earth is not flat. So while he does bring in the idea of probability - more on this later - his example is poor, precisely because a person who refers to the non-flatness of the earth assertion in his book, is not expecting that particular belief or ones like it, to be the problematic ones where he may be wrong. 3) He brings in probability, but then presents a counter argument that it is too complicated to work out the probabilities. But who would argue that we do. We have a sound, gut sense, that even some rather seemingly obvious truths can turn out not to be true. We do not do the math, we intuitively guesstimate. No contradiction. We have beliefs we are totally sure of. We have others that we think are incredibly likely to be the case and so on down. Books are generally not meant to be taken like Bibles and we realize this, most of us. So while Nature magazine might demand that we include in our article the statistics we used to draw the meta-belief that there are likely errors in the book, we do not do this, nor do we need to.

There is no contradiction here.

[u/Shortneckbuzzard]

I interpreted the final question to be this. How can we be right about anything we know, if there is a chance that we can be wrong? My response to the question is this. Because the probability of being right out weighs the probability of being wrong.

[u/mywan]

I take the probabilistic side of the argument. As far as I'm concerned the notion that uncertainty negates knowledge suffers the same logical errors that the notion beliefs represent knowledge do, and implicitly depends on a conflation between validity and truth. A good example is the distinction between a mathematical proof and a well verified physical theory. The reason mathematicians can offer proofs that physicist can't is because they can select belief a&b and define a&b true axiomatically. Then say that c provably follows when a&b are true. That is valid knowledge, even if it's not uniquely valid knowledge.

Take Riemannian geometry for instance. It was created as a purely intellectual exercise that explicitly began by choosing axioms that essentially contradicted those of Euclidean geometry. It wasn't till later that it was used as the foundation for General Relativity. Only we can't say that the validity of Euclidean geometry is falsified just because Riemannian geometry is valid.

Those who would say that reality if non-Euclidean because Riemannian geometry is valid, implying Euclidean geometry is invalid, are conflating validity with capital Truth. Two propositions that take opposing axiomatic propositions can be equally as valid. Understanding that both, and other undefined alternatives, can be equally as valid is knowledge irrespective of any application errors in the use of that knowledge.

Knowledge is not an absolute that you can then automatically reject the validity of any alternative axioms just because they aren't in line with your selected axioms. Validity and capital Truth are very distinct things, are can be valid without being uniquely valid.

[u/SpentitinGenoa]

Fallibility.... Yes, we must take everything with the proverbial grain of salt. As he said we are "almost certain that bosphorous is in turkey".

It's all about becoming familiar with unorthodox perspectives so that ours as an individual can be a well rounded opinion.

[u/tonsofpcs]

I think the problem here is more in the interpretation of the two beliefs. The author believes that the premises A & B & C ... & X are individually true and collectively true. He also believes that one of those is not true, however that latter belief is better stated logically as a belief that a belief is false not a belief that a premise is false. That is to say, he believes A, B, C, D, E, ..., X are true - let's call these beliefs B_A, B_B, B_C, .... Note that we haven't assigned truth values to these beliefs (only the premises, via the beliefs), we have just stated that they exist. Further, he believes that one of these (B_X) is false. Thus, by B_A... B_W, A ... W are true. By the belief of B_X being false, X is false. There is no contradiction.

(My apologies if the explanation is a bit convoluted in this stream-of-consciousness paragraph attempt)

[u/[deleted]]

The biggest contradiction I saw here was the narrator, after acknowledging that when we're being careful, we reason probabilistically, and then proceeds to talk about knowledge requiring absolute certainty.

He just defined himself into irrelevance by writing bad rules to the game-rules that don't allow any progress. Those rules result in a soccer game where the score, in addition to being low by virtue of it being soccer, are made even lower, as if Zenos Paradox was rolling the ball's movement.

[u/[deleted]]

If this philosopher applied his skepticism to his own beliefs concerning this entire video, then by his own logic he could be wrong.

But if he admits what he said could be wrong, then he would actually be admitting that certain knowledge, at least about some things, does in fact exist.

In other words, universal skepticism is self-refuting.

Just because we could be wrong about some things, does not require us to doubt all of our convictions. That is asking too much. It is like a self-directed ad hominem tu quoque fallacy.