If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Theory of Knowledge: Analyzing Knowledge #2 (No-False-Lemma and No-Defeater Approaches)

If we can’t analyze knowledge simply as justified true belief, can we add one more ingredient to produce a successful analysis? In this Wireless Philosophy video, Jennifer Nagel examines two ‘extra ingredient’ analyses of knowledge: Michael Clark’s ‘no false lemma’ analysis, and the fancier ‘no undefeated defeaters’ analysis of Keith Lehrer and Thomas Paxson.

Speaker: Dr. Jennifer Nagel, Associate Professor, University of Toronto.

Want to join the conversation?

  • orange juice squid orange style avatar for user Daniel Rigal
    Could "no false lemma" be fixed just by saying "no indispensable false lemma"?

    What I mean is that if the lemma was false, and that was a vital link in the chain to the final belief, then that is not knowledge, just a belief that is true by chance. Alternatively, if the false lemma was something you can safely throw out without affecting the result (e.g. kicking out the one witness who didn't see the crime and relying on the others) then it is still valid knowledge.

    I know this would be a patch on top of a patch, and that is not great, but it does sound like it could be OK. Am I missing something? Has anybody else tried this? Intuitively this feels better to me than the vague notion of a "defeater".
    (2 votes)
    Default Khan Academy avatar avatar for user
    • spunky sam blue style avatar for user Dalendrion
      How many lemmas are you willing to throw out without affecting the result?
      Say there were 100 witnesses. 50 say Jones dun it, and 50 say Jones didn't dun it.
      If my belief is Jones didn't dun it, can I throw out the 50 witnesses who say he did dun it?
      If my belief is Jones did dun it, can I throw out the 50 witnesses who say he didn't dun it?
      (1 vote)

Video transcript

my name is Jennifer Nagel I teach philosophy at the University of Toronto and today I want to talk to you about analyzing knowledge this video looks at two different ways to do this both of which are modifications of the classical analysis of knowledge as justified true belief the pure JTB analysis of knowledge is not very popular now it's widely agreed that there are effective counter examples to it like the Gettier cases described in the last video the person who looks at a stopped clock at just the moment when it happens to read correctly has a justified true belief without knowledge but some philosophers have felt that we can get a good analysis of knowledge if we just add one thing to the JTB formula today we'll look at two different theories about what that one thing might be the no false belief analysis and the no de feeders analysis you may have noticed that the characters in get ears cases had something in common although they ended up believing something true they relied on a false belief on their way to getting the truth so when Smith believes that the man who will get the job has ten coins in his pocket what he believes is true but he infers this true conclusion from his false belief that Jones will get the job equally the person who tells the time by looking at a broken clock presumably has a false belief that the clock is working right after Gettier published his paper a philosopher named Michael Clarke argued that you could patch the classical analysis just by ruling out reliance on false belief according to Clarke's analysis S knows that P if and only if one p is true two s believes that P 3 as is justified in believing that P and for it is on true grounds that S believes that P one problem with this approach is the condition for seems to rule out some perfectly good cases of knowledge imagine a detective who has eight kind of evidence that a certain person is guilty of a crime videotapes DNA dozens of witness statements and this detective makes a true judgement about the culprit on the basis of all this if even one of the witnesses is lying when he says he saw what happened maybe he wasn't there then no matter how much other evidence she has the detective can never know who is guilty on Clark's theory because she won't be making up her mind on entirely true grounds so Clark's theory is too strict if we want to accept the common-sense view that in some cases people can gain knowledge despite the presence of some false beliefs as long as their overall evidence is strong enough the no false belief theory faces trouble on the other side as well it is designed to handle cases of inference where we believe something on the grounds of something else but not all Gettier cases turn out to involve inference here's an example from the classical Indian tradition a traveler is walking in the desert and has a hallucination of water in the valley ahead he goes down into the valley and by chance there is water there hidden under a rock the traveler never makes an inference from a false belief he just immediately believes there is water in front of him on the basis of his visual experience and that belief is true and in some sense justified will say that his hallucinations totally realistic but it seems wrong to say he knows that there is water in the valley as he stands there hallucinating a more sophisticated version of the no false belief analysis is the no defeater analysis developed by Keith Lehrer and Thomas Paxson in 1969 they divide knowledge into two kinds basic and non-basic basic knowledge is the kind of self-evident awareness you have when you know that you have a headache for example Lehrer and Paxton analyzed basic knowledge as true belief for which there's complete justification that doesn't depend on any justifying statement it's non basic knowledge that generates the trouble in getting your original examples now unbasic knowledge has supporting evidence if someone asks Smith why he believes that the man who will get the job has ten coins in his pocket he'd explain that he saw Jones pocketing the coins and heard what the company president said ordinarily this supporting evidence would be great justification the problem in the Gettier story is that there's a justification destroying fact lurking out there that Smith doesn't know about the fact that Jones won't get the job lera and Paxson call this hidden fact a defeater if Smith knew that Jones wasn't going to get the job Smith wouldn't be justified in believing that the man who will get the job has ten coins in his pocket Lehren Paxson analyzed non basic knowledge as undefeated justified true belief as long as there are no nasty hidden surprises out there in the world waiting to destroy your justification you're justified true belief will be knowledge there is a little complication in their account they don't want to say that knowing requires absolutely no de features at all to show that it's possible to have knowledge despite the presence of a defeater Lehren Paxson offer the following story you're in the library one day and see a man stealing a book you're sure you recognize him as your fellow student Tom Gravatt at this point it seems that you know that Tom Gravatt has just stolen a book from the library but wait here's a hidden fact Tom's mother mrs. Gravatt is sitting at home by her telephone ready to testify to the police or anyone else who calls but actually Tom could not have been in the library today because he's over a thousand miles away she's also going to advise everyone that you might have seen Tom's identical twin brother John Gravatt who told her he was going to the library to get a book he desperately needed so at this point it seems that your justification has now been defeated and you don't know that Tom rabbit has stolen a book from the library after all but wait there's one last twist there's a further hidden fact that cancels out the first hidden fact about mrs. Kravitz testimony the further fact is that mrs. Gravatt is a pathological liar and there never was any twin her only Son Tom really did take the book and you saw him do so your original defeater has itself being defeated and you actually had all along what Lara and Paxton call an undefeated justification for your belief the fact that there was some hidden evidence apparently contrary to your belief doesn't crush its justification because there was also some further hidden evidence showing that you had nothing to worry about at the end of the day defeat ours are okay as long as they ultimately get defeated it's only undefeated the feeders that can stop you from having knowledge this theory faces a number of challenges starting with difficulties cashing out just what is meant by justification without using the concept of knowledge itself this is an especially big problem in the basic knowledge clause what does it mean exactly to say that you have a true belief with complete justification the theory may also have a problem with the desert Mirage case where your belief is true and doesn't seem to rely on you accepting any justifying statement it looks like the theory could classify this as a case of basic knowledge which is a problem if we think the desert traveler doesn't know that there's water in the valley another challenge for the theory lies in explaining which defeatist should count as ultimately undefeated especially in getting your cases where what we believe is ultimately true so any evidence against it should ultimately count as misleading if you like these series you could think about ways of improving them another option is to look at different approaches the next video looks at two fresh ways of analyzing knowledge you