Certainty and ErrorCertainty and Error One thing Russell seems right about is that we dont need certainty in order to know something. In fact, even Descartes grants this. Certainty and ErrorCertainty and Error The Certainty Argument (1)No one is ever certain of anything about the external world. (2) If S knows that p then S is absolutely certain that p. (3)Therefore, no one knows anything about the external world. Possibility of Error Argument (1)For any belief, p, S has about the external world S could be mistaken. (2) If a belief could be mistaken, then it is not a case of knowledge (3)Therefore, S does not know anything about the external world. Certainty and ErrorCertainty and Error It seems very easy to respond to the skeptic if we can just deny the second premise in these arguments. It is true that there is some slight possibility we are wrong. But we have no reason to think that we are. If knowledge does not require absolute certainty or something like it, it seems we have plenty of knowledge! Transmissibility Unfortunately there is another skeptical argument that does not rely on such implausible premises and has the same radical conclusion. Transmissibility Consider the following principle: Transmissibility: If I know p is true, and I also know that p entails q, then I can know that q is true. Is this principle true? Transmissibility It sure seems like it. If I know p, and know that p entails q, then it seems I could simply draw the inference in order to come to know that q! Unfortunately, if this principle is true, we can generate a powerful skeptical argument that does not depend on the requirement that knowledge be absolutely certain. Transmissibility The Transmissibility Argument (Table) 1.I cant know that I am not in the Matrix. 2.If there is a table here, then I am not in the Matrix. 3.I know that 2 is true. 4.If I know that there is a table here, and I also know that this is incompatible with being in the Matrix, then I can know Im not in the Matrix. 5.Therefore, I cant know there is a table here. Transmissibility There is nothing special about the table. I could run the same reasoning for any belief about the external world. One can immediately see that if the argument is sound, then we dont know anything about the external world. A Modern Version: Brain in a Vat Transmissibility The Transmissibility Argument (Hands) 1.I cant know that I am not a BIV. 2.If I have hands, then I am not a BIV. 3.I know that 2 is true. 4.If I know that I have hands, and I also know that this is incompatible with being a BIV, then I can know Im not a BIV. 5.Therefore, I cant know that I have hands. Transmissibility The argument is valid. Unlike the Certainty and Error arguments, none of the premises are obviously false. This is the puzzle that really requires an answer and it has stumped philosophers (and everyone else) for hundreds of years. For Next TimeFor Next Time Finish Bouwsma. Start reading Thomsons A Defense of Abortion (59-79) Jennas office hours today are cancelled. They will be rescheduled for next week. Moores Proof of an External World The proof: 1.Here is a hand. 2.Here is another hand. 3.Hands are external objects. 4.Therefore, external objects exist. A Proof???A Proof??? Moore claims that the proof is perfectly rigorous and that it is perhaps impossible to give a better more rigorous proof of anything whatever. (143) A Proof???A Proof??? Three conditions for a rigorous proof: 1.The premises are different from the conclusion (no question-begging or circular reasoning) 2.One must know that the premises are true. 3.The conclusion is validly deducible from the premises. A Proof???A Proof??? We ordinarily accept proofs of this kind: I dont believe my roommate when he tells me there is beer in the fridge. He can properly prove me to be mistaken by going to the fridge and pointing out a couple of beers. Similarly if we doubt that there are external objects, all that is needed is for us to produce one! Dissatisfaction with the Proof The skeptics argument purports to show that one cannot know things such as that one has hands. So how can Moore claim in response to the skeptic that he does know he has hands? Dissatisfaction with the Proof Moore concedes that he didnt prove that he has hands. However, as we already know proof and certainty are not required for knowledge! I can know things which I cannot prove; and among things which I certainly did know, even if (as I think) I could not prove them, were the premises of my two proofs. (105) Begging the QuestionBegging the Question But Moore seems to beg the question against the skeptic. One begs the question against if one assumes the falsehood of an arguments conclusion in ones premises. The skeptic gives an argument for the conclusion that Moore doesnt know that he has hands. Moore simply assumes that this is false without any argument! Moores ResponseMoores Response Moore thinks that if he is begging the question against the skeptic, the skeptic equally begs the question against him! One Mans Modus Ponens Skeptical Argument (condensed) 1.I cannot know that I am not a BIV. 2.If I know that I have hands, then I can know that I am not a BIV 3.I cannot know that I have hands. Moorean Argument 1.I know that I have hands. 2.If I know that I have hands, then I can know that I am not a BIV. 3.Therefore, I can know that I am not a BIV. One Mans Modus Ponens Skeptical Argument (condensed) 1.I cannot know that I am not a BIV. 2.If I know that I have hands, then I can know that I am not a BIV 3.I cannot know that I have hands. Moorean Argument 1.I know that I have hands. 2.If I know that I have hands, then I can know that I am not a BIV. 3.Therefore, I can know that I am not a BIV. One Mans Modus Ponens Moore thinks that all the premises of both arguments are very plausible. However, the one he is least likely to give up on is the claim that he knows he has hands (and other similar claims). Two Anti-Skeptical ProjectsTwo Anti-Skeptical Projects Ambitious Anti-Skeptical Project: Refute a skeptic on his own terms. Show to the satisfaction of the skeptic that one knows about the external world. Modest Anti-Skeptical Project: Establish to our own satisfaction that we know things about the external world, without contradicting obvious facts about perception and evidence. The Modest Anti-Skeptical Project Does Moore succeed in convincing us by our own standards that we know things about the external world? A Paradox RemainsA Paradox Remains For all of his cleverness, few people are convinced by Moores argument on its own. A Paradox RemainsA Paradox Remains Moore has shown that the following three claims are inconsistent: 1.Transmissibility: If I know p, and know that p entails q, then I can know q. 2.I cant know that I am not in the Matrix/dreaming/a BIV/etc. 3.I know that I have hands. A Paradox RemainsA Paradox Remains He may even be right that most of us wont give up on #3 as the skeptic demands. We still have been given no rational grounds to believe #3. Moore just insists that it is the most plausible. However, both of the other two claims seem extraordinarily plausible on their own. We still have no idea which one is false or why! A Paradox RemainsA Paradox Remains Without an answer to this puzzle, it is hard to shake the feeling that we are just being dogmatic about our supposed knowledge. If we have no rational reason to prefer #3 to the other two propositions, or know which of #1 or #2 are false shouldnt we suspend judgment?