If I Know, do I Know that I Know?by E. J. Lemmon

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<ul><li><p>If I Know, do I Know that I Know? by E. J. LemmonReview by: Risto HilpinenThe Journal of Symbolic Logic, Vol. 38, No. 4 (Dec., 1973), p. 662Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2272022 .Accessed: 14/06/2014 03:45</p><p>Your use of the JSTOR archive indicates your acceptance of the Terms &amp; Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp</p><p> .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.</p><p> .</p><p>Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to TheJournal of Symbolic Logic.</p><p>http://www.jstor.org </p><p>This content downloaded from on Sat, 14 Jun 2014 03:45:32 AMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/action/showPublisher?publisherCode=aslhttp://www.jstor.org/stable/2272022?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>662 REVIEWS </p><p>conjunctive propositions by using the letters A and B as propositional variables and laying down the following metatheorem: If (in a valid syllogism) the premisses are A and the conclusion B, then if A is necessary then B is necessary. </p><p>Here A denotes a conjunction. However, as Geach points out, Aristotle is able to derive in this way apodeictic syllogistic moods from assertoric ones only by the fortunate circumstance that "Necessarily (p and q) " and "Necessarily p and necessarily q" are equivalent. The corre- sponding move in the case of the problematic moods will not work, since "Possibly (p and q)" is not implied by "Possibly p and possibly q." STORRS MCCALL </p><p>E. J. LEMMON. If I know, do I know that I know? Epistemology, New essays in the theory of knowledge, edited by Avrum Stroll, Harper &amp; Row, New York, Evanston, and London, 1967, pp. 54-82. </p><p>ARTHUR C. DANTO. On knowing that we know. Ibid., pp. 32-53. These papers discuss the question whether knowing that p implies knowing that one knows </p><p>that p. If 'a knows that p' is abbreviated 'Kap', the thesis that knowing implies knowing that one knows can be expressed 'Kap -- KaKap'. In the sequel this principle will be termed "the KK-thesis." Both Lemmon and Danto argue that the KK-thesis is not a valid principle of epistemic logic, and present specific counterexamples to it. </p><p>According to Lemmon, 'Kap' can be taken to mean that a has learned that p and a has not forgotten that p. This analysis of knowledge can be expressed in the form (i) Kap +-* Lap &amp; </p><p>Fap, where 'Lap' means that a has learned that p and 'Fap' means that a has forgotten that p. (i) implies (ii) KaKap &lt; * La(Lap &amp; HFap) &amp; -Fa(Lap &amp; HFap). Lemmon accepts the follow- ing principle concerning forgetting: (iii) - Fa(p &amp; q) -H - Fap &amp; -rFaq. By virtue of (iii), (ii) implies (iv) KaKap -- FaLap. Lemmon argues that Lap &amp; HFap is logically consistent with FaLap, and consequently the KK-thesis is not valid. He supports this claim by an example of the following type: Let Q be a question, and assume that p is the correct answer to Q. Suppose that a is unable to answer Q at time t, but later (say at t + 1) realizes that p is the correct answer. According to Lemmon, a's ability to produce the correct answer at t + 1 shows that he had not forgotten even at t that p; thus at t both Lap and Fap are true. However, a's failure to recall the correct answer at t shows that he had (at t) forgotten that he had learned that p, and hence did not know that he knew that p. </p><p>In this case it is indeed natural to say that at t, a knew that p, but did not know that he knew that p. On the other hand, if a at t + 1 recalls the correct answer, he presumably also remembers that he had learned that p. Thus, if a's ability to produce the correct answer at t + 1 is taken as evidence that he at t knew that p, it can also be taken as evidence that he had not really forgotten that he had learned that p. Lemmon's counterexample to the KK-thesis is not entirely convincing. </p><p>Lemmon considers also some other definitions of knowledge and argues that they do not entail the KK-thesis, and criticizes various systems of epistemic logic based on the modal system T of Feys. </p><p>Danto's paper discusses and criticizes arguments by which Prichard, Hintikka, and Malcolm have supported the KK-thesis (or epistemological principles related to it). Danto presents the following counterexample to the KK-thesis: According to Danto, a can know that p only if he understands p, that is, if 'a understands p' is expressed by ' Uap', Kap -* Uap is valid. This implies (v) KaKap - UaKap. Danto says that a can know that he knows that p only if he understands "what knowledge is" and possesses an adequate theory of knowledge (p. 50). Kap does not require this; thus the KK-thesis is not valid. By " understanding p" Danto seems to mean understanding the sentence 'p'. This concept of understanding is relevant to knowledge only if it is assumed that knowing is a relation between persons and sentences, but this is an implausible conception of knowledge. Regardless of the interpretation of' Uap', Danto's claim that UaKap requires a correct philosophical theory of knowledge seems unwarranted: Even if it is conceded that KaKap requires that a (in some sense) understand what it is to know, this understanding hardly presupposes a theory of knowledge. RISTO HILPINEN </p><p>This content downloaded from on Sat, 14 Jun 2014 03:45:32 AMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p><p>Article Contentsp.662</p><p>Issue Table of ContentsThe Journal of Symbolic Logic, Vol. 38, No. 4 (Dec., 1973), pp. 551-752Measurable Cardinals and a Combinatorial Principle of Jensen [pp.551-560]Generic Expansions of Structures [pp.561-570]Equality in F [pp.571-575]Axiom Systems for First Order Logic with Finitely Many Variables [pp.576-578]On Complexity Properties of Recursively Enumerable Sets [pp.579-593]A Converse of the Barwise Completeness Theorem [pp.594-612]Model Existence Theorems for Modal and Intuitionistic Logics [pp.613-627]Prefix Classes of Krom Formulas [pp.628-642]Reviewsuntitled [pp.643-644]untitled [pp.644-646]untitled [pp.646-647]untitled [p.647]untitled [p.647]untitled [pp.647-648]untitled [p.648]untitled [pp.648-649]untitled [p.649]untitled [p.650]untitled [p.650]untitled [p.650]untitled [p.651]untitled [pp.651-652]untitled [p.652]untitled [p.652]untitled [pp.652-653]untitled [p.653]untitled [pp.653-654]untitled [p.654]untitled [p.654]untitled [pp.654-655]untitled [p.655]untitled [p.655]untitled [pp.655-656]untitled [p.656]untitled [pp.656-657]untitled [p.658]untitled [pp.658-660]untitled [p.660]untitled [p.660]untitled [pp.660-661]untitled [p.661]untitled [pp.661-662]untitled [p.662]untitled [p.663]untitled [pp.663-665]untitled [pp.665-668]untitled [pp.668-670]</p><p>Historia Mathematica [p.670]Notice of Summer Institute, Logic Colloquium, and Meeting of the Association for Symbolic Logic [p.671]Fellowship and Research Opportunities in the Mathematical Sciences [p.671]Fourth Biennial Meeting of the Philosophy of Science Association [p.671]Association for Symbolic Logic [pp.672-710]Index of Reviews: Volumes 37, 38 [pp.711-752]</p></li></ul>


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