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 .

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662 REVIEWS

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.

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

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 & Row, New York, Evanston, and London, 1967, pp. 54-82.

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 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.

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 &

Fap, where 'Lap' means that a has learned that p and 'Fap' means that a has forgotten that p. (i) implies (ii) KaKap < * La(Lap & HFap) & -Fa(Lap & HFap). Lemmon accepts the follow- ing principle concerning forgetting: (iii) - Fa(p & q) -H - Fap & -rFaq. By virtue of (iii), (ii) implies (iv) KaKap -- FaLap. Lemmon argues that Lap & 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.

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.

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.

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

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