Knowledge and Belief - An Introduction to the Logic of the Two Notions

by Jaakko Hintikka, Vincent F. Hendricks (Compiler), John Symons (Compiler)

Knowledge and Belief An Introduction to the Logic of the Two Notions by Jaakko Hintikka Prepared by Vincent F. Hendricks & John Symons In 1962 Jaakko Hintikka published Knowledge and Belief: An Introduction to the Logic of the Two Notions with Cornell University Press. Almost every paper or a book on epistemic and doxastic logic that has appeared since then has referred to this seminal work. Although many philosophers working in logic, epistemology, game-theory, economics, computer science and linguistics mention the book, it is very likely that most have never literally had their hands on it, much less owned a copy. After a fourth printing in 1969, Knowledge and Belief went out of print and as many of us have found to our dismay, it has become increasingly difficult to find used copies at our local shops or online. It is our pleasure to provide the interdisciplinary community with this reprint edition of Knowledge and Belief. Knowledge and Belief is a classic on which a generation - my generation - of epistemologists cut their teeth. This reissue is welcome. It will provide something for the next generation to chew on. - Fred Dretske, Duke University It is wonderful to see this classic being reissued after so many years out of print. It was extremely influential in its day; its influence continues to this day, through the impact of epistemic logic in fields as diverse distributed computing, artificial intelligence, and game theory. This reissue should make it possible for a new generation of researchers to appreciate Hintikka's groundbreaking work. - Joseph Halpern, Cornell University

Genres: Philosophy, Logic, Academic

148 pages, Paperback

First published May 18, 2005

Reviews

[Jesse Maurais · Rating 5 out of 5]

All of philosophy, in some way or another, is about knowledge. But it is not in the purview of logic to say what the facts are. So an epistemic logic is not concerned with how we derive knowledge from experience. Rather, it is about how we use terms like "know" and "believe" when we make claims about what is the case, or we state our convictions. This is a qualitatively different thing than stating what facts there are to know. Hintikka is concerned with how we can make knowledge claims in a consistent (defensible) way or how we can determine when what we say is indefensible (when we are being inconsistent.) And to this end Hintikka proposes a set of conditions which trace out precisely what our intuitions do under a limited definition of what it means "to know." (Other connotations such as "to be aware" are something he mentions but does believe his theory is apt for addressing.)

It should be stated up front that his formal system is set down in modal terms. Modal logic is fascinating in its own right. It has a history that goes back to medieval philosophy when Duns Scotus used it to argue for the freedom of the will. And today it is central to machine learning and artificial intelligence algorithms. Modal logics make others look poor in comparison, and applications of these others to many complex problems look naive where modal logics also apply.

Briefly, modal operators are inter-definable by the formula "~□p = ◇~p" where p is any declarative sentence. We read "◇p" as "It is possible that p" and "□p" as "It is necessary that p" where the locution "p is impossible" is translated as "It is not possible that p" or "It is necessary that not p." And we call □ the dual of ◇ and vice versa. One important thing to recognize--and this goes a long way to understanding why modal logics are so useful--is that {p, ◇~p} is a consistent set of sentences. It says that, while p is true, it may have been otherwise; p is contingent, not a necessary truth. This is the general idea of modal logic, where the epistemic logic of Hintikka's book is a special application.

Epistemic logic takes "knowing" denoted by the symbol K as a modal operator analogous to □. But the English language does not have a word for the dual of K. So we reuse the word "possible" in a slightly different sense and write our formula "~Kp = P~p" to draw an equivalence between "It is not the case that I know p" and "It is possible, for all I know, that not p."

Claims to knowledge using the K operator are epistemic. Those of belief use the B operator and are called doxastic. Similar to K, B does not have a dual in the English but we reuse "consistent" denoted by C so that "~Bp = C~p" means "It is consistent, given all that I believe, that not p." But K and B are not merely the same operators in different symbols; there are significant semantic differences that will result in different truth values for certain sentences if we merely swap out one symbol for the other. This difference can be expressed by noting that the implication Kp → p is always true but Bp → p is sometimes false. This is due to the definition of knowledge as justified true belief. You cannot know what is actually false. If what you believed turned out to be false, it wasn't really knowledge. But of course someone can err in believing what is not true. This difference reverberates through all subsequent discussion in the book about epistemic and doxastic logics.

As for the truth conditions Hintikka gives, by which we determine whether statements translated into the above syntax are defensible (i.e. consistent.) I cannot reproduce them here without reproducing a substantial part of his book, so I won't try. But I will give the basic idea. If one utters the statements {~Kp, P~p, Pp} on an occasion, one can be shown to be consistent. The defensibility of the set of sentences can be shown by a super set {p, ~Kp, P~p, Pp} which also asserts that p. That is to say: p is true, but I do not know that p, and for all I know p is true, and for all I know p is false; I simply do not know whether p. This is due to the fact that ~Kp does not imply ~p the way that Kp implies p. It is fallacy to say that "not knowing whether p is knowing that not p." And in fact this is the same crucial difference mentioned about general modal logics above.

The utility of Hintikka's conditions is that we can give definitive answers to several perplexing statements. For example, is "to know that one knows" any different than "knowing" simpliciter? It is not uncommon, after asking how someone knows what they just claimed, to hear in reply that they just know that they know it. It would seem to infer that there is a hierarchy to knowledge, and I would be just as capable of seeing the truth of their claim if only I had access to the same higher sphere of knowing as they. Alas, I do not. But I always felt like such answers were an evasion. In Hintikka's system such answers would not be answers at all because "Kp" and "KKp" can be shown to be equivalent. Anyone making such a statement in defense of a knowledge claim is merely reasserting what they first said, under Hintikka's system.

Another strange statement is G.E. Moore's example "p but I do not believe that p." Under slightly different conditions Hintikka finds that this statement is doxastically indefensible. The set {p, B~p} ought to be written B(p & B~p) if the one uttering it actually believed what they said. But one cannot simultaneously believe p and believe that they believe it to be false. There is a very thorough treatment of this and related sentences in the book.

There are many other interesting consequences of Hintikka's system, some of which are quite deep. But I could not expound enough of his system in a review to even state them appropriately, let alone convince anyone with the same kind of force that the book is capable of doing. It is a classic. I would regard it as required reading for anyone who has an interest in logic.

Addenda.
This is a new printing of the first edition, not a second edition. It contains some typos and errors, including one meandering sentence. Most of the errors are harmless (like a missing bracket where it is obvious from context what was meant. There is at least one typo in a proof that makes it invalid. I wanted to point it out. On p.47 of section 4.1 (Knowing that others know) there is a proof of the statement "(a knows that b knows that p) implies (a knows that p)." Line 25 of the proof has "Ka p" where it should have "Kb p" otherwise the result does not follow.

[Kaidi Pan · Rating 3 out of 5]

A seminal moment of one strand of formal epistemology.

[Joshua Stein · Rating 3 out of 5]

Though it requires an understanding of formal logic, Hintikka is still relatively accessible to the reader who is not as familiar with Epistemic logics. There are some structural problems with Hintikka's writing that make it difficult as an introductory text. For example, Hintikka is often unwilling to show the full proofs he is arguing, leaving some very serious gaps for the reader.

The extent to which I can endorse Hintikka as right about epistemology is very limited. There are some claims that he makes that are controversial (and objectionable) in epistemology. With that consideration, though, it is still worth reading.

[Ninni]

An illuminating account of the logic of knowledge and belief.