Per the title, what are some of the oldest books on logic out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
Update: Doesn't have to be mathematical logic per se. I mean logic at large.
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asked Dec 7, 2019 at 4:35
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$\begingroup$ I do not have it at hand to check (hence this is just a comment instead of an answer), but the first edition of Bourbaki's E.I contains (as far as I can remember) unsolved exercises and is from 1954(?), thus a bit older than the books mentioned by Carlo below. $\endgroup$– Fred RohrerCommented Dec 10, 2019 at 11:52
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9$\begingroup$ By "unsolved exercises" do you mean "exercises without solutions presented in the text" or "exercises which are currently-open problems"? $\endgroup$– Noah SchweberCommented Dec 10, 2019 at 18:35
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4 Answers
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The update to the question now asks for "logic at large" -- rather than specifically mathematical logic. Then one can go back to before the 20th century, as in:
Studies and exercises in formal logic, J.N.Keynes, 1884.
Questions and exercises in elementary logic, deductive and inductive, W.H. Forbes and D. Hird, 1875.
Exercises in logic, J.T. Gray, 1845.
Logic; or, The art of reasoning simplified. With exercises on a variety of interesting topics, to guide and develope the reasoning powers of the youthful inquirer after truth, S.E. Parker, 1837.
one exercise from Keynes
answered Mar 8, 2020 at 22:21
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I have not succeeded in going back much more than 50 years for a textbook on mathematical logic with excercises:
Introduction to Mathematical Logic, by Elliott Mendelson (1964)
Mathematical Logic, by Joseph Shoenfield (1967)
Mathematical Logic: A First Course, by Joel Robbin (1969)
one exercise from the 1964 book
answered Dec 10, 2019 at 11:33
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1$\begingroup$ Which ones of these are unsolved? $\endgroup$– VincentCommented Mar 4, 2020 at 10:46
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$\begingroup$ ? The text gives no solutions, isn’t that what is meant by an “unsolved exercise? $\endgroup$ Commented Mar 7, 2020 at 18:58
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$\begingroup$ It is one of two common meanings, see Noah's comment on the original post. I was thinking about the other meaning $\endgroup$– VincentCommented Mar 7, 2020 at 20:24
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2$\begingroup$ @Vincent -- this particular question is one in a series of questions by the OP, who is clearly interested in problems in a text book without a solution in the same text. $\endgroup$ Commented Mar 8, 2020 at 10:56
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In Symbolic Logic by Lewis Carroll (1896), most of the exercises have solutions, but there are four problems in the appendix (pp. 185-188) that do not. Carroll writes "I shall be very glad to receive, from any Reader, who thinks he has solved any one of them, what he conceives to be its complete Conclusion."
(These four problems were apparently meant as a preview of Part II of the work, which Carroll did not complete before his death in 1898. It seems a version was eventually published in 1977.)
answered Mar 4, 2020 at 3:57
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What about Hilbert/Ackermann: Grundzüge der Theoretischen Logik (1958), 4th edition. This edition definitely has unsolved exercises. I have no access to former editions. The first one is from 1928. There is no remark in the 1958 edition that excercises have been added.
answered Dec 10, 2019 at 12:03