Logic Resources

 

Recommended Texts

Copi, Irwin. Symbolic Logic. (The text is pitched at the same level as Tomassi’s Logic. It covers predicate logic, and then the meta-theory of propositional and predicate logic including the limitative results of Gödel and Skolem. An Indian edition of this copy is available at Saeed Book Bank.)

Hunter, Geoffery. Metalogic: An introduction to the meta-theory of standard first-order logic. (The first few sections of the book are pitched at an elementary level.)

 

Advanced Reading

Enderton, Herbert. A Mathematical Introduction to Logic. (For students intending to study the completeness proofs of propositional and predicate logic, and the limitative results including the Gödel’s Incompleteness Theorems I and II, and Lowenheim-Skolem Theorem. This text is recommended over the ones given below. An Indian edition of this book is available at Saeed Book Bank.)

Bell & Machover. Set Theory, Logic and their Limitations. (pp. 1-9, 101-282) (This is the popular text in university courses. It covers the same material as Enderton’s text. But, it is more terse, and thus harder to follow. Students interested can cover this text and use the Enderton text as a reference.)

Boolos, George. Computability and Logic. (The chapters on limitative results are easier to follow than perhaps ones in Bell & Machover.)

 

Other Links of Interest

Dirk Schlimm’s webpage on History and Philosophy of Mathematics

Michel, Hallett. “Foundations of Mathematics” in Cambridge History of Philosophy. (This is an overview of the revolutionary developments that took place in mathematics at the end of 19th and the beginning of 20th century.)

 

Guidelines for Logic Education from the Association of Symbolic Logic.

Britannica Entries: Logic, History of Logic, Philosophy of Logic, Philosophy of Mathematics, Foundations of Mathematics, Set Theory.

 

Some Logical/Philosophical Questions?

  1. Can actions determine intentions? (Comment on the link between actions and intentions, is the link probable, necessary, certain etc.). Example: Consider this scenario: The eye-witnesses claim (all of their claims are consistent) that Mr. X picked up a gun and shot Mr. Y dead. Is it certain that he intended to kill him? Come up with an alternative interpretation in which X does not intend to kill Y, yet ends up doing so. If you were the judge, and only the eye-witness accounts were available what would you do? If X presents your interpretation of events would you let him go. (Your argument should consider whether in order to give a decision on an event does one’s conclusion be certain or merely highly probable—and according to whose judgment?).
  2. If P ¢ C. The show that P, ~C ¢ X & ~X, i.e. yields some contradiction.
  3. Prove that if P ¢ X & ~X then P ¢ Y & ~Y.
  4. A groups of scholars at the beginning of 20th century claimed that: “Whatever is not empirically testable is meaningless”. Assess their claim.
  5. Analyze the claim: “God is a figment of your imagination”.
  6. Some Orientalists (western scholars of Islam typically hostile to the religion) claim that Abu Bakr, the first caliph, declared wars of Rida (apostacy) for the sake of booty. Analyze their claim. (Hint: You do not need to get into the historical issues. Just pay attention to the language of the claim.)
  7. “Science is truth?” Analyze. (1. Explain what does this claim amount to, by laying out what this statement really implies in terms of scientific theories. 2. Then show if this claim is correct in all such cases. 3. If it is not, then clearly state so.)
  8. If something is logically impossible then can it be physically possible?
  9. If something is physically impossible then can it be logically possible?
  10. X claims that P ¢ C. But C is absurd so P is false. Now when you analyze the argument you realize there is a hidden assumption A which X is using surreptitiously. Show that, because of that assumption, the falsity of C does not entail (by MT) the falsity of P.
  11. What is a world-view? What is a fact? Does our world-view shapes facts? Give examples.
  12. The Batanis, a deviant sect in Islam, claimed that language of the Quran does not mean what people believe, but it means what they know through esoteric knowledge. So, mountain does not mean mountain but means man, and vice versa.
  13. What is wrong with the claim that “Bible is the word of God, because it says so in the Bible”. Does this show that Bible is not the word of God?

 

 

 

 

 

 

 

Hosted by www.Geocities.ws

1