Introduction to Mathematical Logic

July 8 -- August 8

The aforementioned textbook and software introduce the notation mathematicians use to formalize logical reasoning and to give a precise meaning to the notion of "truth". We'll discuss the notion of a "model" of a language (a miniature universe in which statements of the language are true or false) and the possibilities of a statement being true in one world and false in another, or true in several different worlds. We'll discuss the notion of logical consequence (under what circumstances one statement necessarily follows from another), its formalization in mathematical inference rules, and the correspondence of those formal rules to the informal principles of sound reasoning used by real human beings. We'll also mention some of the major paradoxes and problems in the history of logic, and some major breakthroughs of 20th-century logic.

**Homework 1**assigned 9 July, due 16 July:-
problems 2.3,2.4,2.5,2.19 to be turned in on floppy disk

problems 2.6,2.9,2.14,2.18,2.21,2.22,2.24 to be turned in on paper or by email

problems 2.1,2.2,2.15,2.16,2.17 to be done but not turned in or graded (if you specifically want feedback on one of them, turn it in on paper and write a comment in the margin telling me what you'd like me to look at).

**Note:**in problem 2.9, some of the sentences may be**impossible**to translate.

**Note:**in problem 2.19, you are required to build counterexample worlds for the invalid arguments. For the valid ones, try (as an "optional exercise") to write informal proofs of them. **Homework 2**assigned 16 July, due 23 July:-
problems 3.24-3.26,3.32-3.34,3.42,3.43,3.56,3.59,3.60
to be turned in (on disk, paper, or email, as appropriate)

problems 3.5,3.12-3.14,3.18,3.19,3.30,3.31 to be done at your discretion, but not turned in unless you have a specific question. **Homework 3**assigned 23 July, due 30 July:-
problems 4.11,4.14,4.16,4.23,5.8,5.10,5.12,5.18,5.19 to be turned in
**in groups**if you wish. Turn in one disk, and one paper with the names of all the students who "contributed significantly" to the answers.

problems 4.3-4.8,4.18,4.23-4.28,5.1-5.7,5.9,5.11,5.13-5.15,5.21 to be done at your discretion. (Yes, this is a lot of optional problems. I really think they'll help you understand the material, but use your own judgment to decide how much time to spend on which.) **Homework 4**assigned 30 July, due 6 Aug:-
problems 5.25,5.32,5.39,6.34,6.37,6.45 to be turned in
**in groups**as above.

problems 5.23-32,5.36-41,6.2-4,6.11-12,6.18-21,6.29,6.32,6.35,6.52 to be done at your discretion. (Again, this is a lot of optional problems. Do as many as you think you need and have time for.) **Homework 5, aka Take-Home Final Exam**to be assigned 5 Aug, due 8 Aug.

Date(s) | Assignment | Reading | Lecture Subject | |
---|---|---|---|---|

8 July | Introduction, administrivia, history | |||

9 July | HW1 | pp. 1-15, 283-293 | Relationships among objects | |

11 July | pp. 16-34 | First Order languages and proofs | ||

15 July | pp. 35-66,293-295 | Relationships among statements | ||

16 July | HW1 due; HW2 | pp. 67-90 | Formal proofs and other topics | |

18 July | pp. 91-97 | More relationships among statements | ||

22 July | pp. 97-106 | More on conditionals and biconditionals | ||

23 July | pp. 106-122 | Quantifiers | ||

25 July | I'll be at a conference on teaching logic | |||

29 July | pp. 123-134 | Translating and using quantifiers | ||

30 July | HW3 due; HW4 | pp. 134-153 | Proofs with quantifiers | |

1 Aug | pp. 154-171 | Multiple Quantifiers | ||

5 Aug | HW5 | pp. 172-184 | Proofs with multiple quantifiers | |

6 Aug | HW4 due | Review and catch up | ||

8 Aug | HW5 due | pp. 227-240 | Mathematical Induction |

Last modified: Tue Jul 30 10:31:27 EDT 1996 Stephen Bloch / sbloch@boethius.adelphi.edu