- Ted Sider, Fall, 1998

This will be an introductory course on systems of logic whose natural semantics are of the possible worlds variety, including propositional and predicate modal logic, counterfactual conditionals, and tense logic. Additional topics may include counterpart theory, multiple indexing and supervenience.

Any standard introductory course in propositional and predicate logic.

Required text: G. E. Hughes and M. J. Cresswell, *A
New Introduction to Modal Logic*. Note not to panic: we will
*not* cover all of the material in Hughes and Cresswell, not even
all the material in the assigned portions; this course will be a little
less logically "high-powered" than Hughes and Cresswell. **Note on symbolism**:
I will not use the same symbols as used by Hughes and Cresswell, so care
must be taken in integrating class discussion with the discussion in the
text.

Other reading material: If you're interested, you could get a
copy of David Lewis's *Counterfactuals*, but there's no need to buy
this; selections will be placed for copying in the graduate lounge. Similar
remarks apply to L. T. F. Gamut,
*Logic, Language, and Meaning, vol 2*.
Additionally, some or all of my notes will be made available in the graduate
lounge for copying.

Two or three in-class exams; dates and times to be announced. Graduate students may be asked to answer different exam questions than undergraduates. I will hand out homework assignments periodically. These may not be collected or graded; but in any case their completion is highly recommended. I will put answers to selected homework problems on reserve. Exams will consist partly of exercises like those on homework, and partly of short-answer questions.

Note: Hughes and Cresswell readings are listed in the outline; for readings in my notes, simply read the material corresponding to the headings in the outline. Note that since I don't go in exactly the same order as Hughes and Cresswell, sometimes the topics in their readings won't exactly match my presentation.

- Intro stuff
- Logic
- Form and abstraction
- The "correctness" of logical systems
- Modal Logic
- Historical remarks on modal logic
- Metatheory of propositional logic (PL)
- Language of PL
- PL and the axiomatic approach
- semantics for PL
- soundness and completeness
- Limitations of PL
- Modal propositional logic (MPL)
- wffs
- translations
- Axiomatic systems: K, D, T, B, S4, S5
- Semantics for MPL
- A digression: Naive Set Theory
- Models
- Validity
- Semantic validity proofs
- Countermodels
- Soundness
- Completeness
- Tense logic
- Subjunctive/Counterfactual Conditionals
- Features of English counterfactuals
- The rough idea of the Lewis/Stalnaker view
- Stalnaker's system
- syntax
- semantics
- validity proofs
- countermodels
- examples
- features peculiar to MSC
- Lewis's System
- A problem with both
- Quantified Modal Logic
- Tarski-style semantics for LPC
- syntax
- semantics
- Modal LPC
- syntax
- translations
- semantics
- examples
- Inconstant domains
- Identity and Descriptions
- Other systems...

Reading: Hughes and Cresswell, pp. 3-13

Reading: Elliott Mendelson, *Introduction to Mathematical Logic, pp. 27-35*.

Reading: Hughes and Cresswell, pp. 13-17, 23-56

Reading: Hughes and Cresswell, pp. 23-68

Reading: Hughes and Cresswell, chapter 4

Reading: Hughes and Cresswell, chapter 6

Reading: Hughes and Cresswell, 127-134; L. T. F. Gamut, pp. 32-39

Reading: David Lewis, *Counterfactuals*, chapter 1, plus sections 3.4 and 4.2; copy in the graduate lounge

Reading: Hughes and Cresswell, chapter 13

Reading: Hughes and Cresswell, chapters 15-16

Reading: Hughes and Cresswell, chapter 17