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January 26, 2007
Errata
Well, the first 2 weeks of teaching from Fitting and Mendelsohn's First-Order Modal Logic
A couple of minor thoughts on it: it seems to me that after the introduction of semantics for K,T, D, K4, B, S4 and S5 in the first half of the first chapter, the discussion of tense logic from pages 24-27 represents a missed oportunity to draw out the parallels. The section discusses four different ways to understand tensed sentences, two of which involve treating tensed sentences as equivalent to first order classical formulas in which one simply quantifies over time instants, and the suggestion that we use operators like 'G' ( it will always be the case that) and 'F' (it will be the case that) like '[]' (box) and '<>' (diamond) is discussed in less than half a page and left at the intuitive level, e.g.:
For example, the thesis []P->P, fails. Just because it will always be true that P, it does not follow that P is true now. (p. 27)
But this isn't justified with reference to any particular model theory - we're just supposed to get it from our intuitive understanding of 'it will always be the case that.' This would have been understandable if the writer couldn't assume that his reader would be able to follow a discussion involving putting the semantics for those operators into a definition of truth in a model, and considering what formulas involving them come out valid for different classes of frames, but the book has just done exactly that for ordinary modal logic, and considered what formulas come out valid if we assume that the accessibility relation is e.g. transitive and reflextive, or serial and so it would have been a great place to at least mention that you can get different tense logics by putting different restrictions on the "earlier than" relation (partial ordering, total ordering, total ordering with no maximum or minimum, density ... etc). Given this I've been supplementing our discussion of tense logic with John P. Burgess' "Basic Tense Logic" from volume II of the Handbook of Philosophical Logic
A second (even more) minor point: like any logic textbook, there are some typos. Here's one:
p. 26 - the interpretations of
- G John wins the election
- H John wins the election
are given as
and
respectively. But, first of all, 'John wins the election' is an infelicitous atomic sentence to use, (what do we make of: at every time in the future, John wins the election ?) 'John is happy' would have been much less confusing. (There's nothing funny about: at every time in the future, John is happy.)
And secondly, those conjunctions should surely be conditionals, otherwise 'G John is happy', means every time is later than the present time and John is happy at it and 'H John is happy' means every time is earlier than the present and John is happy at it!
This, of course, is small stuff, and so far I would recommend the book to anyone who needs to teach modal logic to philosophers who are not logicians. Also Fitting has his own site of errata for the book here.
Posted by logican at January 26, 2007 12:24 PM
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