Finally following up on some discussion we had a couple of weeks ago, two papers you may want to check out:
Since we did not resolve the issue of how the reduction of an ordered pair <a,b> to the set {{a},{a,b}} worked out for pairs of the form <x,x>, you may want to check out this Wikipedia discussion of different variants of defining pairs as sets, including how we can derive the first and second member of the pair from those definitions for all cases.
The question of how to compute the number of functions from any given set A to any given set B came up in class, with the suggestion that it’s the cardinality of the second set to the power of the cardinality of the first set.
That indeed is correct, at least for non-deviant cases (see some links for interesting discussions on the internet, but beware of some questionable reasoning when it comes to the number of ‘onto’ functions and other more complex questions).
The deviant cases are when one of the sets is empty. In that case the only relation between A and B is the empty set. If one counts that as a function (because it vacuously satisfies the requirements for being a function), that would mean the result in the non-deviant cases is incorrect. Also 0 to the 0th power is undefined. So things don’t seem to work out for these cases in the same way…
The set theory notes, Homework 1, and the reading for next week have now been posted on the schedule. (files available on Zotero)
For additional discussions of functions and relations (in part, not entirely, from a more mathy perspective) in video format, check out the Khan Academy’s video series on functions (I haven’t really looked at them in any detail yet, but I think they’re very good; note that there are some slight terminological divergences concerning domain and range between the videos and Partee, ter Meulen, and Wall)
Welcome to LING 380/580, Fall 2012 edition! First class is Wednesday, 9/5, in the department seminar room.
Class materials will be made available through Zotero. You’ll need to create an account there and request an invitation for joining the group.
The syllabus for the class can be found here.
If you’d like to get a head start, you could take a look at the first two chapters of Larson & Segal’s ‘Knowledge of Meaning‘ (restricted link to screen-only version of entire book; should work from within Penn), as well as the first chapter of Bach 1989 and the article Varieties of Semantic Evidence (draft) by Manfred Krifka. The new book by Paul Elbourne also makes for excellent introductory reading on the side.
On a somewhat more basic, but very intuitive, level, you could also have a look at the first two chapters of Portner 2005.
Chierchia and McConnell-Ginet’s Chapters 1 & 2 also provide a great introduction to the formal semantics enterprise. I highly recommend looking at least some subset of these suggested readings, especially if you have not really had any serious encounters with semantics before. It can be very helpful to see different types of presentation of the general approach underlying most of what we will cover in this course.
Feel free to get in touch if you have any questions in the meantime!