Formal linguistics is essentially the application of formal, or mathematical, or symbolic logic to the study of the semantics of natural languages.
Symbolic logic is itself a simplified kind of language, devised so that the logical relations between sentences written in it are easy to see. It is straightforward to show, for instance, that one statement is a logical consequence of another. This kind of logic was originally devised to explore the fundamental concepts of mathematics.
It was applied to natural language most famously by Richard Montague. The result is a kind of translation between English and a logical language. It is probably easiest to understand the value of doing this by imagining a computer which can perform the translation. If the logical language was complete, the computer would be able to read an English text and then answer questions about it just as well as a native speaker, even though it is only carrying out logical manipulations, and does not "really" understand a human language.
Not surprisingly, computational linguists have taken up "Montague grammar" with even greater enthusiasm than other linguists. Another prominent logician in the field is M.J. Cresswell, whose work has not attracted so much attention although it is arguably more elegant.
Needless to say we shall looking through the works of both these logicians during the course of the year. Handouts will be provided, so it will not be necessary to buy any texts. The first step, though, will be to get to grips with the elements of symbolic logic. We shall start right at the beginning - no prior knowledge of the field is assumed. As long as you have a logical mind, you can master the basics in just a few weeks. Again handouts will be provided, so you do not have to buy any texts, though I will mention here the two books that have most influenced me. The first is "Introduction to Symbolic Logic and its Applications" by Rudolf Carnap (Dover Publications, 1958) and the other W.V. Quine's "Methods of Logic" (Routledge and Kegan Paul). I always use the third edition of the latter, published in 1974, just because I prefer the older notation used in it, on purely aesthetic grounds.
Something I can give you during the course, which as far as I know is not found in any other text, is a method of proof which can be used to determine the implications of even the most complex expressions in the logics of Montague and Cresswell. It is basically an extension of a proof method due to Quine. Let me give you a simple example. The simplest logical translation of the English sentence "someone loves everyone" could be written symbolically as
Another problem arises. If a and b are the people who love everybody, then does that mean that they love themselves? Does the formula imply "love aa" and "love bb" in that case? Again Quine's method can assure us that the answer is "yes". That means that the translation of "love" needs a bit more sophistication. We all know that self love is not the same as other kinds of love, so that "a loves everybody" does not imply "a loves a". But that has to be made explicit for the imaginary computer, so that it also understands the meaning of love, or at least behaves as if it did!
If you click on the class name on my timetable, you can find details of the first handout to download, and also of the first assignment!
There will be no examinations: you will be expected to write out your answers to various exercises from time to time, and hand them in as assignments. Your grade will be calculated on the basis of those.