PHIL808D     Seminar in the Problems of Philosophy
Semester:Spring 2014
Instructor: Paul Pietroski
Room:SKN 1116
Meeting Times:TH, 1:00pm - 3:30pm
Level:Graduate
 
Philosophers often talk about the logical form of an ordinary sentence. Famously, one might 
think that the English sentences (1) and (2) have the logical forms (1a) and (2a), respectively. 
 
 (1) Every number has a successor.              (2) The king is bald. 
 
 (1a) ∀x[Nx ⊃ ∃y(Syx)]                             (2a) ∃x[Kx & ∀y(Ky ⊃ y = x) & Bx] 
 
One might suspect that (3) and (4) have different logical forms, and likewise for (5) and (6), 
 
 (3) That dog is a terrier.                       (4) That dog is a father. 
 
 (5) That dog is your terrier.                   (6) That dog is your father. 
 
since (7) and (3) imply (5), but (7) and (4) do not imply (6). 
 
 (7) That dog is yours. 
 
Or one might think that (8) and (9) have the same logical form, since each implies the other. 
 
 (8) Plum stabbed Green in the hall.            (9) There was a stab of Green by Plum in the hall. 
 
Or one might think that (10) and (11) have the same logical form, since each translates the other. 
 
 (10) Every cat is on a mat.                      (11) Chaque chat est sur un tapis. 
 
But what is it for an ordinary sentence to “have” a logical form, or for two sentences to have the  “same” logical form, or for one sentence to “imply” or “translate” another?  
 
 In the seminar, I want to explore three historically important—and to some extent  overlapping—conceptions of logical form: a “natural logic” conception, according to which  spoken sentences imperfectly indicate mental sentences that actually exhibit logical forms; a  “regimentation” conception, according to which logical forms are invented sentences that  “translate” natural sentences (public or private) into a more scientific idiom; and a “semantic” conception, according to which logical forms are sentences of a meta-language used to specify the truth conditions of natural sentences. Each of these sketchy views can be filled out in various ways. Exactly how we proceed will depend on the interests and background of those enrolled. But as time permits, I hope to develop a version of the “natural logic” approach that borrows a bit from the “semantic” approach.