PHILO 375 Advaned Symbolic LogiC (Cross listed with  MATH 370, 672, CSCI 39584-01

	The core of this course concerns two central results in metaloigc, the theory which takes logic as studied in Symbolic Logic as the subject and establishes theorems about it. Symbolic Logic (PHILO 275, Math 275, CSCI 395.9 then is prerequisite.) In Symbolic Logic we define the concepts of quantificational truth, entailment, and consistency in PD., a system of predicate derivations. The completeness theorem shows that if a statement is entailed by a set of assumptions, it is derivable from those assumptions. Its converse, the Soundness Theorem claims that if a statement is derivable from a set of assumptions, it is entailed by those assumptions. We prove both theorems in the course. 

	Another major 20th century result in metalogic is Godel’s Incompleteness Theorem for elementary arithmetic Given an axiomatization of arithmetic strong enough to express both addition and multiplication, the incompleteness theorem shows that some mathematical truth will be left out, not be derivable from the basic axioms of the theory. No matter how we extend the set of assumptions, we cannot capture every consequence of the basic assumptions.

	Besides these two results, we shall consider and establish a number of supporting theorems and further results. The method of course evaluation will primarily be a series of problem sets, about 7, due over the course of the semester.