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Logic

Logic is the study of formal and informal reasoning. Originally a branch of philosophy, logic has also become a mathematical discipline, a tool of modern linguistics, the core of computer science and an object of study for psychologists and cognitive scientists of every description. The field now reaches into virtually every aspect of human (and nonhuman) thought. Studying logic enhances students’ reasoning ability, analytic reading and writing skills, oral debate skills, and appreciation of the structure of language and argument and of the structure of abstract formal systems. Logic is an excellent foundation not only for the study of philosophy, mathematics, computer science and linguistics, but also for such disciplines as legal studies, government and economics.


Requirements & Courses

Minors in logic, to be designed in consultation with a co-director, will consist of at least 20 credits including:

  • LOG 100 or PHI 202, but not both
  • MTH 153 or CSC 250
  • MTH 217 or PHI 220

Additional courses may be chosen from the following list:

  • CSC 111 Computer Science I
  • CSC 250 Foundations of Computer Science
  • CSC 270 Digital Circuits and Computer Systems
  • CSC 290 Introduction to Artificial Intelligence
  • CSC 294 Introduction to Computational Linguistics
  • LOG 404 Special Studies in Logic
  • MTH 153 Discrete Mathematics
  • MTH 217 Mathematical Structures
  • PHI 203 Topics in Symbolic Logic
  • PHI 220 Logic and the Undecidable
  • PHI 236 Linguistic Structures
  • PHI 322 Topics in Advanced Logic

Depending on the topic, the courses listed below may also be taken for logic minor credit:

  • CSC 390 Seminar in Artificial Intelligence
  • MTH 224 Topics in Geometry
  • MTH 238 Topics in Number Theory
  • MTH 343 Topics in Mathematical Analysis
  • MTH 350 Topics in the History of Mathematics
  • PHI 362 Seminar: Philosophy of Language

Some courses in the Five College system may also be acceptable, such as courses in linguistics and law. Also, learn more about the Five College Logic Certificate Program.

In this century, logic has grown into a major discipline with applications to mathematics, philosophy, computer science, linguistics and cognitive science. The goal of the logic minor is to provide students with the tools, techniques and concepts necessary to appreciate logic and to apply it to other fields.

Logic courses include the following:

LOG 100 Valid and Invalid Reasoning: What Follows from What? 
Formal logic and its application to the evaluation of everyday arguments, the abstract properties of logical systems, the implications of inconsistency. Examples drawn from law, philosophy, economics, literary criticism, political theory, commercials, mathematics, psychology, computer science, off-topic debating and the popular press. Deduction and induction, logical symbolism and operations, paradoxes and puzzles. May not be taken for credit with PHI 202.

LOG 335 Conditionals in Formal and Natural Languages
Consider the following argument: 'If you don't buy a lottery ticket, then you can't win the lottery. But you can win the lottery. Therefore, you do buy a lottery ticket.' Modus tollens is a classically valid argument form. But this appears to be a counterexample. You might well not buy a ticket. In this seminar, we'll study different theories of conditionals - statements of the form 'If A, then B' - in formal and natural languages. We'll do so in the context of the paradox above and others, seeking a theory that can solve them. Enrollment limited to 12. Prerequisities: Logic 100 or equivalent. (E) {M} Credits: 4
Theresa Helke

LOG 404 Special Studies 
Offered both semesters each year.

PHI 101 Plausible and Implausible Reasoning: What Happened? What Will Happen Next? 
This course is designed for students who are uncomfortable with symbolic systems. It will provide an elementary introduction to the structure and function of propositional and predicate logic. This will include translating ordinary language statements and arguments into symbolic form; using truth tables to calculate truth values and determine the validity of arguments in finite universes; quantification in infinite universes; direct, indirect and conditional proof techniques in propositional and predicate logic. The course will also survey topics in inductive logic involving probabilistic and statistical reasoning and elements of decision theory. Enrollment limited to 24.

 

Logic at the Five Colleges

The Five College Logic Certificate program brings together aspects of logic from different regions of the curriculum and is designed to acquaint students with the uses of logic and initiate them in the profound mysteries and discoveries of modern logic.

FIVE COLLEGE LOGIC PROGRAM

 

 

 

Contact The Logic Program

Dewey Hall 106

Smith College

Northampton, MA 01063

Phone: 413-585-3679 Email: cbell@smith.edu

Administrative Assistant: Chrissie Bell

Students who wish to learn more about the logic program may contact Jay Garfield.