Critical Thinking Note 11: Logic


Logic has taken a real hit at BC since the recent changes to the Direct Transfer Agreement. But we just might manage to run two sections of it this fall. We will need some more students though. There are plenty of seats in both the 9:30 and the 11:30 section. In case you know any students who might like to have a better idea what they’d be getting into in a logic class, please pass this note along:

Logic is the science of what follows from what. For instance, if Jose and Mary went to the movies, it follows that Jose went to the movies. Or, if all dogs are K9s and Fido is dog, then it follows that Fido is a K9. In both of these simple arguments, a conclusion is drawn that has to be true if the premises are true. That’s what it is for one thing to follow from another. Just about everybody easily recognizes a handful or so of relatively simple reasoning patterns where one thing follows from some others. But without some training, most of us quickly get lost when things get a bit more complicated. Consider this argument from Patrick Hurley’s logic text:

If quotas are imposed on textile imports only if jobs are not lost, then the domestic textile industry will modernize only if the domestic textile industry is not destroyed. If quotas are imposed on textile imports, the domestic textile industry will modernize. The domestic textile industry will modernize only if jobs are not lost. Therefore, if quotas are imposed on textile imports, the domestic textile industry will not be destroyed.

The last claim in this argument does follow from the prior claims, but without some training in logic, you might have a hard time seeing this. The goal of PHIL& 120 is to build on the foundation of simple reasoning patterns we already get and to learn a variety of techniques for better appreciating when one thing follows from others (or fails to) in more complicated or subtle lines of reasoning.

Logic is a powerful tool for making sense out of math, science, philosophy and much more. Its the class that makes everything else in college make sense. This, at any rate, is what logic instructors have heard from countless former logic students. The logical systems and techniques we now teach in PHIL& 120 are based on advances made just over a century ago in an effort to show that all of mathematics is just an extension of logic. Logic is the central kernel of mathematical reasoning and studying logic gives you a chance to focus on mastering the central kernel of deductive reasoning without the overwhelming barrage of special symbols, theorems and specific algebraic applications. You will encounter a few symbols, 8 to be exact. But these will be used to represent simple everyday notions like “and”, “or” and “all”.

PHIL&120, Introduction to Logic is offered every quarter at BC. BC’s primary logic instructor, Mark Storey, has authored an open source e-text that is available to students for free, so there is no textbook to purchase. PHIL&120 fulfills the Quantitative/Symbolic Reasoning requirement for Direct Transfer degrees. It can also be used as a non-lab science course for the Associates in Arts and Sciences transfer degree. Your specific educational goals might have competing requirements, so be sure to consult with your BC academic adviser. But whatever your educational goals, you might find logic to be a valuable step towards these even if you take the course as an elective. Passing MATH 098 with a C or better is now a pre-requisite for PHIL& 120.

Russ Payne

September 16, 2014

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