LOGIC

 

Logic is one of the most important topics you will ever study. “How could you say such a thing?” you might well protest.  And yet, consider:  logic teaches us many things, and one of these is how to recognize good and bad arguments.  Not just arguments about logic - any argument.

Nearly every undertaking in life will ultimately require that you evaluate an argument, perhaps several. You are confronted with a question:  Should I buy this car or that car?  Should I go to this college or that college? Did that scientific experiment show what the scientist claims it did?  Should I vote for the candidate who promises to lower taxes, or for the one who says she might raise them? And so on. Our lives are a long parade of choices.  When we try to answer such questions, in order to make the best choices, we often have only one tool: an argument. We listen to the reasons for and against various options and must choose between them. And so, the ability to evaluate arguments is an ability that is very useful in everything that you will do - in your work, your personal life, your deepest reflections.

If you are a student, note that nearly every discipline, be it a science, one of the humanities, or a study like business, relies upon arguments.  Evaluating arguments is the most fundamental skill common to mathematics, physics, psychology, literary studies, and any other intellectual endeavour.  Logic alone tells you how to evaluate the arguments of any discipline.

The alternative to developing these logical skills is to be always at the mercy of bad reasoning and, as a result, you will make bad choices.  Worse, you will always be manipulated by deceivers.  Speaking in New York, on August 3, 1857, the escaped slave and abolitionist leader Frederick Douglass observed that:

Power concedes nothing without a demand. It never did and it never will. Find out just what any people will quietly submit to and you have found out the exact measure of injustice and wrong which will be imposed upon them, and these will continue till they are resisted with either words or blows or with both. The limits of tyrants are prescribed by the endurance of those whom they oppress.

We can add to Frederick Douglass’s words that: find out just how much a person can be deceived, and that is just how far he will be deceived.  The limits of tyrants are also prescribed by the reasoning abilities of those they aim to oppress.  And what logic teaches you is how to demand and recognize good reasoning, and so how to avoid deceit.  You are only as free as your powers of reasoning enable.

·         Identify when an argument is good, and when it is bad;

·         Construct good arguments;

·         Evaluate reasons, and know when they should, and should not, be convincing;

·         Describe things with a precision that avoids misunderstanding;

·         Get a sense of how one can construct the foundations of arithmetic;

·         Begin to describe the meaning of “possibility” and “necessity”.

Some philosophers have argued that one cannot define “logic”. Instead, one can only show logic, by doing it and teaching others how to do it. But it is easy to describe the benefits of logic. 

That is by no means a complete list of the many useful things that logic can provide.  Some of us believe that logic and mathematics are ultimately the same things, two endeavours with the same underlying structure distinguished only by different starting assumptions.  On such a view, we can also think of logic as the study of the ultimate foundations of mathematics.  This is a reasonable characterization of logic, but those afraid of mathematics need not fear: logic must become quite advanced before its relation to mathematics becomes evident.

Ultimately, the only way to reveal the beauty and utility of logic is to get busy and do some logic.  You will approach the study of logic by building several precise logical languages and seeing how you can best reason with these.  The first of these languages is called “the propositional logic”.

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