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Symbolic Logic: An Introduction

Studying for the LSAT? Interested in philosophy or artificial intelligence? Learn the basics of logical reasoning and symbolic logic.

What is logic?

Logic is basically the systematic way in which everyone with a brain thinks. Logic is the tool our minds use to make sense of things, make decisions, and live our lives in general. For example, deciding not to step into the road in front of a speeding 18-wheeler is a logical choice. But it is more than that – logic is the subconcious  method we use to decide if an idea sounds plausible, or if a plan is realistic, or if a course of action is worth the time or money, etc. Logic can be described as a “thinking about thinking” and lies at the very center of every human’s thought process.

Symbolic logic

Symbolic logic is exactly what it sounds like. It is a system of symbols that are used to transform normal English into a more condensed easy-to-work-with structure. Symbolic logic is important and useful in deciding whether certain arguments are valid or sound or both. A system of symbolic logic is also relevant to the fields of artificial intelligence and computer science. In fact, one of the fathers of computer science, Alan Turing, was a logician who figured out how to use symbolic language as a system of commands for computers. This system of signs and symbols will be introduced shortly, but first we must look at the most basic foundation of logic and symbolic logic: arguments.

Arguments are the bedrock of any logical system. In fact we often think of arguments as either being logical or illogical. For example using the argument that it is ok to stand in an open field with an umbrella during a lighting storm because you don’t know anyone who has ever been struck by lightning is an illogical argument. Symbolic logic deals strictly with arguments. If you have no arguments, you can not symbolize what you are saying in symbolic logic. So then, what exactly is an argument?

The basic structure of an argument

Before getting into what an argument is, it is important to distinguish what does not count as an argument. An opinion or opinionated statement is not an argument! The “arguments” you had with your brother or sister when you were a child are not arguments. In fact, any kind of bickering or name-calling is not an argument at all. Here are some examples of non-arguments:

                    My favorite color is red, therefore all cars should be red.

                    If you think global warming is an illusion, you’re an idiot.

                    I know what I’m talking about because I went to college.

                    I’m right because I’m a Democrat and you’re wrong because you’re a republican.

                    etc., etc.

All of the above are not arguments. As stated, anything to do with a personal opinion or any statement intended to inflict name-calling is not an argument. Real arguments have a structured form.                  

All arguments have the same basic form. This form includes two or more premises and one conclusion. A premise is a statement that provides evidence for the conclusion. For example, a premise for the conclusion that cars are harmful to the atmosphere is that cars emit carbon monoxide, which is a noxious gas. A conclusion is a statement that follows from the premises that have been given in support of it.
For example, the following is an argument:

                    Premise #1: Bob loves cold weather.
                    Premise #2: It is cold in Antarctica.
                    Conclusion: Bob should move to Antarctica.

The above argument, as you can see, contains two premises and one conclusion. It is just about as basic of an argument as you can get. To some, the above argument may seem strange. Why should Bob move to Antarctica just because he likes cold weather? That seems a little extreme for poor Bob, doesn’t it? This is because, even though it may be valid, the above argument is not sound.

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