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Principia
Logic is the laws of thought. As the laws of nature are to the workings of the universe, logic tells us about the limits of thought. For introductory logic courses, however, most of what a student will see is simple logic that can be applied in any situation. Most semesters of PHIL 110 include very similar material, despite being taught by different professors. Topics include arguments, fallacies, deductive logic, validity, soundness, inductive logic, strong premises, cogency, and truth tables.


ArgumentsEdit

Arguments are composed of statements, which are true or false propositions. Questions, imperatives, and noises are not statements. The statement which the argument is meant to prove or give probable support for is called conclusion and is usually signified by words like "therefore". Statements which are given as reasons to believe the conclusion are called premises.

Most philosophical analysis is best done in standard form, seen below.

  1. All Wildcats are students.
  2. Mary is a Wildcat.
  3. Therefore, Mary is a student.

Philosphers prefer their arguments in standard form because each component of the argument is clear and distinct. Weak premises and invalid conclusions are, then, easier to identify. Ultimately, most professors would like to see their students do this with arguments found in class readings - though most don't require it. In fact, most philosophers don't bother setting out their arguments in standard form, but this is because the skills necessary to extract this form from a reading are expected of the reader.

When reading a text with a student, be sure to have them mark the conclusion and premises. Then have them write the statements in standard form.

FallaciesEdit

Fallacies are errors in reasoning. They are also, unfortunately, very common. Most introductory courses will introduce students to a list of common fallacies. The tutor's job is to help the student understand why these fallacies are erronous.

Fallacies are best learned with examples. First, provide an example for the student and have them explain the error in reasoning. Then, ask the student to come up with a few examples on their own.

An excellent source on common fallacies may be found here.

Deductive LogicEdit

Introductory courses offer a primer in deductive vocabulary and expose the students to deductive argument forms. Nearly all classes will cover precisely the same concepts in deductive logic.

Consider the following argument.

  1. If it is raining, then it is wet outside.
  2. It is wet outside.
  3. Thus, it is raining.

This example provides opportunity to become familar with vocabulary specific to deductive logic. Our conclusion does not follow from the premises in this argument. In other words, the premises do not guarantee the truth of the conclusion - this argument is invalid. Particularly, our conclusion is that it must be raining because it's wet outside. However, other things may cause wetness: sprinklers, car washes, water balloon fights - you name it. Compare this to a valid argument:

  1. If it is raining, then it is wet outside.
  2. It is raining.
  3. Thus, it is wet outside.

In this case the premises guarantee the truth of the conclusion. If the premises are true, then the conclusion must also be true. Of course, the next step in judging this argument is to ask whether the premises are indeed true. This is called checking for soundness. Sound arguments have true premises, unsound arguments have at least one false premise.

Going through a step-by-step process is most helpful in learning about how to use deductive logic. Ask the student to first construct the argument in standard form, if an argument is not already presented. Have the student, then, check for validity. Finally, ask the student if the argument is sound.

Another common concept encountered with deductive argumentation is the form of the argument. The form of an argument shows the relations between atomic statements. For example, any argument of the form

  1. If A, then B.
  2. A.
  3. Thus, B.

will be valid. A list of common argument forms can be found here.

Inductive LogicEdit

Inductive reasoning covers a broad range of concepts. Thus, the material covered in a course may vary widely, but there a few essential concepts which may always be expected. Inductive reasoning differs from deductive reasoning in that its argument are only meant to give probable support to a conclusion and do not guarantee the truth of that conclusion. A technique which may help make this clear to a student is to ask them to imagine the premises of a valid, deductive argument as true and the conclusion as false.

Inductive arguments have properties corresponding to those of deductive arguments. Instead of validity, we speak of how strong the premises of an inductive argument are. Instead of soundness, we speak of cogency. Strong premises give great probable support to an argument, if the premises were true, e.g., "Every person I know will die. You are someone I know. Thus, you will die." Cogent arguments are composed of premises which are actually true. It may not be the case that a strong argument is also cogent, in which case the argument would fail.

Take note of the example above that the argument may be strong and cogent, but the conclusion may still be false. This is how deductive and inductive arguments differ. Valid and sound arguments must have a true conclusion. Strong and cogent arguments do no necessarily have a conclusion that follows from the premises. The negation of the conclusion may be conceived without contradiction.

Inductive reasoning, then, is essentially empirical. Thus, much of scientific and statistical reasoning is inductive. Information from these disciplines will then be seen in introductory logic courses. However, the breadth of information is so great that no discussion here would suffice.