What is formal reasoning?
The most ‘formal’ or ‘strict’ type of reason is usually termed logic. Logic is sometimes used instead of the word reason, but if you substitute it in the sentences above, you will see that it makes the sense of the statement much narrower. For something to make logical sense is a more demanding achievement than for something to make reasonable sense. The use of logic to arrive at an answer implies that that answer will be more measurably correct or not.
For our purposes, let’s define logic as the use of reason according to strict rules to help us determine knowledge (remember our definition of knowledge, after Socrates: justifiable true belief). Logic, therefore, becomes our tool for searching out answers and weighing up conflicting statements, opinions, and ideas. It does so in a range of ways, according to the way in which it uses reason. Some of these ways are tried, tested and accepted; others are lessons in how not to use reason.
Deductive and Inductive Reasoning
The most important way of dividing up logic is into deductive and inductive reasoning. Deduction leads to specific conclusions based on weighing up general principles. Induction is the opposite, and produces a general conclusion from a specific case or cases. Each one can be subdivided into further forms and types.
Probably the best known, and most widely-used form of deductive reasoning is the syllogism. In a syllogism, a primary premise is linked to a secondary premise to arrive at a conclusion. This sounds complicated, but is more easily understood by looking at an example. One that is often cited is:
Primary premise: All humans are mortal.
Secondary premise: Socrates is human.
Conclusion: Socrates is mortal.
This argument is sound because if the two propositions are true, there is no possible way that the conclusion could be false. Another example, slightly more immediate to us, could be:
Primary premise: All IB students must study TOK.
Secondary premise: Gabriel is an IB student.
Conclusion: Gabriel studies TOK.
These involve simple premises, but it also works when you construct a compound premise.
Primary premise: If IB students want to pass their diploma, then they have to pass the TOK course.
Secondary premise: Gabriel wants to pass the Diploma.
Conclusion: Gabriel has to pass the TOK course.
The important thing with a syllogism is to keep the premises precise and accurate. If either one is inaccurate, or uses generalised statements, the conclusion will be unsound. For example:
Primary premise: Many IB Diploma students speak a second language
Secondary premise: Gabriel does the IB Diploma
Conclusion: Gabriel speaks a second language
This is not necessarily true, as the first premise is making a generalised point.
We use induction more often than we use deduction in every day life, because unless we are professional scientists, we simply don’t have time to investigate phenomena by repeating experiments to check that our theories work. In other words, we make generalizations on previous experiences, and those previous experiences are often just based on seeing or feeling a thing once or twice.
One of the most common generalizations is about other people. We sometimes make a statement about another nationality or habits in their country on the flimsiest of evidence. Our perceptions are often coloured by a vivid experience – perhaps you once fell in love with a Swedish girl. Does that mean that Swedish girls are all attractive? Perhaps someone was once extremely rude to you in Rome. Does that mean that all Italian people are arrogant? Generalizing on the basis of one or two experiences can be very dangerous, and lead you down the road towards fallacious reasoning, which we will discuss in a later section.