Definition of Logic

Logic-The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning.


L01.1 A preliminary definition
The term "logic" came from the Greek word logos, which is sometimes translated as "sentence", "discourse", "reason", "rule", and "ratio". Of course, these translations are not enough to help us understand the more specialized meaning of "logic" as it is used today.
So what is logic? Briefly speaking, we might define logic as the study of the principles of correct reasoning. This is a rough definition, because how logic should be properly defined is actually quite a controversial matter. However, for the purpose of this tour, we thought it would be useful to give you at least some rough idea as to the subject matter that you will be studying. So this is what we shall try to do on this page.

L01.3 The principles of logic
So what are these principles of reasoning that are part of logic? There are many such principles, but the main (not the only) thing that we study in logic are principles governing the validity of arguments - whether certain conclusions follow from some given assumptions. For example, consider the following three arguments :

If Tom is a philosopher, then Tom is poor.
Tom is a philosopher.
Therefore, Tom is poor.

If K>10, then K>2.
K>10.
Therefore, K>2.

If Tarragona is in Europe, then Tarragona is not in China.
Tarragona is in Europe.
Therefore, Tarragona is not in China.

These three arguments here are obviously good arguments in the sense that their conclusions follow from the assumptions. If the assumptions of the argument are true, the conclusion of the argument must also be true. A logician will tell us that they are all cases of a particular form of argument known as "modus ponens" :

L01.5 Necessity in logic
A second feature of the principles of logic is that they are non-contingent, in the sense that they do not depend on any particular accidental features of the world. Physics and the other empirical sciences investigate the way the world actually is. Physicists might tell us that no signal can travel faster than the speed of light, but if the laws of physics have been different, then perhaps this would not have been true. Similarly, biologists might study how dolphins communicate with each other, but if the course of evolution had been different, then perhaps dolphins might not have existed. So the theories in the empirical sciences are contingent in the sense that they could have been otherwise. The principles of logic, on the other hand, are derived using reasoning only, and their validity does not depend on any contingent features of the world.
For example, logic tells us that any statement of the form "If P then P." is necessarily true. This is a principle of the second kind that logician study. This principle tells us that a statement such as "if it is raining, then it is raining" must be true. We can easily see that this is indeed the case, whether or not it is actually raining. Furthermore, even if the laws of physics or weather patterns were to change, this statement will remain true. Thus we say that scientific truths (mathematics aside) are contingent whereas logical truths are necessary. Again this shows how logic is different from the empirical sciences like physics, chemistry or biology.

L01.6 Formal and informal logic
Sometimes a distinction is made between informal logic and formal logic. The term "informal logic" is often used to mean the same thing as critical thinking. Sometimes it is used to refer to the study of reasoning and fallacies in the context of everyday life. "Formal logic" is mainly concerned with formal systems of logic. These are specially constructed systems for carrying out proofs, where the languages and rules of reasoning are precisely and carefully defined. Sentential logic (also known as "Propositional logic") and Predicate Logic are both examples of formal systems of logic.
There are many reasons for studying formal logic. One is that formal logic helps us identify patterns of good reasoning and patterns of bad reasoning, so we know which to follow and which to avoid. This is why studying basic formal logic can help improve critical thinking. Formal systems of logic are also used by linguists to study natural languages. Computer scientists also employ formal systems of logic in research relating to Aritificial Intelligence. Finally, many philosophers also like to use formal logic when dealing with complicated philosophical problems, in order to make their reasoning more explicit and precise.