Logic is one of the most important and oldest branches of philosophy and its subject matter falls at the core of philosophizing. Logic studies patterns of reasoning dividing them into those that are valid and invalid with respect to a set of given rules. Classical logic studies those arguments that are valid with respect to some rules as defined by "classical" authors, especially Aristotle. Over the past century, logic has flourished probably like never before, specializing into several sub-branches each of which has some specific domain of interest, such as temporal logic (time), modal logic (possibility and necessity), deontic logic (duty), paraconsistent logic (impossibility) …
History of Western Logic
Important chapters in the history of logic have been written not only by ancient philosophers (Aristotle and the so-called Megaric Stoics), but also by the Scholastic philosophers of the Middle Ages such as Ockham and Buridan, who left us some works of exceptional quality. In modern philosophy, authors such as Leibniz and Wolff were particularly influent, followed by the logic of contradiction as developed by Hegel and Schelling as well as the logic of dialectic materialism proposed by Marx.
Towards the ending of the 1800s logic was off to a new start. The work of authors such as Gottlob Frege (1848-1925) and Charles Sanders Peirce (1839-1914), who reconceived the logical structure of a proposition, opened up the path to both new techniques of evaluating human reasoning and new ways of conceiving of a language. The result is the flourishing of research in logic that has characterized analytic philosophy in the second half of 1900s.
Arguments, Soundness and Validity
An argument is a series of propositions, the latter of which is said to be the conclusion, while the others are the premises. An argument is said to be valid when the truth of the premises entails the truth of the conclusion, that is, if the premises are true the conclusion also is true.
An argument that is valid even when the conclusions are plausibly false and nevertheless, if the premises were true, the conclusion would be true. An argument whose premises are true and that is valid is said to be sound.
For instance, the following is a valid but unsound argument:
(1) If 2+2=5, 5=2+2;
(2) 2+2=5;
(3) Therefore, 5=2+2.
In this case, since premise (2) is evidently false, the argument is invalid. But, the following is instead sound:
(4) If 2+2=4, 4=2+2;
(5) 2+2=4;
(6) Therefore, 4=2+2.
Syllogism
The examples provided above are also instance of arguments of a particular form, called syllogism. A syllogism is an argument composed of three propositions; of the two premises, one is said to be the major premise, because it contains the predicate of the conclusion, and the other the minor premise, because if contains the subject of the conclusion.
Before the logical turn of the end of 1800s, most of logic was concerned with the theory of syllogism, first introduced by Aristotle and the Megaric Stoics in ancient Greek philosophy. The development of logic consisted in great part in devising an analysis of proposition that escaped the subject-predicate analysis presupposed in the theory of syllogism
Deductive vs Inductive Logic
Arguments can be divided between those that proceed from all-or-nothing premises (premises that are either true or false necessarily, such as "2+2=4") and those that proceed from some premises that are probable (for example, "All swans are white"). The former type of arguments are called deductive, the latter inductive. A development of logic which was particularly important for the study of scientific reasoning by philosophers of science is inductive logic.
Further Online Readings
Some logic-related entries at the Internet Encyclopedia of Philosophy.
