Logic, ancient

By Thom, Paul

Western antiquity produced two great bodies of logical theory – those of Aristotle and the Stoics. Both aim to explain what distinguishes good arguments from bad. Both see ...

Łukasiewicz, Jan (1878–1956)

By Wolenski, Jan

Before 1918, Łukasiewicz’s interests centred on logic (in the broad sense) and philosophy, and he worked on induction and probability. He also wrote an important historical book on ...

Stoicism

By Sedley, David

Stoicism is the Greek philosophical system founded by Zeno of Citium c.300 bc and developed by him and his successors into the most influential philosophy of ...

Stoicism

Stoicism is the Greek philosophical system founded by Zeno of Citium c.300 bc and developed by him and his successors into the most influential philosophy of ...

Theophrastus (c.372–c.287 BC)

By Huby, Pamela M.

Theophrastus, the pupil and successor of Aristotle, shared all the latter’s interests, and produced a large number of works on the same topics. Some, like the extant botanical ...

Ancient philosophy

By Sedley, David

The philosophy of the Greco-Roman world from the sixth century bc to the sixth century ad laid the foundations for all subsequent Western philosophy. Its greatest ...

Philo the Dialectician (late 4th–early 3rd centuries BC)

By Denyer, Nicholas

A member of the Dialectical school, Philo was a Greek philosopher whose claim to fame is twofold. First, he maintained that one proposition implies another if and only ...

Formal and informal logic

By Walton, Douglas

Formal logic abstracts the form of an argument from an instance of it that may be encountered, and then evaluates the form as being valid or invalid. The ...

Aristotle (384–322 BC)

By Irwin, T.H.

Aristotle of Stagira is one of the two most important philosophers of the ancient world, and one of the four or five most important of any time or ...

Second-order logic, philosophical issues in

By Shapiro, Stewart

Typically, a formal language has variables that range over a collection of objects, or domain of discourse. A language is ‘second-order’ if it has, in addition, variables that ...

Fallacies

By Walton, Douglas

Fallacies are common types of arguments that have a strong tendency to go badly wrong, or to be used as deceptive tricks when two parties reason together. In ...

Logic, philosophy of

By Forbes, Graeme

Philosophy of logic can be roughly characterized as those philosophical topics which have emerged either from the technical development of symbolic (mathematical) logic, or from the motivations that ...

Platonism, Early and Middle

By Dillon, John

Platonism is the body of doctrine developed in the school founded by Plato, both before and (especially) after his death in 347 bc. The first phase, usually ...

Quantifiers

By Hintikka, Jaakko; Sandu, Gabriel

The quantifiers ‘some’ and ‘every’ were the object of the very first logical theory, Aristotelian syllogistic. An example of a syllogism is ‘Every Spartan is Greek, every Greek ...

Chrysippus (c.280–c.206 BC)

By Sedley, David

The Greek philosopher Chrysippus of Soli was the third and greatest head of the Stoic school in Athens. He wrote voluminously, and in particular developed Stoic logic into ...

Diodorus Cronus (late 4th–early 3rd centuries BC)

By Denyer, Nicholas

The most famous member of the Dialectical school, the Greek philosopher Diodorus Cronus maintained various paradoxical theses. He argued that any attempt to divide space, time or matter ...

Logic in Islamic philosophy

By Black, Deborah L.

Islamic logic was inspired primarily by Aristotle’s logical corpus, the Organon (which according to a late Greek taxonomy also included the Rhetoric and Poetics). Islamic authors were also ...

Polish logic

By Zygmunt, Jan

The term ‘Polish logic’ was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of ...

Logic, medieval

By Ashworth, E.J.

Medieval logic is crucial to the understanding of medieval philosophy, for every educated person was trained in logic, as well as in grammar, and these disciplines provided techniques ...

Logical form

By Menzel, Christopher

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with ...

Logical laws

By Restall, Greg

There are at least three different kinds of answer to the question ‘What is a logical law?’ One establishes what it means for something to be a logical ...

Logic in the second half of the twentieth century

By Cook, Roy T.; Logan, Shay Allen

By the end of the first half of the twentieth century, logic had become a mature philosophical and mathematical discipline. As happens in mature disciplines, in the second ...

Logic, Renaissance

By Ashworth, E.J.

Renaissance logic is often identified with humanist logic, which is in some ways closer to rhetoric than to the study of formal argumentation. This is a mistake, for ...

Modal logic

By Kuhn, Steven T.

Modal logic, narrowly conceived, is the study of principles of reasoning involving necessity and possibility. More broadly, it encompasses a number of structurally similar inferential systems. In this ...

Quantifiers, generalized

By Westerstahl, Dag

Generalized quantifiers are logical tools with a wide range of uses. As the term indicates, they generalize the ordinary universal and existential quantifiers from first-order logic, ‘∀x’ and ...