LogicLogic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language.
Square of oppositionIn term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram; this was done several centuries later by Apuleius and Boethius.
DefinitionA definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
SyllogismA syllogism (συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book Prior Analytics), a syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across.
Peripatetic schoolThe Peripatetic school was a philosophical school founded in 335 BC by Aristotle in the Lyceum in Ancient Athens. It was an informal institution whose members conducted philosophical and scientific inquiries. After the middle of the 3rd century BC, the school fell into decline, and it was not until the Roman Empire that there was a revival. The term peripatetic is a transliteration of the ancient Greek word περιπατητικός (peripatētikós), which means "of walking" or "given to walking about".
Porphyry (philosopher)Porphyry of Tyre (ˈpɔrfɪri; Πορφύριος, Porphýrios; فُرْفُورِيُوس, Furfūriyūs; 234 – 305 AD) was a Neoplatonic philosopher born in Tyre, Roman Phoenicia during Roman rule. He edited and published The Enneads, the only collection of the work of Plotinus, his teacher. He wrote original works in the Greek language on a wide variety of topics, ranging from music theory to Homer to vegetarianism. His Isagoge or Introduction, an introduction to logic and philosophy, was the standard textbook on logic throughout the Middle Ages in its Latin and Arabic translations.
William of OckhamWilliam of Ockham, OFM (ˈɒkəm; also Occam, from Gulielmus Occamus; 1287 – 10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and Catholic theologian, who is believed to have been born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century. He is commonly known for Occam's razor, the methodological principle that bears his name, and also produced significant works on logic, physics and theology.
IsagogeThe Isagoge (Εἰσαγωγή, Eisagōgḗ; 'aisəgo:dZi:) or "Introduction" to Aristotle's "Categories", written by Porphyry in Greek and translated into Latin by Boethius, was the standard textbook on logic for at least a millennium after his death. It was composed by Porphyry in Sicily during the years 268–270, and sent to Chrysaorium, according to all the ancient commentators Ammonius, Elias, and David.
A priori and a posterioriA priori ("from the earlier") and a posteriori ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, tautologies, and deduction from pure reason. A posteriori knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in Organon, a collection of works by Aristotle.
Semantics of logicIn logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment. The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences.
