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Islamic Logic
Early Islamic law placed importance on formulating standards of argument, which gave rise to a "novel approach to logic" ( ''manṭiq'' "speech, eloquence") in Kalam (Islamic scholasticism). However, with the rise of the Mu'tazili philosophers, who highly valued Aristotle's ''Organon'', this approach was displaced by the older ideas from Hellenistic philosophy. The works of al-Farabi, Avicenna, al-Ghazali and other Muslim logicians who often criticized and corrected Aristotelian logic and introduced their own forms of logic, also played a central role in the subsequent development of European logic during the Renaissance. Scholars who have studied Islamic logic include Nicholas Rescher, who in a 1964 work contextualized some 170 Arabic-language logicians, without the book being exhaustive. There have been hundreds of original treatises in the subject as well thousands of later commentaries or supra-commentaries. According to the Routledge Encyclopedia of Philosophy: Importa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Islamic Law
Sharia, Sharī'ah, Shari'a, or Shariah () is a body of religious law that forms a part of the Islamic tradition based on scriptures of Islam, particularly the Qur'an and hadith. In Islamic terminology ''sharīʿah'' refers to immutable, intangible divine law; contrary to ''fiqh'', which refers to its interpretations by Islamic scholars. Sharia, or fiqh as traditionally known, has always been used alongside customary law from the very beginning in Islamic history; has been elaborated and developed over the centuries by legal opinions issued by qualified jurists – reflecting the tendencies of different schools – and integrated and with various economic, penal and administrative laws issued by Muslim rulers; and implemented for centuries by judges in the courts until recent times, when secularism was widely adopted in Islamic societies. Traditional theory of Islamic jurisprudence recognizes four sources for Ahkam al-sharia: the Qur'an, ''sunnah'' (or authentic ahadi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Rescher
Nicholas Rescher (; ; 15 July 1928 – 5 January 2024) was a German-born American philosopher, polymath, and author, who was a professor of philosophy at the University of Pittsburgh from 1961. He was chairman of the Center for Philosophy of Science and chairman of the philosophy department. Rescher served as president of the American Catholic Philosophical Association, Leibniz Society of North America, American Metaphysical Society, American Philosophical Association, and Charles S. Peirce Society. He was the founder of '' American Philosophical Quarterly'', '' History of Philosophy Quarterly'', and '' Public Affairs Quarterly''. He died in Pittsburgh on January 5, 2024, at the age of 95. Early life and education Rescher was born in Hagen in the Westphalia region of Germany. In his autobiography he traces his descent to Nehemias Rescher (1735–1801), a founder of the Hochberg-Remseck Jewish community in Swabian Germany. He relocated to the United States when he was 10 an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Citation
Scientific citation is the process of systematically acknowledging sources from which information, data, ideas, or direct quotations are drawn in Academic writing, scholarly work.Sources in science are typically previously-published Peer review, peer-reviewed Academic journal, journal articles, books, Thesis, theses or dissertations, Conference proceedings, conference papers, and rarely private or public communications. Citations connect a researcher’s work with existing Literature review, literature, ensuring transparency, academic integrity, and safe outcomes such as in medical science. Effective citation practices require clear, standardized mechanisms for referencing materials, particularly crucial as electronic publishing and online data repositories expand rapidly. Scientists generate Epistemology, new knowledge by practicing the scientific method on the thoughts, ideas, and work that scientists did before them. By applying scholarly principles, scientists may report thei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Reasoning
Inductive reasoning refers to a variety of method of reasoning, methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike Deductive reasoning, ''deductive'' reasoning (such as mathematical induction), where the conclusion is ''certain'', given the premises are correct, inductive reasoning produces conclusions that are at best ''probable'', given the evidence provided. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from premises about a Sample (statistics), sample to a conclusion about the statistical population, population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Temporal Logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I eat something"). It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians. Temporal logic has found an important application in formal verification, where it is used to state requirements of hardware or software systems. For instance, one may wish to say that ''whenever'' a request is made, access to a resource is ''eventually'' granted, but it is ''never'' granted to two requestors simultaneously. Such a statement can conveniently be expressed in a temporal logic. Motivation Consider the statement "I am hungry". Though it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothetical Syllogism
In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms. Types Hypothetical syllogisms come in two types: mixed and pure. A ''mixed'' hypothetical syllogism has two premises: one conditional statement and one statement that either affirms or denies the antecedent or consequent of that conditional statement. For example, :If P, then Q. :P. :∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid. A mixed hypothetical syllogism has four possible forms, two of which are valid, while the other two are invalid. A valid mixed hypothetical syllogism either affirms the anteceden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System Of Logic
A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Concepts A formal system has the following: * Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). * Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal language. A formal system is said to be recursive (i.e. effective) or recursively enumerable if the set of axioms and the set of inference rules are decidable sets or semid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
A syllogism (, ''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 deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proposition (philosophy)
A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky is blue" expresses the proposition that the sky is blue. Unlike sentences, propositions are not linguistic expressions, so the English sentence "Snow is white" and the German "Schnee ist weiß" denote the same proposition. Propositions also serve as the objects of belief and other propositional attitudes, such as when someone believes that the sky is blue. Formally, propositions are often modeled as functions which map a possible world to a truth value. For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value T if given the actual world as input, but would return F if given some alternate world where the sky is green. However, a number of alternative formalizations have been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terminology
Terminology is a group of specialized words and respective meanings in a particular field, and also the study of such terms and their use; the latter meaning is also known as terminology science. A ''term'' is a word, Compound (linguistics), compound word, or multi-word Expression (language), expression that in specific context (language use), contexts is given specific meanings—these may deviate from the meanings the same words have in other contexts and in everyday language. Terminology is a discipline that studies, among other things, the development of such terms and their interrelationships within a specialized domain. Terminology differs from lexicography, as it involves the study of concepts, conceptual systems and their labels (''terms''), whereas lexicography studies words and their meanings. Terminology is a discipline that systematically studies the "labelling or designating of concepts" particular to one or more subject fields or domains of human activity. It does t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaphysics
Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of human understanding. Some philosophers, including Aristotle, designate metaphysics as first philosophy to suggest that it is more fundamental than other forms of philosophical inquiry. Metaphysics encompasses a wide range of general and abstract topics. It investigates the nature of existence, the features all entities have in common, and their division into categories of being. An influential division is between particulars and universals. Particulars are individual unique entities, like a specific apple. Universals are general features that different particulars have in common, like the color . Modal metaphysics examines what it means for something to be possible or necessary. Metaphysicians also explore the concepts of space, time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
