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The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters".
Loglan is a logical constructed language originally designed for linguistic research, particularly for investigating the Sapir–Whorf hypothesis. The language was developed beginning in 1955 by Dr. James Cooke Brown with the goal of making a language so different from natural languages that people learning it would think in a different way if the hypothesis were true. In 1960, Scientific American published an article introducing the language. Loglan is the first among, and the main inspiration for, the languages known as logical languages, which also includes Lojban.
In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is not vague since every number is definitively either prime or not. Vagueness is commonly diagnosed by a predicate's ability to give rise to the Sorites paradox. Vagueness is separate from ambiguity, in which an expression has multiple denotations. For instance the word "bank" is ambiguous since it can refer either to a river bank or to a financial institution, but there are no borderline cases between both interpretations.
A syllogism 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.
An artistic language, or artlang, is a constructed language designed for aesthetic and phonetic pleasure. Constructed languages can be artistic to the extent that artists use it as a source of creativity in art, poetry, calligraphy or as a metaphor to address themes such as cultural diversity and the vulnerability of the individual in a globalizing world. They can also be used to test linguistical theories, such as Linguistic relativity.
The T-schema is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it as the "Equivalence Schema", a synonym introduced by Michael Dummett.
The Latin term characteristica universalis, commonly interpreted as universal characteristic, or universal character in English, is a universal and formal language imagined by Gottfried Leibniz able to express mathematical, scientific, and metaphysical concepts. Leibniz thus hoped to create a language usable within the framework of a universal logical calculation or calculus ratiocinator.
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.
In philosophy—more specifically, in its sub-fields semantics, semiotics, philosophy of language, metaphysics, and metasemantics—meaning "is a relationship between two sorts of things: signs and the kinds of things they intend, express, or signify".
In generative grammar and related approaches, the logical form (LF) of a linguistic expression is the variant of its syntactic structure which undergoes semantic interpretation. It is distinguished from phonetic form, the structure which corresponds to a sentence's pronunciation. These separate representations are postulated in order to explain the ways in which an expression's meaning can be partially independent of its pronunciation, e.g. scope ambiguities.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought.
The grammar of Lojban is based on predicate logic. The majority of the grammar is borrowed from the prior "logical language" Loglan, and some of its features come from Láadan. The characteristic regularity, unambiguity, and versatility of Lojban grammar owes much to modern linguistics and computer programming—resources that were unavailable to the designers of earlier languages. Lojbanist Bob LeChevalier summarized one advantage of Lojban grammar as follows: "Lojban moves beyond the restrictions of European grammar. It overtly incorporates linguistic universals, building in what is needed to support the expressivity of the whole variety of natural languages, including non-European ones."
Lojban is a logical, constructed, human language created by the Logical Language Group which aims to be syntactically unambiguous. It succeeds the Loglan project.
A constructed language is a language whose phonology, grammar, and vocabulary, instead of having developed naturally, are consciously devised for some purpose, which may include being devised for a work of fiction. A constructed language may also be referred to as an artificial, planned or invented language, or a fictional language. Planned languages are languages that have been purposefully designed; they are the result of deliberate, controlling intervention and are thus of a form of language planning.
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in the formal languages studied in mathematics and logic, the term "symbol" refers to the idea, and the marks are considered to be a token instance of the symbol. In logic, symbols build literal utility to illustrate ideas.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines 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. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
References
- ↑ "Glossopoeia & Glossopoeic Languages". www.carolandray.plus.com. Retrieved 2021-05-26.
- ↑ "Ygyde Language". May 15, 2024.
- ↑ "Ygyde Language". Archived from the original on February 1, 2016.