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Propositions
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] |
Logic
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 based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Attitudes
A propositional attitude is a mental state held by an agent or organism toward a proposition. In philosophy, propositional attitudes can be considered to be neurally realized, causally efficacious, content-bearing internal states (personal principles/values). Linguistically, propositional attitudes are denoted by a verb (e.g. ''believed'') governing an embedded "that" clause, for example, 'Sally believed that she had won'. Propositional attitudes are often assumed to be the fundamental units of thought and their contents, being propositions, are true or false from the perspective of the person. An agent can have different propositional attitudes toward the same proposition (e.g., "''S'' believes that her ice-cream is cold," and "''S'' fears that her ice-cream is cold"). Propositional attitudes have directions of fit: some are meant to reflect the world, others to influence it. One topic of central concern is the relation between the modalities of assertion and belief, as well as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, philosophy of logic, logic, and Philosophy of mathematics, mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the History of logic#Rise of modern logic, development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in computing as well as various types of logic. Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null are treated as false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called falsy and truthy. For example, in Lisp, nil, the empty list, is treated as false, and all other values are treated as true. In C, the number 0 or 0.0 is false, and all other values are treated as true. In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intentionality
Intentionality is the mental ability to refer to or represent something. Sometimes regarded as the ''mark of the mental'', it is found in mental states like perceptions, beliefs or desires. For example, the perception of a tree has intentionality because it represents a tree to the perceiver. A central issue for theories of intentionality has been the problem of ''intentional inexistence'': to determine the ontological status of the entities which are the objects of intentional states. An early theory of intentionality is associated with Anselm of Canterbury's ontological argument for the existence of God, and with his tenets distinguishing between objects that exist in the understanding and objects that exist in reality. The idea fell out of discussion with the end of the medieval scholastic period, but in recent times was resurrected by empirical psychologist Franz Brentano and later adopted by contemporary phenomenological philosopher Edmund Husserl. Today, intentionalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platonist
Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism has had a profound effect on Western thought. At the most fundamental level, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism." Philosophers who affirm the existence of abstract objects are sometimes called platonists; those who deny their existence are sometimes called nominalists. The terms "platonism" and "nominalism" have established senses in the history of philosophy, where they denote positions that have little to do with the modern notion of an abstract object. In this connection, it is essential to bear in mind that modern platonists (with a small 'p') need not accept any of the doctrines of Plato, just as modern nominal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internalism
Internalism and externalism are two opposite ways of integrating and explaining various subjects in several areas of philosophy. These include human motivation, knowledge, justification, meaning, and truth. The distinction arises in many areas of debate with similar but distinct meanings. Internal–external distinction is a distinction used in philosophy to divide an ontology into two parts: an internal part concerning observation related to philosophy, and an external part concerning question related to philosophy. Internalism is the thesis that no fact about the world can provide reasons for action independently of desires and beliefs.Giuseppina D'Oro"Collingwood, psychologism and internalism,"''European Journal of Philosophy'' 12(2):163–177 (2004). Externalism is the thesis that reasons are to be identified with objective features of the world. Moral philosophy Motivation In contemporary moral philosophy, motivational internalism (or moral internalism) is the view that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Image
In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f". Similarly, the inverse image (or preimage) of a given subset B of the codomain Y is the set of all elements of X that map to a member of B. The image of the function f is the set of all output values it may produce, that is, the image of X. The preimage of f is the preimage of the codomain Y. Because it always equals X (the domain of f), it is rarely used. Image and inverse image may also be defined for general binary relations, not just functions. Definition The word "image" is used in three related ways. In these definitions, f : X \to Y is a function from the set X to the set Y. Image of an element If x is a member of X, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indicator Function
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , then the indicator function of is the function \mathbf_A defined by \mathbf_\!(x) = 1 if x \in A, and \mathbf_\!(x) = 0 otherwise. Other common notations are and \chi_A. The indicator function of is the Iverson bracket of the property of belonging to ; that is, \mathbf_(x) = \left x\in A\ \right For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers. Definition Given an arbitrary set , the indicator function of a subset of is the function \mathbf_A \colon X \mapsto \ defined by \operatorname\mathbf_A\!( x ) = \begin 1 & \text x \in A \\ 0 & \text x \notin A \,. \end The Iverson bracket provides the equivalent notation \left x\in A\ \right/math> or that can be used instead of \mathbf_\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mind
Philosophy of mind is a branch of philosophy that deals with the nature of the mind and its relation to the Body (biology), body and the Reality, external world. The mind–body problem is a paradigmatic issue in philosophy of mind, although a number of other issues are addressed, such as the hard problem of consciousness and the nature of particular mental states.Siegel, S.: ''The Contents of Visual Experience''. New York: Oxford University Press. 2010.Macpherson, F. & Haddock, A., editors, ''Disjunctivism: Perception, Action, Knowledge'', Oxford: Oxford University Press, 2008. Aspects of the mind that are studied include mental events, mental functions, mental property, mental properties, consciousness and neural correlates of consciousness, its neural correlates, the ontology of the mind, the nature of cognition and of thought, and the relationship of the mind to the body. Dualism (philosophy of mind), Dualism and monism are the two central schools of thought on the mind–bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inquisitive Semantics
Inquisitive semantics is a framework in logic and Formal semantics (linguistics), natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and the issue that it raises. The framework provides a foundation for the linguistic analysis of statements and questions. It was originally developed by Ivano Ciardelli, Jeroen Groenendijk, Salvador Mascarenhas, and Floris Roelofsen. Basic notions The essential notion in inquisitive semantics is that of an ''inquisitive proposition''. * An ''information state'' (alternately a ''classical proposition'') is a set of possible worlds. * An ''inquisitive proposition'' is a nonempty downward closure, downward-closed set of information states. Inquisitive propositions encode informational content via the region of logical space that their information states cover. For instance, the inquisitive proposition \ encodes the information that is the actual world. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
