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Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a '' possible world''. A formula's truth value ...
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Formal System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an " axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought. 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. Background Each formal system is described by primitive symbols (which collectively form an alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the primitive symbols—combinations that are forme ...
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Saul Kripke
Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic, modal logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and recursion theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts. Kripke made influential and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics. He received the 2001 Schock Prize in Logic and Philosophy. Kripke was also partly responsible for the revival of metaphysics after the decline of logical positivism, claimi ...
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Permission (philosophy)
Permission, in philosophy, is the attribute of a person whose performance of a specific action, otherwise ethically wrong or dubious, would thereby involve no ethical fault. The term "permission" is more commonly used to refer to consent. Consent is the legal embodiment of the concept, in which approval is given to another party. Permissions depend on norms or institutions. Many permissions and obligations are complementary to each other, and deontic logic Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It ... is a tool sometimes used in reasoning about such relationships. Further reading * Alexy, Robert, ''Theorie der Grundrechte'', Suhrkamp, Frankfurt a. M.: 1985. Translation: ''A theory of constitutional rights'', Oxford University Press, Oxford: 2002. * Raz, Joseph, ''Practical rea ...
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Determinism
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. The opposite of determinism is some kind of indeterminism (otherwise called nondeterminism) or randomness. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible.For example, see Determinism is often used to mean ''causal determinism'', which in physics is known as cause-and-effect. This is the concept that events within a given paradigm are bound by causality in such a way that any state of an object or event is completely determined by its prior states. This meaning can be distinguished from other varieties of determinism mentioned below. Debates about determinism often concern the scope of determined systems; some maintain that the entire universe is a single determ ...
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Knowledge
Knowledge can be defined as awareness of facts or as practical skills, and may also refer to familiarity with objects or situations. Knowledge of facts, also called propositional knowledge, is often defined as true belief that is distinct from opinion or guesswork by virtue of justification. While there is wide agreement among philosophers that propositional knowledge is a form of true belief, many controversies in philosophy focus on justification: whether it is needed at all, how to understand it, and whether something else besides it is needed. These controversies intensified due to a series of thought experiments by Edmund Gettier and have provoked various alternative definitions. Some of them deny that justification is necessary and replace it, for example, with reliability or the manifestation of cognitive virtues. Others contend that justification is needed but formulate additional requirements, for example, that no defeaters of the belief are present or that t ...
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Obligation
An obligation is a course of action that someone is required to take, whether legal or moral. Obligations are constraints; they limit freedom. People who are under obligations may choose to freely act under obligations. Obligation exists when there is a choice to do what is morally good and what is morally unacceptable. There are also obligations in other normative contexts, such as obligations of etiquette, social obligations, religious, and possibly in terms of politics, where obligations are requirements which must be fulfilled. These are generally legal obligations, which can incur a penalty for non-fulfilment, although certain people are obliged to carry out certain actions for other reasons as well, whether as a tradition or for social reasons. Obligations vary from person to person: for example, a person holding a political office will generally have far more obligations than an average adult citizen, who themselves will have more obligations than a child. Obligations ...
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Operator (mathematics)
In mathematics, an operator is generally a Map_(mathematics), mapping or function (mathematics), function that acts on elements of a space (mathematics), space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an ''operator'', but the term is often used in place of ''function'' when the domain of a function, domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to be explicitly characterized (for example in the case of an integral operator), and may be extended to related objects (an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation). See Operator (physics) for other examples. The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are the same space, for example \R^n to \R^n. Such operators oft ...
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Social Epistemology
Social epistemology refers to a broad set of approaches that can be taken in epistemology (the study of knowledge) that construes human knowledge as a collective achievement. Another way of characterizing social epistemology is as the evaluation of the social dimensions of knowledge or information. As a field of inquiry in analytic philosophy, social epistemology deals with questions about knowledge in social contexts, meaning those in which knowledge attributions cannot be explained by examining individuals in isolation from one another. The most common topics discussed in contemporary social epistemology are testimony (e.g. "When does a belief that x is true which resulted from being told 'x is true' constitute knowledge?"), peer disagreement (e.g. "When and how should I revise my beliefs in light of other people holding beliefs that contradict mine?"), and group epistemology (e.g. "What does it mean to attribute knowledge to groups rather than individuals, and when are such kno ...
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Multiverse (set Theory)
In mathematical set theory, the multiverse view is that there are many models of set theory, but no "absolute", "canonical" or "true" model. The various models are all equally valid or true, though some may be more useful or attractive than others. The opposite view is the "universe" view of set theory in which all sets are contained in some single ultimate model. The collection of countable transitive models of ZFC (in some universe) is called the hyperverse and is very similar to the "multiverse". A typical difference between the universe and multiverse views is the attitude to the continuum hypothesis In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZF .... In the universe view the continuum hypothesis is a meaningful question that is either true or false though we have not yet bee ...
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Web Design
Web design encompasses many different skills and disciplines in the production and maintenance of websites. The different areas of web design include web graphic design; user interface design (UI design); authoring, including standardised code and proprietary software; user experience design (UX design); and search engine optimization. Often many individuals will work in teams covering different aspects of the design process, although some designers will cover them all. The term "web design" is normally used to describe the design process relating to the front-end (client side) design of a website including writing markup. Web design partially overlaps web engineering in the broader scope of web development. Web designers are expected to have an awareness of usability and be up to date with web accessibility guidelines. History 1988–2001 Although web design has a fairly recent history, it can be linked to other areas such as graphic design, user experience, and multimed ...
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Legal Theory
Jurisprudence, or legal theory, is the theoretical study of the propriety of law. Scholars of jurisprudence seek to explain the nature of law in its most general form and they also seek to achieve a deeper understanding of legal reasoning and analogy, legal systems, legal institutions, and the proper application of law, the economic analysis of law and the role of law in society. Modern jurisprudence began in the 18th century and it was based on the first principles of natural law, civil law, and the law of nations. General jurisprudence can be divided into categories both by the type of question scholars seek to answer and by the theories of jurisprudence, or schools of thought, regarding how those questions are best answered. Contemporary philosophy of law, which deals with general jurisprudence, addresses problems internal to law and legal systems and problems of law as a social institution that relates to the larger political and social context in which it exists ...
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Moral Theory
Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns matters of value; these fields comprise the branch of philosophy called axiology. Ethics seeks to resolve questions of human morality by defining concepts such as good and evil, right and wrong, virtue and vice, justice and crime. As a field of intellectual inquiry, moral philosophy is related to the fields of moral psychology, descriptive ethics, and value theory. Three major areas of study within ethics recognized today are: # Meta-ethics, concerning the theoretical meaning and reference of moral propositions, and how their truth values (if any) can be determined; # Normative ethics, concerning the practical means of determining a moral course of action; # Applied ethics, concerning what a person is obligated (or permitted) to do in a sp ...
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