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Certain Equation
Certainty (also known as epistemic certainty or objective certainty) is the epistemic property of beliefs which a person has no rational grounds for doubting. One standard way of defining epistemic certainty is that a belief is certain if and only if the person holding that belief could not be mistaken in holding that belief. Other common definitions of certainty involve the indubitable nature of such beliefs or define certainty as a property of those beliefs with the greatest possible justification. Certainty is closely related to knowledge, although contemporary philosophers tend to treat knowledge as having lower requirements than certainty. Importantly, epistemic certainty is not the same thing as psychological certainty (also known as subjective certainty or certitude), which describes the highest degree to which a person could be convinced that something is true. While a person may be completely convinced that a particular belief is true, and might even be psychologically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistemic
Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowledge in the form of skills, and knowledge by acquaintance as a familiarity through experience. Epistemologists study the concepts of belief, truth, and justification to understand the nature of knowledge. To discover how knowledge arises, they investigate sources of justification, such as perception, introspection, memory, reason, and testimony. The school of skepticism questions the human ability to attain knowledge while fallibilism says that knowledge is never certain. Empiricists hold that all knowledge comes from sense experience, whereas rationalists believe that some knowledge does not depend on it. Coherentists argue that a belief is justified if it coheres with other beliefs. Foundationalists, by contrast, maintain that the justi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lawrence M
Lawrence may refer to: Education Colleges and universities * Lawrence Technological University, a university in Southfield, Michigan, United States * Lawrence University, a liberal arts university in Appleton, Wisconsin, United States Preparatory & high schools * Lawrence Academy at Groton, a preparatory school in Groton, Massachusetts, United States * Lawrence College, Ghora Gali, a high school in Pakistan * Lawrence School, Lovedale, a high school in India * The Lawrence School, Sanawar, a high school in India Research laboratories * Lawrence Berkeley National Laboratory, United States * Lawrence Livermore National Laboratory, United States People * Lawrence (given name), including a list of people with the name * Lawrence (surname), including a list of people with the name * Lawrence (band), an American soul-pop group * Lawrence (judge royal) (died after 1180), Hungarian nobleman, Judge royal 1164–1172 * Lawrence (musician), Lawrence Hayward (born 1961), British mus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency Proof
In deductive logic, a consistent theory (mathematical logic), theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no Formula (mathematical logic), formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences of T. Let A be a set of Closed-form expression, closed sentences (informally "axioms") and \langle A\rangle the set of closed sentences provable from A under some (specified, possibly implicitly) formal deductive system. The set of axioms A is consistent when there is no formula \varphi such that \varphi \in \langle A \rangle and \lnot \varphi \in \langle A \rangle. A ''trivial'' theory (i.e., one which proves every sentence in the language of the theory) is clearly inconsistent. Conversely, in an principle of explosion, explosive formal system (e.g., classical or intuitionistic propositional or first-order logics) every inconsistent theory is trivial. Consistency of a theory is a sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russell's Paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. According to the unrestricted comprehension principle, for any sufficiently well-defined property, there is the set of all and only the objects that have that property. Let ''R'' be the set of all sets that are not members of themselves. (This set is sometimes called "the Russell set".) If ''R'' is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox. In symbols: : Let R = \. Then R \in R \iff R \not \in R. Russell also showed that a version of the paradox co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found set theory on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship such objects have with physical reality consists. Major themes that are dealt with in philosophy of mathematics include: *''Reality'': The question is whether mathematics is a pure product of human mind or whether it has some reality by itself. *''Logic and rigor'' *''Relationship with physical reality'' *''Relationship with science'' *''Relationship with applications'' *''Mathematical truth'' *''Nature as human activity'' (science, the arts, art, game, or all together) Major themes Reality Logic and rigor Mathematical reasoning requires Mathematical rigor, rigor. This means that the definitions must be absolutely unambiguous and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radical Skepticism
Radical skepticism (or radical scepticism in British English) is the philosophical position that knowledge is most likely impossible. Radical skeptics hold that doubt exists as to the veracity of every belief and that certainty is therefore never justified. To determine the extent to which it is possible to respond to radical skeptical challenges is the task of epistemology or "the theory of knowledge". See also *Pyrrhonism * Cratylism * Epistemological nihilism *Nihilism *Skepticism *Ajñana ''Ajñāna'' (, (Vedic) IPA: /ɐd͡ʑ.ɲɑː.nɐ/; (Classical) IPA: /ɐd͡ʑˈɲɑː.n̪ɐ/) was one of the Āstika and nāstika, ''nāstika'' or "heterodox" schools of Hindu philosophy, ancient Indian philosophy, and the ancient school of rad ... References Leavitt, Fred (2021) If Ignorance is Bliss We Should All be Ecstatic. Open Books ;NotesThe Epistemology Page {{DEFAULTSORT:Radical Skepticism Philosophical skepticism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evidence
Evidence for a proposition is what supports the proposition. It is usually understood as an indication that the proposition is truth, true. The exact definition and role of evidence vary across different fields. In epistemology, evidence is what Justification (epistemology), justifies beliefs or what makes it rational to hold a certain wikt:doxastic, doxastic attitude. For example, a perceptual experience of a tree may serve as evidence to justify the belief that there is a tree. In this role, evidence is usually understood as a private mental state. In Phenomenology (philosophy), phenomenology, evidence is limited to intuitive knowledge, often associated with the controversial assumption that it provides indubitable access to truth. In the science, scientific evidence is information gained through the scientific method that confirms or disconfirms Hypothesis#Scientific hypothesis, scientific hypotheses, acting as a neutral arbiter between competing Scientific theory, theories. Mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legal Burden Of Proof
In a legal dispute, one party has the burden of proof to show that they are correct, while the other party has no such burden and is presumed to be correct. The burden of proof requires a party to produce evidence to establish the truth of facts needed to satisfy all the required legal elements of the dispute. It is also known as the onus of proof. The burden of proof is usually on the person who brings a claim in a dispute. It is often associated with the Latin maxim ''semper necessitas probandi incumbit ei qui agit'', a translation of which is: "the necessity of proof always lies with the person who lays charges." In civil suits, for example, the plaintiff bears the burden of proof that the defendant's action or inaction caused injury to the plaintiff, and the defendant bears the burden of proving an affirmative defense. The burden of proof is on the prosecutor for criminal cases, and the defendant is presumed innocent. If the claimant fails to discharge the burden of proof t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychological
Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feelings, and motivation, motives. Psychology is an academic discipline of immense scope, crossing the boundaries between the Natural science, natural and social sciences. Biological psychologists seek an understanding of the Emergence, emergent properties of brains, linking the discipline to neuroscience. As social scientists, psychologists aim to understand the behavior of individuals and groups.Hockenbury & Hockenbury. Psychology. Worth Publishers, 2010. A professional practitioner or researcher involved in the discipline is called a psychologist. Some psychologists can also be classified as Behavioural sciences, behavioral or Cognitive science, cognitive scientists. Some psychologists attempt to understand the role of mental functions in i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjectivity
The distinction between subjectivity and objectivity is a basic idea of philosophy, particularly epistemology and metaphysics. Various understandings of this distinction have evolved through the work of countless philosophers over centuries. One basic distinction is: *Something is subjective if it is dependent on a mind (biases, perception, emotions, opinions, imagination, or conscious experience). Solomon, Robert C.br>"Subjectivity" in Honderich, Ted. '' Oxford Companion to Philosophy'' (Oxford University Press, 2005), p.900. If a claim is true exclusively when considering the claim from the viewpoint of a sentient being, it is subjectively true. For example, one person may consider the weather to be pleasantly warm, and another person may consider the same weather to be too hot; both views are subjective. *Something is objective if it can be confirmed independently of a mind. If a claim is true even when considering it outside the viewpoint of a sentient being, then it may be lab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
