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Certainty (also known as epistemic certainty or objective certainty) is the
epistemic Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Episte ...
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 Justification may refer to: * Justification (epistemology), a property of beliefs that a person has good reasons for holding * Justification (jurisprudence), defence in a prosecution for a criminal offenses * Justification (theology), God's act of ...
. 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 incapable of entertaining its falsity, this does not entail that the belief is itself beyond rational doubt or incapable of being false. While the word "certainty" is sometimes used to refer to a person's ''subjective'' certainty about the truth of a belief, philosophers are primarily interested in the question of whether any beliefs ever attain ''objective'' certainty. The philosophical question of whether one can ever be truly certain about anything has been widely debated for centuries. Many proponents of philosophical skepticism deny that certainty is possible, or claim that it is only possible in '' a priori'' domains such as logic or mathematics. Historically, many philosophers have held that knowledge requires epistemic certainty, and therefore that one must have
infallible Infallibility refers to an inability to be wrong. It can be applied within a specific domain, or it can be used as a more general adjective. The term has significance in both epistemology and theology, and its meaning and significance in both fi ...
justification in order to count as knowing the truth of a proposition. However, many philosophers such as René Descartes were troubled by the resulting skeptical implications, since all of our experiences at least seem to be compatible with various
skeptical scenario Philosophical skepticism ( UK spelling: scepticism; from Greek σκέψις ''skepsis'', "inquiry") is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even reject ...
s. It is generally accepted today that most of our beliefs are compatible with their falsity and are therefore fallible, although the status of being certain is still often ascribed to a limited range of beliefs (such as " I exist"). The apparent fallibility of our beliefs has led many contemporary philosophers to deny that knowledge requires certainty.


History


Ancient Greece

Major elements of philosophical skepticismthe idea that things cannot be known with certainty, which the ancient Greeks expressed by the word '' acatalepsia''are apparent in the writings of several ancient Greek philosophers, particularly Xenophanes and Democritus. The first Hellenistic school that embraced philosophical skepticism was
Pyrrhonism Pyrrhonism is a school of philosophical skepticism founded by Pyrrho in the fourth century BCE. It is best known through the surviving works of Sextus Empiricus, writing in the late second century or early third century CE. History Pyrrho of E ...
, which was founded by Pyrrho of Elis. Pyrrho's skepticism quickly spread to Plato's Academy under Arcesilaus, who abandoned Platonic dogma and initiated Academic Skepticism, the second skeptical school of
Hellenistic philosophy Hellenistic philosophy is a time-frame for Western philosophy and Ancient Greek philosophy corresponding to the Hellenistic period. It is purely external and encompasses disparate intellectual content. There is no single philosophical school or cu ...
. The major difference between the two skeptical schools was that Pyrrhonism's aims were psychotherapeutic (i.e., to lead practitioners to the state of ataraxiafreedom from anxiety, whereas those of Academic Skepticism were about making judgments under uncertainty (i.e., to identify what arguments were most truth-like).


Descartes – 17th century

In his '' Meditations on First Philosophy'', Descartes first discards all belief in things which are not absolutely certain, and then tries to establish what can be known for sure. Although the phrase " Cogito, ergo sum" is often attributed to Descartes' ''Meditations on First Philosophy'', it is actually put forward in his ''Discourse on Method''. Due to the implications of inferring the conclusion within the predicate, however, he changed the argument to "I think, I exist"; this then became his first certainty. Descartes' conclusion being that, in order to doubt, that which is doing the doubting certainly has to existthe act of doubting thus proving the existence of the doubter.


Ludwig Wittgenstein – 20th century

'' On Certainty'' is a series of notes made by Ludwig Wittgenstein just prior to his death. The main theme of the work is that context plays a role in epistemology. Wittgenstein asserts an anti-foundationalist message throughout the work: that every claim can be doubted but certainty is possible in a framework. "The function ropositionsserve in language is to serve as a kind of framework within which empirical propositions can make sense".


Degrees of certainty

Physicist
Lawrence M. Krauss Lawrence Maxwell Krauss (born May 27, 1954) is an American theoretical physicist and cosmologist who previously taught at Arizona State University, Yale University, and Case Western Reserve University. He founded ASU's Origins Project, now cal ...
suggests that the need for identifying degrees of certainty is under-appreciated in various domains, including policy-making and the understanding of science. This is because different goals require different degrees of certaintyand politicians are not always aware of (or do not make it clear) how much certainty we are working with.
Rudolf Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. He ...
viewed certainty as a matter of degree ("degrees of certainty") which could be objectively measured, with degree one being certainty. Bayesian analysis derives degrees of certainty which are interpreted as a measure of
subjective Subjective may refer to: * Subjectivity, a subject's personal perspective, feelings, beliefs, desires or discovery, as opposed to those made from an independent, objective, point of view ** Subjective experience, the subjective quality of conscio ...
psychological Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between t ...
belief. Alternatively, one might use the legal degrees of certainty. These standards of
evidence Evidence for a proposition is what supports this proposition. It is usually understood as an indication that the supported proposition is true. What role evidence plays and how it is conceived varies from field to field. In epistemology, evidenc ...
ascend as follows: no credible evidence, some credible evidence, a preponderance of evidence, clear and convincing evidence, beyond reasonable doubt, and beyond any shadow of a doubt (i.e. ''undoubtable''recognized as an impossible standard to meetwhich serves only to terminate the list). If knowledge requires absolute certainty, then knowledge is most likely impossible, as evidenced by the apparent fallibility of our beliefs.


Foundational crisis of mathematics

The ''foundational crisis of mathematics'' was the early 20th century's term for the search for proper foundations of mathematics. After several schools of the philosophy of mathematics ran into difficulties one after the other in the 20th century, the assumption that mathematics had any foundation that could be stated within
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
itself began to be heavily challenged. One attempt after another to provide unassailable foundations for mathematics was found to suffer from various paradoxes (such as Russell's paradox) and to be
inconsistent In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent i ...
. Various schools of thought were opposing each other. The leading school was that of the formalist approach, of which
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
was the foremost proponent, culminating in what is known as Hilbert's program, which sought to ground mathematics on a small basis of a formal system proved sound by metamathematical finitistic means. The main opponent was the intuitionist school, led by
L.E.J. Brouwer Luitzen Egbertus Jan Brouwer (; ; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and compl ...
, which resolutely discarded formalism as a meaningless game with symbols. The fight was acrimonious. In 1920 Hilbert succeeded in having Brouwer, whom he considered a threat to mathematics, removed from the editorial board of ''
Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
'', the leading mathematical journal of the time.
Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research i ...
, proved in 1931, showed that essential aspects of Hilbert's program could not be attained. In Gödel's first result he showed how to construct, for any sufficiently powerful and consistent finitely axiomatizable systemsuch as necessary to axiomatize the elementary theory of
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
a statement that can be shown to be true, but that does not follow from the rules of the system. It thus became clear that the notion of mathematical truth cannot be reduced to a purely formal system as envisaged in Hilbert's program. In a next result Gödel showed that such a system was not powerful enough for proving its own consistency, let alone that a simpler system could do the job. This proves that there is no hope to ''prove'' the consistency of any system that contains an axiomatization of elementary arithmetic, and, in particular, to prove the consistency of Zermelo–Fraenkel set theory (ZFC), the system which is generally used for building all mathematics. However, if ZFC is not consistent, there exists a proof of both a theorem and its negation, and this would imply a proof of all theorems and all their negations. As, despite the large number of mathematical areas that have been deeply studied, no such contradiction has ever been found, this provides an almost certainty of mathematical results. Moreover, if such a contradiction would eventually be found, most mathematicians are convinced that it will be possible to resolve it by a slight modification of the axioms of ZFC. Moreover, the method of
forcing Forcing may refer to: Mathematics and science * Forcing (mathematics), a technique for obtaining independence proofs for set theory *Forcing (recursion theory), a modification of Paul Cohen's original set theoretic technique of forcing to deal with ...
allows proving the consistency of a theory, provided that another theory is consistent. For example, if ZFC is consistent, adding to it the continuum hypothesis or a negation of it defines two theories that are both consistent (in other words, the continuum is independent from the axioms of ZFC). This existence of proofs of relative consistency implies that the consistency of modern mathematics depends weakly on a particular choice on the axioms on which mathematics are built. In this sense, the crisis has been resolved, as, although consistency of ZFC is not provable, it solves (or avoids) all logical paradoxes at the origin of the crisis, and there are many facts that provide a quasi-certainty of the consistency of modern mathematics.


See also

* Almost surely *
Fideism Fideism () is an epistemological theory which maintains that faith is independent of reason, or that reason and faith are hostile to each other and faith is superior at arriving at particular truths (see natural theology). The word ''fideism'' c ...
*
Gut feeling Feelings are Subjectivity, subjective self-contained phenomenal experiences. According to the ''APA Dictionary of Psychology'', a feeling is "a self-contained phenomenal experience"; and feelings are "subjective, evaluative, and independent of t ...
* Infallibility * Justified true belief * Neuroethological innate behavior,
instinct Instinct is the inherent inclination of a living organism towards a particular complex behaviour, containing both innate (inborn) and learned elements. The simplest example of an instinctive behaviour is a fixed action pattern (FAP), in which a v ...
* Pascal's Wager * Pragmatism *
Scientific consensus Scientific consensus is the generally held judgment, position, and opinion of the majority or the supermajority of scientists in a particular field of study at any particular time. Consensus is achieved through scholarly communication at confe ...
*
Skeptical hypothesis Philosophical skepticism ( UK spelling: scepticism; from Greek σκέψις ''skepsis'', "inquiry") is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even reject ...
* As contrary concepts ** Fallibilism ** Indeterminism **
Multiverse The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The di ...


References


External links

*
certainty
The American Heritage Dictionary of the English Language. Bartleby.com * *
The certainty of belief
{{Sufism terminology Cognition Concepts in epistemology Concepts in logic Concepts in metaphilosophy Concepts in metaphysics Concepts in the philosophy of mind Concepts in the philosophy of science Critical thinking Epistemological theories Epistemology History of logic History of mathematics History of philosophy History of religion History of science Intellectual history Logic Metaphilosophy Metaphysical theories Metaphysics Metaphysics of mind Ontology Philosophy of mathematics Philosophy of mind Philosophy of religion Philosophy of science Pyrrhonism