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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
belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take i ...
s 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 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 distinc ...
, 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 Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
question of whether one can ever be truly certain about anything has been widely debated for centuries. Many proponents of
philosophical skepticism 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 ...
deny that certainty is possible, or claim that it is only possible in ''
a priori ("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ex ...
'' 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 René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
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 Originally, fallibilism (from Medieval Latin: ''fallibilis'', "liable to err") is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified,Haack, Susan (1979)"Fallibilism and Nece ...
, 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 skepticism 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 ...
the idea that things cannot be known with certainty, which the ancient Greeks expressed by the word ''
acatalepsia In philosophy, acatalepsy (from the Greek ἀκαταληψία "inability to comprehend" from alpha privative and καταλαμβάνειν, "to seize") is incomprehensibleness, or the impossibility of comprehending or conceiving a thing. It ...
''are apparent in the writings of several ancient Greek philosophers, particularly
Xenophanes Xenophanes of Colophon (; grc, Ξενοφάνης ὁ Κολοφώνιος ; c. 570 – c. 478 BC) was a Greek philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φ ...
and
Democritus Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. No ...
. 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 of Elis (; grc, Πύρρων ὁ Ἠλεῖος, Pyrrhо̄n ho Ēleios; ), born in Elis, Greece, was a Greek philosopher of Classical antiquity, credited as being the first Greek skeptic philosopher and founder of Pyrrhonism. Life ...
. Pyrrho's skepticism quickly spread to Plato's
Academy An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy ...
under
Arcesilaus Arcesilaus (; grc-gre, Ἀρκεσίλαος; 316/5–241/0 BC) was a Greek Hellenistic philosopher. He was the founder of Academic Skepticism and what is variously called the Second or Middle or New Academy – the phase of the Platonic Acade ...
, who abandoned Platonic
dogma Dogma is a belief or set of beliefs that is accepted by the members of a group without being questioned or doubted. It may be in the form of an official system of principles or doctrines of a religion, such as Roman Catholicism, Judaism, Islam ...
and initiated
Academic Skepticism Academic skepticism refers to the skeptical period of ancient Platonism dating from around 266 BCE, when Arcesilaus became scholarch of the Platonic Academy, until around 90 BCE, when Antiochus of Ascalon rejected skepticism, although individua ...
, 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
ataraxia ''Ataraxia'' (Greek: ἀταραξία, from ("a-", negation) and ''tarachē'' "disturbance, trouble"; hence, "unperturbedness", generally translated as "imperturbability", "equanimity", or "tranquility") is a Greek term first used in Ancient Gre ...
freedom from anxiety, whereas those of Academic Skepticism were about making judgments under
uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or ...
(i.e., to identify what arguments were most truth-like).


Descartes – 17th century

In his ''
Meditations on First Philosophy ''Meditations on First Philosophy, in which the existence of God and the immortality of the soul are demonstrated'' ( la, Meditationes de Prima Philosophia, in qua Dei existentia et animæ immortalitas demonstratur) is a philosophical treatise ...
'', 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 The Latin , usually translated into English as "I think, therefore I am", is the "first principle" of René Descartes's philosophy. He originally published it in French as , in his 1637 ''Discourse on the Method'', so as to reach a wider audien ...
" 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 ''On Certainty'' (german: Über Gewissheit, original spelling ) is a philosophical book composed from notes written by Ludwig Wittgenstein over four separate periods in the eighteen months before his death on 29 April 1951. He left his initial not ...
'' is a series of notes made by
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...
just prior to his death. The main theme of the work is that
context Context may refer to: * Context (language use), the relevant constraints of the communicative situation that influence language use, language variation, and discourse summary Computing * Context (computing), the virtual environment required to su ...
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 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 Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and ...
derives degrees of certainty which are interpreted as a measure of subjective
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 A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take i ...
. 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 The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's ...
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
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 premises, leads to a seemingly self-contradictory or a logically u ...
es (such as
Russell's paradox In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains a ...
) 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 ...
. 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 In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathema ...
, which sought to ground mathematics on a small basis of a
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 form ...
proved sound by metamathematical finitistic means. The main opponent was the
intuitionist In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fu ...
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 In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as ...
(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 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 In mathematics, 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 (ZFC), this is equivalent to ...
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 In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. ...
*
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 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 ...
*
Justified true belief Definitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philoso ...
* 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 Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...
*
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 Originally, fallibilism (from Medieval Latin: ''fallibilis'', "liable to err") is the philosophical principle that Proposition, propositions can be accepted even though they cannot be conclusively proven or Justification (epistemology), justifie ...
**
Indeterminism Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or do not cause deterministically. It is the opposite of determinism and related to chance. It is highly relevant to the philosophical probl ...
**
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 ''The American Heritage Dictionary of the English Language'' (''AHD'') is an American English, American dictionary of English published by Boston publisher Houghton Mifflin Harcourt, Houghton Mifflin, the first edition of which appeared in 1969. ...
.
Bartleby.com Bartleby.com was an electronic text archive, headquartered in Los Angeles (USA) and named for Herman Melville's story "Bartleby, the Scrivener". It was initiated with the name "Project Bartleby" in January 1993 as a collection of classic literatur ...
* *
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