Related concepts and fundamentals:
Certainty is perfect knowledge that has total security from error, or
the mental state of being without doubt.
Objectively defined, certainty is total continuity and validity of all
foundational inquiry, to the highest degree of precision. Something is
certain only if no skepticism can occur.
Philosophy (at least,
historical Cartesian philosophy) seeks this state.
Pyrrho – ancient Greece
1.2 Ibn-Rushd – Averroes
Descartes – 17th century
Ludwig Wittgenstein – 20th century
2 Degrees of certainty
3 Foundational crisis of mathematics
5 See also
7 External links
Pyrrho – ancient Greece
Main article: Pyrrho
Pyrrho is credited as being the first Skeptic philosopher. The main
principle of Pyrrho's thought is expressed by the word acatalepsia,
which denotes the ability to withhold assent from doctrines regarding
the truth of things in their own nature; against every statement its
contradiction may be advanced with equal justification. Secondly, it
is necessary in view of this fact to preserve an attitude of
intellectual suspense, or, as Timon expressed it, no assertion can be
known to be better than another.
Ibn-Rushd – Averroes
Main article: Ibn Rushd
Averroes was a purveyor of certain parts of Aristotelian philosophy.
His philosophy was considered controversial in Muslim circles. as
well as in West with thinkers like St. Thomas Aquinas who said of
Averroes, "the Arabian commentator as one who had, indeed, perverted
the Peripatetic tradition, but whose words, nevertheless, should be
treated with respect and consideration." Averroes' contribution to
epistemology is only noted for the fact that he was one of the first
to write on the topic and acted as a comparison for the traditional
and definitive works of the Western tradition.Turner, William.
"Averroes". Catholic Answers. Catholic Answers. Retrieved February 28,
Descartes – 17th century
Descartes' Meditations on First
Philosophy is a book in which
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.
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 [propositions]
serve in language is to serve as a kind of framework within which
empirical propositions can make sense".
Degrees of certainty
See also: Inductive reasoning,
Probability interpretations, and
Philosophy of statistics
Lawrence M. Krauss
Lawrence M. Krauss suggests that 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 certainty—and politicians are not
always aware of (or do not make it clear) how much certainty we are
Rudolf Carnap viewed certainty as a matter of degree ("degrees of
certainty") which could be objectively measured, with degree one being
Bayesian analysis derives degrees of certainty which are
interpreted as a measure of subjective psychological belief.
Alternatively, one might use the legal degrees of certainty. These
standards of evidence 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
meet—which serves only to terminate the list).
Foundational crisis of mathematics
Main article: Foundations of mathematics § Foundational crisis
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 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.
Various schools of thought were opposing each other. The leading
school was that of the formalist approach, of which
David Hilbert 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,
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, the leading mathematical journal of the time.
Gödel's incompleteness theorems, 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 system—such as
necessary to axiomatize the elementary theory of arithmetic—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 can not 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 dealt a final
blow to the heart of Hilbert's program, the hope that consistency
could be established by finitistic means (it was never made clear
exactly what axioms were the "finitistic" ones, but whatever axiomatic
system was being referred to, it was a weaker system than the system
whose consistency it was supposed to prove). Meanwhile, the
intuitionistic school had failed to attract adherents among working
mathematicians, and floundered due to the difficulties of doing
mathematics under the constraint of constructivism.
In a sense, the crisis has not been resolved, but faded away: most
mathematicians either do not work from axiomatic systems, or if they
do, do not doubt the consistency of Zermelo–Fraenkel set theory,
generally their preferred axiomatic system. In most of mathematics as
it is practiced, the various logical paradoxes never played a role
anyway, and in those branches in which they do (such as logic and
category theory), they may be avoided.
Doubt is not a pleasant condition, but certainty is absurd.
In this world nothing can be said to be certain, except death and
— Benjamin Franklin
There is no such thing as absolute certainty, but there is assurance
sufficient for the purposes of human life.
— John Stuart Mill
I don't know what to say
Ludwig Wittgenstein #115 from On Certainty
Gut feeling[clarification needed]
Justified true belief
Neuroethological innate behavior, instinct
As contrary concepts
^ "Averroës (Ibn Rushd) > By Individual Philosopher >
Philosophy". Philosophybasics.com. Retrieved 2012-10-13.
^ Wittgenstein, Ludwig. "On Certainty". SparkNotes.
^ "question center, SHAs – cognitive tools". edge.com.
Look up certainty or certain in Wiktionary, the free dictionary.
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"Certitude". Catholic Encyclopedia. 1913.
certainty, The American Heritage Dictionary of the English Language.
"certainty vs. doubt". About.com. Retrieved 2008-02-23.
Reed, Baron. "Certainty". In Zalta, Edward N. Stanford Encyclopedia of
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