Certainty
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- A related article is titled uncertainty.
- For statistical certainty, see probability.
Certainty is the state of being without doubt. It is total security from error. Certainty is the continuity and validity of all foundational inquiry. Something is certain only if no skepticism can occur. Philosophy (at least historically) seeks this state. Epistemology is the study of knowledge, certainty, and truth. Contemporary views of knowledge, both in philosophy and in general, do not demand certainty. It is widely held that certainty is a failed historical enterprise.[1] A common alternative is "justified true belief".
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[edit] Problems
It is generally believed that some reasoning, specifically Deductive reasoning, does make conclusions which are certain. An example:
- P or Q.
- not P.
- Therefore, Q is true (and certain)
The conclusion of Q however, relies on its premises, "P or Q" and "not P" to be true. Logic can only extend certainty to the conclusion but cannot establish certainty of the premises- this is because they have their own premises.
This is where philosophers find the problem of proving a first premise, or the validity of reason itself, independently from reason. A popular analogy in philosophy describing the inability of logic to supply arguments for its own validity is that of Baron Münchhausen, who fell into a swamp and escaped by pulling up on his own hair.
[edit] History
[edit] Socrates- ancient Greece
Socrates, often thought to be the first true philosopher, had a higher a criterion for knowledge than others before him. The skeptical problems that he encountered in his philosophy were taken very seriously. As a result, he claimed to know nothing. Socrates often said that his wisdom was limited to an awareness of his own ignorance.
[edit] Al-Ghazali- middle ages
Al-Ghazali was a professor of philosophy in the 11th century. His book titled The Incoherence of the Philosophers marks a major turn in Islamic epistemology, as Ghazali effectively discovered philosophical skepticism that would not be commonly seen in the West until René Descartes, George Berkeley and David Hume. He described the necessary of proving the validity of reason- independently from reason. He attempted this and failed. The doubt that he introduced to his foundation of knowledge could not be reconciled using philosophy. Taking this very seriously, he resigned from his post at the university, and suffered serious psychosomatic illness. It was not until he became a religious sufi that he found a solution to his philosophical problems, which are based on Islamic religion; this encounter with skepticism led Ghazali to embrace a form of theological occasionalism, or the belief that all causal events and interactions are not the product of material conjunctions but rather the immediate and present will of God.
[edit] Descartes- 18th 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. It is a famous pursuit of certainty by Descartes, in which he claims Cogito, ergo sum (I think, therefore I am) as a certain truth.
[edit] Ludwig Wittgenstein- 20th Century
On Certainty, is a book by Ludwig Wittgenstein. 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".[2]
[edit] 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 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: an undesirable situation in which every mathematical statement that can be formulated in a proposed system (such as 2 + 2 = 5) can also be proved in the system.
Various schools of thought on the right approach to the foundations of mathematics were fiercely 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 thought 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[citation needed]. 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. 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 ZFC, 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.
[edit] Quotes
| “ | There is no such thing as absolute certainty, but there is assurance sufficient
for the purposes of human life. — John Stuart Mill | ” |
| “ | Doubt is not a pleasant condition, but certainty is absurd. — Voltaire | ” |
| “ | In this world nothing can be said to be certain, except death and taxes. — Benjamin Franklin | ” |
[edit] See also
[edit] External links
- "Certitude". Catholic Encyclopedia. (1913). New York: Robert Appleton Company.
- http://www.bartleby.com/61/41/C0214100.html
- http://atheism.about.com/library/glossary/general/bldef_certainty.htmde:Gewissheit
fr:Certitude pl:Pewność pt:Certeza ru:Уверенность uk:Впевненість
