In the
philosophy of scienceThe philosophy of science is concerned with the assumptions, foundations, and implications of science. The field is defined by an interest in one of a set of "traditional" problems or an interest in central or foundational concerns in science...
inductivism exists both in a classical naive version, which has been highly influential, and in various more sophisticated versions. The naive version, which can be traced back to thinkers such as Abū Rayhān al-Bīrūnī and
David HumeDavid Hume was a Scottish philosopher, economist, historian and a key figure in the history of Western philosophy and the Scottish Enlightenment...
, says that general statements (theories) have to be based on empirical observations, which are subsequently generalized into statements which can either be regarded as true or probably true.
The classical example goes from a series of observations:
Swan no.
In the
philosophy of scienceThe philosophy of science is concerned with the assumptions, foundations, and implications of science. The field is defined by an interest in one of a set of "traditional" problems or an interest in central or foundational concerns in science...
inductivism exists both in a classical naive version, which has been highly influential, and in various more sophisticated versions. The naive version, which can be traced back to thinkers such as Abū Rayhān al-Bīrūnī and
David HumeDavid Hume was a Scottish philosopher, economist, historian and a key figure in the history of Western philosophy and the Scottish Enlightenment...
, says that general statements (theories) have to be based on empirical observations, which are subsequently generalized into statements which can either be regarded as true or probably true.
The classical example goes from a series of observations:
Swan no. 1 was white, Swan no. 2 was white… Swan no. k was white… to the general statement: All swans are white.
In support of this view it can be said that we often appear to think in this manner.
In science the proof that there is a law of gravity would then consist in having recorded a large number of observations of things falling, or of bodies attracting one another. Typically classical inductivism will require large and varied amounts of data, which also means that it has difficulties in explaining the importance of singular observations, such as the one in 1918 where light could be observed to be bent around the sun in accordance with Einstein's prediction in his General theory of relativity.
Another problem is that no inductive conclusion can yield certainty, and here
David HumeDavid Hume was a Scottish philosopher, economist, historian and a key figure in the history of Western philosophy and the Scottish Enlightenment...
also famously pointed out that it can not even be shown that inductive conclusions yield probable conclusions as one gets involved in a circular argument in that case, trying to prove the value of induction through induction.
Karl PopperSir Karl Raimund Popper, CH, FRS, FBA was an Austrian and British philosopher and a professor at the London School of Economics. He is considered one of the most influential philosophers of science of the 20th century, and also wrote extensively on social and political philosophy...
in
The Logic of Scientific DiscoveryLogik der Forschung is a 1934 book by Karl Popper. It was originally written in German, but reformulated in English by Popper himself some years later, to be published as The Logic of Scientific Discovery in 1959. This forms the rare case of a major work to appear in two languages, both written by...
emerged as a major critic of classical inductivism, which he saw as an essentially conservative strategy. He replaced induction with
falsificationFalsification may mean:*The act of disproving a proposition, hypothesis, or theory. *Forgery, the act of producing something that lacks authenticity with the intent to commit fraud or deception...
. His simplest argument here says that no induction can prove that all swans are white, since this will require an infinite number of observations, but that the observation of a single non-white swan will falsify the statement that all swans are white. The logical rule invoked here is
modus tollensIn classical logic, modus tollens has the following argument form:...
.
A more detailed discussion of induction involves the whole theory of
probabilityProbability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy...
.
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