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Induction

Related: generalization - reason - science

Contrast: deduction

Inductive reasoning works the other way from deduction, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach. [Aug 2006]

Definition (philosophy)

Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the conclusion of an argument is very likely to be true, but not certain, given the premises. It is to ascribe properties or relations to types based on limited observations of particular tokens; or to formulate laws based on limited observations of recurring phenomenal patterns. --http://en.wikipedia.org/wiki/Inductive_reasoning [May 2005]

Deductive, inductive, abductive

Reasoning has been classified as either deductive reasoning, meaning "from the general to the particular", or inductive reasoning, meaning "from the particular to the general". In the 19th century, Charles Peirce, an American philosopher, added a third classification, abductive reasoning, by which he meant "from the best available information to the best explanation" --http://en.wikipedia.org/wiki/Reason [Feb 2005]

Benjamin and Virilio: induction

If Walter Benjamin had one true intellectual descendant who extended his inquiries into the second half of the twentieth century, this must be Paul Virilio. Indeed, Benjamin and Virilio share a number of crucial affinities both in terms of their method and the themes they explore.

The method: both are able to practice the most difficult philosophical method of all -- that of induction -- inferring general laws of culture and history from the minute details of everyday life. (This sets them apart from most critics who are predisposed to see such details through the filters of already existing theoretical paradigms.)

Both also abandon the conventional method of theoretical exposition which requires the writer to first clearly state general arguments and then support them by particular examples in favor of another method, borrowed from cinema: montage of images. --Lev Manovich

Black swans and inductive reasoning

There are seven species of swans in the world, all pure white except for the Australian Black Swan and the South American Black-necked Swan. The first European to see a Black Swan is believed to be the Dutch sailor Antonie Caen who described the species during his visit to the Shark Bay area in 1636. Later, the Dutch explorer Willem de Vlamingh captured several birds on the Swan River, Western Australia in 1697, but many people in Europe did not believe him, as at that time it was believed that all swans were white. Three of the captured birds were taken to Batavia, where they lived for some time. However, the species wasn't reported again until the arrival of the 'First Fleet' in 1788. The Black Swan was first described scientifically by Dr. John Latham in 1790. --http://www.nzbirds.com/BlackSwan.html [Jun 2005]

No matter how many times 17th Century biologists observed white swans, and in how many different locations, there is no deductive path that can lead them to the conclusion that all swans are white. This is just as well, since, as it turned out, that conclusion would have been wrong. --http://en.wikipedia.org/wiki/Philosophy_of_science#Induction [Jun 2005]

see also: induction - reason

Induction (science)

Inductive reasoning maintains that if a situation holds in all observed cases, then the situation holds in all cases. So, after completing a series of experiments that support the Third Law, one is justified in maintaining that the Law holds in all cases.

Explaining why induction commonly works has been somewhat problematic. One cannot use deduction, the usual process of moving logically from premise to conclusion, because there is simply no syllogism that will allow such a move. No matter how many times 17th Century biologists observed white swans, and in how many different locations, there is no deductive path that can lead them to the conclusion that all swans are white. This is just as well, since, as it turned out, that conclusion would have been wrong. Similarly, it is at least possible that an observation will be done tomorrow that shows an occasion in which an action is not accompanied by a reaction; the same is true of any scientific law.

One answer has been to conceive of a different form of rational argument, one that does not rely on deduction. Deduction allows one to formulate a specific truth from a general truth: all crows are black; this is a crow; therefore this is black. Induction merely allows one to formulate a probability of truth from a series of specific observations: this is a crow and it is black; that is a crow and it is black; therefore our sample shows crows are black.

The problem of induction is one of considerable debate and importance in the philosophy of science: is induction indeed justified, and if so, how? --http://en.wikipedia.org/wiki/Philosophy_of_science#Induction [May 2005]

Problem of induction

The problem of induction is the philosophical issue involved in deciding the place of induction in determining empirical truth. The problem of induction is whether inductive reason works. That is, what is the justification for either:

However, any series of observations, however large, may be taken to logically imply any particular conclusion about some future event only if 'induction' itself works. And that may be concluded only inductively. So, for instance, from any series of observations that water freezes at 0C it is valid to infer that the next sample of water will do the same only if induction works. That such a prediction comes true when tried merely adds to the series; it does not establish the reliability of induction, except inductively. The problem is, then, what justification can there be for making such an inference?

David Hume addressed this problem in the 18th century in a particularly influential way, and no analysis since has managed to evade Hume's critique. Hume looked at ways to justify inductive thinking. He pointed out that justifying induction on the grounds that it has worked in the past begs the question. That is, it is using inductive reasoning to justify induction. Circular arguments are valid, but do not provide a satisfactory justification for the supposition they claim to support. Prior to Hume, Sir Francis Bacon had made a strong claim that science was based on induction. Sir Karl Popper sought to 'bypass' the problem in the philosophy of science by arguing that science does not actually rely on induction, developing the notion of falsification instead. Popper replaced induction with deduction, in effect making modus tollens the centerpiece of his theory. On this account, when assessing a theory one should pay greater heed to data which is in disagreement with the theory than to data which is in agreement with it. Popper went further and stated that a hypothesis which does not allow of such experimental test is outside the bounds of science.

Isaac Newton considered induction the basis of scientific method at least in his "Opticks".

Nelson Goodman presented a different description of the problem of induction in the article "The New Problem of Induction" (1966). Goodman proposed a new colour, "grue". Something is grue if it is green up until some given time, and blue thereafter. The "new" problem of induction is, how can one know that grass is indeed green, and not grue? --http://en.wikipedia.org/wiki/Problem_of_induction [May 2005]

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