In five pages this paper discusses the formation of beliefs and the importance of induction in a consideration of its validity as well as its drawbacks. Six sources are cited in the bibliography.
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continues to be used in those areas that do not lend themselves to the requirements of deduction, particularly the requirement that something be experienced before it can be known.
While useful, induction does have its limitations. It is not the best way to form beliefs, but there are times it is the only way.
Mathematical Bases Until the turn of the century just past, the study of mathematics was a purely theoretical pursuit
and discipline largely inaccessible to all but those steadfastly determined to study it. The transformation to modern mathematics began in the late 19th century (Gray, 1993), much of it
having remained intact and unquestioned literally for millennia. Euclids Elements was one such blindly accepted area: "For more than 2000 years they
remained unquestioned, yet it should have been obvious that some, at least, were open to doubt. For instance, the famous fifth postulate--that parallel lines never meet--is not true on curved
surfaces" (Gray, 1993; p. 30). When examining the qualities and properties of lines, debate could be much more esoteric before flight was possible than after. In the earliest
days of the space race, knowing this exception to Euclids fifth postulate was a critical issue for those involved, as well as for those in training.
The very definition of inductive reasoning allows individuals to describe and relate laws of nature, and it also requires that the one doing the reasoning take on
some assumption about the issue at hand. Despite the need to make assumptions about topics and issues that cannot be known without question, Mauro writes that the "method