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In this case, the modified hypothesis needs to be tested again and if it passes the test, it will be considered a corroborated hypothesis and can be published. The sixth and final step is to construct, support or cast doubt on a scientific theory which is not a guess, speculation or suggestion which is the proper definition of the term theory.
Mathematics is an essential discipline due to its practical role to the individual and society, as a result of its problem solving approach. Applied mathematics loosely designates a wide range of studies with significant current use in the empirical sciences. It includes numerical methods and computer science that seeks concrete solutions, sometimes approximate, to explicit mathematical problems for instance differential equations, large systems of linear equations (Moyal 240). Descartes, in his search for certainty, found that none of the senses, individually or jointly, provides experience so "clear and distinct" that it is beyond all doubt. He implied that if he could find one thing which was unquestionably true of his experience, it would serve as a foundation for all the other elements of knowledge that were less in certainty. It was for this reason that he turned to the intangible precision of mathematics (Rene & Ian 148). He was able to show that the possibility of being wrong in one's assumptions of mathematics. One may assume that they are right in their calculations due to having learnt the wrong way and even continue to teach others the wrong way. This can be compared to everyone originally thinking that the earth was flat and was the centre of the solar system. If a hypnotist can be able to make an entire group of people swear that there is a pink elephant in the room, it should not be difficult to accept that mathematics is equally suspect.
Mathematics may be more reliable and produce more consistent results than other sensory knowledge, but it still casts a shadow of doubt. Descartes adopted a dualistic philosophy by separating the rational realm of self-awareness, abstract thought and mathematical processes from the experiential realm of sounds, colors, textures, tastes and smells. The mind/body problem describes a view in which an immaterial and intellectual dimension is held to be separate from the dimension of one's physical existence. Descartes held that the rational, intellectual dimension is primary, which is ultimately more reliable since at least one truth derived by the mind is beyond doubt. He then connected the "clear and distinct" truth of reason to the less reliable realm of bodily experience by applying the truths of mathematics and logic to the corporeal realm. In his mediations, Descartes even doubted logic and math by his introduction of the hypothesis of an Evil Genie who created, through deception, a virtual reality makes us suppose our numbers and measurement are correct ("Descartes' Deductions").
In conclusion, doubt is the key to knowledge as if one has doubt, they will have questions which they will want answered and in the pursuit of these answers they will gain knowledge. Just as in the areas of science and mathematics, when one has doubts, they will continue to carry out experiments or find other ways of approaching the problem, respectively, as they tackle the problem. Doubt also plays an important role in that we experience ignorance and doubt and uncertainty. This usually leaves us with a feeling of ignorance and this feeling can only be overcome and progress achieved once we recognize the ignorance and leave room for doubt.
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