The hypothesis logic is the antecedent of a conditional proposition. An extensive mathematical or scientific investigation often assumes the form of a vast conditional proposition. The hypothesis is usually stated once and for all at the beginning and taken for granted throughout the investigation. The study of hypotheses of this type and the deduction of their logical consequences is what mathematics is all about.
Thus, the axioms of Euclidean geometry form the hypothesis on the basis of which the principles of geometry are proved. In natural science, the truth of the hypothesis, which is a matter of indifference to the mathematician, is of fundamental importance. It is rare, if ever, for this to be examined directly, and cannot always be deduced from known generalizations, so a hypothesis is usually established or disproven by studying its logical implications. An unfulfilled consequence of a hypothesis is sufficient to refine it, but no number of verified consequences, however large, is sufficient for its complete demonstration.
The hypothesis logic is the antecedent of a conditional proposition. An extensive mathematical or scientific investigation often assumes the form of a vast conditional proposition.
The hypothesis logic is the antecedent of a conditional proposition. An extensive mathematical or scientific investigation often assumes the form of a vast conditional proposition. Source
However, hypotheses have certain properties, through which their degrees of difference or similarity may be compared. It is, moreover, a widely accepted rule that the fewer and less significant the details in which a hypothesis breaks down, the slighter will be the difference between it and the true hypothesis. Thus, scientific hypothesis, which at first furnishes only a very crude approximation to the observed facts, by the gradual remodeling of detail after detail, comes as close to the truth of the matter as desired.
Natural selection is a good example of this: slow variations have been found to be insufficient for evolutionary change, so mutations have replaced them. These changes in opinion have resulted in the discarding of the theory of inheritance of acquired characteristics, as well as the adjustment of the survival of the fittest concept. The modern theory of evolution is thus more firmly established than its predecessor, though it still remains a hypothesis capable of further rectifying.
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