In enumerative induction, there is no contradiction in accepting the premiss while denying the conclusion.282 But in the case of deductive reasoning (mathematical induction) the denial of the conclusion would entail a contradiction. The reason for this is that while mathematical induction deals with formal relations, strictly formal concepts, strictly formal definitions, and formal knowledge of this - analytic knowledge - enumerative induction deals with, either or both, predictions regarding the future anddescriptions of observed cases (with the implicit aim of this description serving as a foundation for the prediction of future cases and observations). Consequently, in both the predictive and the descriptive cases, enumerative induction is concerned with physical reality and the establishment of synthetic knowledge regarding this reality - a reality whose content is empirically determined but not formally determined, two spheres of reality that have little or nothing to do with one another. If, for example, one considers the fact that n +1 is a necessarily valid law of mathematics and thus an apodictically certain law, then one can accept this as a premiss and yet deny the assertion that there actually does exist an unlimited number of humans (n +1 humans), which would constitute synthetic knowledge.The assertion denied in the former sentence is a conclusion that must be empirically determined in order to be verified or validated (which itself would constitute an impossibility).A further example of how it is possible to accept a premiss while denying its consequence is that it is possible to deny a general rule, for example, that the sun rises in the mornings, which follows from enumerative induction, by stating that that the sun will not rise tomorrow as the Earth will not rotate or the observer lives above the polar circle and so on.There is nothing logically self-contradicting in denying an empirically a ca l l f o r s c i e n t i f i c p u r i t y 131 4 . 2 . 2 . 3 Denying Inductive Inferences:A Logical Impossibility? 282 A Companion to Epistemology, Dancy and Sosa, eds., Induction: enumerative and hypothetical.

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