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Although inductive reasoning is– as we shall see - not logically continuous, it is nevertheless a seemingly parsimonious avenue for the formation of theories and conceptions about the world around us. The sun has risen and fallen every day up until this point in time and while this may not logically prove that it will do the same tomorrow, the popular belief is that this repetition gives us a firm ontological grounding for expecting it to do so. This does not seem unreasonable, at least in one sense of the word; indeed, if you happened to meet an individual who claimed to possess an agnostic belief about whether or not the sun is likely to reappear tomorrow, then you would most likely consider them to be a very odd person. So inductive inferences are all around us, they are the functional basis of our understanding of the world. For the sake of this paper, then, it is important to understand what we mean when we talk about an inductive inference.
Presented in its most rudimentary construct, the inductive inference appears in the logical form:
(I) Pa1,..., Pan Pan+1, or
(II) Pa1,…, Pan AxPx.
Let us briefly explore these two statements. In statement (I), an+1 denotes a different object or form from those denoted by a1 ,…., an. During the application of these principles (I) and (II), we are to assume that we do not know any non-P’s, and furthermore that the class of a1 ,..., an are the sole objects for which we know that they are P’s.
Now,

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