# The Incommensurability of Inductive Support and Mathematical Probability

# The Incommensurability of Inductive Support and Mathematical Probability

This chapter provides an elaboration on the incommensurability of inductive support and mathematical probability. It begins by presenting the argument from the possibility of anomalies. If inductive support-grading is to allow for the existence of anomalies, it cannot depend on the mathematical probabilities involved. A second argument for the incommensurability of inductive support with mathematical probability may be built up on the basis of the conjunction principle for inductive support. If s[H,E] conforms to this principle, the actual value of p_{M}[H] must be irrelevant to that of s[H,E] unless intolerable constraints are to restrict the mathematical probability of one conjunct on another. Since the actual value of p_{M}[E,H] must also be irrelevant to that of s[H,E], and s[H,E] cannot possibly be a function of p_{M}[E] alone, it follows that s[H,E] cannot be a function of the mathematical probabilities involved.

*Keywords:*
inductive support, mathematical probability, incommensurability, inductive support-grading, conjunction principle

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