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It is not the case that The application of probability concepts does not involve any presuppositions about the external world or the law of causality.
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Reasons For
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Reason for 1 of 2
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1.
Applying probability to empirical events requires assuming that past frequencies are relevant to future outcomes, which presupposes causal regularity.
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2.
Hume's problem of induction shows that no purely a priori reasoning can license inference from observed to unobserved cases without causal assumptions.
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3.
Therefore, the application—as distinct from the formal calculus—necessarily imports presuppositions about the world's causal structure.
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Reason for 2 of 2
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1.
Frequentist interpretations of probability, defended by Venn and von Mises, define probability as the limiting frequency of events in physical sequences.
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2.
A limiting frequency is a fact about the external world, not a consequence derivable from the concept of probability alone.
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3.
Any application of probability under the frequentist interpretation thus presupposes stable, law-governed regularities in nature.
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Reasons Against
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1.
The calculus of probability is purely a priori.
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2.
The calculus of probability is solely derived from the concept of probability itself.
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