Anti Hume - A Critical Note on Hume's Problem of Induction

Background:David Hume's problem of induction has exerted enormous influence on epistemology and philosophy of science, purportedly demonstrating that inductive reasoning lacks rational foundation. However, Hume's argument rests on premises that are both logically fallacious and empirically untenable.Material and methods:We analyze Hume's original texts — the \textit{Treatise of Human Nature} (1739) and the \textit{Enquiry Concerning Human Understanding} (1748) — identifying the logical structure of his argument and its hidden assumptions. We then apply the mathematical theory of probability, specifically the binomial right-tailed test, to quantify inductive uncertainty. Jacob Bernoulli's \textit{Ars Conjectandi} (1713) provides the foundational framework for this analysis.Results:Hume's critique commits the \textit{post hoc, ergo propter hoc} fallacy and rests on the internally inconsistent assertion that nature is both eternally uniform and capable of change. His argument against induction is itself inductively grounded, rendering it circular. The right-tailed binomial test, by contrast, yields precise probabilistic measures of evidential support:\[p\text{-value} = \sum_{i=k}^{n} \binom{n}{i} \pi_0^{i} (1-\pi_0)^{n-i},\]with closed-form expressions for boundary cases such as \(n = k+1\). This framework quantifies confidence without demanding certainty.Conclusion:Hume's problem dissolves when examined through the lens of probability theory. The mathematical apparatus for sound inductive inference existed decades before Hume wrote, yet he failed to engage with it. His critique is not a genuine philosophical insight but a pseudo-problem arising from logical confusion and disciplinary isolation. The binomial model demonstrates that induction, properly understood, provides rigorous and measurable probabilistic guarantees.