The core of statistics is concerned with the solution of special types of problems of induction following special modes of reasoning. In the inductive process, some at least of the premises are empirical, and there is always an element of uncertainty about the truth of the conclusion. Historically, examination of the basis of inductive and empirical reasoning started in the 17th century with Francis Bacon and John Locke, but later encountered a stumbling block when Hume raised a serious objection about the logic underlying such reasoning. Statistical inference seeks to get round Hume’s objection pragmatically by invoking probability calculus at various stages of the inductive process.
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