The Scottish Enlightenment figure David Hume (pictured above) makes four important preliminary observations about the relationship between evidence and probability in the first part his essay “Of Miracles” (paragraphs 3 to 8). For reference, I will restate Hume’s main points as follows:

• First off, Hume describes belief as a continuous variable, not a binary one, because one’s belief about a “matter of fact” — i.e. the probability that the fact might, or might not, be true — can vary from very high (i.e. near certainty) to very low (i.e. total disbelief), or in the immmortal words of David Hume: “in our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence” (Hume, Of Miracles, para. 3, emphasis added).
• From this fundamental premise (i.e. belief is a continuous variable), Hume concludes that the actual level of your degree of belief about a disputed fact should correspond to the amount of relevant evidence available to you: “A wise man, therefore, proportions his belief to the evidence” (para. 4, emphasis added). And he then illustrates this relationship between belief and evidence with a specific example: “A hundred instances or experiments on one side, and fifty on another, afford a doubtful expectation of any event; though a hundred uniform experiments, with only one that is contradictory, reasonably beget a pretty strong degree of assurance” (ibid.).
• Next, Hume observes that in ordinary life the most common type of evidence we use when making our probability judgments (i.e. when determining how strong or weak our degree of belief should be) are not scientific experiments or clinical trials. The most common forms of evidence we rely on are historical reports and eyewitness testimony: “there is no species of reasoning more common, more useful, and even necessary to human life, than that which is derived from the testimony of men, and the reports of eye-witnesses and spectators” (para. 5).
• Lastly (and most importantly), Hume says that we judge the credibility of such evidence (i.e. historical reports or eyewitness testimony) in light of our own understanding of how the world works: “the ultimate standard, by which we determine all disputes, that may arise concerning them [eyewitnesses testimony], is always derived from experience and observation” (para. 6, emphasis added). In other words, we don’t automatically accept a person’s testimony at face value. Instead, we ask ourselves whether his testimony is consistent with our own personal experience of the world and, I might add, with common sense:

“The reason, why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive à priori, between testimony and reality, but because we are accustomed to find a conformity between them.” (para. 8)

To be continued …