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Review of Probability and Certainty in Seventeenth-Century England by Barbara J. Shapiro (Princeton, NJ: Princeton Univ Press, 1983). (Note that this Amazon page seems to contain information about two different books, one by Shapiro of which I write, and another by Abrahamian.)
This book is about knowing. The concept of science evolved dramatically in the seventeenth century. What interests me in particular about this period is evolution in the idea of what constitutes knowledge and the circumstances surrounding the emergence of mathematical probability as a scientific tool (the two are closely related).
This book is not about mathematical probability. It is an examination of changes in various aspects of English culture attendant to the phenomenon of the broadening of the philosophical concept of "knowing" to embrace things not provable mathematically or geometrically.
While not discussed in Shapiro's book, this change in the definition of what was admissible as knowledge would give legitimacy to mathematical probability as a valid means to extend knowledge. Not coincidentally, I guess, the foundations of mathematical probability were developed at this time, attributed to Pascal and Fermat in 1654.
In England, two philosophers provide the defining end points for this period of change, namely Francis Bacon (1561-1626) and John Locke (1632-1704), but the time immediately surrounding the Restoration (1660-ish), seems especially significant.
Shapiro's goal is to show how the same evolving ways of thinking operated in philosophy, physics, biology, law, religion, etc., driven by a cast of characters who, in true renaissance tradition, were involved in many of these areas simultaneously.
Knowledge in the Eye of the Beholder
Before this period, most philosophers (scientists) felt that the only valid way to know anything was to be able to prove it. Such proofs "compelled assent." No dispute about the length of the hypotenuse of a right triangle, given the lengths of the other two sides is possible once the Pythagorean Theorem had been proved. Any other type of claim to knowledge, anything else at all, is just opinion. Kinda stifling, but definitely a "bright line."
That all changed when it was allowed that if some fact could be believed with a "moral certainty", then it could be claimed as knowledge. The probability of an alleged "matters of fact" referred to the degree to which the fact might be believed. Facts for which the inferential evidence (based on new emerging definitions of what was acceptable as evidence) was overwhelming could be granted "moral certainty." If less compelling, then the fact might be judged probable or highly probable.
Establishing knowledge in this new empirical way could have resulted in a highly contentious atmosphere, so rules for proper presentation and discussion of scientific claims were established and promoted (by the Royal Society, founded in 1661-ish). It is interesting that England in 1660 was emerging from a period of civil strife and religious factionalism, and that some of the leading thinkers, who also happened to be Anglican clergy and public figures, therefore had multiple motives, for seeking to promote agreement on rules for non-belligerent discussion over disputed facts.
The book contains some very interesting insights. For example, Anglican clergy were heavily involved in the new kind of empiricist knowledge generation, in part because they believed that science could be employed to obtain evidence supporting the fundamental tenets of their religion (including existence of God in the world). Shapiro argues that because the Anglicans had rejected Rome and papal infallibility, they needed to find other means to both ground their religion and defend it against not only Rome but also the fundamentalist religious factions at home.
The chapter on natural philosophy and experimental science is of most interest. Bacon set the stage with his empiricist philosophy, allowing that sense experience could be a valid form of knowledge. Shapiro asserts that following Bacon, for the generation of Robert Boyle and Robert Hooke and others, "Phenomenal matters of fact derived from observation and experiment became a, if not the, central concern of English natural philosophers. Knowledge could be expanded through empirical study of the sensory world, even if the resulting matters of fact could not be established through mathematical proof. Locke, closing the century, synthesized the change in philosophical thinking in his theory of knowledge.
Much of the experimental philosophy conducted in this period was ostensibly for the purpose of establishing matters of fact not about validating theory. [Discussion about what matters of fact might mean in the context of a given theory was declared to be outside the realm of natural philosophy.] Hence it seems to me that no mathematical concept of hypothesis testing would have been a natural outgrowth of this work, and Shapiro mentions none.
Still, there was apparently much discussion about hypothesis and explanations of established matters of fact. Shapiro, describing Boyle's view, states that a `Good Hypothesis' should be "intelligible, assume nothing impossible or demonstrably false, be sufficient to explicate the phenomena, be consistent with related phenomena, and not contradict any known phenomena," and that an "'Excellent Hypothesis' must not only be the simplest one to `Explicate the Phaenomena,' but must also permit prediction."
This view of hypothesis as a component of science is decidedly empirical, broadening the preexisting mathematical (or syllogistic) view and, significantly, subsuming some of what previous periods' philosophers would have labeled opinion or speculation.
This has been a superficial and highly impressionistic summary of a thorough and detailed piece of research. As it used to be said, God is in the details. What I have glossed or omitted is not insignificant to Shapiro's narrative. Here I have focused only on a few points salient with respect to my narrow interests.