Language, Proof and Logic, 2nd edition

Book Preface

What do the elds of astronomy, economics, nance, law, mathematics, medicine, physics, and sociology have in common? Not much in the way of subject matter, that’s for sure. And not all that much in the way of methodology. What they do have in common, with each other and with many other elds, is their dependence on a certain standard of rationality. In each of these elds, it is assumed that the participants can dierentiate between rational argumentation based on assumed principles or evidence, and wild speculation or nonsequiturs, claims that in no way follow from the assumptions. In other words, these elds all presuppose an underlying acceptance of basic principles of logic.

For that matter, all rational inquiry depends on logic, on the ability of logic and rational people to reason correctly most of the time, and, when they fail to reason inquiry correctly, on the ability of others to point out the gaps in their reasoning. While people may not all agree on a whole lot, they do seem to be able to agree on what can legitimately be concluded from given information. Acceptance of these commonly held principles of rationality is what dierentiates rational inquiry from other forms of human activity.

Just what are the principles of rationality presupposed by these disciplines? And what are the techniques by which we can distinguish correct or valid” reasoning from incorrect or invalid” reasoning? More basically, what is it that makes one claim follow logically” from some given information, while some other claim does not?

Many answers to these questions have been explored. Some people have claimed that the laws of logic are simply a matter of convention. If this is so, logic and convention we could presumably decide to change the conventions, and so adopt dierent principles of logic, the way we can decide which side of the road we drive on. But there is an overwhelming intuition that the laws of logic are somehow more fundamental, less subject to repeal, than the laws of the land, or even the laws of physics. We can imagine a country in which a red trac light means go, and a world on which water  ows up hill. But we can’t even imagine a world in which there both are and are not nine planets.