Abstract
Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.
Highlights
Sophists, and the exercise of their profession-sophistry, have received very bad press, ever since Plato, who, together with his mentor Socrates, was an implacable foe of the sophists' ideas and methods
Those who oppose the statisticians' dictum, including me, do not propose that we infer causal relations which do not respect temporal ordering; rather, we propose that causal relations may be inferred even lacking explicit temporal knowledge
Despite the fact that probability theory applies a formal calculus and, as such, comes no more naturally to people than do mathematical logic or the differential and integral calculus, it should be clear that probability theory offers a useful guide to much of correct human inference
Summary
The exercise of their profession-sophistry, have received very bad press, ever since Plato, who, together with his mentor Socrates, was an implacable foe of the sophists' ideas and methods. Despite the claims of psychologists that many of these forms of reasoning fail to match our best normative standards, including Bayesian reasoning principles, and so are fallacious, they are to be endorsed as good, if imperfect, discoverers ofthe truth. Arguments along these lines are due to LJ. Bayesian reasoning fully or partially endorses the "fallacy." This kind ofpoint is perfectly compatible with the possibility that less than fully normative heuristics provide evolutionarily useful guidance in decision making It is a continuing difficulty for Bayesian theory that its principles are very easy to misunderstand and misapply, as has been repeatedly demonstrated in the philosophical, statistical and psychological literatures. I hope that my treatment ofthe fallacies may help in this regard
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