Edwin Coleman

I argue that there is no fallacy of argument from authority. I first show the weakness of the case for there being such a fallacy: text-book presentations are confused, alleged examples are not genuinely exemplary, reasons given for its alleged fallaciousness are not convincing. Then I analyse arguing from authority as a complex speech act. Rejecting the popular but unjustified category of the "part-time fallacy", I show that bad arguments which appeal to authority are defective through breach of some felicity condition on argument as a speech act, not through employing a bad principle of inference

The specific characteristics of mathematical argumentation all depend on the centrality that writing has in the practice of mathematics, but blindness to this fact is near universal. What follows concerns just one of those characteristics, justification by proof. There is a prevalent view that long proofs pose a problem for the thesis that mathematical knowledge is justified by proof. I argue that there is no such problem: in fact, virtually all the justifications of mathematical knowledge are ‘long proofs’, but because these real justifications are distributed in the written archive of mathematics, proofs remain surveyable, hence good.

My real position is that logic is a mere sub-branch of rhetoric, but in this paper I only try to show an area of overlap. Certain usages in logical work are metaphorical, and I argue that this has pernicious effects in a discipline assumed strictly literal. Among these pernicious effects are the bizarre and fruitless focus of philosophy of mathematics on the pseudo-problems of foundations and objects. I mostly examine the locution 'logical construction' and a range of associated metaphors. Some sketchy remarks on the history of rhetoric are offered in explanation.