Wednesday, April 07, 2010
Some remarks on a passage by Botha
In Rudolf Botha's The Justification of Linguistic Hypotheses: A Study of Nondemonstrative Inference in Transformational Grammar, Chapter 2, he postulates three levels of merit for nondemonstrative arguments, viz., the level of support, the level of acceptability, and the level of persuasive power. I here will be concerned with the first two only.
As factors affecting the level of support, he lists, among others, "the number of the evidential statements that bear positively on the proposition", and "the number of evidential statements that bear negatively on the proposition", the former increasing the rank and the latter lowering the rank of said proposition. When he considers fators affecting the level of acceptability, he lists, among others, "the (rank/degree of) support for the proposition underlying the hypothesis", and "the truth of the evidential statements which bear positively on the proposition underlying the hypothesis". Let's ignore the confused writing (rank of support? rank of the proposition?) and concentrate on the abysmal incoherence of what has been said. First of all, if he regards the truth of certain statements as a distinct item, one must logically deduce that, when he had mentioned said statements earlier, he was not presupposing their truth. Therefore, we must deduce that statements which have some bearing on the proposition are to be considered relevant for the level of support even when they are false. But this is absurd, since the number of positively bearing propositions is exactly the same as the number of negatively bearing ones: you have, for every true proposition, a false one which is its negative. The absurd is made more evident by the following: if he must consider "the truth of the evidential statements which bear positively on the proposition", why hasn't he considered "the falsity of the evidential statements which bear negatively on the proposition"?
As factors affecting the level of support, he lists, among others, "the number of the evidential statements that bear positively on the proposition", and "the number of evidential statements that bear negatively on the proposition", the former increasing the rank and the latter lowering the rank of said proposition. When he considers fators affecting the level of acceptability, he lists, among others, "the (rank/degree of) support for the proposition underlying the hypothesis", and "the truth of the evidential statements which bear positively on the proposition underlying the hypothesis". Let's ignore the confused writing (rank of support? rank of the proposition?) and concentrate on the abysmal incoherence of what has been said. First of all, if he regards the truth of certain statements as a distinct item, one must logically deduce that, when he had mentioned said statements earlier, he was not presupposing their truth. Therefore, we must deduce that statements which have some bearing on the proposition are to be considered relevant for the level of support even when they are false. But this is absurd, since the number of positively bearing propositions is exactly the same as the number of negatively bearing ones: you have, for every true proposition, a false one which is its negative. The absurd is made more evident by the following: if he must consider "the truth of the evidential statements which bear positively on the proposition", why hasn't he considered "the falsity of the evidential statements which bear negatively on the proposition"?
