Inductive Arguments and True Conclusions
Wednesday, 28. June 2006, 13:36:57
I started "Notes on Logic" as a way of note-taking for updating the superficial logic tutorials at philosophy.lander.edu--without doubt, this purpose accounts in good measure for the unimaginative writing style of this blog.
While trying to clarify the fallacy versions of hasty generalization, converse accident, composition, accident, and division, I am looking at a bit of the logic literature. At present, I'm reviewing an insightful analysis of these fallacies by Douglas Walton, which, undoubtedly, will be cited with admiration in future blogs.
But, at one point, I was startled to read an offhand remark concluding an analysis of an argument from the Sherlock Holmes literature:
Also available online from this link:
Douglas Walton: Papers, "Ignoring Generalizations Secundum Quid as a Subfallacy of Hasty Generalization," n.d. URL=<http://io.uwinnipeg.ca/~walton/p_and_p.htm>
It's well known that Sir A. Conan Doyle referred to Holmes's arguments as "deductive," when, in fact, the arguments usually only provided probable conclusions and so are properly classified as inductive arguments. Correct or good inductive argument claim that their conclusion follows with probability. In valid deductive arguments the conclusion follows with certainty.
Prof. Walton points out Holmes's reasoning concluded in a statement which proved to be true later in the story. He infers from that reason, "...it turned out to be a good argument of that type." However, the later discovery of the truth of the conclusion of an inductive argument has no logical connection with the "goodness" or the "correctness" of the argument.
Correct inductive arguments sometimes have false conclusions because the reasoning is only probable. Incorrect inductive argument (and, indeed, informal fallacies) sometimes have true conclusions.
In other words, Prof. Walton's reasoning can be summarized as follow:
(1) Holmes's argument was clever and plausible.
(2) Holmes's conclusion turned out to be true.
(3) Therefore, Holmes's argument was a good argument.
But, as pointed out above, many invalid and incorrect arguments happen to have true conclusions. There is no necessary connection between the conclusion of an inductive argument and the truth of its premisses.
Perhaps, my disagreement with Prof. Walton is simply over the distinction between an inductive argument and a "plausible conjecture based on presumptive reasoning." Even so, the later discovery of the truth of the conclusion of a "plausible conjecture" is independent of the plausibility of the conjecture.
Just as past events cannot influence the probability of future events, so likewise, I would think, future events cannot influence the logical adequacy of a conjecture.
While trying to clarify the fallacy versions of hasty generalization, converse accident, composition, accident, and division, I am looking at a bit of the logic literature. At present, I'm reviewing an insightful analysis of these fallacies by Douglas Walton, which, undoubtedly, will be cited with admiration in future blogs.
But, at one point, I was startled to read an offhand remark concluding an analysis of an argument from the Sherlock Holmes literature:
Douglas N. Walton, "Ignoring Generalizations Secundum Quid as a Subfallacy of Hasty Generalization," Logique & Analyse 129-139 (1990), 119.To say that Holmes'argument was fallacious because he could possibly have been mistaken is to insist, unsympathetically and unfairly, that Holmes' argument must be interpreted as a deductively valid argument, or perhaps a very strong kind of induction.
But far from that, Holmes' argument was evidently meant to be a clever guess, a plausible conjecture based on presumptive reasoning. And as such, at least as far as we are told in the story, it turned out to be a good argument of that type.
Also available online from this link:
Douglas Walton: Papers, "Ignoring Generalizations Secundum Quid as a Subfallacy of Hasty Generalization," n.d. URL=<http://io.uwinnipeg.ca/~walton/p_and_p.htm>
It's well known that Sir A. Conan Doyle referred to Holmes's arguments as "deductive," when, in fact, the arguments usually only provided probable conclusions and so are properly classified as inductive arguments. Correct or good inductive argument claim that their conclusion follows with probability. In valid deductive arguments the conclusion follows with certainty.
Prof. Walton points out Holmes's reasoning concluded in a statement which proved to be true later in the story. He infers from that reason, "...it turned out to be a good argument of that type." However, the later discovery of the truth of the conclusion of an inductive argument has no logical connection with the "goodness" or the "correctness" of the argument.
Correct inductive arguments sometimes have false conclusions because the reasoning is only probable. Incorrect inductive argument (and, indeed, informal fallacies) sometimes have true conclusions.
In other words, Prof. Walton's reasoning can be summarized as follow:
(1) Holmes's argument was clever and plausible.
(2) Holmes's conclusion turned out to be true.
(3) Therefore, Holmes's argument was a good argument.
But, as pointed out above, many invalid and incorrect arguments happen to have true conclusions. There is no necessary connection between the conclusion of an inductive argument and the truth of its premisses.
Perhaps, my disagreement with Prof. Walton is simply over the distinction between an inductive argument and a "plausible conjecture based on presumptive reasoning." Even so, the later discovery of the truth of the conclusion of a "plausible conjecture" is independent of the plausibility of the conjecture.
Just as past events cannot influence the probability of future events, so likewise, I would think, future events cannot influence the logical adequacy of a conjecture.
WIDGETIZE