I must dissent from "A logical proof is 100% true. It always trumps a statistical proof." It is a gross over-statement. A logical proof can be certainly (100%) true only: 1. When all the underlying premises are absolutely, unconditionally true; and 2. When the logical process is flawless. Logical proof trumps statistical inference (We don't say "proof"; all such inferences must recognize the element of doubt.) only when those rigid conditions are met. This, it turns out, is a rare phenomenon and often exists only in the abstract. For very many real things in this world, underlying premises are - at best - fuzzy and rife with unknown qualifications. Here is an example of logical proof gone awry: o Men are taller than women. o John is a man; Carol is a woman. o Therefore, John is taller than Carol. However, it is quite possible that John is not taller than Carol; he might be 5'2" tall and she 6'4", as might be if he were a jockey and she a professional basketball player. This is not an instance of "exception proves the rule"; it is a case of an inadequate rule (premise). A statistical inference or prediction applies when only some things about the subject of interest are known and those with less precision. Statistical inferences & predictions reach into places where logic can not go. Damon Runyon stated the principle as "The race goes not always to the swift.., but that's the way to bet." -ralph_/)

> -----Original Message----- > From: y-dna-projects-bounces@rootsweb.com [mailto:y-dna-projects- > bounces@rootsweb.com] On Behalf Of Ralph Taylor > Sent: Friday, August 13, 2010 5:51 PM > To: y-dna-projects@rootsweb.com > Subject: [Y-DNA-projects] Logic vs. Statistics > > I must dissent from "A logical proof is 100% true. It always trumps a statistical > proof." It is a gross over-statement. Not at all. It's true by definition. > A logical proof can be certainly (100%) true only: > 1. When all the underlying premises are absolutely, unconditionally true; and 2. When > the logical process is flawless. Yes, of course, that's the definition of a logical proof. > Logical proof trumps statistical inference (We don't say "proof"; all such inferences > must recognize the element of doubt.) only when those rigid conditions are met. Call it what you like, but the point of logical deduction is that -- if the premises are true and the logic is valid -- the conclusion has no element of doubt. That's the reason it trumps a statistical conclusion. > This, it turns out, is a rare phenomenon and often exists only in the abstract. For very > many real things in this world, underlying premises are - at best - fuzzy and rife with > unknown qualifications. Logical deductions are not rare, at all. We all make logical deductions every day, hundreds of them in fact. To use my computer, it must be turned on. My computer is not currently turned on (no pun intended). Currently, I cannot use my computer. > Here is an example of logical proof gone awry: > o Men are taller than women. > o John is a man; Carol is a woman. > o Therefore, John is taller than Carol. > > However, it is quite possible that John is not taller than Carol; he might be 5'2" tall > and she 6'4", as might be if he were a jockey and she a professional basketball player. > This is not an instance of "exception proves the rule"; it is a case of an inadequate > rule (premise). You have deliberately constructed a syllogism with a premise that is untrue and, thus, a conclusion that is untrue. That doesn't mean valid logical deductions can't be made, it means you have to follow the rules for forming them. I'm talking about conclusions that fulfill the requirements of valid logical deductions. > A statistical inference or prediction applies when only some things about the subject > of interest are known and those with less precision. Statistical inferences & > predictions reach into places where logic can not go. I never said statistics weren't valuable research tools. I said statistical proofs/inferences/deductions/conclusions/whatever (things that are "true" only to some degree of probability) are weaker than valid logical ones (which are, by their nature, 100% true). > Damon Runyon stated the principle as "The race goes not always to the swift.., but > that's the way to bet." Yes, of course, if you're a rational person you bet the odds -- and you don't go to Vegas with the expectation of returning rich. But when the odds are 100%, it ceases to be a betting matter. I'm going to be a little unfair here and call an end to this thread with my having had the last word (listadmin's prerogative). We are off topic for the list; and, in any case, we're just repeating the same arguments in different words. There's nothing constructive to be accomplished by a prolonged "Yes, it is" - "No, it isn't" exchange. Diana