tag:blogger.com,1999:blog-3634628224045926034.post5954759913921437733..comments2023-08-29T01:27:13.772-07:00Comments on Magpie's Asymmetric Warfare: Circular ReasoningMagpiehttp://www.blogger.com/profile/07528637318288802178noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3634628224045926034.post-495066324422126622011-12-15T02:43:27.908-08:002011-12-15T02:43:27.908-08:00Okay, let's see if this is what you meant with...Okay, let's see if this is what you meant with your first paragraph.<br /><br />Although the text uses Predicate Logic statements (cleverly disguised, of course), this logically valid proof of the Sentential Logic statement S => S could do the trick:<br /><br />1 ! ! S_____Assumption<br />. ! !-----<br />2 ! ! S_____1 Reiteration<br />. !<br />3 ! S=>S____1-2 =>Introd.<br /><br />This is a valid proof, therefore the statement cannot be fallacious. It is, however, trivial in most contexts: obviously, S always entails S (i.e. S => S).<br /><br />As this follows my own reasoning, Version 2 is not fallacious, but trivial.<br /><br />Is that what you meant?Magpiehttps://www.blogger.com/profile/07528637318288802178noreply@blogger.comtag:blogger.com,1999:blog-3634628224045926034.post-15520255852319176702011-12-15T01:54:08.475-08:002011-12-15T01:54:08.475-08:00You are... I mean, this is... uh... err... "C...You are... I mean, this is... uh... err... "Circular reasoning! CIRCULAR REASONING!!!" ;-) Just kidding.<br /><br />Thanks for the input! I'll have to give your first paragraph a lot more thought. I think I get some of your idea.<br /><br />The second paragraph I think I understand your point and you are right. Although, if I understand your point, in the case of the set of men, of course, it is not an uncountably infinite set.Magpiehttps://www.blogger.com/profile/07528637318288802178noreply@blogger.comtag:blogger.com,1999:blog-3634628224045926034.post-59102335275587280062011-12-15T01:22:44.310-08:002011-12-15T01:22:44.310-08:00@Magpie: I don't really agree with you here (b...@Magpie: I don't really agree with you here (but I won't shout "circular reasoning"). As it stands, your Version 2 is not in fact an example of circular reasoning. If I accept as true that "Socrates is a man" it may be trivial to conclude that "Socrates is a man" but it is not circular reasoning. Circular reasoning arises when you try to establish propositions A and B by arguing that A entails B and B entails A. Of course if you (and everyone else) accepts A and you establish that A entails B, then you can logically deduce that B is true (and, trivially, that A is as well...but that's not much fun). <br /><br />As a technical aside, in a mathematical context, you can not always switch from a version 1 to a version 2 form. For example, if your initial statement is "all real numbers have property P", you cannot switch to a list of statements for "x has property P" for every real number x (because real numbers are uncountably infinite).Sean Carmodyhttps://www.blogger.com/profile/16916053833912846761noreply@blogger.com