tag:blogger.com,1999:blog-22301740.post3088604649809851047..comments2024-03-26T09:49:07.212-07:00Comments on The Scratching Post: On Open-mindedness And Gay MarriageK T Cathttp://www.blogger.com/profile/10259428595745509790noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-22301740.post-70972584180058946642016-09-20T09:25:23.570-07:002016-09-20T09:25:23.570-07:00First, " 'true by definition' is not ...First, " 'true by definition' is not the same as true": I can accept that. Effectively we decide if such definitions lead to a consistent system (inconsistency voids at least one assumption). In other words we use an empirical verification to determine possible untruth. So in that sense the Axioms are always subject to proof of inconsistency, i.e., disproof.<br /><br />I have never liked seeing " 1/0 = infinity ". It is completely true that 1/0 is not solvable within the set of Complex numbers. As to actually using infinity in an equation one must be VERY careful about using other information to maintain consistency (truth), so I am always very cautious about writing such.<br /><br />I don't think Godel's incompleteness theorem supports your case. Yes, it shows that there are things that are provably true (empirically verifiable) just not provable inside the formal system. But we verified it, so it is true. There are cases where we cannot prove things. In some of those cases we can choose more than one truth (see Euclidin vs non-Euclidian geometries). Which one is true? All of them are. We can choose any one, at a time, but in the end the truth in a specific case is determined with empirical verification against observation and/or consistency. <br /><br />I'm not trying to argumentative here. I completely agree that lots of "axioms" (like KT's argument against Relativism) which are demonstrably untrue. However, I have yet to see a TRUE statement, i.e., one we know must be true, that isn't empirically verified or accepted as axiomatic.Ohioan@Hearthttps://www.blogger.com/profile/08650494620853971183noreply@blogger.comtag:blogger.com,1999:blog-22301740.post-68053438539190535582016-09-20T05:39:50.736-07:002016-09-20T05:39:50.736-07:00O@H,
"True by definition" is not the sa...O@H,<br /><br />"True by definition" is not the same thing as "true"Ilíonhttps://www.blogger.com/profile/15339406092961816142noreply@blogger.comtag:blogger.com,1999:blog-22301740.post-48692775051158261022016-09-20T05:36:37.845-07:002016-09-20T05:36:37.845-07:00"But to say that there are truths that are un..."<i>But to say that there are truths that are unprovable, and yet not axiomatic assumptions seems to me to be unsupportable.</i>"<br /><br />Here is one statement that is true and totally unprovable -- 1 / 0 = "infinity"<br /><br />"<i>How do we know it is true?</i>"<br /><br /><a href="https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems" rel="nofollow">Gödel's incompleteness theorems</a><br />Ilíonhttps://www.blogger.com/profile/15339406092961816142noreply@blogger.comtag:blogger.com,1999:blog-22301740.post-18028836113235779122016-09-19T15:02:08.968-07:002016-09-19T15:02:08.968-07:00Your argument about relativism shows that some ide...Your argument about relativism shows that some ideas are demonstrably false (they lead to contradiction, classic proof by assuming a contradictory position and show that that must be false - which boils down to an Empirical Verification of the opposite). I have no issue with such. But to say that there are truths that are unprovable, and yet not axiomatic assumptions seems to me to be unsupportable. How do we know it is true? Because it is "obvious"? That's an axiom. Because it's opposite leads to contradiction? Just covered that. Because I (or other authority) says so? Axiom. I really don't see the middle ground that you are claiming.Ohioan@Hearthttps://www.blogger.com/profile/08650494620853971183noreply@blogger.comtag:blogger.com,1999:blog-22301740.post-67723748133880097512016-09-19T10:55:44.477-07:002016-09-19T10:55:44.477-07:00But what you haven't shown is that these are t...But what you haven't shown is that these are the only things that are true. That's where this falls apart. It's neither one nor the other.K T Cathttps://www.blogger.com/profile/10259428595745509790noreply@blogger.comtag:blogger.com,1999:blog-22301740.post-4891577150933474242016-09-19T09:08:10.102-07:002016-09-19T09:08:10.102-07:00Actually I would tend towards a mathematical like ...Actually I would tend towards a mathematical like version of the Axiom of Empirical Verifibility. Some things are true by definition (these are our Axioms). One of those Axioms is the "Principle" of Empirical Verification, to wit: Other true things, i.e., true but non-axiomatic things, can only be identified by Emperical Verification from Axioms and other true statements already proven via Empirical Verification.<br /><br />Now perhaps I don't see the issue here but it seems the problem from above is completely eliminated (since all Geisler did is say that it could not be an axiom, and I assert it as such).<br />Ohioan@Hearthttps://www.blogger.com/profile/08650494620853971183noreply@blogger.com