tag:blogger.com,1999:blog-22363645.post1149446582795019957..comments2021-04-20T04:35:44.650-07:00Comments on armchair investigations: The Sixth WayBrian Rabernhttp://www.blogger.com/profile/05189164021937523325noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-22363645.post-81250341405761351722008-02-13T19:16:00.000-08:002008-02-13T19:16:00.000-08:00I thought of a way to side step the "universal con...I thought of a way to side step the "universal conjunction" problem (if it is really a problem).<BR/><BR/>A simple truth is a truth such that nothing follows from it by simplification (i.e. conjunction elimination). Let Z be the conjunction of all simple truths. If all truths are known, then someone knows Z. Thus, someone knows each of Z's conjuncts.<BR/><BR/>Note: Every truth follows from Z, including truths like Z & Z.Brian Rabernhttps://www.blogger.com/profile/05189164021937523325noreply@blogger.comtag:blogger.com,1999:blog-22363645.post-48413689135923003242008-02-12T22:43:00.000-08:002008-02-12T22:43:00.000-08:00Atkin's suggested trying to prove that if every tr...Atkin's suggested trying to prove that if every truth is known, then there is an omniscient being in the following way.<BR/><BR/>Assume every truth is known. Consider the conjunction V of all true propositions. V is true. Thus, someone knows V. Hence, someone knows each conjunct of V. So, someone is omniscient.<BR/><BR/>The problem, it seems, is with the assumption that there is a conjunction of all true propositions. If V is the conjunction of all true propositions, then one of its conjuncts is V itself, since surely V & V is a true proposition.<BR/><BR/>This is all reminiscent of problems with the universal set. There is no "universal conjunction". Right? Or is there some trick I'm missing here.Brian Rabernhttps://www.blogger.com/profile/05189164021937523325noreply@blogger.comtag:blogger.com,1999:blog-22363645.post-84936004735651891882008-02-11T22:50:00.000-08:002008-02-11T22:50:00.000-08:00Yeah, the Bigelow paper is cool. For those who hav...Yeah, the Bigelow paper is cool. For those who haven't read it the basic proof (originally from Humberstone, "collective omniscience") goes like this: <BR/><BR/>Assume that for every truth p there is someone who knows it and that no being is omniscient (i.e. for each being i there is some truth p_i that i does not know). Consider the conjunction H of all the truths of the form [p_i and i does not know that p_i]. H is true. Hence, someone (say j) knows H. But one of the conjuncts of H is of the form [p_j and j does not know that p_j]. This leads to a contradiction.<BR/><BR/>Thus, if for every truth there is someone who knows it, then there is someone who knows every truth.<BR/><BR/>Now what? The Sixth Way looks like it could be turned into a valid proof that an omniscient being exists. If so, then I guess I would be tempted to deny the first premise...but haven't thought about it a lot.Brian Rabernhttps://www.blogger.com/profile/05189164021937523325noreply@blogger.comtag:blogger.com,1999:blog-22363645.post-87199856652631604252008-02-11T15:17:00.000-08:002008-02-11T15:17:00.000-08:00Yeah, we thought the quantifier fallacy made it pe...Yeah, we thought the quantifier fallacy made it perfectly Aquinas-esque. I hadn't thought about the further move you suggest. Thanks for the reference...Brian Rabernhttps://www.blogger.com/profile/05189164021937523325noreply@blogger.comtag:blogger.com,1999:blog-22363645.post-3305466920049621432008-02-11T14:50:00.000-08:002008-02-11T14:50:00.000-08:00Nice! But like most of Aquinas' arguments for the...Nice! But like most of Aquinas' arguments for the existence of God, this one contains a fallacy. If the argument is sound and valid through step 4, then it shows that for each truth there is someone who knows it. It doesn't show that there is someone who knows each truth. However, the last step can be gotten once we notice that the conjunction of all truths is itself a truth. Since someone (but no human) knows it, there is at least one non-human that knows all truths. John Bigelow has a <A HREF="http://www.blackwell-synergy.com/doi/pdf/10.1111/j.1467-8284.2005.00548.x" REL="nofollow">nice discussion</A> of this last step.Joe Salernohttps://www.blogger.com/profile/15060173423563404276noreply@blogger.com