tag:blogger.com,1999:blog-7844827880580229020.post4089126106048895408..comments2015-12-18T06:03:42.615-08:00Comments on Director's cut: Burden of proofSKhttp://www.blogger.com/profile/03473150367386722079noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-7844827880580229020.post-55332680765445176292014-04-28T17:50:31.083-07:002014-04-28T17:50:31.083-07:00No, it can't. It cannot establish the existenc...No, it can't. It cannot establish the existence of God nor can it rule it out, because it's not about that.<br /><br />Gödel's incompleteness theorem states that any formal theory of arithmetic (with certain specifications, irrelevant here) which is consistent is incomplete, that is, there is a mathematical truth which cannot be proved in the theory.<br /><br />This theorem has been misunderstood as saying something about knowledge. As if the theorem states that complete knowledge of arithmetic is impossible, as there will always be unprovable truths. <br /><br />So one could extrapolate that if that happens in arithmetic, it happens in other fields and we should learn to live without expecting to be able to prove everything that is true. Worse, I even heard somebody say once, in a lecture, that Gödel's incompleteness theorem proves that knowledge is impossible!! Not at all...<br /><br />That is not what Gödel's incompleteness theorem says. It is not about knowledge, it is about formal theories formalised in certain kind of languages known as first-order languages. The theorem is stating a limitation of those languages. So one might take it as an indication that we should try to find more powerful languages, languages with more expressive power, so that one could find axioms in those languages and define theories capable of proving all arithmetical truths.<br /><br /><br /><br /><br /><br />Yolitahttps://www.blogger.com/profile/02115609535199782762noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-53580269062046187222014-04-28T08:55:25.385-07:002014-04-28T08:55:25.385-07:00But that is not how most people refer to agnostici...But that is not how most people refer to agnosticism, which is why I took the most favorable definition I could to reflect it being a position on knowledge, even if I expressed that statement incorrectly at first. Ask an agnostic that question. The fact that it is a position on knowledge and not belief does not change the fact that the agnostic cannot hold a belief on the matter. And what would such a belief be, if he insisted that existence is unknown.Shripathi Kamathhttps://www.blogger.com/profile/03473150367386722079noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-36857120742248287692014-04-28T08:50:40.240-07:002014-04-28T08:50:40.240-07:00Ok, can it establish existence of God anymore than...Ok, can it establish existence of God anymore than it can rule it out? The point being, your circle of existence requires a true proposition which cannot be proven with what is known in that circle. So if that is true for existence, you have no proof.Shripathi Kamathhttps://www.blogger.com/profile/03473150367386722079noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-20585675314771014732014-04-28T05:40:41.423-07:002014-04-28T05:40:41.423-07:00"There may be, as the diagram in your link sh..."There may be, as the diagram in your link shows, an agnostic theist who says: "It's impossible to know whether 'p' is true or false, yet I believe 'p'", but I haven't met any of those."<br /><br />I have. And I fail to see any basis by which I could argue that their belief constitutes knowledge!<br /><br />Now, you say this is a pointless semantic distinction, but I disagree. I think the treatment of agnosticism as some sort of philosophical no man's land by which someone takes the best of both sides while eschewing the worst or - even worse - as merely a noncommittal atheist, misses the point of agnosticism.<br /><br />Theism and atheism are statements about the existence of a god. Agnosticism is not. Agnosticism says nothing about whether a god exists, precisely because it makes the claim that we can't know whether a god exists!<br /><br />I'll concede that this is tangential to the topic of this post, but this is something I see crop up from time to time and I think it's important to try and quash the misconception.Scott Rollisonhttps://www.blogger.com/profile/13663467927122221623noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-72820330515996393492014-04-27T19:33:14.399-07:002014-04-27T19:33:14.399-07:00Sorry about the typos. I tried to type Gödel´´ and...Sorry about the typos. I tried to type Gödel´´ and it came out as Gódel´´. :-)Yolitahttps://www.blogger.com/profile/02115609535199782762noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-34699885478359476042014-04-27T19:31:41.002-07:002014-04-27T19:31:41.002-07:00"Clearly that is wrong on many levels. Gödel&..."Clearly that is wrong on many levels. Gödel's incompleteness theorem basically rules out proof of existence just as much as it rules out proof of non-existence or a disproof of existence."<br /><br />I don't see the need to bring Gödel's incompleteness theorem here. It doesn't add to the discussion or to the point that you are making.<br /><br />But I have to say that Gödel's incompleteness theroem doesn't rule out proof of existence, nor does it rule out proof of non.existence. In fact, in the proof of Gödel's theorem one gets to see a proof of existence and a proof of non-existence.<br /><br />Gódel proves that any system that contains Peano´s arithmetic an which has a set of axioms of a certain kind, is incomplete. And this means that there is a formula which is true and non-provable in the system. So Gódel proves the existence of this formula in the best way one can prove existence: by exhibiting it, by constructing it.<br /><br />One can use that construction to prove that there is no proof of the consistency of arithmetic, unless one is prepared to use much stronger systems, whose consistency is even more doubtful. And one proves the non-existence of the proof by reductio ad absurdum. That's the only way to prove non-existence: to show that assuming existence leads to a contradiction.<br /><br />That's the beauty of Gódel´s theorem: it proves existence of certain objects, it proves non-existence of other objects and in 22 pages it destroyed 2 philosophical programs. As good a theorem as it gets. <br /><br />But irrelevant here, sadly. :-)<br /><br />Yolitahttps://www.blogger.com/profile/02115609535199782762noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-82804388122838506412014-04-27T19:13:46.381-07:002014-04-27T19:13:46.381-07:00I think you're right, that a belief under thos...I think you're right, that a belief under those circumstances is not tenable. That's why I don't think that there are any agnostic theists. At least I haven't met any, it would be a very difficult position to hold. <br /><br />Agnostics basically claim that it is not possible to decide about the truth value of the proposition "God exists" because it's unknowable. So they don't believe it and the don't believe its negation. Yolitahttps://www.blogger.com/profile/02115609535199782762noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-34798010887769338402014-04-27T19:07:28.616-07:002014-04-27T19:07:28.616-07:00Of course one can believe something without knowin...Of course one can believe something without knowing it, so strictly speaking Shripathi's phrase was indeed wrong as stated. But I think he's capturing the spirit of agnosticism better than the diagram in the link you provided.<br />That classical definition of knowldege as justified true belief (which is by no means accepted by the totality of the philosophical community, it must be said) refers to propositional knowledge and I think it is very useful to focus on the proposition rather than on the subject believing it. So if 'p' is a proposition and S is a subject, when we say that S knows 'p', what we mean is that 'p' is true, S believes 'p' and 'p' has been duly justified. Of course there are many problems here: What do we mean by 'true'? What is a belief? What counts as adequate justification? But let's go with the simplest definition of belief: to believe 'p' is to consider 'p' to be true. <br />Now let p be the proposition "God exists"<br />An atheist would say: "I don't believe p", that is, "I don't consider 'p' to be true". Whether that implies that he believes not-p will depend on his underlying logic (i.e. whether he accepts the Principle of the Excluded Middle or not). That will make the difference between strong and weak atheism<br />An agnostic, according to the definitions (1) and (2) provided by Shripathi, would say: "I don't have an opinion as to whether 'p' is true or false, because it is unknowable". I think that's the spirit of agnosticism.<br />There may be, as the diagram in your link shows, an agnostic theist who says: "It's impossible to know whether 'p' is true or false, yet I believe 'p'", but I haven't met any of those. Usually people who believe 'p' claim that there is another kind of knowledge, very personal, accesible through inspiration and meditation, mystical. In the same way, I haven't met a gnostic atheist who claims to *know* that there aren't any gods.<br />So the diagram looks neat, but in fact it just adds labels that are not all that useful. They turn the discussion into as semantical one.<br />It reminds me of my communist youth, when we spent hours obsessing on what it meant to be a Trotskyist, a Maoist, a Titoist, a neo-Stalinist, a revisionist, a Marxist... :-)<br />In that sense, I think the emphasis should be on discussing who has the burden of proof, people who believe 'p' to be true or people who believe 'p' to be false. Independently of what we call them.Yolitahttps://www.blogger.com/profile/02115609535199782762noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-28771803040671253742014-04-27T11:25:24.221-07:002014-04-27T11:25:24.221-07:00I need to clarify this, because my focus is not on...I need to clarify this, because my focus is not on knowledge vs belief, and it is raising tangents,Shripathi Kamathhttps://www.blogger.com/profile/03473150367386722079noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-26170947738254094252014-04-27T10:32:09.101-07:002014-04-27T10:32:09.101-07:00Knowledge is justified true belief. So agnostics b...Knowledge is justified true belief. So agnostics believing something that is not knowledge is possible if it is either not true, or not justified. Given that they claim that it is not knowable, they are committing to one of those two positions and know it. They are either not justified, or know it to be false. A belief under either of those cases is not tenable. Shripathi Kamathhttps://www.blogger.com/profile/03473150367386722079noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-24125815343582305882014-04-27T05:58:32.335-07:002014-04-27T05:58:32.335-07:00I wish I could edit...
In this vein agnosticism, ...I wish I could edit...<br /><br />In this vein agnosticism, dealing only with knowledge, is **separate from** theism/atheism, which deals with belief.<br />Scott Rollisonhttps://www.blogger.com/profile/13663467927122221623noreply@blogger.comtag:blogger.com,1999:blog-7844827880580229020.post-68571388318070272882014-04-27T05:57:43.058-07:002014-04-27T05:57:43.058-07:00"Agnostics cannot believe in something they d..."Agnostics cannot believe in something they do not even acknowledge knowing."<br /><br />This flies in the face of the entire field of epistemology, which formulates knowledge as a type of belief. Specifically it is a belief which is also true and you have justification in believing it to be true. It is a justified true belief. Thus you can believe in something without knowing it (by recognizing you lack justification).<br /><br />http://upload.wikimedia.org/wikipedia/commons/2/2b/Classical-Definition-of-Kno.svg<br /><br />In this vein agnosticism, dealing only with knowledge, is a subset to theism/atheism, which deals with belief.<br /><br />http://actok.org/wp-content/uploads/2012/10/Agnostic+v+Gnostic+v+Atheist+v+Theist.png<br /><br />This is actually a more fruitful definition. After all, what is the value in highlighting a subset of atheists that claim to know? While, commonly, agnostics may be found within the population of atheists, there are agnostic theists out there.Scott Rollisonhttps://www.blogger.com/profile/13663467927122221623noreply@blogger.com