tag:blogger.com,1999:blog-36959219.post6364368503744654346..comments2023-05-10T08:55:47.701-07:00Comments on Richard Carrier Blogs: Defining NaturalismRichard Carrierhttp://www.blogger.com/profile/17577206926510030146noreply@blogger.comBlogger24125tag:blogger.com,1999:blog-36959219.post-32162661834920960632010-08-09T21:02:35.811-07:002010-08-09T21:02:35.811-07:00OK, I see where we are disagreeing - your definiti...OK, I see where we are disagreeing - your definition is wider than I had understood it, so I concede to your argument.<br /><br />(I'll have to reserve judgement on how useful I think those definitions are; that'll require a lot more thought.)Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-20254448730837926942010-08-05T15:05:34.332-07:002010-08-05T15:05:34.332-07:00Andrew G. said... Swapping elements is only part o...<b>Andrew G. said...</b> <i>Swapping elements is only part of the story; a topological space consists of two things: a set, and a collection of subsets (satisfying certain rules) of that set.</i><br /><br />Which is a set. <br /><br />That's not two things. It's one thing, in different iterations.<br /><br />Hence unless a logical inconsistency is created when swapping elements of these Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-14095931461629754092010-07-30T14:04:36.476-07:002010-07-30T14:04:36.476-07:00Swapping elements is only part of the story; a top...Swapping elements is only part of the story; a topological space consists of two things: a set, and a collection of subsets (satisfying certain rules) of that set.<br /><br />The set captures the abstraction "point". The collected subsets are called the "open sets", and in a certain way they capture the abstraction of "close to" or "connected to". Concepts Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-51649333047135296472010-07-30T02:41:35.439-07:002010-07-30T02:41:35.439-07:00Holy crap, I really did learn some maths today.
A...Holy crap, I really did learn some maths today.<br /><br />Andrew: Likewise, you can combine a particle with a charge of +1 (e.g. a proton) with a particle of charge -1 (e.g. an electron) and produce a particle of charge 0 (e.g. a neutron).<br /><br />Okay, I'm fine with that, but electrons don't actually have 'negative' value in the same way that negative numbers do. However, I Pikemann Urgehttps://www.blogger.com/profile/02587558012877707537noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-7949730977026020972010-07-29T18:55:44.431-07:002010-07-29T18:55:44.431-07:00Andrew G. said... I'm getting the impression t...<b>Andrew G. said...</b> <i>I'm getting the impression that you're out of your depth when talking about transfinites. Do you not understand the important distinction between a countably infinite number of cats and an uncountably infinite number?</i><br /><br />Yes. Hence my example directly paralleled Cantor's set theoretic argument for higher cardinality infinities.<br /><br /><i>If Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-9323143094657905172010-07-29T17:58:30.181-07:002010-07-29T17:58:30.181-07:00I'm getting the impression that you're out...I'm getting the impression that you're out of your depth when talking about transfinites. Do you not understand the important distinction between a countably infinite number of cats and an uncountably infinite number?<br /><br />If you put a countably infinite number of line segments together end-to-end you just have an infinitely long line like the ordinary real line. The idea of having Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-49266594616813873632010-07-29T16:02:33.743-07:002010-07-29T16:02:33.743-07:00Andrew G. said... Mathematics is stranger than you...<b>Andrew G. said...</b> <i>Mathematics is stranger than you imagine.</i><br /><br />The issue is not how strange it is, but simply this: either you can logically construct a given line, or you can't. If you can't, there is no sense in which it exists, even potentially. Period. But if you can, it's logically necessary that that construction can be realized physically (just substitute Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-12554073016825442392010-07-29T13:12:45.175-07:002010-07-29T13:12:45.175-07:00Mathematics is stranger than you imagine :-)
Here...Mathematics is stranger than you imagine :-)<br /><br />Here's an example. Imagine the real half-line, i.e. starting from some point 0 and continuing infinitely (assuming an infinite universe, or if you prefer we can treat it as the time axis and assume it to be open and unbounded in the future direction).<br /><br />We can traverse this line as follows: take one step (of one unit length) in Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-22101638123575682962010-07-29T09:25:55.989-07:002010-07-29T09:25:55.989-07:00Andrew G. said... The long line does not appear to...<b>Andrew G. said...</b> <i>The long line does not appear to be something that can possibly "exist" in any concrete sense (it's not an abstraction of anything in the physical universe, even conceptually).</i><br /><br />It is potentially. If it can be coherently defined, it can be potentially realized. For example, if the line has length, then that length can be divided into cats (Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-47516732149124557392010-07-29T08:09:49.690-07:002010-07-29T08:09:49.690-07:00If [the long line is] not possible, it doesn't...<i><br />If [the long line is] not possible, it doesn't exist. I don't have to account for the existence of things that can't possibly exist.<br /><br />Hence I assumed you weren't asking me to do that.<br /></i><br /><br />My point is this:<br /><br />1). The long line does not appear to be something that can possibly "exist" in any concrete sense (it's not an Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-1239828833426047092010-07-28T13:14:40.958-07:002010-07-28T13:14:40.958-07:00Andrew G. said...
Even in a universe of infinite ...<b>Andrew G. said...</b><br /><br /><i>Even in a universe of infinite duration, there is no time t=omega, since every value of t (assuming t is representing an ordering of discrete physical events, as otherwise it is a category error to talk about it taking ordinals as values) must be zero or a successor ordinal (since any time after the beginning of the universe must have a predecessor), and Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-20370543646850076772010-07-28T13:13:57.947-07:002010-07-28T13:13:57.947-07:00Pikemann Urge said... I don't mean to say that...<b>Pikemann Urge said...</b> <i>I don't mean to say that it's useless, but it's still a label.</i><br /><br />...for something that actually exists and obeys the mathematics of negative numbers, i.e. negative numbers are words that refer to those things and the mathematical rules for negative numbers describe how such things behave. Nothing more. Nothing less. That's my point.<br Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-3543578136944656252010-04-01T07:43:08.517-07:002010-04-01T07:43:08.517-07:001. 'Negative' and 'positive' in th...<i>1. 'Negative' and 'positive' in the physical world are labels. Electrons are 'negatively charged' but it's just a label. I don't mean to say that it's useless, but it's still a label.</i><br /><br />It's not just a label, it's also a set of properties. For example, electric charge is conserved: if you produce charged particles from uncharged Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-44051323223375398282010-04-01T07:33:05.514-07:002010-04-01T07:33:05.514-07:00then there will eventually in actual fact be, at t...<i>then there will eventually in actual fact be, at t = omega</i><br /><br />Even in a universe of infinite duration, there is no time t=omega, since every value of t (assuming t is representing an ordering of discrete physical events, as otherwise it is a category error to talk about it taking ordinals as values) must be zero or a successor ordinal (since any time after the beginning of the Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-62317938813980212332010-03-31T21:22:14.337-07:002010-03-31T21:22:14.337-07:00LOL... look what I wrote in point 5. I wasn't ...LOL... look what I wrote in point 5. I wasn't really thinking was I... ::facepalm::Pikemann Urgehttps://www.blogger.com/profile/02587558012877707537noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-64578201995884947392010-03-31T21:21:26.187-07:002010-03-31T21:21:26.187-07:00Some quick assertions for Andrew & Richard'...Some quick assertions for Andrew & Richard's consideration (keep in mind I'm not extremely well versed in maths or logic):<br /><br />1. 'Negative' and 'positive' in the physical world are labels. Electrons are 'negatively charged' but it's just a label. I don't mean to say that it's useless, but it's still a label.<br /><br />2. Magnets have Pikemann Urgehttps://www.blogger.com/profile/02587558012877707537noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-38945580663883251912010-03-31T16:55:29.669-07:002010-03-31T16:55:29.669-07:00N.B. Teapot Atheist replied to this blog. I respon...N.B. Teapot Atheist replied to this blog. I responded in kind in the following blog: <a href="http://richardcarrier.blogspot.com/2010/03/defining-naturalism-ii.html" rel="nofollow">Defining Naturalism II</a>.Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-9631387019232374242010-03-31T15:44:59.759-07:002010-03-31T15:44:59.759-07:00Pikemann Urge said... Once I challenged a couple o...<b>Pikemann Urge said...</b> <i>Once I challenged a couple of people by saying that mathematics describes more than what can exist in this universe. I gave the example of negative numbers. There's no such thing, AFAIK, as negative things. I didn't get a single successful refutation (e.g. I got: temperature, electrons, money etc.). Maybe Richard will give it a shot!</i><br /><br />Of Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-37586065369905551712010-03-31T15:38:23.583-07:002010-03-31T15:38:23.583-07:00Does the Supernatural Potentially Exist?
Andrew G...<b>Does the Supernatural Potentially Exist?</b><br /><br /><b>Andrew G. said...</b> <i>[Some concepts] arise, as I see it, as higher-order abstractions</i><br /><br />Sure. But higher-order abstractions are entirely composed of lower-order abstractions. So in every possible universe, where there are lower-order abstractions, there are necessarily higher-order abstractions (i.e. there is no Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-65951100816714398602010-03-31T15:34:38.925-07:002010-03-31T15:34:38.925-07:00Are There Abstractions That, Even Potentially, Onl...<b>Are There Abstractions That, Even Potentially, Only Exist in the Mind?</b><br /><br /><b>Andrew G. said...</b> <i>But I wouldn't claim that these concepts are in any way supernatural or have any "existence" other than as ideas in the minds of mathematicians or as descriptions written in the language of mathematics.</i><br /><br />TPA’s point is that this can’t be true of Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-37509479832323641732010-03-31T15:31:53.716-07:002010-03-31T15:31:53.716-07:00Are There Any Coherent Mathematical Formalisms Tha...<b>Are There Any Coherent Mathematical Formalisms That Do Not Correspond Even Potentially with Anything Physical?</b><br /><br /><b>Andrew G. said...</b> <i>I would say that there are concepts in mathematics which do not correspond, even potentially, to any physical quantity or property.</i><br /><br />Everyone who says that, isn't aware of the actual physical underpinnings of mathematical Richard Carrierhttps://www.blogger.com/profile/17577206926510030146noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-54721117170775243492010-03-31T06:11:31.085-07:002010-03-31T06:11:31.085-07:00If you don't accept negative electric charges ...If you don't accept negative electric charges as an instance of physical existence of negative numbers I'm not sure what you would accept - it seems clear enough to me.<br /><br />Numbers larger than the number of particles in the universe are indeed useful; a famous example is the number of possible chess games (or for an even larger number, the number of possible Go games).<br /><br />(Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-86353799989473587642010-03-31T00:16:01.194-07:002010-03-31T00:16:01.194-07:00Andrew, I'd say you're right. Once I chall...Andrew, I'd say you're right. Once I challenged a couple of people by saying that mathematics describes more than what can exist in this universe. I gave the example of negative numbers. There's no such thing, AFAIK, as negative things. I didn't get a single successful refutation (e.g. I got: temperature, electrons, money etc.). Maybe Richard will give it a shot!<br /><br />It is Pikemann Urgehttps://www.blogger.com/profile/02587558012877707537noreply@blogger.comtag:blogger.com,1999:blog-36959219.post-13274387570660206212010-03-30T17:20:55.798-07:002010-03-30T17:20:55.798-07:00I would say that there are concepts in mathematics...I would say that there are concepts in mathematics which do not correspond, even potentially, to any physical quantity or property. In this category I would include numbers like aleph-omega, or concepts like the topology of the long line; these are unphysical in a very fundamental way.<br /><br />(Some might argue that these things are in fact meaningless; there is some justification for this Andrew G.https://www.blogger.com/profile/12284971176688746388noreply@blogger.com