tag:blogger.com,1999:blog-15005476.post3762105175454702604..comments2023-10-10T08:02:18.073-04:00Comments on Rationally Speaking: What does it mean for something to be metaphysically necessary?Unknownnoreply@blogger.comBlogger111125tag:blogger.com,1999:blog-15005476.post-78012274530473093382014-03-09T08:47:42.887-04:002014-03-09T08:47:42.887-04:00Hi Pete,
Again, it's an analogy to try to com...Hi Pete,<br /><br />Again, it's an analogy to try to communicate something about how I think of it, not an argument. It's not the same thing as language, but I think it is in some respects more appropriate to think of it like a language than a place. My view of this does not in fact depend on human communications at all.<br /><br />One interesting thing I think languages and formal systems share is that just like languages, different formal systems can be used to describe the same mathematical objects. ZFC and ZF can both be used to describe the Mandelbrot Set even though these are different formal systems, and in my view there is only one Mandelbrot Set.<br /><br />Even better than a language would be to think of it as a context. The distance between geodesics remains constant in the context of Euclidian geometry, but not in the context of Hyperbolic geometry, but there is no conflict because we are talking about different contexts. This is perhaps reasonably easy to understand. You seem to think that the Continuum Hypothesis is fundamentally different, but I will only accept that if its affirmation or its negation turns out to be logically incoherent. The CH is true in the context of ZFC+CH and false in ZFC+¬CH, just as the parallel postulate is true in Euclidean and false in Hyperbolic geometry.Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-29234186584872334042014-03-09T00:20:25.009-05:002014-03-09T00:20:25.009-05:00DM -
Thanks for clarifying. I must say that the ...DM - <br /><br />Thanks for clarifying. I must say that the language analogy is a bid misplaced as well. Languages are used for communicating and there are many different ways of doing this. However, as far as being descriptive of certain aspects of the world around us, they still refer to objective features of existence that are unique and constant. Mathematical truth shouldn't have anything to do with the context of human beings communicating with each other. petehttps://www.blogger.com/profile/12969621709127674152noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-24103523736736126972014-03-08T22:48:10.556-05:002014-03-08T22:48:10.556-05:00@Thomas Jones:
“I searched SEP for articles that m...@Thomas Jones:<br />“I searched SEP for articles that mention "concreteness," and found at least 32 articles in which it was mentioned in one context or another. I am clearly in over my head. I am sorry I cannot engage in a fruitful discussion with you regarding your comments.”<br /><br /><br />As these were just short comments, I did not give out more precise description about what I mean on ‘concreteness’, although I did know that it can be described in many different contexts. Thus, I took an easy way out, by using an operational definition, the “I”-concreteness (similar to Descartes' "Cogito ergo sum"). I further hinted that the u-concreteness is the ‘ultimate reality’ without giving details. <br /><br /><br />In addition to the operational definition, ‘concreteness’ has special meanings to me. <br />One, mathematically, it is a precise procedure of how an infinity concretizes into a finite ‘object’. Thus, a finitude (finite universe) can be risen from infinity. Please see http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html .<br /><br /><br />Two, with Cantor’s theorem, it is a precise procedure of how multi-dimensional universe arose from one-dimension. See, http://prebabel.blogspot.com/2012/04/origin-of-spatial-dimensions-and.html .<br /><br /><br />Three, for u-concreteness, it must have, at least, the following attributes.<br />a. It must be eternal and immutable,<br />b. It must give rise to all the followings: (the cosmological constant (Λ), the Cabibbo angle, the Weinberg angles, the Alpha, the Neff = 3, the Planck data, the particle zoo of the Standard Model, the Baryongenesis, the quantum principle, the unified force equation (including gravity), the life, the Quantum-Spin, Why is here something rather than nothing? And more.) See, http://www.quantumdiaries.org/2014/02/07/interpretations-of-quantum-mechanics/#comment-172443 .<br /><br /><br />With these, my ‘concreteness’ is now better defined.<br />Tienzenhttps://www.blogger.com/profile/05842156512465678309noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-56031447852328526342014-03-08T13:12:36.774-05:002014-03-08T13:12:36.774-05:00@Thomas Jones:
“I'm not being sarcastic. I...@Thomas Jones:<br /><br />“I'm not being sarcastic. I'm just wondering how to reconcile this concreteness with Buddhist notions of impermanence and change.”<br /><br />Excellent question. In fact, my definition does not meet the requirement that the metaphysically necessary of ‘my concreteness’ is true in all possible worlds, at the first glance.<br /><br /><br />Let’s start with your concreteness. Before I know you, your concreteness has no ‘meaning’ to my concreteness, that is, I can deny your concreteness without violating any physical or moral laws. Yet, as soon as I click the ‘reply’ button, a new concreteness arose, the interaction between us. There are two issues about this new concreteness.<br />First, your concreteness can no longer be denied by my concreteness.<br />Second, there is a ‘metaphysical necessity’ for this newly arose concreteness, and it consists of at least the followings:<br />a. There must be a space which separate us.<br />b. There must be a thing called ‘individuality’ which separate us in addition to space.<br />c. Massimo Pigliucci must be a concreteness which I no longer can deny.<br /><br /><br />Very quickly, this ‘local’ and transient concreteness is no longer local and transient anymore. Now, I will introduce the 2nd metaphysics law.<br /><br />Law 2: If concreteness B is undeniable by concreteness A, then the ‘metaphysical necessity’ of concreteness B cannot be denied by concreteness A.<br /><br />Very soon, this ‘metaphysical necessity’ of concreteness B cannot be denied by many, and it is not too difficult to show that it cannot be denied in all possible worlds if they are also concreteness.<br /><br /><br />Yet, I showed that there are two different types of concreteness.<br />One, the “I”-type concreteness which can be denied in practice although not in principle because of the Law 2.<br />Two, the ‘ultimate’ concreteness (the ‘u’-type) which by definition must give rise to all I-type concreteness.<br /><br />Now, I must introduce the Law 3 --- The ‘metaphysical necessity’ of an I-concreteness must also be a concreteness.<br /><br />By definition, there is a u-type concreteness. But, is there a u-concreteness? Let me start with a subset of set (UC), the set (4), and it consists of only four concreteness.<br />C1 = Alpha fine structure constant<br />C2 = (Dark/visible) mass ratio<br />C3 = particle zoo of Standard Model<br />C4 = I am here (a “life”)<br /><br />Theorem one: If concreteness X is the ‘metaphysical necessity’ of set (4), it is a u-concreteness. <br />Is concreteness X a concreteness? Can we find it? Of course, we can.<br />How about the “Buddhist notions of impermanence and change”? A good ancient ‘opinion’, it does describe one point of view.<br />Tienzenhttps://www.blogger.com/profile/05842156512465678309noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-52549132252212018552014-03-08T10:36:15.960-05:002014-03-08T10:36:15.960-05:00If you mean computationalism, then I think they st...If you mean computationalism, then I think they stand on their own. If, as you say, mathematical platonism is a consequence, then all the more reason for accepting platonism, I'd say.Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-18311199626981951362014-03-08T02:35:27.457-05:002014-03-08T02:35:27.457-05:00All that seems to say is that mathematical platomi...All that seems to say is that mathematical platomism is a consequence of certain sorts of theories of mind. All the more reason for rejecting those theories I say.Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-46417181454276314972014-03-07T18:40:47.558-05:002014-03-07T18:40:47.558-05:00“…metaphysicians these days seem to make sense of ...“…metaphysicians these days seem to make sense of the notion of metaphysical necessity by saying that something is metaphysically necessary if it is true in all possible worlds. … I am leaning toward the conclusion that there is no such thing as metaphysical necessity. That’s in part because one cannot find metaphysical laws, and in part because I doubt there is such a thing as necessity, period. Nothing is physically or logically necessary - only possible or impossible.”<br /><br />You have given two different ‘definitions’ for ‘metaphysical necessity’ while they are internal consistent between them. Of course, I cannot disagree with you if I use these two definitions to discuss this issue. Thus, if you allow, I will make a new definition.<br /><br />I will define this issue with two steps.<br />First, finding out the concreteness.<br />Two, finding out the ‘ultimate’ concreteness.<br />It will take a 200 page book to talk about this concreteness. Thus, I will not go into the details of it in this short comment but just point out a few key points. The concreteness does not depend on the physics laws, math theory, reasoning, logic, time, eternal, or space. I am here now [will definitely be gone in a future time, that is, my being is just a possible outcome in Buddhism], and it is ‘concreteness’ for me and to anyone who interacts with me. A 126 Gev. particle were seen by 6,000 physicists at LHC, it is a concrete object for them. Now, we can make the ‘first’ metaphysical law (FML).<br /><br />FML --- for every concreteness, there is a something as the ‘metaphysical necessity’ for that concreteness.<br /> Corollary --- if a concreteness is not the ‘ultimate’ concreteness, it cannot be its own metaphysical necessity.<br /><br />Now, with a unlimited concreteness set (UC) = {C1, C2, … Cn,…}, C(u) is a standalone single concreteness, and there is a set (in finite numbers) of rules which allows the C(u) to give rise to all members of set (UC), then C(u) is the ‘ultimate’ concreteness. <br /><br />Of course, there is a big issue about whether such an ultimate concreteness can be found. Yet, with these new definitions, we might be able to address this issue in a new direction.<br />Tienzenhttps://www.blogger.com/profile/05842156512465678309noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-86264585250588229892014-03-07T15:31:30.633-05:002014-03-07T15:31:30.633-05:00An axiom is part of the definition of a mathematic...An axiom is part of the definition of a mathematical object. If you view an axiom as a statement for human minds to appreciate and interpret, you are thinking about the representation in symbols of a mathematical concept and not about the mathematical concept itself. The axiom is the meaning agreed upon by those who use it, not the statement used to represent it.Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-32885794177602833182014-03-07T14:40:13.353-05:002014-03-07T14:40:13.353-05:00But an aciom is a statement that has no meaning ex...But an aciom is a statement that has no meaning except for the meaning agreed upon by those who use it. What sort of thing is an axiom that is independent of any mind?Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-72382595413283525202014-03-07T09:25:01.900-05:002014-03-07T09:25:01.900-05:00Hi Robin,
My claim is that all mathematical objec...Hi Robin,<br /><br />My claim is that all mathematical objects exist. Since formal systems can be treated as mathematical objects, they also exist. Mathematical objects exist independently of any intelligent mind.Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-53568078230508721152014-03-07T08:55:36.859-05:002014-03-07T08:55:36.859-05:00I think that you need to unpack what sort of thing...I think that you need to unpack what sort of thing an axiom or a formal system would be in the mathematical universe.<br /><br />In terms of the mathematics I do on paper these are sets of rules in a language and depend upon an intelligent mind to interpret them and agree on meanings.<br /><br />Unless you are positing a default mathematician, which I know you are not, then you need to be clearer about what is the analog of these things you are proposing in the self existing mathematical realm.Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-29421396686119577332014-03-07T07:56:30.953-05:002014-03-07T07:56:30.953-05:00Hi Robin,
This blog post ought to explain my atti...Hi Robin,<br /><br />This blog post ought to explain my attitude.<br /><br />http://disagreeableme.blogspot.co.uk/2013/10/mathematical-platonism-is-true-because.htmlDisagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-32178893869214843162014-03-07T07:55:38.860-05:002014-03-07T07:55:38.860-05:00>Seriously???<
Tongue firmly planted in che...>Seriously???<<br /><br />Tongue firmly planted in cheek.<br /><br />But yeah, maybe in some respects, in that it's not immediately obvious if it's coherent.Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-30910195072419177962014-03-07T07:48:56.024-05:002014-03-07T07:48:56.024-05:00Seriously???Seriously???Anonymoushttps://www.blogger.com/profile/09099460671669064269noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-71555852836973096462014-03-07T05:22:59.480-05:002014-03-07T05:22:59.480-05:00Robin:So Harry Potter is a bit like M Theory?
Exa...Robin:So Harry Potter is a bit like M Theory?<br /><br />Exactly!Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-82888091259406038532014-03-07T05:22:13.067-05:002014-03-07T05:22:13.067-05:00Hi Pete,
"I can definitely understand where ...Hi Pete,<br /><br />"I can definitely understand where you're coming from in suggesting FBP and trying to tie it back into the example of different universes with different laws of physics. The problem with this is that it doesn't actually work. See, in the idea of a multiverse where different physical laws are instantiated in different universes (think of the 10^500 possible Calabi-Yau configurations or whatnot), there is still actually a meta-theory or meta-laws of physics."<br /><br />I think you may be mistaking my analogy to physics for an argument when it is intended only as a means of illustrating my position. Yes, there are differences between the set of formal systems and the set of universes within a specific kind of multiverse. That doesn't necessarily kill the analogy though. All analogies involve aspects of similarity and aspects of difference. The question is whether the differences are more relevant than the similarities, and I don't think they are, at least not if I'm only trying to explain my meaning.<br /><br />Besides, there is an underlying meta-theory for the set of all formal systems, and that is the rule that mathematical objects described by consistent formal systems exist.<br /><br />A core idea of the MUH is to discard all unnecessary axioms and metaphysical laws. The one law that remains is arguably not a law at all but a principle with respect to how we regard the concept of existence. In the multiverse of the MUH, therefore, your criticism does not apply.<br /><br />"It makes no sense to think that over here a particular mathematical statement is true, but over there its not (in the abstract mathematical universe)"<br /><br />I agree, which is why I think that there are different interpretations of my position at play.<br /><br />I think of the different formal systems not in terms of being different places but more like being different languages. It makes no sense to imagine that the correct word for "Hello" is "Hola" in Spain and "Bonjour" in France. But it does make sense to say that the correct word is "Hola" in the context of Spanish, and "Bonjour" in the context of French.<br /><br />So the idea is that there is no absolute mathematical truth without context. Every mathematical utterance is made in the context of some formal system whether implicit or explicit, and its truth is evaluated accordingly.Disagreeable Mehttps://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-88252428051432028402014-03-07T04:20:21.592-05:002014-03-07T04:20:21.592-05:00Hi DM,
Can you identify even one thing that would...Hi DM,<br /><br />Can you identify even one thing that would be different about mathematics if numbers didn't exist?Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-25558325272175858522014-03-07T03:24:41.393-05:002014-03-07T03:24:41.393-05:00But I wonder why you link a background in science ...But I wonder why you link a background in science to a bias toward utility. Engineering maybe, but scientists are generally more likely to be moved by thinga like fascination, awe and the inherent value of knowledge than they are by utility.Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-78355009790525953002014-03-06T23:55:54.901-05:002014-03-06T23:55:54.901-05:00But there are no laws of metaphysics, just like th...But there are no laws of metaphysics, just like there are no laws of philosophy, so this endeavor is one of critically making sense of things, not of discovering or dictating how things are.<br /><br /><br />That would be correct, but who know whether you know why? The answer is you can only arrive at such speculations using rationality and they only persist as long as rationally satisfying to you in making sense of logic and physics. Rationality is a means, or ongoing process, with no end of laws in itself. Strictly speaking.Anonymoushttps://www.blogger.com/profile/12115337703424786486noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-76958552604091337182014-03-06T22:09:54.593-05:002014-03-06T22:09:54.593-05:00Pete, I can put the idea of it all being a symbol ...Pete, I can put the idea of it all being a symbol manipulation to rest just as soon as someone gives me a good reason for doing so.<br /><br />What gives the symbol manipulation it's predictive power? Nobody knows, because you cannot get past the symbol manipulation.<br /><br />We may refer speculatively to the "thing in itself", the "somewhat" the "physical world" as it has variously been called, but the most information we have about it, probably that we will ever have about it, is a symbol manipulation.<br /><br />There is no logical requirement for there to be something that the symbol manipulations are referring to. There is no need for that hypothesis in science. In fact some of our most important science was done by physicists who made no assumption about this.<br /><br />We could not in any account know anything about the "what the symbol manipulation describes" beyond the symbol manipulation itself and the sensations we have of it.Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-60048497959617173422014-03-06T21:41:42.981-05:002014-03-06T21:41:42.981-05:00DM wrote: "Again, I'm not saying it is ca...DM wrote: "<i>Again, I'm not saying it is categorically impossible. I am saying that the rules as stated are too simple, too naive. The rules as presented are not workable in the state they are in and need to be refined and made more precise in order for us to figure out if they make sense.</i><br /><br />So Harry Potter is a bit like M Theory?Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-74325089265512991152014-03-06T21:38:24.718-05:002014-03-06T21:38:24.718-05:00Do numbers exist?Do numbers exist?Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-42742749045835691662014-03-06T21:20:21.879-05:002014-03-06T21:20:21.879-05:00Isn't "there are no laws of metaphysics&q...Isn't "there are no laws of metaphysics" a law of metaphysics?mregnorhttps://www.blogger.com/profile/11431770851694587832noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-19611482373548631632014-03-06T21:14:12.199-05:002014-03-06T21:14:12.199-05:00So I guess it is a little like science or mathemat...So I guess it is a little like science or mathematics. This discussion may have no utility at all, or it may have utility in ways which we are not expecting but all ideas, no matter how apparently unrealistic, can have utility as the Anselm example above shows.<br /><br />For me it has an inherent value which can also be utility since the concept of utility also involves personal utility.Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-18764066182100309222014-03-06T20:20:47.941-05:002014-03-06T20:20:47.941-05:00Hi,
Happy to answer your question. The particula...Hi,<br /><br />Happy to answer your question. The particular topic at hand is, at least tangentially, logic.<br /><br />Logic is what underlies mathematics and mathematics is what underlies physics which has quite a good deal of utility.<br /><br />There have been completely pointless sounding arguments which have proved to have utility. For example a twelfth century monk comes up with an ingenious argument for the existence of God.<br /><br />It sounds like rubbish but no-one can quite say why it is rubbish and the eventual refutation of it led to the biggest development in logic since Aristotle.<br /><br />Much of our mathematics could not be stated without this advancement in logic and mathematics is, as I said before the basis of physics which has quite a lot of utility.<br /><br />I could make a good case that the whole movement of Logical Positivism had an influence on science in that physicists of the early 20th century focussed less on concepts of reality and more on whether models worked.Robinhttps://www.blogger.com/profile/16015911138886238144noreply@blogger.com