tag:blogger.com,1999:blog-7324805351517740683.post5306974891931487352..comments2023-07-19T15:38:01.618+03:00Comments on Perhaps: Fictionalism and existenceAatu Koskensiltahttp://www.blogger.com/profile/10999226899475411504noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7324805351517740683.post-38099932782926155402009-03-16T19:42:00.000+02:002009-03-16T19:42:00.000+02:00Yes, as you noted Captain Planet or the Silver Sur...Yes, as you noted Captain Planet or the Silver Surfer doensn`t exist. They do exist as fantasies. But existence is existence and physicalist will claim that every kind of existence is reducible to physical beings, so in priciple we can see all fantasies as finite bits of information. If we say that there are infinitely many sets, it might very well be false if we take that claim empirically. <BR/> What I am puzzled is what gives mathematics it`s meaning, because in one sense I don`t believe it is the objects "out there". I am somewhat open to claims that some infinitary mathematical theorems are objectively true, but I can`t see that there exist "really" eg. physical sense infinitary beings. I think much depends how we see semantics. In Tarskian semantics there exists objects which correlate with the consepts of our language and because that semantics depends heavily on set theory and also obviously from law of ecluded middle we interpret usually mathematics realistically (platonistically). This is why I can`t see model theory as other than a technicality. How I see mathematics is that we have some informal collective theory of mathematics and laws of logic. I see the law of logics realistically, specially what Kant calls the law of contradiction which is prior to all mathematics, this I understand to mean objective logical consequence. I don`t care that much respect to my philosophy if logical consequence in the some trong sense can`t be or can be formalized in some theory or logic, because I see that these theories allready depend on this notion. <BR/><BR/>-GcAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-7324805351517740683.post-19633828793144009112009-03-16T15:04:00.000+02:002009-03-16T15:04:00.000+02:00That "humans somehow create non-computable infinit...That "humans somehow create non-computable infinities" is weird only if we take this creation to amount to something substantial. If we take it to mean nothing more than that humans routinely fantasise about such infinities there's nothing more problematic about it than the fact that we fantasise about time-travel, omniscient and omnipotent beings such as those found in the Marvel universe, and so on.<BR/><BR/>As to existence and truth, on a classical fictionalist account most mathematical statements are simply false since they are, on the face of it, about objects that simply do not exist. This again is not problematic. What is problematic is accounting for the fact that we do in fact accept some mathematical statements (with existential import) and reject others. There are many ways of answering this conundrum, some covered in the Stanford Encyclopedia article. In the blog post my point was simply that there is no need to tie a view naturally called "fictionalist" with the claim that mathematical objects do not exist. We may view "fictionalism" broadly understood rather as a sketchy observation about how mathematical objects exist, in light of what sort of considerations we take to be germane, sensible, and so on, when pondering this existence. The observation, then, is just that when pondering the existence of mathematical objects we do not take our task to be similar to that of determining whether Sherlock Holmes or Captain Planet exist.Aatu Koskensiltahttps://www.blogger.com/profile/10999226899475411504noreply@blogger.comtag:blogger.com,1999:blog-7324805351517740683.post-6685895455050593182009-02-27T01:42:00.000+02:002009-02-27T01:42:00.000+02:00If someone says that some mathematical sentences a...If someone says that some mathematical sentences are true, but there is not necessarily nothing that correlates with those sentences I really don`t understand what the world true means in that contex. Classically as I understand it you need consept of existence to define the consept truth. Of course we might think that the existence of that something depends on the human beings, but then it looks quite weird that humans some how create non computable infinities.<BR/><BR/>Philosophy of mathematics might be more fun to mathematicians if doensn`t deal with so called metaphysical questions. Some finnish positivist once said that theology is a science which studies a thing that doensn`t exist. So analogously with theology philosophy of mathematics depends epistemologically from ontology.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7324805351517740683.post-83823165801406249402009-02-21T08:00:00.000+02:002009-02-21T08:00:00.000+02:00Interesting read, thanks.Interesting read, thanks.Rotwanghttps://www.blogger.com/profile/05166697482509062607noreply@blogger.com