> On 28 Sep 2018, at 06:51, Brent Meeker <meeke...@verizon.net> wrote: > > > > On 9/27/2018 9:29 PM, Bruce Kellett wrote: >> From: Bruno Marchal <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>> >>> >>> But now, let us move forward. Stop saying “realism or platonism”, in pour >>> metaphysical context this lead to misunderstanding. >>> >>> Assuming classical arithmetic = arithmetical realism. >> >> It is becoming clear that we have very different understandings of what is >> meant by arithmetical (or mathematical) realism. I gathered a few statements >> about realism from your recent post -- included here: >> >> "Realism = classical. Realism means that I use the axiom (A v ~A)." >> >> "All scientific theories use arithmetical realism, but you are still using >> it in a philosophical/metaphysical sense, when it means simply that we >> accept the excluded middle principle in arithmetic." >> >> "Of course, given what I mean by arithmetical realism (which I thought I >> already told you), this would mean that you reject the use of (A v ~A) in >> arithmetic" >> >> >> My understanding of 'realism' comes from the idea of scientific realism. >> This can have a number of nuanced interpretations, but the basic idea of >> scientific realism is a cluster of views about the nature of scientific >> theories and theorizing. A common core might be the following: >> (1) The aim of scientific inquiry is to produce theories that provide >> description of the world that are literally true. >> (2) Theories in the 'mature sciences' are usually approximately true, and >> the entities postulated by those theories usually exist. >> >> One of the most popular arguments for scientific realism is the so-called >> 'miracle argument'. Following Putnam, scientific realism is capable of >> explaining why a predictively successful theory is predictively successful, >> whereas the success of a theory would be miraculous if scientific realism >> were not true. >> >> Stathis Psillos adds a metaphysical component: the world has a definite >> mind-independent structure; and a semantic component: scientific theories >> are truth-conditioned descriptions of their intended domain, so the >> theoretical terms in theories have factual reference -- the unobservable >> entities they posit populate the world -- form the 'furniture' of reality. >> >> The Oxford Dictionary of Philosophy, in the section on the philosophy of >> mathematics, gives the following definitions: >> >> "There are two distinct types of realism in the philosophy of mathematics. >> Realism-in-ontology is the view that the subject matter of mathematics is >> the realm of objects that exist independent of the mind, conventions, and >> language of the mathematician. Most advocates of this view hold that >> mathematical objects -- numbers, functions, points, sets, etc. -- are >> abstract, eternal, and do not enter into causal relationships with material >> objects. Because of this, realism-in-ontology is sometimes called platonism. >> "Realism-in-truth-value is the view that unambiguous assertions of >> mathematics are non-vacuously true or false, independent of the mind, >> language, and conventions of the mathematician. (This would seem to be close >> to the view that you, Bruno, espouse.) >> >> "There is a natural connection between the two varieties of realism. >> Consider the following statement: >> >> 'There is a prime number greater than 1,000,000.' >> >> "The realist-in-truth-value holds that this is an objective truth. But what >> does it mean? Prima facie, '1,000,000' is a singular terms, and 'prime >> number' is a common noun. If the surface grammar of this sentence reflects >> its logical form, and if 'there is' means 'there exists', then the sentence >> entails that both the number 1,000,000 and a greater prime number exist. For >> the realist-in-truth-value, this existence is objective, and so we are led >> to realism-in-ontology. In sum, if one is a realist-in-truth-value, then >> realism-in-ontology is the result of taking mathematical assertions at face >> value." >> >> Other references that I have looked up, such as entries in the Stanford >> Encyclopedia of Philosophy on "Realism" and "Platonism in the Philosophy of >> Mathematics", say similar things. Though, of course, there are probably more >> nuances in the understanding of mathematical realism than there are >> philosophers of mathematics. >> >> >> Given the above references, I think it should be clear why I say "realism or >> platonism", and refer to "an independently existing mathematical realm". In >> Western philosophy at least, that is what realism in mathematics means -- >> although things might be different in Gallic philosophy. >> >> It seems that your idea of arithmetical (mathematical) realism is entirely >> from classical logic and is, therefore, essentially a >> 'realism-in-truth-value' understanding. It is interesting, in that case, >> that you make no reference to mathematical objects. You claim that the truth >> of propositions such as '2+2=4' is independent of the mind, language, and >> conventions of arithmetic, as in the definition of 'realist-in-truth-value' >> above. But you do not seem to go the additional step of saying that >> mathematical objects, numbers and so on, are objects that actually exist >> (which would be a form of platonism). If you want to reject platonism, and >> the idea that mathematical concepts are objects that actually exist -- that >> there is a mathematical realm of objects that exist independently of any >> physical existence -- then I suppose you are entitled to any view that you >> wish to hold. But you cannot claim that any such view is uniquely necessary. >> >> If you reject platonism, it is hard to see how you can make sense of claims >> such as "All calculations exist in arithmetic", or that physics arises from >> the statistics of computations in the universal dovetailer. Since I reject >> all forms of arithmetical realism, particularly platonism, I do not think >> that your arguments for 'comp' have any merit. >> >> However, the philosophy of mathematics is not an area in which I have had >> any particular interest, so apart from rejecting mathematical realism and >> platonism, I do not have any strong views about which of the many >> alternatives on offer might be an acceptable philosophical attitude to >> arithmetic. >> >> Bruce > > I don't see any problem in saying that "2+2=4" while denying that numbers > exist.
See my answer to Bruce. This means only I will not use contemporary logic. In both predicate logic (classical, say) we have a rule which makes it possible to derive Ex(x+2=4) from 2+2=4. Changing the logic will hardly change the reality, or the consequence of computationalism, although it could make some result less intelligible. > ISTM analogous to saying "A unicorn has a single horn." without implying that > unicorns exist. Yes, but as the theory is given, you will be unable to derive the existence of a unicorn. You will derive only the existence of a number believing in the existence of a unicorn. > The truth that is maintained by mathematical proof is just a marker which > is analytically preserved by the rules of inference. Yes. It is only a machine’s belief. > The fact that there are true but unprovable sentences in arithmetic Unprovable is relative to a theory or machine, note. > , in just a logical inference in meta-mathematics. Which is embeddable in arithmetic. That is the whole point of Gödel arithmétization of metamathematics. > It's not something outside mathematics that is true OK. > in the sense that ice is cold. That is also a belief by some machine, and it might be recovered in their phenomenology, in arithmetic. We cannot discuss in the abstract. Doing metaphysics with the scientific method as for theory and means of verifying empirically the theory. The mechanist theory predicts both matter and consciousness. Materialist theory assume matter, with some magical attribute, and miss consciousness. So … Bruno > > Brent > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
