--- In Wittrs@xxxxxxxxxxxxxxx, "jrstern" <jrstern@...> wrote: >> The word "numbers" appears in the title of the paper. > The historical value of the paper turned out to be in the > billions of computers that have been built since, which are > not purchased and operated in order to prove out any theory > about computable numbers, in spite of the paper's title. I sometimes wonder about that. I'm inclined to suspect that von Neumann would have come up with the same architecture at about the same time, even without the influence of Turing. >> Talk about alphabetic letters does not help you here. What >> makes something a letter "O" or a digit "0" or a round doodling >> mark is the intention of the user. > We are wandering way away from the point, I fear. We clearly have some disagreements, and we are focusing on the points of disagreement. > My curiosity is still about what you might have meant, > by intend, or intention, or intentionality. > And about whether Turing was writing about symbols, > or just using them, as he used the alphabet. Clearly, Turing was writing about symbols, and using them in similar ways to those symbols that we refer to as the alphabet. >> I did not even use the word "intentionality" in this thread, >> except when quoting you. I did use "intentional" and "intention". >> The main point here is that what makes a physical mark a symbol is >> that the person using that mark intends it as a symbol. > What about the mark on the tape of a TM. > Do you want to assert that only has its value by > means of a human outside the TM? The TM is an ideal object which is itself the product of human thought and intentions. > I am certainly asserting otherwise. I recognize that, and I am disagreeing. >> Let me comment on the idea of symbols that don't actually >> symbolize anything. That seems to confuse you. > Of course. > The squiggle becomes a symbol only when it symbolizes, > even if all you've said is, "Take some variable X". Some people do have difficulty with the idea of symbols that don't symbolize. It seems to me that mathematical platonism is there to deal with such a difficulty. Just invent an imaginary platonic realm, and have those symbols refer to ideal objects in the platonic realm. What seems strange to me, is that you say you are a nominalist. And I take nominalism to say that universals do not exist, we merely have names for them. So those names are then symbols that don't symbolize. So I would think a nominalist should be quite comfortable dealing with non-referring symbols. The letters of the alphabet are symbols that don't symbolize. I'm not understanding why you have a problem there. > Symbol, to me, is first of all a physical particular. But it isn't. I'll make a separate post to discuss that. Regards, Neil Group Home Page: http://seanwilson.org/wittgenstein.discussion.html Group Discussion Board: http://seanwilson.org/forum/ Google Archive: http://groups.google.com/group/Wittrs FreeList Archive: //www.freelists.org/archive/wittrs FreeList for September: //www.freelists.org/archive/wittrs/09-2009 FreeList for August: //www.freelists.org/archive/wittrs/08-2009 Group Creator's Page: http://seanwilson.org/ Today's Messages: http://alturl.com/whcf Messages From Last 3 Days: http://alturl.com/d9vz This Week's Messages: http://alturl.com/yeza Yahoo Archive: http://groups.yahoo.com/group/Wittrs/