On Tue, Apr 8, 2008 at 10:24 PM, Gabriel Dos Reis wrote: > > | On Tue, Apr 8, 2008 at 8:59 PM, Gabriel Dos Reis wrote: > | > Bill Page writes: > | > > | > | I can not agree. Because something cannot always be computed > | > | does not mean that it is therefore ill-defined. This is especially > | > | true in mathematics. > | > > | > I believe you're putting confusing the issues. Function equality > | > is well-defined in classic mathematics (set theoretical). But > | > that definition is almost useless from algorithmic perspective. > | > > | > | I do not think "almost unless" is synonymous with ill-defined even > | from an algorithmic perspective. > > So?
So, I was waiting for you to present the reason why earlier you said: "From computational (there algorithmic) perspective, function equality is ill-defined." But so far I have been disappointed. > > | In reply to a similar comment by > | Waldek in this thread I characterized the current fully computable > | syntactic definition of equality for functions as an "approximation" > | to the actual equality. > > The problem I have with that `characterization' is that it does not > make any sense from principled computations point of view. If the > game is to just hack up something, we know how to do that. But I > cannot marry your `charaterization' with the nearly worship in > category theory. > You have injected the words "hack" and "worship" here but I do not think they are appropriate. What reason do you have to believe that I worship anything in particular? When have I ever proposed a simple "hack" just to make something work without asking why it works the way that it does? > > | I think what it means to be approximate can in > | principle be rigorously defined. > > I'm awaiting an *actual* rigorously defined one -- not one that > `can be in principle'. Bcause, after all, I have feed the machine > with an actual algorithm. > > > | > | For example, the assumed equality of functions, i.e. the > | > | concept of a commutative diagram, is essential for category theory. > | > > | > `category theory' is a medium, not the message. By itself it is void > | > of content. > | > > | > | You would have a hard time convincing me of this > > Then we just have to agree to disagree. I don't believe in worship in > category theory. I do believe category is an extremely sophisticated > and powerful tool... when one has actual *matter* to work with. > I do not believe in "worship" of category theory either but I do not understand what you mean by "actual matter". What counts as *matter* to you? > [...] > > | Would you say that classical set theory is similarly "devoid of > | content"? > > The problem with `set theory' is not that it is devoid of content. It > is that it has a overweight non-constructive content. In essence, it > concludes that `bubble sort' and `heap sort' are the same function. > That is why it is so inadequate from (algorithmic) computational > perspectives. > I agree. Regards, Bill Page. ------------------------------------------------------------------------- This SF.net email is sponsored by the 2008 JavaOne(SM) Conference Don't miss this year's exciting event. There's still time to save $100. Use priority code J8TL2D2. http://ad.doubleclick.net/clk;198757673;13503038;p?http://java.sun.com/javaone _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
