Date: Tue, 28 Jan 1997 18:33:53 -0500 (EST) Subject: M-I: Re: [Rakesh Bandari] Sohn-RethalOn Tue, 28 Jan 1997, malgosia askanas wrote: > What in the world is "real abstraction"? As opposed to what, "unreal > abstraction"? What are these categories designed to express/accomplish? > > Fernando, you write: > > > The real abstraction in mathematics is what? The mathematical axioms. > > You ask an incomprehensible question and then, not surprisingly, give an > incomprehensible answer. Aren't the concept of "rational number" or "the > number 2" or "straight line" or "right angle" or "area" abstractions? Or are > they abstractions, but not "real abstractions"? > Axioms are definitions of mathematical concepts. The axioms of Euclidean > geometry define the concepts "line", point", "angle", "plane" through > elaborating a system of relationships between them. The Peano axioms of > arithmetic define the concepts "natural number", "addition", "multiplication". > Does abstraction, for you, reside in definitions? A thing, then, is concrete > until one defines it? <snip> > > What does Engels mean by "analysis of magnitude"? What is he going to > go out and analyze? -- I assume it won't be any of the things that mathematics > offers him, since he's so lame at understanding them. What does he mean > by "necessary determinations of magnitude"? What does he mean by saying > that these determinations are "provable dialectically"? What does it mean, > to prove a determination? What are the goals of this Engelsian project, and > what is it supoosed to be good for? > > I am also curious about all these "rounds" of which, according to you, we are > in the fifth. Are we in a boxing match or something? If so, do we get > paid? Are there prizes? Is the match fixed? Are there referees? How did > we, unknowingly, get into it? Could we unknowingly get out and find ourselves, > all of a sudden, simply having a conversation on an e-mail list? > > > -m Here is an experiment you can try out quickly. Stand in front of a large mirror. Ask a friend to look at your reflection in the mirror. What your friend will see in the mirror will be an abstraction of the real "you", that is, if you are "real" yourself. If you are unreal in the sense that you are actually a reflection of a real "-m", then your friend will be seeing an "unreal" abstraction doubly removed from the real "you". This only if you are again "real" and twice removed from the abstraction which your friend saw. And so on and on -- ad infinitum. The degree of unreality of the abstraction that your friend sees will increase linearly with the farther the real "you" is removed from her/him. This is the wilderness of mirrors in which our social "scientists" dwell. Case closed. PS: Please drop a line about the success/failure of your experiment. Thanks. --- from list marxism-international-AT-lists.village.virginia.edu ---