Sylvain Baron wrote: > In 1902, in a book called "Science and Hypothesis" Henri Poincare > wrote about physical and mathematical continuum : " We cannot believe that two quantities which are equal to a third are not " equal to one another
Is this an axiom? Trivial counter-examples are easy to find (though, granted, it could be said that they do not constitute examples of continuum). For example, if I have 3 dollars, and you have 3 dollars, you could say that these two quantities are equal. But the same object can't exist in two places at the same time, so either: (a) the three dollars that I have are different from the three dollars that you have, or (b) we don't really each have three dollars. If two quantities which are equal really represent something different from each other, why should that quality cease to exist when a third quantity is introduced? Put differently, as long as the concepts exist purely in one's mind, equality is easy to manage. However, in the real world there is no such thing as absolute equality. Even the same object is different from two different perspectives. This is not simply a matter of appearance, and is not simply because it is changing over time. But, also because the distinction between what is a part of the object and what is not is an artifact of the mind. For example, is that photon or that oxygen molecule or whatever other small thing near the surface of the object a part of it or not? Granted, concepts of equality are incredibly useful tools of thought. But I think Henri Poincare talked about this as an issue of belief for a very good reason. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
