* * [1][IMG] [2]El Ch* You said "How do you capture the concept that two apples are both two apples and also different to which using them for numerical quantity would be ultimately dishonest?". I have tried to explain that same issue to other mathematicians. We can do it with different classes of equivalence relations with varying degrees of intensionality/extensionality (the level of composition of what is being compared in the equivalence relation). [3]46 mins * [4]Unlike * [5]1 * [6][IMG] [7]Kenneth Udut [8]El Ch* - That makes sense. I like that solution. I'm amazed that I completely understand every word that you're saying, considering I have no background in math; but a year and a half of being buried 'til 5am in Wikipedia, studying the nature of ambiguity and uncertainty from various perspectives.. and finding the "holes" in various philosophies and worldviews... I guess I picked up a few vocabulary words. Thank you El Che - I think you've given me validation from a more specific perspective. I like validation. Gives warm fuzzies and a restoration of purpose. [9]37 mins * [10]Like * [11]1 * [12][IMG] [13]Kenneth Udut [14]El Ch* I wonder though, is it ever possible to have a point where no one could say, "yeah, but what about ______ ?" without having a ready and satisfying answer? Hm. Somebody recently asked that question somewhere in a different form and you were part of it.. what *was* that? Where was that? ugh,silly memory. [15]33 mins * [16]Edited * [17]Like * [18]1 * [19][IMG] [20]El Ch* [21]Kenneth Udut - I have gotten kicked out of math communities/groups. There are mathematicians who can't see past what's written in the books, and when you start talking about creating different equivalence relations other than the intensional '=' sign, they get their panties in a bunch. [22]28 mins * [23]Unlike * [24]1 * [25][IMG] [26]Kenneth Udut [27]El Ch* Same, although my approach tends to be cultural-historical-deconstructionalist-absurdist-etc but ends up with the same result: "You! OUT!" What the "get out"ers don't realize, is that it's precisely BECAUSE I hold mathematics to such a high esteem that I _expect_ more out of it. It's the road we've been taking and are continuing to take... and .. well.. it needs some important tweaks as it dives into more complicated realms of human thought. [28]2 mins * [29]Edited * [30]Like * [31][IMG] [32]Kenneth Udut