* 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). [1]13 mins * [2]Unlike * [3]1 * [4][IMG] [5]Kenneth Udut [6]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. [7]4 mins * [8]Like * [9][IMG] [10]Kenneth Udut [11]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. References Visible links 1. https://www.facebook.com/groups/neoacademiaannex/permalink/636368136484987/?comment_id=636370319818102&offset=0&total_comments=1 2. Unlike this comment https://www.facebook.com/groups/neoacademiaannex/636368136484987/?comment_id=636370319818102¬if_t=group_comment# 3. https://www.facebook.com/browse/likes?id=636370319818102 4. https://www.facebook.com/kenneth.udut?fref=ufi 5. https://www.facebook.com/kenneth.udut?fref=ufi 6. https://www.facebook.com/profile.php?id=100007796295516 7. https://www.facebook.com/groups/neoacademiaannex/permalink/636368136484987/?comment_id=636373599817774&offset=0&total_comments=2 8. Like this comment https://www.facebook.com/groups/neoacademiaannex/636368136484987/?comment_id=636370319818102¬if_t=group_comment# 9. https://www.facebook.com/kenneth.udut?fref=ufi 10. https://www.facebook.com/kenneth.udut?fref=ufi 11. https://www.facebook.com/profile.php?id=100007796295516