:::::I think the problem is a lack of imprecision when using words like "same" or "equal". In mathematics such terms have very precisely defined meanings and so to say that all groups of order three are the same or are equal (or, equivalently, to say that "there is only one group of order 3") is not to say that all such groups are the same in all respects (obviously, this isn't true or they would all have the same name/description and we wouldn't even doubt there were more than one such group), but instead only says that all such groups behave similarly in all the ways that are (currently) important to mathematicians. When dealing with real world situations like mathematical aptitude and gender, it's much easier to speak imprecisely (either mistakenly or maliciously) and thus much more plausible that some suggested equivalences are the result of liberal bias and not some underlying similarities. I just don't see how that is possible, however, in the realm of mathematics, at least with respect to homomorphisms. | :::::I think the problem is a lack of imprecision when using words like "same" or "equal". In mathematics such terms have very precisely defined meanings and so to say that all groups of order three are the same or are equal (or, equivalently, to say that "there is only one group of order 3") is not to say that all such groups are the same in all respects (obviously, this isn't true or they would all have the same name/description and we wouldn't even doubt there were more than one such group), but instead only says that all such groups behave similarly in all the ways that are (currently) important to mathematicians. When dealing with real world situations like mathematical aptitude and gender, it's much easier to speak imprecisely (either mistakenly or maliciously) and thus much more plausible that some suggested equivalences are the result of liberal bias and not some underlying similarities. I just don't see how that is possible, however, in the realm of mathematics, at least with respect to homomorphisms. |