I agree, but I also believe we have an innate capacity for morality - one that seems rooted in empathy - and such a capacity is consistent with natural selection.I've found incredible rhetorical and persuasive success by appealing to NUMVs (nearly universal moral values). To continue living, to be free from oppression, to be free to pursue happiness, etc... Moral agreements between agents with shared moral values are objectively true in the same sense that a good strategy is objectively likely to lead to victory. — VagabondSpectre
Case in point. When you say "schmets can have infinite members" do you mean "schmets can have infinitely many members" or do you mean "schmets can have infinity as a member"?Okay, so sets are by definition, conceptually finite collections so any attempt to define or talk about infinite collections is incoherent on pain of contradiction. But let's create a new concept and a word to refer to it: "Schmets". Schmets are just like sets, except some schmets can have infinite members provided they are defined appropriately. So now the question is, are there sets or are there schmets? Well, since sets are, by hypothesis, necessarily finite, they aren't very useful in mathematics since nearly every standard and non-standard maths uses infinity in some form or fashion (ultrafinitism doesn't look very promising). So it seems mathematicians are using Schmets and so we can just dispense with using sets in maths.
I agree with what you said, but it's beside the point. We agree that infinity is not reached to or from, but that just implies we need look elsewhere for our conception of an infinite future. The future is NOT the destination, it is the unending causal process following the arrow of time. The concept of "completeness" is key: the process for the future is never complete. On the other hand, the past is certainly complete - there is no continuing process - the process has completed (except for the finite process of appending an additional day every 24 hours). That is another way that the past has ontologically distinct properties from the future.The reason a temporal process will never reach infinitely far into the future is that there is nothing for it to reach: a process can start at point A and reach point B, but if there is no point B, then talk about reaching something doesn't make sense. Turn this around, and you get the same thing: you can talk about reaching the present from some point in the past, but if there is no starting point (ex hypothesi), the talk about reaching from somewhere doesn't make sense, unless you implicitly assume your conclusion (that time has a starting point in the past).
A "sphere" (or "ideal sphere") is an abstraction, not an actually existing thing. You bring up another abstraction: the number of possible paths being infinite. This is hypothetical; in the real world, you cannot actually trace an infinite number of paths. So in the real world you cannot actually COLLECT an infinity. All you can do is to conceptualize.That's an ideal sphere. Nowhere did I mention an ideal sphere. Now why don't you address the point. You want a collected "infinity"? Take any sphere-like object. The number of possible paths on the sphere is not less than aleph-c. — tim wood
It's not true that the "normal operations" can be performed with transfinite numbers. Analogous operations can be defined, but the are not the SAME operation. The fact that transfinite numbers have mathematical properties has no bearing on whether or not they have a referent in the real world - mathematics deals with lots of things that are pure abstraction with no actual referent (look into abstract algebra).It doesn't behave non-numerically, that doesn't make sense. The normal operations can be performed with such numbers, but that doesn't mean you'll get the results you would expect with finite numbers. And the reason is clear: Because you're dealing with a different type of number.
