(February 15, 2018 at 8:16 am)polymath257 Wrote:(February 14, 2018 at 10:55 pm)RoadRunner79 Wrote: The term actual infinity is contradictory.
Infinite of course refers to limitless or endless. It cannot be ended, or completed. It cannot be contained or actualized in it's entirety or limited. Therefore when you put the two together, it is a contradiction.
Infinity means that there is no limit, that there is always something more. You cannot bind it and say "here is infinity" at any given point. You will have a potential infinity, which may be increased.
So, infinite, in your personal language, is not the same as simply not being finite, i.e, countable with some positive integer.
1.) What, precisely, do you mean by 'completed'? 2.) Is there some process going on? 3.) Why do you assume that? 4.) What do you mean by 'actualized'?
5.) Might I suggest that you update your definition of the term 'infinity' to the more modern one for discussion sake?
If you mean that it is simply uncountable as in really large and impossible to quantify then no. And I don't believe that this view would make sense in regards to the discussion on actual vs potential infinite.
1.) I mean that it is a completed or whole thing, that you can say here is infinity.
2.) By definition an endless one, or one without limit.
3.) See definition.
4.) To be made actual or real
5.) If you have difficulty, then propose how you would like to discuss it. As long as the ideas are the same, it doesn't matter to me. Just because something is new or novel however, doesn't mean that it is better.
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. - Alexander Vilenkin
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther