(February 15, 2018 at 1:28 pm)polymath257 Wrote:(February 15, 2018 at 1:15 pm)SteveII Wrote: Therefore the the abstraction of actual infinity (from the first quote) is based on an axiom that there exists at lease one infinite set. Appropriately, an axiom in mathematics is defined as: a statement or proposition on which an abstractly defined structure is based. In case we are still unclear, the third quote defines an Abstraction. I highlighted the key theme all the way through this. Abstract.
You have NOT made an argument (in this or the previous thread) where you show how this abstract concept in mathematics applies to the real world. It should be simple to propose some thought experiments or examples for us all to consider. I understand your point that the concept in mathematics exists--now you need to provide some evidence that it applies to real objects. Re-iterating infinite set theory from mathematics will not further this discussion.
Yes, I get that. I will happily admit (as I have done repeatedly) that we do not *know* if there is an actual infinity in the real world. None has been given, I agree.
But that is distinct from the question of whether it is *logically contradictory*. The fact that it works in the abstract is enough to show there is no *logical* problem with the concept.
Also, all claimed 'dis-proofs' are based on a confusion between 'size' in terms of subsets, 'size' in terms of cardinality, and attempting to 'subtract' when it isn't well-defined. In other words, the claimed 'dis-proofs' simply don't manage to disprove the concept.
You are answering a metaphysical question with a mathematical axiomatically-driven abstraction. Mathematical axiomatically-driven abstractions are not part of the pool where logic goes for information. By the definition of the terms, you have not *shown* anything to be logical.
