RE: Can I just say, and I'm just being honest...
March 4, 2018 at 2:54 pm
(This post was last modified: March 4, 2018 at 3:02 pm by Kernel Sohcahtoa.)
CIJS,
The activity in the thread, Actual Infinite in Reality, has been interesting. There have been attempts to invalidate mathematical axioms and concepts, such as set theory (infinite). The opponents of the possibility of an actual infinity existing in reality claim that the concept leads to absurdities and contradictions. From my understanding, the opponents of the possibility of an actual infinity existing in reality claim that infinite set theory cannot be used to justify this possibility and that this possibility must be examined via means of logic and reasoning that are independent of mathematics; yet, they derive their alleged contradictions via basic mathematical operations, which are grounded in set theory (we need to know what collections of objects that the particular objects belong to in order to understand their properties and if performing the operations will be valid/invalid), and so, they have invited math, along with set theory (finite and infinite), into the discussion. Thus, IMO, they seem to be selectively using math: they use math that supports their position (while claiming that it isn't math), while ignoring/dismissing math that challenges their position.
More importantly, they have incorrectly applied mathematical concepts. For example, it seems that they treat infinite as a number (infinity is not a number; it is a concept) that obeys basic arithmetic laws; they also seem to think that the rules of finite sets should be exactly the same as the rules of infinite sets because that seems to fit with their intuition. Consequently, the alleged contradictions that they have generated are the result of a misapplication of fundamental mathematical ideas. Hence, if they are going to successfully reach a contradiction, then they need to strictly adhere to mathematical definitions, theorems, lemmas, concepts, etc., because any contradiction that is reached via incorrectly applying mathematical ideas is invalid.
P.S. This thread is unfortunate. It had the potential to be an exciting intellectual adventure that encourages people to challenge their preconceptions. However, it seems that some posters are more interested in confirming their preconceptions; they don't seem to be interested in learning.
The activity in the thread, Actual Infinite in Reality, has been interesting. There have been attempts to invalidate mathematical axioms and concepts, such as set theory (infinite). The opponents of the possibility of an actual infinity existing in reality claim that the concept leads to absurdities and contradictions. From my understanding, the opponents of the possibility of an actual infinity existing in reality claim that infinite set theory cannot be used to justify this possibility and that this possibility must be examined via means of logic and reasoning that are independent of mathematics; yet, they derive their alleged contradictions via basic mathematical operations, which are grounded in set theory (we need to know what collections of objects that the particular objects belong to in order to understand their properties and if performing the operations will be valid/invalid), and so, they have invited math, along with set theory (finite and infinite), into the discussion. Thus, IMO, they seem to be selectively using math: they use math that supports their position (while claiming that it isn't math), while ignoring/dismissing math that challenges their position.
More importantly, they have incorrectly applied mathematical concepts. For example, it seems that they treat infinite as a number (infinity is not a number; it is a concept) that obeys basic arithmetic laws; they also seem to think that the rules of finite sets should be exactly the same as the rules of infinite sets because that seems to fit with their intuition. Consequently, the alleged contradictions that they have generated are the result of a misapplication of fundamental mathematical ideas. Hence, if they are going to successfully reach a contradiction, then they need to strictly adhere to mathematical definitions, theorems, lemmas, concepts, etc., because any contradiction that is reached via incorrectly applying mathematical ideas is invalid.
P.S. This thread is unfortunate. It had the potential to be an exciting intellectual adventure that encourages people to challenge their preconceptions. However, it seems that some posters are more interested in confirming their preconceptions; they don't seem to be interested in learning.