# Mackies critique of KalamCAs & impossible "actual infinites"

Hello,

Perhaps I am mistaken but I fail to see how W. Craig’s argument for the impossibility of an actual infinite constitutes anything other than a contradiction. That is, that the following argument isn’t sound:

Infinite Library analogy

(A) (Set of all books) [1,2,3…]
(B) (Set of all red books) [1,2,3…]

If A & B are both infinite then: (i) A = B
(ii) A > B

(i) & (ii) = a contradiction. Thus (by RAA) |- actual infinites (and actual infinite Libraries) are impossible.

Mackie argues that the relation of (i) “equals to” & (ii) “smaller than” doesn’t evoke such a contradiction - but how could that be? It appears to make no sense. His objection goes almost entirely unsupported.

IMH/SO, “A = B” is false.

IMH/SO, Infinities do not equate unless you declare a cardinality.

IMH/SO, Standard mathematics doesn’t apply to infinities or infinitesimals.
IMH/SO, They are “indeterminate”, because they are not quantities, but stated qualities (that of being unbounded, having no specific value).

Hello James, thankyou for your reply.

Please excuse me for my rather limited expertise of cantorian set theory - I wonder if you could please elucidate what it is you mean?

Thanks

IMH/SO, Georg Cantor was merely expressing the limitation of a mono-decimal system in saying that infinity squared was the largest possible number (that could be represented in such a system).

IMH/SO, The idea of cardinality refers to the idea of having an infinite set, but then taking each member also as an infinite set. With each step in doing that, a new “cardinality” is declared. In reality, one can have an infinite number of cardinalities. They merely cannot represent them in a mono-decimal form, “1234.5678” - single decimal.

IMH/SO, But the issue here is that when something is declared infinite, it is merely declaring that there is no highest value. It is not saying anything about it being equal to another infinite value. Saying “infinite” does not give a quantitative value with which one can use standard mathematics.

IMH/SO, So the whole “A = B” bit doesn’t apply at all. That would like saying that object A is too big and object B is too big, therefore object A is equal to object B.

Aha. I see. Thankyou for your help James. Most appreciated.