On Hell and Forgiveness

[SteveII]

Ultimately, as I said to Neo in the thread on delusion and religion, number, and the concepts it is dependent on, are a mystery.  I can suggest that number, being an example of reasoning using parts and wholes, only exists in so far as we make arbitrary identity judgements, about what is a part of what, and what is a whole.  But our intuitions tend to marshall against us, at the very least, and it's not entirely clear that number is subjective in its entirety, that it doesn't have an independent, objective substance of some sort.  Yet when we go the other direction, and assert that number, and part/whole distinctions are objective, we run into problems in that direction as well, problems which seem equally intractable.  So we're left with a mystery, I think, and to declare that number, or parts & wholes, is definitely objective, is, to my mind, to embrace an opinion that is not in any sense fully justified.  At minimum, if you can't prove that number is objective, that leaves the door open, no matter how slightly, that number is subjective, as it must be one or the other, it can't be both.  So, QED, as it were, I think I've shown that number and parts & wholes being a product of mind is not a view that is as far fetched as Neo and Steve made it sound.  If you disagree, please explain why.

(To rephrase in terms of your example, what makes two hydrogen atoms and an oxygen atom, close together, strongly interacting, a molecule of water, and the same group of atoms, separated by several light years of empty space, not a molecule of water?)

After a little research...

We don't reason from parts to a whole with numbers. Frege did a lot of work still respected today in the field of philosophy of mathematics and write an important work (in that field anyway) called The Foundation of Arithmetic.  All references from: https://en.wikipedia.org/wiki/The_Founda...Arithmetic

Psychologistic accounts of mathematics[edit]

Frege objects to any account of mathematics based on psychologism, that is the view that math and numbers are relative to the subjective thoughts of the people who think of them. According to Frege, psychological accounts appeal to what is subjective, while mathematics is purely objective: mathematics are completely independent from human thought. Mathematical entities, according to Frege, have objective properties regardless of humans thinking of them: it is not possible to think of mathematical statements as something that evolved naturally through human history and evolution. He sees a fundamental distinction between logic (and its extension, according to Frege, math) and psychology. Logic explains necessary facts, whereas psychology studies certain thought processes in individual minds.[2]

Jorm, specific to your point above, I think this is an interesting point:

Frege roundly criticizes the empiricism of John Stuart Mill.[6][7] He claims that Mill's idea that numbers correspond to the various ways of splitting collections of objects into subcollections is inconsistent with confidence in calculations involving large numbers.[8][9] He also denies that Mill's philosophy deals adequately with the concept of zero.[10] He goes on to argue that the operation of addition cannot be understood as referring to physical quantities, and that Mill's confusion on this point is a symptom of a larger problem of confounding the applications of arithmetic for arithmetic itself.
 
...further down...

Frege's definition of a number[edit]

Frege argues that numbers are objects and assert something about a concept. Frege defines numbers as extensions of concepts. 'The number of F's' is defined as the extension of the concept G is a concept that is equinumerous to F. The concept in question leads to an equivalence class of all concepts that have the number of F (including F). Frege defines 0 as the extension of the concept being non self-identical. So, the number of this concept is the extension of the concept of all concepts that have no objects falling under them. The number 1 is the extension of being identical with 0. 

You also might be interested in the paragraph labeled KANT, there this is discussed: He criticizes him mainly on the grounds that numerical statements are not synthetic-a-priori-, but rather analytic-a priori.