On Hell and Forgiveness

[polymath257]

Why do you think that the law of identity is not thought through very well?  It would seem that without it; we cannot have a rational conversation. Tree is a language concept as well.

As Neo pointed out, you seem to be assuming the answer to your question in your argument (that if you cannot observe the number it ildoesnt exist). In any case the number as a description is not dependent on the subject. It is describing an external part of reality, not giving information about the person who holds the view.

Well, first of all, most people who use that identity don't distinguish well between *logical* identity (p if and only if q) and *equality* (p=q). They are very different notions and applicable in very different situations.

So, *logical* identity describes the logical statement that "p is true if and only if p is true". This is something that is the case in most logical systems, including classical logic.

Equality is a much more complex and interesting thing. We can use the 'identity of indistinguishables' definition and say that x=y whenever x and y have exactly the same properties. This forms an equivalence relation (x=x, x=y implies y=x, x=y and y=z implies x=z). But there is a problem doing the quantitifcation over *all* properties. What constitutes a property?

Furthermore, most people, when they think they are using equality, are actually using some other equivalence relation. And it is NOT the case that two things equivalent via an equivalence relation must be equal. It isn't just *one* criterion that determines 'indistinguishability'.

In math, the allowed properties are carefully spelled out, so there is no ambiguity. But there are also undefined notions (typically, set membership). Only after the development of set theory does it become possible to define the concept of 'number'.

And you fell into the equivalence relation/identity trap in your next statement when you said that trees are a language concept also. No, trees are wooden plants. They are not part of language. What is part of language is the *word* 'tree'. This is usually called the 'use/mention' distinction. There is noting inherent in reality or in tees that forces us to use the vocalization 'tree' or the English word 'tree'. The word is NOT an objective part of reality. It is a subjective tradition that we adopt for communication. But, you would use a different word for the same reality if you spoke a different language.

And, you also bring up another very important issue: how do you define the verb 'to exist'? A LOT of care is required here. We need a definition that allows us to talk about non-existent things like Sherlock Holmes while also allowing us to say that the chair in my room really exists. But we can have that for another discussion, or later in this one.