I don't think you can consider one without considering them all. In your head you can contemplate whatever, but as soon as it becomes interpersonal we are bound by the rules of language. If we're talking about infinity, we have to adhere to the commonly accepted definition of the word. If you or the OP mean to discuss something else, or your personal conception of infinity, then it has to be explicitly stated.
I am not taking a strictly mathematical approach. I feel like I've taken a few here, and what you just said is more or less what I've been saying. We have to start from a common ground and only use things which are understood and accepted by everyone. This is ancient philosophic theory.
Perhaps, since you seem to be adequately versed in philosophy, you'd care to give us this grounding, and then we can all work together to come to some sort of conclusion. (Most likely not, but hey).
Will you present us with the definition of infinity (that we should discuss) and propose a method we should use to resolve this question? There will be no more debates on what infinity means, and from there on in Infinity will be used to refer to the item defined by you.
__________________
In the end we are but wisps
|