I say otherwise because the apples that we see have all of the facts present while our memories have less of the facts present (being precise relates to having more/most of the facts present that makes it specific).Philosophy Explorer wrote:In response to Wyman:
But you said earlier that your definition of 'abstraction' was:
It didn't have to do with extra-sensory phenomena. See how being precise and utilizing definitions can keep a discussion focused and meaningful, rather than shifting mid-discussion?By abstract means to speak in general terms rather than specifically
PhilX[/quote]
That is a very good answer, actually. Ignore Hexhammer.
I distinguish between general and specific, as well as abstract versus concrete. You seem to merge them. So be it. (We'll ignore the hybrids of general concretes, such as water and red, or the specific abstracts such as quarks).
I think some of us challenge you as to how 'abstract' can be quantified, or said to exhibit 'levels.' I can see clearly how something can be more general. For instance, natural numbers are less general than integers, and rational more general than integers, and real numbers more general than rational numbers, etc.. In this sense, the kind of 'number' we're speaking of becomes broader, encompassing (predicating) more and more classes or kinds of numbers. However, I don't know that these broader generalities are necessarily more abstract than the less general categories.
Having said that, with more understanding of what you mean by 'abstract,' I think the answer to your original question is no. Abstractness has nothing to do with usefulness. If a physicist can successfully model reality based upon very abstract mathematics, so be it. I suppose if the mathematics becomes so abstract that no physicist could understand it, that would be a problem, but that's the only limit I can see. In which case, he or she would have to enlist mathematicians to help with the difficult stuff, like Einstein was forced to do.