Hey, I was reading the 1994 Aquinas Lecture, Realism and Nominalism Revisited, and the point was made that numbers like 6 are in the same category of terms as more impresice things like ‘some’ and ‘more than’. I found this interesting because when contemplating universals, it’s a lot easier to believe that ‘70’ refers to something real than it is to believe that ‘some’ does. Any thoughts on this?
I suppose it depends what categories have been defined. They both are involved in counting, and they are also both human constructs. Really, the only difference between them is the degree of precision. But that can be very important and give rise to different categories worth considering. Unfocused sunlight won’t set paper on fire, but focused sunlight will. I mean, if we are creating artificial categories, we can lump things together pretty much however we want.
But in terms of the category we put them in intuitively, yeah, that makes sense. Huh, never thought about it that way. Neat.
The weird thing is, I don’t even know if there’s a degree of precision difference anymore. You can explicitly define ‘some’ as ‘at least one’, and taken that way, there’s certainly situations in which only that term will do. I’d always been on the fence about whether to consider numbers real or artificial, and I think this comparison makes up mind for me.
it is a question of laziness…
which is more believable?
there are some apples in that tree
there are 70 apples in that tree
which is more easily verified?
-Imp
Personally, I disagree - intuitively, i find it much easier to believe that the concept underlying “some” corresponds to something “real” than the number 70 - which is a uniquely human concept. As I talked about in another thread - i don’t think what you’re calling “imprecise quantification” requires counting, which is a methodology involving a much higher level of cognitive abstraction than simple size-based comparisons - e.g., things like more and less, single things and groups, some and none, etc. Most mammals can make size-based comparisons, but very few can count.
Isn’t it better to know precise amounts? I don’t see the dilemma here…
I suppose it depends. Precise amounts are far more subject to change than imprecise amounts. Let’s say compound X blocks activity Y to the extent of A. If am being precise, I would have to provide a whole bunch of qualifiers, you know, statistics. A plus-or-minus B. Because I’m limited by the tools I am using to observe the situation and the situation itself could be undergoing various processes of change that I am not accounting for. On the other hand, saying “some” can be assumed and sorta drop out. Compound X blocks activity Y [to some extent], period/full stop. Both have their merits. Sometimes it is better to qualify things, other times it is better to leave quantities unqualified.
you’re right, there’s no real dilemma as such - i would just object to making the presumption that mathematics is a universal - that numbers exist independently of human cognition - or that there even is any absolute precision - i think it’s more likely that numbers are something we assign rather than discover, so to speak.