Seems like yet another confusion about the definition of “exist”, which you conveniently don’t give.
If you rephrase it as “Can infinite quantities be observed?” then the answer is negative. If you phrase it as “Can models with infinities in them fit the observations better then those without?”, then the answer is affirmative. If you are interested in a metaphysical answer, such as “Do numbers exist?”, then you have to be clear in what you mean by each term.
some quite smart people disagree on the meaning of this term
We have an apparently very deep philosophical difference here. Some “quite smart people” have offered different accounts of existence: Quine’s, that we are committed to the existence of those variables we quantify over in our best theory, comes to mind. My use of “exists” is ordinary enough that most any reasonable account will serve. I think the intuition of “existence” is really extremely clear, and we argue about accounts, not concepts. Existence is very simple
Maybe addressing your specific examples will clarify. “Can infinite quantities be observed?” as a meaning of existing. Clearly doesn’t mean the same thing. Whether something exists or it can be observed are two different questions, existence being a necessary but insufficient condition for observability. “Can models with infinities in them fit the observations better than those without?” Still not existence. There are instrumentalist models and realist models. (Realists will agree; some intrumentalists will consider all theory instrumental, but that’s another question.) There’s a difference between saying something predicts the data and saying that the model describes reality (what exists) even if the latter claim is justified by the former. “Do numbers exist?” There the dispute isn’t about existence but about numbers, and it’s only because we do have a clear intuition of “existence” that the question about numbers can arise. So, we get different theories about numbers, which imply that numbers exist or don’t.
So, even when it comes to numbers, I don’t think there’s much problem with the concept of existence. Sometimes one sees an unphilosophical tendency to treat problems regarding concepts as though they could be resolved by a mere choice of definition. Such flaws so easily corrected rarely arise in sophisticated thought. The question here is whether our intuition of existence implies that only the finite can exist. In analyzing an intuition, it rarely helps to start with a definition.
This is the worst answer possible, given that some quite smart people disagree on the meaning of this term, and it renders your post meaningless. Consider rereading Skill: The Map is Not the Territory for one possible answer.
Seems like yet another confusion about the definition of “exist”, which you conveniently don’t give.
If you rephrase it as “Can infinite quantities be observed?” then the answer is negative. If you phrase it as “Can models with infinities in them fit the observations better then those without?”, then the answer is affirmative. If you are interested in a metaphysical answer, such as “Do numbers exist?”, then you have to be clear in what you mean by each term.
We have an apparently very deep philosophical difference here. Some “quite smart people” have offered different accounts of existence: Quine’s, that we are committed to the existence of those variables we quantify over in our best theory, comes to mind. My use of “exists” is ordinary enough that most any reasonable account will serve. I think the intuition of “existence” is really extremely clear, and we argue about accounts, not concepts. Existence is very simple
Maybe addressing your specific examples will clarify. “Can infinite quantities be observed?” as a meaning of existing. Clearly doesn’t mean the same thing. Whether something exists or it can be observed are two different questions, existence being a necessary but insufficient condition for observability. “Can models with infinities in them fit the observations better than those without?” Still not existence. There are instrumentalist models and realist models. (Realists will agree; some intrumentalists will consider all theory instrumental, but that’s another question.) There’s a difference between saying something predicts the data and saying that the model describes reality (what exists) even if the latter claim is justified by the former. “Do numbers exist?” There the dispute isn’t about existence but about numbers, and it’s only because we do have a clear intuition of “existence” that the question about numbers can arise. So, we get different theories about numbers, which imply that numbers exist or don’t.
So, even when it comes to numbers, I don’t think there’s much problem with the concept of existence. Sometimes one sees an unphilosophical tendency to treat problems regarding concepts as though they could be resolved by a mere choice of definition. Such flaws so easily corrected rarely arise in sophisticated thought. The question here is whether our intuition of existence implies that only the finite can exist. In analyzing an intuition, it rarely helps to start with a definition.
If that’s what you think, maybe you are on a wrong site then.
Something’s got to be primitive, and I can’t think of a candidate better than existence.
This is the worst answer possible, given that some quite smart people disagree on the meaning of this term, and it renders your post meaningless. Consider rereading Skill: The Map is Not the Territory for one possible answer.
If you’re going to dodge defining existence, please at least clarify your point by telling us which of these things “exist”:
a) irrational numbers
b) sets
c) postmodernism
d) the number of Langford pairings of length 100
e) negative numbers
f) quaternions