In that vein, do you recognize that there's a conceptual distinction between an "actual infinity" and a "potential infinity"?
— Relativist
Yes, it corresponds to the difference between metaphysical actuality and logical possibility. Again, mathematical existence refers to the latter, not the former. — aletheist
It is not; as I said, mathematical existence--including the potential infinity of the natural numbers--is not metaphysical actuality, it is logical possibility. From your other comments, I think that we agree on this; perhaps you misread my previous post.But how is that metaphysical actuality? — fishfry
No, I said exactly the opposite of that.But you said that potential infinity has metaphysical actuality. — fishfry
In that vein, do you recognize that there's a conceptual distinction between an "actual infinity" and a "potential infinity"? — Relativist
Actual infinity corresponds to metaphysical actuality, while potential infinity and mathematical existence correspond to logical possibility.Yes, it corresponds to the difference between metaphysical actuality and logical possibility. Again, mathematical existence refers to the latter, not the former. — aletheist
It is not; as I said, mathematical existence--including the potential infinity of the natural numbers--is not metaphysical actuality, it is logical possibility — aletheist
That is not what I mean by "metaphysical actuality." I just mean the modal property of being actual, rather than merely possible or strictly necessary — aletheist
So, combining "metaphysical" with "actual" means someone is thinking a metaphysical thought? Or does the expression imply an interaction with physical reality? I am going on a classical definition of the expression. What do you really mean? Please clarify with examples. Thanks. — jgill
What does thinking have to do with anything? Metaphysics is a branch of philosophy, within which "actual" has a technical meaning that distinguishes it from "possible" and "necessary."So, combining "metaphysical" with "actual" means someone is thinking a metaphysical thought? — jgill
That is closer, since whatever is physical is actual in the relevant sense. However, just to be clear, I hold that reality is not coextensive with actuality; there are also real possibilities and real necessities.Or does the expression imply an interaction with physical reality? — jgill
If I say that I have an apple, what I usually mean is that I have an actual apple. If I posit a set of apples in the strictly mathematical sense, then I am talking about something that is logically possible, but not (necessarily) actual. :smile:Please clarify with examples. — jgill
If I say that I have an apple, what I usually mean is that I have an actual apple. If I posit a set of apples in the strictly mathematical sense, then I am talking about something that is logically possible, but not (necessarily) actual — aletheist
No, these are all numbers; and again, existence in mathematics entails only logical possibility, not actuality in metaphysics.Are the natural numbers metaphysically actual? The complete set of natural numbers? The square root of 2? Chaitin's constant, which is known to be noncomputable? — fishfry
Yes, in accordance with how I was using that term.Is a brick metaphysically actual? — fishfry
That depends on whether one is a scientific realist about each of these entities. I am currently inclined to say yes, probably, and maybe.How about an electron? A quark? A string? — fishfry
Do abstractions exist at all? I suggest they don't. A number line "exists" only as an abstraction, but this is not true existence. It's just a concept, in which a set of logical/mathematical properties are considered abstractly. The same is true of numbers, whether rational or irrational. "3" doesn't exist, but collections of 3 objects exist - so we can think abstractly about 3-ness. Neither does Pi exist; nevertheless we can abstractly consider the fact that all "circles" (another abstraction) have Pi as the ratio between their circumference and diameter. — Relativist
LOLOL. — fishfry
LOLOL.But in relating ontology to mathematics, aletheist employs intentional vaguery and ambiguity in terms, as well as outright contradiction to support unreasonable mathematical principles. — Metaphysician Undercover
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