In Chapter 2 of the Proslogion, Anselm defines God as a "being than which no greater can be conceived." — Wikipedia
Infinity is that which is boundless or endless, or something that is larger than any real or natural number. — Wikipedia
Yeah, it fails but, first and foremost, because it is, at most, merely valid and not sound, only the idea of God (essence) is 'demonstrated' but not the existence of the idea's referent as "the proof" also sets out to do. And, as an 'a priori argument', the OA (Proslogion) is only 'true by definition', thus vacuous with respect to a posteriori facts of the matter. So again, my friend, I think your "potential infinity vs actual infinity" argument misses the forest for the trees (& what said :smirk: ).Anselm's ontological argument fails! — TheMadFool
Note the underline bit, "...larger than any real or natural number". Sounds remarkably similar to "...no greater can be conceived" the main premise in the ontological argument. — TheMadFool
There might be a hair to split between what is conceived versus what is realized or actual. But, I would approach it as God must be slightly less than infinity and greater than everything else. However uncountable infinity would move the scale in a way that frustrates that conjecture. — Cheshire
Yeah, it fails but, first and foremost, because it is, at most, merely valid and not sound, only the idea of God (essence) is 'demonstrated' but not the existence of the idea's referent as "the proof" also sets out to do. And, as an 'a priori argument', the OA (Proslogion) is only 'true by definition', thus vacuous with respect to a posteriori facts of the matter. So again, my friend, I think your "potential infinity vs actual infinity" argument misses the forest for the trees (& what ↪fishfry said :smirk: ). — 180 Proof
No :sweat: ... read Popper or Peirce, my friend. No scientific entity is 'true by definition'. — 180 Proof
Note the underline bit, "...larger than any real or natural number". Sounds remarkably similar to "...no greater can be conceived" the main premise in the ontological argument. — TheMadFool
I don't think that Anselm was defining God as being "larger than any real or natural number." That would be a category error.
When Anselm talks about "a being than which no greater can be conceived" by "greater" he means something like "better" or "more awesome." — Michael
Mathematical infinity is the numerical representation of "that than which nothing greater can be conceived." — TheMadFool
Mathematizing Anselm's god is not just a trick-shot, it's germane to the ontological argument as the word "greater" in "...that than which nothing greater can be conceived" is inherently quantitative.
greater — Michael
Jane is a greater piano player than Jim. Jim is a greater friend than Sam. — Michael
is quantitative. If you don't believe me, in math "greater"' is symbolized as ">". Nothing more need be said. — TheMadFool
I can, given some leeway, easily mathematize that in terms of,
1. The length of time a person spends listening to either Jane's or Jim's piano pieces.
or
2. How large the audience is each of their performances
or
3. How many times their performances have been viewed on youtube
.
.
.
so on and so forth
premises of my argument that God can't exist! — TheMadFool
..no greater can be conceived." — TheMadFool
Anselm isn't using the mathematician's notion of "greater than" when he uses the phrase. You're equivocating.
I can, given some leeway, easily mathematize that in terms of,
1. The length of time a person spends listening to either Jane's or Jim's piano pieces.
or
2. How large the audience is each of their performances
or
3. How many times their performances have been viewed on youtube
.
.
.
so on and so forth
None of these are a measure of a person's piano-playing ability. — Michael
From where I'm sitting, it isn't necessary to invoke mathematics — EricH
To tell you the truth though, this entire discussion is ultimately about the existence of actual infinities! — TheMadFool
And what exactly does this mean? Any and every line segment is an actual infinity of points - each point having an address that can be written down. — tim wood
If God is less than anything he can't be "that than which nothing greater can be conceived." Infinity is the numerical representation of that than which nothing greater can be conceived (God). Ergo, since actual infinities don't exist, God too can't exist. — TheMadFool
If they are controversial, how are you justified in asserting, without supporting reasoning, that they don't exist? Or, conversely, if they don't exist, how can they be controversial?However, actual infinity is highly controversial.
Actual infinities don't exist. — TheMadFool
Attempt at a coherent question here. Maybe best to leave it simple. What is an infinite ordinal? — tim wood
How do you go about conceiving infinity? — Cheshire
Did we really though? I think we conceived the conditions for an infinity. I can conceive 10s or maybe hundreds and infer about millions and billions, but saying I'm thinking about the impossible whole of infinity seems reaching.So why would it be difficult to conceive infinity? We did it in grade school. — fishfry
Potential infinity is a matter that's settled. However, actual infinity is highly controversial.
My refutation of Anselm's argument:
Actual infinities don't exist.
Did we really though? I think we conceived the conditions for an infinity. I can conceive 10s or maybe hundreds and infer about millions and billions, but saying I'm thinking about the impossible whole of infinity seems reaching. — Cheshire
Yeah, it fails but, first and foremost, because it is, at most, merely valid and not sound, o
— 180 Proof
Relative to your belief system, please share what would make it sound (if you can) ?
1hOptions — 3017amen
Anyway, in layman's terms, unfortunately he's all bark and no bite. — 3017amen
I believe I may have found a problem with one of your premises though.
"Actual infinities don't exist," doesn't seem to follow from their being controversial. — Count Timothy von Icarus
The transcendental number pi is encoded in and manifest (instantiated) by every non-abstract, or concrete, circular object which makes it an uncountable actual infinity, no?There are no actual infinities. — TheMadFool
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.