This is a long post, but please bear with me.
I only glimpsed at the end of this thread, but I’ll take a look at the rest a little later (maybe tomorrow night. I was in the middle of writing a response for another thread, which will actually include my introduction, but this caught my eye and I decided to post this first. I’ll post a link to my other post when do end up posting it).
In response to Camron’s last post here (#314):
I believe the point emotel was attempting to make but failed to articulate (and if not, I’ll make that point) was that, Logically, if a subject’s definition is illogical, the domain is an empty set. Meaning that an illogical definition directly implies that the subject cannot exist. The confusion comes from no one taking that definition to it’s logical implications and consequences.
John L. Pollock, in his paper “Proving the Non-Existence of God”, begins with Anselm’s Ontological Arguments (the topic of your misunderstandings) and shows how God cannot possibly exist.
The most commonly quoted version of Anselm’s Ontological Argument basically goes like this:
- God is greater than anything that can be conceived.
- Existence is greater than non-existence.
- Therefore, God must exist.
However, Anselm later clarified this, with the introduction of the concept of “Necessary Existence” (originally put forth by the Persian philosopher Avicenna, but made famous here). Something with Necessary Existence must exist by virtue of it’s definition. When applied to God, this usually implies that God is a Necessary Existence because he created everything and is a part of everything. Therefore, nothing that exists could possibly exist without Him. Therefore He Exists Necessarily.
Necessity is represented by the Logic symbol ‘☐’ and is also used for various other things in Logic syntax. (If your fonts don’t display it, it’s an empty square. I’ll be using ‘]’ for the sake of simplicity.) Anselm’s Ontological Argument then became:
- God is greater than anything that can be conceived.
- Necessary Existence is greater than non-existence.
- Therefore, God must Necessarily Exist.
The reason for the change is that critics were quick to point out that, basically, mere existence is not necessarily a Perfection, meaning that there’s no actual argument being made. (Perfection, or “Absolute Perfection”, is a common characteristic attributed to God. Saying “God is greater than anything that can be conceived” is simply implying the characteristic of Absolute Perfection with different wording. This is a core component of Theologic debate.) However, if God exists necessarily, if nothing could possibly exist without God existing, that
would be a Perfection.
So looking at Anselm’s original argument we have:
note: ‘]’ = ‘☐’ (necessity), ‘>’ = ‘⊃’ (proper subset, NOT “greater than”)
(1) g = Df(the x such that Px);
(2) therefore, Pg;
(3) ](x)(Px > Ex);
(4) therefore, ](Pg > Eg);
(5) therefore, Eg.
If that’s all Greek to you, here’s an approximate translation:
(1) God is defined as that which is Perfect.
(2) Therefore, God is Perfect.
(3) By necessity, something must Exist to be Perfect.
(4) Therefore, by necessity, God’s Existence is required by God’s Perfection.
(5) Therefore, God Exists.
If that seems overly meticulous, it’s because formal Logic requires that everything be strictly defined, lest the entire proposition fail. When reading formal Logic proofs, it isn’t uncommon to see a page of boolean algebra explained over the next dozen pages, only to be summarized in a matter of a few simple sentences at the end.
Anselm’s revised argument looks like this:
(1) g = Df(the x such that Px);
(2) therefore, Pg;
(3) ](x)(Px > ]Ex);
(4) therefore, ](Pg > ]Eg);
(5) therefore, ]Eg.
Just take my approximate translation above and replace “Existence” in (3) and (4) with “Necessary Existence” and “Exists” in (5) with “Necessarily Exists”.
But, Mr. Pollock notes, there is a problem here. In both versions, Anselm relies on a basic logical fallacy. (2) does not directly follow from (1). The fallacy employed is that of “Begging the Question” (petitio principii), “in which the proposition to be proved is assumed implicitly or explicitly in one of the premises” (to quote Wikipedia, as I don’t have access to any real texts at the moment). What happened here is that Anselm skipped a step**-- and this is the mistake Camron makes without realizing–** Anselm gave a definition for g (God) but then automatically assumed g was not an empty set (that God exists, or more precisely, that something exists to satisfy the definition of God). This is a very major and very basic Logic “no-no”. To illustrate why, simply imagine that we define an object as something that simultaneously possesses a characteristic and lacks that same characteristic. Well, that doesn’t make sense, does it? Obviously that’s impossible and no such thing exists, which is why the strongest assertion you can make from any mere definition is “if something exists to satisfy this definition, then…”. After that, you must show that something does indeed exist that fits the definition.
This is a simple fix to implement, but it changes the argument entirely. We are forced to revise (2), which drastically changes (5):
(1) g = Df(the x such that Px);
(2) therefore, ](Eg > Pg);
(3) ](x)(Px > ]Ex);
(4) therefore, ](Pg > ]Eg);
(5) therefore, ](Eg > ]Eg).
(2) now translates somewhat literally to “Therefore, by necessity, God must Exist to be Perfect”, but when you read it, red flags go up because it is more simply interpreted as “Therefore,
if God Exists, he is Perfect”. (5) now translates to “Therefore, by necessity, a God that Exists must Exist Necessarily”. So we’ve gone from the conclusion of “God Exists” to “If God Exists, he Exists Necessarily”.
But it gets worse. The definition for God tells us that He is Perfect. We then show that Perfection requires not just Existence, but Necessary Existence. The “necessary” bit is a problem. We were forced to insert conditions where God might not exist. Being Necessary requires that there be no conceivable alternative cause. If something Necessarily Exists, there cannot, under any circumstances, be an alternative, no question of it’s existence. So our argument can be followed through thusly:
(6) (g = Df(the x such that Px)) → ](Eg > ]Eg);
Translation: “The definition of God explicitly implies that if God Exists, he Exists Necessarily.”
(7) ~(g = Df(the x such that Px) → Eg).
Translation: “The definition of God does not explicitly imply that God Exists.” (Remember the logical fallacy earlier.)
(8) ]Eg == ((g = Df(the x such that Px) → Eg)).
Translation: “Necessary Existence implies that something Exists by virtue of it’s constituent terms (it’s definition)”.
(9) ~]Eg.
Translation: “God does not Necessarily Exist.”
(In an attempt to avoid the inevitable confusion, please note the capitalization. This is VERY different from saying, in casual conversation, “not necessarily”. This is saying that God cannot Exist Necessarily. From this and (6), we can get a simpler “~Eg”, but it is a redundant step because it has already been defined in (6) that they are the same thing.
Often, when people are faced with this outcome, they regress to rejecting the “Necessary Existence” bit entirely, but as I already mentioned, simple Existence was long ago shown not be a Perfection, resulting in conclusion that basically says “there is no reason to suggest that God exists”. Then you still have to add in the existence conditional to fix the logical fallacy, so you get “If God exists, there’s reason to suggest He exists”, which goes nowhere fast. The Necessary Existence bit is akin to plugging a leak with your finger: you can’t just take out your finger without fixing the hole or you’ll end up back where you started.)
So, to summarize, if you define God to be “that which is greater than anything conceivable”, or any other definition that involves the Perfection characteristic, you are forced to realize that such a definition quickly comes to a Logical impasse and that, as defined, God cannot possibly exist.
[And then I had a little rant here about dismantling Faith, but I decided it would be best not to post it. I don’t mean to anger anybody, here, merely invoke a bit of rational discourse.]
issue just logic.