Godel's Ontological Theorem.

[LiamOS]

This thread is both for discussion of Godel's Ontological Theorem and a continuation of a debate which was in another thread.

Godel's Ontological Argument is expressed symbolically as:

For those unfamiliar with modal-logic, there is an article on the general Ontological Argument here.


With respect to the theorem's axioms, WikiPedia tells us the following:

We first assume the following axiom:

Axiom 1: It is possible to single out positive properties from among all properties. Gdel defines a positive property rather vaguely: "Positive means positive in the moral aesthetic sense (independently of the accidental structure of the world)... It may also mean pure attribution as opposed to privation (or containing privation)." (Gdel 1995)

We then assume that the following three conditions hold for all positive properties (which can be summarized by saying "the positive properties form a principal ultrafilter"):

Axiom 2: If P is positive and P entails Q, then Q is positive.
Axiom 3: If P₁, P₂, P₃, ..., P_n are positive properties, then the property (P₁ AND P₂ AND P₃ ... AND P_n) is positive as well.
Axiom 4: If P is a property, then either P or its negation is positive, but not both.

Finally, we assume:

Axiom 5: Necessary existence is a positive property (Pos(NE)). This mirrors the key assumption in Anselm's argument.

Now we define a new property G: if x is an object in some possible world, then G(x) is true if and only if P(x) is true in that same world for all positive properties P. G is called the "God-like" property. An object x that has the God-like property is called God.

For debate:
-Is the Ontological Theorem logically valid?
-Are all the axioms of the theorem valid?
-Can the argument hold without the axioms being valid, if they are not necessarily so?

[McCulloch]

...Unless Trinitarians accept polytheism, or that God is a set, they must abandon logic.

According to Christian tradition, the Triune God is one Divinity comprised of three persons. This claim sounds strange to us, but no more strange than a two-dimensional "flatlander" would find in her attempt to grasp the mysteries of a "cube" consisting of multiple two-dimensional "squares."

The parallel is not valid. While higher order spacial dimensions are difficult to imagine, we do know how the three evident spacial dimensions work and we can, and others have, do the mathematics and the logic with regard to Extra Dimensions. It may seem strange to us, as you point out. But it strictly follows all of the rules of logic and mathematics.

Trinity, on the other hand, in its orthodox expression, is not merely strange, it defies logic. Tritheism is explicitly denied.

[Goat]

.
When one resorts to philosophy and metaphysics to "prove" their point, there must be little actual evidence to support what they say -- only mental constructs or mental gymnastics. Philosophy and metaphysics don't prove anything except what one THINKS about a topic (i.e., opinion).

This is not to say that there is no place for philosophy, but rather to say that it emphasizes conceptualization rather than evidence. The term "philosophy" is defined as: a quest for truth through logical reasoning rather than factual observation.

Bold added for emphasis

One can "logically reason" about fairies, leprechauns and goblins (or how many angels can dance on the head / point of a pin) -- with absolutely no tie to reality and no indication that such things exist.

The scientific method in large part stems from philosophy so if you say that metaphysics is assumption, then to be consistent, so is the metaphysics that scientists assume every day, naturalism and materialism. Scientific observations and logical reasoning aren't necessarily mutually exclusive. I mean they can be but I usually find scientific observations in the premises of logical arguments, especially when it comes to inductive and deductive reasoning. I would be reluctant to use an argument that's based 'solely' on metaphysics/ontology to conclusively establish the reality of some matter (not that I'd outrule it).

While there is a philosphy of science, science is not philosophy. To try to equate the two is trying two is the logical fallacy of equivocation. The item that distinguishes the two is the little detail known as 'tangible results'. Science attempts to pass the 'show me' test... by making predictions , and designing experiments that other people can do to confirm the predictions of the results.

It the case of Godel's proof, if you wanted to simplify the argument to terms that the average person can understand it says 'If god exists, then it is logical that God can exist'.

Now, that isn't any kind of proof, but just a tautology that assumes that God exists.
What can't be done using these word games, or in the case of Godel's mathematical symbols, is show that 'God exists'.

[EduChris]

...Trinity, ... in its orthodox expression, is not merely strange, it defies logic...

Isn't that exactly what Einstein first said about Quantum theory?

[Cathar1950]

...Trinity, ... in its orthodox expression, is not merely strange, it defies logic...

Isn't that exactly what Einstein first said about Quantum theory?

No, because they don't mean the same things and QT is not about the the mystery of the Trinity which was used to explain how Jesus was fully God (of the same substance) and fully human. Because this was a logical impossibility as it would make some one 200% they decided it was three Masks (the meaning of persons) and one substance pretty much ignoring what it means to be human.

Except you have limited some arbitrary positive properties to three there is no connection what so ever to the Trinity.

Existence, Differentiation, and Relationality????
Do relationships exist?
Does Differentiation exist?

[LiamOS]

It's what a lot of people said.

Subsequently, I've determined that 'logic' as a philosopher or theologian might know it cannot be considered fundamental to the universe.

[EduChris]

...I've determined that 'logic' as a philosopher or theologian might know it cannot be considered fundamental to the universe.

Is that your opinion, or do you have logical arguments to back that up?

[LiamOS]

It's not my claim that it isn't. but I claim that it cannot be held to be without sufficient evidence.

"A piece of matter has a position at any given time."
Is a pretty logical statement in conventional terms, but appears to break down.

"Everything that begins to exist has a cause."
This is another, more common, logical statement. I cannot hold this to be true, given the nature of particle interactions, though.

[EduChris]

It's not my claim that it isn't. but I claim that it cannot be held to be without sufficient evidence.

"A piece of matter has a position at any given time."
Is a pretty logical statement in conventional terms, but appears to break down.

"Everything that begins to exist has a cause."
This is another, more common, logical statement. I cannot hold this to be true, given the nature of particle interactions, though.

I grant you that all human knowledge breaks down eventually--even the scientist's knowledge.

But are you prepared to say that we cannot reasonably conclude that if "X is not Y" is true, then "X is Y" cannot also be true in the same sense at the same time?

[Cathar1950]

It's not my claim that it isn't. but I claim that it cannot be held to be without sufficient evidence.

"A piece of matter has a position at any given time."
Is a pretty logical statement in conventional terms, but appears to break down.

"Everything that begins to exist has a cause."
This is another, more common, logical statement. I cannot hold this to be true, given the nature of particle interactions, though.

Even the language is misleading. Have you ever seen anything "begin to exist"?
Conservation of energy?

[McCulloch]

...Trinity, ... in its orthodox expression, is not merely strange, it defies logic...

Isn't that exactly what Einstein first said about Quantum theory?

Yes, but the consensus of physicists is that quantum theory is correct. Why? Evidence and the application of logic and mathematics. Yes, quantum theory is strange and counter-intuitive, but ultimately it does not defy logic.

Can the same be said for Trinity? No, in order to accept Trinity, you must abandon logic.