Cerpin Taxt
Lifer
- Feb 23, 2005
- 11,943
- 541
- 126
No, it isn't.
Finally, we defined God (g) to be the conceivable thing such that
nothing greater is conceivable:
g =df ıx!1
The first two non-logical premises
needed are:Connectedness of Greater Than: #x#y(Gxy % Gyx % x=y)
Premise 1 : !x(Cx & ¬!y(Gyx & Cy))
Lemma 2 asserts that if there is a conceivable thing such that nothing greater can be conceived, then there is a unique conceivable thing such that nothing greater can be conceived. The proof of Lemma 2 was provided in our paper.2 As we shall see below, Lemma 2 helps to justify the introduction of the description that (conceivable thing) than which nothing greater is conceivable (ıx!1) into the ontological argument. The final non-logical premise needed in Anselms argument is:
Premise 2: ¬E!ıx!1 $ !y(Gyıx!1 & Cy)
Premise 2 asserts: if that than which nothing greater is conceivable fails to exist, something greater than it is conceivable.
With these premises, theorems, and definitions we then formulated Anselms ontological argument as follows:
1.!x!1 Premise 1
2. !!x!1 from (1), by Lemma 2
3. !y(y=ıx!1) from (2), by Description Thm 1
4. Cıx!1 & ¬!y(Gyıx!1 & Cy) from(3),byDescriptionThm2
5. ¬E!ıx!1 Assumption, for Reductio
6.!y(Gyıx!1 & Cy) from (5), by Premise 2
7. ¬!y(Gyıx!1 & Cy) from (4), by &E
8. E!ıx!1 from (5), (6), and (7), by Reductio
9.E!g from (8), by the definition of g
Note that, strictly speaking, we need not have used free logic to reconstruct the argument because we establish at line (3) that our descriptionıx!1 is well-defined. Its logic is therefore classical, and the ontological argument proceeds along classical lines.3
Clearly then, the ontological argument directly rests on the logical
theorems Description Theorems 1 and 2 and on the non-logical premises
Premise 1, Lemma 2, and Premise 2. It indirectly rests on the Description
Axiom (which yields both Description Theorem 1 and Lemma 1, the latter
yielding Description Theorem 2), and on the connectedness of thegreater
than relation (which together with Premise 1, yields Lemma 2).
When we input the above representations of the logical and non-logicalpremises to prover9, we thought it would proveGods existence from the
following non-logical premises: the definition ofnone greater, Premise 1,
Lemma 2, Premise 2, and the definition of God (with the connectedness
of greater than being used in a separate proof of Lemma 2). However,
we were surprised to find that prover9 did not require all of these nonlogical elements.
prover9easily discovers a proof of the claim that God exists from
the above representations. However, much to our surprise, the proof it
discovered used only a few of the premises we formulated above. prover9
reports that it used only the following premises in the proof:all F (Relation1(F) -> ((exists x (Object(x) & Is_the(x,F))) ->
(all y (Object(y) -> (Is_the(y,F) -> Ex1(F,y)))))).all x all F (Is_the(x,F) -> (Relation1(F) & Object(x))).
all x (Object(x) -> (Ex1(none_greater,x) <->
(Ex1(conceivable,x) & -(exists y (Object(y) &
Ex2(greater_than,y,x) & Ex1(conceivable,y)))))).
all x (Object(x) -> ((Is_the(x,none_greater) & -Ex1(e,x)) ->
(exists y (Object(y) & Ex2(greater_than,y,x) &
Ex1(conceivable,y))))).
Is_the(g,none_greater).As you can see by inspection, the first of these is Description Theorem 2,
the second is the sorting principle onIs the, the third is the definition
of none greater, the fourth is Premise 2, and the last is the definition
of g. prover9 did not need to use Description Theorem 1, Premise 1,
or Lemma 2. Moreover, since it didnt use Lemma 2, it didnt require
the connectedness of greater than. Indeed, prover9 didnt need the full
content of the premises that it did use in its proof; each of these premises gets turned into multiple clauses and only some of the resulting clauses are used in the proof.
The resulting simplified ontological argument for the existence of God is:
1.¬E!ıx!1 Assumption, for Reductio
2.!y(Gyıx!1 & Cy) from (1), by Premise 2 and MP
3. Ghıx!1 & Ch from (2), by !E, h arbitrary
4. Ghıx!1 from (3), by &E
5. !y(y=ıx!1) from (4), by Desc. Thm. 3
6. Cıx!1 & ¬!y(Gyıx!1 & Cy) from(5),byDesc.Thm.2
7. ¬!y(Gyıx!1 & Cy) from (6), by &E
8. E!ıx!1 from (1), (2), (7), by Reductio
9. E!g from (8), by the definition of g
Thus, we have a valid argument for the existence of God that doesnt
require that any conditions be placed on thegreater than relation, and
doesnt require that we assert Premise 1 or establish Lemma 2 in order
to justify the introduction of the definite description ıx!1. Instead, all
the reasoning about the description takes place inside a Reductio assumption, except at the very end, after it is established that the description is well-defined. The question of the soundness of the ontological argument now reduces to the question of the truth of Premise 2!
In the case in which the description ıx!1 denotes and the object it denotes
exists, the antecedent of Premise 2 is false, making Premise 2 true. But
the defender of the ontological argument can take no comfort from such
an observation, since it defends Premise 2 by using the conclusion of the
ontological argument. That is, if she uses the existence of the conceivable
thing than which no greater thing is conceivable to prove Premise 2, she
is guilty of circular reasoning. She needs an independent argument to
support the premise. Thus, arguments (1) and (2) above show that the defender of the ontological argument needs independent support for two claims: that the definite description denotes and that Premise 2 is true.
I read all of that. It doesn't answer my question. I'll repeat it:
Greatest what?
I will repost the answer again.
Finally, we defined God (
g) to be the conceivable thing such that
nothing greater is conceivable:
g =df ıx!1
1.) Iff Mary is a woman, then Einstein was president of the United StatesThis shows that it is not illogical to assert God exists. Independant support is needed, yes, but that does not make it illogical.
My question remains unanswered.
1.) Iff Mary is a woman, then Einstein was president of the United States
2.) Mary is a woman.
C.) Therefore, Einstein was President of the United States.
Is it logical or illogical to assert that Einstein was President of the United States?
Cerpin Taxt: Greatest what?It was answered, you simply do not understand the answer. It is quite clear, which makes it strange you do not understand it.
I have no problem understanding your responses. The problem is that your responses are not answers.Which words do you not understand, I can post definitions to them. Maybe it is a string of words you do not understand, post the string and I will explain it to you.
Irrelevant. If you insist on being obtuse I can reformulate another syllogism.Premise one is false.
Which rule of logic does it violate?Therefor your deduction, C, is illogical.
Cerpin Taxt: Greatest what?
cybrsage: The greatest.
Cerpin Taxt: Greatest what?
cybrsage: I answered you.
Uh huh.
I have no problem understanding your responses. The problem is that your responses are not answers.
Irrelevant. If you insist on being obtuse I can reformulate another syllogism.
1.) Iff squares have four corners, then invisible space aliens will destroy the planet tomorrow.
2.) Squares have four corners.
C.) Therefore, invisible space aliens will destroy the planet tomorrow.
Is is logical or illogical to assert that invisible space aliens will destroy the planet tomorrow?
Which rule of logic does it violate?
You do not know that, but you are invited to take a stab at proving it.Premise one is still false.
The rule where you say something which is false is true. Logic does not allow lying.
You do not know that, but you are invited to take a stab at proving it.
Still as disingenuous as ever. Ok, fine, wonderful person, how about this?
1.) If P -> Q
2.) P
C.) Therefore Q
Is it logical or illogical to assert Q?
1.) A being that has won the Tour de France is greater than a being that has not won the Tour de France.God is the greatest conceivable being.
The point, which you are either too inept or too obtuse to acknowledge, is that "greatness" is not an objective property, yet it is treated as one in the argument.There is a point where you have to simply say you cannot understand something for whatever reason and move on with your life with the knowledge that others do understand it. Sometimes that has to be good enough. I am sure you do this already for a great host of things (everyone does), simply add one more item to the list.
You claimed the premise was false. It is your onus to prove your claim. Premises are not claims. They are simply premises.The onus on proving it true is on the person making the claim. You made the claim.
Do you know if the premises of the argument in the paper are true or false?It depends, is premise 1 true of false? Pretending it does not matter is silly.
1.) A being that has won the Tour de France is greater than a being that has not won the Tour de France.
2.) Lance Armstrong has won the Tour de France.
3.) God has not won the Tour de France.
4.) Lance Armstrong is greater than God
5.) God is not the greatest conceivable being.
QED
The point, which you are either too inept or too obtuse to acknowledge, is that "greatness" is not an objective property, yet it is treated as one in the argument.
You claimed the premise was false. It is your onus to prove your claim. Premises are not claims. They are simply premises.
I'll repeat my earlier question which you ignored:
Which rule(s) of logic have been violated?
You must define the question prior to being able to answer the question, yes? I assume you said yes, since no is ludicrous.
Moving on, since the study was specific to the Abramamic gods, we would need to use the definition of said gods. It would be quite stupid to use an incorrect definition when discussion a specific type of god.
The first line is simply providing the subject which is being discussed. Without it, there can be no discussion.
Buddhism, at least Zen Buddhism is not a faith, as I understand it. When you say this about faith I think you are just saying that you would not identify yourself as an adherent. However, Zen Buddhism is simply a means to achieving wisdom and personal liberation, the goal being release from the bondage of illusory ideas and life styles (the quest being satori, enlightenment). Thus, there's no ideology associated with it whatsoever. There is nothing to worship. Here's an interesting quote from Albert Einstein concerning Buddhism:I've always had trouble as to what term to use to describe my religious belief, but I found this on Wikipedia and it's extremely close:
https://en.wikipedia.org/wiki/Ietsism
I do have a fondness for Buddhist teachings in regards to my personal conduct, but I've never considered it my faith.
Buddhism, at least Zen Buddhism is not a faith, as I understand it. When you say this about faith I think you are just saying that you would not identify yourself as an adherent. However, Zen Buddhism is simply a means to achieving wisdom and personal liberation, the goal being release from the bondage of illusory ideas and life styles (the quest being satori, enlightenment). Thus, there's no ideology associated with it whatsoever. There is nothing to worship. Here's an interesting quote from Albert Einstein concerning Buddhism:
Buddhism has the characteristics of what would be expected in a cosmic religion for the future: It transcends a personal God, avoids dogmas and theology; it covers both the natural and the spiritual, and it is based on a religious sense aspiring from the experience of all things, natural and spiritual, as a meaningful unity.
You claimed the premise was false. It is your onus to prove your claim. Premises are not claims. They are simply premises.
Do you know if the premises of the argument in the paper are true or false?
I'll repeat my earlier question which you ignored:
Which rule(s) of logic have been violated?
Sage, I agree that you have to define something, but the problem is that they are using the definition as a truth instead of an assertion. That proof essentially just proves that the concept of what God could be is not invalid.
Don't even bother, no matter what you say he won't understand.
Oh no, are you one of those "I claim something is true and if you disagree YOU have to prove me wrong...I am not required to support my claim" type of people, are you?