ParaclitosLogos

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Quote from: Maydole´s deductively valid formalization of Anselm´s Ontological Argument

 lexicon: 

Ux =df x is understood
Sy =df the concept of y exists-in-the-understanding
Ex =df x exists-in-reality
Gxy =df x is greater than y
Fxy =df x refers to y
 Dx =df x is a definite description
d =df the definite description “(ix) ~©(∃y)Gyx”
g =df (ix)~©(∃y)Gyx
P(Y) =df Y is a great-making property

©. . . =df it is conceivable that . . .

 Here then is our logical reconstruction of Anselm’s ontological argument:

A1 The definite description “that than which it is not conceivable for something to be greater” is understood. (Premise) (Dd & Ud )

 A2 “That than which it is not conceivable for something to be greater” refers to that than which it is not conceivable for something to be greater.
 (Premise) Fdg


A3 The concept of whatever a definite description that is understood refers to has existence-in-the-understanding.
(Premise) (x)(y)((Dx & Fxy & Ux) ⊃ Sy)

 A4 It is conceivable that something is greater than anything that lacks a great-making property that it conceivably has.
(Premise) (x1)(Y)[(P(Y)&∼Yx1&©Yx1)⊃©(∃x2)Gx2x1 ]

A5 Existence-in-reality is a great making property.
(Premise)P(E)

A6 Anything the concept of which has existence-in-the-understanding conceivably has existence-in-reality. (Premise) (x)(Sx ⊃ ©Ex)

A7 It is not conceivable that something is greater than that than which it is not conceivable for something to be greater.
(Premise) ∼©(∃y)Gyg

Therefore,

A8 That than which it is not conceivable for something to be greater exists-in-reality.

QED: Eg





« Last Edit: May 14, 2016, 11:58:17 pm by ontologicalme »

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grosso

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What does ix mean in your definition of d?

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ParaclitosLogos

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What does ix mean in your definition of d?

I couldn´t copy the correct symbol for definite description, it means definite description.
This/that (which) ....
« Last Edit: May 14, 2016, 11:58:57 pm by ontologicalme »

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Jenna Black

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Quote from: Maydole´s deductively valid formalization of Anselm´s Ontological Argument

 lexicon: 

Ux =df x is understood
Sy =df the concept of y exists-in-the-understanding
Ex =df x exists-in-reality
Gxy =df x is greater than y
Fxy =df x refers to y
 Dx =df x is a definite description
d =df the definite description “(ix) ~©(∃y)Gyx”
g =df (ix)~©(∃y)Gyx
P(Y) =df Y is a great-making property

©. . . =df it is conceivable that . . .

 Here then is our logical reconstruction of Anselm’s ontological argument:

A1 The definite description “that than which it is not conceivable for something to be greater” is understood. (Premise) (Dd & Ud )

 A2 “That than which it is not conceivable for something to be greater” refers to that than which it is not conceivable for something to be greater.
 (Premise) Fdg


A3 The concept of whatever a definite description that is understood refers to has existence-in-the-understanding.
(Premise) (x)(y)((Dx & Fxy & Ux) ⊃ Sy)

 A4 It is conceivable that something is greater than anything that lacks a great-making property that it conceivably has.
(Premise) (x1)(Y)[(P(Y)&∼Yx1&©Yx1)⊃©(∃x2)Gx2x1 ]

A5 Existence-in-reality is a great making property.
(Premise)P(E)

A6 Anything the concept of which has existence-in-the-understanding conceivably has existence-in-reality. (Premise) (x)(Sx ⊃ ©Ex)

A7 It is not conceivable that something is greater than that than which it is not conceivable for something to be greater.
(Premise) ∼©(∃y)Gyg

Therefore,

A8 That than which it is not conceivable for something to be greater exists-in-reality.

QED: Eg



I agree. JB
Philippians 4:8 Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue, and if there be any praise, think on these things.

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grosso

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What does ix mean in your definition of d?

I couldn´t copy the correct symbol for definite description, it means definite description.
This/that (which) ....

Cool. I'm not familiar with the symbol. Is it discussed online somewhere that you can link me to it?

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ParaclitosLogos

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What does ix mean in your definition of d?

I couldn´t copy the correct symbol for definite description, it means definite description.
This/that (which) ....

Cool. I'm not familiar with the symbol. Is it discussed online somewhere that you can link me to it?

Found this, looks ok

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grosso

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Thanks. I get what you mean with it now. I hate to be pedantic but is it equivalent to (∃x!)?

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ParaclitosLogos

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Thanks. I get what you mean with it now. I hate to be pedantic but is it equivalent to (∃x!)?

Logically, yes, gramatically, no.

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grosso

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Got it. I'm tempted to ask why not grammatically, but I don't want to derail.

One sticking point for me is A5. How do we determine whether we should treat an existence claim as a quantified proposition or as a property?

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ParaclitosLogos

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Some additional info on Anselm´s metaphysical world view.


St. Anselm plausibly was a ultra realist (Neo-Platonist)

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grosso

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I'm hoping there's an easier way to resolve the issue than to open the universals can of worms.

Have you seen Alston's The Ontological Argument Revisited? He discusses the issue in that paper.

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ParaclitosLogos

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I'm hoping there's an easier way to resolve the issue than to open the universals can of worms.

Have you seen Alston's The Ontological Argument Revisited? He discusses the issue in that paper.

My objective is more humble. It seems to me, that if Anselm was assuming a certain metaphysics, and, under such metaphysics the argument simply works just fine, he deserves the fair treatment of his reasonable, at the time, assumptions instead of the usual disdain.

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Language-Gamer

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Yeah but then I can prove unicorns exist! Anselm's refuted!
I told her all about how we been livin' a lie
And that they love to see us all go to prison or die
Like, "Baby, look at how they show us on the TV screen"
But all she ever want me to do is unzip her jeans

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Jenna Black

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Yeah but then I can prove unicorns exist! Anselm's refuted!
No, you can't and you know it.
Philippians 4:8 Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue, and if there be any praise, think on these things.

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grosso

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I'm hoping there's an easier way to resolve the issue than to open the universals can of worms.

Have you seen Alston's The Ontological Argument Revisited? He discusses the issue in that paper.

My objective is more humble. It seems to me, that if Anselm was assuming a certain metaphysics, and, under such metaphysics the argument simply works just fine, he deserves the fair treatment of his reasonable, at the time, assumptions instead of the usual disdain.
That's a good point.

It's been too long since I've looked at Anselm. Philosophy 101 maybe.

What are the standard objections to him? Gaunilos island or is there more?