See what Mr. Kant  says! Surely you will listen to him if not me! (And, frankly, I think you already know what Mr. Kant says...)

[Quotations from Immanuel Kant, Critique of Pure Reason, Transcendental Doctrine of Method, Chapter I. The Discipline of Pure Reason, SECTION IV. The Discipline of Pure Reason in Relation to Proofs (@ Wikisource)  - Adelphe #381]

…to which my reply was …

I must admit that you have done a good research, and you have hit me were it hurts, because you know that I am a great admirer of Immanuel Kant.

I also admit that the in section of his Critique of Pure Reason, from where you have taken your quotations, "The Discipline of Pure Reason in Relation to Proofs", Kant explains why

[FONT=Georgia]“ ... all transcendental proofs must never be apagogic or indirect, but always ostensive or direct. (I. Kant)”

This argument therefore is serious. In fact it is too serious to confront it here, in few lines. I will therefore confront it separately.

I promise I will, as the Fair Combatant Warrior that I am. [MdS #396]

[/FONT]
Over the ensuing months, and even recently, Adelphe has not missed a single opportunity for reminding me of my promise. (which is perfectly fair)
 
  It was my intention to make this an occasion for examining in depth the motivation for Kant’s objection to the recourse to apagoge (bka reductio ad absurdum, from the Latin equivalent expression), a logical procedure whose perfect philosophical character is confirmed by its being often used by Aristotle, and the perfect validity of which is confirmed by its being often used Euclid in demonstrating many theorems of his magnum opus,Elements, “the most successful textbook in the history of mathematics.”
 
  But, while this would be very interesting from a philosophical POV, it would take us to far from the original purpose of the thread which, let’s recall it here was and is to prove what to me is a self-evident set of axioms, that is …

Axioms of God’s Foreknowledge vs. Human Freedom

[1] God’s total foreknowledge is incompatible with genuine human freedom.

[2] God is with us at all times but does NOT know in advance what we'll think or do.

  This I have done by apagoge, viz. by proving that the opposite of [1], that is …

[3] God’s total foreknowledge is compatible with genuine human freedom.

… leads to an absurdity, that is (having assumed, as Adelphe does, God’s total Omniscience) the the affirmation AND to the denial of God's total Omniscience.
 
  I have therefore decided to ... ... and to provide a syllogistic demonstration of [1].
 
  I have already anticipated that I may not proceed to do this without setting a condition. I confirm that I intend to set a condition, which is the following.
 
  Herebelow is the demonstration per absurdum of [1], viz. of the incompatibility of God’s total foreknowledge with genuine human freedom, which I have proposed in many “variants”, and was already essentially present at the end of post #2.

(D0) “On day D+0, Ambrose Bierce knows that the following day D+1, as on every week-day, he will get the train from Albany to New York”

(D1) “On day D+1, Ambrose freely decides not to go from Albany to New York, but to go to Saratoga Springs instead”. (see map)

(D2) If God, at day D (or even from eternity, for that matter), knew already that Ambrose, at day D+1 would have gone to Saratoga Springs, the freedom of Ambrose’s  decision (apparently freely taken on day D+1), is a pure delusion.

(D3) If God, at day D, did not know that Ambrose, at day D+1 would have gone to Saratoga   Springs, then God’s omniscience is NOT total: the definition of His omniscience is NOT total BUT inherent, viz. limited.
 
  Conclusion:
.
[LIST]
[*]according to (D2) God is Totally Omniscient; [/LIST][LIST]
[*]according to (D3) God is NOT Totally Omniscient.[/LIST].
  Quod Est Absurdum

  I will ONLY proceed to provide a syllogistic demonstration of [1] (God’s total foreknowledge is incompatible with genuine human freedom) on condition that Adelphe affirms and confirms that, although, under the “high patronage” of Professor Immanuel Kant she may not like a demonstration of [1] by apagoge (reductio ad absurdum) nevertheless …

  “Adelphe recognizes that the demonstration per absurdum of [1] is perfectly clear, consistent and compelling”
 
  No more (bur also no less) is required by Miguel_de_Servet to proceed as promised to a syllogistic demonstration of [1]. :cool:
 
  RSVP

See what Mr. Kant  says! Surely you will listen to him if not me! (And, frankly, I think you already know what Mr. Kant says...)

[Quotations from Immanuel Kant, Critique of Pure Reason, Transcendental Doctrine of Method, Chapter I. The Discipline of Pure Reason, SECTION IV. The Discipline of Pure Reason in Relation to Proofs (@ Wikisource)  - Adelphe #381]

…to which my reply was …

I must admit that you have done a good research, and you have hit me were it hurts, because you know that I am a great admirer of Immanuel Kant.

I also admit that the in section of his Critique of Pure Reason, from where you have taken your quotations, "The Discipline of Pure Reason in Relation to Proofs", Kant explains why

[FONT=Georgia]“ ... all transcendental proofs must never be apagogic or indirect, but always ostensive or direct. (I. Kant)”

This argument therefore is serious. In fact it is too serious to confront it here, in few lines. I will therefore confront it separately.

I promise I will, as the Fair Combatant Warrior that I am. [MdS #396]

[/FONT]
Over the ensuing months, and even recently, Adelphe has not missed a single opportunity for reminding me of my promise. (which is perfectly fair)
 
  It was my intention to make this an occasion for examining in depth the motivation for Kant’s objection to the recourse to apagoge (bka reductio ad absurdum, from the Latin equivalent expression), a logical procedure whose perfect philosophical character is confirmed by its being often used by Aristotle, and the perfect validity of which is confirmed by its being often used Euclid in demonstrating many theorems of his magnum opus,Elements, “the most successful textbook in the history of mathematics.”
 
  But, while this would be very interesting from a philosophical POV, it would take us to far from the original purpose of the thread which, let’s recall it here was and is to prove what to me is a self-evident set of axioms, that is …

Axioms of God’s Foreknowledge vs. Human Freedom

[1] God’s total foreknowledge is incompatible with genuine human freedom.

[2] God is with us at all times but does NOT know in advance what we'll think or do.

  This I have done by apagoge, viz. by proving that the opposite of [1], that is …

[3] God’s total foreknowledge is compatible with genuine human freedom.

… leads to an absurdity, that is (having assumed, as Adelphe does, God’s total Omniscience) the the affirmation AND to the denial of God's total Omniscience.
 
  I have therefore decided to ... ... and to provide a syllogistic demonstration of [1].
 
  I have already anticipated that I may not proceed to do this without setting a condition. I confirm that I intend to set a condition, which is the following.
 
  Herebelow is the demonstration per absurdum of [1], viz. of the incompatibility of God’s total foreknowledge with genuine human freedom, which I have proposed in many “variants”, and was already essentially present at the end of post #2.

(D0) “On day D+0, Ambrose Bierce knows that the following day D+1, as on every week-day, he will get the train from Albany to New York”

(D1) “On day D+1, Ambrose freely decides not to go from Albany to New York, but to go to Saratoga Springs instead”. (see map)

(D2) If God, at day D (or even from eternity, for that matter), knew already that Ambrose, at day D+1 would have gone to Saratoga Springs, the freedom of Ambrose’s  decision (apparently freely taken on day D+1), is a pure delusion.

(D3) If God, at day D, did not know that Ambrose, at day D+1 would have gone to Saratoga   Springs, then God’s omniscience is NOT total: the definition of His omniscience is NOT total BUT inherent, viz. limited.
 
  Conclusion:
.
[LIST]
[*]according to (D2) God is Totally Omniscient; [/LIST][LIST]
[*]according to (D3) God is NOT Totally Omniscient.[/LIST].
  Quod Est Absurdum

  I will ONLY proceed to provide a syllogistic demonstration of [1] (God’s total foreknowledge is incompatible with genuine human freedom) on condition that Adelphe affirms and confirms that, although, under the “high patronage” of Professor Immanuel Kant she may not like a demonstration of [1] by apagoge (reductio ad absurdum) nevertheless …

  “Adelphe recognizes that the demonstration per absurdum of [1] is perfectly clear, consistent and compelling”
 
  No more (bur also no less) is required by Miguel_de_Servet to proceed as promised to a syllogistic demonstration of [1]. :cool:
 
  RSVP

Miguel_de_Servet wrote:

This thread is started in response to multiple … solicitations by Adelphe to deliver on a promise that I made, as far back as 07-06-2008, after Adelphe’s initial prompting …

…to which my reply was …
Over the ensuing months, and even recently, Adelphe has not missed a single opportunity for reminding me of my promise. (which is perfectly fair)

It was my intention to make this an occasion for examining in depth the motivation for Kant’s objection to the recourse to apagoge (bka reductio ad absurdum, from the Latin equivalent expression), a logical procedure whose perfect philosophical character is confirmed by its being often used by Aristotle, and the perfect validity of which is confirmed by its being often used Euclid in demonstrating many theorems of his magnum opus,Elements, “the most successful textbook in the history of mathematics.”

But, while this would be very interesting from a philosophical POV, it would take us to far from the original purpose of the thread which, let’s recall it here was and is to prove what to me is a self-evident set of axioms, that is …
This I have done by apagoge, viz. by proving that the opposite of [1], that is …… leads to an absurdity, that is (having assumed, as Adelphe does, God’s total Omniscience) the the affirmation AND to the denial of God's total Omniscience.

I have therefore decided to ... ... and to provide a syllogistic demonstration of [1].

I have already anticipated that I may not proceed to do this without setting a condition. I confirm that I intend to set a condition, which is the following.

Herebelow is the demonstration per absurdum of [1], viz. of the incompatibility of God’s total foreknowledge with genuine human freedom, which I have proposed in many “variants”, and was already essentially present at the end of post #2. I will ONLY proceed to provide a syllogistic demonstration of [1] (God’s total foreknowledge is incompatible with genuine human freedom) on condition that Adelphe affirms and confirms that, although, under the “high patronage” of Professor Immanuel Kant she may not like a demonstration of [1] by apagoge (reductio ad absurdum) nevertheless …

“Adelphe recognizes that the demonstration per absurdum of [1] is perfectly clear, consistent and compelling”

No more (bur also no less) is required by Miguel_de_Servet to proceed as promised to a syllogistic demonstration of [1]. :cool:

RSVP

Mario,

So this is...it?

This is what I have been waiting for?

The resurrection of your lame Ambrose that we already covered in several of the 800+ some posts?

Your argument is circular.

This is what is under discussion:

(D2) If God, at day D (or even from eternity, for that matter), knew already that Ambrose, at day D+1 would have gone to Saratoga Springs, the freedom of Ambrose’s decision (apparently freely taken on day D+1), is a pure delusion.

:o

Adelphe #4 wrote:

So this is...it?

This is what I have been waiting for?

The resurrection of your lame Ambrose that we already covered in several of the 800+ some posts?

Your argument is circular.

This is what is under discussion:

(D2) If God, at day D (or even from eternity, for that matter), knew already that Ambrose, at day D+1 would have gone to Saratoga Springs, the freedom of Ambrose’s decision (apparently freely taken on day D+1), is a pure delusion.

If you read coolly, calmly and collectedly, I am not saying that what I have presented at the OP is something new. I said clearly that what I have presented is ...

“the demonstration per absurdum of ... the incompatibility of God’s total foreknowledge with genuine human freedom, which I have proposed in many “variants”, and was already essentially present at the end of post #2”

What is new is that I have made "synoptically explicit" the absurdity of the the opposite affirmation, viz:

“[3] God’s total foreknowledge is compatible with genuine human freedom.”

Now, you, under the “high patronage” of Professor ... ... may not like a demonstration of [1] by apagoge (reductio ad absurdum), nevertheless it is a perfectly valid demonstration, and, if you clumsily call it "circular", you simply have no clue what "circular reasoning" (bka "begging the question") is that is, viz. "'begging the question' ... refers to an argument where the premises are as questionable as the conclusion."

Where, pray tell, would be the "questionable premises"? Certainly (D0) and (D1) are NOT "questionable". :o

Adelphe #5 wrote:

... hopefully Mario will come up with something better than presenting old news--something that's already been argued that lead to the particular request he referenced in the OP.

What can be concluded here with this piffle?  He is between a rock and a hard place.

I am certainly NOT in the ... uncomfortable position you would love to see me in.

You, not me, my dear Adelphe, are ...

Once again, being evident that  ...
.[LIST]
[*] my demonstration per absurdum is perfectly legitimate;[/LIST].[LIST]
[*] your rejection thereof is ONLY a matter of dislike, backed up with a "big name";[/LIST].
... I am most adamant  that I will proceed to provide a syllogistic demonstration of [1] (God’s total foreknowledge is incompatible with genuine human freedom) ONLY on condition that Adelphe affirms and confirms that, although, under the “high patronage” of a. m. Professor Immanuel Kant she may not like a demonstration of [1] by apagoge (reductio ad absurdum) nevertheless …

  “Adelphe recognizes that the demonstration per absurdum of [1] is perfectly clear, consistent and compelling”
 
  No more (but also no less) is required by Miguel_de_Servet to proceed as promised to a syllogistic demonstration of [1]. :cool:
 
  RSVP

Mario

Adelphe wrote:

I gave you the nature of the circularity in my post #4.

Again:

D2) If God, at day D (or even from eternity, for that matter), knew already that Ambrose, at day D+1 would have gone to Saratoga Springs, the freedom of Ambrose’s decision (apparently freely taken on day D+1), is a pure delusion.

Let's break it down to its essence, shall we?:
.[LIST]
[*] If God knew[/LIST][LIST]
[*] Then Ambrose wasn't free[/LIST].
That is precisely what you are (trying) to prove.

This is no reductio ad absurdum argument.

This is no argument at all.

[Patiently, as to an exceptionally stubborn and obtuse child...]

We both know (we ALL know ...) how much you love to indulge in preliminaries, rather than going for a good ... syllogism (:p) ... so we can stay here for another 800 posts, AFAIAC. :cool:

Just answer this simple question, if you please: "Did Ambrose still have, on day D+1, the freedom to decide to go to New York, instead of going to Saratoga Springs? YES OR NO?

Mario