Author Topic: Does St. Anselm's Ontological Argument work with modern modal logic?  (Read 416 times)

Offline Xavier

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In recent decades, there has been a revival of interest in Archbishop St. Anselm of Canterbury's Ontological Argument: https://en.wikipedia.org/wiki/Ontological_argument It is usually formulated using modal premises on possibility and necessity.

1. The existence of a Necessarily Existing Being is possible.
2. If the existence of a Necessarily Existing Being is possible, a Necessarily Existing Being exists in some possible world.
3. But by nature of Necessary Existence, if a Necessarily Existing Being exists in some possible world, He exists in every possible world.
4. Therefore, the Necessarily Existent Being exists in every possible world.
5. So, the Necessarily Existent Being exists in the actual world. God exists.

Now, an argument very close to this is still defended by some Christian philosophers like Alvin Plantinga and William Lane Craig. What is the argument saying, in simple terms? It is this: God's existence cannot be merely possible, without being actual; nor merely actual, without being necessary. It must be either necessary or impossible.

Necessary here in a broad sense means a Being Who exists non-contingently i.e. without beginning or end, and so unlike any creature. It is also used in its modal sense, i.e. a necessary being is One Who exists in every possible world. Hence, if a necessary Being is possible, He exists necessarily. He must be impossible or necessary.

Thoughts on this argument? It si said that if the argument at least shows that if God is not impossible, He must exist; then it's atheists and agnostics who now have to shoulder the burden of proof. Moreover, it seems to render agnosticism inconsistent. Agnostics don't believe God's existence is impossible. But then His existence is necessary.

A final point: it is said St. Thomas did not accept the argument in the form it was proposed to him, for St. Thomas said, "Therefore I say that this proposition, "God exists," of itself is self-evident, for the predicate is the same as the subject, because God is His own existence as will be hereafter shown (I:3:4). Now because we do not know the essence of God, the proposition is not self-evident to us; but needs to be demonstrated by things that are more known to us, though less known in their nature namely, by effects."

Hence, St. Thomas prefers a demonstration of God's existence by observed visible effects, what are sometimes called "a posteriori" arguments" rather than "a priori" ones like the ontological argument. But if we read the response carefully, St. Thomas is not denying the existence of God is self-evident - St. Thomas says God's Existence is self-evident because Essence and Existence are the same in God. Hence, God's very nature is Eternal Existence, and God cannot be conceived, by one who understands that, as non-existent.

St. Thomas uses another argument in the Third Way, which can also be summarized in terms of contingency and necessity thus: (1) visible observed beings exist contingently, for they could cease to be, and once did not exist. (2) But an infinite regress of contingent beings is not possible, i.e. it cannot be that every contingent being is caused by contingent beings only. (3) hence, the first cause of all contingent beings exists non-contingently, i.e. necessarily. This is another means, "a posteriori" to arrive at the Necessary Being.

Thoughts?
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Offline Daniel

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Well if we define "possible" to mean "exists in some possible world", then it becomes a question of scientific investigation. Go out and search in every possible world for a necessarily-existing being. (Good luck with that!) If at least one world has such a being in it then you can call off the search and affirm God's existence... yet until you find such a being you have no choice but to keep searching through the infinitely-many possible worlds and only once you've managed to do that may you conclude that God does not exist. This is problematic for two reasons: 1.) if we need to search through infinitely-many possible worlds in order to disprove God's existence, then it becomes literally impossible to disprove God's existence even if God does not exist (which seems to raise epistemological issues concerning falsifiability and burden of proof), and 2.) our science can't even prove the existence of a necessarily-existing being existing in this world. So it's not in our favour to turn this into a question of science. If we leave the question up to science, it's never going to be answered.


That said, I don't think this formulation of the argument really proves the existence of God so much as it divides the theists from the agnostics from the atheists. Theists are going to accept the first premise while atheists are going to deny it, so it basically comes down to question-begging. As for the agnostics, they'll neither accept it nor deny it (at least not as certain). Maybe that was the point, to show that atheism is just as much a matter of belief as theism is. Even so, the proof doesn't work without accepting the first premise.
« Last Edit: May 26, 2020, 07:48:54 AM by Daniel »
 

Offline Philip G.

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In recent decades, there has been a revival of interest in Archbishop St. Anselm of Canterbury's Ontological Argument: https://en.wikipedia.org/wiki/Ontological_argument It is usually formulated using modal premises on possibility and necessity.

1. The existence of a Necessarily Existing Being is possible.
2. If the existence of a Necessarily Existing Being is possible, a Necessarily Existing Being exists in some possible world.
3. But by nature of Necessary Existence, if a Necessarily Existing Being exists in some possible world, He exists in every possible world.
4. Therefore, the Necessarily Existent Being exists in every possible world.
5. So, the Necessarily Existent Being exists in the actual world. God exists.

Now, an argument very close to this is still defended by some Christian philosophers like Alvin Plantinga and William Lane Craig. What is the argument saying, in simple terms? It is this: God's existence cannot be merely possible, without being actual; nor merely actual, without being necessary. It must be either necessary or impossible.

Necessary here in a broad sense means a Being Who exists non-contingently i.e. without beginning or end, and so unlike any creature. It is also used in its modal sense, i.e. a necessary being is One Who exists in every possible world. Hence, if a necessary Being is possible, He exists necessarily. He must be impossible or necessary.

Thoughts on this argument? It si said that if the argument at least shows that if God is not impossible, He must exist; then it's atheists and agnostics who now have to shoulder the burden of proof. Moreover, it seems to render agnosticism inconsistent. Agnostics don't believe God's existence is impossible. But then His existence is necessary.

A final point: it is said St. Thomas did not accept the argument in the form it was proposed to him, for St. Thomas said, "Therefore I say that this proposition, "God exists," of itself is self-evident, for the predicate is the same as the subject, because God is His own existence as will be hereafter shown (I:3:4). Now because we do not know the essence of God, the proposition is not self-evident to us; but needs to be demonstrated by things that are more known to us, though less known in their nature namely, by effects."

Hence, St. Thomas prefers a demonstration of God's existence by observed visible effects, what are sometimes called "a posteriori" arguments" rather than "a priori" ones like the ontological argument. But if we read the response carefully, St. Thomas is not denying the existence of God is self-evident - St. Thomas says God's Existence is self-evident because Essence and Existence are the same in God. Hence, God's very nature is Eternal Existence, and God cannot be conceived, by one who understands that, as non-existent.

St. Thomas uses another argument in the Third Way, which can also be summarized in terms of contingency and necessity thus: (1) visible observed beings exist contingently, for they could cease to be, and once did not exist. (2) But an infinite regress of contingent beings is not possible, i.e. it cannot be that every contingent being is caused by contingent beings only. (3) hence, the first cause of all contingent beings exists non-contingently, i.e. necessarily. This is another means, "a posteriori" to arrive at the Necessary Being.

Thoughts?

Is this exact argument attributed to St. Anselm? 
« Last Edit: May 26, 2020, 12:50:08 PM by Philip G. »
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Offline St.Justin

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This brings up a point I have been trying to make for years. One of the big problems in the Church today ( not just the Church but the world) is no one understand terms the way they have always been understood and the way the Church has always understood them. In this particular case everyone in St. Anselm's time would have understood exactly what he meant. In opposition to that we have Daniel trying to make sense of St. Anselm's words in the way he perceives the wording. In Theology and philosophy words have very specific meanings. We seem to have lost all grasp of that even among modern theologians and particularly want to be theologians who really have no grasp of philosophy or logic.
 

Offline Daniel

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Is this exact argument attributed to St. Anselm?

It's not. St. Anselm was the first person to come up with the "ontological argument", but the argument has been adapted time and time again over the centuries. This just happens to be the version that's popular today.


The original version, off the top of my head, was basically:
1. We can conceive of some being X such that no greater being exists.
2. Stuff that exists both outside our mind and inside our mind is greater than stuff that exists only in our mind.
3. Therefore, X must exist both outside our mind and inside our mind.
It's hard to identify, but something about the argument seems faulty.
 

Offline Daniel

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This brings up a point I have been trying to make for years. One of the big problems in the Church today ( not just the Church but the world) is no one understand terms the way they have always been understood and the way the Church has always understood them. In this particular case everyone in St. Anselm's time would have understood exactly what he meant. In opposition to that we have Daniel trying to make sense of St. Anselm's words in the way he perceives the wording. In Theology and philosophy words have very specific meanings. We seem to have lost all grasp of that even among modern theologians and particularly want to be theologians who really have no grasp of philosophy or logic.

In modal logic, that is what the words mean. "Possibility" simply means "exists in at least one possible world". The original argument wasn't framed in terms of modal logic though.
 

Offline Philip G.

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1. The existence of a Necessarily Existing Being is possible.
2. If the existence of a Necessarily Existing Being is possible, a Necessarily Existing Being exists in some possible world.
3. But by nature of Necessary Existence, if a Necessarily Existing Being exists in some possible world, He exists in every possible world.
4. Therefore, the Necessarily Existent Being exists in every possible world.
5. So, the Necessarily Existent Being exists in the actual world. God exists.

I think number three is where this argument becomes clearly deceptive.  It introduces the concept of nature, which poses that it cannot merely be referring to a spiritual world/aka the initial differentiated "possible" world.  But, it also introduces the concept that a male necessarily exists.  Yet, God said it is not good that man be alone, so God made Man a woman, Eve.

In order to accept number three, which is twofold, you have to reject that there can exist being which is solely spiritual, which is surely a basis for establishing number one and two.   

It is possible that a "he" exist, for Adam existed by himself for a short time. But, it was only temporary.  For God said, it is not Good that man be alone.  So, he made woman/Eve.  If I had to jump to a conclusion, this argument basically asserts that God is not Good, and that God is not Good by nature.  It also stinks of aliens and alternate universes.   I cannot but say that it is a blasphemous argument.
« Last Edit: May 26, 2020, 01:30:45 PM by Philip G. »
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Offline St.Justin

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possibility

a chance that something may happen or be true:

something that you can choose to do in a particular situation:

probability

the level of possibility of something happening or being true:

used to mean that something is very likely:




 
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Offline Xavier

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Daniel, in order to show God's existence is possible, it doesn't seem necessary to investigate every possible world, but only the actual world. Now, St. Thomas' Third Way arguably shows not merely that a Necessary Being is possible, but even that He certainly exists: "The third way is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary ... Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God."

I would argue even this argument itself likely shows it is close to 100% certain that the Necessary Being exists, from the impossibility of infinite regress of contingent beings. But let us suppose it is only 90% probable, or for that matter 50% probable or even 10% probable. If so, it is not impossible but has some probability. Only 0% probability is impossible e.g. a dice calibrated from 1 to 6 throwing up a 7. But if you now combine the Third Way, with the Ontological Argument, we arrive at the conclusion that, God's existence not being impossible, must be ontologically necessary. Suppose you and I were among the first human beings in existence. That is not the actual world, but is one possible world from many possibilities. But even in all those many possible worlds, it would be necessary to deduce the existence of One Necessary Being, Who is perfect in every perfection, Who caused all other beings and all their perfections, and greater than Whom none can exist. That appears to me to be what St. Anselm has been saying.

Philip, the arguments (neither of St. Anselm nor of St. Thomas) do not say that God is not Good. In fact, St. Thomas shows God is Perfect Goodness in the Fourth Way, and the argument of St. Anselm is that God's Goodness is greater than that of all creatures, whether actual or possible. St. Anselm's argument is that God's Goodness necessarily exists, not merely possibly. I would personally go with St. Thomas' Third and Fourth Ways, from effects, to begin with; but St. Anselm's is worth considering imo.
« Last Edit: May 26, 2020, 09:30:21 PM by Xavier »
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Offline aquinas138

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Is this exact argument attributed to St. Anselm?

It's not. St. Anselm was the first person to come up with the "ontological argument", but the argument has been adapted time and time again over the centuries. This just happens to be the version that's popular today.


The original version, off the top of my head, was basically:
1. We can conceive of some being X such that no greater being exists.
2. Stuff that exists both outside our mind and inside our mind is greater than stuff that exists only in our mind.
3. Therefore, X must exist both outside our mind and inside our mind.
It's hard to identify, but something about the argument seems faulty.

If I recall correctly from philosophy classes many moons ago, one objection is that statement 2 seems like it needs to be more than simply asserted. Why is something outside our mind "greater" than something only in our mind? It seems to mean that "actually existing" is greater than "merely conceivable," but I doubt many modern philosophers let that pass unchallenged.

ETA: It was Kant who first objected to the idea that existence is a "great-making property."
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