With the help of Mickey, from A Philosopher's Blather, I've been able to improve one of the modal cosmological arguments I've been working on.
1. Every existing being (thing, entity) is either contingent or necessary.
(1) is true by definition.
2. There is a possible state of affairs in which nothing contingent exists. (Premise)
"State of affairs" refers to the instantiation or non-instantiation of some concrete object or objects. Excluded are abstract objects, like numbers and propositions. There are many apples, for example, but it is possible for there to be no apples.
3. It is necessarily the case that possible states of affairs are possibly caused.
Assume that there is no cause of the non-existence of apples. Even granting this scenario, there is still a possible world in which the non-existence of apples is caused. Applied to the argument, then, there is a possible world in which the non-existence of contingent things is caused.
In fact, we may weaken the premise even further. Instead of being a sufficient explanation, suppose the cause in question is merely a partial explanation, such that:
3*. It is necessarily possible that possible states of affairs are at least partially caused. (Premise)
For instance, oxygen is a partial cause of water. Oxygen alone is not sufficient to cause water, but it is something needed.
4. It is possible for the non-existence of contingent beings to have at least a partial cause. (From 2 and 3)
5. Therefore, a necessary being exists. (From 1, 4 and S5)
Q.E.D.
Tuesday, April 20, 2010
Saturday, April 17, 2010
Metaphysics, Essence and Existence
Philosophers in the Aristotelian tradition have arguably offered the best account of metaphysics. What Thomas, Averroes, Maimonides and others, were able to champion much later after Aristotle was the distinction between essence and existence. It was Parmenides who stated that nothing can differ. All must be one, since things either differ by being or non-being. But, to be distinct from being by being is to be non-being, and to be distinct from being by non-being is to be not-distinct at all. Parmenides concluded that all is one.
What Aristotelians were able to accomplish is: 1) a demonstration that things differ; and 2) that Pure Being is needed to ground each essence that isn't identical to its existence.
1. Something exists.
This is undoubtedly true. In order to doubt that I exist, I must first exist in order to doubt it.
2. Something exists only if there is such a thing as existence.
Again, this doesn't need any extensive argumentation. If there is no existence, then nothing can exist.
3. Existence is Pure Being.
Let's first define a couple of terms:
essence: what something is
existence: that something is (its being, actuality, or reality)
For example, what is the difference between a real dollar bill and an imaginary one? The essence of each is the same (a dollar bill has a specific shape, color, smell, etc.), so obviously the difference is that the real dollar bill has existence!
Now, if the essence of a dollar bill is a dollar bill, then the essence of existence must be existence itself. "Pure Being" or "Pure Existence" are the common philosophical terms for existence itself, so premise (3) is true by definition. I have chosen the term "Pure Being" since that is the most used term by metaphysicians, in addition to the fact that this way we may avoid a linguistic redundancy.
4. Therefore, Pure Being exists.
(4) follows from (1)-(3). So, what else can be known about Pure Being? At least five things:
First, Pure Being must have necessary existence. Imagine a state of affairs in which nothing exists. Is such a state of affairs possible? If the state of affairs exists, then something exists. If the state of affairs does not exist, then it's meaningless to talk about a state of affairs in which nothing exists. In short, it is contradictory to posit an existing state of affairs in which nothing exists. Finally, if something exists, then Pure Being exists, as was shown above.
Secondly, Pure Being must be unique. If there were more than one Pure Being, then there would be distinctions between them. However, to be distinct from existence is to be non-existence. Therefore, what is fully existence (Pure Being) must be one and not many.
Third, Pure Being must be omnipresent (all-present). In every existing place, something exists. Yet, something can only exist if it is grounded in Pure Being. Hence, Pure Being exists everywhere.
Fourth, Pure Being is eternal. We have already seen that Pure Being has necessary existence. Now, what exists necessarily cannot at any time fail to exist; otherwise, it would be contingent and not-necessary. Because Pure Being is necessary, it must exist at all times and therefore must be eternal.*
Fifth, Pure Being must be distinct from everything else that exists. Pure Being has an essence that is identical to its existence, since the essence of existence is existence itself. However, every other existing thing has an essence distinct from its existence (a dollar bill does not have necessary existence, but may or may not exist).
What all of this implies is that while things may not differ by existence, they can (and do) differ by essence. Something either exists or it doesn't, but things may differ by what type of things they are.
This is also the basic metaphysical proof of God's existence found in St. Thomas Aquinas' De Ente et Essentia ("On Being and Essence"). It's not entirely original with Thomas, but I think he puts it the best way. So far, this is the easiest summary I've been able to come up with.
You can be sure of at least three things, then: 1) I exist; 2) God exists; and 3) I am not God.**
*Whether Pure Being is timeless or omnitemporal is up for debate.
**Feel free to read "I" in the first-person, rather than in the sense that "Doug Benscoter exists."
What Aristotelians were able to accomplish is: 1) a demonstration that things differ; and 2) that Pure Being is needed to ground each essence that isn't identical to its existence.
1. Something exists.
This is undoubtedly true. In order to doubt that I exist, I must first exist in order to doubt it.
2. Something exists only if there is such a thing as existence.
Again, this doesn't need any extensive argumentation. If there is no existence, then nothing can exist.
3. Existence is Pure Being.
Let's first define a couple of terms:
essence: what something is
existence: that something is (its being, actuality, or reality)
For example, what is the difference between a real dollar bill and an imaginary one? The essence of each is the same (a dollar bill has a specific shape, color, smell, etc.), so obviously the difference is that the real dollar bill has existence!
Now, if the essence of a dollar bill is a dollar bill, then the essence of existence must be existence itself. "Pure Being" or "Pure Existence" are the common philosophical terms for existence itself, so premise (3) is true by definition. I have chosen the term "Pure Being" since that is the most used term by metaphysicians, in addition to the fact that this way we may avoid a linguistic redundancy.
4. Therefore, Pure Being exists.
(4) follows from (1)-(3). So, what else can be known about Pure Being? At least five things:
First, Pure Being must have necessary existence. Imagine a state of affairs in which nothing exists. Is such a state of affairs possible? If the state of affairs exists, then something exists. If the state of affairs does not exist, then it's meaningless to talk about a state of affairs in which nothing exists. In short, it is contradictory to posit an existing state of affairs in which nothing exists. Finally, if something exists, then Pure Being exists, as was shown above.
Secondly, Pure Being must be unique. If there were more than one Pure Being, then there would be distinctions between them. However, to be distinct from existence is to be non-existence. Therefore, what is fully existence (Pure Being) must be one and not many.
Third, Pure Being must be omnipresent (all-present). In every existing place, something exists. Yet, something can only exist if it is grounded in Pure Being. Hence, Pure Being exists everywhere.
Fourth, Pure Being is eternal. We have already seen that Pure Being has necessary existence. Now, what exists necessarily cannot at any time fail to exist; otherwise, it would be contingent and not-necessary. Because Pure Being is necessary, it must exist at all times and therefore must be eternal.*
Fifth, Pure Being must be distinct from everything else that exists. Pure Being has an essence that is identical to its existence, since the essence of existence is existence itself. However, every other existing thing has an essence distinct from its existence (a dollar bill does not have necessary existence, but may or may not exist).
What all of this implies is that while things may not differ by existence, they can (and do) differ by essence. Something either exists or it doesn't, but things may differ by what type of things they are.
This is also the basic metaphysical proof of God's existence found in St. Thomas Aquinas' De Ente et Essentia ("On Being and Essence"). It's not entirely original with Thomas, but I think he puts it the best way. So far, this is the easiest summary I've been able to come up with.
You can be sure of at least three things, then: 1) I exist; 2) God exists; and 3) I am not God.**
*Whether Pure Being is timeless or omnitemporal is up for debate.
**Feel free to read "I" in the first-person, rather than in the sense that "Doug Benscoter exists."
Friday, April 2, 2010
A More Accessible Modal Cosmological Argument
1. Something exists.
2. Every existing being is either contingent or necessary.
3. There is a possible state of affairs in which no contingent being exists.
4. It is necessarily the case that possible states of affairs are explicable.
5. Hence, a necessary being is possible.
6. Whatever is possibly necessary exists in all possible worlds.
7. Therefore, a necessary being exists.
(1) and (2) are easily granted. I cannot doubt my own existence without first existing to doubt it. As for (2), something can either exist in at least one (but not all) possible worlds (contingent existence), or else exist in all possible worlds (necessary existence). Existence in no possible worlds would yield that a thing is impossible, and therefore necessarily non-existent.
(3) is highly plausible. If we represent the sum total of all contingent beings as C, and if all the members of C can at some time fail to exist, it's reasonable to infer that C itself may at some time fail to exist. By analogy, if every part of a house can possibly fail to exist, then the house as a whole can also fail to exist.
(4) doesn't entail that every state of affairs must have an explanation in the actual world. Rather, a state of affairs is defined as "explicable" so long as it is explained in at least one possible world W. Yet, the only thing that is left to explain ~C in W would be a necessary being. So, if it is possible that ~C obtains and that ~C has an explanation in some possible world, then a necessary being exists in some possible world, in confirmation of (5).
(6) and (7) are necessary inferences under the S5 axiom of modal logic. If something necessary does not exist in some possible world, then it is not necessary at all, but contingent, which is contradictory.
Maydole argues very similarly, here. The key difference (besides the use of S5 in the argument above) is that Maydole narrows the scope of his argument to the possibility of C not obtaining in the past, whereas the argument above is more general.
2. Every existing being is either contingent or necessary.
3. There is a possible state of affairs in which no contingent being exists.
4. It is necessarily the case that possible states of affairs are explicable.
5. Hence, a necessary being is possible.
6. Whatever is possibly necessary exists in all possible worlds.
7. Therefore, a necessary being exists.
(1) and (2) are easily granted. I cannot doubt my own existence without first existing to doubt it. As for (2), something can either exist in at least one (but not all) possible worlds (contingent existence), or else exist in all possible worlds (necessary existence). Existence in no possible worlds would yield that a thing is impossible, and therefore necessarily non-existent.
(3) is highly plausible. If we represent the sum total of all contingent beings as C, and if all the members of C can at some time fail to exist, it's reasonable to infer that C itself may at some time fail to exist. By analogy, if every part of a house can possibly fail to exist, then the house as a whole can also fail to exist.
(4) doesn't entail that every state of affairs must have an explanation in the actual world. Rather, a state of affairs is defined as "explicable" so long as it is explained in at least one possible world W. Yet, the only thing that is left to explain ~C in W would be a necessary being. So, if it is possible that ~C obtains and that ~C has an explanation in some possible world, then a necessary being exists in some possible world, in confirmation of (5).
(6) and (7) are necessary inferences under the S5 axiom of modal logic. If something necessary does not exist in some possible world, then it is not necessary at all, but contingent, which is contradictory.
Maydole argues very similarly, here. The key difference (besides the use of S5 in the argument above) is that Maydole narrows the scope of his argument to the possibility of C not obtaining in the past, whereas the argument above is more general.
Monday, March 29, 2010
Axiology and Anselm's Cosmological Argument
St. Anselm is usually known for his ontological argument, but he also supported various other arguments for God's existence. One of these is a version of the cosmological argument, which seeks to establish that, "there is . . . some one being which is supremely good, and supremely great, that is, the highest of all existing beings." [1]
1. Something good exists.
The axiological realist will grant this premise. However, it will not be accepted by moral nihilists. The audience of this proof, then, will be restricted to those who acknowledge that there really are, objectively-speaking, good things.
2. That which is good is either good through itself or through another.
Premise (2) will be accepted by those who adhere to even a minimal Principle of Sufficient Reason. Only if some attribute of a thing is inexplicable would (2) be false, or possibly false.
3. Different things are good by virtue of a single principle.
Anselm anticipates an objection, here. A horse is said to be good because he is both strong and swift. Yet, a robber can also be strong and swift, but surely the robber is not good. It's at this point that Anselm appeals to teleology: the horse's strength and swiftness is good due to its usefulness, whereas the robber's strength and swiftness is bad because his actions are harmful. It is the end, goal or purpose, then, that Anselm appeals to.
Further, two things are said to be just because they both participate in the single quality of justness. Likewise, then, two (or more) things are said to be good because they participate in the single quality of goodness. Now, this quality of goodness is itself a great good, Anselm says. Therefore, there is a single principle of goodness, the Supreme Being (God), which is the cause of all goodness in good things.
4. Therefore, a single principle of goodness exists.
Q.E.D.
Works Cited
[1] St. Anselm, "Monologium," Ch. 1, from Basic Writings, translated by S.N. Deane, Open Court Publishing Company, 1962, p. 86.
1. Something good exists.
The axiological realist will grant this premise. However, it will not be accepted by moral nihilists. The audience of this proof, then, will be restricted to those who acknowledge that there really are, objectively-speaking, good things.
2. That which is good is either good through itself or through another.
Premise (2) will be accepted by those who adhere to even a minimal Principle of Sufficient Reason. Only if some attribute of a thing is inexplicable would (2) be false, or possibly false.
3. Different things are good by virtue of a single principle.
Anselm anticipates an objection, here. A horse is said to be good because he is both strong and swift. Yet, a robber can also be strong and swift, but surely the robber is not good. It's at this point that Anselm appeals to teleology: the horse's strength and swiftness is good due to its usefulness, whereas the robber's strength and swiftness is bad because his actions are harmful. It is the end, goal or purpose, then, that Anselm appeals to.
Further, two things are said to be just because they both participate in the single quality of justness. Likewise, then, two (or more) things are said to be good because they participate in the single quality of goodness. Now, this quality of goodness is itself a great good, Anselm says. Therefore, there is a single principle of goodness, the Supreme Being (God), which is the cause of all goodness in good things.
4. Therefore, a single principle of goodness exists.
Q.E.D.
Works Cited
[1] St. Anselm, "Monologium," Ch. 1, from Basic Writings, translated by S.N. Deane, Open Court Publishing Company, 1962, p. 86.
Tuesday, March 23, 2010
The Imago Dei
We say that man is created in the image of God. Does this mean that God is just a big man? The Maverick Philosopher has recently provided a helpful analogy:
1. Man is made in God’s image.
2. Man is a physical being with a digestive tract, etc.
Therefore
3. God is a physical being with a digestive tract, etc.
But that’s like arguing:
1. This statue is made in Lincoln’s image.
2. This statue is composed of marble.
Therefore
3. Lincoln is composed of marble.
The point is that "being made in the image of" something does not require us to share physical attributes. Rather, this is a spiritual likening, which culminates in humanity's ability to reason. Reason finds its locus in God, and the fact that we are able to know things about ourselves and the ordered world around us is evidence of the order that God has created in us and the world. We reason because God reasons.
1. Man is made in God’s image.
2. Man is a physical being with a digestive tract, etc.
Therefore
3. God is a physical being with a digestive tract, etc.
But that’s like arguing:
1. This statue is made in Lincoln’s image.
2. This statue is composed of marble.
Therefore
3. Lincoln is composed of marble.
The point is that "being made in the image of" something does not require us to share physical attributes. Rather, this is a spiritual likening, which culminates in humanity's ability to reason. Reason finds its locus in God, and the fact that we are able to know things about ourselves and the ordered world around us is evidence of the order that God has created in us and the world. We reason because God reasons.
Monday, March 8, 2010
The Modal Cosmological Argument's Possibility Premise
I have been working on a Modal Cosmological Argument (MCA) for some time now, and I'm convinced that the key premise - the possibility premise - is rationally acceptable. However, given recent attempts at proving that a maximally great being is possible (see my previous post), demonstrating the possibility of a necessary being ought to be even easier, assuming that such a proof is correct. Before I provide the possibility proof, here's another look at the MCA:
1. Contingent beings exist.
2. It is possible that the collection of all contingent beings (CCB) has an external cause.
3. If an external cause exists, that cause is a necessary being.
4. Hence, a necessary being possibly exists.
5. Whatever is possibly necessary is necessary.
6. Therefore, a necessary being exists.
Let's reformulate the three axioms listed earlier:
A1. If a property is a great-making property, its negation is not a great-making property.
A2. If a property A is a great-making property and the property B is a necessary condition for A, then B is a great-making property.
A3. Being a necessary being is a great-making property.
Following these axioms is the proof that a necessary being possibly exists:
P1. If it's not possible that a necessary being exists, then every being has the property of being contingent.
P2. If every being has the property of being contingent, then being contingent is a necessary condition.
P3. If being contingent is a necessary condition, then being contingent is a great-making property. (From A2)
P4. Being contingent is not a great-making property. (From A1 and A3)
P5. Therefore, it is possible that a necessary being exists.
1. Contingent beings exist.
2. It is possible that the collection of all contingent beings (CCB) has an external cause.
3. If an external cause exists, that cause is a necessary being.
4. Hence, a necessary being possibly exists.
5. Whatever is possibly necessary is necessary.
6. Therefore, a necessary being exists.
Let's reformulate the three axioms listed earlier:
A1. If a property is a great-making property, its negation is not a great-making property.
A2. If a property A is a great-making property and the property B is a necessary condition for A, then B is a great-making property.
A3. Being a necessary being is a great-making property.
Following these axioms is the proof that a necessary being possibly exists:
P1. If it's not possible that a necessary being exists, then every being has the property of being contingent.
P2. If every being has the property of being contingent, then being contingent is a necessary condition.
P3. If being contingent is a necessary condition, then being contingent is a great-making property. (From A2)
P4. Being contingent is not a great-making property. (From A1 and A3)
P5. Therefore, it is possible that a necessary being exists.
Sunday, March 7, 2010
Proof of the Possibility Premise of the Modal Ontological Argument?
Plantinga has followed in the steps of Leibniz, who stated that if God possibly exists, then God actually exists. This is because God is defined as a being who possesses all great-making properties. So, God either necessarily exists or is impossible. The Modal Ontological Argument goes like this:
1. It is possible that a maximally great being exists.
2. A being is maximally great only if it is maximally excellent in all possible worlds.
3. A being is maximally excellent only if it is omnipotent, omniscient, and perfectly good.
4. Hence, a maximally excellent being exists in all possible worlds.
5. Therefore, a maximally excellent being exists.
The four great-making properties listed are: omnipotence, omniscience, perfect goodness, and necessary existence. The first three are covered by what Plantinga calls "maximal excellence." Only if a maximally excellent being exists necessarily is it maximally excellent.
Now, Kant objected that existence is not a predicate. However, the proponent of the MOA can grant this and go merrily on his way. For, existence is not assumed to be a great-making property anyway. Rather, it is necessary existence, as opposed to contingent existence, that is deemed a great-making property. Kant's objection, therefore, while interesting, is irrelevant.
Yet, if a maximally great being (God) is possible, then it must exist. For, if God were to exist only in some possible worlds, then He would be contingent and not necessary, which means He is not maximally great. That, of course, is contradictory.
The opponent of the MOA can only conclude that God (defined not just as "First Cause" or "Creator," but as a maximally great being) is impossible. In fact, if one starts a counter-argument like this:
1*. It is possible that a maximally great being does not exist
it follows that a maximally great being does not exist.
The only two options, then, are that a maximally great being necessarily exists, or else impossibly exists. A maximally great being cannot exist contingently, for then it would not be maximally great.
Is there any compelling reason to believe (1) or (1*)? Robert Maydole's recent formulation of the ontological argument - what he calls the "Modal Perfection Argument" - attempts to establish the possibility premise. With some word-substitution, I believe we can transform Plantinga's rationally acceptable argument into a compelling proof.
Three axioms:
A1. If a property is a great-making property, it's negation is not a great-making property.
A2. If a property A is a great-making property and the property B is a necessary condition for A, then B is a great-making property.
A3. Being a maximally great being is a great-making property.
Now, the proof that a maximally great being is possible:
P1. If it's not possible that a maximally great being exists, then every being has the property of not being maximally great.
P2. If every being has the property of not being maximally great, then not being maximally great is a necessary condition.
P3. If not being maximally great is a necessary condition, then not being maximally great is a great-making property. (From A2)
P4. Not being maximally great is not a great-making property. (From A1 and A3)
P5. Therefore, it is possible that a maximally great being exists.
1. It is possible that a maximally great being exists.
2. A being is maximally great only if it is maximally excellent in all possible worlds.
3. A being is maximally excellent only if it is omnipotent, omniscient, and perfectly good.
4. Hence, a maximally excellent being exists in all possible worlds.
5. Therefore, a maximally excellent being exists.
The four great-making properties listed are: omnipotence, omniscience, perfect goodness, and necessary existence. The first three are covered by what Plantinga calls "maximal excellence." Only if a maximally excellent being exists necessarily is it maximally excellent.
Now, Kant objected that existence is not a predicate. However, the proponent of the MOA can grant this and go merrily on his way. For, existence is not assumed to be a great-making property anyway. Rather, it is necessary existence, as opposed to contingent existence, that is deemed a great-making property. Kant's objection, therefore, while interesting, is irrelevant.
Yet, if a maximally great being (God) is possible, then it must exist. For, if God were to exist only in some possible worlds, then He would be contingent and not necessary, which means He is not maximally great. That, of course, is contradictory.
The opponent of the MOA can only conclude that God (defined not just as "First Cause" or "Creator," but as a maximally great being) is impossible. In fact, if one starts a counter-argument like this:
1*. It is possible that a maximally great being does not exist
it follows that a maximally great being does not exist.
The only two options, then, are that a maximally great being necessarily exists, or else impossibly exists. A maximally great being cannot exist contingently, for then it would not be maximally great.
Is there any compelling reason to believe (1) or (1*)? Robert Maydole's recent formulation of the ontological argument - what he calls the "Modal Perfection Argument" - attempts to establish the possibility premise. With some word-substitution, I believe we can transform Plantinga's rationally acceptable argument into a compelling proof.
Three axioms:
A1. If a property is a great-making property, it's negation is not a great-making property.
A2. If a property A is a great-making property and the property B is a necessary condition for A, then B is a great-making property.
A3. Being a maximally great being is a great-making property.
Now, the proof that a maximally great being is possible:
P1. If it's not possible that a maximally great being exists, then every being has the property of not being maximally great.
P2. If every being has the property of not being maximally great, then not being maximally great is a necessary condition.
P3. If not being maximally great is a necessary condition, then not being maximally great is a great-making property. (From A2)
P4. Not being maximally great is not a great-making property. (From A1 and A3)
P5. Therefore, it is possible that a maximally great being exists.
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