The version of the modal cosmological argument (MCA) that I defend goes like this:
1. Every contingent entity possibly has an external cause. (Premise, W-PSR)
2. If the sum total of contingent entities C has an external cause, that cause is a necessary, eternal, and enormously powerful entity. (Premise)
3. C is a contingent entity. (Premise)
4. Possibly, C has an external cause. (From 1 and 3)
5. Therefore, the external cause of C is a necessary, eternal, and enormously powerful entity. (From 2, 4, and S5)
The argument is logically sound, but are its premises more likely true than their negations? Prima facie, almost nobody questions (1). Assuming it's possible for a brick to pop into existence uncaused out of nothing, it's still reasonable to conclude that the brick could have had an external cause of its existence.
(2) is largely analytical. If there is a cause outside the sum total of C that causes C, that cause must have necessary existence. Otherwise, it too would be contained within C. Moreover, this necessary entity would have to be eternal, since there is no time at which a necessary entity can fail to exist. Finally, the entity in question must also be enormously powerful, since a cause's power is at least as great as its effect. The sheer vastness and order of C warrants this conclusion.
Notice what the skeptic cannot argue. He cannot start by reversing the W-PSR:
1*. Every contingent entity possibly does not have an external cause.
The existence of a necessary, eternal, and enormously powerful entity is consistent with its not having caused what exists contingently. What the skeptic would have to do is begin by saying that a necessary entity possibly does not exist. However, this possibility premise entails the much stronger conclusion that C cannot possibly have an external cause. This brings the original W-PSR back into question. So, the skeptic will have to pick their poison.
At any rate, I could argue that a necessary entity's possible non-existence is contradictory (and I think it is), but for now, it's important to realize that not all contradictions are as immediately obvious as the next. "The Prime Minister is a prime number" is necessarily false, but it's nowhere near as obvious as, "X is ~X."
Sunday, March 20, 2011
Friday, March 18, 2011
A Modal Ontological Argument in the tradition of Rene Descartes
With all of the recent modalizations of St. Anselm's ontological argument, I was surprised to see how few attempts have been made to do the same with Descartes' arguments from First Meditations.
In short, Descartes reasons that he has the concept of God in his mind. He then asks, what is the cause of this conception? For example, we have the concept of an apple because we know such things exist. We have the concept of a unicorn, not because they exist, but because we composite different parts (a horse's body, the horn of any number of animals, and the wings of a majestic bird). For Descartes, then, the ability to have a clear and distinct conceptualization of a thing points to that thing's having existence in reality.
Here's how a modal version of the argument might look:
1. If a concept of C is held by person S, then C possibly corresponds to an objective reality. (Premise)
2. The concept of a maximally great being is a concept of S. (Premise)
3. Hence, the concept of a maximally great being possibly corresponds to an objective reality. (From 1 and 2)
4. A maximally great being possibly exists. (3, simplification)
5. A being is maximally great if and only if it is maximally excellent in every possible world. (Premise)
6. A being is maximally excellent if and only if it is omnipotent, omniscient, and morally perfect. (Premise)
7. Hence, an omnipotent, omniscient, and morally perfect being exists in all possible worlds. (From 5, 6, and S5)
8. Therefore, an omnipotent, omniscient, and morally perfect being exists. (From 7)
9. Therefore, God exists. (From 8)
In short, Descartes reasons that he has the concept of God in his mind. He then asks, what is the cause of this conception? For example, we have the concept of an apple because we know such things exist. We have the concept of a unicorn, not because they exist, but because we composite different parts (a horse's body, the horn of any number of animals, and the wings of a majestic bird). For Descartes, then, the ability to have a clear and distinct conceptualization of a thing points to that thing's having existence in reality.
Here's how a modal version of the argument might look:
1. If a concept of C is held by person S, then C possibly corresponds to an objective reality. (Premise)
2. The concept of a maximally great being is a concept of S. (Premise)
3. Hence, the concept of a maximally great being possibly corresponds to an objective reality. (From 1 and 2)
4. A maximally great being possibly exists. (3, simplification)
5. A being is maximally great if and only if it is maximally excellent in every possible world. (Premise)
6. A being is maximally excellent if and only if it is omnipotent, omniscient, and morally perfect. (Premise)
7. Hence, an omnipotent, omniscient, and morally perfect being exists in all possible worlds. (From 5, 6, and S5)
8. Therefore, an omnipotent, omniscient, and morally perfect being exists. (From 7)
9. Therefore, God exists. (From 8)
Tuesday, March 1, 2011
The Traditional Third Way
I have spent quite a bit of time defending the Modal Third Way. However, I think the traditional argument is compelling, as well. What Maimonides, Thomas, and others have argued is the following:
1. Every existing entity is either contingent or necessary. (Definition)
2. Something has always existed. (Premise)
3. There was a past time at which nothing contingent existed. (Premise)
4. Therefore, a necessary entity exists. (From 1 - 3)
Before moving on to a defense of each of the premises, a few words of "necessity" are in order. First, the conclusion is not necessarily to a logically necessary entity. It's not as if "nothing necessary exists" is contradictory in the same vein as "John is a married bachelor." Rather, the argument seeks to establish the existence of some temporally necessary entity, e.g. something indestructible, or incorruptible, if it exists at all. Moreover, as I have said on more than one occasion, a necessary entity must also be eternal and enormously powerful (if not omnipotent). After all, the weaker a thing is, the more inclined it is toward corruptibility.
Now, what about the argument's premises? (1) is obviously true: an existing thing either possibly fails to exist (contingency) or cannot fail to exist (necessity). (2) is based on ex nihilo nihil fit (out of nothing comes nothing). If there were a past time at which nothing exists, then nothing would exist now, which is patently false.
(3) is likely the most controversial premise, but "controversial" is not synonymous with "improbable." Given infinite time, all non-zero probabilities will be actualized at some point. The Scholastics put it like this: given infinite time, all real potentialities will be actualized. After all, infinity is just inexhaustible. In fact, it could even be argued that there are infinitely-many points at which nothing contingent exists. Either way, (3) appears to be in good shape. Yet, if nothing contingent existed at a past time, and something existed at the same time - per premise (2) - it follows that a necessary entity exists.
Therefore, something necessary, eternal, and enormously powerful exists. Whether or not this entity is the Christian God, or the deity of any other religion, is a matter for further inquiry.
Of course, one could always say that the universe's past is finite, and I would agree. However, that does nothing to undermine the Third Way. In fact, it actually gives us another argument for God's existence: the Kalam Cosmological Argument (KCA).
1. Every existing entity is either contingent or necessary. (Definition)
2. Something has always existed. (Premise)
3. There was a past time at which nothing contingent existed. (Premise)
4. Therefore, a necessary entity exists. (From 1 - 3)
Before moving on to a defense of each of the premises, a few words of "necessity" are in order. First, the conclusion is not necessarily to a logically necessary entity. It's not as if "nothing necessary exists" is contradictory in the same vein as "John is a married bachelor." Rather, the argument seeks to establish the existence of some temporally necessary entity, e.g. something indestructible, or incorruptible, if it exists at all. Moreover, as I have said on more than one occasion, a necessary entity must also be eternal and enormously powerful (if not omnipotent). After all, the weaker a thing is, the more inclined it is toward corruptibility.
Now, what about the argument's premises? (1) is obviously true: an existing thing either possibly fails to exist (contingency) or cannot fail to exist (necessity). (2) is based on ex nihilo nihil fit (out of nothing comes nothing). If there were a past time at which nothing exists, then nothing would exist now, which is patently false.
(3) is likely the most controversial premise, but "controversial" is not synonymous with "improbable." Given infinite time, all non-zero probabilities will be actualized at some point. The Scholastics put it like this: given infinite time, all real potentialities will be actualized. After all, infinity is just inexhaustible. In fact, it could even be argued that there are infinitely-many points at which nothing contingent exists. Either way, (3) appears to be in good shape. Yet, if nothing contingent existed at a past time, and something existed at the same time - per premise (2) - it follows that a necessary entity exists.
Therefore, something necessary, eternal, and enormously powerful exists. Whether or not this entity is the Christian God, or the deity of any other religion, is a matter for further inquiry.
Of course, one could always say that the universe's past is finite, and I would agree. However, that does nothing to undermine the Third Way. In fact, it actually gives us another argument for God's existence: the Kalam Cosmological Argument (KCA).
A Heraclitean Cosmological Argument
The ancient Greek philosopher, Heraclitus, held views that are very consonant with what many today hold. He was a commonsense philosopher who is famous for his quote, "you cannot step into the same river twice." Rivers, like all natural things, are in a constant state of flux. However, there is an order to how each of these things change, and the ordering principle (or "Logos") is distinguished from these changing things. As A.H. Armstrong summarizes, "[The] world of change and conflict pictured by Heraclitus is not however a mere chaos. It is governed by an immanent principle of order and measure. . . . [H]is name for the ruling principle is the Logos." [1]
There are several ways of formalizing Heraclitus' thought into a cosmological argument. I wish to present two of these ways:
I. The Heraclitean Cosmological Argument (HCA) based on correspondence
1. Nature is in constant flux. (Premise)
2. There is order throughout nature. (Premise)
3. The order throughout nature is either in flux or not in flux. (Definition)
4. The order throughout nature is not in flux. (Premise)
5. Every fact of concrete reality corresponds to some existing concrete reality. (Premise, correspondence principle)
6. Hence, the fact of order in nature corresponds to some existing concrete reality. (From 2 and 5)
7. The corresponding concrete reality is itself either in flux or not in flux. (Definition)
8. It cannot be in flux. (From 4 and 5)
9. Therefore, an immutable ordering principle (Logos) exists. (From 6 - 8)
10. Therefore, the Logos is distinct from nature. (From 1 and 9)
The Logos that Heraclitus concludes to is immutable, eternal (for something can only cease to exist at some time if it changes), and enormously powerful, given that it is the cause of change throughout nature. More precisely, though, his thought is that the Logos is part of nature, but distinct from those aspects of nature that are in flux.
II. The HCA based on the Principle of Sufficient Reason (PSR)
With some modifications of Leibniz' argument, we can reformulate the syllogism to be Heraclitean-friendly:
1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, PSR)
2. If the order of nature has an explanation of its existence, that explanation is the Logos. (Premise)
3. The order of nature exists. (Premise)
4. Hence, the order of nature has an explanation of its existence. (From 1 and 3)
5. Therefore, the order of nature is explained by the Logos. (From 2 and 4)
What I like about this version is the awkwardness that results in rejecting the existence of the Logos. If the skeptic takes the view that the order of the universe has an external cause, then we have something supernatural. If, however, the other horn of the dilemma is preferred, then the order of the universe has necessary existence. This entails that something is immutable, eternal, and enormously powerful, anyway.
This means that either (1) and/or (3) must be rejected. That's not an issue for me, though.
[1] A.H. Armstrong, An Introduction to Ancient Philosophy, Rowman and Littlefield Publishers, 1989 edition, p. 10.
There are several ways of formalizing Heraclitus' thought into a cosmological argument. I wish to present two of these ways:
I. The Heraclitean Cosmological Argument (HCA) based on correspondence
1. Nature is in constant flux. (Premise)
2. There is order throughout nature. (Premise)
3. The order throughout nature is either in flux or not in flux. (Definition)
4. The order throughout nature is not in flux. (Premise)
5. Every fact of concrete reality corresponds to some existing concrete reality. (Premise, correspondence principle)
6. Hence, the fact of order in nature corresponds to some existing concrete reality. (From 2 and 5)
7. The corresponding concrete reality is itself either in flux or not in flux. (Definition)
8. It cannot be in flux. (From 4 and 5)
9. Therefore, an immutable ordering principle (Logos) exists. (From 6 - 8)
10. Therefore, the Logos is distinct from nature. (From 1 and 9)
The Logos that Heraclitus concludes to is immutable, eternal (for something can only cease to exist at some time if it changes), and enormously powerful, given that it is the cause of change throughout nature. More precisely, though, his thought is that the Logos is part of nature, but distinct from those aspects of nature that are in flux.
II. The HCA based on the Principle of Sufficient Reason (PSR)
With some modifications of Leibniz' argument, we can reformulate the syllogism to be Heraclitean-friendly:
1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, PSR)
2. If the order of nature has an explanation of its existence, that explanation is the Logos. (Premise)
3. The order of nature exists. (Premise)
4. Hence, the order of nature has an explanation of its existence. (From 1 and 3)
5. Therefore, the order of nature is explained by the Logos. (From 2 and 4)
What I like about this version is the awkwardness that results in rejecting the existence of the Logos. If the skeptic takes the view that the order of the universe has an external cause, then we have something supernatural. If, however, the other horn of the dilemma is preferred, then the order of the universe has necessary existence. This entails that something is immutable, eternal, and enormously powerful, anyway.
This means that either (1) and/or (3) must be rejected. That's not an issue for me, though.
[1] A.H. Armstrong, An Introduction to Ancient Philosophy, Rowman and Littlefield Publishers, 1989 edition, p. 10.
Tuesday, February 15, 2011
Mortimer Adler's Cosmological Argument
Mortimer Adler came to the Christian faith fairly late in life, and to the Catholic faith in particular, even later. Nevertheless, even before his conversion and throughout his professional career, Adler made no apologies for defending his belief in God (or a Supreme Being of some kind) based on the existence of a contingent universe. His own argument goes roughly like this:
1. If X is an effect in need of a sustaining cause Y, then the existence of X implies the existence and action of Y. (Premise)
2. The universe is an existing effect. (Premise)
3. The universe is radically contingent. (Premise)
4. Whatever is radically contingent requires a sustaining cause. (Premise, PSR)
5. Therefore, the universe has a sustaining cause. (From 1 - 4)
(1) and (2) are indubitably true. (3) seems fairly benign upon consideration. Adler distinguishes between radical contingency and superficial contingency, the former of which entails the possibility of one or more alternative states of affairs. For example, the universe as it presently exists could logically exist differently. The laws of nature could be different; my desk could be yellow instead of black; the Steelers could have beaten the Packers in the Super Bowl; and so forth.
(4) is Adler's interpretation of the Principle of Sufficient Reason (PSR). Instead of going into a defense of the PSR, it is worth considering a common objection. It is often alleged that these arguments commit a composition fallacy. Just because each part of a mountain is small, that doesn't mean the mountain as a whole is small. Likewise, it is thought, even though each part of the universe has a sustaining cause, that doesn't mean the universe as a whole has a sustaining cause.
The disparity in this analogy is evident whenever we try to apply causal explanations. Would it be wise to suggest that even though each part of the mountain has a causal explanation, the mountain as a whole does not? Surely the mountain itself has been formed by geological processes, etc. What this illustrates is that while there are cases in which the whole is not like its parts, there are other cases in which the whole is like its parts.
Adler then reasons that the sustaining cause of the universe must have the usual transcendent attributes of timelessness, immutability, and immateriality, in addition to enormous power.
It turns out that Adler's argument is pretty close to Leibniz's own formulation of the cosmological argument.
1. If X is an effect in need of a sustaining cause Y, then the existence of X implies the existence and action of Y. (Premise)
2. The universe is an existing effect. (Premise)
3. The universe is radically contingent. (Premise)
4. Whatever is radically contingent requires a sustaining cause. (Premise, PSR)
5. Therefore, the universe has a sustaining cause. (From 1 - 4)
(1) and (2) are indubitably true. (3) seems fairly benign upon consideration. Adler distinguishes between radical contingency and superficial contingency, the former of which entails the possibility of one or more alternative states of affairs. For example, the universe as it presently exists could logically exist differently. The laws of nature could be different; my desk could be yellow instead of black; the Steelers could have beaten the Packers in the Super Bowl; and so forth.
(4) is Adler's interpretation of the Principle of Sufficient Reason (PSR). Instead of going into a defense of the PSR, it is worth considering a common objection. It is often alleged that these arguments commit a composition fallacy. Just because each part of a mountain is small, that doesn't mean the mountain as a whole is small. Likewise, it is thought, even though each part of the universe has a sustaining cause, that doesn't mean the universe as a whole has a sustaining cause.
The disparity in this analogy is evident whenever we try to apply causal explanations. Would it be wise to suggest that even though each part of the mountain has a causal explanation, the mountain as a whole does not? Surely the mountain itself has been formed by geological processes, etc. What this illustrates is that while there are cases in which the whole is not like its parts, there are other cases in which the whole is like its parts.
Adler then reasons that the sustaining cause of the universe must have the usual transcendent attributes of timelessness, immutability, and immateriality, in addition to enormous power.
It turns out that Adler's argument is pretty close to Leibniz's own formulation of the cosmological argument.
Thursday, February 3, 2011
The Indispensability Argument for the Existence of Abstract Objects
Numbers, sets, laws of logic, and so forth are all abstract objects. What makes something abstract as opposed to concrete is known with some imprecision, but it is generally agreed that one aspect that distinguishes abstract objects from concrete objects is that the former do not stand in causal relations. Now, should we admit that such objects actually exist? Here is one reason to think they do.
Our scientific knowledge of the world can be reduced in some cases to basic "laws," axioms composed of mathematical formulas. For instance, Newton's law of universal gravitation states that: F = G (m1 * m2 / r^2). The distance between the masses is "r" and the axiom requires that r be squared - hence, r^2. The mathematical function of squaring the distance is therefore an indispensable aspect of Newton's law. The same indispensability can be shown for all kinds of abstract objects. This leads us to the following argument:
1. Whatever is indispensable possesses the attribute of indispensability. (Definition)
2. Abstract objects are indispensable. (Premise)
3. Hence, abstract objects possess the attribute of indispensability. (From 1 and 2)
4. Non-existent objects cannot possess any attribute. (Premise)
5. Therefore, abstract objects exist. (From 3 and 4, plus negation)
All that's left is to defend the certainly uncontroversial premise (4). Something non-existent cannot possess any attributes, since attributes are themselves existing qualities. Therefore, at least some abstract objects, at any rate, exist.
Our scientific knowledge of the world can be reduced in some cases to basic "laws," axioms composed of mathematical formulas. For instance, Newton's law of universal gravitation states that: F = G (m1 * m2 / r^2). The distance between the masses is "r" and the axiom requires that r be squared - hence, r^2. The mathematical function of squaring the distance is therefore an indispensable aspect of Newton's law. The same indispensability can be shown for all kinds of abstract objects. This leads us to the following argument:
1. Whatever is indispensable possesses the attribute of indispensability. (Definition)
2. Abstract objects are indispensable. (Premise)
3. Hence, abstract objects possess the attribute of indispensability. (From 1 and 2)
4. Non-existent objects cannot possess any attribute. (Premise)
5. Therefore, abstract objects exist. (From 3 and 4, plus negation)
All that's left is to defend the certainly uncontroversial premise (4). Something non-existent cannot possess any attributes, since attributes are themselves existing qualities. Therefore, at least some abstract objects, at any rate, exist.
Monday, January 24, 2011
The Modal First Way
Inspired by Maydole's Modal Third Way, as well as Gale and Pruss' Modal Cosmological Argument, I think there is promise in constructing a modalized version of the argument from motion - the Modal First Way (MFW). Let's start with three modal axioms:
A1. Everything in motion is possibly moved by another.
A2. The regress of movers is possibly finite.
A3. Whatever is contingent is possibly moved by another.
Motion, or change, is the transition of a potentiality to an actuality, as in the case of an acorn becoming an oak tree. Now, for a reductio ad absurdum:
P1. Assume that a First Mover does not possibly exist.
P2. If a First Mover does not possibly exist, then it is either necessarily the case that a) something in motion cannot be moved by another; or b) the regress of movers is infinite. (From 1, A1 and A2)
P3. It is not necessarily the case that (2a) or (2b). (From A1 and A2)
P4. Hence, it is possible that a First Mover exists. (From 1 - 3)
P5. Whatever is possible is either contingent or necessary. (Definition)
P6. Whatever is contingent is possibly moved by another. (From A3)
P7. A First Mover cannot be moved by another. (Premise)
P8. Therefore, a First Mover necessarily exists. (From 1 - 7)
Of course, one may imagine a possible world in which nothing is in motion. However, this wouldn't undermine our conclusion that a First Mover necessarily exists. For, without motion the First Mover would just exist a se and without any effect, much like George Washington would still be the same person had he not been the first president of the United States.
Let's sum up the argument in simpler terms:
1. Pure Act possibly exists. (Premise)
2. Whatever is possible is either contingent or necessary. (Definition)
3. Whatever is contingent is possibly actualized. (Premise)
4. Hence, Pure Act is necessary. (From 1 - 3)
5. Therefore, Pure Act exists. (From 4)
Then, in closing the gap between Pure Act and God:
6. Pure Act is either omnipotent or non-omnipotent. (Definition)
7. Whatever is non-omnipotent exemplifies the potentiality to grow in power. (Premise)
8. Pure Act does not exemplify any potentiality. (Definition)
9. Therefore, Pure Act is omnipotent. (From 6 - 8)
A1. Everything in motion is possibly moved by another.
A2. The regress of movers is possibly finite.
A3. Whatever is contingent is possibly moved by another.
Motion, or change, is the transition of a potentiality to an actuality, as in the case of an acorn becoming an oak tree. Now, for a reductio ad absurdum:
P1. Assume that a First Mover does not possibly exist.
P2. If a First Mover does not possibly exist, then it is either necessarily the case that a) something in motion cannot be moved by another; or b) the regress of movers is infinite. (From 1, A1 and A2)
P3. It is not necessarily the case that (2a) or (2b). (From A1 and A2)
P4. Hence, it is possible that a First Mover exists. (From 1 - 3)
P5. Whatever is possible is either contingent or necessary. (Definition)
P6. Whatever is contingent is possibly moved by another. (From A3)
P7. A First Mover cannot be moved by another. (Premise)
P8. Therefore, a First Mover necessarily exists. (From 1 - 7)
Of course, one may imagine a possible world in which nothing is in motion. However, this wouldn't undermine our conclusion that a First Mover necessarily exists. For, without motion the First Mover would just exist a se and without any effect, much like George Washington would still be the same person had he not been the first president of the United States.
Let's sum up the argument in simpler terms:
1. Pure Act possibly exists. (Premise)
2. Whatever is possible is either contingent or necessary. (Definition)
3. Whatever is contingent is possibly actualized. (Premise)
4. Hence, Pure Act is necessary. (From 1 - 3)
5. Therefore, Pure Act exists. (From 4)
Then, in closing the gap between Pure Act and God:
6. Pure Act is either omnipotent or non-omnipotent. (Definition)
7. Whatever is non-omnipotent exemplifies the potentiality to grow in power. (Premise)
8. Pure Act does not exemplify any potentiality. (Definition)
9. Therefore, Pure Act is omnipotent. (From 6 - 8)
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