I'm of the opinion that Euthyphro should have been the one asking Socrates the questions. Roughly, the modern defender of the alleged dilemma asks, "is something good because God wills it, or does God will something because it is good?" Let's tackle this question by separating each part of the disjunction:
A. X is good because God wills it.
B. God wills X because X is good.
Now, in order for this to be a true dilemma, B must be the negation (or the equivalent to the negation) of A. Otherwise, the disjunction that Socrates presents is a false dilemma. Euthyphro should have asked Socrates why A and B are contradictory. Why can it not be the case that both A and B?
In debating the question over the years, it has become clear to me that defenders of the dilemma are making a very crucial assumption. What the Euthyphro Dilemma requires in order to work properly is the implication that B entails independence of God. A and B should really be rephrased like this:
A'. X, which is good, is dependent on God.
B'. X, which is good, is independent of God.
Obviously, A' and B' are mutually incompatible, but this raises an even more obvious question: why not simply state the dilemma like this? The answer is likely that Euthyphro would have simply affirmed A'. Hence, there is no dilemma for him to consider. What Socrates and his modern counterpart have to defend is that B entails B'. Are there any forthcoming arguments to support this? I doubt it. In any case, the theist should not accept the burden of proof in trying to explain away the (false) dilemma. Rather, the dilemma's defender ought to accept responsibility for arguing that B and B' are ultimately identical.
Wednesday, October 12, 2011
Monday, September 26, 2011
A Leibnizian Kalam Argument?
Staying with my recent approach of tossing up new arguments and seeing what sticks, I thought I'd give this a try. I've defended several modal cosmological arguments before, but this time I want to take some Leibnizian and kalam considerations into account.
1. Possibly, everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, W-PSR)
2. Necessarily, whatever begins to exist is contingent. (Premise)
3. Possibly, the universe began to exist. (Premise)
4. Possibly, the universe is contingent. (From 2 and 3)
5. Hence, the universe is contingent. (From 4 and S5)
6. Possibly, whatever is contingent has an external cause. (Premise, implied by W-PSR)
7. Possibly, the universe has an external cause. (From 5 and 6)
8. Necessarily, if the universe has an external cause, that cause is a timeless, changeless, immaterial, and very powerful first cause. (Premise)
9. Possibly, a timeless, changeless, immaterial, and very powerful first cause exists. (From 7 and 8)
10. Necessarily, a first cause is either necessary or contingent. (Definition)
11. Necessarily, a first cause cannot be explained by anything else. (Premise)
12. Necessarily, a first cause is explained by a necessity of its own nature. (From 1 and 11)
13. Therefore, a timeless, changeless, immaterial, and very powerful first cause exists. (Implied by 12)
1. Possibly, everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, W-PSR)
2. Necessarily, whatever begins to exist is contingent. (Premise)
3. Possibly, the universe began to exist. (Premise)
4. Possibly, the universe is contingent. (From 2 and 3)
5. Hence, the universe is contingent. (From 4 and S5)
6. Possibly, whatever is contingent has an external cause. (Premise, implied by W-PSR)
7. Possibly, the universe has an external cause. (From 5 and 6)
8. Necessarily, if the universe has an external cause, that cause is a timeless, changeless, immaterial, and very powerful first cause. (Premise)
9. Possibly, a timeless, changeless, immaterial, and very powerful first cause exists. (From 7 and 8)
10. Necessarily, a first cause is either necessary or contingent. (Definition)
11. Necessarily, a first cause cannot be explained by anything else. (Premise)
12. Necessarily, a first cause is explained by a necessity of its own nature. (From 1 and 11)
13. Therefore, a timeless, changeless, immaterial, and very powerful first cause exists. (Implied by 12)
Monday, September 19, 2011
Modalizing Descartes
1. Whatever is conceivable C is possibly caused by an existing C's impression. (Premise)
2. A perfect being is conceivable. (Premise)
3. Hence, the conception of a perfect being is possibly caused by a perfect being's impression. (From 1 and 2)
4. Hence, a perfect being possibly exists. (Implied by 3)
5. Therefore, a perfect being exists. (From 4 and S5)
Besides the usual unpackaging of (4), this argument is defensible. Descartes held that in order to conceive of something, there had to be an impression of that conception caused by the entity being conceived. That's a bit of a mouthful, but the idea can be illustrated by connotation, as opposed to strict denotation. The reason I can conceive of a horse is because I have seen an existing horse. Even imaginary entities, such as a unicorn, are just an amalgamation of existing things, e.g. a horse (which exists) and a horn (which exists on other animals).
Now, instead of contending that Descartes' strong principle is correct, we can actually weaken it and still arrive at the same conclusion. If it is even possible for a conception to be caused in the manner described above, it follows that a perfect being (omnipotent, omniscient, and morally perfect in every possible world) possibly exists. All that's left is a defense of the rather uncontroversial S5 axiom, and we have a successful ontological argument for God's existence.
Of course, I don't expect anyone to be persuaded by this argument if they're not persuaded by similar ones, e.g. the modal third way, that have arguably even more modest premises.
2. A perfect being is conceivable. (Premise)
3. Hence, the conception of a perfect being is possibly caused by a perfect being's impression. (From 1 and 2)
4. Hence, a perfect being possibly exists. (Implied by 3)
5. Therefore, a perfect being exists. (From 4 and S5)
Besides the usual unpackaging of (4), this argument is defensible. Descartes held that in order to conceive of something, there had to be an impression of that conception caused by the entity being conceived. That's a bit of a mouthful, but the idea can be illustrated by connotation, as opposed to strict denotation. The reason I can conceive of a horse is because I have seen an existing horse. Even imaginary entities, such as a unicorn, are just an amalgamation of existing things, e.g. a horse (which exists) and a horn (which exists on other animals).
Now, instead of contending that Descartes' strong principle is correct, we can actually weaken it and still arrive at the same conclusion. If it is even possible for a conception to be caused in the manner described above, it follows that a perfect being (omnipotent, omniscient, and morally perfect in every possible world) possibly exists. All that's left is a defense of the rather uncontroversial S5 axiom, and we have a successful ontological argument for God's existence.
Of course, I don't expect anyone to be persuaded by this argument if they're not persuaded by similar ones, e.g. the modal third way, that have arguably even more modest premises.
Friday, September 16, 2011
An Epistemological Argument Against a Beginningless Universe
Suppose that a beginningless universe is metaphysical possible. With this assumption in mind, it may still be shown that it is irrational to believe in such a universe.
1. If the universe is beginningless, then its past is infinite. (Premise)
2. An infinite past yields infinitely-many actualities. (Premise)
3. If there are infinitely-many actualities, then it is epistemically impossible to weigh any probability. (Premise)
4. Probability can be epistemically weighed. (Premise)
5. Therefore, it is irrational to believe in an infinite universe. (From 1 - 4)
The logic of the argument as stated is pretty loose, but one can follow the reasoning of the premises to the conclusion fairly naturally, I think. (1) is obviously true, and (2) is almost entirely uncontroversial. (4) must be true in order for probability and induction to survive, and these principles are indispensable toward rationality. This leaves us with (3).
Imagine the lines of evidence both for and against a beginningless universe. Further, imagine that the evidence on both sides is inexhaustible. We can represent the evidence for a beginningless universe with the set of all odd numbers {1, 2, 3, . . . n}, and the evidence against a beginningless universe with the set of all even numbers {2, 4, 6, . . . 2n}. This scenario should be expected, given the existence of infinitely-many actualities.
But if this is the case, how can the probability of either hypothesis be reasonably assessed? For every line of evidence for a beginningless universe, there is an equally strong line of evidence against it. Yet, we all know that the probability of a hypothesis can be reasonably assessed. If this is correct, then it follows that it is inconsistent with probability for there to be infinitely-many actualities to take into account. Because of the epistemic warrant for probability, then, it seems that the rejection of infinitely-many actualities, and therefore a beginningless universe, is preferable.
1. If the universe is beginningless, then its past is infinite. (Premise)
2. An infinite past yields infinitely-many actualities. (Premise)
3. If there are infinitely-many actualities, then it is epistemically impossible to weigh any probability. (Premise)
4. Probability can be epistemically weighed. (Premise)
5. Therefore, it is irrational to believe in an infinite universe. (From 1 - 4)
The logic of the argument as stated is pretty loose, but one can follow the reasoning of the premises to the conclusion fairly naturally, I think. (1) is obviously true, and (2) is almost entirely uncontroversial. (4) must be true in order for probability and induction to survive, and these principles are indispensable toward rationality. This leaves us with (3).
Imagine the lines of evidence both for and against a beginningless universe. Further, imagine that the evidence on both sides is inexhaustible. We can represent the evidence for a beginningless universe with the set of all odd numbers {1, 2, 3, . . . n}, and the evidence against a beginningless universe with the set of all even numbers {2, 4, 6, . . . 2n}. This scenario should be expected, given the existence of infinitely-many actualities.
But if this is the case, how can the probability of either hypothesis be reasonably assessed? For every line of evidence for a beginningless universe, there is an equally strong line of evidence against it. Yet, we all know that the probability of a hypothesis can be reasonably assessed. If this is correct, then it follows that it is inconsistent with probability for there to be infinitely-many actualities to take into account. Because of the epistemic warrant for probability, then, it seems that the rejection of infinitely-many actualities, and therefore a beginningless universe, is preferable.
Tuesday, August 30, 2011
A Mereological Argument Based on Alethic Realism
1. There are true propositions. (Premise)
2. Every true proposition is part of a maximally alethic state of affairs A. (Premise)
3. The contents of A are possibly known by a mind. (Premise)
4. Hence, an omniscient mind possibly exists. (implied by 1 - 3)
5. A possibly existent omniscient mind either has necessary or contingent existence. (Premise)
6. An omniscient mind cannot exist contingently. (Premise)
7. Therefore, a necessary and omniscient mind exists. (From 4 - 6)
I currently accept (6) solely on intuition. I'm sure some argument can be forged for its plausibility, but I wonder if such an argument would be persuasive and (more importantly) sound.
2. Every true proposition is part of a maximally alethic state of affairs A. (Premise)
3. The contents of A are possibly known by a mind. (Premise)
4. Hence, an omniscient mind possibly exists. (implied by 1 - 3)
5. A possibly existent omniscient mind either has necessary or contingent existence. (Premise)
6. An omniscient mind cannot exist contingently. (Premise)
7. Therefore, a necessary and omniscient mind exists. (From 4 - 6)
I currently accept (6) solely on intuition. I'm sure some argument can be forged for its plausibility, but I wonder if such an argument would be persuasive and (more importantly) sound.
Friday, August 19, 2011
The Transcendental Argument
That's right: a classical Aristotelian is defending a version of the so-called "transcendental argument" for God's existence. First, what does it mean for something to be transcendental? In a few quick words, the term refers to a thing's necessary preconditions. In order for water to exist, it must be composed of hydrogen and oxygen. H2O is, therefore, a transcendental of water.
More seriously, we might ask: how do we know X is true? Before determining whether X corresponds to reality in fact, we must determine whether X is logically coherent. Unless something is consistent with the laws of logic, then, it cannot exist. I realize I'm dumbing it down a bit here, but believe it or not, there are actually people who reject this line of thought. I won't pursue such a radical perspectivism at this juncture, though. In any case, the laws of logic are a necessary precondition of rational inquiry. Let's start our argument like this:
Axiom 1. One cannot be rational while rejecting rational inquiry.
Axiom 2. One cannot be rational while undermining the necessary preconditions of rational inquiry.
Here, now, is the first part of the proof, via reductio ad absurdum:
Prove A: The laws of logic are universal.
Assume ~A: The laws of logic are not universal.
~A --> B: If the laws logic are not universal, X can be ~X.
~B: X cannot be ~X.
~~A: by modus tollens.
Therefore, A: by negation, the laws of logic are universal.
Q.E.D.
Most fundamental to the laws of logic are the laws of identity, non-contradiction, and excluded middle. I would also add the transitive axiom (if A = B, and B = C, then A = C) to that list. In order to engage in rational inquiry, one must be consistent with at least these four laws of logic. They are transcendentals of rational inquiry.
Now comes the next part: from universality to existence. Does the universality of logic entail that it exists? One reason to think it does is that if X possesses the attribute of universality (I've also mentioned indispensability in the past), then X must exist. For, non-existent entities cannot possess any attributes whatsoever. The positive attribute of universality provides us with solid ground to accept the laws of logic as having an ontological instantiation throughout reality.
However, the laws of logic are abstract objects. They don't stand in any causal relations to other entities. For example, the number 5 cannot mow my lawn or pick up my laundry. So in what sense do these abstract objects, especially the laws of logic, exist?
We have already ruled out a strong form of nominalism. We are left Platonism and conceptualism. The argument may go something like this:
1. Abstract objects are either a) non-existent, b) mind-independent entities, or c) mental concepts.
2. Abstract objects exist. (contrary to 1a)
3. Abstract objects are not mind-independent. (contrary to 1b)
4. Therefore, abstract objects are mental concepts. (From 1 - 3)
Now, why think premises (2) and (3) are correct? We have already given a defense the ontological instantiation of abstract objects, based on their having the attributes of universality and indispensability. As I stated above, the real meat of the debate is between the Platonist and the conceptualist. I concede that I find the arguments for the existence of abstract objects so compelling that if, hypothetically, I were to abandon conceptualism, I would gladly embrace Platonism.
Nevertheless, I think there are good arguments in favor of conceptualism, as well as good arguments against Platonism. Assuming that abstract objects are mind-independent entities that also lack any causal relations, how can we possibly have knowledge of them? There is a causal relationship between the mind knowing and the object being known by the mind. For example, as I look into my laptop's monitor, my eyes act as part of a bridge in the causal relationship between my mind and the monitor.
But on Platonism, there just is no causal relationship to appeal to because abstract object are causally effete. It is for this reason alone that I believe Platonism should be abandoned in favor of conceptualism.
The really interesting part here is that abstract objects cannot be grounded in just any mind. For there are contingent minds, much as myself, who are incapable of grounding any necessary truths. Instead, we ought to conclude that there exists a necessary mind that grounds abstract objects. But not only is this necessary mind the ground of abstract objects. Still further, this necessary mind must know all true propositions. The union of all true propositions is itself an abstract object. Since only an omniscient mind could know all true propositions, it follows that a necessary, eternal, omniscient mind exists.
More seriously, we might ask: how do we know X is true? Before determining whether X corresponds to reality in fact, we must determine whether X is logically coherent. Unless something is consistent with the laws of logic, then, it cannot exist. I realize I'm dumbing it down a bit here, but believe it or not, there are actually people who reject this line of thought. I won't pursue such a radical perspectivism at this juncture, though. In any case, the laws of logic are a necessary precondition of rational inquiry. Let's start our argument like this:
Axiom 1. One cannot be rational while rejecting rational inquiry.
Axiom 2. One cannot be rational while undermining the necessary preconditions of rational inquiry.
Here, now, is the first part of the proof, via reductio ad absurdum:
Prove A: The laws of logic are universal.
Assume ~A: The laws of logic are not universal.
~A --> B: If the laws logic are not universal, X can be ~X.
~B: X cannot be ~X.
~~A: by modus tollens.
Therefore, A: by negation, the laws of logic are universal.
Q.E.D.
Most fundamental to the laws of logic are the laws of identity, non-contradiction, and excluded middle. I would also add the transitive axiom (if A = B, and B = C, then A = C) to that list. In order to engage in rational inquiry, one must be consistent with at least these four laws of logic. They are transcendentals of rational inquiry.
Now comes the next part: from universality to existence. Does the universality of logic entail that it exists? One reason to think it does is that if X possesses the attribute of universality (I've also mentioned indispensability in the past), then X must exist. For, non-existent entities cannot possess any attributes whatsoever. The positive attribute of universality provides us with solid ground to accept the laws of logic as having an ontological instantiation throughout reality.
However, the laws of logic are abstract objects. They don't stand in any causal relations to other entities. For example, the number 5 cannot mow my lawn or pick up my laundry. So in what sense do these abstract objects, especially the laws of logic, exist?
We have already ruled out a strong form of nominalism. We are left Platonism and conceptualism. The argument may go something like this:
1. Abstract objects are either a) non-existent, b) mind-independent entities, or c) mental concepts.
2. Abstract objects exist. (contrary to 1a)
3. Abstract objects are not mind-independent. (contrary to 1b)
4. Therefore, abstract objects are mental concepts. (From 1 - 3)
Now, why think premises (2) and (3) are correct? We have already given a defense the ontological instantiation of abstract objects, based on their having the attributes of universality and indispensability. As I stated above, the real meat of the debate is between the Platonist and the conceptualist. I concede that I find the arguments for the existence of abstract objects so compelling that if, hypothetically, I were to abandon conceptualism, I would gladly embrace Platonism.
Nevertheless, I think there are good arguments in favor of conceptualism, as well as good arguments against Platonism. Assuming that abstract objects are mind-independent entities that also lack any causal relations, how can we possibly have knowledge of them? There is a causal relationship between the mind knowing and the object being known by the mind. For example, as I look into my laptop's monitor, my eyes act as part of a bridge in the causal relationship between my mind and the monitor.
But on Platonism, there just is no causal relationship to appeal to because abstract object are causally effete. It is for this reason alone that I believe Platonism should be abandoned in favor of conceptualism.
The really interesting part here is that abstract objects cannot be grounded in just any mind. For there are contingent minds, much as myself, who are incapable of grounding any necessary truths. Instead, we ought to conclude that there exists a necessary mind that grounds abstract objects. But not only is this necessary mind the ground of abstract objects. Still further, this necessary mind must know all true propositions. The union of all true propositions is itself an abstract object. Since only an omniscient mind could know all true propositions, it follows that a necessary, eternal, omniscient mind exists.
Sunday, August 14, 2011
A Plausible Ontological Argument
1. Necessarily, something exists. (Premise)
2. There is a possible state of affairs at which nothing contingent exists. (Premise)
3. If something exists and nothing contingent exists, then something necessary exists. (From 1 and 2)
4. Hence, something necessary possibly exists. (From 2 and 3)
5. Therefore, something necessary exists. (From 4 and S5)
Like all ontological arguments, it is really premise (1) that is most controversial. However, I think that the above premise (1) is quite obviously true, and not nearly as controversial as the usual "a maximally great being possibly exists." In its denial of ontological nihilism, the proponent may simply stress that a state of affairs at which nothing at all exists would itself be an existing entity. Of course, this commits us to either realism or conceptualism, the latter of which I prefer.
I would argue further that this necessary entity is a mental concept, which could only be grounded in a necessary mind, e.g. God. However, I don't want to pursue that argument at the moment.
For those skeptical of S5, let's instead consider the following reductio, having already granted the truth of (1) and (2):
Assume (6): a necessary entity does not exist. (6) and (2) imply that there is a possible state of affairs at which nothing exists. However, this contradicts (1), which states that something or other must exist. Therefore, (6) is false, and (5) is true. An appeal to S5, while legitimate, is unnecessary in this case.
Naturally, the Platonist will gladly accept the conclusion of this argument. If he is also an atheist, though, then he will presumably insist that the necessary entity concluded to in (5) is one of the forms, and not a concrete entity, such as God. The debate, then, turns upon whether one should adopt Platonism or conceptualism, but I regress.
2. There is a possible state of affairs at which nothing contingent exists. (Premise)
3. If something exists and nothing contingent exists, then something necessary exists. (From 1 and 2)
4. Hence, something necessary possibly exists. (From 2 and 3)
5. Therefore, something necessary exists. (From 4 and S5)
Like all ontological arguments, it is really premise (1) that is most controversial. However, I think that the above premise (1) is quite obviously true, and not nearly as controversial as the usual "a maximally great being possibly exists." In its denial of ontological nihilism, the proponent may simply stress that a state of affairs at which nothing at all exists would itself be an existing entity. Of course, this commits us to either realism or conceptualism, the latter of which I prefer.
I would argue further that this necessary entity is a mental concept, which could only be grounded in a necessary mind, e.g. God. However, I don't want to pursue that argument at the moment.
For those skeptical of S5, let's instead consider the following reductio, having already granted the truth of (1) and (2):
Assume (6): a necessary entity does not exist. (6) and (2) imply that there is a possible state of affairs at which nothing exists. However, this contradicts (1), which states that something or other must exist. Therefore, (6) is false, and (5) is true. An appeal to S5, while legitimate, is unnecessary in this case.
Naturally, the Platonist will gladly accept the conclusion of this argument. If he is also an atheist, though, then he will presumably insist that the necessary entity concluded to in (5) is one of the forms, and not a concrete entity, such as God. The debate, then, turns upon whether one should adopt Platonism or conceptualism, but I regress.
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