On the Aristotelian account of ethics, what is "good" for an agent depends on that agent's essence/nature/form as well as that form's characteristic natural ends. For example, it is good for a dog to reproduce, eat and drink, and have fully working senses, the reason being that reproduction, internal equilibrium, and various types of perception are some of the natural ends (in Greek, 'teloi') of a dog. When it comes to us humans the general outline remains the same, though we will have some differences insofar as humans are essentially different from dogs, and hence characterized by different natural ends.
Now, it seems plausible to think that there are necessary ethical truths. For instance, it is always wrong for people to torture little children just for the sake of it. But could the above Aristotelian account contradict this? It seems that, given human evolution, the conditions whereby natural selection brought about the existence of humans might have brought about evil counterparts, call them "anti-humans." All of their natural ends would be inverse to ours. For instance, while it is good and fulfilling of our ends to protect others, for the anti-humans it might be good and fulfilling of their ends to commit murder. Similarly, it might be good for them to rape, torture children, commit genocide, etc. Hence, what is good or bad is simply relative to whether you are a human or anti-human. Call this idea "Aristotelian Relativism."
There are a couple of ways an Aristotelian could get out of this relativism. First off, there is the theistic route. Given God's existence and the idea that goodness is grounded in his nature, this would provide an objective basis for the good which holds across all possible worlds. This prevents the instantiation of any species whose ends include raping and murdering their young, or something of that sort, thus making the anti-human scenario strictly speaking impossible.
There are also a couple of ways for a non-theist Aristotelian to respond. The first is to bite the bullet and say that such things which appear horrendous to us (and indeed are horrendous for us) would not be horrendous for some other kind of thing. It's not a reply we might like, but that's exactly what we should expect given that it is contrary to our nature to do these sorts of actions. When we see rape, cannibalism, and slaughter in the lower animals, though we are likely to be disturbed, we nevertheless admit that it is natural to those animals to bring about and flourish from these types of suffering.
A second and maybe more satisfying way to respond is to say that such a scenario is not metaphysically possible for a species of rational animals. Remember, though they may disturb us, we already acknowledge that cannibalism, slaughter, and forced sex can be fulfilling for some lower animals, as there are examples of this found in the natural world. But with rational animals it is different. Aristotle understood the essence of man not to consist in our purely biological properties, but rather in our rationality; hence, "rational animals". It is from this that he derived the virtues and goods that we already acknowledge. But that means that for anything which can be classified as a rational animal, it will be wrong for it to do the things such as murder, rape, and torture. Hence, the idea of an "anti-human" turns out to be contradictory. If anti-humans are rational animals, and Aristotle's derivation of the natural ends of rational animals is correct, then it's metaphysically impossible for murder, rape, and torture to be good for such creatures. Anti-humans, then, are metaphysically impossible, and the things we understand to be good for persons are necessarily good after all.
Tuesday, June 21, 2011
Monday, June 13, 2011
Friday, June 10, 2011
Aquinas' Intellectualism
From Mike Flynn: "The will is determined always to the good, but the intellect does not always know perfectly what is good, and a particular object may not be good from every perspective. If it were good from every perspective, the will could not freely withhold consent."
Question: What if the intellect did know perfectly what was good? If I'm understanding the Thomistic intellectualist position right, in that case we would make perfectly good choices.
For one, this appears to contradict Christian theology. God is all-good from every perspective. Yet the fallen angels are in their state because of their choice to sin against God. This is inexplicable given the framework where the will would be unable to freely withhold consent.
It also appears to cause problems for our personal responsibility. After all, what we choose depends on what is in our intellect. What is in our intellect is what first comes through our senses (according to Aquinas in De Veritate). So what we choose is dependent on what comes through our senses. This would imply that whether we make good or bad choices and become good or bad people is ultimately dependent on our "sensory history", i.e. whether or not we are fortunate enough to have had the types of sensations which would lead to our apprehending the types of truths which would cause us to act well. And if that's the case, it seems our action is ultimately just a matter of our having this flux of sensory stimuli rather than another. This isn't much better than the materialist picture; we're not the proper source of our actions.
Another problem is that some people have better intellects, if that makes sense. Of course, someone with a good intellect may not have a very congenial sensory history. This would explain why smart people can turn out wicked. But for those who have better intellects and better sensory histories, being directed to the good will come much easier to them insofar as they can apprehend truth and goodness more clearly than others. Thus, by chance, they're at an unfair advantage.
It seems safe to say that this means when we're punishing criminals we're ultimately (a) punishing them for not being gifted with a good intellect or (b) punishing them for not having the right sensory history. However, one should not be punished for external contingencies beyond one's control.
Question: What if the intellect did know perfectly what was good? If I'm understanding the Thomistic intellectualist position right, in that case we would make perfectly good choices.
For one, this appears to contradict Christian theology. God is all-good from every perspective. Yet the fallen angels are in their state because of their choice to sin against God. This is inexplicable given the framework where the will would be unable to freely withhold consent.
It also appears to cause problems for our personal responsibility. After all, what we choose depends on what is in our intellect. What is in our intellect is what first comes through our senses (according to Aquinas in De Veritate). So what we choose is dependent on what comes through our senses. This would imply that whether we make good or bad choices and become good or bad people is ultimately dependent on our "sensory history", i.e. whether or not we are fortunate enough to have had the types of sensations which would lead to our apprehending the types of truths which would cause us to act well. And if that's the case, it seems our action is ultimately just a matter of our having this flux of sensory stimuli rather than another. This isn't much better than the materialist picture; we're not the proper source of our actions.
Another problem is that some people have better intellects, if that makes sense. Of course, someone with a good intellect may not have a very congenial sensory history. This would explain why smart people can turn out wicked. But for those who have better intellects and better sensory histories, being directed to the good will come much easier to them insofar as they can apprehend truth and goodness more clearly than others. Thus, by chance, they're at an unfair advantage.
It seems safe to say that this means when we're punishing criminals we're ultimately (a) punishing them for not being gifted with a good intellect or (b) punishing them for not having the right sensory history. However, one should not be punished for external contingencies beyond one's control.
Friday, May 20, 2011
Is Nihilism Self-Refuting?
Woo, been a while since a post. Okay. Consider the following argument, contra moral nihilism, i.e. the view that nothing is moral or immoral:
(1) If a belief is true, then we ought to believe it.
(2) Nihilism is a belief.
So, (3) If nihilism is true, then we ought to believe it.
(4) It is not the case that we ought to believe nihilism.
Therefore, (5) Nihilism is not true.
Is there something to 1 such that, if a nihilist were to deny it, he would be leading himself to irrationality? It would seem so. The denial of 1 is, after all, "It is not the case that if a belief is true, we ought to believe it." This seems to almost undercut the entire idea of rational argument. Denying 1 would also mean that it's not the case that, if nihilism were true, then we ought to believe it. Maybe they're fine with that, but I'm sure as heck not becoming a moral nihilist if I don't have any obligation to.
The nihilist seems to be committed to 4, since any "oughts" related to things like intellectual virtue or intellectual honesty are false on nihilism; these are, after all, ethical ideas (honesty is a virtue).
Maybe the nihilist could find some way of understanding "ought" which is entirely unrelated to ethics, making it possible to affirm that if a belief is true, then we ought to believe it, along with an obligation to believe nihilism. All of this without committing to the truth of any moral theses. This already seems implausible as such. Questions of epistemic justification, intellectual responsibility, and warrant are probably inseparable from ethics in some way. Nevertheless, suppose the nihilists pull it off. This leads to there being at least some normativity and responsibility, and the possibility of normativity and obligation in one sphere makes it harder to see why the nihilist would deny normativity and obligation in the sphere of ethics.
The situation looks grim for the nihilist then. They can (A) deny 1, implying that we're free to believe whatever we please (including the falsity of nihilism), as well as making the whole project of rational argumentation dubitable, or (B) deny 4 and accept that there is some normativity and obligation, putting them at odds with their claims about ethics. Or maybe they'll come to terms and accept all our premises. :-)
That's all a little sloppy I think, but I hope it makes sense. If not, please tell me.
P.S., birthday in two days! Would be a nice birthday present if I could figure out the soundness of this argument.
(1) If a belief is true, then we ought to believe it.
(2) Nihilism is a belief.
So, (3) If nihilism is true, then we ought to believe it.
(4) It is not the case that we ought to believe nihilism.
Therefore, (5) Nihilism is not true.
Is there something to 1 such that, if a nihilist were to deny it, he would be leading himself to irrationality? It would seem so. The denial of 1 is, after all, "It is not the case that if a belief is true, we ought to believe it." This seems to almost undercut the entire idea of rational argument. Denying 1 would also mean that it's not the case that, if nihilism were true, then we ought to believe it. Maybe they're fine with that, but I'm sure as heck not becoming a moral nihilist if I don't have any obligation to.
The nihilist seems to be committed to 4, since any "oughts" related to things like intellectual virtue or intellectual honesty are false on nihilism; these are, after all, ethical ideas (honesty is a virtue).
Maybe the nihilist could find some way of understanding "ought" which is entirely unrelated to ethics, making it possible to affirm that if a belief is true, then we ought to believe it, along with an obligation to believe nihilism. All of this without committing to the truth of any moral theses. This already seems implausible as such. Questions of epistemic justification, intellectual responsibility, and warrant are probably inseparable from ethics in some way. Nevertheless, suppose the nihilists pull it off. This leads to there being at least some normativity and responsibility, and the possibility of normativity and obligation in one sphere makes it harder to see why the nihilist would deny normativity and obligation in the sphere of ethics.
The situation looks grim for the nihilist then. They can (A) deny 1, implying that we're free to believe whatever we please (including the falsity of nihilism), as well as making the whole project of rational argumentation dubitable, or (B) deny 4 and accept that there is some normativity and obligation, putting them at odds with their claims about ethics. Or maybe they'll come to terms and accept all our premises. :-)
That's all a little sloppy I think, but I hope it makes sense. If not, please tell me.
P.S., birthday in two days! Would be a nice birthday present if I could figure out the soundness of this argument.
Saturday, April 9, 2011
Does Conceivability Entail Possibility?
The following should probably be pretty clear to some people. Just another way of showing that conceivability does not imply possibility. The proof will go somewhat informally with a few hidden premises, and I'm not even sure if it's any good.
Suppose
(1) If I can conceive of a possible world, then such a world exists. (This doesn't mean it's actual of course.)
Further,
(2) I can conceive of a possible world which is empty.
(3) Therefore, there is an empty possible world.
(4) I can conceive of a necessary being.
One can easily deduce from (4) that
(5) Therefore, there is no empty possible world.
(6) Therefore, there is an empty possible world and there is no empty possible world.
(7) Therefore, ~(1). (because 1 implies a contradiction, viz. 6)
By "empty possible world" I mean a world in which no entities exist. Some may object that this is harder to understand than at first sight, and may in fact be inconceivable. For those who agree that it is conceivable we've shown that (1) is false. For the skeptic's sake let's take a less controversial example. Let's say that in every possible world there exists at least one entity. This isn't to say that in each world it is the same entity, i.e. we're not saying there exists something x such that x exists in all possible worlds. To illustrate the point let's use a little bit of basic sets. Take two sets A = {1,2} and B = {3,4). These two sets are disjoint. If you tried to find a set which has as its elements/members all x such that x is in A and x is in B you'd come up with an empty set. In other words, they have no members in common. In an analogous way we can conceive of two possible worlds being "disjoint", that is, not having any entities in common. So we can say
(8) I can conceive of two "disjoint" possible worlds.
(9) Therefore, there are two disjoint possible worlds.
Remember, this is consistent with our rejection of (2).
(10) If there are two disjoint possible worlds, then there are no entities common to all possible worlds.
(11) Therefore, there are no entities common to all possible worlds
(12) If a necessary being is possible, then there are some entities which are common to all possible worlds.
(13) Therefore, there are some entities common to all possible worlds. (One could easily show that this follows.)
We've of course come to our flat contradiction with (11) and (13) and shown (1) to be false.
Without (1) how can we learn about metaphysical possibility? It seems to me that we'll have to go back to those good ol' essences, thus raising the further question of how we can know both essences and their implications. I wonder though how we can figure out why anything exists at all. We can't turn to essences to learn about the modal properties of being. Being has no "essence", since it's a transcendental. The falsity of (1) also has implications for those who want to create modal arguments for God. We can't just go based on God's conceivability. It's interesting to note that Robert Maydole's proof of the Maximally Great Being's (MBG) metaphysical possibility seems to rely on the very essence of the MGB.
P.S. Now we've got Ss. Augustine, Anselm, and Bonaventure praying for us on the side. :-)
Suppose
(1) If I can conceive of a possible world, then such a world exists. (This doesn't mean it's actual of course.)
Further,
(2) I can conceive of a possible world which is empty.
(3) Therefore, there is an empty possible world.
(4) I can conceive of a necessary being.
One can easily deduce from (4) that
(5) Therefore, there is no empty possible world.
(6) Therefore, there is an empty possible world and there is no empty possible world.
(7) Therefore, ~(1). (because 1 implies a contradiction, viz. 6)
By "empty possible world" I mean a world in which no entities exist. Some may object that this is harder to understand than at first sight, and may in fact be inconceivable. For those who agree that it is conceivable we've shown that (1) is false. For the skeptic's sake let's take a less controversial example. Let's say that in every possible world there exists at least one entity. This isn't to say that in each world it is the same entity, i.e. we're not saying there exists something x such that x exists in all possible worlds. To illustrate the point let's use a little bit of basic sets. Take two sets A = {1,2} and B = {3,4). These two sets are disjoint. If you tried to find a set which has as its elements/members all x such that x is in A and x is in B you'd come up with an empty set. In other words, they have no members in common. In an analogous way we can conceive of two possible worlds being "disjoint", that is, not having any entities in common. So we can say
(8) I can conceive of two "disjoint" possible worlds.
(9) Therefore, there are two disjoint possible worlds.
Remember, this is consistent with our rejection of (2).
(10) If there are two disjoint possible worlds, then there are no entities common to all possible worlds.
(11) Therefore, there are no entities common to all possible worlds
(12) If a necessary being is possible, then there are some entities which are common to all possible worlds.
(13) Therefore, there are some entities common to all possible worlds. (One could easily show that this follows.)
We've of course come to our flat contradiction with (11) and (13) and shown (1) to be false.
Without (1) how can we learn about metaphysical possibility? It seems to me that we'll have to go back to those good ol' essences, thus raising the further question of how we can know both essences and their implications. I wonder though how we can figure out why anything exists at all. We can't turn to essences to learn about the modal properties of being. Being has no "essence", since it's a transcendental. The falsity of (1) also has implications for those who want to create modal arguments for God. We can't just go based on God's conceivability. It's interesting to note that Robert Maydole's proof of the Maximally Great Being's (MBG) metaphysical possibility seems to rely on the very essence of the MGB.
P.S. Now we've got Ss. Augustine, Anselm, and Bonaventure praying for us on the side. :-)
Saturday, March 26, 2011
False Senses of God's Goodness
Introduction:
What does God's omnibenevolence consist in? I think that we need to do a little more work on fully explaining what we mean by this. In fact I'm somewhat distraught, because it seems that if we affirm God's all-goodness we should already know what we're talking about. I think that some of the notions which are typically bound up with omnibenevolence really don't make sense.
In a post a while back I presented the Prussian Free Will Defense. I think the argument is sound. The conclusion that we end up drawing from it is the following. It will be important in determining what omnibenevolence can be and what it cannot be:
(C1) It is not the case that there is some moral principle in the nature of an omnibenevolent and omnipotent being which prevents him from creating a creature who does something immoral.
"Actualizing all possible goods":
I think it's relatively easy to understand omnipotence and omniscience. Omnipotence is just the ability to do all that is possible. Omniscience is just the knowing of all things. So does omnibenevolence consist in the actualizing of all good things?
I'm convinced that this notion is incoherent. (C1) shows that God's omnibenevolence is compatible with God's not actualizing worlds which he could have actualized in which all moral agents always freely choose to do the right thing. And that is certainly incompatible with God's omnibenevolence meaning that he actualizes all possible goods.
The idea that omnibenevolence means "actualizing every possible good" is probably in contradiction with the idea of omnipotence anyhow. One could think of two goods which are mutually exclusive but are both within the range of God's power. For example, my marrying Lucy and my marrying Edith are both goods which are mutually exclusive and possible for God to actualize. However, God can only bring about one of these. Hence, if God is omnipotent, he can't be omnibenevolent if that means that he actualizes every possible good; there are some goods which God could actualize but doesn't.
"Preventing all unnecessary evil":
It seems that the existence of an all-good being must preclude the existence of unnecessary evil. Responses to the problem of evil like Plantinga's Free Will Defense say that some evils which take place are justified by greater goods. But the atheist objects that there are some evils which are probably not justified by greater goods, and in general, the theist agrees that if this were true then an omnibenevolent God would not exist. The typical attempt to solve the problem is to claim that no evils are unnecessary.
But what if the theist were to take a different route and say that even if there were evils which could have been prevented that this doesn't rule out the existence of an all-good God? In fact, I think (C1) shows that this is true. For take again the possible world W1 in which all agents always freely choose to do what is good. (C1) shows that there is no moral principle in the nature of an omnibenevolent being which prevents him from actualizing a world W2 where an evil is committed even though he could have actualized W1 instead. But in that case, some of the evils which take place are unnecessary; they could have been prevented by God's actualizing W1.
A Problem:
So we see that, based on (C1), omnibenevolence cannot imply the actualizing of all possible goods. Neither does it imply the preventing of all unnecessary evils. Yet this seems to sap omnibenevolence of any real content. How could we call something "all-good" which allows needless suffering and withholds a great many good things from us?
To me this is a big problem. I want to find some possible ways in which we can understand omnibenevolence in light of these objections. Any thoughts?
What does God's omnibenevolence consist in? I think that we need to do a little more work on fully explaining what we mean by this. In fact I'm somewhat distraught, because it seems that if we affirm God's all-goodness we should already know what we're talking about. I think that some of the notions which are typically bound up with omnibenevolence really don't make sense.
In a post a while back I presented the Prussian Free Will Defense. I think the argument is sound. The conclusion that we end up drawing from it is the following. It will be important in determining what omnibenevolence can be and what it cannot be:
(C1) It is not the case that there is some moral principle in the nature of an omnibenevolent and omnipotent being which prevents him from creating a creature who does something immoral.
"Actualizing all possible goods":
I think it's relatively easy to understand omnipotence and omniscience. Omnipotence is just the ability to do all that is possible. Omniscience is just the knowing of all things. So does omnibenevolence consist in the actualizing of all good things?
I'm convinced that this notion is incoherent. (C1) shows that God's omnibenevolence is compatible with God's not actualizing worlds which he could have actualized in which all moral agents always freely choose to do the right thing. And that is certainly incompatible with God's omnibenevolence meaning that he actualizes all possible goods.
The idea that omnibenevolence means "actualizing every possible good" is probably in contradiction with the idea of omnipotence anyhow. One could think of two goods which are mutually exclusive but are both within the range of God's power. For example, my marrying Lucy and my marrying Edith are both goods which are mutually exclusive and possible for God to actualize. However, God can only bring about one of these. Hence, if God is omnipotent, he can't be omnibenevolent if that means that he actualizes every possible good; there are some goods which God could actualize but doesn't.
"Preventing all unnecessary evil":
It seems that the existence of an all-good being must preclude the existence of unnecessary evil. Responses to the problem of evil like Plantinga's Free Will Defense say that some evils which take place are justified by greater goods. But the atheist objects that there are some evils which are probably not justified by greater goods, and in general, the theist agrees that if this were true then an omnibenevolent God would not exist. The typical attempt to solve the problem is to claim that no evils are unnecessary.
But what if the theist were to take a different route and say that even if there were evils which could have been prevented that this doesn't rule out the existence of an all-good God? In fact, I think (C1) shows that this is true. For take again the possible world W1 in which all agents always freely choose to do what is good. (C1) shows that there is no moral principle in the nature of an omnibenevolent being which prevents him from actualizing a world W2 where an evil is committed even though he could have actualized W1 instead. But in that case, some of the evils which take place are unnecessary; they could have been prevented by God's actualizing W1.
A Problem:
So we see that, based on (C1), omnibenevolence cannot imply the actualizing of all possible goods. Neither does it imply the preventing of all unnecessary evils. Yet this seems to sap omnibenevolence of any real content. How could we call something "all-good" which allows needless suffering and withholds a great many good things from us?
To me this is a big problem. I want to find some possible ways in which we can understand omnibenevolence in light of these objections. Any thoughts?
Wednesday, March 23, 2011
What Does It Take to Be An Atheist?
Consider some valid theistic arguments and what an atheist must do to deny their soundness.
Argument A - A Necessary Concrete Entity:
(1) Possibly a necessary concrete being exists implies a necessary concrete being exists.
(2) Possibly, a necessary concrete being exists.
(3) Therefore, a necessary concrete being exists.
Assume further that it can be shown that the necessary being is God.
What must the atheist do to deny this argument? (1) is just axiom S5. Therefore they must deny (2). This implies that (a) possibly nothing exists or (b) necessarily, there exists at least one contingent entity. This also implies that all concrete entities are contingent.
Atheist Theorem 1 (AT1): It is not possible that a necessary concrete being exists.
Atheist Theorem 2 (AT2): Either (a) possibly nothing exists or (b) necessarily there exists at least one contingent entity.
Atheist Theorem 3 (AT3): For any concrete entity x, x is contingent.
Disproving AT1, AT2 or AT3 is sufficient for refuting atheism.
Argument B - The Scotistic Cosmological Argument:
(1') Whatever is possible is contingent or necessary.
(2') A first cause is possible.
(3') Therefore, a first cause is contingent or necessary.
(4') Any contingent substance is possibly actualized by another substance.
(5') A first cause is not possibly actualized by another substance.
(6') Therefore a first cause is not contingent.
(7') Therefore, a first a cause is necessary.
What must the atheist do to deny this argument? The atheist can only really deny either (2) or (4).
Atheist Theorem 4 (AT4): Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
Hence, disproving this disjunction AT4 is sufficient for refuting atheism. Saying that (b) is false also leads to some interesting consequences about infinite regresses.
Argument C – A Modal Cosmological Argument:
(1*) Every contingent entity possibly has an external cause.
(2*) If the sum total of contingent concrete entities C has an external cause, that cause is necessary.
(3*) C is a contingent concrete entity.
(4*) Possibly, C has an external cause.
(5*) Therefore, possibly there is a necessary cause of C.
(6*) Therefore, there is a necessary cause of C.
What must the atheist deny? All premises seem quite strong. He must then deny (1*).
Atheist Theorem 5 (AT5): For some concrete contingent entity x it is impossible that x is caused.
Disproving AT5 is sufficient for disproving atheism.
Thus far we have Atheist Theorems 1-5:
AT1: It is not possible that a necessary concrete being exists.
AT2: Either (a) possibly nothing exists or (b) necessarily at least one contingent entity exists.
AT3: For any concrete entity x, x is contingent.
AT4: Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
AT5: For some concrete contingent entity x it is impossible that x is caused.
Disproving one of these theorems is sufficient for disproving atheism. Showing a contradiction between these beliefs and other atheist beliefs is sufficient for showing atheism as such to be incoherent. To me all of these propositions seem quite implausible in their own right.
Argument A - A Necessary Concrete Entity:
(1) Possibly a necessary concrete being exists implies a necessary concrete being exists.
(2) Possibly, a necessary concrete being exists.
(3) Therefore, a necessary concrete being exists.
Assume further that it can be shown that the necessary being is God.
What must the atheist do to deny this argument? (1) is just axiom S5. Therefore they must deny (2). This implies that (a) possibly nothing exists or (b) necessarily, there exists at least one contingent entity. This also implies that all concrete entities are contingent.
Atheist Theorem 1 (AT1): It is not possible that a necessary concrete being exists.
Atheist Theorem 2 (AT2): Either (a) possibly nothing exists or (b) necessarily there exists at least one contingent entity.
Atheist Theorem 3 (AT3): For any concrete entity x, x is contingent.
Disproving AT1, AT2 or AT3 is sufficient for refuting atheism.
Argument B - The Scotistic Cosmological Argument:
(1') Whatever is possible is contingent or necessary.
(2') A first cause is possible.
(3') Therefore, a first cause is contingent or necessary.
(4') Any contingent substance is possibly actualized by another substance.
(5') A first cause is not possibly actualized by another substance.
(6') Therefore a first cause is not contingent.
(7') Therefore, a first a cause is necessary.
What must the atheist do to deny this argument? The atheist can only really deny either (2) or (4).
Atheist Theorem 4 (AT4): Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
Hence, disproving this disjunction AT4 is sufficient for refuting atheism. Saying that (b) is false also leads to some interesting consequences about infinite regresses.
Argument C – A Modal Cosmological Argument:
(1*) Every contingent entity possibly has an external cause.
(2*) If the sum total of contingent concrete entities C has an external cause, that cause is necessary.
(3*) C is a contingent concrete entity.
(4*) Possibly, C has an external cause.
(5*) Therefore, possibly there is a necessary cause of C.
(6*) Therefore, there is a necessary cause of C.
What must the atheist deny? All premises seem quite strong. He must then deny (1*).
Atheist Theorem 5 (AT5): For some concrete contingent entity x it is impossible that x is caused.
Disproving AT5 is sufficient for disproving atheism.
Thus far we have Atheist Theorems 1-5:
AT1: It is not possible that a necessary concrete being exists.
AT2: Either (a) possibly nothing exists or (b) necessarily at least one contingent entity exists.
AT3: For any concrete entity x, x is contingent.
AT4: Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
AT5: For some concrete contingent entity x it is impossible that x is caused.
Disproving one of these theorems is sufficient for disproving atheism. Showing a contradiction between these beliefs and other atheist beliefs is sufficient for showing atheism as such to be incoherent. To me all of these propositions seem quite implausible in their own right.
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