It's often said that Plantinga *refuted* the logical problem of evil -- i.e., that he demonstrated that' there's no logical inconsistency between the existence of an all-knowing, all-powerful, and perfectly good god, on the one hand, and evil on the other. This is extremely misleading. To see why, consider the following three claims, in descending order in terms of strength of claim:
1. The following is a fact: Possibly, every creature that God can create would freely perform at least one morally wrong action.
2. Here is a story that we have decent reason to believe is true: Possibly, every creature that God can create would freely perform at least one morally wrong action.
3. Here is a claim that we can't rule out for sure as false: Possibly, every creature that God can create would freely perform at least one morally wrong action.
Now many apologists talk as though Plantinga has shown that (1) or (2) is true. These are the sorts of claims that Plantinga would have to have vindicated for the apologists to be right. However, Plantinga has only shown that (3) is true.
As you can see, (3) is a bit less interesting than (1) and (2). According to the latter two claims, it would be true, or at least more reasonable to believe than not, that there are possible worlds in which it's possible that God and evil can co-exist, in which case the logical problem of evil would indeed be defeated in a way that would make the agument a failure. For on either of these two claims, it would be true, or more reasonable than not, to think that God and evil are compatible.
However, (3) doesn't show anything as strong as this. Consider the following two claims:
4. Theist to the non-theist: I've shown that *you are unreasonable* to think that God and evil can't coexist. I've shown that the deductive argument from evil is unsound.
5. Theist to the non-theist: I've shown you that *I'm not unreasonable* to think that God and evil can coexist, given that I also have strong enough evidence or warrant for thinking that theism is true. I've shown that we can't be absolutely sure that God and evil can coexist.
(1) and (2) give reason to accept (4); (3) only gives reason to accept (5). And the latter is all that Plantinga has done. But establishing (5) isn't sufficient to show that the deductive version of the problem of evil argument is unsound -- i.e., it may well be sound; it's just that we're not sure that it is.
Three relatively recent works have been published that underscore the point above:
-Michael Bergmann's "Might-Counterfactuals, Transworld Untrustworthiness, and Plantinga's Free Will Defense", Faith and Philosophy 16:3 (1999), 336-351.
-Daniel Howard-Snyder and John Hawthorne, "Transworld Sanctity and Plantinga's Free Will Defense", Int'l. Journal for Philosophy of Religion 44 (1998), 1-21.
-The chapter on Plantinga on the logical problem of evil in James F. Sennett's book on Plantinga's Philosophy, viz., Modality, Probability, and Rationality
Interestingly, all of these philosophers are fairly conservative christians.
A Critique of the Kalam Cosmological Argument
(Note: I've posted this previously at Debunking Christianity.
You can go to the archives at that site and read the follow-up of objections
and replies in the "comments" section below the post)
On the Possibility of a Beginningless Past: A Reply to Craig
William Lane Craig has argued vigorously that, cosmological discoveries aside, it’s reasonable to believe on purely a priori grounds that the set of past events is finite in number.1 He offers two main types of a priori arguments for this claim: (i) that it’s metaphysically impossible for an actually infinite set of concrete things to exist, in which case the set of past events can’t be actually infinite, and (ii) that even if such a set could exist, it’s impossible to traverse it even in principle. Craig doesn’t pursue this claim for it’s own sake, however. Rather, he does so as a means to demonstrating that a theistic god exists. He reasons that if the set of past events is finite, then the universe as a whole had an absolute beginning with the first moment of time2. But since nothing can come into existence without a cause, the universe as a whole has a cause. From here, he goes on to argue that such a cause must be timeless (at least sans creation), immaterial, immensely powerful, and a person of some sort.
I intend to show that one of Craig’s most popular versions of (ii) is unsound. In this essay, I’ll state this argument, prefacing it with an explanation of the concepts crucial to understanding it. Then, I’ll examine a common objection to his argument, along with Craig’s response to it, in order to shed light on an unstated assumption of the argument. Finally, I’ll show that the unstated assumption is false, and how this is fatal to his argument.
I
As I mentioned above, several concepts that are crucial for understanding the argument need clarification.3 First of all, one needs a fairly perspicuous idea of a set and of a proper subset. A set is a collection of entities, called members of the set. The precise number of members contained in a set is its cardinal number. A proper subset is a part of another set, the former lacking at least one member which the latter contains, and which contains no other members (e.g., from a totally distinct set). More formally, a set A is a proper subset of a set B if and only if every member of A is a member of B, and some member of B isn’t a member of A. To illustrate: Suppose you have ten bottlecaps, five of which are from Pepsi bottles and five of which are from Coke bottles. Then we can call this the set of bottlecaps, the cardinal number of which is 10. Let’s call this set, A. Furthermore, the set of Pepsi caps (call it B) is a proper subset of A, since B consists in a collection of members that belong to A, and A has members that B does not (i.e., the Coke caps).
Another concept that plays an important role in the argument is that of a one-to-one-correspondence. This is a concept used to determine whether two sets have the same number of members (or, the same cardinal number). So there is a one-to-one correspondence between two sets, A and B, if and only if each member of A can be paired up with exactly one member of B, and each member of B can be paired up with exactly one member of A. To illustrate this concept, consider our set of bottlecaps. Now suppose that you didn’t know how to count, but you wanted to know if your had just as many Coke caps as you had of Pepsi caps. You could accomplish this task by pairing each Coke cap with each Pepsi cap, and each Pepsi cap with each Coke cap. If this can be accomplished with no remaining bottlecaps, then there is a one-to-one correspondence between the set of Pepsi caps and the set of Coke caps. If follows that the respective sets of bottlecaps have the same cardinal number.
The concept most important for our purposes is that of actual infinity. To obtain a grasp of this concept, consider the set of all the natural numbers (i.e., {1, 2, 3, …}). This set, as well as any set that can be put into a one-to-one correspondence with it, is an actually infinite set (It’s actually the “smallest” of the infinite sets, but we won’t be concerned with “larger” infinites here). An actual infinite has several interesting features. First of all, it is complete, in the sense that it has an infinite number of members; it is not merely increasing in number without limit. Second, any actually infinite set (of the “size” we’re here considering) can be put into a one-to-one correspondence with one of its proper subsets. This can be demonstrated by putting the set of natural numbers in a one-to-one correspondence with its proper subset of even numbers:
1 2 3 4…
2 4 6 8…
This example shows that a part of an actually infinite set can have as many members as the whole set! The cardinal number of an actually infinite set that can be put into a one-to-one correspondence with the natural numbers is called “aleph null” (let’s use ‘A0’ for brevity).
The final concept relevant to our discussion is order-type. I won’t talk at length about this concept here. Rather, I’ll barely do more than mention the order-types of certain sets containing A0 members. Four our purposes, it will suffice to know that sets can be sequentially ordered according to certain patterns or types. The order-type given to the set of natural numbers so ordered that, beginning with 1, each natural number is succeeded by the next largest natural number – i.e., {1, 2, 3, …} – is ‘omega’, or 'w’, and the set of negative integers so ordered that they are sequentially the opposite of w is w* (i.e., {…-3, -2, -1}). Sets with A0 members can have other order-types, however. For example, an A0 set can have the order type w+1 (i.e., {1, 2, 3, ..., 1}), or the order-type w+2 (i.e., {1, 2, 3, …, 1, 2}), etc. In fact, a set with A0 members can have the order-type w+w (i.e., {1, 2, 3, …, 1, 2, 3, …}), or the order-type w+w+w (i.e., {1, 2, 3, …., 1, 2, 3, …, 1, 2, 3, …}), etc.! To see this, recall that any set that can be put into a one-to-one correspondence with the natural numbers has a cardinal number of A0. But sets with the order-types mentioned above can be put into such a correspondence. So, for example, a set with the order-type w+1 can be put into a one-to-one correspondence with the natural numbers as follows:
1 1 2 3…
1 2 3 4…
Similarly, a set with the order-type w+w+w can be put into a one-to-one correspondence with the natural numbers as follows:
1 2 3…1 2 3…1 2 3…
1 4 7…2 5 8…3 6 9…
Therefore, since sets with such order-types can be put into a one-to-one correspondence with the natural numbers, it follows that their cardinal number is A0.
At this point, an interesting feature of certain sets with A0 members emerges. For consider any A0 set with an order-type other than w. For example, consider a set of A0 offramps on an infinitely long freeway, such that a distance of one mile separates each offramp from its predecessor and successor (except, of course, the first offramp, since it has no predecessor). Suppose further that the order-type of the offramps is w+1 ({1, 2, 3, …, 1}). The offramp assigned the first 1 would seem to be infinitely distant from the offramp assigned the second 1. Such a set has the interesting feature of being non-traversable in principle – it cannot, even in principle, be exhaustively counted through one offramp at a time. This is because it is logically impossible to count to a number that has no immediate predecessor. But the offramp assigned the second 1 has no immediate predecessor. Therefore, a driver on such a freeway could never reach the offramp assigned the second 1. Call this particular logical ban on traversing sets with w+1 or “higher” order-types ‘LB’.
Now it may be tempting to think that this consideration is decisive for the view that the past must be finite, since any set with A0 members can be ordered according to the order-type w+1. In this way, one might think, LB infects all actually infinite sets, and thus no set with A0 members is traversable. This reasoning can be expressed as follows:
1. A set is LB non-traversable if and only if it contains at least one member A0 distant from at least one of the other of its members.
2. Any set with the order-type w+1 is such that it contains a member A0 distant from at least one of the other of its members.
3. Therefore, any set with the order-type w+1 is LB non-traversable.
4. Any set with A0 members can be assigned the order-type w+1.
5. Therefore, any set with A0 members is LB non-traversable.
But this would be rash. For the inference from (3) and (4) to (5) is a non sequitur. For consider a set with A0 members that is assigned the order-type w. A set with this order-type is such that (i) no member is infinitely distant from any other member, and (ii) each member does have an immediate predecessor, as so is immune to LB. But any set with A0 members can be assigned the order-type w. So if the inference from (3) and (4) to (5) were valid, then by similar reasoning the following inference should go through as well:
3’. Any set with the order-type w is not LB non-traversable.
4’. Any set with A0 members can be assigned the order-type w.
5’. Therefore, any set with A0 members is not LB non-traversable.
But (5’) contradicts (5). Therefore, since the same pattern of reasoning yields contradictory results, it’s faulty. So, just because an A0 set can be assigned a non-traversable order-type, it doesn’t follow that such a set is non-traversable. What really follow from (3) and (4) is rather
5’’. Any set with A0 members can be assigned an LB non-traversable order-type.
Which, needless to say, doesn’t help to establish the finitude of the set of past events.
The arguments above suffer from another problem as well. For (2) is clearly false. To see this, consider again our infinitely long freeway. No suppose that it only has one lane, and that it has an infinitely long traffic jam. Finally, suppose that each car in the jam is assigned a number from the order-type w+1. Does it follow that there is a car A0 distant from any other car? No. For the car assigned the second 1 could be immediately in front of the first car. This illustration shows that the order-type assigned to a set of objects doesn’t necessarily affect the distances between its members. To drive this implication home, suppose that the cars of the traffic jam were assigned the order-type w. Would it follow that no car is A0 distant from any other car? Not in the least. For the first and second cars may be infinitely distant from one another. One might reply that we could just stipulate that the distances between the cars and the order-type assigned to the cars correspond. In such a case, each car would only be finitely distant from every other car when assigned the order-type w (e.g., the second car is 2 meters from the end of the traffic jam, the third car is 3 meters from the end of the jam, etc. [these are small cars!]). One could then reassign the cars with the order-type w+1, but then the correspondence between the order-type and the distances of the cars would break down. This is because no car assigned a number from the w order-type in our scenario is infinitely distant from any other car. Therefore, the second 1 of the newly assigned w+1 reordering would be assigned to a car that is only finitely distant from any other car. These illustrations show that (i) some sets assigned the order-type w+1 are such that no member is infinitely distant from any other, and (ii) we can know a priori than an A0 set of concrete objects cannot be reordered from w to w+1 in such a way that the distances between the members of such a set correspond to their order-type. Therefore, if a set of objects has A0 members (arranged linearly), it does not follow from this that it has members infinitely distant (whether in time or in space) from other members (and is therefore LB non-traversable).4 Thus, to show that an A0 past is non-traversable, Craig must show that no A0 set with either the order-type w or w* (and is such that no member is infinitely distant from any other) is traversable. Let’s consider one of Craig’s main attempts to do this.
II
Craig advances an argument for the proposition that one cannot traverse a beginningless past and end at the present moment.5 To do this, Craig assumes, for the sake of argument, that there could be a beginningless past, conceived as a set of events with the cardinal number A0 and the order-type w* (i.e., {…,. -3, -2, -1}), where each negative integer represents an event of the past. He then argues,
“…suppose we meet a man who claims to have been counting down from eternity and who is now finishing:…,-3, -2, -1, 0. We could ask, why didn’t he finish counting yesterday or the day before or the year before? By then an infinite amount of time had already elapsed, so that he should already have finished. Thus, at no point in the infinite past could we ever find the man finishing his countdown, for by that point he should already be done! In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will already be finished. But if at no point in the past do we find him counting, this contradicts the hypothesis that he has been counting down from eternity.”6
Craig’s argument is a reductio ad absurdum, where we suppose that a beginningless past is possible in order to show that it entails a contradiction. The argument can be expressed as follows, with (1) as the premise set up for reduction:
1. The past is beginningless (conceived as a set of events with the cardinality A0, and the order-type w*).
2. If the past is beginningless, then there could have been an immortal counter who counts down from such a past at the rate of one negative integer per day.
3. The immortal counter will finish counting if and only if he has an infinite number of days in which to count them.
4. If the past is beginningless, then there are an infinite number of days before every day.
5. Therefore, the immortal counter will have finished counting before every day.
6. If the immortal counter will have finished counting before every day, then he has never counted.
7. Therefore, the immortal counter has both never counted and has been counting down from a beginningless past (contradiction)
8. Therefore, the past is not beginningless (from 1-7, reductio)
In short, Craig argues that the past must -- logically must -- have a beginning. For the very notion of traversing a beginningless past entails a contradiction. Craig’s underlying intuition here is that if the past is beginningless, then it must contain an actually infinite proper subset of events that was not formed by successive addition, and that this is absurd.
Critics typically attack (3), arguing that Craig mistakenly assumes that to count an infinite number of negative integers is to count all of them. However, critics of Craig’s argument point out that one can count an infinite set of numbers without counting them all.7 For example, suppose our eternal counter just finished counting all the negative integers down to -3. Then it would be true that he has counted an infinite number of integers, and yet he has not counted all the integers. This can be demonstrated by the following one-to-one correspondence:
Days counted: -3 -4 -5…
Nat. numbers: 1 2 3…
In this case, the set of days counted has the cardinal number A0, since its members can be put into a one-to-one correspondence with the natural numbers. Yet he clearly hasn’t counted all the negative integers, since he has failed to count -2 and -1. Therefore, since counting an infinite number of things is not synonymous with counting them all, Craig’s (3) is based on an equivocation.
Craig has denied that he is guilty of this charge8:
“I do not think the argument makes this alleged equivocation, and this can be made clear by examining the reason why our eternal counter is supposedly able to complete a count of the negative numbers, ending at zero. In order to justify this intuitively impossible feat, the argument’s opponent appeals to the so-called Principle of Correspondence…On the basis of the principle the objector argues that since the set of past years can be put into a one-to-one correspondence with the set of negative numbers, it follows that by counting one number a year an eternal counter could complete a countdown of the negative numbers by the present year. If we were to ask why the counter would not finish next year or in a hundred years, the objector would respond that prior to the present year an infinite number of years will have elapsed, so that by the Principle of Correspondence, all the numbers should have been counted by now.
But this reasoning backfires on the objector: for on this account the counter should at any point in the past have already finished counting all the numbers, since a one-to-one correspondence exists between the years of the past and the negative numbers.”9
From this passage, we see Craig’s rationale for (3):
(R) The counter will have finished counting all of the negative integers if and only if the years of the past can be put into a one-to-one correspondence with them.
Furthermore, from the passage cited, we see that Craig thinks that the defender of an A0 past agrees with (R). But since the type of correspondence depicted in (R) can be accomplished at the present moment, it follows that the counter should be finished by now. Therefore, Craig’s opponent is committed to a view that entails the absurdity surfaced by the above reductio.
III
It isn’t clear that Craig hasn’t made his case, however. For consider the following scenario. Suppose God timelessly numbers the years to come about in a beginningless universe. Suppose further that He assigns the negative integers to the set of events prior to the birth of Christ, and then the positive integers begin at this point. Then the timeline, with its corresponding integer assignment, can be illustrated as follows:
…-3 -2 -1 Birth of Christ 1 2 3…
Suppose yet further that God assigned Ralph, an immortal creature, the task of counting down the negative integers assigned to the years BCE, and stopping at the birth of Christ. Call this task ‘(T)’. With this in mind, suppose now that Ralph has been counting down from eternity past and is now counting the day assigned (by God) the integer -3. In such a case, Ralph has counted a set of years that could be put into a one-to-one correspondence with the set of negative integers, yet he has not finished all the negative integers. This case shows that, while it is a necessary condition for counting all of the events that one is able to put them into a one-to-one correspondence with the natural numbers, this is not sufficient. For if the events that are to be counted have independently “fixed”, or, “designated” integer assignments set out for one to traverse, one must count through these such that, for each event, the number one is counting is the same as the one independently assigned to the event. In the scenario mentioned above, God assigned an integer to each year that will come to pass. In such a case, Ralph must satisfy at least two conditions if he is to accomplish (T): (i) count a set of years that can be put into a one-to-one correspondence with the natural numbers, and (ii) for each year that elapses, count the particular negative integer that God has independently assigned to it. According to Craig’s assumption (R), however, Ralph is supposed to be able to accomplish (T) by satisfying (i) alone. But we have just seen that he must accomplish (ii) as well. Therefore, being able to place the events of the past into a one-to-one correspondence with the natural numbers does not guarantee that the counter has finished the task of counting all the negative integers. In other words, (R) is false. But recall that (R) is Craig’s rationale for (3). Thus, (3) lacks positive support. But more importantly, (3) is false. This is because the scenario above is a counterexample to both (R) and (3). For (3) asserts that it is sufficient for counting down all the negative integers that one has an infinite amount of time in which to count them. But our scenario showed that one could have an infinite amount of time to count, and yet not finish counting all of the negative integers (e.g., one can count down to -3 in an infinite amount of time, and yet have more integers to count).
To sum up: We’ve looked at an argument that Craig repeatedly gives for the impossibility of a beginningless past. We then saw that one of its premises is false, in which case it is unsound. Thus, this argument, at least, cannot be used to offer a priori support for the key premise in his Kalam argument.
1 See, for example, his The Kalam Cosmological Argument (London: Macmillan, 1979); Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Clarendon Press, 1995). See also Craig’s popular-level book, Reasonable Faith (Wheaton: Crossway Books, 1994).
2 I should mention a wrinkle here: the possibility that the universe did not begin to exist with the first event of time, but rather existed eternally in a quiescent, eventless mode of existence “prior” to the first event. Craig addresses this worry in “The Kalam Cosmological Argument and the Hypothesis of a Quiescent Universe”, Faith and Philosophy 8 (1991), pp. 104-8.
3 My discussion of the following set-theoretic concepts is indebted to J.P. Moreland’s Scaling the Secular City (Grand Rapids: Baker, 1987)
4 The points and illustrations are similar to those made and conceded by Craig in “Reply to Smith: On the Finitude of the Past”, International Philosophical Quarterly 33 (1993), pp. 228-9.
5 Actually, he advances two arguments for this proposition. One is a variation on the famous Tristam Shandy Paradox. In Craig’s construal of it, Shandy writes his autobiography from the beginningless past at the rate of one year of writing per day of autobiography. It seems that Shandy would never finish his autobiography, getting farther behind with each passing day. But since one can put the days of his life into a one-to-one correspondence with the set of past years, it (paradoxically) seems that he should have finished his autobiography by now. The other version is virtually the same as the one I consider here. It asserts that Shandy should be finished by now, irrespective of the rate at which he is writing. However, I won’t consider the former version here. See Craig and Smith’s Theism, Atheism, and Big Bang Cosmology, pp. 99-100, and Craig’s “Feature Review of Time, Creation, and the Continuum”, International Philosophical Quarterly 25 (1985), pp. 319-26. For a briefer exposition, see Craig, Reasonable Faith, pp. 98-9.
6 Craig, Reasonable Faith, p. 99.
7 This objection can be found in David A. Conway. “’It Would Have Happened Already’: On One Argument for a First Cause”, Analysis 44 (1984), pp. 159-66; Richard Sorabji. Time, Creation, and the Continuum (Ithaca: Cornell University Press, 1983), pp. 219-24.
8 See, for example, Craig and Smith, Theism, Atheism, and Big Bang Cosmology, pp. 105-6; Craig, “Review of Time, Creation, and the Continuum”, p. 323.
9 Craig, “Review of Time, Creation, and the Continuum”, p. 323.
You can go to the archives at that site and read the follow-up of objections
and replies in the "comments" section below the post)
On the Possibility of a Beginningless Past: A Reply to Craig
William Lane Craig has argued vigorously that, cosmological discoveries aside, it’s reasonable to believe on purely a priori grounds that the set of past events is finite in number.1 He offers two main types of a priori arguments for this claim: (i) that it’s metaphysically impossible for an actually infinite set of concrete things to exist, in which case the set of past events can’t be actually infinite, and (ii) that even if such a set could exist, it’s impossible to traverse it even in principle. Craig doesn’t pursue this claim for it’s own sake, however. Rather, he does so as a means to demonstrating that a theistic god exists. He reasons that if the set of past events is finite, then the universe as a whole had an absolute beginning with the first moment of time2. But since nothing can come into existence without a cause, the universe as a whole has a cause. From here, he goes on to argue that such a cause must be timeless (at least sans creation), immaterial, immensely powerful, and a person of some sort.
I intend to show that one of Craig’s most popular versions of (ii) is unsound. In this essay, I’ll state this argument, prefacing it with an explanation of the concepts crucial to understanding it. Then, I’ll examine a common objection to his argument, along with Craig’s response to it, in order to shed light on an unstated assumption of the argument. Finally, I’ll show that the unstated assumption is false, and how this is fatal to his argument.
I
As I mentioned above, several concepts that are crucial for understanding the argument need clarification.3 First of all, one needs a fairly perspicuous idea of a set and of a proper subset. A set is a collection of entities, called members of the set. The precise number of members contained in a set is its cardinal number. A proper subset is a part of another set, the former lacking at least one member which the latter contains, and which contains no other members (e.g., from a totally distinct set). More formally, a set A is a proper subset of a set B if and only if every member of A is a member of B, and some member of B isn’t a member of A. To illustrate: Suppose you have ten bottlecaps, five of which are from Pepsi bottles and five of which are from Coke bottles. Then we can call this the set of bottlecaps, the cardinal number of which is 10. Let’s call this set, A. Furthermore, the set of Pepsi caps (call it B) is a proper subset of A, since B consists in a collection of members that belong to A, and A has members that B does not (i.e., the Coke caps).
Another concept that plays an important role in the argument is that of a one-to-one-correspondence. This is a concept used to determine whether two sets have the same number of members (or, the same cardinal number). So there is a one-to-one correspondence between two sets, A and B, if and only if each member of A can be paired up with exactly one member of B, and each member of B can be paired up with exactly one member of A. To illustrate this concept, consider our set of bottlecaps. Now suppose that you didn’t know how to count, but you wanted to know if your had just as many Coke caps as you had of Pepsi caps. You could accomplish this task by pairing each Coke cap with each Pepsi cap, and each Pepsi cap with each Coke cap. If this can be accomplished with no remaining bottlecaps, then there is a one-to-one correspondence between the set of Pepsi caps and the set of Coke caps. If follows that the respective sets of bottlecaps have the same cardinal number.
The concept most important for our purposes is that of actual infinity. To obtain a grasp of this concept, consider the set of all the natural numbers (i.e., {1, 2, 3, …}). This set, as well as any set that can be put into a one-to-one correspondence with it, is an actually infinite set (It’s actually the “smallest” of the infinite sets, but we won’t be concerned with “larger” infinites here). An actual infinite has several interesting features. First of all, it is complete, in the sense that it has an infinite number of members; it is not merely increasing in number without limit. Second, any actually infinite set (of the “size” we’re here considering) can be put into a one-to-one correspondence with one of its proper subsets. This can be demonstrated by putting the set of natural numbers in a one-to-one correspondence with its proper subset of even numbers:
1 2 3 4…
2 4 6 8…
This example shows that a part of an actually infinite set can have as many members as the whole set! The cardinal number of an actually infinite set that can be put into a one-to-one correspondence with the natural numbers is called “aleph null” (let’s use ‘A0’ for brevity).
The final concept relevant to our discussion is order-type. I won’t talk at length about this concept here. Rather, I’ll barely do more than mention the order-types of certain sets containing A0 members. Four our purposes, it will suffice to know that sets can be sequentially ordered according to certain patterns or types. The order-type given to the set of natural numbers so ordered that, beginning with 1, each natural number is succeeded by the next largest natural number – i.e., {1, 2, 3, …} – is ‘omega’, or 'w’, and the set of negative integers so ordered that they are sequentially the opposite of w is w* (i.e., {…-3, -2, -1}). Sets with A0 members can have other order-types, however. For example, an A0 set can have the order type w+1 (i.e., {1, 2, 3, ..., 1}), or the order-type w+2 (i.e., {1, 2, 3, …, 1, 2}), etc. In fact, a set with A0 members can have the order-type w+w (i.e., {1, 2, 3, …, 1, 2, 3, …}), or the order-type w+w+w (i.e., {1, 2, 3, …., 1, 2, 3, …, 1, 2, 3, …}), etc.! To see this, recall that any set that can be put into a one-to-one correspondence with the natural numbers has a cardinal number of A0. But sets with the order-types mentioned above can be put into such a correspondence. So, for example, a set with the order-type w+1 can be put into a one-to-one correspondence with the natural numbers as follows:
1 1 2 3…
1 2 3 4…
Similarly, a set with the order-type w+w+w can be put into a one-to-one correspondence with the natural numbers as follows:
1 2 3…1 2 3…1 2 3…
1 4 7…2 5 8…3 6 9…
Therefore, since sets with such order-types can be put into a one-to-one correspondence with the natural numbers, it follows that their cardinal number is A0.
At this point, an interesting feature of certain sets with A0 members emerges. For consider any A0 set with an order-type other than w. For example, consider a set of A0 offramps on an infinitely long freeway, such that a distance of one mile separates each offramp from its predecessor and successor (except, of course, the first offramp, since it has no predecessor). Suppose further that the order-type of the offramps is w+1 ({1, 2, 3, …, 1}). The offramp assigned the first 1 would seem to be infinitely distant from the offramp assigned the second 1. Such a set has the interesting feature of being non-traversable in principle – it cannot, even in principle, be exhaustively counted through one offramp at a time. This is because it is logically impossible to count to a number that has no immediate predecessor. But the offramp assigned the second 1 has no immediate predecessor. Therefore, a driver on such a freeway could never reach the offramp assigned the second 1. Call this particular logical ban on traversing sets with w+1 or “higher” order-types ‘LB’.
Now it may be tempting to think that this consideration is decisive for the view that the past must be finite, since any set with A0 members can be ordered according to the order-type w+1. In this way, one might think, LB infects all actually infinite sets, and thus no set with A0 members is traversable. This reasoning can be expressed as follows:
1. A set is LB non-traversable if and only if it contains at least one member A0 distant from at least one of the other of its members.
2. Any set with the order-type w+1 is such that it contains a member A0 distant from at least one of the other of its members.
3. Therefore, any set with the order-type w+1 is LB non-traversable.
4. Any set with A0 members can be assigned the order-type w+1.
5. Therefore, any set with A0 members is LB non-traversable.
But this would be rash. For the inference from (3) and (4) to (5) is a non sequitur. For consider a set with A0 members that is assigned the order-type w. A set with this order-type is such that (i) no member is infinitely distant from any other member, and (ii) each member does have an immediate predecessor, as so is immune to LB. But any set with A0 members can be assigned the order-type w. So if the inference from (3) and (4) to (5) were valid, then by similar reasoning the following inference should go through as well:
3’. Any set with the order-type w is not LB non-traversable.
4’. Any set with A0 members can be assigned the order-type w.
5’. Therefore, any set with A0 members is not LB non-traversable.
But (5’) contradicts (5). Therefore, since the same pattern of reasoning yields contradictory results, it’s faulty. So, just because an A0 set can be assigned a non-traversable order-type, it doesn’t follow that such a set is non-traversable. What really follow from (3) and (4) is rather
5’’. Any set with A0 members can be assigned an LB non-traversable order-type.
Which, needless to say, doesn’t help to establish the finitude of the set of past events.
The arguments above suffer from another problem as well. For (2) is clearly false. To see this, consider again our infinitely long freeway. No suppose that it only has one lane, and that it has an infinitely long traffic jam. Finally, suppose that each car in the jam is assigned a number from the order-type w+1. Does it follow that there is a car A0 distant from any other car? No. For the car assigned the second 1 could be immediately in front of the first car. This illustration shows that the order-type assigned to a set of objects doesn’t necessarily affect the distances between its members. To drive this implication home, suppose that the cars of the traffic jam were assigned the order-type w. Would it follow that no car is A0 distant from any other car? Not in the least. For the first and second cars may be infinitely distant from one another. One might reply that we could just stipulate that the distances between the cars and the order-type assigned to the cars correspond. In such a case, each car would only be finitely distant from every other car when assigned the order-type w (e.g., the second car is 2 meters from the end of the traffic jam, the third car is 3 meters from the end of the jam, etc. [these are small cars!]). One could then reassign the cars with the order-type w+1, but then the correspondence between the order-type and the distances of the cars would break down. This is because no car assigned a number from the w order-type in our scenario is infinitely distant from any other car. Therefore, the second 1 of the newly assigned w+1 reordering would be assigned to a car that is only finitely distant from any other car. These illustrations show that (i) some sets assigned the order-type w+1 are such that no member is infinitely distant from any other, and (ii) we can know a priori than an A0 set of concrete objects cannot be reordered from w to w+1 in such a way that the distances between the members of such a set correspond to their order-type. Therefore, if a set of objects has A0 members (arranged linearly), it does not follow from this that it has members infinitely distant (whether in time or in space) from other members (and is therefore LB non-traversable).4 Thus, to show that an A0 past is non-traversable, Craig must show that no A0 set with either the order-type w or w* (and is such that no member is infinitely distant from any other) is traversable. Let’s consider one of Craig’s main attempts to do this.
II
Craig advances an argument for the proposition that one cannot traverse a beginningless past and end at the present moment.5 To do this, Craig assumes, for the sake of argument, that there could be a beginningless past, conceived as a set of events with the cardinal number A0 and the order-type w* (i.e., {…,. -3, -2, -1}), where each negative integer represents an event of the past. He then argues,
“…suppose we meet a man who claims to have been counting down from eternity and who is now finishing:…,-3, -2, -1, 0. We could ask, why didn’t he finish counting yesterday or the day before or the year before? By then an infinite amount of time had already elapsed, so that he should already have finished. Thus, at no point in the infinite past could we ever find the man finishing his countdown, for by that point he should already be done! In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will already be finished. But if at no point in the past do we find him counting, this contradicts the hypothesis that he has been counting down from eternity.”6
Craig’s argument is a reductio ad absurdum, where we suppose that a beginningless past is possible in order to show that it entails a contradiction. The argument can be expressed as follows, with (1) as the premise set up for reduction:
1. The past is beginningless (conceived as a set of events with the cardinality A0, and the order-type w*).
2. If the past is beginningless, then there could have been an immortal counter who counts down from such a past at the rate of one negative integer per day.
3. The immortal counter will finish counting if and only if he has an infinite number of days in which to count them.
4. If the past is beginningless, then there are an infinite number of days before every day.
5. Therefore, the immortal counter will have finished counting before every day.
6. If the immortal counter will have finished counting before every day, then he has never counted.
7. Therefore, the immortal counter has both never counted and has been counting down from a beginningless past (contradiction)
8. Therefore, the past is not beginningless (from 1-7, reductio)
In short, Craig argues that the past must -- logically must -- have a beginning. For the very notion of traversing a beginningless past entails a contradiction. Craig’s underlying intuition here is that if the past is beginningless, then it must contain an actually infinite proper subset of events that was not formed by successive addition, and that this is absurd.
Critics typically attack (3), arguing that Craig mistakenly assumes that to count an infinite number of negative integers is to count all of them. However, critics of Craig’s argument point out that one can count an infinite set of numbers without counting them all.7 For example, suppose our eternal counter just finished counting all the negative integers down to -3. Then it would be true that he has counted an infinite number of integers, and yet he has not counted all the integers. This can be demonstrated by the following one-to-one correspondence:
Days counted: -3 -4 -5…
Nat. numbers: 1 2 3…
In this case, the set of days counted has the cardinal number A0, since its members can be put into a one-to-one correspondence with the natural numbers. Yet he clearly hasn’t counted all the negative integers, since he has failed to count -2 and -1. Therefore, since counting an infinite number of things is not synonymous with counting them all, Craig’s (3) is based on an equivocation.
Craig has denied that he is guilty of this charge8:
“I do not think the argument makes this alleged equivocation, and this can be made clear by examining the reason why our eternal counter is supposedly able to complete a count of the negative numbers, ending at zero. In order to justify this intuitively impossible feat, the argument’s opponent appeals to the so-called Principle of Correspondence…On the basis of the principle the objector argues that since the set of past years can be put into a one-to-one correspondence with the set of negative numbers, it follows that by counting one number a year an eternal counter could complete a countdown of the negative numbers by the present year. If we were to ask why the counter would not finish next year or in a hundred years, the objector would respond that prior to the present year an infinite number of years will have elapsed, so that by the Principle of Correspondence, all the numbers should have been counted by now.
But this reasoning backfires on the objector: for on this account the counter should at any point in the past have already finished counting all the numbers, since a one-to-one correspondence exists between the years of the past and the negative numbers.”9
From this passage, we see Craig’s rationale for (3):
(R) The counter will have finished counting all of the negative integers if and only if the years of the past can be put into a one-to-one correspondence with them.
Furthermore, from the passage cited, we see that Craig thinks that the defender of an A0 past agrees with (R). But since the type of correspondence depicted in (R) can be accomplished at the present moment, it follows that the counter should be finished by now. Therefore, Craig’s opponent is committed to a view that entails the absurdity surfaced by the above reductio.
III
It isn’t clear that Craig hasn’t made his case, however. For consider the following scenario. Suppose God timelessly numbers the years to come about in a beginningless universe. Suppose further that He assigns the negative integers to the set of events prior to the birth of Christ, and then the positive integers begin at this point. Then the timeline, with its corresponding integer assignment, can be illustrated as follows:
…-3 -2 -1 Birth of Christ 1 2 3…
Suppose yet further that God assigned Ralph, an immortal creature, the task of counting down the negative integers assigned to the years BCE, and stopping at the birth of Christ. Call this task ‘(T)’. With this in mind, suppose now that Ralph has been counting down from eternity past and is now counting the day assigned (by God) the integer -3. In such a case, Ralph has counted a set of years that could be put into a one-to-one correspondence with the set of negative integers, yet he has not finished all the negative integers. This case shows that, while it is a necessary condition for counting all of the events that one is able to put them into a one-to-one correspondence with the natural numbers, this is not sufficient. For if the events that are to be counted have independently “fixed”, or, “designated” integer assignments set out for one to traverse, one must count through these such that, for each event, the number one is counting is the same as the one independently assigned to the event. In the scenario mentioned above, God assigned an integer to each year that will come to pass. In such a case, Ralph must satisfy at least two conditions if he is to accomplish (T): (i) count a set of years that can be put into a one-to-one correspondence with the natural numbers, and (ii) for each year that elapses, count the particular negative integer that God has independently assigned to it. According to Craig’s assumption (R), however, Ralph is supposed to be able to accomplish (T) by satisfying (i) alone. But we have just seen that he must accomplish (ii) as well. Therefore, being able to place the events of the past into a one-to-one correspondence with the natural numbers does not guarantee that the counter has finished the task of counting all the negative integers. In other words, (R) is false. But recall that (R) is Craig’s rationale for (3). Thus, (3) lacks positive support. But more importantly, (3) is false. This is because the scenario above is a counterexample to both (R) and (3). For (3) asserts that it is sufficient for counting down all the negative integers that one has an infinite amount of time in which to count them. But our scenario showed that one could have an infinite amount of time to count, and yet not finish counting all of the negative integers (e.g., one can count down to -3 in an infinite amount of time, and yet have more integers to count).
To sum up: We’ve looked at an argument that Craig repeatedly gives for the impossibility of a beginningless past. We then saw that one of its premises is false, in which case it is unsound. Thus, this argument, at least, cannot be used to offer a priori support for the key premise in his Kalam argument.
1 See, for example, his The Kalam Cosmological Argument (London: Macmillan, 1979); Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Clarendon Press, 1995). See also Craig’s popular-level book, Reasonable Faith (Wheaton: Crossway Books, 1994).
2 I should mention a wrinkle here: the possibility that the universe did not begin to exist with the first event of time, but rather existed eternally in a quiescent, eventless mode of existence “prior” to the first event. Craig addresses this worry in “The Kalam Cosmological Argument and the Hypothesis of a Quiescent Universe”, Faith and Philosophy 8 (1991), pp. 104-8.
3 My discussion of the following set-theoretic concepts is indebted to J.P. Moreland’s Scaling the Secular City (Grand Rapids: Baker, 1987)
4 The points and illustrations are similar to those made and conceded by Craig in “Reply to Smith: On the Finitude of the Past”, International Philosophical Quarterly 33 (1993), pp. 228-9.
5 Actually, he advances two arguments for this proposition. One is a variation on the famous Tristam Shandy Paradox. In Craig’s construal of it, Shandy writes his autobiography from the beginningless past at the rate of one year of writing per day of autobiography. It seems that Shandy would never finish his autobiography, getting farther behind with each passing day. But since one can put the days of his life into a one-to-one correspondence with the set of past years, it (paradoxically) seems that he should have finished his autobiography by now. The other version is virtually the same as the one I consider here. It asserts that Shandy should be finished by now, irrespective of the rate at which he is writing. However, I won’t consider the former version here. See Craig and Smith’s Theism, Atheism, and Big Bang Cosmology, pp. 99-100, and Craig’s “Feature Review of Time, Creation, and the Continuum”, International Philosophical Quarterly 25 (1985), pp. 319-26. For a briefer exposition, see Craig, Reasonable Faith, pp. 98-9.
6 Craig, Reasonable Faith, p. 99.
7 This objection can be found in David A. Conway. “’It Would Have Happened Already’: On One Argument for a First Cause”, Analysis 44 (1984), pp. 159-66; Richard Sorabji. Time, Creation, and the Continuum (Ithaca: Cornell University Press, 1983), pp. 219-24.
8 See, for example, Craig and Smith, Theism, Atheism, and Big Bang Cosmology, pp. 105-6; Craig, “Review of Time, Creation, and the Continuum”, p. 323.
9 Craig, “Review of Time, Creation, and the Continuum”, p. 323.
Problems for PSR (Slightly Revised)
This post completes my discussion of the deductive cosmological argument from contingency. In my previous post, I considered a set of objections to the argument that didn't seem to be persuasive. The moral of that discussion seemed to be that the argument stands or falls with the viability of PSR.
Here, I offer objections to PSR that seem to have some force. These criticisms aren’t original with me, but rather are standard objections (except perhaps the last one, although it's based on ideas of other authors). Furthermore, I don’t mean to imply that there aren’t other versions of the argument from contingency that may avoid these criticisms. However, they do seem to apply to the variants of the argument that one finds in standard “intermediate-level” apologetics books. The criticisms can be divided into two broad categories: (i) those that undercut the reasons offered for accepting PSR, and (ii) those that indicate that PSR is positively false or unreasonable.
1. Type-(i) Criticisms:
1.1 Contrary to what its proponents often assert, PSR does not seem to be supported by reflection on cases. Rather what such reflections support is the weaker principle that objects and events are explained in terms of antecedent causes and conditions. In actual practice, ordinary individuals and scientists explain the existence of objects and events in terms of antecedent causes and conditions, provisionally taking the latter things to be brute facts unless or until they, too, can be further explained. But the prinicple implicit in this sort of search for explanations isn't sufficient to generate the need for an explanation of the universe as a whole in terms of a necessary being.[1]
1.2 Contrary to what some of its proponents assert, PSR does not seem to be self-evident. For what makes a proposition self-evident is that grasping its meaning is sufficient for seeing that it’s true. Consider the two standard categories of self-evident propositions: analytic a priori propositions and synthetic a priori propositions. Both sorts of propositions are knowable independently of empirical investigation of the world. But they differ in that the former (analytic a priori propositions) are tautologous and uninformative, while the latter are not. So, for example, "All bachelors are unmarried" is an analytic a priori proposition, while "Nothing can be red all over and green all over at the same time" is arguably a synthetic a priori proposition.
Now consider PSR: (a) For every object, there is a sufficient reason for why it exists; (b) for every positive state of affairs, there is a sufficient reason for why it obtains. This isn't a tautology; so it's not analytic a priori. Furthermore, although it's a substantive claim, its truth or falsity is not evident merely by reflecting on its constituent conceps. Thus, it doesn't seem to be synthetic a priori, either. Perhaps there is another category of self-evident propositions, but if so, PSR seems not to belong to it. For what makes a proposition self-evident is that one can see that it's true merely be reflecting on its contituent concepts, and we have seen that PSR doesn't safisfy this condition.
1.3 Even if PSR were a presupposition of reason, it wouldn’t follow that it would then be true. But in any case, PSR does not seem to be a presupposition of reason. Rather, again, reason only seems to demand that the existence of each object or fact is explained in terms of antecedent causes and conditions, which are provisionally taken as brute facts unless or until they, in turn, can be explained. Reason does not seem to require anything beyond this.[2]
2. Type-(ii) Criticisms:
2.1 PSR absurdly entails that everything obtains of necessity. The argument for this can be stated as follows. Consider the conjunction of all contingent facts (CCF). By PSR, there is a sufficient reason for CCF. Now the sufficient reason for CCF is itself either contingent or necessary. But it can’t be contingent, because then it would represent a contingent fact, in which case it would itself be a part of the CCF. But contingent facts don’t contain within themselves the sufficient reason for why they obtain – let alone the sufficient reason for why the CCF obtains. Thus, the sufficient reason for CCF must be necessary. But whatever is entailed by a necessary truth is itself necessary, in which case all truths would be necessary truths, and the referents they represent would obtain of necessity. But this is absurd. Therefore, PSR is false. [3]
2.2 The following scenario is prima facie possible: there are just two kinds of beings that exist: contingent-and-dependent beings (e.g., rocks, trees, planets, galaxies, you and me) and contingent-yet-independent, “free-standing” beings, out of which all contingent-and-dependent beings are made (perhaps matter-energy is like this). If so, then even though there are possible worlds at which the contingent-yet-independent beings don’t exist, they are eternal and indestructible at all possible worlds in which they do exist (interestingly, some theists -- e.g., Richard Swinburne -- take God to be just such a being). On this account, then, there are contingent beings that come to be and pass away – viz., the contingent-and-dependent beings. But the beings out of which they’re made – i.e., the contingent-yet-independent beings -- do not; nor can they.[4] This scenario seems possible. But if so, then since PSR entails that such a state of affairs is impossible, then so much the worse for PSR.[5]
The basic point here is that PSR assumes that dependent beings must have their ultimate explanation in terms of necessarily existent independent beings (beings who exist in all possible worlds), when in fact essentially independent beings (beings that are independent at all possible worlds in which they exist) are all that are needed to do the requisite explanatory work. PSR entails that this isn't enough: if there are any essentially independent, indestructible, free-standing beings, then these must be further explained in terms of a necessarily existent being. But surely this is explanatory overkill, and since PSR entails that such further explanations are required, this implication undercuts any prima facie plausibility PSR may seem to have had.
These criticisms have varying degrees of force. However, it seems to me that criticism 2.2 is an undercutting defeater for PSR, and that criticism 2.1 is a rebutting defeater of PSR. But if these things are so, then the argument from contingency is defeated.
=============================
Appendix: Recent Defenses of PSR
A number of philosophers have attempted to revive the Leibnizian cosmological argument in recent years by advancing a weaker version of PSR.[6] According to their version of PSR, every contingent being has a possible explanation in terms of something else. That is, every contingent being is such that there is at least one possible world at which it has an explanation for why it exists. Call this version of PSR, 'Modal PSR'.
Now some authors, such as Garrett DeWeese and Joshua Rasmussen[7] -- offer an argument for Modal PSR. Now I think their argument has a couple of problems, but here I just want to mention one that I think is decisive: The argument uses Modal PSR as a premise to derive the standard version of PSR we discussed above. But this premise is implausible at best, and outright false at worst. For unless they just beg the question and assume that there are no possible beings that lack a sufficient reason, then they must be claiming that, even if there are possible worlds at which a given contingent beings lacks a sufficient reason, there are *other* possible worlds at which it does. But this is implausible, For It seems to me that the only way to accept Modal PSR is to reject origin essentialism. Allow me to me unpack and explain this criticism below:
Suppose origin essentialism is true, and suppose we've got our hands on a universe, and we give it a Kripkean baptism: (pointing to the universe) "Let that be called 'Uni'. 'Uni' is now a Kripkean rigid designator -- it refers to that universe in all possible worlds in which it exists.
So now we have a way to hold Uni fixed, so we can start considering modal claims about it. Given this, there are two relevant possibilities for us to consider: (i) Uni has its origin in the causal power of a divine being, and (ii) Uni has no origin. If (i) is true, then, by origin essentialism, this is an essential property of Uni, in which case there is no possible world in which Uni lacks such an origin. On the other hand, if (ii) is true, then Uni lacks an origin in the causal activity of a divine being, and so this fact about Uni is essential to it, in which case there is no possible world in which it has an origin in the causal activity of a divine being.
The moral, then, is that if we accept origin essentialism like good Kripkeans, then whether a universe has an explanation in terms of a divine being doesn't vary from world to world. But if so, then Modal PSR is of no help unless we know beforehand whether our universe has its origin in the causal activity of a divine being. But if we already knew that, then the contingency argument would be superfluous.
Of course, one could always reject origin essentialism, or restrict its scope in a way favorable to the argument, but then the audience for the argument shrinks considerably.
----------------------------------------
[1] This is a rough paraphrase of one of J.L. Mackie’s objections in The Miracle of Theism (Oxford: Oxford UP, 1983), pp. 84-87.
[2] See ibid.
[3] This objection is a rough paraphrase of one of Peter Van Inwagen’s objections in his textbook, Metaphysics, 2nd edition (Boulder: Westview Press, 2002), pp. 119-122.
[4] Here are a couple of possible ways this could be:
(i) The Strong Version: at least one possible independent being x has indestructibility as an essential property: x is indestructible at all possible worlds in which x exists. This is because nothing has what it takes to destroy x at each possible world in which it exists. Now consider the set S of worlds at which x exists. Suppose at least one member of S -- call it 'W' -- is such that x never began to exist in W, and that. It follows from this and the above-mentioned properties that x is independent, indestructible and everlasting in W. However, since x isn't a metaphysically necessary being, there are possible worlds at which x doesn't exist. X is therefore a contingent-yet-independent being of the requisite sort.
(ii) A Weaker Version: there is a being y like x, except that y's indestructibility is world-indexed: it has the property of being indestructible-at-W, where 'W' denotes a possible world. How can y's indestructibility be indexed to W? Because nothing in W has what it takes to destroy y (although things may well have such an ability at other worlds in which y exists). Thus, y is not destroyed at W. This W-indexed fact about y then grounds the fact that W is not destroyed at all worlds counterfactual to W. And if that's right, then y is indestructible in W. Now suppose that, at W, Y never began to exist. Then y is independent, indestructible, and everlasting at W. Y is therefore a contingent-yet-independent being of the requisite sort.
[5] If one is skeptical that this is possible, one could re-construe it as an epistemic possibility, and thus re-categorize it as an undercutting (instead of a rebutting) defeater of PSR along with the other type-(i) criticisms.
[6] See, for example: Gale, Richard and Pruss, Alexander. "A New Cosmological Argument", Religious Studies 35 (1999), pp. 461–476; “Hume and the Kalam Cosmological Argument”, in In Defense of Natural Theology: A Post-Humean Reassessment, ed. Douglas Groothuis and James Sennett (IVP, 2005)
[7] “Hume and the Kalam Cosmological Argument”.
Here, I offer objections to PSR that seem to have some force. These criticisms aren’t original with me, but rather are standard objections (except perhaps the last one, although it's based on ideas of other authors). Furthermore, I don’t mean to imply that there aren’t other versions of the argument from contingency that may avoid these criticisms. However, they do seem to apply to the variants of the argument that one finds in standard “intermediate-level” apologetics books. The criticisms can be divided into two broad categories: (i) those that undercut the reasons offered for accepting PSR, and (ii) those that indicate that PSR is positively false or unreasonable.
1. Type-(i) Criticisms:
1.1 Contrary to what its proponents often assert, PSR does not seem to be supported by reflection on cases. Rather what such reflections support is the weaker principle that objects and events are explained in terms of antecedent causes and conditions. In actual practice, ordinary individuals and scientists explain the existence of objects and events in terms of antecedent causes and conditions, provisionally taking the latter things to be brute facts unless or until they, too, can be further explained. But the prinicple implicit in this sort of search for explanations isn't sufficient to generate the need for an explanation of the universe as a whole in terms of a necessary being.[1]
1.2 Contrary to what some of its proponents assert, PSR does not seem to be self-evident. For what makes a proposition self-evident is that grasping its meaning is sufficient for seeing that it’s true. Consider the two standard categories of self-evident propositions: analytic a priori propositions and synthetic a priori propositions. Both sorts of propositions are knowable independently of empirical investigation of the world. But they differ in that the former (analytic a priori propositions) are tautologous and uninformative, while the latter are not. So, for example, "All bachelors are unmarried" is an analytic a priori proposition, while "Nothing can be red all over and green all over at the same time" is arguably a synthetic a priori proposition.
Now consider PSR: (a) For every object, there is a sufficient reason for why it exists; (b) for every positive state of affairs, there is a sufficient reason for why it obtains. This isn't a tautology; so it's not analytic a priori. Furthermore, although it's a substantive claim, its truth or falsity is not evident merely by reflecting on its constituent conceps. Thus, it doesn't seem to be synthetic a priori, either. Perhaps there is another category of self-evident propositions, but if so, PSR seems not to belong to it. For what makes a proposition self-evident is that one can see that it's true merely be reflecting on its contituent concepts, and we have seen that PSR doesn't safisfy this condition.
1.3 Even if PSR were a presupposition of reason, it wouldn’t follow that it would then be true. But in any case, PSR does not seem to be a presupposition of reason. Rather, again, reason only seems to demand that the existence of each object or fact is explained in terms of antecedent causes and conditions, which are provisionally taken as brute facts unless or until they, in turn, can be explained. Reason does not seem to require anything beyond this.[2]
2. Type-(ii) Criticisms:
2.1 PSR absurdly entails that everything obtains of necessity. The argument for this can be stated as follows. Consider the conjunction of all contingent facts (CCF). By PSR, there is a sufficient reason for CCF. Now the sufficient reason for CCF is itself either contingent or necessary. But it can’t be contingent, because then it would represent a contingent fact, in which case it would itself be a part of the CCF. But contingent facts don’t contain within themselves the sufficient reason for why they obtain – let alone the sufficient reason for why the CCF obtains. Thus, the sufficient reason for CCF must be necessary. But whatever is entailed by a necessary truth is itself necessary, in which case all truths would be necessary truths, and the referents they represent would obtain of necessity. But this is absurd. Therefore, PSR is false. [3]
2.2 The following scenario is prima facie possible: there are just two kinds of beings that exist: contingent-and-dependent beings (e.g., rocks, trees, planets, galaxies, you and me) and contingent-yet-independent, “free-standing” beings, out of which all contingent-and-dependent beings are made (perhaps matter-energy is like this). If so, then even though there are possible worlds at which the contingent-yet-independent beings don’t exist, they are eternal and indestructible at all possible worlds in which they do exist (interestingly, some theists -- e.g., Richard Swinburne -- take God to be just such a being). On this account, then, there are contingent beings that come to be and pass away – viz., the contingent-and-dependent beings. But the beings out of which they’re made – i.e., the contingent-yet-independent beings -- do not; nor can they.[4] This scenario seems possible. But if so, then since PSR entails that such a state of affairs is impossible, then so much the worse for PSR.[5]
The basic point here is that PSR assumes that dependent beings must have their ultimate explanation in terms of necessarily existent independent beings (beings who exist in all possible worlds), when in fact essentially independent beings (beings that are independent at all possible worlds in which they exist) are all that are needed to do the requisite explanatory work. PSR entails that this isn't enough: if there are any essentially independent, indestructible, free-standing beings, then these must be further explained in terms of a necessarily existent being. But surely this is explanatory overkill, and since PSR entails that such further explanations are required, this implication undercuts any prima facie plausibility PSR may seem to have had.
These criticisms have varying degrees of force. However, it seems to me that criticism 2.2 is an undercutting defeater for PSR, and that criticism 2.1 is a rebutting defeater of PSR. But if these things are so, then the argument from contingency is defeated.
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Appendix: Recent Defenses of PSR
A number of philosophers have attempted to revive the Leibnizian cosmological argument in recent years by advancing a weaker version of PSR.[6] According to their version of PSR, every contingent being has a possible explanation in terms of something else. That is, every contingent being is such that there is at least one possible world at which it has an explanation for why it exists. Call this version of PSR, 'Modal PSR'.
Now some authors, such as Garrett DeWeese and Joshua Rasmussen[7] -- offer an argument for Modal PSR. Now I think their argument has a couple of problems, but here I just want to mention one that I think is decisive: The argument uses Modal PSR as a premise to derive the standard version of PSR we discussed above. But this premise is implausible at best, and outright false at worst. For unless they just beg the question and assume that there are no possible beings that lack a sufficient reason, then they must be claiming that, even if there are possible worlds at which a given contingent beings lacks a sufficient reason, there are *other* possible worlds at which it does. But this is implausible, For It seems to me that the only way to accept Modal PSR is to reject origin essentialism. Allow me to me unpack and explain this criticism below:
Suppose origin essentialism is true, and suppose we've got our hands on a universe, and we give it a Kripkean baptism: (pointing to the universe) "Let that be called 'Uni'. 'Uni' is now a Kripkean rigid designator -- it refers to that universe in all possible worlds in which it exists.
So now we have a way to hold Uni fixed, so we can start considering modal claims about it. Given this, there are two relevant possibilities for us to consider: (i) Uni has its origin in the causal power of a divine being, and (ii) Uni has no origin. If (i) is true, then, by origin essentialism, this is an essential property of Uni, in which case there is no possible world in which Uni lacks such an origin. On the other hand, if (ii) is true, then Uni lacks an origin in the causal activity of a divine being, and so this fact about Uni is essential to it, in which case there is no possible world in which it has an origin in the causal activity of a divine being.
The moral, then, is that if we accept origin essentialism like good Kripkeans, then whether a universe has an explanation in terms of a divine being doesn't vary from world to world. But if so, then Modal PSR is of no help unless we know beforehand whether our universe has its origin in the causal activity of a divine being. But if we already knew that, then the contingency argument would be superfluous.
Of course, one could always reject origin essentialism, or restrict its scope in a way favorable to the argument, but then the audience for the argument shrinks considerably.
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[1] This is a rough paraphrase of one of J.L. Mackie’s objections in The Miracle of Theism (Oxford: Oxford UP, 1983), pp. 84-87.
[2] See ibid.
[3] This objection is a rough paraphrase of one of Peter Van Inwagen’s objections in his textbook, Metaphysics, 2nd edition (Boulder: Westview Press, 2002), pp. 119-122.
[4] Here are a couple of possible ways this could be:
(i) The Strong Version: at least one possible independent being x has indestructibility as an essential property: x is indestructible at all possible worlds in which x exists. This is because nothing has what it takes to destroy x at each possible world in which it exists. Now consider the set S of worlds at which x exists. Suppose at least one member of S -- call it 'W' -- is such that x never began to exist in W, and that. It follows from this and the above-mentioned properties that x is independent, indestructible and everlasting in W. However, since x isn't a metaphysically necessary being, there are possible worlds at which x doesn't exist. X is therefore a contingent-yet-independent being of the requisite sort.
(ii) A Weaker Version: there is a being y like x, except that y's indestructibility is world-indexed: it has the property of being indestructible-at-W, where 'W' denotes a possible world. How can y's indestructibility be indexed to W? Because nothing in W has what it takes to destroy y (although things may well have such an ability at other worlds in which y exists). Thus, y is not destroyed at W. This W-indexed fact about y then grounds the fact that W is not destroyed at all worlds counterfactual to W. And if that's right, then y is indestructible in W. Now suppose that, at W, Y never began to exist. Then y is independent, indestructible, and everlasting at W. Y is therefore a contingent-yet-independent being of the requisite sort.
[5] If one is skeptical that this is possible, one could re-construe it as an epistemic possibility, and thus re-categorize it as an undercutting (instead of a rebutting) defeater of PSR along with the other type-(i) criticisms.
[6] See, for example: Gale, Richard and Pruss, Alexander. "A New Cosmological Argument", Religious Studies 35 (1999), pp. 461–476; “Hume and the Kalam Cosmological Argument”, in In Defense of Natural Theology: A Post-Humean Reassessment, ed. Douglas Groothuis and James Sennett (IVP, 2005)
[7] “Hume and the Kalam Cosmological Argument”.
Some Criticisms of the Argument from Contingency that Don’t Seem to Work
In this post, I continue the task of giving the contingency argument its due. To that end, I briefly discuss three criticisms of the deductive argument from contingency that don’t seem to work. Here I’m just summarizing William Rowe’s points from his Philosophy of Religion (Belmont, Ca: Wadsworth, 1978), pp. 16-30.
1. Dependence and the fallacy of composition:
1.1 The argument fallaciously assumes that because each member of the collection of beings within the universe is dependent, that therefore the whole collection of such beings is itself dependent. But this doesn’t follow.
1.2 Reply: It would be fallacious to assume this, but the defender of the cosmological argument need not assume it for the argument to work. Rather, since the existence of the collection of dependent beings is a positive fact, then it follows from PSR alone – i.e., without the need to rely on an inference from dependence of the parts to dependence of the whole -- that there must be a sufficient reason for why the collection exists.
2. Causation and the fallacy of composition:
2.1 The argument fallaciously assumes that because each member of the collection of dependent beings has a cause, that therefore the whole collection of dependent beings has a cause. But this doesn’t follow.
2.2 Reply: It would be fallacious to assume this, but the defender of the cosmological argument need not assume it for the argument to work. Rather, since the existence of the collection of dependent beings is a positive fact, then it follows from PSR alone – i.e., without the need to rely on an inference from the need for a cause of the parts to a need from a cause of the whole -- that there must be a sufficient reason for why the collection exists.
3. Nothing’s left to explain
3.1 The defender of the cosmological argument fails to see that once the existence of each member of a collection of dependent beings is explained, the existence of the whole collection is thereby explained.
3.2 Reply: It’s not true that explaining why each member of *any* collection of dependent beings exists entails an explanation for why the whole collection exists – why there are dependent beings at all. True, there are cases *of certain sorts* in which explaining the former entails explaining the latter. For example, if a necessary being were the direct cause of each dependent being in the universe, then it would be true that explaining why each dependent being exists would thereby entail an explanation for why the whole collection exists, and why there are dependent beings at all. However, there are cases in which it wouldn’t; just take the necessary being out the previous case, and imagine each dependent being as caused by one of the others. In such a case, explaining why each dependent being exists wouldn’t explain why there are dependent beings at all.
1. Dependence and the fallacy of composition:
1.1 The argument fallaciously assumes that because each member of the collection of beings within the universe is dependent, that therefore the whole collection of such beings is itself dependent. But this doesn’t follow.
1.2 Reply: It would be fallacious to assume this, but the defender of the cosmological argument need not assume it for the argument to work. Rather, since the existence of the collection of dependent beings is a positive fact, then it follows from PSR alone – i.e., without the need to rely on an inference from dependence of the parts to dependence of the whole -- that there must be a sufficient reason for why the collection exists.
2. Causation and the fallacy of composition:
2.1 The argument fallaciously assumes that because each member of the collection of dependent beings has a cause, that therefore the whole collection of dependent beings has a cause. But this doesn’t follow.
2.2 Reply: It would be fallacious to assume this, but the defender of the cosmological argument need not assume it for the argument to work. Rather, since the existence of the collection of dependent beings is a positive fact, then it follows from PSR alone – i.e., without the need to rely on an inference from the need for a cause of the parts to a need from a cause of the whole -- that there must be a sufficient reason for why the collection exists.
3. Nothing’s left to explain
3.1 The defender of the cosmological argument fails to see that once the existence of each member of a collection of dependent beings is explained, the existence of the whole collection is thereby explained.
3.2 Reply: It’s not true that explaining why each member of *any* collection of dependent beings exists entails an explanation for why the whole collection exists – why there are dependent beings at all. True, there are cases *of certain sorts* in which explaining the former entails explaining the latter. For example, if a necessary being were the direct cause of each dependent being in the universe, then it would be true that explaining why each dependent being exists would thereby entail an explanation for why the whole collection exists, and why there are dependent beings at all. However, there are cases in which it wouldn’t; just take the necessary being out the previous case, and imagine each dependent being as caused by one of the others. In such a case, explaining why each dependent being exists wouldn’t explain why there are dependent beings at all.
The Cosmological Argument from Contingency
The deductive cosmological argument from contingency has a long and illustrious history. It’s been exposited and defended by the likes of, e.g., G.W. Leibniz, Samuel Clarke, and recently (e.g.) Stephen C. Davis, Ronald Nash, Robert Koons, and Alexander Pruss. However, a number of contemporary theists seem to shy away from defending it, such as J.P. Moreland, Peter Van Inwagen, and William Lane Craig (although Craig seems to have warmed up to it slightly in recent years, given his more-positive-than-usual assessment of it in his essay in The Rationality of Theism).
This version of the cosmological argument has been given a number of construals, depending on how its proponents spell out the notions of a contingent being and the Principle of Sufficient Reason (PSR). One common way to spell out these notions is as follows:
A contingent being or state of affairs is a being or state of affairs that exists, but doesn’t have to – its nonexistence is logically (or metaphysically) possible. So, for example, rocks, trees, and you and I are contingent beings, and George W. Bush being the current U.S. President is a contingent state of affairs. By contrast, a necessary being or state of affairs is a being or state of affairs that exists or obtains of logical (or metaphysical) necessity – to use possible worlds talk, one that exists or obtains in all possible worlds. So, for example, if Anselm’s God exists, then it is a necessary being.
Finally, PSR states that (a) for every being that exists, there is a sufficient reason for why it exists, and (b) for every state of affairs, there is a sufficient reason for why it obtains. PSR has prima facie plausibility, and is often defended by offering one or more of the following three considerations. First, it seems to make sense of our intuitions when we reflect on sample cases. So, for example, suppose there is a ball on the lawn in your front yard. No one would say that there is no sufficient reason for why the ball exists, or why it’s there on the lawn. Obviously, the ball has an explanation for its origin (in a toy factory), its continued existence (in terms of, e.g., the properties of the particles that constitute the ball), and its being on the lawn now (your daughter left it there). The same sorts of explanations seem to generalize to any case we can think of. Therefore, we have some support for PSR based on reflection on cases. Second, some have argued that PSR is self-evident. Self-evident propositions are those that can be seen to be true merely by coming to understand what they assert. That is, once you understand what they mean, you can see that they’re true. So, for example, consider the proposition, “all triangles have three angles”. Once I understand the constituent concepts of this proposition, I can see that it’s true. Similarly for “nothing can be red all over and green all over at the same time.” And similarly, say some proponents of the contingency argument, for PSR. Third, even if one remains unpersuaded by the previous two considerations, one may think that it’s a presupposition of rational thought. Compare: Although it's notoriously difficult to justiify the existence of material objects, and the existence of a past, it nonetheless seems pathological to deny that material objects exist, or to deny that the universe has existed for more than ten minutes (as opposed to thinking that it was created ten minutes ago, with an appearance of age, and with false memories of a longer past). All sane people accept these propositions, and -- say some proponents of the argument from contingency -- the same is true of PSR. Thus, even if you think we can’t prove it, you must accept it to be a rational agent. Given these notions, we may now state the argument.
It’s undeniable that contingent beings exist. After all, we came into existence, and could go out of existence without much trouble. The same is true of rocks, trees, our planet, and in fact every object in the universe. In fact, the universe itself seems to be just one big contingent being. If so, then by PSR, it has a sufficient reason for its existence. Now since it’s a contingent being, it can’t account for it’s own existence in terms of its own nature, even if it has existed forever. For even if the contingent universe existed forever, the following contingent state of affairs would obtain:
(CF1) There being an eternally existent contingent universe.
But if so, then by PSR, there is a sufficient reason for why CF1 obtains, in which case we must look for a reason beyond our contingent universe.
Now whatever that “something” is, it can’t just be more contingent beings. For even our universe is explained in terms of an infinite series of contingent beings, the following contingent state of affairs would obtain:
(CF2) There being an infinite series of contingent beings.
But if so, then by PSR, there is a sufficient reason for why the infinite series of contingent beings exists or why CF2 obtains. In short, no matter how many contingent beings we throw into the explanatory “pot”, the existence of our contingent universe – or any contingent being whatever, for that matter – cannot be sufficiently accounted for purely in terms of contingent beings. But if not, then the sufficient reason for the existence of our contingent universe must be in terms of at least one necessary being. And, as Aquinas would say, “this we all call ‘God’.
This version of the cosmological argument has been given a number of construals, depending on how its proponents spell out the notions of a contingent being and the Principle of Sufficient Reason (PSR). One common way to spell out these notions is as follows:
A contingent being or state of affairs is a being or state of affairs that exists, but doesn’t have to – its nonexistence is logically (or metaphysically) possible. So, for example, rocks, trees, and you and I are contingent beings, and George W. Bush being the current U.S. President is a contingent state of affairs. By contrast, a necessary being or state of affairs is a being or state of affairs that exists or obtains of logical (or metaphysical) necessity – to use possible worlds talk, one that exists or obtains in all possible worlds. So, for example, if Anselm’s God exists, then it is a necessary being.
Finally, PSR states that (a) for every being that exists, there is a sufficient reason for why it exists, and (b) for every state of affairs, there is a sufficient reason for why it obtains. PSR has prima facie plausibility, and is often defended by offering one or more of the following three considerations. First, it seems to make sense of our intuitions when we reflect on sample cases. So, for example, suppose there is a ball on the lawn in your front yard. No one would say that there is no sufficient reason for why the ball exists, or why it’s there on the lawn. Obviously, the ball has an explanation for its origin (in a toy factory), its continued existence (in terms of, e.g., the properties of the particles that constitute the ball), and its being on the lawn now (your daughter left it there). The same sorts of explanations seem to generalize to any case we can think of. Therefore, we have some support for PSR based on reflection on cases. Second, some have argued that PSR is self-evident. Self-evident propositions are those that can be seen to be true merely by coming to understand what they assert. That is, once you understand what they mean, you can see that they’re true. So, for example, consider the proposition, “all triangles have three angles”. Once I understand the constituent concepts of this proposition, I can see that it’s true. Similarly for “nothing can be red all over and green all over at the same time.” And similarly, say some proponents of the contingency argument, for PSR. Third, even if one remains unpersuaded by the previous two considerations, one may think that it’s a presupposition of rational thought. Compare: Although it's notoriously difficult to justiify the existence of material objects, and the existence of a past, it nonetheless seems pathological to deny that material objects exist, or to deny that the universe has existed for more than ten minutes (as opposed to thinking that it was created ten minutes ago, with an appearance of age, and with false memories of a longer past). All sane people accept these propositions, and -- say some proponents of the argument from contingency -- the same is true of PSR. Thus, even if you think we can’t prove it, you must accept it to be a rational agent. Given these notions, we may now state the argument.
It’s undeniable that contingent beings exist. After all, we came into existence, and could go out of existence without much trouble. The same is true of rocks, trees, our planet, and in fact every object in the universe. In fact, the universe itself seems to be just one big contingent being. If so, then by PSR, it has a sufficient reason for its existence. Now since it’s a contingent being, it can’t account for it’s own existence in terms of its own nature, even if it has existed forever. For even if the contingent universe existed forever, the following contingent state of affairs would obtain:
(CF1) There being an eternally existent contingent universe.
But if so, then by PSR, there is a sufficient reason for why CF1 obtains, in which case we must look for a reason beyond our contingent universe.
Now whatever that “something” is, it can’t just be more contingent beings. For even our universe is explained in terms of an infinite series of contingent beings, the following contingent state of affairs would obtain:
(CF2) There being an infinite series of contingent beings.
But if so, then by PSR, there is a sufficient reason for why the infinite series of contingent beings exists or why CF2 obtains. In short, no matter how many contingent beings we throw into the explanatory “pot”, the existence of our contingent universe – or any contingent being whatever, for that matter – cannot be sufficiently accounted for purely in terms of contingent beings. But if not, then the sufficient reason for the existence of our contingent universe must be in terms of at least one necessary being. And, as Aquinas would say, “this we all call ‘God’.
The Current Agenda
As the sub-title of my blog suggests, my goal is to fairly exposit the arguments of christian apologists, and then to fairly evaluate them. I ask those who wish to join me to please stick to the arguments of the actual apologists themselves, and not to discuss those of your own, or those you've seen floating around the internet. I also ask that you refer to the relevant apologetics book and its author. I promise I'll do my best to do the same.
To borrow a scale from the apologists in the Suggested Reading lists in their books, the range of authors discussed will be wide -- from "entry-level" authors like Josh McDowell, to "advanced-level" authors such as Alvin Plantinga and Richard Swinburne. I plan the sequence of discussion of apologetics arguments to begin with the philosophical arguments of natural theology and reformed epistemology. Then, I'll shift focus to historical apologetics, which will include arguments involving the reliability of the New Testament and the resurrection of Jesus of Nazareth. Finally, I'll shift to a discussion of scientific apologetics. This will include discussion of the critique of evolution, the case for intelligent design, as well as general issues in the philosophy of science (e.g., the scientific status of creation science and intelligent design, and the nature of science in general). I will probably occassionally jump out of sequence, but this will be the general pattern of discussion.
My posts in the foreseeable future will involve some preliminary discussion of the standard arguments of natural theology (e.g., a representative sampling of the common versions of the cosmological, teleological, ontological arguments for the existence of a god). I'll start with some cosmological arguments.
I should note that my posts may be slow and intermittent, as I am trying to hurry and finish my graduate studies this year -- I'd hate to run out of funding before I finish! In any case, my ideal for discussion would be to post or comment on something no more than a couple of times a week. After all, this is just a blog; our family, our friends, and our jobs should come first.
Regards,
exapologist
To borrow a scale from the apologists in the Suggested Reading lists in their books, the range of authors discussed will be wide -- from "entry-level" authors like Josh McDowell, to "advanced-level" authors such as Alvin Plantinga and Richard Swinburne. I plan the sequence of discussion of apologetics arguments to begin with the philosophical arguments of natural theology and reformed epistemology. Then, I'll shift focus to historical apologetics, which will include arguments involving the reliability of the New Testament and the resurrection of Jesus of Nazareth. Finally, I'll shift to a discussion of scientific apologetics. This will include discussion of the critique of evolution, the case for intelligent design, as well as general issues in the philosophy of science (e.g., the scientific status of creation science and intelligent design, and the nature of science in general). I will probably occassionally jump out of sequence, but this will be the general pattern of discussion.
My posts in the foreseeable future will involve some preliminary discussion of the standard arguments of natural theology (e.g., a representative sampling of the common versions of the cosmological, teleological, ontological arguments for the existence of a god). I'll start with some cosmological arguments.
I should note that my posts may be slow and intermittent, as I am trying to hurry and finish my graduate studies this year -- I'd hate to run out of funding before I finish! In any case, my ideal for discussion would be to post or comment on something no more than a couple of times a week. After all, this is just a blog; our family, our friends, and our jobs should come first.
Regards,
exapologist
A Place for Honesty, Civility, and Clarity in the Discussion of Christian Theism
Hi all,
This is my first post on my own blog. As such, I should say a few words about my aims. Although I enjoy scrolling through a number of blogs regarding theism in general, and christian theism in particular, I'm often discouraged at the tone of the discussion. It's all too easy for interlocutors to be so caught up in "dueling" their "opponents" that they lose sight of the goal, viz., the pursuit of truth and understanding and the avoidance of falsehoods and incomprehension. I have no illusions about changing all of this, but at least I can try to make a difference, however trifling. Let me just say what should be obvious: any one of us, including myself, may be completely wrong about our views on some matter. Therefore, it's important to cultivate truth-conducive intellectual virtues that will increase the likelihood that we'll come to have more true beliefs than false ones. Thus, one of my main goals for this blog will be to exercise, as best as I can, the virtues of honesty, civility, humility, and clarity. I take these to involve the following: giving the best and most powerful construal of the points of one's interlocutor; giving one's interlocutor the benefit of the doubt; pursuing truth instead of "victory"; aiming to understand and internalize one's interlocutor's views before a critique ever occurs to one. In doing so, I ask those who may choose to join the discussion here to do the same. In the unlikely event that someone chooses to join the discussion, yet expresses their points in a way that plainly goes against these aims, I'm afraid that their comments will be removed.
Regards,
exapologist
This is my first post on my own blog. As such, I should say a few words about my aims. Although I enjoy scrolling through a number of blogs regarding theism in general, and christian theism in particular, I'm often discouraged at the tone of the discussion. It's all too easy for interlocutors to be so caught up in "dueling" their "opponents" that they lose sight of the goal, viz., the pursuit of truth and understanding and the avoidance of falsehoods and incomprehension. I have no illusions about changing all of this, but at least I can try to make a difference, however trifling. Let me just say what should be obvious: any one of us, including myself, may be completely wrong about our views on some matter. Therefore, it's important to cultivate truth-conducive intellectual virtues that will increase the likelihood that we'll come to have more true beliefs than false ones. Thus, one of my main goals for this blog will be to exercise, as best as I can, the virtues of honesty, civility, humility, and clarity. I take these to involve the following: giving the best and most powerful construal of the points of one's interlocutor; giving one's interlocutor the benefit of the doubt; pursuing truth instead of "victory"; aiming to understand and internalize one's interlocutor's views before a critique ever occurs to one. In doing so, I ask those who may choose to join the discussion here to do the same. In the unlikely event that someone chooses to join the discussion, yet expresses their points in a way that plainly goes against these aims, I'm afraid that their comments will be removed.
Regards,
exapologist
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