Classical mereology and causal regresses

Assume classical mereology with arbitrary fusions.

Further assume two plausible theses:

1. If each of the ys is caused by at least one of the xs and there is no overlap between any of the xs and ys, then the fusion of the ys is caused by a part of the fusion of the xs.

2. It is impossible to have non-overlapping objects A and B such that A is caused by a part of B and B is caused by a part of A.

It follows that:

3. It is impossible to have an infinite causal regress of non-overlapping items.

For suppose that A₀ is caused by A₋₁ which is caused by A₋₂ and so on. Let E be a fusion of the even-numbered items and O a fusion of the odd-numbered ones. Then by (1), a part of E causes O and a part of O causes E, contrary to (2).

This is rather like explanatory circularity arguments I have used in the past against regresses, but it uses causation and mereology instead.

An argument against the Thomistic primary/secondary causation account of strong providence

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed. Some like me think one cannot have circularity in the order of explanation at all. I argued for this thesis in my previous post today. Now I want to draw an interesting application.

On one influential (and I think exegetically correct, pace Eleonore Stump) reading of Aquinas, God decides what our free choices will be. Our free choices cannot be determined by created causes, but they are determined by God. This is because God’s causation is primary causation which is of a different sort from the secondary causation which is creaturely causation. God can primarily cause you to freely secondarily cause something, and this is how providence and free will interact. Often the analogy between an author and a character is given: the author decides what the character will freely do and this does not infringe on the character’s freedom.

But now observe this (which was brought home to me by a paper of one of our grad students). On this picture, God will presumably sometimes providentially make earlier actions happen because of later ones. Thus, God may want you to perform some heroic self-sacrifice in ten years. So, right now God prepares you for this by having you freely engage in small self-sacrifices now. In the “because” corresponding to the explanatory order of providence and primary causation, we thus have:

1. You engage in small self-sacrifices because you will engage in a great self-sacrifice.

However, divine primary causation does not undercut secondary causation, and we have the standard Aristotelian story of habituation at the level of secondary causation in light of which we have:

2. You will engage in a great self-sacrifice because you are engaging in small self-sacrifices.

These explanations form a heterotypic explanatory loop (i.e., we have explanations of two different sorts in opposite directions). But if I am right that no explanatory loop is possible, the above story is not possible. However, there is nothing to rule out the above story if the above Thomistic account of primary and secondary causation’s role in providence is correct. Hence, I think we should reject that account.

If no homotypic circles of explanation, no heterotypic ones either

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed, i.e., there are no homotypic circles of explanation. Some like me think one cannot have circularity in the order of explanation at all. Why? One intuition might be that explanations of all types are still explanations, and so the circularity is still an explanatory circularity. :-) (Yes, that begs the question.) More seriously, heterotypic explanations (namely, explanations of different types) can be combined, sometimes chainwise (A explains B and B explains C, and thereby A explains C) and sometimes in parallel (A explains B and C explains D so A-and-C explains B-and-D). This means that the types of explanation are not quite as separate as they might seem.

Here is an argument building on the second intuition. We need two concepts. First, we can talk of two sets of explanatory relations as independent, namely without any interaction between the explanatory relations in the two sets. Second, given two type of explanation₁ and explanation₂, I will say that explanation_1|2 is a type of explanation where explanation₁ and explanation₂ are combined in parallel.

1. If circularity in explanation is possible, it is possible to have a two-item heterotypic explanatory loop.

2. If it is possible to have a two-item heterotypic explanatory loop, it is possible to have two independent two-item heterotypic explanatory loops where each loop involves the same pair of explanation types as the other loop.

3. Necessarily, if A explains₁ B and C explains₂ D, and the two explanatory relations here are independent, then A-and-C explains_1|2 B-and-D.

4. Necessarily, the relations explains_1|2 and explains_2|1 are the same.

5. It is not possible to have a circle of explanations of the same type.

6. Suppose circularity in explanation is possible. (Assume for reductio)

7. There is a possible world w, such that at w: there are A, B, C and D such that A explains₁ B, B explains₂ A, D explains₁ C and C explains₂ D, and the above explanatory relations between A and B are independent of the above explanatory relations between C and D. (6,1,2)

8. At w: A-and-C explains_1|2 B-and-D. (3,7)

9. At w: B-and-D explains_2|1 A-and-C. (3,7)

10. At w: B-and-D explains_1|2 A-and-C. (4,9)

11. At w: there is a circle of explanations of type 1|2. (8,10)

12. Contradiction! (5,11)

13. So, circularity in explanation is impossible.

I think the most problematic premise in this argument is (4). However, if (4) is not true, we have a vast multiplication in types of explanation.

Motivating panpsychism

There is something attractive about an ontology where all the properties are powers, but it seems objectionable.

First, a power is partly defined by the properties it can produce. But if these in turn are powers, then we have a vicious regress or circularity.

At the same time, mental properties do not seem to be purely powers: they seem to have a categorical qualitative character that is not captured by the power to produce something else.

What is attractive about a pure powers ontology is the conceptual simplicity, and the fact that categorical properties seem really mysterious.

There is, however, a modification we can make to a pure powers ontology that gets us out of the problem. There are two kinds of properties: powers and qualia. The mysteriousness objection does not apply to qualia, because we experience them. On this ontology, powers bottom out in the ability to produce qualia.

For this to avoid implausible anthropocentrism, we need panpsychism—only then will there be enough qualia outside of living things for the powers of fundamental physics to bottom out in. So we have an interesting motivation for panpsychism: it yields an attractive ontology for reasons that have nothing to do with the usual concerns in the philosophy of mind.

It’s worth noting that this ontology is similar to Leibniz’s. Leibniz had two kinds of properties: appetitions and perceptions. The appetitions are (deterministic) powers. Perceptions are similar to qualia, but not quite the same, because (a) perceptions need not be conscious, and (b) perceptions are always representational. Unfortunately, the representational aspect leads to a regress or circularity problem, much as the power powers ontology did, since representationality will define a perception in terms of other appetitions and perceptions.

A simple moral preference circle with infinities

Here is a simple moral preferability circle. Suppose there are infinite many human strangers numbered ..., −3, −2, −1, 0, 1, 2, 3, ... all of whom, in addition to two cats, are about to drown. Consider these options:

A. Save the strangers numbered 0, 1, 2, ....

B. Save the strangers numbered −1, −2, −3, ... and one cat.

C. Save the strangers numbered 1, 2, 3, ... and both cats.

Option B beats Option A: If we had to choose between strangers 0, 1, 2, ... and strangers −1, −2, −3, ..., we should clearly be indifferent. Toss in the cat, and now it looks like we have a reason to save the second set of strangers.

Option C beats Option B: If we had to choose between strangers −1, −2, −3, ... and strangers 1, 2, 3, ..., we should be indifferent. But now observe that in Option C one more cat is saved, and it sure looks like we should go for C.

Option A beats Option C: Option A replaces the two cats with stranger 0, and surely it’s better to save one human over two cats.

If you don’t think we have moral reasons to save cats, replace saving the cats from drowning with saving two human strangers from ten minutes of pain.

I am now toying with an intuitively very appealing solution to problems like the above: we have no moral rules in such outlandish cases. I think this can be said on either natural law or divine command theory. On natural law, it is unsurprising if our nature does not provide guidance in situations where we are far from our natural environment. On divine command theory, why would God bother giving us commands that apply to situations so far from ones we are going to be in?

Final and efficient causation

It is sometimes said that:

1. One can have p explain q and q explain p when the types of explanation are different.

I think (1) is mistaken, but in this post I want to focus not on arguing against (1), but simply on arguing against one particular and fairly common form of argument for (1):

2. In cases of Aristotelian final causation, it typically happens that y is a final cause of its own efficient cause.

3. If y is a final cause of x, then that y occurred finally explains that x occurred.

4. If x is an efficient cause of y, then that x occurred efficiently explains that y occurred.

5. So, it’s possible to have p explain q and q explain p when the types of explanation are final and efficient, respectively.

I want to argue that this argument fails (bracketing the interpretive question whether Aristotle or Aquinas accepts its premises).

First, explanation is factive: if p explains q, then both p and q are true. This is because explanations provide correct answers to why questions, and a false answer isn’t correct. But final explanations are not factive. I can offer an argument in order to convince you and yet fail to convince you. (Indeed, perhaps this post is an example.) Therefore, (3) is not always true. That doesn’t show that (3) is false in the case that the argument needs. But it is plausible that an action that fails for extrinsic reasons has exactly the same explanation as a successful action. The failed action cannot be explained by its achieving its goal, since it doesn’t achieve its goal. Therefore, the successful action cannot be explained in terms of its achieving its goal, either.

Second, efficient causation is a relation between tokens. If I turn on the lights in order to alert the burglars, then my token turning-on-the-lights is the efficient cause of the token alerting-the-burglars. But final causation is not a relation between tokens. For suppose that I fail to alert the burglars, say because the burglars are blindfolded (they were challenged to rob me blind, and parsed that phrase wrong) and don’t see the lights. Then there are infinitely many possible tokens of the alerting-the-burglars type any one of which would pretty much equally well serve my goals. For instance, I could alert the burglars at 10:44:22.001, at 10:44:22.002, etc. In the case of action failure, no one of these tokens can be distinguished as “the final cause”, the token I am aiming at. Indeed, if one particular possible token a₀ were the final cause, then if I happened to produce another token, say a₇, my action would have been a failure—which is absurd. Thus, either all the infinitely many possible tokens serve as the final causes of the action or none of them do. It seems wrong to say that there are infinitely many final causes of the action, so none of the tokens is.

Given that explanation of the failed action is the same as of the successful action, it follows that even in the successful case, none of the tokens provides the final cause.

Therefore, we should see final causation as a relation between a type, say alerting the burglars at some time or other near 10:44:22, and a token, say my particular turning on of the lights. But if so, then (2) is false, for it is false that in the successful case the same things are related by final and efficient causation: the final causation relates the outcome type with a productive token and efficient causation relates the productive token with the outcome token.

As I said, this doesn’t show that (1) is false, but it does show that efficient and final explanation do not provide a case of (1).

Acknowledgments: I am grateful to Tim Pawl for discussion of these questions.

A puzzle about being and being-caused

These claims are really plausible:

1. I exist because I was caused by my parents.
2. My having been caused by my parents is a fact about me.
3. My existence is explanatorily prior to all other facts about me.
4. There are no loops of explanatory priority.

But they seem to be contradictory. My being caused by my parents is explanatorily prior to my existence, but my existence is explanatorily prior to that, and that surely looks like a loop.

But actually there is no contradiction. To get the claim that my existence is explanatorily prior to my being caused out of (3), we need to add the premise that my being caused is a different fact about me from my existing. But why add a premise that makes for a contradiction? We should instead conclude that the fact of my existence is the same fact as my being caused by my parents.

But if it's the same fact, then we have an interesting ontological conclusion: My existing is my being caused by my parents (and presumably by all the other causes cooperating with them, including especially God). I've argued for something like this conclusion here, but this is a much neater argument.

There may be another corollary. It seems that my esse, my existence, is modally essential to me--I couldn't exist with a different esse. But if my esse is my being caused by my parents, then I couldn't have had other parents.

Objection 1: We should restrict (3) to facts about the present time. But my having been caused by my parents isn't like that.

Response: Run the argument in the first moment of my existence (assuming there is one; if not, run it for some creature which has a first moment of existence; presumably if the ontological thesis I am arguing for is true for some creature, it's true for them all).

Objection 2: If my existing is the same as my being caused by my parents, how can (1) be true: isn't (1), then, a claim that I exist because I exist?

Response: Even if the fact (or state of affairs or event--there are multiple ways to formulate the argument) of my existence is the same as the fact of my being caused by my parents, the proposition that I exist is not the same as the proposition that I am caused by my parents.

An interesting preference structure

Sam invites me to a home-sewn costume party. While I'd love to come, I would much rather not spend the time to sew costume. Sam offers to do it for me. I know that it would take many hours for him to do it, and I would feel bad having him put this effort in when I could do it myself.

This generates a circular preference structure if we restrict to pairwise comparisons, assuming in each case that the third option is not available:

• Not coming to party beats sewing a costume.
• Sam's sewing a costume for me beats not coming to the party.
• My sewing a costume for me beats Sam's sewing a costume for me.

But if all three options are available, then I think I am stuck sewing a costume for me. For I just can't let Sam do the work for me simply because it's a lot of trouble for me, assuming I can do the work myself. Initially my choices were between sewing for myself and missing the party, and I preferred missing the party. But Sam's offering of a third option forced me to switch.

This kind of thing is a way for Sam to manipulate my behavior if I am a nice guy who doesn't want to put Sam to the trouble. In the case at hand, this means that Sam probably should not make me the offer to sew the costume, since by offering, he brings it about that I will go to the trouble myself. In cases where it is important that I go to the party, this manipulation may be perfectly fine—I've used it in an important case several years ago.

Grounding graphs

Consider three propositions:

1. (2) or (3) is true.
2. (1) or (3) is true.
3. The sky is blue.

Then, clearly, (3) grounds (1) and (2). But there is also another path to grounding (1). We could say that (3) grounds (2), and then (2) grounds (1). But if (2) grounds (1), then by an exact parallel (1) grounds (2). And that violates the noncircularity of grounding.

What should we say about (1)-(3)? It was plausible to say that (3) grounds (1) and (2). But the line of thought that (3) grounds (2) and (2) grounds (1) was also plausible. We might say that there are three pathways to grounding among (1)-(3):

• (3) to both (1) and (2)
• (3) to (2) to (1)
• (3) to (1) to (2)

All pathways seem acceptable. But we had better not confuse the pathways, since if we mix up grounding claims that belong to the last two pathways, we get (2) grounding (1) and (1) grounding (2).

There are multiple grounding pathways. Here is one way to formalize this. Take as the primitive notion that of a grounding graph. A grounding graph encodes a particular mutually compatible grounding pathway. Each grounding graph is a directed graph whose vertices are propositions. It will often be a contingent matter whether a given graph is or is not a grounding graph: the same graph can be a grounding graph in one world but not in another. The notion is not a formal one. Moreover, grounding graphs will be backwards-complete: they will go as far back as possible. But their futures may be incomplete.

Say that a parent of a vertex b in a directed graph G is any vertex a such that a→b is an arrow of G, and then b is called a child of a. An ancestor is then a parent, or a parent of a parent, or .... An initial vertex is one that has no vertices.

We can say that a partly grounds b in G if and only if a is an ancestor of b in G and that a is fundamental in G if and only if a is initial in G. We say that a proposition a partly grounds b provided that there is a grounding graph G such that a partly grounds b in G, and that a proposition p is fundamental if and only if there is a grounding graph G such that p is fundamental in G. We say that the a partly grounds b compatibly with c partly grounding a provided that there is a single grounding graph in which both partial grounding relations hold.

We say that a finite or infinite sequence of vertices is a chain in G provided that there is an arrow from each element of the sequence to the next. We say that b is the terminus of a chain C provided that b is the last element of C.

We stipulate that a set S of vertices grounds b in G provided that (a) every vertex in S is an ancestor of b and (b) every chain whose terminus is b can be extended to a chain still with terminus b and that contains at least one member of S. In particular, the set of all the parents of b grounds b if it is non-empty.

We now have some bridge axioms that interface between the notion of a grounding graph and other notions:

• Truth: Every vertex of a grounding graph G is true.
• Explanation: Every non-initial vertex is explained by its parents.
• Partial Explanation: Every parent partly explains each of its children.

We add this very metaphysical axiom, which is a kind of Principle of Sufficient Reason:

• Universality: Every true proposition is a vertex of some grounding graph.

Now we add some structural axioms:

• Noncircularity: There is no grounding graph G in which a is a parent of b and b is a parent of a.
• Lower Bound: If C is a chain in a grounding graph G, then there is a vertex p of G which is the ancestor of all the vertices in C, other than p itself if p is in C.
• Wellfoundedness: No vertex of a grounding graph is the terminus of an infinite chain.
• Absoluteness of Fundamentality: No vertex is initial in one grounding graph and non-initial in another.
• Truncation: If G₁ is a grounding graph and G₂ is a subgraph of G₁ relatively closed under the parent relation (if b is in G₂ and a is a parent of b in G₁ then a is in G₂ and a is a parent of b in G₂), then G₂ is a grounding graph.

Absoluteness of Fundamentality says that if a proposition is fundamental, it is fundamental in every grounding graph where it is found. Of course Wellfoundedness entails Noncircularity and Lower Bound. And Noncircularity plus Absoluteness of Fundamentality entails that if a partly grounds b and b partly grounds a, then (a) these two grounding relations do not hold in the same grounding graph and (b) in every grounding graph where one of these relations holds, at least one of a and b is grounded in something other than a and b, so that there are no fundamental circles.

We can now add some "logical axioms". These are just a sampling.

• Disjunction Introduction: If a grounding graph G contains a vertex <p> but not the vertex <p or q>, then the graph formed by appending <p or q> to G together with an arrow from <p> to it is also a grounding graph.
• Conjunction Introduction: If a grounding graph G contains vertices <p> and <q> but not the vertex <p&q>, then the graph formed by appending <p&q> to G toegther with arrows from <p> and <q> to it is also a grounding graph.
• Existential Introduction: If a grounding graph G contains a vertex <Fa> but no vertex <(∃x)Fx>, then the graph formed by appending <(∃x)Fx> together with an arrow from <Fa> to <(∃x)Fx> is a grounding graph.
• Conjunctive Concentration: If a grounding graph G contains a vertex b with distinct parents <p> and <q> but no vertex <p&q>, then the graph formed by removing the arrows from <p> and <q> to b, adding the vertex <p&q> and inserting arrows from <p> and <q> to <p&q>, and from <p&q> to b is a grounding graph.
• No Disjunctive Overdetermination: If a grounding graph contains <p or q>, then it contains at most one of the arrows <p>→<p or q> and <q>→<p or q>.

Go back to our original example. There will be at least three distinct grounding graphs corresponding to the different grounding pathways. There will be a grounding graph where we have (3)→(2)→(1), and another where we have (2)→(3)→(1), and a third which contains (3)→(1) and (2)→(1). But there won't be a graph that contains both (2)→(1) and (1)→(2).

I don't really insist on this list of axioms. Probably the "logical axioms" are incomplete. Nor am I completely sure of all the axioms. But the point here is to indicate a way to structure further discussion.

[Definition of universality edited to fix problem pointed out in discussion.]

A circle

I just gave out our comprehensive exams in Ancient and Early Modern Philosophy. I did this by first saying: "If you are getting the Ancient exam, please put up your hand", and giving the Ancient exam to those who did, and then saying: "If you are getting the Modern Exam, please up your hand", and giving the Modern exam to those who did.

So, if x got the Ancient exam:

1. x put up her hand because x was getting the Ancient exam.
2. x was getting the Ancient exam because x put up her hand.

This surely looks like an explanatory circularity!

Fortunately, this one is easy to resolve: x put up her hand because x was supposed to get the Ancient exam, or because x thought she was getting the Ancient exam.

Self-referential properties

The following is even rougher than is usual for posts.  It's notes to self mainly.

Consider this anti-self-referentiality (ASR) thesis about properties:

• There is no property P and relation R (complex or not) such that a component (say, a conjunct or disjunct) of P is the property of being R-related to P.

Suppose ASR is true.  Then we may well get the following consequences:  

1. Property-identity forms of divine command theory are in trouble.  On these theories, being obligatory is identical with being commanded by God.  But being commanded by x is a complex property one component of which is being intended by x have obligatoriness.  And that's a way of being related to obligatoriness.  And hence property-identity forms of divine command theory likely violate ASR.
2. For the same reason, property-identity forms of legal positivism and moral prescriptivism are in trouble.  For in both cases, we identify a species of obligation with a species of being commanded, and it is plausible that the property of being commanded in the relevant way will include a relation to obligation.
3. The property of being asserted (requested, commanded, etc.) by x is not identical with any complex property that includes a conjunct like being intended to be taken as asserted (requested, commanded, etc.) by x.  Thus various accounts of illocutionary force fail.
4. No property P is identical with being taken to have P, being properly taken to have P, being felt to have P, etc.  All sorts of projectionist views are in trouble.

A fair amount of work would be needed to substantiate the inference from ASR to the above claims. 

I suspect quite a bit of other stuff is ruled out by ASR.  For instance, no property P can have a component of being R-related to Q while Q has a component of being S-related to P.  

I don't know if ASR is true.  I suspect it is.

Epistemically otiose appeals to authority

Suppose I am an art graduate student.  After careful study, a certain well-known painting of uncertain provenance looks very much to me like it is by Rembrandt.  Kowalska is the world expert on Rembrandt.  I have never heard what Kowalska thinks about this painting.  But I reason thus: "This painting is almost certainly by Rembrandt.  Kowalska is very reliable at identifying Rembrandt paintings and has no doubt thought about this one.  Therefore, very likely, Kowalska thinks that the painting is by Rembrandt."  I then tell people: "I have evidence that Kowalska thinks this painting is by Rembrandt."

What I say is true--the evidence for thinking that the painting is by Rembrandt combined with the evidence of Kowalska's reliability is evidence that Kowalska thinks the painting is by Rembrandt.  But there is a perversity in what I say.  (Interestingly, this perversity is a reversal of this one.)  By implicature, I am offering Kowalska's Rembrandt authority as significant evidence for the attribution of the pointing, while in fact all the evidence rests on my own authority.  Kowalska's authority on matters of Rembrandt is epistemically otiose.

This kind of rhetorical move occurs in religious and moral discourse to various degrees.  In its most egregious form, one reasons, consciously or not: "It is true that p.  Jesus knows the truth at least about matters of this sort.  Therefore, if the subject came up, Jesus would say that p."  And so one says: "Jesus would say that p."  (I am grateful to my wife for mentioning this phenomenon to me.)  Here it seems one is implicating that Jesus' theological or moral authority supports one's own view, but in fact all the evidential support for the view comes from one's initial reasons for believing that p.  One's reason for thinking that Jesus would say that p is that one thinks that it is true that p and one therefore thinks that Jesus would say it.

At the same time, there are contexts where this rhetorical move is legitimate, namely when the question is not primarily epistemic but motivational--when the point is not to convince someone that it is true that p, but to motivate her to act accordingly.  In this case, the imaginative exercise of visualizing Jesus saying that p may be helpful.  But when the question is primarily epistemic, there is a danger that one is cloaking one's own epistemic authority with that of Jesus.

Still, sometimes it is epistemically legitimate to appeal to what Jesus would say.  This is when one has grounds for believing that Jesus would say that p that go over and beyond one's other reasons for believing that it is true that p.  We can know about Jesus' character from Scripture and cautiously extrapolate what he would say about an issue.  (Likewise, we might know that Kowalska judged paintings relevantly like this one to be by Rembrandt, and this gives us additional confidence that she thinks this one is Rembrandt's.)  But we need to be very cautious with such counterfactual authority.  For one of the things that we learn from the New Testament is that what Jesus would say on an issue is likely to surprise people on both sides of the issue.  In particular, even if it is true that p and Jesus knows that p, Jesus might very well not answer in the affirmative if asked whether it is true that p.  He might, instead, question the motivations of the questioner or point to a deeper issue.

Here is a particularly unfortunate form of this epistemically otiose appeal to authority.  One accepts sola scriptura and one thinks that it is an important Christian doctrine that p.  So one concludes that Scripture somewhere says that p.  With time one might even forget that one's main reason for thinking that Scripture says that p was that one oneself thought that p, and then one can sincerely but vaguely (or perhaps precisely if  eisegesis has occurred) cite Scripture as an authority that p.  This is, I think, a danger for adherents of sola scriptura.  (Whether this danger is much of a reason not to accept sola scriptura, I don't know.)

But religious authority is not the only area for this.  This also happens with science.  One accepts the proposition that p for some reason, good or bad.  That proposition is within the purview of science, or so one thinks.  So, one concludes that one day science will show that p or that science will make disagreement with the claim that p ridiculous, and one says this.  Here, the appeal to a future scientific authority is epistemically otiose and has only rhetorical force, though one may well be implicating that it has more than rhetorical force.

Here is another interesting issue in the neighborhood.  Suppose I know some philosophical, theological or scientific theory T to be true, and I know that God believes all truths.  Then I should be able to know that God believes T (barring some special circumstances that make for a counterexample to closure).  But it sounds presumptuous to say: "I know that God himself believes T."  I think the above considerations suggest why such a statement is inappropriate.  It is inappropriate because in standard contexts to say that one knows what an expert believes implicates that one believes it in part because of the expert's opinion--one is covering oneself with the expert's mantle of authority.  Still, inappropriateness is not the same as presumptuousness, and so the above still isn't a very good explanation of why "I know that God himself believes T" sounds bad.  Maybe a part of the explanation of the apparent presumptuousness is that by saying that one knows what God believes one is suggesting that one is one of God's intimates?  (Still, surely no theist would balk at: "God believes that 2+2=4.")

Johnson's framework for theistic arguments

Occasionally, I've been offering theistic arguments that border on begging the question. Here, for instance, is one that's basically due to Kant, but transposed into an argument in a way that Kant would not approve of:

1. (Premise) We should be grateful for the wondrous universe.
2. (Premise) If something is not the product of agency, we should not be grateful for it.
3. Therefore, the wondrous universe is the product of agency.

The argument is indisputably valid.[note 1] Moreover, if theism is true, it is also sound, and I do take theism to be true. But soundness is, of course, not enough for a good argument. While premise (2) is pretty plausible (in the objective sense of "should"), it feels like premise (1) "begs the question".

Nonetheless, I think there could be something to (1)-(3). Dan Johnson, in the January 2009 issue of Faith and Philosophy has a fascinating little article on the ontological and cosmological arguments. He argues that a certain kind of circularity is not vicious. Suppose that I know p₁. I then infer p₂ from p₁ in such a way that I also know p₂. I then non-rationally (or irrationally) stop believing p₁, but as it happens, I continue to believe p₂. It will then often be the case that there will be a good argument from p₂ back to p₁ (perhaps given some auxiliary premises), and if I use that argument, I will be able to regain my knowledge of p₁. This is true even though there is a circularity: from p₁, to p₂, and back to p₁. Here is an uncontroversial example: I am told my hotel room is 314. I infer that my hotel room is the first three digits of pi. I then forget that my hotel room is 314, but continue to believe it is the first three digits of pi. I then infer that my hotel room is 314.

Johnson proposes that by the sensus divinitatis one may come to know that God exists (actually, throughout this, I can't remember if he talks of knowledge or justified belief). One may then infer from this various things, such as that possibly God exists. Then, one irrationally rejects the existence of God (it does not have to be a part of the theory that every rejection of the existence of God is irrational), but some of the things one inferred from that belief remain. And arguments like the S5 ontological argument then make it possible to recover the knowledge of the existence of God from the things that one had inferred from that belief. Johnson also applies this to the cosmological argument.

This same structure may be present in my Kantian argument. By the sensus divinitatis one comes to know that God exists (obviously this is not a Kantian idea!). One infers that the universe is such that we should be grateful for it. One then irrationally comes to be an atheist (again, there is need be no claim that every atheist is irrationally such), but one continues to believe that gratitude is an appropriate response to the universe. And if that belief is sufficiently deeply engrained, one can reason back from it to theism or at least to agency behind the universe.

Now let me move a little beyond the Johnson paper. I think it is not necessary for this structure that the initial knowledge of God's existence come from the sensus divinitatis. Any other way of having knowledge of God's existence will do—say, by argument or testimony. In fact, it is not even necessary for this structure that one oneself ever had the knowledge or even belief that God exists. Suppose, for instance, one's parents knew that God exists (in whatever way), and inferred from this that the universe is worthy of gratitude. They then instilled this belief in one, and did so in such a way as to be knowledge-transmitting. (Surely, value beliefs can be instilled in such a way.) But they did not instill the belief that God exists (maybe because they thought that the existence of God was something everybody should figure out for themselves). One then knows (1), and can infer (3).

This transmission can be mediated by the wider culture, too. Culture can transmit knowledge, whether scientific or normative, and arguments can work at a cultural level. It could be that a theistic culture where the existence of God was known grew into a culture where (1) was known. The knowledge of (1) can remain even if the culture non-rationally rejects the existence of God (as American culture has not done, and might or might not do in the future). And then the individual can acquire the knowledge of (1) from the culture (we don't need to attribute knowledge to the culture if we don't want to; we can just talk of knowledge had by individuals participating in the culture), and then infer (3).

I think there are probably many consequences of theism that are embedded in the culture, from which consequences one can infer back to theism. If the participants in the culture knew theism to be true when these consequences were derived, then it is perfectly legitimate to reason back from these consequences to theism.

Grandfather paradox

Suppose I went back in time and tried to shoot my grandfather before my father was conceived. Then either I would hit or I would miss. If I hit, absurdity results. What is less discussed in the literature is that if I miss, absurdity also results. Suppose that I miss due to sloppy aiming. (This is the case most favorable to my argument. But I think a similar story can be told for other causes of missing.) Then, my sloppy aiming is explanatorily prior to my grandfather's survival. But my grandfather's survival is explanatorily prior to my existence, and hence to my sloppy aiming. Hence, we get an explanatory circle, which is absurd.

A fun circularity

Yesterday, I was interested in a paper because I was interested in that paper. Here's the story. I was interested in a paper by John Norton. A colleague mentioned that he had come across a paper and described the topic it was on. It was closely related to the topic of the paper that interested me, and hence I became interested in the paper that the colleague had come across. However, as it turned out, it was the same paper, though in a revised version.

Sometimes an enthymematic explanation is circular, but the circularity disappears once the details are filled in.

Circularity and regress

I am not entirely convinced of the arguments below. But they are fun.

Say that p is explanatorily prior to q provided that p contributes to some explanation of q. I shall assume that explanatory priority only holds between true propositions. Let us suppose that:

1. No contingent proposition is explanatorily prior to itself.

Thus, anybody who thinks that explanatory priority among contingent propositions could be circular—for instance, p prior to q, q prior to r, and r prior to p—is committed to denying the transitivity of explanatory priority.

Now, let us posit two plausible formal principles for explanatory priority:

2. If p is prior to q, and r is prior to s, then p&q is prior to q&s.
3. If p and q are conjunctions, and differ only in the order of the conjuncts, and p is prior to r, then q is prior to r.

For a reductio, suppose a circle of size three (the argument works in general): p is prior to q, q is prior to r and r is prior to p, where all three are contingent and true. Using (1) twice, we conclude that p&q&r is prior to q&r&p. Using (3), we conclude that q&r&p is prior to q&r&p, which contradicts (1), since the conjunction of contingent truths is a contingent truth.

Now suppose that a backwards infinite regress of contingently true propositions is possible:

4. ... p₋₃ prior to p₋₂, p₋₁ prior to p₀.

Then a doubly infinite regress is surely also possible:

5. ..., p₋₃ prior to p₋₂, p₋₁ prior to p₀, p₀ prior to p₁, p₁ prior to p₂, p₂ prior to p₃, ....

(Here is a quick way to go from (4) to (5): let p_n be the proposition that 1+1=3 or p_n−1 for n>0. Then, p_n−1 is explanatorily prior to p_n.) Suppose that all the propositions in the regress are distinct (otherwise, there is a circularity, which has already been ruled out). Suppose that the infinitary analog of (2) holds:

6. If A and B are two sets of propositions, with a one-to-one correspondence c between the members of A and those of B, such that c(a) is prior to a for every member a of A, and if p is the conjunction of all the members of A, and q is the conjunction of all the members of B, then q is prior to p.

Now, let A be the set of all the p_n for n an integer (positive, negative or zero). Let B=A. Let c(p_n)=p_n−1. The antecedents in (6) are satisfied. Hence, the conjunction of all the members of B is prior to the conjunction of all the members of A. But A=B. Thus, we have a violation of (1), once again.

The weakness of this argument is that (6) seems less plausible than the finite version (2).

An argument against (2) (and hence also against (6)) is that (2) implies that p can be prior to q even though p and q have a conjunct in common. (Suppose p is prior to q and q is prior to r; then p&q is prior to q&r.) And that might be implausible.

Circular lives and time travel

1. Necessarily, having the same kind of genuine bliss for an infinite amount of time is intrinsically better for one than having it for a finite amount of time. (Premise)
2. Leading a genuinely blissful life over a temporal circle that wraps around from t₀ to t₁ (you have a blissful life from t₀ to t₁, and time wraps around so that t₁ is actually the same as t₀) would be intrinsically just as good as living out an eternal recurrence of a genuinely blissful life of the same kind and length as the temporally circular life. (Premise)
3. If both of the scenarios in (2) are possible, then (1) is violated. (Premise)
4. The scenario of an eternal recurrence of a blissful life is possible. (Premise)
5. The scenario of a life arranged on a temporal circle is impossible. (By (1)-(4))
6. If a circular life is possible, so is a blissful circular life. (Premise)
7. Therefore, a circular life is impossible. (By (5) and (6))
8. If circular time is possible, so is a circular life. (Premise)
9. Therefore, circular time is impossible. (By (7) and (8))
10. If time travel is possible, so is a circular life. (Premise)
11. Therefore, time travel is impossible. (By (7) and (10))

In (2), the life of infinite recurrence is the circular life "unwrapped". I am open to the possibility that (2) in the argument is false, and that it is due to the "infinitely many times around" misapprehension of what circular time would be. It could also be that experiencing the same kind of bliss twice is no better than experiencing it once. I am also open the possibility that (8) is false—maybe there can be circular time, but lives of persons might not be circularly arrangeable. Likewise, I am not that sure of (10).

In any case, the thought experiment embodied in (2) seems worth thinking about. As you approach t₁, you become more and more like you were at t₀, and then, lo and behold, t₁ is t₀. If I lived on a circular time, I would never be facing death. Yet my life would be finite. It would not only be finite in the objective way of a life of someone whose functions got faster and faster, thereby ensuring that over a finite span of objective time he accomplished a life that was of infinite subjective span (i.e., a super-task life), but the circular life would be a life that has only a finite subjective span, though no beginning or end.

A non-vicious circle in the order of explanation

Say that p is prior to q in the order of explanation provided that p enters into some explanation of q. One might think that a circle in the order of explanation is impossible. (Some background: Robert M. Adams has once constructed an elegant argument against Molinism that, among other premises, assumed that there were no circles in the order of explanation. William Lane Craig, however, has responded by arguing that circles in the order of explanation are quite possible, but the examples of his that I've seen I've found unconvincing.)

Suppose I promise that if this year you make a donation either to CRS or Caritas of Waco, I will this year make a donation to CRS. You make a donation to Caritas. I thus make a donation to CRS. This example inspires you, and you respond with a donation to CRS yourself. Let p be the proposition that you made a donation to CRS or Caritas. Let q be the proposition that I made a donation to CRS. Let r be the proposition that you made a donation to CRS. Then, p helps explain q, and q helps explain r. But r is a disjunct in p, so it seems q helps explain p. Thus, it seems, p is explanatorily prior to q and q is explanatorily prior to p.

Is this a good argument? I am not so sure. One problem is that the thesis that the truth of a disjunct a explains the truth of a disjunction a-or-b may not be true when a is itself explained by b.

But suppose one accepts the example. Is there still a way of capturing the intuition behind the idea that there can't be circular explanations? I think so, but it will take some hard work. And that I want to leave for another post.

Note, also, that the above example fits with a principle I've defended that if there is a circle of explanations, then the circle also has an explanation from beyond the circle. (If this principle is true, then Adams can probably regroup and defend his anti-Molinist argument.) In this case, your initial choice to make a donation to Caritas together with my promise are an explanation for the circle.

Circles of justification

This is a fun little riddle, coming from a discussion with Dan Johnson. At t2 Mary believes q because she believes p. At t1 (t1<t2), she had come to believe p because she had believed q. No new evidence came in after t1 for p. Yet her beliefs that p and q are both justified and, indeed, knowledge. How could this be?

One solution: p and q are mathematical theorems. At t0 (t0<t1), Mary saw a proof of q. At t1, she saw that p easily follows from q. Between t1 and t2, Mary forgot all about q, the proof of q, and the fact that she derived p from q. She continued to know p, since we know mathematical theorems that we once had known the proofs of even if we do not remember these proofs. At t2, Mary realized that q easily follows from p, and came to believe q. Since she knew p, she now has knowledge of q.

Comments: This appears to involve a circularity in the order of justification, but only if we confuse the contents of beliefs with believings (or types of belief with belief tokens). Mary has three relevant, believings: (1) her believing between t0 until after t1 that q, (2) her believing starting at t1 that p, and (3) her new believing that q starting at t2. Here, (1) has independent justification; the justification of (2) depends on the justification of (1); the justification of (3) depends on the justification of (2). There is no real circularity.