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"It is widely held that the Principle of Sufficient Reason (PSR) proves too much. It is conceded that, if the PSR were true, then on its basis we could conclude a great deal, including that a necessary being exists. For everyone grants that contingent beings exist, and if the PSR were true, then the existence of the contingent would have to have an explanation, which only a necessary being could provide. It is also argued, however, that the PSR couldn’t possibly be true. For it implies not just that the existence of contingent beings has an explanation but that every true proposition has an explanation. And it is argued that, necessarily, there are certain true propositions that couldn’t possibly have explanations.
In what follows, I will argue that the position sketched in the above paragraph is wrong on all counts, and I will defend a very different view of the PSR and its implications. My chief aim will be to defend the PSR against arguments to the effect that, necessarily, there are true propositions that can’t have explanations. Each of the arguments I will be considering puts forward some particular proposition (which I will call the Grand Inexplicable) and argues that it constitutes a counterexample to the PSR, since the supposition that this proposition has an explanation leads to a contradiction. These arguments fall into two types. First, there are arguments where the proposition that plays the role of the Grand Inexplicable is a conjunction of some vast collection of propositions, such as the conjunction of all contingently true propositions. Second, there are arguments where the Grand Inexplicable is an existential claim, such as the claim that the universe exists or that something exists. I will consider these two kinds of arguments in the first and second sections of my paper, respectively. I will argue that none of these arguments succeeds, and I will provide a diagnosis for why they fail. In the third section, having considered arguments against the PSR, I will turn to one of the most prominent arguments that employs the PSR, namely the argument from contingency for the existence of a necessary being. And I will argue that this argument requires the very same kind of false assumption that serves as the basis for Grand Inexplicable arguments against the PSR. Once we recognize that we must reject this kind of assumption, we can defend the PSR against the view that it leads to contradiction, but at the same time we deprive the PSR of much of the power it has been traditionally thought to have. In the concluding section, I will argue that while the PSR lacks some of the implications that have traditionally been ascribed to it, it has others that are no less surprising." (pp.80-81)
"Consider the following argument from Peter van Inwagen:
(A1) Suppose the following thesis is true.
PSR: For every true proposition A, there is a true proposition B
that is sufficient to explain A.
(A2) Let C be the conjunction of all true contingent propositions.
(A3) Since any conjunction with contingent conjuncts is contingent, C
is contingent.
(A4) Since C is a true proposition, it follows from our supposition that
there is a true proposition (call it D) such that D is sufficient to
explain C.
(A5) Since only contingent propositions can suffice to explain contin-
gent propositions, D is contingent.
(A6) For any propositions A and B, if A is sufficient to explain B, then
B is true in every possible world in which A is true.
(A7) Thus, C is true in every possible world where D is true.
(A8) The only possible world in which C is true is the actual world.
(A9) Thus, D is true in every possible world in which C is true.
(A10) For any propositions A and B, if A and B are true in exactly the
same possible worlds, then A = B.
(A11) Thus, C = D.
(A12) Thus, from (A3) and (A11), D is sufficient to explain D.
(A13) But no contingent proposition is sufficient to explain itself.
(A14) Hence, the supposition that the PSR is true entails a contradiction,
namely the conjunction of (A4), (A12), and (A13).
(A15) Therefore, the PSR is false." (p.81)
"This argument relies crucially on a coarse-grained conception of propositions, according to which, for every set of worlds, there is at most one proposition that is true in all and only these worlds. For such an account is implied by premise (A10)." (pp.81-82)
"Van Inwagen states his argument not in terms of propositions but in terms of states of affairs. Hence he is arguing not against the PSR as we have defined it but rather against the following:
PSR*: For every state of affairs that obtains, there is a sufficient reason for its obtaining.
On van Inwagen’s version of the argument, the analog of premise (A10) is as follows:
(A10*) States of affairs are identical whenever they obtain in exactly the same set of possible worlds.
However, on van Inwagen’s conception of states of affairs, they stand in a one-to-one relation with propositions (1983: 171), and so, for him, (A10*) stands and falls with (A10). Of course, one might hold a coarse-grained account of states of affairs while holding a fine-grained account of propositions. Hence, one might accept (A10*) and endorse van Inwagen’s argument against the PSR*, while rejecting (A10) and hence rejecting the argument given above against the PSR. But if one adopts this kind of position, then one will be left without an argument against the defender of the PSR who understands the latter as a claim about propositions. Moreover, as I will go on to argue, there is strong reason to understand explanation as a relation that obtains between fine-grained entities. Hence, if one adopts the position in question and holds that states of affairs are coarse-grained while propositions are fine-grained, then one will have strong reason to state the PSR in terms of propositions, and hence to regard PSR, not PSR*, as the best formulation." (note 2 p.82)
"But the defender of the PSR needn’t accept such a coarse-grained account of propositions, as she may instead accept an account on which propositions are more fine-grained than sets of possible worlds. She might, for example, adopt a view on which every proposition consists in, or at least is representable by, an ordered series of constituents corresponding to the constituents of the sentences by which they would be expressed in a canonical language. And there are well-known advantages in adopting a more fine-grained conception of propositions. For the coarse-grained account that van Inwagen assumes implies that the two sentences in each of the following pairs express the same proposition:
(B1) All bachelors are unmarried.
(B2) Fermat’s Last Theorem is true.
(C1) Jack runs.
(C2) Jack runs and Jack is a mammal.
Hence, assuming that propositions are the objects of belief and assertion, this view has the problematic implication that one couldn’t believe or assert that all bachelors are unmarried without believing or asserting that Fermat’s Last Theorem is true, and similarly that one couldn’t believe or assert that Jack runs without believing or asserting that Jack runs and Jack is a mammal." (p.82)
"Moreover, when we consider the nature of explanation, we can see that the entities that stand in the explanation relation must be more fine-grained than sets of possible worlds, and hence that the propositions that figure in the PSR can’t be coarse-grained entities. This can be seen if we consider the following sets of propositions:
(D1) If the other two sides of a right triangle are 3 and 4 units long, respectively, then the hypotenuse is 5 units long.
(D2) In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(D3) All bachelors are unmarried.
Here, (D2) explains (D1), but (D3) does not. Similarly, consider an example involving a posteriori propositions:
(E1) When water molecules are divided, oxygen and hydrogen are formed.
(E2) Water is H2O.
(E3) Hesperus is Phosphorus.
Here, (E2) explains (E1), but (E3) does not. Similarly, consider an example involving contingent propositions:
(F1) Ten billion years after the Big Bang, the universe is in state S2.
(F2) The universe is governed by deterministic laws L, and at the time of the Big Bang, the universe is in state S1.
(F3) The universe is governed by deterministic laws L, and twenty billion years after the Big Bang, the universe is in state S3 .
Once again, given the right values of L, S1, S2, and S3, (F2) will explain (F1), but (F3) will not. Note, however, that in each of these cases, the second and third propositions in each trio are true in exactly the same possible worlds. Thus, if we want to maintain that the second proposition explains the first, whereas the third proposition does not, then we need to maintain that the second and third propositions are distinct, and so we need to reject premise (A10)." (p.83)
"However, not all Grand Conjunction arguments against the PSR require (A10). Consider an argument that begins with (A1) through (A5), and then continues as follows:
Argument 2
(G1) Since C is the conjunction of all true contingent propositions, and D is a true contingent proposition, D is a conjunct of C.
(G2) For any propositions A and B, if A is sufficient to explain B, then A is sufficient to explain every conjunct of B.
(G3) Thus, since D is sufficient to explain C, and D is a conjunct of C, D is sufficient to explain D.
(G4) But no contingent proposition is sufficient to explain itself.
(G5) Hence, the supposition that the PSR is true entails a contradiction, namely the conjunction of (A5), (G3), and (G4).
(G6) Therefore, the PSR is false." (pp.83-84)
"Like Argument 1, Argument 2 aims to show that if every proposition had a sufficient explanation, then D (the proposition that explains the conjunction of all true propositions) would have to explain itself. But this time this claim is supported not on the basis of D’s supposed identity with C but rather on the basis of D’s being a conjunct of C. Furthermore, like Argument 1, Argument 2 relies on the stipulation that C is the conjunction of all true contingent propositions. Is this a legitimate stipulation ? That will depend on our conception of propositions. Suppose we identify a proposition with the set of all possible worlds in which it is true. Then we can define the conjunction of any propositions as the set of worlds that are contained in each of these propositions. Since, on this view, the true propositions will be the sets of possible worlds that contain that actual world, and since the only world that all these sets have in common is the actual world, it follows that, on this view, the conjunction of all true contingent propositions is the set containing only the actual world. Since, presumably, there is such a set, it follows that on this coarse-grained account of propositions, there will indeed be a conjunction of all true propositions.
But recall that our reason for moving from Argument 1 to Argument 2 was in order to be able to adopt a more fine-grained account of propositions. And so suppose we adopt such an account and regard propositions as consisting in, or at least representable by, an ordered series of constituents corresponding to the constituents of the sentences by which they would be expressed in a canonical language. On such an account, for every proposition, there will be a corresponding set of the constituents of this proposition. And a conjunction will have its conjuncts as constituents. And so it follows that, for every proposition, there will be a set that includes all of its conjuncts. On such a view, therefore, there will be a conjunction of all true contingent propositions only if there is a set of all true contingent propositions. But is there a set of all true contingent propositions ? Alexander Pruss offers an argument that there can be no such set. His argument requires the controversial assumption that for every cardinality k, it is possible that k is the cardinality of objects in the universe. Later in this paper I will be arguing that the defender of the PSR should reject this kind of assumption. But we don’t need this kind of controversial assumption. For, given the structured account of propositions we are considering, it’s easy to argue that there can be no set of all true contingent propositions, without any assumptions about what the world might be like. For it is well known that there are too many sets for there to be a set of all sets." (p.84)
"And for every set S, there is a distinct necessary proposition of the form S = S. And for each of these necessary propositions, we can form a true contingent proposition by conjoining it with a given true contingent proposition (say, the proposition that Caesar crossed the Rubicon). These contingent propositions will all be distinct, since they will differ in one of their constituents. And there will be one such proposition for every set. Hence, since there are too many sets to fit in a set, it follows that there are too many true contingent propositions to fit into a set. Hence, on the account of propositions we are considering, we should deny that there is any conjunction of all true propositions." (p.85)
"Pruss has proposed a variant of Argument 2 that dispenses with the assumption that there is a conjunction of all true contingent propositions. In this alternative argument, the Grand Conjunction is instead the conjunction of all propositions of the following kinds:
(i) All true basic contingent propositions
(ii) All logically uncompounded true propositions reporting causal relations
His argument can be reconstructed as follows:
Argument 3
(H1) Suppose the following thesis is true.
PSR: For every true proposition A, there is a true proposition B that is sufficient to explain A.
(H2) Let E be the conjunction of all propositions of kinds (i) and (ii).
(H3) Since any conjunction with contingent conjuncts is contingent, E is contingent.
(H4) Since E is a true proposition, it follows from our supposition that there is a true proposition (call it F) such that F is sufficient to explain E.
(H5) Since only contingent propositions can suffice to explain contingent propositions, F is contingent.
(H6) Every proposition that explains any of the propositions of kinds (i) and (ii) is constructable out of propositions of kinds (i) and (ii).
(H7) Hence, since F is explanatory, and since E is the conjunction of all propositions of kinds (i) and (ii), F is constructable out of the conjuncts of E.
(H8) For any propositions A, B, and C, if A is sufficient to explain B, and B is a conjunction out of whose conjuncts C is constructable, then A is sufficient to explain C.
(H9) Therefore, since F is sufficient to explain E, and E is a conjunction out of whose conjuncts F is constructable, F is sufficient to explain F.
(H10) But no contingent proposition is sufficient to explain itself.
(H11) Hence, the supposition that the PSR is true entails a contradiction, namely the conjunction of (A5), (H9), and (H10).
(H12) Therefore, the PSR is false." (pp.85-86)
"I believe Pruss’s revised argument is not convincing, for it faces a dilemma. If we have a sufficiently narrow conception of “basic propositions,” then while (H2) is acceptable, (H6) is dubious ; but if we don’t have such a narrow conception of basic propositions, then while (H6) may be acceptable, (H2) is dubious. Let’s begin with the first horn of the dilemma. On a natural construal of “basic propositions,” the true contingent basic propositions will state the Humean facts ; that is, they will indicate what qualities are present at what spacetime points. Assuming there are only continuum many spacetime points, there will presumably be only continuum many such true basic contingent propositions. Or, in any case, there will be few enough such propositions to fit into a set. Similarly, we should expect the propositions of type (ii) reporting causal relations to be manageable in number as well, since presumably there won’t be more of those than there are pairs of events, and there will be only continuum many events. And so if the basic propositions are understood in this Humean manner, then we should expect all the propositions of types (i) and (ii) together to form a set, and so we should expect there to be a conjunction of such propositions, as (H6) requires." (p.86)
"But in this case, premise (H6) will be suspect. For it seems there could be law-stating propositions that explain the Humean and causal propositions without supervening on, and hence without being constructible in terms of, the Humean and causal propositions they explain. Here’s an illustration.
Imagine two worlds, w1 and w2, that have identical initial conditions, and whose laws differ in only the following respect. In w1, it is a law of nature (call it L1) that the attractive force a struon exerts on a fluon is proportional to the charge of the struon. Thus, if a struon is positively charged, then it attracts fluons, and the greater the charge the greater the attraction ; but if a struon is negatively charged, then it repels fluons, and the greater the charge the greater the repulsion.
By contrast, in w2, it is a law of nature (call it L2) that the attractive force a struon exerts on a fluon is proportional to the absolute value of the struon’s charge. Thus, the greater the charge of a struon, be it positive or negative, the more strongly it attracts fluons. In
both worlds, struons pick up their charge by colliding with thruons (which give them positive charge) and shmuons (which give them negative charge). It just so happens that in both worlds, the struons never collide with the shmuons, and so, while they could easily have acquired negative charge, they never do.
Now, since these two worlds have the same initial conditions, and with respect to their laws differ only in that L1 prevails in w1 and L2 prevails in w2, and since these laws diverge only when struons have negative charge, which never obtains in either world, these two worlds will be identical with respect to true Humean propositions and with respect to the true propositions concerning causal relations between particular events. But these worlds will differ with respect to what explains these true propositions. When a struon attracts a fluon in w1, this is explained by L1, whereas when a struon attracts a fluon in w2, this is explained by L2. And so these laws explain some of the Humean and causal propositions without being constructable out of the Humean and causal propositions. And so (H6) is false.
Now consider the second horn of the dilemma. Suppose we adopt a broader conception of the basic contingent propositions. Suppose we hold that these include not only the Humean and causal propositions but also the law-stating propositions. In this case, there’s no guarantee that there will be few enough basic propositions for them all to fit into a set. And so there’s no guarantee that there is any conjunction of the kind stipulated in H2. Moreover, the proponent of the PSR is likely to deny that there are so few propositions. For she may hold that for every set of laws, there is a further law that explains the conjunction of these laws. And from this it follows, on pain of paradox, that there must be too many laws to include in any set. Thus, if the basic propositions include the laws, then it can’t be assumed, without argument, that there are few enough laws to fit into a set, since such an assumption appears to beg the question against the PSR.
To sum up, in order to provide a Grand Conjunction argument against the PSR, one would need to assume that there is some set of contingent propositions such that any proposition that explains any proposition within this set would have to be somehow included within this set (either by being one of its elements or by being constructable out of these elements). But the defender of the PSR can simply deny this. She can maintain that while every contingent proposition is explained by another contingent proposition, these contingent propositions are too numerous to form a set, and for any set of propositions one must go beyond this set to find the proposition that explains their conjunction." (pp.86-87)
"In the preceding section, we considered Grand Inexplicable arguments against the PSR in which the proposition that served as the Grand Inexplicable was a conjunction of vastly many contingent propositions. In the present section, we will consider a different kind of Grand Inexplicable argument where this role is played by some existential proposition that is of cosmic significance. One such proposition, which will no doubt be salient to the reader of this volume, is the proposition that there exists anything at all. It might seem that this proposition does not admit of any explanation, and hence that it can serve as a counterexample to the PSR. One could argue as follows:
Argument 4
(I1) Suppose the following thesis is true.
PSR: For every true proposition A, there is a true proposition B that is sufficient to explain A.
(I2) Let G be the proposition that there exists some being.
(I3) Thus, by our supposition, there is a true proposition (call it H) that is sufficient to explain G.
(I4) For any kind K of beings, the proposition that there exists something of kind K can be explained only by a proposition that appeals to the existence of beings that are not of kind K.
(I5) Thus, since H is sufficient to explain G, and since G is the proposition that there exists something that is a being, H must appeal to the existence of beings that are not beings.
(I6) And so, since no true proposition appeals to the existence of beings that are not beings, H is not true.
(I7) Hence, the supposition that the PSR is true entails a contradiction, namely the conjunction of (I3) and (I6).
(I8) Therefore, the PSR is false." (pp.87-88)
"The crucial premise of this argument is (I4). This premise has some prima facie plausibility. After all, one might hold that any explanation of an existential claim would need to involve another existential claim. But if one attempted to explain the existence of Bs by appealing to the existence of Bs, then this putative explanation would appear to be viciously circular. And so it may seem, prima facie, that any explanation of the existence of Bs must appeal to the existence of non- Bs. And so (I4) has some plausibility. Nonetheless, we should reject (I4). Here’s a counterexample. Consider the following proposition:
(J1) There is something that undergoes gravitational attraction. This proposition could be explained by the following proposition:
(J2) There are at least two massive bodies, and every massive body is gravitationally attracted to every other massive body.
But while (J2) explains (J1), (J2) doesn’t appeal to the existence of anything that is not of the kind posited by (J1). For the only objects to whose existence (J2) appeals are massive bodies, and all these objects undergo gravitational attraction. And so this pair of propositions constitutes a counterexample to (I4).
But maybe there’s a way of construing the claim that something exists in such a way that it can serve to refute the PSR without appealing to (I4). Perhaps it can be understood not as the claim that there exists something in the kind beings but rather as the claim that there exists something in set S, where S happens to be the set of all beings. For there is an important difference between explaining why there are things of kind K and explaining why there are members of set S: it seems you can explain why there are things of kind K without explaining why any of the things in kind K exist—this is what the case above illustrates, for here we explain why there are things that undergo gravitational attraction, without explaining why it’s true that any of the things that happen to undergo gravitational attraction exist. By contrast, since sets contain their members essentially, you can’t explain why there are members of a given set without explaining why it’s true that any of the members of the set exist." (pp.88-89)
"It seems, therefore, that we could solve the problem faced by Argument 4 by replacing premises (I2) and (I4) with the following two premises respectively, and by revising the other premises accordingly:
(K2) Let S be the set of all beings, and let G be the proposition that there exists at least one member of S.
(K4) For any set S of beings, the proposition that there exists at least one member of S can be explained only by a proposition that appeals to the existence of beings that are not in S.
Premise (K4) is much more plausible than (I4), and it is immune to the counterexample that (I4) faces. To see why, let S be the set of objects that undergo gravitational attraction. Suppose there were three objects that undergo such attraction, and call them Peter, Paul, and Mary. Thus, S = {Peter, Paul, Mary}. While (J2) may explain why there are objects that undergo gravitational attraction, it doesn’t explain why Peter, Paul, or Mary exists, and so it doesn’t explain why there exists at least one member of S. And so this example is not a counterexample to (K4)." (p.89)
"But there’s a problem. While (K4) is perfectly acceptable, (K2) is not. For (K2) assumes the existence of a set of all objects. But there is no such set. For there are too many objects to fit into a set. This follows from the fact that there are too many sets to fit into a set, and the fact that all sets are objects. Thus, it’s not so easy to refute the PSR using the claim that something exists. For, where this is understood as the proposition affirming the existence of something in the kind beings, an appeal to this proposition can refute the PSR only when combined with something like (I4), which, as we have seen, is false. If, on the other hand, the claim that something exists is understood as the proposition affirming the existence of something in the set of beings, then it is doubtful that this could be a true proposition, for it is doubtful that there is any such set.
What about the proposition, not that something exists, but that everything exists ? Could this serve as a Grand Inexplicable in an argument against the PSR ? Might we argue that, if there were an explanation of the existence of everything, it would have to appeal to the existence of something outside of everything, which is impossible, and hence that there can be no explanation of the existence of everything ?" (pp.89-90)
-Jacob Ross, « The Principle of Sufficient Reason and the Grand Inexplicable », dans The Puzzle of Existence: Why Is There Something Rather Than Nothing ?, édité par Tyron Goldschmidt, Routledge, 2013, 80-94 : https://www.academia.edu/63061588/Jacob_Joshua_Ross_The_Principle_of_Sufficient_Reason_and_the_Grand_Inexplicable_in_Tyron_Goldschmidt_ed_The_Puzzle_of_Existence_Why_Is_There_Something_Rather_Than_Nothing_New_York_and_London_Routledge_2013_80_94#:~:text=This%20chapter%20explores%20an%20objection%20to%20explanatory%20universalism,%20the%20doctrine
Dernière édition par Johnathan R. Razorback le Dim 6 Oct - 13:28, édité 4 fois
