6 The Strength of Russell’s Modal Logic

I discussed Russell’s theory of modality in chapters 2–4. It is time to discuss Russell’s modal logics and their strength. First, I sketch my methodology for imputing a modal logic to Russell. Then I distinguish Russell’s modal theory from his modal logic in general. Then I define seven modal logics which may be implicitly attributed to Russell, including three alethic logics, a causal logic, an epistemic logic, and two deontic logics, and assess their strength. I save the deontic logics for last because they are the most difficult. Next, I discuss grades of modal involvement and problems of paraphrase of ordinary de re modal talk, especially problems of quantification into modal contexts. Last, I refute Thomas Magnell’s critique of my 1990 Erkenntnis paper. My methodology is this. I shall impute a modal logic to Russell if either of two tests is met: (i) it is more reasonable than not to paraphrase Russell’s thinking into the modal logic, or (ii) it is more reasonable than not to suppose that Russell would have substantially assented to the modal logic as a paraphrase of his thought. Test (i) is Russell’s own philosophy of paraphrase applied to whole theories. Paraphrase is regimentation of informal discourse into a formal notation. Some replacement of vague thoughts by a more determinate notation is permissible, if that replacement is more reasonable than not. This involves our judgment in balancing the letter and the spirit of the discourse, in assessing what Russell meant or intended. It is ultimately a matter of philosophical interpretation. Russell states test (i) in his famous “Mr Strawson on Referring” (MPD 178–79). Test (i) is met to the extent that a certain modal logic is logically implicit in Russell’s thinking. Test (ii) boils down to test (i), if we suppose that Russell would have substantially assented to formal paraphrases of his thinking which are more reasonable than not. I think that supposition is fairly safe. But no one is perfectly rational all the time, so it may be safer to say only that tests (i) and (ii) are not wholly distinct in the case of thinkers such as Russell. I think there is a sense in which test (ii) is more speculative. Namely, test (ii) calls for express speculation about what Russell would or might have said, if asked. This is good. Such speculation is involved in applying test (i), and it

61 62 Bertrand Russell on Modality and Logical Relevance should be brought out expressly. But test (i) is the more basic, because more purely rational, test. It is not always the case that philosophers would assent to what is logically implicit in their thinking; it might, for example, lead to a reductio ad absurdum of their beliefs. To that extent there is tension between tests (i) and (ii). But the tension is resolved by the very fact that test (i) is more basic. My disjunctive two-prong test is somewhat weaker than a test of finding it more reasonable than not that Russell actually did admit the modal logics I impute to him. On the other hand, my test is far stronger than a test of merely finding these modal logics to be logically consistent with everything or nearly everything he says. On either prong, my test requires finding a substantial positive basis in Russell for imputing the logics to him. In fact, it may be called a substantial positive basis test. This concludes my discussion of methodology. We are after fair philosophical game, if not game to a mere historian’s taste. I distinguish Russell’s modal theory from his modal logic in general. Russell’s full modal theory is MDL {1,2,3}, in which MDL appears as level (3). MDL defines a propositional function F(x) as possible with respect to x just in case F(x) is not always false. From the ontological perspective, MDL {1} is basic to understanding Russell’s theory of modality. But from the logical point of view, MDL {3} is only the stepping-stone to the modal logics. I proceed to the task of imputing modal logics to Russell and assessing their strength. I do not impute a modal logic to Principles of Mathematics. I do impute the full range of Leibniz’s possible worlds as logically implicit in that work. In fact, the 1903 Russell takes such worlds far more seriously than Leibniz does. For Leibniz, they are mere ideas in God’s mind. For Russell, they would be mind-independent complex entities. Such worlds could very easily be the semantic basis for a modal logic. But in Principles, Russell expressly adopts G. E. Moore’s theory of logical necessity as being degrees of implication among propositions. I conclude that there is no possible worlds modal logic in Principles. There are only the possible worlds themselves. I suppose you could call the totality of degrees of implication among propositions a modal logic. But that seems too remote from what is ordinarily meant by the term “modal logic.” Russell’s first modal logic is FG–MDL, meaning fully generalized MDL. Russell presents FG–MDL in his unpublished paper, “Necessity and Possibility” (Russell 1994a; c. 1903–5). FG–MDL defines logical truths as truths which are fully general, i.e., truths containing nothing but logical The Strength of Russell’s Modal Logic 63 constants and bound individual and predicate variables. I follow Gregory Landini in proposing these definitions for FG–MDL:

~A =Df (F1...Fm, x1...xn)AF1...Fm, x1...xn and

A =Df (›F1...›Fm, ›x1...›xn)AF1...Fm, x1...xn (Landini 1993)

It is easy to see how FG–MDL is based on MDL. In FG–MDL, truths are necessary (“~”) or possible (“”) with respect to all the variables they contain. Russell’s second and mature modal logic is FG–MDL* (“*” is pro- nounced “star”). FG–MDL* defines logical truths as truths which are both (i) fully general in accordance with Landini’s definitions and (ii) true in virtue of their form, i.e.. tautologous. I explained why Russell abandoned FG–MDL and adopted FG–MDL* in chapter 1. I proceed to define the modal operators, using the usual boxes and diamonds to represent “Necessarily” by ~ and “Possibly” by . The modal operators, ~ and , must be defined differently in the two modal logics. In FG–MDL, “~” means “true when fully generalized using only universal quantifiers.” In FG–MDL*, “~” means “true when fully generalized using only universal quantifiers and true in virtue of its form.” Both interpreta- tions are modally innocent. They contain no modal notions. In FG–MDL*, the operator for necessity might be informally called “Analytically,” or even “Logically.” That will not cover the whole field of necessary truths, but Russell aims to cover only logically necessary truths. Iteration of modal operators is admissible in both FG–MDL and FG–MDL*, since we are prefixing whole propositions with the operators. We can iterate operators all we want. Theory of types is not a problem, since an iterated operator is never predicated of itself, but always of a proposition. I shall now discuss the strength of Russell’s two modal logics for logical necessity, beginning with FG–MDL*.1 The distinguishing axiom of alethic S1 is that if P, then it is logically possible that P. That is, P 6 P. That is trivially true in FG–MDL*, due to considerations of logical form. The distinguishing axiom of alethic S2 is that if it is logically possible that P and Q, then it is logically possible that P. That is, (P & Q) 6 P. That is trivially true in FG–MDL* as well. 64 Bertrand Russell on Modality and Logical Relevance

The distinguishing axiom of alethic S3 is that if P deductively implies Q, then the logical possibility of P deductively implies the logical possibility of Q. That is, (P 6 Q) 6 (P 6 Q). That is clearly true in FG–MDL*. Iteration of logical modal operators is syntactically possible in FG–MDL*, since they are predicated of statements. Thus we may proceed to consider S4 and S5. Iterated modal operators entirely of the same kind will be trivially collapsible in FG–MDL*, since they will all have the same conditions of application, namely appropriate kind of logical form. Thus ~~P 6 ~P, and P 6 P. The only way it could be logically necessary for P to be logically necessary is if P is logically necessary in virtue of its logical form. And the only way it could be logically possible for P to be logically possible is if P is not logically impossible in virtue of its logical form. The distinguishing axiom of alethic S4 is that if it is logically possible that P is logically possible, then P is logically possible. That is, P 6 P. That is true in FG–MDL*, as we just saw. The distinguishing axiom of alethic S5 is that if P is logically possible, then it is logically necessary that P is logically possible. That is, P 6 ~P. In FG–MDL*, if a statement is possible, then it is necessarily possible, since its possibility is in virtue of its logical form, which is an essential part of the statement’s being the statement it is, and which is timeless and unchanging. And if a statement is necessary, then it is both necessarily possible and necessarily necessary, in virtue of its tautological character. Thus FG–MDL* is closest to S5; note that Arthur Prior and Kit Fine compare standard quantificational logic to S5 (Prior 1977: chapter 1). As far as Russell’s intentions go, FG–MDL seems best compared to S5 too. That is because it seems best to say that in FG–MDL Russell had not yet clearly separated the two notions, (i) being a true full generalization, and (ii) being true in virtue of logical form. He would have had no need to. In fact, if asked about the matter, the 1905 Russell might well have said he believed that true fully generalized propositions were true in virtue of their form. That is because he thought he could logically prove that there are infinitely many objects, i.e., that the axiom of infinity is a logical truth. And if that axiom were a logical truth, then true full generalizations such as “There exist at least 30,000 objects” would not be counterexamples to FG–MDL. They would be logical truths just like the axiom itself, since they are logically implied by the axiom. Thus the 1905 Russell might well have thought that full generalization simply is the form in virtue of which logical truths were true. Indeed, if his attempt to prove the axiom of infinity had succeeded, he would have been right. The Strength of Russell’s Modal Logic 65

My argument is simply that the 1905 Russell took true full generalization to constitute logical truth, and hence to analyze logical necessity. If I am right, then the 1905 Russell would have also said, if asked, that all logically possible propositions are necessarily possible in virtue of their form. And that, again, is the hallmark of S5. That the counterexamples are valid and the 1905 Russell therefore failed to achieve an S5 modal logic is criticism, not scholarship. My second argument is also simple. When Russell finally admitted that the axiom of infinity is a logically contingent proposition, he admitted that “There exist at least 30,000 objects” is a valid counterexample to FG–MDL, and he modified FG–MDL into FG–MDL* accordingly. This speaks volumes about his intent all along to analyze logically necessary truths as true in virtue of form. In fact, FG–MDL* is stronger than S5. Insofar as Russell admits (x)(x = x) as a logical truth (PM 216/*24.01), FG–MDL* is most like the system Hughes and Cresswell call S5 + I (Hughes 1968: 190), where thesis I is ~(x)(x = x). Thesis I cannot be proved in S5. Thesis I is not what distinguishes S5, is not in any of the historic S-logics, and indeed is not anywhere in C. I. Lewis’s books (C. Lewis 1932; 1918). Decisively, Russell holds that any true identity statement whose subject-terms are logically proper names is a tautology, i.e. a necessary truth (PLA 245–46; see 231; PM 216/*24.01). FG–MDL* is not stronger than S5 in virtue being any of the systems S6 through S8. S1–S2–S3–S4–S5 is one series of progressively stronger systems, made stronger by the addition of a new axiom at each stage. S1–S2–S6–S7–S8 is a second such series. S6 is S2 plus the axiom p. S7 is S3 plus the axiom p. S8 is S3 plus the axiom ~p. The distinguishing axiom of S6 and S7 asserts that any well-formed statement is possibly possible. The distinguishing axiom of S8 asserts that any well-formed statement is necessarily possibly possible. Russell would have rejected these axioms for FG–MDL* because well-formed but self-contradictory statements are not possibly possible, due to their logical form. Another way to put it is that a semantic model interpretation of S6 would have to include “non-normal” possible worlds in which self- contradictory statements are true (Hughes 1968: 279–82). Russell would never accept such worlds, not even as mere “Leibnizian phraseology” (IMP 141, 192). Landini notes that if the five howlers were not disposed of before, they are certainly disposed of in FG–MDL* (Landini 1993). Needless to say, Russell’s deductively valid inferences can all be rewritten as logically true implications in FG–MDL*. 66 Bertrand Russell on Modality and Logical Relevance

FG–MDL* does not attempt to cover the whole field of necessary truth. Specifically, FG–MDL* does not capture any synthetic a priori truths, and we know Russell admits them. They include “If a thing is good, it is not bad” and “If a thing is yellow, it is not red” (Russell 1994a: 517; see PP 76, 82). An expansion of FG–MDL* to include synthetic a priori truths seems easy in Russell’s case, if we apply his doctrine in The Problems of Philosophy that “All a priori knowledge deals exclusively with the relations of universals” (PP 103). That includes synthetic a priori knowledge as well as all logic and mathematics (PP 74–77, 82, 102–3, 117), and may be regarded as an expansion of the notion of tautological logical form to a new notion of a priori universal form. Call this logic “FG–MDL**” (double star). If FG–MDL* is closest to S5 among the S-logics due to the character of tautological truths, then FG–MDL** must be correspondingly closest to S5 due to the character of a priori truths. (Even logic is synthetic in Kant’s strict sense; see page 11.) We have done well indeed. But what about causal necessity? While Russell accepts a Humean assay of causation, he does accept causal laws as true empirical generalizations. Perhaps then there is also an implicit Russellian causal logic. Russell’s causal laws may be defined as true universal statements which are not fully generalized, and which are neither true in virtue of their logical form nor true synthetic a priori. They will generally be relational statements, and not merely conditional statements, so as to describe complex systems of interacting variables (ONC 187–93). We will have to interpret causal modal operators appropriately for Russell, so as to reflect what we know of his views on both modality and causation. Our interpretation will determine the modal strength of what we may call Russell’s causal logic, or “MDL–C”. We may prefix a causal necessity operator of a universal statement just in case the corresponding propositional function is necessary in MDL, i.e., is always true, with respect to all the universally quantified variables. We may call any particular or general statement causally necessary if it is deductively implied by any combination of causal laws and true particular statements. This includes particular statements which are true predictions, as well as true quantified statements which are deductively implied as described. There are four approaches we might take to defining causal possibility. (1) As is well-known, the four modal operators of necessity, possibility, impossibility, and contingency are interdefinable. Hence we may define P as causally possible just in case not-P is not causally necessary. (2) Or we may prefix a causal possibility operator of any existentially quantified statement just in case the corresponding propositional function is possible in MDL, i.e., The Strength of Russell’s Modal Logic 67 is sometimes true, with respect to all the quantified variables. (3) In fact, we may as well call any true particular or general statement causally possible. Obviously no true statement can violate a causal law in the sense of contradict- ing it, since causal laws are true statements themselves. (4) Or if we wish to let Russell speak of alternative causally possible worlds, we may count a statement as causally possible if it is consistent with the conjunction of all causal laws. The following discussion is applicable to any of the four approaches. Indeed, there is not much difference between (1)–(3), insofar as that all of them confine causal possibilities to the actual world, assuming that everything happens according to some causal law. That being so, I shall count a statement as causally possible if it is causally possible on any of approaches (1)–(3). That might be deemed approach (5), but it really devolves to (3). Perhaps the most helpful discussion of causal possibility is not in External World or “On the Notion of Cause,” but in the 1910 essay “The Elements of Ethics.” There Russell finds the case for determinism “overwhelming” (PE 37, 38, 45, 59). And “if determinism is true, there is a sense in which no action is possible except the one actually performed” (PE 39, 59). This is the sense with which we are concerned in discussing Russell’s causal logic. Clearly we are on track in taking approaches (1)–(3). MDL is the éminence grise, the power behind the causal throne. There is nothing intrinsically causally modal about the causal modal operators. In keeping with Russell’s Humean assay of causation and his general approach to modality, MDL–C is eliminative of causal modal entities and causal modal notions across the board. In fact, there is no difference in MDL–C between a causal law and a true accidental generalization. Following Russell, we will assume that at least one thing exists, and that deductive implication is strict implication. Now, let P and Q be any statements. The modal truism, ~P : ¬¬P, is true in MDL–C. So is the modal truism, ~P 6 P, thanks to the rules of universal instantiation and existential generalization. The distinguishing axiom of causal S1 is that if P, then it is causally possible that P. That is, P 6 P. That is true in MDL–C. Indeed, it defines alternative (3). The distinguishing axiom of causal S2 is that if it is causally possible that P and Q, then it is causally possible that P. That is, (P & Q) 6 P. That is true in MDL–C. The distinguishing axiom of causal S3 is that if P deductively implies Q, then the causal possibility of P deductively implies the causal possibility of Q. That is, (P 6 Q) 6 (P 6 Q). That is clearly true in MDL–C as well. 68 Bertrand Russell on Modality and Logical Relevance

Iteration of causal modal operators is syntactically possible in MDL–C, since they are predicated of statements. Thus we may proceed to consider S4 and S5. The chief question is the appropriate interpretation of iterated operators. Of course, a modal operator should mean the same thing whether it is iterated or not. Indeed, I think that here iterated operators can make sense only if defined as we have already defined the operators. For example, “It is causally necessary that it is causally necessary that P” can only mean that it is universally the case that it is universally the case that P. Thus iterated modal operators entirely of the same kind will be trivially collapsible, since they will all have the same conditions of application. Thus ~~P 6 ~P, and P 6 P. The distinguishing axiom of causal S4 is that if it is causally possible that P is causally possible, then P is causally possible. That is, P 6 P. That is true in MDL–C, as we just saw. The distinguishing axiom of causal S5 is that if P is causally possible, then it is causally necessary that P is causally possible. That is, P 6 ~P. I think that will be true in MDL–C too. For P is causally possible if and only if P is causally necessary. That is because it is Russell’s view that particular events can always be brought under uniform laws. Russell holds that infinitely many rival theories predicting future empirical observations, “all of which have exactly the same inductive evidence in their favour,” are compatible with any given finite set of past observations, notably with the set of all human observations up to any given date. Most of these theories will involve artificial predictions of changes in the course of nature (HK 312–13; see AMA 232; OP 111; ONC 197–98). Thus MDL–C is trivially S5. More substantively, Russell finds the case for determinism “overwhelming” (PE 37, 38, 45, 59). And “if determinism is true, there is a sense in which no action is possible except the one actually performed” (PE 39, 59). Decisively, Russell says, “Causality belongs to the existing world” (PE 39). But a very slightly later Russell merely says that the evidence that our volitional behavior is determined in the sense of being uniform is “strong but not conclusive” (ONC 201; see KEW 163–83). I suppose this would mean that the evidence that MDL–C is S5 remains strong but is no longer conclusive for Russell. My conclusion is that MDL–C is closest to S5. This is a desirable result, since it is in keeping with the fact that MDL–C is not, and is not intended to be, significantly different from Russell’s logic as ordinarily understood, and we have already found FG–MDL and FG–MDL* to be closest to S5. No false statements are causally possible in MDL–C. This too is a desirable result, since it comports well with the Parmenidean-Diodorean character of Russell’s logic. A causal law is a universal statement that ranges The Strength of Russell’s Modal Logic 69 over all possible individuals in the sense that there are no merely possible individuals. Russell uses subjunctive conditionals to speak of causal relations (PM 475–76, ONC 196). This too tends to confirm my interpretation. If I am right, then Russell has the right strength for a causal logic. We want our causal logic to be S5. “Iterated operators are needed in causal logic, e.g. to express...that if a certain causal law were false, such-and-such would be the case, or that it is a causal law that a certain kind of habit...arises under certain circumstances” (Føllesdal 1971: 57). Thus in general, if something is causally possible, then it should be causally necessary that that thing be caus- ally possible. There is only one other analysis which seems even remotely possible. That is to analyze causal laws directly as formal implications. This lowers the strength to S2. But the path is filled with difficulties. 2 MDL–E is the theory of epistemic possibility noted in chapter 2. It is the theory that when we say “It is possible that it may rain tomorrow,” using the word “possible” in an ordinary sense, this may be analyzed as: “We do not know if it will rain tomorrow; ‘It will rain tomorrow’ is a value of the propositional function, ‘It rains at time t’; and that propositional function is not always false” (PLA 254–55). The best way to analyze this would seem to be as follows. P is epistemically impossible, and ¬P is epistemically necessary, if we know that ¬P or if propositional function Px1, x2,....xn is always false. It would seem that MDL–E is closest to S5, since the conditions specified in the analysis must be known if we are to apply the concept of epistemic possibility meaningfully. Note the Parmenidean aspect of MDL–E. False statements cannot be known to be true, and propositional functions which are always false are epistemically impossible, since there are no merely possible objects. MDL–D is Russell’s early deontic logic. I shall confine my discussion of MDL–D to the early Russell’s major work of neo-Moorean objectivist ethics, his 1910 “The Elements of Ethics.” In a deontic logic, necessity is moral necessity, and possibility is moral possibility. To use more familiar terms, moral necessity is moral obligation, and moral possibility is moral permissibility. Russell’s philosophical writings on ethics concern what it is to be ethically desirable (meta-ethics), and what things are ethically desirable (ethics). That is, they concern what it is to be an ethically desirable alternative world, and the contents of such worlds. This is expressly so in “The Elements of Ethics.” Just as Russell expressly adopts Leibnizian talk of logically possible worlds, he also expressly adopts talk of moral worlds—even in the 70 Bertrand Russell on Modality and Logical Relevance course of rejecting Leibnizian optimism that the actual world is the best of all possible worlds:

Hence the position of some optimists, that all the evil in the world is necessary to constitute the best possible whole, is not logically absurd, though there is, so far as I know, no evidence in its favour. Similarly the view that all the good is an unavoidable ingredient in the worst possible whole is not logically absurd.... (PE 56; boldface emphasis mine)

Again:

To live in a fool’s paradise is commonly considered a misfortune; yet in a world which allows no paradise of any other kind a fool’s paradise is surely the happiest habitation. (PE 57; boldface emphasis mine)

Again:

We may admit at once that in a well-ordered world [the doctrine that every man will best serve the general good by pursuing his own good] would be true.... (PE 49; boldface emphasis mine)

Again:

If two bitter enemies lived in different countries, and each falsely believed that the other was undergoing tortures, each might feel pleasure; yet we should not consider such a state of things good. We should even think it much worse than a state in which each derived pain from the belief that the other was in torture. (PE 57–58; boldface emphasis mine)

Again:

And when Christians affirm that a world created by a good God must be a good world, they do not mean that it must be to their taste.... (PE 21; boldface emphasis mine)

Furthermore, the reasons we ordinarily give for actions are that their conse- quences are “likely to be...at least the best possible under the circumstances” (PE 15). Leibniz is the source of Russell’s talk of better or worse worlds. Just ten years earlier, Russell had written a whole book on Leibniz; the last chapter is a discussion of Leibniz’s ethics (PL chapter 16). The Strength of Russell’s Modal Logic 71

The paradoxes of moral implication are similar to those of strict implication. “¬P e (P 6 Q)” would mean “Doing what is forbidden commits us to doing everything” (Snyder 1971: 193). “~Q e (P 6 Q)” would mean “What is obligatory is morally implied by everything” (Snyder 1971: 193). These, of course, require no special treatment. Indeed, one might simply accept them, much as Lewis—and I think eventually Russell—accepted the paradoxes of strict implication. Deontic logic sharply departs from other modal logics in the relationship of moral modalities to what is actually the case. It would be implausible to say that whatever is necessary is actual, or ~P P P. That would mean that whatever is morally obligatory actually happens, which is absurd. Likewise, it would be implausible to say that whatever is actual is possible, or P P P. That would mean that whatever actually happens is morally permissible, which is absurd. In colloquial terms, it means “Anything goes.” Call these the moral absurdi- ties. The standard way to avoid the moral absurdities is to avoid imputing moral characteristics to the actual world (Snyder 1971: 192–93). Historically, that is just Hume’s view that no ‘ought’ can be derived from an ‘is’, or Moore’s open question fallacy. Russell would avoid these absurdities in this standard way, since he adopts the Hume-Moore view (PE 21–25, 58; Russell 1962: 19). The avoidance can be technically accomplished simply by allowing no plain atomic statements in the deontic logic, and requiring that all atomic statements be prefixed by modal operators. This means that the logic will not be used to describe the actual world, which is considered ethically neutral, but only to describe alternative ethically desirable worlds (Snyder 1971: 193 on CMn, 195). This too might be found implied in Russell by reasonable extension, though of course without ontological commitment to alternative worlds. The 1910 Russell would have to rely on descriptions of alternative ethical worlds. My generous approach to assessing MDL–D’s strength will be guided by my agreement with D. Paul Snyder that deontic logic in general ought to be S5, pace Georg Henrik von Wright, who has argued against the iterability of deontic operators (Snyder 1971: 197).3 The distinguishing axiom of deontic S1 is that if P, then it is morally possible that P. That is, P 6 P. That is one of the two moral absurdities. I have suggested that Russell could admit this axiom. But he could also accept much of a stronger S-logic without accepting the distinguishing axiom of S1. 72 Bertrand Russell on Modality and Logical Relevance

The distinguishing axiom of deontic S2 is that if it is morally possible that P and Q, then it is morally possible that P. That is, (P & Q) 6 P. That is trivially true in MDL–D. The distinguishing axiom of deontic S3 is that if P deductively implies Q, then the moral possibility of P deductively implies the moral possibility of Q. That is, (P 6 Q) 6 (P 6 Q). That is trivially true in MDL–D as well. The distinguishing axiom of deontic S4 is that if it is morally possible that P is morally possible, then P is morally possible. That is, P 6 P. That would seem trivially true in MDL–D. The distinguishing axiom of deontic S5 is that if P is morally possible, then it is morally necessary that P is morally possible. That is, P 6 ~P. I think that will be trivially true in MDL–D too. Model semantics for an S5 deontic logic can be constructed only with a specialized set of assumptions (Snyder 1971: 192–98). Unusual assumptions need to be made about the transitivity, symmetry, and especially the reflexivity of the ethical alternativeness relationship, so as to complete the avoidance of the moral absurdities by avoiding relationships back to the actual world, which is treated as the fixed model. Also, exclusively deontic operators need to be defined, if the deontic logic is to be integrated with an alethic modal logic such as FG–MDL*. I shall not describe the details (Snyder 1971: 196–98). All this might be imputed to Russell more reasonably than not, in the name of protecting his adoption of the Hume-Moore separation of is from ought, and of facts from values. Indeed, since Russell rejects the moral absurdities, does this not logically imply he would accept the special reflexivity assumptions of deontic logic? After all, their sole mission is to forestall the absurdities. But you can see why I said that the deontic logic would be the most difficult of my imputations to Russell. I do not impute model semantics to Russell. That Russell lacks formal model semantics is criticism, not scholarship. Where Jean van Heijenoort and Jaakko Hintikka contrast model semantics with Frege-Russell universal logic, they tacitly admit that the Frege-Russell intended model is simply the actual world (Dummett 1995: 12, 12 n.6). I am imputing the axioms of S5 to Russell, not the latest semantics for them. That is work enough. Note that for Russell, the set of moral worlds is not a proper subset of the set of logically possible worlds. Even lifeless worlds can illuminate moral theory. Such worlds need not have ontological status even in model semantics (Forrester 1996: 90). The 1910 Russell never states that it is good that there are good things, or that it is our duty to do our duty. In fact, some might think he may have had two positive reasons for not finding it good that things are good. (i) He may The Strength of Russell’s Modal Logic 73 have mistakenly thought that would violate theory of types by committing us to an infinite number of type-levels of goodness. Of course, if he positively rejected the concept of an iterable modal operator, that would go against all the modal logics I impute to Russell. But we do see at least the casual locution “necessarily possible” in Principia (PM 40). This indicates that not only does he possess the concept of iteration, but he applies it. (ii) The early Russell may have thought that since goodness is an existing quality (PE 20, 21) and since nothing ethical can be inferred merely from what exists (PE 21–25, 58), we are not entitled to infer that it is good that there are existent goods. The problem with this reason is that we can still intuit that the quality of goodness is itself good, without considering goodness as one of the things that exist. Russell does much intuiting of goodness in other things. Why not in goodness itself? In fact, I can hardly see how Russell could fail to intuit that the goodness of good things is itself good. Russell comes close to iteration of the same operator when he says, “I do not wish to deny that right conduct is among the things that are good on their own account” (PE 37). This amounts to saying that it is good to do acts which probably will produce the best results. And that is virtually the same as saying it is good to do good, which is trivially true. What is more, intellectual intuition of the quality of goodness is merely acquaintance with a universal through the usual process of intellectual abstraction. At least, I assume the 1912 The Problems of Philosophy sheds definitive light on the 1910 “The Elements of Ethics” on this score. (PP 48, 51–52, 101–2). The 1912 Russell adds, “Judgements of intrinsic ethical or aesthetic value are apt to have some self-evidence, but not much” (PP 117). I can also hardly see how Russell could fail to intuit that we have a duty to do our duty. For Russell, the objectively right act is “that one, of all the acts that are possible, which will probably produce the best results” (PE 59). It follows that “It is objectively right to do what is objectively right” means the same as “Of all the acts that are possible, it will probably produce the best results to do, out of all the acts that are possible, the act which will probably produce the best results.” That is trivially true. The distinguishing axiom of deontic S4 was that if it is morally possible that P is morally possible, then P is morally possible. That is, P 6 P. This is equivalent to ¬~¬(¬~¬P) 6 (¬~¬P). That is, “If it is not objectively right that it not be the case that (it is not objectively right that not-P), then (it is not objectively right that not-P).” Or, more fully, “If it is not the case that out of all the acts that are possible, it would probably produce the best results that it not be the case that (it is not the case that out of all the acts that are possible, not-P will probably produce the best results), then (it is not the case that out 74 Bertrand Russell on Modality and Logical Relevance of all the acts that are possible, not-P will probably produce the best results).” You do not need to figure this out to see that the substitutions will not eliminate the trivial character of the truth in question. Looking to the symbolic version, you can eliminate the double negation in the antecedent. That will result in an iterated necessity operator which can be collapsed to a single necessity operator in accordance with what I said in the previous paragraph. And that will make the antecedent and the consequent identical. That is, the axiom is now of the form “If Q, then Q.” Alternatively, you can work backward through the substitutions to the intuitively correct thesis that if it is morally permissible that P be morally permissible, then P is morally permissible. Criticism of working backward is criticism of Russell’s theory, not scholarship. I am using only the most elementary implications of his theory. Certainly Russell’s intent is to state what moral obligation is, if not to state by implication what moral permissibility is. I am merely formalizing his intent in accordance with his own philosophy of paraphrase. The distinguishing axiom of deontic S5 was that if P is morally possible, then it is morally necessary that P is morally possible. That is, P 6 ~P. That is, ¬~¬P 6 ~(¬~¬P). That is, if I may simplify, “If it is not probably best that not-P, then it is probably best that (it is not probably best that not-P).” That seems true enough, at least working backward to the intuitively correct thesis that if P is morally permissible, then it is a moral obligation to ensure that P be morally possible. Again, working backward is innocent from the scholarly point of view. One might object to my attribution of MDL–D to Russell as follows. Russell treats ethics separately from his logic, ontology, and metaphysics. The formal requirements of a plausible deontic logic are simply too remote from Russell’s ethical concerns. None of Russell’s ethical writings concerns the formal machinery of a plausible deontic logic. And while the relationship of MDL–C and MDL–E to MDL is obvious, the relationship of Russell’s ethical theory to MDL is not. MDL is the gateway to FG–MDL and FG–MDL*, where it is very easy to imply the iteration of modal operators. But here we see no gateway. My reply would make four points. First, Russell’s ethical thought is closely connected with his ontology and metaphysics, both early and late. Second, the dearth of formal deontic machinery really does not matter to my methodology. What matters is whether test (i) or test (ii) is met. Third, Russell finds the case for determinism “overwhelming” (PE 37, 38, 45, 59). And “if determinism is true, there is a sense in which no action is possible except the one actually performed” (PE 39, 59). Thus there is a The Strength of Russell’s Modal Logic 75 fundamental sense in which one’s actual moral act is the only causally possible moral act. And that implicates MDL through MDL–C. MDL is the éminence grise, the power behind the ethical throne and the causal throne alike, so much so that Russell is driven to admit a second sense of “possible” in which alternative actions are possible. The possibility of alternative actions in this sense is compatible with determinism, and is also the sort of possibility relevant to ethical theory. Russell calls acts which are possible in this sense “physically possible.” The basic idea is that an act is physically possible if it “will be performed if we will to perform it” (PE 59; see 36–45 for an extended discussion). Fourth, what is morally possible must be logically possible. This implicates MDL through FG–MDL, Russell’s alethic logic until 1914. This must not be confused with the second moral absurdity, that whatever is actual is morally permissible. I think enough universality can be attributed to the early Russell’s moral duties that something is a duty for a given person in a certain type of consequential situation in the actual world if and only if it is a duty in the same type of consequential situation for all persons in all moral alternative worlds, and in fact in all logically possible worlds. That is, for Russell moral duties are nondefeasible, where a moral duty is defeased if it is trumped by another, higher-level, moral duty in a certain situation. Russell in a sense admits defeasible moral duties, a main topic of deontic logic. Russell admits subjective moral duties which surely can be defeased (PE 33–36, 38, 59). Donald Nute distinguishes between prima facie duties, actual duties, and apparent moral duties:

By a prima facie obligation, I mean something that is binding other things being equal....By an actual obligation I will mean any obligation that is binding when all relevant circumstances are considered....[T]here may be situations in which we cannot know all morally relevant circumstances before deciding what we ought to do. In such a situation, we are expected to fulfill those obligations which bind us given all we know about morally relevant circumstances. These are what I call our apparent obligations. (Nute 1997: 287)

Apparent obligations can be defeased in the light of new information. Here a new and better justified apparent obligation can defease the old apparent obligation (Nute 1997: 288). Evidently a prima facie obligation can be defeased by a greater obligation even where all relevant circumstances are considered. 76 Bertrand Russell on Modality and Logical Relevance

For the 1910 Russell, what is objectively right is our actual obligation, and what is subjectively right is our apparent obligation. What is objectively right is what is most likely to produce the greatest amount of good, and what is subjectively right is what a moral agent would believe to be objectively right after an appropriate amount of reflection in the light of available information (PE 38, 59; see 27–37). Surely Russell’s subjectively right duties are defeasible in just the manner Nute suggests. The more difficult question is whether Russell would admit prima facie duties which can conflict with and be overridden by greater obligations. This would concern only the realm of objectively right acts, i.e. objective duties. Can we subdivide this realm into prima facie duties and actual duties? Russell says, “Whenever a question is at all complicated, [it] cannot be settled by following some simple rule” (PE 28). Even simple rules which we admit are justified only as being right “in the vast majority of instances” (PE 28), and we tend to reclassify exceptional acts as not falling under the rule. For example, “Thou shalt not murder” will generally not be treated as including killing in war or in self-defense (PE 28–29). Thus a “moral code is never itself ultimate; it is based upon an estimate of probable consequences” (PE 30). “Right and wrong, since they depend upon consequences, will vary as men’s circumstances vary” (PE 54). This may sound like defeasibility of prima facie duties. But the existence of an exception to a rule does not imply the defeasement of that rule by another rule. It might be an unprincipled exception. Of course, you could always treat Russell’s definition of objective rightness as a supreme rule to do whatever will probably maximize goodness, and Russell would admit only lesser rules and exceptions which fall under that supreme rule. But Russell’s talk of moral codes is always of specific historical moral codes, and it may be that none of them is objectively right in the first place. And precisely because all lesser rules must conform to the supreme rule in order to be objective rules at all, there is no sense of conflict among objective rules. At bottom, no subdivision of objectively right acts into prima facie duties and actual duties is possible for Russell, “since in fact everything either ought to exist or ought not” (PE 18). “Everything” presumably includes moral acts and moral duties. And intrinsic goodness is a property which either a thing has or it has not (PE 20). Thus in a dispute about whether a thing is good or not, one person will be right and the other wrong (PE 21). This too presumably includes moral acts and moral duties. Also, Russell does all he can to explain away moral disagreements as merely apparent (PE 54–56), while defeasement The Strength of Russell’s Modal Logic 77 of prima facie obligations is a philosophical theory which aims to resolve genuinely objective moral conflicts. Another main topic of deontic logic is the use of dyadic modal operators to formalize conditional moral duties (Nute 1997a: 7; Forrester 1996: 23, 48–49; Snyder 1971: 194). Russell’s moral duties are conditional in that they are contingent on what happens. This is the utilitarian side of Russell’s ethic. Here Russell requires dyadic or, more accurately, polyadic modal operators. For Russell, moral rightness is conditional on good consequences, and is thus conditional on causality, whether assayed á la Hume or not. “If causality is doubted, morals collapse” (PE 38). “Right and wrong, since they depend upon consequences, will vary as men’s circumstances vary” (PE 54). And since causality involves systems of interacting variables (ONC 187–93), polyadicity is needed. Moral acts are also conditional on their physical possibility, as explained earlier (PE 39–40). The conditionality of moral duties must not be confused with their defeasibility. Also, it must be noted that in any utilitarian ethic such as Russell’s, moral duties are temporally and causally postconditional, and only logically or definitionally preconditional. That is because their present rightness is defined in terms of their future consequences. To sum up, I find it more reasonable than not to impute a deontic logic to the 1910 Russell. Some readers may find this a close call. But I find a substantial positive basis in his talk of alternative moral worlds, his rejection of the moral absurdities, his separation of is from ought, and his acceptance of an intuited quality of goodness which could hardly fail to be itself intuited as good. Could goodness fail to be itself good, and still remain goodness? What kind of existing, intrinsic quality of goodness is it that is not itself good? Similarly for moral duties. What kind of moral obligations are not themselves morally obligatory? Of course, we might construct a deontic logic consistent with everything or nearly everything the early (or later) Russell says. Indeed, it seems that Snyder has done so without any reference to Russell (Snyder 1971: 192–98). But that would not meet test (i) or test (ii) of my methodology. MDL–D* is Russell’s later deontic logic. Russell’s major later ethical work, the 1954 Human Society in Ethics and Politics (mainly written in 1946), is not a pure and simple subjectivism as some have thought (HS vii, 20, 59–72 90–96, pace viii on reason as the slave of the passions). I show elsewhere that from 1921 on, Russell equates degree of publicity with degree of objectivity in his ontology and metaphysics (Dejnoñka 1991: 22–23, 26, 28–29, 30–34). In Human Society, Russell finds moral objectivity in widespread moral agreement. Nor is Human Society emotivist. Russell finds that ethical 78 Bertrand Russell on Modality and Logical Relevance statements are, or can be, true or false (HS 94–96, pace 19, 72; see Dejnoñka 1997: 53). There is considerable continuity in Russell’s ethical thinking from 1910 to 1954. Russell continues to think in terms of alternative moral worlds:

Borrowing a term from Leibniz’s account of possible worlds, we may call two desires or impulses “compossible” when both can be satisfied, and “conflicting” when the satisfaction of the one is incompatible with that of the other....It is obvious that a world in which the aims of different individuals or groups are compossible is likely to be happier than one in which they are conflicting. It follows that it should be part of a wise social system to encourage compossible purposes, and discourage conflicting ones.... (HS xiv–xv, boldface emphasis mine)

Again:

That feelings are relevant to ethics is easily seen by considering the hypothesis of a purely material universe, consisting of matter without sentience. Such a universe would be neither good not bad, and nothing in it would be right or wrong. (HS 19, boldface emphasis mine)

Again:

Without civic morality communities perish; without personal morality their survival has no value. Therefore civic and personal morality are equally necessary to a good world. (HS 22, boldface emphasis mine)

Again:

In an inanimate world there would be nothing good or bad. (HS 44, boldface emphasis mine)

Again:

Borrowing a term from Leibniz, I call a number of desires “compossible” when all can be satisfied by the same state of affairs; when they are not compossible, I call them incompatible. (HS 47, boldface emphasis mine)

Again: The Strength of Russell’s Modal Logic 79

It may be urged that hate generates hate, and that a world in which hate is encouraged will be so full of strife that nobody will be able to enjoy a good life. (HS 70, boldface emphasis mine)

Again:

What is meant, if anything, by saying that a world in which humans are happy is better than a world in which they are unhappy? (HS 90, boldface emphasis mine; Russell “find[s] it intolerable to suppose” that something subjective is meant)

Again:

I can make these robots do all the things that are usually praised. I can make them read the Bible. I can make them preach eloquent sermons....But if A said to B, “You ought to substitute robots for human beings, because robots do not sin,” almost everybody would reply that the robot world, since it would be destitute of sentience, would be neither good nor bad, and would be in no way better than a world of ordinary matter unable to perform the robots’ imitative tricks. (HS 100, boldface emphasis mine)

Again:

[Abstract considerations might make it seem that the road to universal contentment requires only] that the desires actuating the conduct of individuals should be compossible desires.... (HS 127, boldface emphasis mine)

That is a total of nine texts in Human Society describing possible worlds or compossible things. Two of the texts expressly cite Leibniz. Another major continuity in Russell’s ethical thinking from 1910 to 1954 is that the objectively right act is defined the same as before, namely, as the act probably producing the best consequences (HS 95). The only change is that instead of wanting to maximize the production of things having an intuited quality of goodness, we want to maximize the general happiness or sense of satisfaction. Goodness, in the sense of a felt sense of satisfaction, remains an intrinsic quality as before (HS 41; see 93). And presumably we have acquaintance with the quality of goodness as before, though now the acquaintance is through introspection of a feeling, or more generally of a state of mind (HS 107), rather than through a process of intellectual abstraction (PP 48, 51–52, 101–2). Since the strength of MDL–D* depends on the definition 80 Bertrand Russell on Modality and Logical Relevance and not on the substituted change, we may apply our analysis of the strength of MDL–D to MDL–D* wholesale and without further ado. Thus MDL–D* is S5 in strength. The robot world and the purely material world suggest a separation of ought from is, as before. Russell says that ethical judgments state feelings not facts, should be imperative not indicative in mood, and “clearly cannot be proved or disproved merely by amassing facts” (HS 19; this is consistent with 94–96, rejecting emotivism). Russell’s fourth ‘fundamental proposition’, “It is right to feel approval of a right act and disapproval of a wrong act” (HS 95), suggests that he would allow the iteration of the moral necessity operator, if he is not actually iterating it in that proposition. The 1954 Russell still distinguishes objectively right acts from subjec- tively right acts (HS 71). Again, there seems to be room for defeasing apparent obligations. The 1954 Russell also still speaks of exceptions to rules (HS 37). But he seems to reject any distinction between prima facie and actual obligations within the realm of objective rightness. He thinks of moral rules as universal (HS 71). And he still aims to minimize the theoretical possibility of ethical disagreement, while defeasement is a way to resolve theoretically genuine ethical conflicts. As before, the moral rightness of an act is contingent on its probable consequences. Polyadic modal operators are still needed. The 1954 Russell states much the same theory of free will and determin- ism as before, though not in the same detail (HS 79–80). Morality is consistent with determinism. Once again, there is a fundamental sense in which one’s actual moral act is the only causally possible moral act, implicating MDL through MDL–C and driving Russell to find a second sense of “possible” which is consistent with determinism. Again, morally possible acts must be logically possible acts. This implicates MDL through FG–MDL*, and more broadly through FG–MDL**. Surveying now all seven of Russell’s modal logics—FG–MDL, FG–MDL*, FG–MDL**, MDL–C, MDL–E, MDL–D, and MDL–D*— all seem closest to S5. If I am right, Russell has achieved a tremendous theoretical simplification due to his always interpreting modality in terms of quantifi- cational logic. MDL is a basic element of, or moving power behind, all seven. Whether the modalities are logical, causal, epistemic, or moral is irrelevant to the question of strength. The Strength of Russell’s Modal Logic 81

This makes historical sense. FG–MDL** is close to the early modern theory of necessary truths as relations of ideas, which is best seen as S5 for similar reasons. FG–MDL* has an antecedent in the Leibniz-Kant subject- contains-predicate test of analyticity, which is best seen as S5 for similar reasons. All this helps place Russell in the modern tradition of theory of necessary truth. The reader may object that surely causal necessity should be weaker than logical necessity or synthetic a priori necessity, yet here I am making all three sorts of necessity out to have the same strength, S5. This is not quite correct, since logical necessity is S5 + I and causal necessity is only S5. But of course that does not begin to answer the objection. The answer is that the necessity operator is interpreted differently in all seven modal logics. In FG–MDL, “~P” means “P is a fully general truth.” In FG–MDL*, “~P” means “P is a fully general truth and is true in virtue of its logical form.” In FG–MDL**, “~P” means “P is a synthetic a priori truth.” In MDL–C, “~P” means, “P is deducible from the set of all causal laws and true particular statements.” In MDL–E, “~P” means “¬¬P”, where “P” means “We do not know if P; ‘P’ is a value of the propositional function, ‘Px’; and that propositional function is not always false.” In MDL–D and MDL–D*, “~P” means, “It ought to be that P,” this being interpreted in different ways. I think that should answer the objection. Note that all seven necessity operators are referentially opaque. That is, none of them is a truth-functional operator on P. That is, merely replacing true P with true Q does not guarantee that the operator still applies, if it applied to P (or still does not apply, if it did not apply to P). The reason is simple. Truth- functional statement operators treat statements as mere atoms of truth or falsehood. But the first five necessity operators in Russell’s modal logics make reference to the form or internal structure of statements—and not all true statements have the same internal structure. Even the sixth and seventh operators are connected to the form of statements, in that what is logically impossible cannot be morally necessary. Russell, of course, can easily accommodate referential opacity with respect to modal contexts such as are created by the use of modal operators. He already admits referential opacity with respect to epistemic contexts. That is, he admits “Smith believes that P” is a non-truth-functional statement. This is his famous theory of propositional attitudes in Principia Mathematica (PM 8). While the modal operators in all seven modal logics are referentially opaque, none of the modal logics involves any modal entities or notions except for MDL–D, which is based on a primitive modal entity, goodness. This entity 82 Bertrand Russell on Modality and Logical Relevance vanishes in the later Russell’s MDL–D*, and may be regarded as an anomalous modal holdover from Russell’s neo-Moorean Principles realism. The reason for opacity in the other six modal logics is not the presence of modal notions, but the reference to the forms or internal structures of statements. Even the deontic operators of duty and permissibility are related to the logical forms of statements. What is logically impossible or physically impossible cannot be a moral obligation. What is morally permissible must be both logically possible and physically possible. Mark W. Dickson (1998) observes that Russell permits quantification into epistemic contexts as early as “On Denoting”:

[W]hen we say, ‘George IV wished to know whether Scott was the author of Waverley’, we normally mean ‘George IV wished to know whether one and only one man wrote Waverley and Scott was that man’; but we may also mean: ‘One and only one man wrote Waverley and George IV wished to know whether Scott was that man’. In the latter, ‘the author of Waverley’ has a primary occurrence; in the former, a secondary. (OD 52)

Evidently this is a scope distinction that Russell does apply to epistemic contexts and logically could apply to modal contexts. That “wished” is intentional, not epistemic, seems insignificant casual writing. But Russell evidently permits quantification into intentional contexts here as well. I need not add that epistemic contexts are modal contexts, insofar as knowledge is epistemic necessity. Since Russell technically (formally) can quantify into modal contexts, the only remaining question is whether Russell has sufficient positive reason to justify quantification into modal contexts. I shall argue later that he does. We are now able to discuss the grade of modal involvement of Russell’s seven modal logics in terms of Willard Van Orman Quine’s essay “Three Grades of Modal Involvement.” The lowest grade or least involvement occurs when “is necessary” is viewed as a semantical predicate of names. Quine argues that its seeming referential opacity is no genuine threat to extensionality, that is, to truth- functionality, since such modal contexts are not significantly different from mere quotational contexts (Quine 1976a: 161–63). The second grade occurs when “is necessary” is viewed as a statement operator. The commitment here is to modal statement operators. Note that the later Frege construes sentences as names of truth-values, and has no use- mention confusions. The Strength of Russell’s Modal Logic 83

The third grade occurs when quantification is permitted into modal contexts. This is the highest grade of modal involvement. Quine characterizes it as a commitment to Aristotelian essentialism. Quine means a commitment to things in the world as having some properties necessarily. While in the lower two grades, modality was only part of how we talk about the world, here the locus of modality is in the world we talk about (Quine 1976a). A model will succeed in being anti-essentialist only if it makes de re quantified form- ulas equivalent to de dicto formulas (see Parsons 1971; McKay 1975). All seven of Russell’s modal logics are of the second grade at the very least, since all of them have iterable referentially opaque statement operators. Landini observes that in MDL, necessity with respect to x would be best viewed as a semantical predicate of names (Landini 1993: 4). I presume that is because x can be replaced by logically proper names. I agree that this assigns to MDL the lowest grade of modal involvement. But as Landini is well aware, MDL is not Russell’s modal logic. MDL is only the stepping-stone. I shall now argue that Russell has a sufficient positive reason to permit quantification into modal contexts in a proper sub-part of FG–MDL**, the modal logic of synthetic a priori truths. Namely, at least on my interpretation, the 1903–18 Russell’s theory of particulars and universals is that sensible particulars are essentially instances of sensible universals. Such particulars would not be the particulars they are unless they were instances of the sensible universals of which they are instances. For them to change their sensible qualities is for them to cease to exist and to be replaced by new and wholly different particulars (RUP 119; PLA 119; Dejnoñka 1996: 159–60). This is Russell’s Aristotelian essentialism. Note that Russell speaks of sensible particulars as being substances logically speaking (PLA 201–2, 203–4). In fact, ignoring one’s own mind and looking only to sensed and unsensed sensibilia, the 1914–18 Russell is best described as a superessentialist, where superessentialism is the view that every monadic property of a real particular is an essential part of its nature (modifying Blumenfeld 1982: 103). This exceeds Aristotle. Yet it is wrong to say with Quine that now the ontological locus of modality is in the world we talk about. For here in the third grade of modal involvement, Russell is as eliminative of modal entities and modal notions as ever. Here the necessity operator in “(›x)~(Fx)” means only “It is a relation- ship of instantiation that.” It is instantiational relationships which have their locus in the world. This is very closely analogous to eliminative analyses of modal relationships as whole-part relationships, as in the whole-part theory of deductively valid inference. After all, the sole difference between a universal 84 Bertrand Russell on Modality and Logical Relevance and its instances is that it is one and they are many. They are distinct only in reason. Even if the 1903–18 Russell’s particulars were bare particulars and not (sensible quality) instances, their individual identities would be just as essentially connected to the sensible qualities they exemplify. The only thing that would change is that the necessity operator in “(›x)~(Fx)” would mean, “It is a relationship of exemplification that.” Placing this sort of instantiational quantification into modal contexts in FG–MDL** might seem to blur Gustav Bergmann’s threefold distinction among three sorts of necessity. These are categorial necessity, analytic necessity, and synthetic a priori necessity, where the first would be shown not said in an ideal language perfectly mirroring the categorial structure of the world in its syntactical structure (Bergmann 1967: 23–24). The reason for the seeming blur is this. At least on my interpretation of Russell’s individuals as all being particulars, the mere fact “a” is a logically proper name shows that “a” denotes a sensible particular, since it is only by acquaintance that we could grasp the meaning of “a”. And the only way to achieve Aristotelian essential necessity here would be in case F is a monadic property of individuals such as a. Thus the fact that a essentially has F would be shown not said. Thus such de re predication would seem to be a categorial necessity. But I classify such de re predication as synthetic a priori necessity. The reason is that the criterion of categorial impossibility is that an attempt to express it in the formal notation would be syntactically ill-formed. Well-formed “(›x)~(Fx)” would be the best paraphrase of “There exists a particular which is necessarily red.” And where Fx =Df ¬Gx, “(›x)~(Fx)” is logically equivalent to “(›x)¬(¬Gx),” which is also well-formed. Hence the necessity is merely synthetic a priori. This result should not appear strange. Some philosophers might well argue that all three sorts of necessity are de re. Even we might accept that not all de re predication occurs at the deepest level of categories. Using the box symbol is always an interpretive gloss on Russell, who uses no such symbols himself. I feel it is shallow and uncharitable to interpret Russell or anyone as limited by his formal notation if some of his metaphysical views would be better expressed in a different notation. Again, this use of the box does not commit us to interpreting the box as expressing a modal meaning. Here it is best understood as meaning only “It is a relation of instantiation that,” where the notion of instantiation is not intrinsically a modal notion. It is the relation of a particular being a certain universal, in a sense almost that of identity. The Strength of Russell’s Modal Logic 85

Perhaps the grossest inconsistency I have found in Russell’s philosophy is that between his essentialism and his anti-essentialism. The later Russell lambastes essentialism:

The “essence” of a thing appears to have meant “those of its properties which it cannot change without losing its identity”....In fact, however, this is a verbal convenience. The “essence” of Socrates thus consists of those properties in the absence of which we should not use the name “Socrates.” The question is purely linguistic: a word may have an essence, but a thing cannot. (HWP 200–1)

Yet the 1940–59 Russell admits sensible qualities as recurrent particulars and predicates generic universals of them which they could only have essentially. For example, a certain shade of red is a particular which essentially has the generic properties of having a color, of being visible, and of being sensible (IMT 98, 100, 227; Dejnoñka 1996: 161–62, 292–95 n.4). The only rescue I can think of is that Russell is attacking traditional essentialism while embracing his own new essentialism. But that seems a fig leaf. As late as 1959, Russell says, “Traditionally, qualities, such as [a certain sort of] white or hard or sweet, counted as universals, but if [my 1940–59] theory is valid, they are syntactically more akin to substances” (MPD 127). Substance and essence are revised, not rejected, in the early Russell (instances) and in the later Russell (qualities) alike. That this essentialism is not entirely shown in the formal notation does not detract from this point. At least, logically proper names always denote the post-1910 Russell’s substance substitutes. They always denote individuals, that is, particulars. I proceed to discuss another problem of paraphrase. Dickson asks how Russell might translate:

1. “The author of Hamlet might not have written Hamlet.”

Following Saul A. Kripke, Dickson says that if Russell admits only de dicto modality, then Russell can only interpret this sentence as meaning,

1* “It is possible that the author of Hamlet did not write Hamlet,” which Dickson says is a mere contradiction (Dickson 1998). This aptly poses the problem; of course, logical possibility is meant. I think this problem can be solved if we understand Russell’s theory of paraphrase and his metaphysics as well as his formal logic. 86 Bertrand Russell on Modality and Logical Relevance

For Russell, paraphrase is the art of reasonably replacing unclear ordinary thoughts with canonical notation. Dickson is looking for a strong Kripkean solution in which the first occurrence of “the author of Hamlet” in (1) involves rigid designation, and the second occurrence is attributive. I think this type of strong solution is available to Russell, though the rigid designation will be not of the author of Hamlet so much as of a sensible aspect of him. As to metaphysics, for the 1918 Russell a man is a temporal series of classes of sensed and unsensed sensibilia. My paraphrase would be, “The sense-datum s I now sense belongs to class c in temporal series t (where t is Russell’s metaphysical analysis of William Shakespeare as he actually lived and wrote Hamlet) and it is logically possible that there exists at least one class c1 and at least one temporal series t1 such that s belongs to c1 and c1 belongs to t1 (where t1 is the metaphysical analysis of some possible way Shakespeare might have lived in which he did not write Hamlet). The fact that classes and series are logical fictions which have no ontological status, so that quantifica- tion over them is purely nominal, does not detract from the correctness of the paraphrase. It is quantification over s that involves quantification into the modal subcontext. The situation is actually much more complicated than my paraphrase suggests, since there will be many ways in which what we ordinarily call the same man might have lived without writing Hamlet. Also, people today can no longer sense sense-data which are sensible aspects of Shakespeare. But I think my paraphrase conveys the gist of how Russell would approach the problem. We might even simply define c as the class of Hamlet authors and ignore nice- ties such as t. A simpler solution would be to substitute another description for the first occurrence of “the author of Hamlet.” We must allow Russell charity in paraphrasing ordinary language sentences into his canonical notation. No first year student of neo-Russellian predicate logic would dream of making (1) self-contradictory by translating it as (1*). Considerations of paraphrase include not only analysis into particulars and logical fictions, but the use of plain common sense. For example, we should not translate the ordinary definite description “the charlady who ain’t never done no harm to no one” as ‘the charlady who in at least one moment injured the entire human race’. Russell’s famous reply to Strawson makes it clear that Russell would find that literal translation ludicrous. Russell gives the charlady example as a parody of logicians with no common sense. The message of the charlady example is that “My theory of descriptions was never intended as an analysis of the state of mind of those who utter sentences containing descriptions....I was concerned The Strength of Russell’s Modal Logic 87 to find a more accurate and analyzed thought to replace the somewhat confused thoughts which most people at most times have in their heads” (MPD 179). A third solution is to use the “On Denoting” scope distinctions directly to solve the Hamlet problem, by parity of reason with epistemic contexts (Dickson 1998). This is the solution Arthur Smullyan adopts (Smullyan 1971). Leonard Linsky and Quine argue that Smullyan’s solution is not enough (Smullyan 1971, citing Principia Mathematica; L. Linsky 1971: 94–95); see L. Linsky 1971a: 3–4 quoting Quine). Up to a certain point we need not be detained, since in the present context, this is criticism, not scholarship. Only if Smullyan’s solution is truly inadequate should we be worried about making Russell into a truly inadequate modal logician, if we find Smullyan’s solution the most natural solution for Russell. Quine has two arguments. First, the adoption of the scope distinction already requires the possibility of quantifying into modal contexts. Thus “the appeal to scopes of descriptions does not justify such quantification, it just begs the question” (L. Linsky 1971a: 4, quoting Quine). My response is that the adoption of scopes and of quantification are so much the same thing that begging the question is not the right phrase. You simply do both or do neither. This is a stand-off of opposing logical intuitions. Neither Quine nor Smullyan has a decisive upper hand on this level of argument. Quine’s second argument is that eliminating singular terms and using only descriptions, modal features appear to shift as descriptions shift. Therefore modality appears to be a feature not of things themselves, but of how we describe them (L. Linsky 1971a: 4). Quine says:

Mathematicians may conceivably be said to be necessarily rational and not necessarily two-legged; and cyclists necessarily two-legged and not necessarily rational. But what of an individual who counts among his eccentricities both mathematics and cycling? Just insofar as we are talking referentially of the object, with no special bias toward a background grouping of mathematicians as against cyclists or vice versa, there is no semblance of sense in rating some of his attributes as necessary and others as contingent. (Quine 1975: 199)

Quine brings out the tension latent in his second reason with a famous example which will be our final problem of paraphrase:

(a) 9 is necessarily greater than 7. (b) The number of planets is 9. (c) Therefore the number of planets is necessarily greater than 7. 88 Bertrand Russell on Modality and Logical Relevance

The paradox is that (a) and (b) are true, and the inference form seems valid (it uses the principle of the indiscernibility of identicals), yet (c) seems false (FLPV 143; see L. Linsky 1971a: 2). Resolving this paradox will require us to understand Russell’s metaphysical analysis of numbers as logical fictions. I shall consider the three solutions to the Hamlet problem in order. The first Hamlet solution seems hard to apply to numbers. For the 1918 Russell, numbers are logical fictions which have no sensible aspects. Yet the heart of Russell’s critique of Giuseppe Peano’s numbers has always been that Peano disassociates numbers from the empirical experience of counting (POM 127; IMP 9; HK 237). In fact, Russell treats numbers much the same as bodies or minds (PLA 277). Thus rigid designation of groups of four sheep or two oranges may permit a Kripkean paraphrase á la Hamlet. But what about large numbers? As René Descartes observed, we cannot distinguish a 1,000 sided figure from a 1,001 sided figure perceptually, but only intellectually. The answer is that Russell defines large numbers in terms of small numbers. The second Hamlet solution may seem inapplicable. The planet paradox depends directly on the description “the number of planets.” To borrow a phrase from Russell, changing this description would have all the advantage of theft over honest toil. Even worse, any reasonable paraphrase should leave the logical contingency of (b) intact. Third, there is the bare Smullyanian solution of relying directly on the scope distinctions in “On Denoting.” At least Russell has this third Hamlet solution. His motivation might be the bare negative one of avoiding the planet paradox. It may be a poor solution. But that is criticism, not scholarship. Quine criticizes Smullyan’s solution, which is to divide names into proper names and covert descriptions such that proper names which name the same object are always synonymous. This is certainly true of Russell’s logically proper names; any identity statement flanked by logically proper names is tautologous (PLA 245, 246). It is such names which justify extending Russell’s “On Denoting” scope distinction to modal contexts. Quine’s criticism is that referential opacity still occurs even when “[definite] descriptions and other singular terms are eliminated altogether” (FLPV 154). He means that referential opacity occurs even when we quantify into modal contexts, placing variable expressions instead of constant expressions within modal contexts. This strikes me as an ostrich-like criticism, burying our heads in the sand when logically proper names come wandering around. It is the presence of logically proper names within modal contexts which legitimates quantification over variables within those contexts. It is not the latter which somehow avoids or invalidates the former. Worse, Quine’s criticism would eliminate the very The Strength of Russell’s Modal Logic 89 plausible applic-ation of the scope distinction to belief-contexts as well. It is hard to deny that there are things about which we have beliefs.4 Similarly for the query how logical fictions such as numbers can have essential properties and accidental properties. That is criticism, not scholarship. And again I would defend Russell. The planet paradox involves not so much properties as relationships. Numbers, even as logical fictions, have definitional relationships among each other. And definitional relationships are essential relationships. This is why large numbers can be rigidly identified if small numbers can be. On the other hand, the relationship of the number 9 to the class of planets is neither definitional nor a priori. For Russell, the number 9 is a class of classes. It is the class of all classes having nine members. There is nothing essential about the class of planets’ being a member of that class of classes. Therefore it seems to me that Russell is entitled to an Aristotelian essentialism even for numbers as logical fictions. While numbers are not entities, they remain as objective as ever. Traditionally some descriptions reflect essences, others reflect accidents. Essences belong to metaphysics, not to language. They would not shift as descriptions shift, unless you assume they are unreal to begin with. Granted, they are ascribed in metaphysical theories. But does this mean that every such theory has a “special bias” and cannot hope to be objective? At the very least, Russell’s understanding of epistemology, metaphysics, realism, and objectivity is so different from Quine’s that we cannot say a Russellian use of Smullyan’s solution is truly inadequate merely because it appears so from the perspective of Quine’s philosophy. Quine has nothing like Russell’s sense-data which are fully known by nonlinguistic acquaintance and which are instances of sensible universals. Russell has nothing like Quine’s weak verificationism, which surely underwrites Quine’s argument against essentialism. Curiously enough, Quine admits classes and, by extension, numbers as abstract objects, yet wishes to deny them essences, while Russell rejects numbers as logical fictions, yet assigns them logically smooth, logically determinate defined and essential characteristics. At one time, Quine conceded that in a world consisting only of intensional objects, there would be no problem quantifying into modal contexts. Here an intensional object is an object x “such that any two conditions uniquely determining x are analytically equivalent” (FLPV 152). That would eliminate the planet paradox. Quine gives as examples of such objects “what Frege called senses of names, and Carnap and Church called individual concepts” (FLPV 152). But Quine came to reject his earlier concession: 90 Bertrand Russell on Modality and Logical Relevance

For, where A is any intensional object, say an attribute, and ‘p’ stands for any arbitrary true sentence, clearly...

(35) A = (4x)[p @ (x = A)].

Yet, if the true sentence represented by ‘p’ is not analytic, then neither is (35), and its sides are no more interchangeable in modal contexts than are ‘Evening Star’ and ‘Morning Star’, or ‘9’ and ‘the number of the planets’ (FLPV 153).

Quine goes on to observe that the same consideration shows that intensional objects are not always uniquely determined by analytically equivalent conditions, since where ‘Fx’ uniquely determines x, so will ‘Fx @ p’ (FLPV 153). I note that the same consideration also shows that Quine’s “lately italicized” definition of intensional objects, which I quoted from FLPV 152, is far too narrow. In fact, the consideration shows that there are no intensional objects at all, on that definition of intensional objects. I find Quine’s consideration technically ingenious but philosophically uninteresting. I cannot think that anyone committed to intensional objects would be impressed by it. Perhaps Quine set up a straw man, a definition that is far too exclusive in the first place. In any case, arbitrary, contingent p is logically irrelevant to the properties of A in any serious sense of the word “property.” No wonder it kills intensional objects so easily. I suggest that Russell’s sensibilia are intensional objects, as much as senses and individual concepts are. For the meaning of a logically proper name is its denotation. And the sensible qualities of a sensibile are intensional. Even if all and only red things were round, red and round would be two properties, not one (roundness is a “common sensible” quality which can be seen or felt). Perhaps an intensional object is best defined as an object whose essential properties are intensional, where properties are intensional if they logically can map the same individuals onto the same truth-values, yet be different properties. That would explain why a logically proper name, which “is merely a means of pointing to the thing” (PLA 245), can occur with referential transparency in a modal, intentional, or epistemic context. Note that where “a” is a logically proper name, and only a is red and round, the properties red, round, and identical to a are intensional. All three map a alone onto the truth- value of truth, and all three are different properties from each other. Note also the tie between intentionality (“pointing to”) and intensionality. An interesting question I shall not pursue is whether we should polarize the alternatives into objects which are either totally intensional or totally extensional. Why not say The Strength of Russell’s Modal Logic 91 that essential properties are intensional and accidental properties extensional? That is virtually Quine’s own suggestion when he says that “Aristotelian essentialism” is required for quantification into modal contexts (FLPV 155). Indeed, why not call the essential properties of even an essentially extensional object (defined, say, in terms of certain truth-functional mappings onto truth- values) intensional? Suppose a world of four sense-data, a, b, c, and b. Only a and b are blue. We can define a purely extensional Fregean mapping function F as mapping only a and b onto the True. Then, perhaps in different senses of “essentially,” a and b will be essentially F and essentially blue. It will be an informative statement that a sense-datum is F if and only if it is blue, since F and blue are different properties. But then both F and blue are intensional properties in sense (ii) of intensionality as defined on page 7, since they are two different properties had by all and only the same objects. However, F is not intensional in sense (iii), since we do have to specify which objects are F in order to state what F is. Thus not all propositional functions intensional in sense (ii) are intensional in sense (iii) after all. I have been emphasizing the similarities between Russell’s quantification into epistemic and intentional contexts and my extension of that quantification into modal contexts. It is time to look at the other side of the scholarly coin. In “The Philosophy of Logical Atomism,” there are an apparent difference and three genuine differences which might seem to invalidate my extension. The apparent difference is that beliefs seem to be predicated of proposi- tions, while modalities seem to be predicated of propositional functions. In fact beliefs are not predicated of propositions, since beliefs are real and there are no propositions (PLA 214, 223–24). Beliefs actually tie together the constitu- ents which propositions only seem to. And modalities are predicated of propositional functions only in MDL, not in the completed modal logics. The first genuine difference is that beliefs are real facts in the real world (PLA 214, 216–17; see 218–22), while logically necessary truths are nothing, since they are propositions, and propositions are nothing (PLA 214, 223). The second genuine difference is that beliefs include true contingent beliefs which describe specific facts in the real world, while modal proposi- tions never describe anything in the real world (compare PLA 239–41), except in the sense of describing relationships among universals. Here I count logical forms among universals. Granted, one might drive a wedge between the concept of a tautology and the concept of saying nothing about the world, not only by characterizing tautologies as describing relations among universals, but by characterizing true universal tautologies as saying something necessarily true of all individuals. But Russell drives no such wedge. For Russell, true 92 Bertrand Russell on Modality and Logical Relevance universal tautologies are true of any individuals, in the sense that they are true even if there exist no individuals. Like Frege, Russell rejects the Aristotelian all with its existential import (though of course he can reconstruct it). The third genuine difference is that beliefs are psychological while modalities are logical. In fact, since a “map-in-space” cannot be made of a belief (PLA 225–26), “nothing that occurs in space is of the same form as belief” (PLA 226). By implication, beliefs are the cutting edge of Russell’s mental-physical distinction. Russell admits it is logically possible that not all propositional attitudes are psychological. He merely says he does not know of any that are not psychological (PLA 227). This leaves room for modalities as propositional attitudes. In fact, I am surprised he did not think of them. He goes almost directly from wondering whether there are any propositional attitudes besides psychological ones (PLA 227) to defining modalities (PLA 231) in “The Philosophy of Logical Atomism,” but the idea never dawns on him. Of course, since modalities are nothing, they will not be the cutting edge of the physical-mental distinction, but at best of the real-nothing distinction. I speculate that this is precisely what threw him off track. Namely, he did not discover that modalities are propositional attitudes because he was looking only for other real attitudes such as beliefs and wishes. No wonder he could find only psychological ones. The very term “attitude” suggests this. That modalities and propositions are nothing does not preclude modalities from being propositional attitudes or from constituting a modal logic. “A propositional function is nothing, but, like most of the things one wants to talk about in logic, it does not lose its importance through that fact” (PLA 230). Therefore the three genuine differences make no difference in the end. Dagfinn Føllesdal raises a parallel problem with quantification into causal contexts:

(a*) It is causally necessary that the man who drank from that well got poisoned. (b*) The man who drank from that well is the man born at p at t. (c*) Therefore it is causally necessary that the man born at p at t got poisoned. (Føllesdal 1971: 53)

The problem is that the two descriptions of the man are not causally equivalent (Føllesdal 1971: 54). Føllesdal presents the paradox of quantification into causal contexts in terms of our ordinary pre-philosophical understanding of causation. But the paradox persists on Russell’s Humean analysis of causation as nothing but natural uniformity. To that extent the Humean analysis is a worthy analysis of The Strength of Russell’s Modal Logic 93 our pre-philosophical understanding, since it preserves the paradox. To see this, we may apply Humean analysis to Føllesdal’s own example. Namely, even if drinking water from a certain well causes death only in the Humean sense that everyone who drinks it dies, the paradox remains, since there is no Humean necessity that the man born at p at t be poisoned. Thus MDL–C faces the paradox. I proceed to suggest how Russell, if not also Hume, can resolve the paradox. Føllesdal’s solution is to restrict definite descriptions to those that describe the same events in all physically possible worlds (Føllesdal 1971: 60). That solution is available to Russell for MDL–C. Of course, we must remember that merely possible worlds have no ontological status for Russell, and that Russell’s physically possible worlds are merely worlds having the same uniformities as the actual world. But Russell has a stronger solution. The 1914–18 Russell analyzes both natural uniformities and lawfully behaving ordinary physical things in terms of temporal series of classes of sensed and unsensed sensibilia. And any sensibile we sense we can name with a logically rigid logically proper name, which is far more than we need for causally rigid designation. Føllesdal’s example is of physical causation. The paradox arises equally well for mental causation. Gustav Bergmann once gave this example: thinking of the death of a friend mentally causes me to feel sad. Where the thought of my friend’s death is the thought I have now, it is not causally necessary that the thought I have now cause me to feel sad. This alone is not enough to destroy Russell’s attempt to use propositional attitudes to divide the mental from the physical, since the question of maps-in-space remains. I presume that there can be maps-in-space of natural uniformities. Føllesdal’s paradox arises for all four kinds of traditional Aristotelian causation. Føllesdal’s example concerns efficient physical causation, which I just expanded to include efficient mental causation. That leaves formal, material, and final (or teleological) causation. As to formal causation, the form of Socrates is humanity. Where the human Socrates is the thing in the Forum, it is formally causally necessary that the human Socrates eat and breathe. But it is not formally causally necessary that the thing in the Forum eat and breathe. As to material causation, the material of the Eiffel Tower is iron. Where the iron Eiffel Tower is the tallest structure in Paris, it is materially causally necessary that the iron Eiffel Tower have a certain atomic structure and be heavier than water. But it is not materially causally necessary that the tallest structure in Paris have that atomic structure or be heavier than water. 94 Bertrand Russell on Modality and Logical Relevance

As to final causation, the final form of an acorn is oak treehood. Where the acorn in my hand is the thing I just picked up off the ground, it is teleologically necessary that the acorn in my hand tend to grow into an oak tree. But it is not teleologically necessary that the thing I just picked up off the ground tend to grow into an oak tree. It seems clear that the paradox arises for agential action as well as efficient mental causation, where an action is a matter of choice and delibera- tion. In fact, this is a superfluous point. It is merely to add choice and deliberation to the paradox as it arises for intentional contexts. More generally:

[While Quine’s paradox] is directed against the logical modalities, it can be paralleled for any type of nonextensional construction. In fact it would show that any attempt to build up adequate theories of causation, counterfactuals, probability, preference, knowledge, belief, action, duty, responsibility, rightness, goodness etc. must be given up, since, presumably, any such theory would require quantification into non-extensional contexts. (Føllesdal 1987: 101)

All forms of causation and action would appear to be nonextensional. But an even more general point might be made. Any informative identity statement—which for Russell always involves at least one description—trivially gives rise to versions of the paradox. For example, the Evening Star as such is believed to appear, evidently appears, and necessarily appears in the evening, or else we would not use that descriptive name seriously. To this extent, it seems that all descriptions are intensional. And this suggests a deeper level of analysis. So far we have been following Russell in treating informative objectual identities as facts to be discovered and to be described by informative identity statements. (I use the word “fact” loosely, so as not to imply commitment specifically to Russell’s metaphysical category of facts.) This is a Russellian presupposition of the Quine-Smullyan-Føllesdal discussion. But for Panayot Butchvarov, the concept of identity is something we find ourselves imposing on the objects of our perception or thought, so as to organize and classify them into entities (Butchvarov 1994: 46–47; 1979: 44–45). And when we impose the concept of identity, so as to identify some objects as being the same entity, we also enforce indiscernibility (Butchvarov 1979: 66). That is, we adjudicate which, if any, properties of the various objects we attribute to the entity. For example, when I identify the Evening Star with the Morning Star, treating both objects of perception as being the planet Venus, I attribute both appearing in the morning and appearing in the evening to the planet. But where the object The Strength of Russell’s Modal Logic 95 of perception I singled out yesterday was red and the object of perception I single out today is white, and where I judge that my object of perception yesterday was red only because the entity before me was bathed in a red light, and I judge that the entity before me today is bathed in white light, and that both objects are the same unchanging entity, I attribute whiteness and not redness to the entity. We might use Butchvarov’s analysis to go back through all the examples with various results, depending on how we enforce indiscernibility in any particular case. In an important sense this would be nothing more than philosophical dialectics as usual. For example, consider the consciousness- brain process identity thesis of. If a yellowish-orange after-image really is a brain process, then perhaps there is a sense in which some brain processes are yellowish-orange (compare and contrast Place 1970; Smart 1970). Or if beliefs are brain processes, then perhaps there is a sense in which there are maps-in- space of brain processes. As Hilary Putnam says in another context, one philosopher’s modus ponens is another philosopher’s modus tollens. The 1914 Russell is congenial to this in his own way. For he holds that sense-data are physically real. Admittedly he merely constructs the brain process as a temporal series of indefinitely many sensed and unsensed sensibilia, one of which is the yellowish-orange sense-datum in question. There may be no physical brain at all lurking behind the cognitively impenetra- ble barrier of sensibilia. Yet the yellowish-orange sense-datum is as mind- independently real as anything can be for the 1914 Russell, and belongs in Russell’s analysis of physical causation. For Russell, something physical is yellowish-orange. In like manner, if the number of planets really is nine, then perhaps there is a sense in which the number of planets is necessarily greater than seven (Butchvarov 1979: 127–28). There is also a sense for Butchvarov in which the number of planets is not nine, insofar as these are different objects of thought (Butchvarov 1979: 127). This revives the second Hamlet solution. Butchvarov’s essences are not Aristotelian in the sense of being de re simpliciter. Indeed, Butchvarov finds the distinction between de dicto and de re confused (Butchvarov 1979: 124–26). For Butchvarov, the essence of an object is the entity or the kind of entity we classify it as being. And while things never force us to classify them in a certain way, and classification is a conceptual as opposed to experimental activity, classifications are factually based on objective similarities in the world, and some classifications are more reasonable than others (Butchvarov 1979: chapter 5; 1970: 6–11). In fact, it is theoretically possible that there is a single most reasonable classification. We 96 Bertrand Russell on Modality and Logical Relevance cannot dismiss a priori the possibility of a true classification of things in this sense. In contrast, Quine polarizes the essence question into a simplistic yes- no, realist-relativist dilemma. I profess surprise because Quine has plenty of dialectically accommodating approaches of his own on other subjects. Indeed, waiving the difference between Quine’s neural stimulus patterns and Butchvarov’s phenomenology of objects, Quine’s theories of naturalism and of the immanence of truth would seem congenial to Butchvarov’s theory of essence. All this is a measure of the depth of Butchvarov’s theory of identity. However, this book is not the place to discuss his theory in detail. I shall merely mention that I find room both for our impositions of the concept of identity and for objectual identities out there in the world independently of our impositions. Another Russellian presupposition of the Quine-Smullyan discussion is that descriptions are always used attributively and never referentially. Keith Donnellan identified and questioned this presupposition in his landmark paper, “Reference and Definite Descriptions” (Donnellan 1972). Of course, this only postpones the discussion to the level of referential uses and attributive uses of descriptions. However, the referential use of descriptions does explain how the number of planets can be said to be necessarily greater than seven. Namely, we can use “the number of planets” referentially to refer to the number nine. This is another theory I cannot discuss in detail in this book. But I do not under- stand why Quine never mentions Donnellan. The weight of everything we have discussed carries over to deontic logic. The reason for quantifying into moral contexts is to assert that there are people who have moral obligations (Forrester 1996: 91–92). James W. Forrester raises a parallel problem with quantification into moral contexts:

(a**) Smith ought to kill Brown. (b**) Brown is the finest man in town. (c**) Therefore Smith ought to kill the finest man in town. (Forrester 1996: 78)

The 1910 Russell of “The Elements of Ethics” is not a logical fictionalist. But there will be rigid designation of a sense-datum causally connected with Brown, while “the finest man in town” is purely a description. There will also be rigid designation of the intrinsic quality of goodness, since we are acquainted with that universal through a process of abstraction. The distinction The Strength of Russell’s Modal Logic 97 between acquaintance and description goes back at least to “On Denoting” (OD 41, 56). Similarly for the 1954 Russell of Human Society, who is not a logical fictionalist either. There will be rigid designation of sensed events causally connected with the probably existing Brown, and rigid designation of the intrinsic quality of goodness, since we are acquainted with satisfying states of mind through introspection. In general, all the goods of this world will be causally connected with sensed events which can be rigidly designated. Forrester argues for resolution of the deontic Quinean paradox with a semantics of morally possible worlds. He notes that such worlds need not have any ontological status (Forrester 1996: 90). In light of Russell’s repeated use of possible worlds talk in his two greatest ethical writings, Russell would seem highly sympathetic. Forrester discusses alternative moral worlds similar to the actual world, so as to pursue moral casuistry. Russell does that, but he also discusses worlds very different from the actual world, so as to make deep theoretical points. For Russell, even a robot world is a way the actual world ethically might have been. This concludes my discussion of Russell’s grades of modal involvement. Everything is at least second grade. There are at least two things which are third grade: quantification into contexts involving either instantiation of sensible qualities or definitions of logical fictions. Now, besides sensibilia (sensible instances) and logical fictions, the only other things the 1918 Russell has are universals (including relations) and his own mind. No doubt universals and one’s own mind (a mental instance) have essential and accidental features or relationships as well. Thus we may as well say that everything is third grade for the 1918 Russell. Once again we see that without studying Russell’s writings on metaphysics and ontology, we have no hope of determining his best positions on modal logic. Note that the puzzles we considered were not fully generalized; thus they were technically not in FG–MDL or FG–MDL*. My final topic is Magnell’s reply to my 1990 Erkenntnis paper. Magnell raises two main objections to my claim that Russell has a modal logic. First, “if Russell ever had a modal logic, we might expect him to have advanced a systematic study of valid forms of modal inference....[But] Russell did not set out a modal logic in any of his writings that I am aware of.” Second, “If there is a modal logic implicit in Russell’s work, it need not, of course, be equivalent to one of the S-logics. But if there is even a vague outline of a modal logic to be found, we should be able to indicate its position, whether below S1, between S1 and S5, or beyond S5 with some degree of confidence.” But Magnell cannot find even a vague outline. He says that MDL “cannot be 98 Bertrand Russell on Modality and Logical Relevance more than a small part of even a modest theory” (Magnell 1991: 172–73, 176).5 As to the first point, Magnell must be unaware of Principia Mathematica. Far from modest, MDL is as grand and robust as Principia itself. For MDL is an interpretation of Principia. MDL is a formula for reinterpreting Principia as a modal theory. FG–MDL* is the set of logical truths in Principia. And modal inferences in FG–MDL* are the set of deductively valid inferences in Principia. Has a more comprehensive study of forms of modal inference ever been given? As to Magnell’s second point, Magnell’s question is misplaced. MDL is but a building block. It is of FG–MDL* that we properly ask what degree of strength it has. The answer is that FG–MDL* is stronger than S5. The fault is mine, not Magnell’s. In my 1990 Erkenntnis paper, I failed to distinguish MDL from FG–MDL*, and mistakenly portrayed MDL as the modal logic. Magnell merely followed my mistaken portrayal. How could FG–MDL, FG–MDL*, and FG–MDL** be closest to S5, yet fail to be modal logics? Those who deny that they are modal logics are committed to denying that S5 is a modal logic. Denying that Principia is a modal logic because it does not admit any primitive, irreducible modal properties is exactly as absurd as denying that Principia is an existential logic because it does not admit any primitive, irreducible property of existence. Russell defines both “is possible” and “exists” as “sometimes true,” which Russell takes as “the fundamental logical idea, the primitive idea” in “The Philosophy of Logical Atomism.” This ‘sometimes true’ is what Charles H. Kahn would call a “veridical ‘is’,” and does not indicate either a modal or an existential property of propositional functions (Kahn 1986: 3–4, 8–9, 12–13, 16–17, 20–22, 26–27). That Principia, as FG–MDL*, is closest to an S5 logic was surely unintentional on Russell’s part. Even by 1919, he seems to have known only two papers by Lewis (IMP 153). But Russell’s express statement in The Analysis of Matter that deductively valid inference is strict implication seems very much intentional (AMA 199). And I think it was very much intentional that Russell wanted Principia to be understood as a comprehensive modal theory. What would one expect the poor man to do, sit down and literally rewrite the whole of Principia when he could explain how to read Principia modally in three brief lines? This is precisely what Russell does in famous works such as “The Philosophy of Logical Atomism,” Introduction to Mathematical Philosophy, and The Analysis of Matter. Surely it must have occurred to this great logician that in writing those lines he was showing us The Strength of Russell’s Modal Logic 99 how to reinterpret Principia. Granted, the best of us sometimes cannot add one and one, or see what is staring us in the face. But could Russell have missed that?—Could he have missed it eight times? There is at least one good argument for the affirmative: everybody else missed it eight times. Russell did not only publish MDL after Principia in 1913, 1918, 1919, 1927, and 1940. He published MDL twice in 1908 during the writing of Principia, and in 1906 before writing Principia. As we know, Russell and Whitehead wrote Principia vol. 1 from 1907 to 1910. Thus Russell published MDL eight times: before, during, and after the writing of the fundamental volume of Principia. How could interpreting Principia modally by means of MDL have failed to ‘occur’ to him? How could it have failed to occur to any Russell scholar? Russell handed us his Principia modal theory on a silver platter eight published times. Those who hold that Principia is a fortress of nonmodality might wish to explain why Russell and Whitehead use the following phrases the number of times indicated in the first sixty pages of Principia:

“possible determination(s) (of...variable(s))”: 4 times, p. 5 “every possible determination to x”: 1 time, p. 15 “all possible values [of x, x and y, i]”: 6 times, pp. 21, 41, 49, 50, 51 (twice), 52 “whatever possible value % may have”: 1 time, p. 25 “there are necessarily possible arguments with which we are unacquainted”: 1 time, p. 40 (perhaps Russell is committed to iteration after all!) “every possible value of x”: 1 time, p. 40 “possible values of x”: 1 time, p. 40 “all possible arguments”: 1 time, p. 41 “possible values of iz^“: 1 time, p. 49 “some (undetermined) possible values”: 1 time, p. 49 “all possible propositions and functions”: 1 time, p. 51 “all possible functions”: 1 time, p. 53 “the totality of its possible arguments”: 1 time, p. 54 “the possible arguments”: 1 time, p. 54.

Are these the expressions of authors who hate modal logic? Those who are in the grip of the standard picture of Principia may refuse to see it, but these expressions should now appear in a different light. Obviously, Russell uses “possible” to mean ‘of the proper logical type’. But my question is, Why does he use the word “possible” to mean that? Most readers of Principia will assume that type-possibility is all that Russell has in mind. But recall primary level modal feature (ii), that there are no merely possible entities. Thus surely 100 Bertrand Russell on Modality and Logical Relevance

Russell also has in mind that only actual entities of the proper logical type are possible entities of that type. Primary level modal feature (ii) dates back to “On Denoting” (OD 45), well before Principia, and is thoroughly Parmen-idean. Naturally, the argument of the previous paragraph is not to bear any weight of proof that Russell intended Principia to be interpretable as a modal logic. It proves nothing by itself. It is the icing on the cake. It is a retrospective point of interpretation to be considered only after the real arguments are given; and these arguments have already been given.