1 Introduction

Dissatisfied with the material conditional, C. I. Lewis began exploring strict implication in 1912, with “Implication and the Algebra of Logic.” A series of papers and the 1918 book A Survey of Symbolic Logic followed, and then finally, with C. H. Langford, Symbolic Logic in 1932, in which five formal systems of modal logic were presented. From this start modal logic has had an impressive career. By the twenty-first century, the techniques of modal logic and the attendant vocabulary of possible worlds are ubiquitous in almost all branches of philosophy. Modal logic is widely used in computer science, linguistics, and other disciplines. But how could this have happened? Didn’t W. V. O. Quine destroy modal logic halfway through the twentieth century, in 1953, in From A Logical Point of View—at least as something that any naturalist or empiricist could take seriously?

Quine distinguished between Aristotelian Essentialism and Analyticity. The former is a metaphysical position that seems needed for a full-blown modal logic, but, Quine supposes, would be unattractive to any empiricist or naturalist. The latter is an attempt to have necessity without this unattractive metaphysics, based simply on the theory of meaning. It is this last ditch attempt to explain necessity in terms of meaning that Quine destroyed in “Two Dogmas of Empiricism” (1951). On a later paper, Quine concludes,

Most of the logicians, semanticists, and analytical philosophers who discourse freely of attributes, propositions, or logical mod­alities betray failure to appreciate that they thereby imply a metaphysical position which they themselves would scarcely condone. (Quine 1953a, 157)

Quine’s work was very influential. For a while, it seemed that modal logic, if not given a death blow, had been gravely injured. But, in the Transcript,¹ Dreben points out that this seems to have been a Pyrrhic Victory:

… it’s true almost everybody today will say “Yes the notion of analytic as used by the positivists … goes by the board” … [But] many of the people who say “yes analyticity can’t be made sense of and that whole attempt failed” in no way give up the notion of necessity… [T]he whole movement from Kripke onward … Van has won a tremendous Pyrrhic victory … (38)

Right after these remarks on Quine’s Pyrrhic victory, Davidson and Quine insist on the need to understand the everyday uses of “necessity” and “necessarily.” After all, even if one accepts Quine’s argument against modality, it is a fact that we all use modal terms in our everyday talk.² It is, however, also a fact that, by 1986, modal terms were widely used in philosophy and in most cases untroubled by Quine’s concerns, or so it seems:

Quine’s criticisms were taken very seriously, and a large number of philosophers tried to show that quantified modal logic does not commit its proponents to Aristotelian Essentialism. But with the development of a semantics for modal logic, attempts to answer Quine became less and less frequent. Philosophers came to see that if we take a realistic interpretation of possible worlds semantics, we have a perfectly coherent framework for expressing the content of an essentialist metaphysics. (Loux 1979, 25)

Strangely absent from the Transcript is mention of this possible framework to express the “content of an essentialist metaphysics” and of its several philosophical implications.³ Even more strangely absent, however, is mention that the effective resistance to Quine that eventually allowed modal logic to continue to blossom did not start with Kripke, but with Dagfinn Føllesdal, Quine’s student and a participant in the Conference. In his 1961 dissertation, Føllesdal undermines Quine’s arguments against modal logic. The dissertation, Referential Opacity and Modal Logic, was not published until much later, so almost no one read it until then. But Føllesdal and his advisor, Quine, must have done so!

In what follows, we briefly discuss Quine’s problems with modal logic (Section 2) and Føllesdal’s answer. We then argue that Føllesdal’s proposal has all the tools necessary to deal with modal concepts and terms, without having to accept “a realist interpretation of possible worlds,” as Loux proposes (Section 3). Finally, after a discussion of their reluctance towards reference (Section 4) and the uses both Davidson and Quine make of the expressions “necessary,” “necessarily,” and “necessity” in the Transcript (Section 5), we outline our own proposal for necessity (Section 6). It is not our intention to offer an account in the spirit of Quine’s or Davidson’s remarks about the indexicality of “necessary” and cognate expressions, or to be faithful to Føllesdal’s views on the matter. Our aim is rather to sketch an explanation of modal properties that, assuming Føllesdal’s two-sorted semantics and, therefore, a benign form of Aristotelian Essentialism, would lack metaphysical implications grave enough to discard modal logic and, in particular, would have no need of possible worlds.

We finish the paper (Section 7), with some conclusions on the surprisingly little time they spent on these in the Conference. Had Quine and Davidson paid more attention to Føllesdal’s solution, philosophy would have avoided quite a lot of discussion about issues and pseudo-problems, like the ontological status of possible worlds, trans-world identity and the like.

2 Quine Versus Modal Logic

According to Diogenes Laertius, Plato defined a human being as a featherless biped, so that “is a human being” and “is a featherless biped” would have the same extension. Diogenes of Sinope questioned Plato’s definition, and so do we:

Plato had defined the human being as an animal, biped and featherless, and was applauded. Diogenes plucked a fowl and brought it into the lecture-room with the words, “Here is Plato’s human being.” In consequence of which there was added to the definition, “having broad nails.” (Diogenes Laertius, Lives of Eminent Philosophers, Book 6, Chapter 40)

We ignore the shape of fingernails and toenails in this paper. But we assume that an implication of his definition is correct: being a human being and being a featherless biped have the same extension. If so, then both (1) and (2) are true:

1. Paul McCartney is a human being

2. Paul McCartney is a featherless biped

Presumably, a human could grow feathers—or so we assume. So (3) is true but (4) is false:

3. □ (Paul McCartney is a human being)

4. □ (Paul McCartney is a featherless biped)

So modal logic corresponds with the view of the “Aristotelian essentialist.” Objects have some of their properties essentially, others only contingently.

The difference between (3) and (4) is the replacement of one predicate by another that is, in fact, at least on Plato’s authority, co-extensional with it. So it seems that the semantic contribution of predicates, when in the scope of “□,” must be something other than their extensions; i.e., the semantic contribution of predicates in standard logic.

For a Fregean, this contribution would be their senses, that is, roughly, their defining properties. So we can say that “□” is extensionally opaque and not, like operators such as negation or ordinary quantification, extensionally transparent. Similarly with respect to sentences, whose extension in the accepted semantics for predicate calculus is their truth-value. In the scope of “□,” a sentence seems to provide a proposition, rather than a truth-value.

Consider now:

5. □ (7 is a prime number).

6. □ (The number of seas is a prime number)

The embedded sentences are both true, but (5) seems true while (6) seems false. Here the difference comes from the replacement of singular terms with the same designation. So it seems “□” is also designationally opaque.

In “Three Grades of Modal Involvement” (1953b), Quine claimed that modal logicians clearly need extensional opacity, but that they face a dilemma. On the one hand, if they combine extensional opacity with designational opacity, they will be committed to a non-orthodox treatment of variables. On the other hand, if they combine extensional opacity with designational transparency, they will be committed to all true sentences being necessary, if any are.

Quine’s argument makes use of a form of argument now often called “the slingshot.”⁴ The slingshot is an argument, or a group of arguments, to the effect that truth value is the sole semantic contribution of statements. The conclusion of the slingshot argument is that any two true sentences refer (stand for, designate) to the same thing, i.e., their truth-value. The slingshot was suggested by Frege, but was first given careful formulation by Alonzo Church:⁵

1. Sir Walter Scott is the author of Waverly.
2. Sir Walter Scott is the man who wrote the twenty-nine Waverley novels altogether.
3. The number, such that Sir Walter Scott is the man who wrote that many Waverley novels altogether is 29.
4. The number of counties in Utah is twenty-nine.

The argument is that (C2) results from (C1) by substitution of co-designating terms, and so must stand for the same thing. (C3) redistributes the content of (C2) in such way that the truth-conditions remain the same, so, again, they must stand for the same thing. And then (C4) results from (C3) by substitution of co-designating terms. So all four sentences stand for the same thing. But what could be found, other than their truth-values, that all four sentences have in common?

Quine’s version of the slingshot is pretty similar to Church’s, but whereas Church developed it to conclude that all sentences with the same truth-value designate the same thing, Quine developed it to set a pressing dilemma for modal logic, one involving extensional and designational opacity. In Føllesdal’s terms, “Quine’s argument is much more disastrous than Church’s, and it concerns not just the status of logical equivalents, but also the nature of singular terms” (Føllesdal 1983, 93).

Quine’s argument goes as follows (for simplicity we ignore contemporary astronomy—Pluto was still a planet when Quine wrote):

1. 9 > 7
2. {x is & 9 > 7} = {}
3. {x is & the number of planets > 7} = {}
4. The number of planets > 7.

If (A) is true, so is (B), because they are logically equivalent. If (B) is true, so is (C), because (C) results from (B) by substitution of co-designating terms. And if (C) is true, so is (D), because they are logically equivalent (Quine 1953b, 163–64).⁶

Given this, Quine argues that all sentences are necessarily true if any sentence is. Consider:

1. □ (9 > 7)
2. □ ({x is & 9 > 7} = {})
3. □ ({x is & the number of planets > 7} = {})
4. □ (The number of planets > 7).

If (A*) is true, so is (B*), because the embedded sentences are logically equivalent, and so are either both necessary or both contingent. If (B*) is true then, given designational transparency, (C*) will be true, as it results from the substitution of terms that designate the same set in (B*). The embedded sentences in (C*) and (D*) are logically equivalent, so (D*) is true if (C*) is.

So, according to Quine, modal logic collapses. By 1961, however, Føllesdal had given us all that we seem to need for a modal logic that does not violate orthodox logic and avoids the slingshot argument, that is, it does not lead to all true statements being necessary, contrary to Quine’s argument.

3 Føllesdal’s Solution

Now consider:

7. Let x be the number of seas

8. Let y be 7

Here we have assigned the variables x and y to the same entity, the number 7. But we have done so in quite different ways. In orthodox logic, the way the variables are assigned makes no difference, only what they are assigned to. So it seems that (9) and (10) should both be true, given the way the variables were assigned:

9. □ (x is prime)

10. □ (y is prime)

So, unless we are going to adopt an unorthodox treatment of variables, it seems we should say that, relative to a given assignment, variables are designationally transparent.

Føllesdal points out that this is possible. Variables in modal logic can be assigned directly to objects via variable assignments, in a completely orthodox fashion. He extends the idea and proposes a

two-sorted semantics, where general terms and sentences behave as in standard Fregean semantics, while singular terms keep their reference in all possible worlds. (Føllesdal 2004b, xvii)

He notes the lexicon may assign objects to other singular terms, without any mediation of descriptions or senses, in basically the same way that variable assignments do, but once and for all. Nothing in orthodox logic prevents this. He calls such singular terms “genuine singular terms”: terms that stick with the object they pick out or, rather, terms whose designation remains intact as the term is embedded in larger expressions that might include modal operators. Føllesdal defines genuine singular terms as expressions that

are intended to keep on referring to the same object throughout all its changes and throughout our changing opinions and theories concerning the object. When used in modal contexts, these expressions are intended to relate to the same object in all “possible worlds” where that object occurs (Føllesdal 1986, 102).⁷

We avoid mention of possible worlds in the definition. First, because the distinction does not depend on using possible worlds semantics to analyze necessity and possibility. Second, because one might be led to believe that genuine singular terms pick up their objects across worlds through their essential properties, leading to the so-called “trans-world identity” problem and to much stronger forms of essentialism. We discuss this in Sections 6 and 7.⁸

So the issue of designational transparency has two answers. Variables and genuine singular terms are (referentially) transparent, while general terms and descriptions, whether explicit or hidden, are (extensionally) opaque. We’ll call the first phenomenon referential transparency, the second designational opacity.⁹

On Føllesdal’s account, variables are transparent. Singular terms all of whose constituents are transparent will be transparent. Singular terms that are built from general terms and open sentences that are opaque will also be opaque. Thus the variables and the singular terms in (11) and (12) are transparent, but that in (13) is opaque:

11. y is skeptical about necessity & z is a big fan of necessity

12. {x is prime & x ≠ 2} ⊂ {y is odd}

13. {x is the number of seas} = {y is the number of continents}

With respect to ordinary proper names, if, like Frege and Russell (in different ways) we think that they are connected with conditions that an object must satisfy to be the referent, we would regard them as opaque. But if, like Donnellan, Wettstein, Kripke, Kaplan and many others, we take ordinary proper names to be, in Føllesdal’s terms, genuine singular terms, we would regard them as transparent.

So Føllesdal gives an interpretation of modal logic that treats variables in an orthodox way, and allows for extensional opacity, and the opacity of some singular terms—namely, descriptions and terms that behave like hidden descriptions; that is, the sort that seem to fit Frege’s idea of terms associated with senses, which determine reference.

Consider again:

1. □ (9 > 7)
2. □ ({x is & 9 > 7} = {})
3. □ ({x is & the number of planets > 7} = {})
4. □ (The number of planets > 7).

Quine argues that if (A*) is true, so is (B*), because the embedded sentences are logically equivalent, and so are either both necessary or both contingent. If (B*) is true then, given designational transparency, (C*) will be true, as it results from the substitution of terms that designate the same set in (B*). The embedded sentences in (C*) and (D*) are logically equivalent, so (D*) is true if (C*) is.

Given Føllesdal’s distinctions, however, (C*) does not follow from (B*). The singular terms in the expression “{x is & 9 > 7}” are transparent, and so is it. But the singular terms in “{x is & the number of planets > 7}” are not all transparent, so neither is it. Hence, the substitution that leads from (B*) to (C*) does not preserve truth.

Quine, in the second edition of From a Logical Point of View, acknowledges some of Føllesdal’s claims, and introduces some modifications in the text. His overall view on modality, however, seems pretty unmoved by Føllesdal’s proposal.¹⁰

In great part, this is due to Quine’s views on reference. In 1986, the same year in which the Conference took place in Stanford, and answering to Føllesdal’s comments in The Philosophy of W. V. Quine, Quine writes:

Føllesdal celebrates reference, according it priority over predication. I have tended increasingly to depreciate reference, what with my ontological relativity and proxy functions. I have come, like Davidson, to accord primacy to sentences. (Quine 1986, 115)

So we turn to two questions. What do Quine and Davidson have against reference? And what, if anything, do they say about necessity?

4 What is Wrong with Reference?

That fully understanding Davidson’s view on reference would be a daunting task is suggested by Robert G. William’s opening remarks in his essay “Davidson on Reference”:

Reference leads a strange double life in Donald Davidson’s philosophy of language. On the one hand, it is at the heart of his account of the meaning of words and the learnability of language. On the other, he is concerned to combat overly “realist” views about the relation. And he explicitly endorses the seemingly incredible position that reference is wildly inscrutable. There is no fact of the matter at all about what our words refer to. (Williams 2013, 264)

We don’t take on that daunting task, nor on the no doubt equally daunting task of understanding Quine’s views. We merely wish to point out that both philosophers rely on the slingshot, an argument that, as we explained above, Føllesdal destroyed in his thesis. This is one more issue that we find it puzzling not to be discussed in the Transcript.

We already discussed one of Quine’s uses of the slingshot, in “Three Grades of Modal Involvement.” Davidson uses a much simpler version in his 1967 essay “Truth and Meaning”:

But now suppose that “R” and “S” abbreviate any two sentences alike in truth value. Then the following four sentences have the same reference:

(1) R

(2) (x = x & R) = (x = x)

(3) (x = x & S) = (x = x)

(4) S

Davidson describes the two assumptions on which the argument rests as reasonable:

… that logically equivalent singular terms have the same reference; and that a singular term does not change its reference if a contained singular term is replaced by another with the same reference. (Davidson 1967, 19)

Davidson notes that the argument is essentially Frege’s, cites Church, and says that “the argument does not depend on any particular identification of the entities to which sentences are supposed to refer.” (1967, 305–06 n 3) If sentences stand for truth-values, so that all true sentences stand for the same thing and so do all false statements, then in a compositional semantics, the particular objects and conditions that parts of a sentence stand for won’t matter to larger expression that embed them. It will be truth-functional.

So the whole idea of operators that are not truth-functional won’t get off the ground. But this all depends on the slingshot, which Føllesdal had destroyed. However, Quine and Davidson seem not to find this a reason to rethink their skepticism about the importance of reference, and indeed both continued to use the slingshot long after Føllesdal’s dissertation.

5 What’s Wrong with Necessity?

Shortly after Dreben’s comment about Quine having won a “Pyrrhic victory,” Quine explains that he thinks of “necessarily” as an indexical, or at any rate its use is context dependent in the way that indexicals are. Quine says,

As you know, I see the notion of necessity making its main sense at the level of indicator words that are relative to the context purposes of a particular exposition or argument. So there’s no place for it in metaphysics, no place for metaphysical necessity, no place for it in the formulations of scientific theory. What more is there? What further ideas are there on necessity? (39, our italics)

According to Quine, by using “necessarily,” one is essentially pointing at a sentence, and implicitly citing earlier parts of the conversation, and saying the pointed at sentence has some relation, perhaps being implied by, to the earlier material that makes it undeniable. Davidson seems to agree:

… I think actually of the sentential operator as an utterance operator, that is, if somebody says “necessarily,” he’s introducing something he’s about to say and referring to that next remark and making certain comments on it … This works in your suggestion automatically, so to speak, by making “necessarily” govern utterances. And they’re tied down to situations (42).¹¹

But Quine and Davidson also use the word “necessary” as part of their conversation, not just as a topic of conversation. For example, Davidson claims that “[i]ndeterminacy is not necessary to making the point about the analytic/synthetic distinction” (19, our italics); and Quine says: “I don’t think that would be a necessary condition because in any event there has to be a residue. Otherwise you go round and round” (34, our italics). We doubt, however, that these uses support the indexical theory.

In Davidson’s statement, being necessary seem to amount to being required. This use of “necessary” is not limited to philosophical or metaphysical discussion. It is the same use made in ordinary statements such as “Money is necessary to buy food in a Supermarket” or “Good food is necessary for healthy living.”

This use is related to “can,” as in:

1. You can’t send email without a computer
2. A computer is needed for sending email
3. A computer is necessary for sending email
4. You can’t pound in a nail without a hammer
5. A hammer is needed for pounding in a nail
6. A hammer is necessary to pound in a nail.

In these examples the relation of being necessary holds between having an object, or type of object, and an accomplishment. It doesn’t seem to mean anything metaphysically problematic, that naturalists and empiricists need to be embarrassed about.

Quine uses a expression that is ubiquitous in philosophy, but also in the rest of life, “necessary condition,” which, of course, is often paired with “sufficient condition.” This seems a bit more threatening, metaphysically speaking, as it involves conditions. Intuitively, conditions are properties, which Quine and Davidson aren’t fond of. But Quine and Davidson have other ways of handling conditions, as open sentences, or as sets, which they consider unproblematic, since they are determined by an open sentence. Do we need any other, more problematic, concept of what conditions are to be able to talk about necessary conditions? Or is it enough with the concept of conditions, required for other things; one that doesn’t seem metaphysically threatening?

Talk of necessary and sufficient conditions in ordinary language is explained by “if … then,” and the other way around. “If P then Q” means that P is sufficient for Q, and that Q is necessary for P. In using both locutions, we often presuppose a background, something given for the sake of an argument or a conversation. If we are playing poker, I might say to you, “Unless you ante, you can’t bet,” or “If you are going to bet, you have to ante,” or more pompously—perhaps in a game among philosophers—“Ante-ing is a necessary condition for betting.” This all makes sense in the situation in which we are playing poker, given the rules of poker.

C. I. Lewis noted, in the article we cited a the beginning as initiating the twentieth-century debates over necessity and modal logic,

One of the important practical uses of implication is the testing of hypotheses whose truth or falsity is problematic. The algebraic implication has no application here. (Lewis 1912, 529)

By “algebraic implication” he meant the truth functional connective used in predicate logic, often symbolized with “⊃.” A new poker player, trying to figure out what anteing is all about may make two hypotheses: “If I don’t ante, they won’t let me bet” and “if I don’t ante, they won’t let me eat potato chips.” If he doesn’t ante and he’s not allowed to bet, but is still allowed to eat potato chips, he would be confirming the first hypothesis and disconfirming the second. But if his hypotheses amounted to “If I don’t ante ⊃ they won’t let me bet” and “If I don’t ante ⊃ they won’t let me eat potato chips,” this wouldn’t work. He doesn’t ante, so both hypotheses are true.

Lewis argued that we need a stricter notion of implication than “⊃.” His paradigm cases where those where the meaning of the sentences made the connections—cases “for which ‘p implies q’ is equivalent to ‘q can validly be inferred from p’.” (Lewis 1912, 529) But we think that, for ordinary purposes, a less strict notion is required, as illustrated by our poker case. What we need can be captured in four conditions: the deep background (DB); what is given in the conversation (G); the antecedent (P); and the consequent (Q).

The deep background (DB) are basic facts about how things work on earth and in the universe, and we think it is involved in virtually all conversations, so we’ll set it aside. Why is my statement “if you don’t ante, you can’t bet” true? Because given the rules of game of poker we are playing (G), anteing is a necessary condition for being allowed to bet; that is, not anteing is a sufficient condition for not being allowed to bet.

We think the uses of “if … then,” “necessary and sufficient conditions,” “necessarily,” and many other common locutions can be understood in terms of this framework, or some improved descendant of it. We think that, in many of their uses, “if … then,” “necessary and sufficient conditions,” and “necessarily” are relative to a G parameter which is implicit in the context. So, Quine is right that there is some indexical or context sensitive ingredient about “necessarily.” Does this mean we subscribe to some dubious notion of analyticity? Or to Aristotelian Essentialism? We think not.

6 Modal Logic at a Low Metaphysical Price

Modal properties and facts are involved in all kinds of explanations, both everyday and philosophical explanations. A child has to learn what the world is like to learn to do things. Roughly, given a certain goal and a certain desire to achieve that goal, the child needs some sort of understanding of how the world is like and how it works—some beliefs—in order to know what to do to get what they want. This involves grasping the relevant possibilities: possible ways things could be and possible actions they could perform.

Most of the possibilities, and necessities, that we care about are situated or relational properties. The child need only be concerned with possibilities with regard to their situation and with regard to their desires. If they want a cookie, for instance, they do not need to worry about what could happen if they turn the shower on, or about what is or could be in the roof of the house.

Adults usually need to worry about wider situations than children. But not much wider, at least in our everyday lives. Philosophers and scientists try to use modality in the widest and less constrained way possible. But philosophers and scientists still need to distinguish between things that are possible or necessary in limited situations, in not-so limited ones and, whenever is possible, in all situations.

Philosophers, it seems to us, are concerned with ways things could have been, or things that are possible in situations that are relevant for animals, or even plants; but also, or mostly, with things that are possible in situations relevant for humans, with things that are possible in much wider situations (planets or galaxies, say) and, finally, with things that are necessary in all situations (like 2 + 2 = 4) or not possible at all (like 2 + 2 = 5).

Modal properties, understood this way, fit into a spectrum of situated properties, which we use all the time. Philosophers qualms and understanding is also about situated possibilities. We wonder about what we can know (given X, or in certain situations, or even in any situation), what we can do (given X, or in certain situations), what can be or happen (given X, or in certain situations), etc. The concern for metaphysical possibility (or necessity) can be seen as the concern for what is possible at all. Or, more precisely, with independence of any situation—and of physical possibility—but within the boundaries of what is logically possible.

Questions about what is metaphysically possible or metaphysically impossible might not be satisfactorily answerable. But they are not essentially different from everyday questions about what is possible or not in a situation. And they are sensible, legitimate questions when they are understood as part of the search for properties of the type: “these kinds of things X never/always/sometimes happen in situations of the kind S, because situations S have the property P.” In other words, questions concerning modal properties and facts make sense not as normative or linguistic ones, but rather as searches for modal (situation-related) features of reality.

In our own complex world there are many complex devices, institutions, bodies of law, ways of doing things, and the like. These are all contingent, but extremely useful. In conversation that assumes the existence of these things, the concept of necessary and sufficient conditions arises quite naturally. For example, to make an omelet, one needs eggs. If Fred’s spouse wants him to make an omelet, he might say, “I can’t make an omelet, for I have no eggs.” If a philosopher, Fred might go on: “Having eggs is a necessary condition for making an omelet. If I make an omelet, I need eggs.” Perhaps his spouse, also a philosopher, says, “It sounds like you are saying this,” writes on a chalkboard:

∀x□ (x makes an omelet, x has eggs)

and adds “But Quine has shown us that such modal logic makes no sense. So what are you saying?”

Well, Fred replies,

I think it makes perfectly good sense. In the background of my remark there is something I assume and you should too: how one makes an omelet. One breaks some eggs into a pan, stirs them around until the yolks and white are mixed together, and then, if wanted, tosses some other stuff on top, lets it fry for a while and then folds it over, and fries it a little more until brownish. I claim that given that that’s how one makes an omelet, having eggs is a necessary condition of making an omelet. What’s mysterious about that?

Nothing, we believe. We basically have a relation between three things: how one makes an omelet, the condition of having eggs, and the accomplishment of making an omelet. Given the first, anyone who does the third has to meet the second.

This relation gives rise to non-extensional contexts. At the moment, eggs are the food the price of which has risen the most since the drought. But Fred wouldn’t say that, given the way one makes an omelet, having the food the price of which has risen the most since the drought is necessary to make an omelet.

7 Conclusion

Føllesdal’s accomplishments include providing a framework that does not violate ordinary logic with respect to variables and allows for extensional and designational transparency and the possibility of referential transparency for singular terms in additional to variables. By doing so, he also provides the tools to dismantle the slingshot argument.

The price to pay for all of this was acceptance of a two-sorted semantics and of Aristotelian Essentialism. In Føllesdal’s work, however, it was clear that Aristotelian Essentialism was a relatively benign view. It basically involves the combination of modal operators being extensionally opaque and referentially transparent. This combination is required for quantified modal logic to be coherent, as we saw. The referential transparency guarantees that whatever is true (or false) of an object, is true (or false) of that object, independently of how we refer to it. But this is what Quine calls “essentialism,”

An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from some ways of specifying the objects as the former traits do from other ways of specifying it. (Quine 1953a, 155)

The essentialism needed for modal logic, and rejected by Quine, thus simply required the view that an object had some properties necessarily, and others not. This is compatible with empiricist treatments of the nature of objects and individuation, and its metaphysical implications certainly don’t seem to be grave enough to give up on modal logic. Not, at least, if we include genuine singular terms.

Genuine singular terms, as Føllesdal defined them, do not refer by picking out objects by their essences, in the sense of essential properties that uniquely identified them. Føllesdal’s genuine singular terms are, at least in this point, philosophically clearer than Kripke’s rigid designators, and they ask or involve only the weak essentialism described above. Quine, however, tended to identify both:

A term thus qualified is what Føllesdal called a genuine name and Kripke has called a rigid designator. It is a term such that ∃x□(x = a), that is, something is necessarily a, where ‘a’ stands for the term.

… A rigid designator differs from others in that it picks out its object by its essential traits. It designates the object in all possible worlds in which it exists. Talk of possible worlds is a graphic way of waging the essentialist philosophy, but it is only that; it is not an explication. Essence is needed to identify an object from one possible world to another. (Quine 1977, 118, Føllesdal’s italics)

As Føllesdal (1986) rightly claims, in this text Quine seems to be conflating what he had achieved with his arguments against modal logic up to 1961, with what the situation was with regard to quantification into modal contexts, essentialism and reference by 1977. The kind of essentialism Quine is discussing here has nothing to do with the mild Aristotelianism supported by Føllesdal’s account. If essence is necessary to identify and thus pick out an object from one possible world to another, it has to be maintained across worlds, bringing in issues of the trans-world identity, counterparts, etc.

In the Transcript, Dreben talks about a Pyrrhic victory, and of a resistance to Quine that started with Kripke and continued with the blossoming of modal logic and the development of possible worlds semantics. He was referring, we assume, to the type of attitude exemplified by Loux’s quote in the introduction of this paper: “with the development of a semantics for modal logic, attempts to answer Quine became less and less frequent.” None of the participants in the Conference were particularly fond of the way these “new” developments accounted for “the content of an essentialist metaphysics.” Davidson, for instance, when asked by Dreben, answers “I have no truck at all with possible worlds.” (42)

Quine, on the other hand, kept a skeptical attitude towards possible worlds semantics. And attitude that we share, but that we do not find problematic to accept modal properties and facts, as we explained before. Føllesdal summarises Quine’s take on possible worlds semantics quite clearly:

Quine found the so-called “possible world semantic” question-begging. Surely, such semantics are formulated in an extensional metalanguage, but since in this metalanguage one quantifies over possible worlds, the semantics do not bring us any further toward understanding the modal notions unless the notion of possible worlds is made clear. (Føllesdal 2004a, 201)

As far as we know, the notion of possible worlds has not been made clear. Or, at least not clear enough to offer an understanding of modal notions. But this should not be a serious problem for modal logic because, way before Kripke, and way before the tremendous development of possible world semantics and modal logic in the 70’s, Føllesdal had provided a means to solve Quine’s problems with modal logic and essentialism. Føllesdal provided a way to grant Quine the victory over Carnap and Lewis, and a way to avoid both the catastrophic consequences of Quine’s argument—collapse of modality—and the many problems generated by other attempts to avoid this. Possible worlds semantics, useful as it is, is not needed to give a solution to Quine’s challenge and an explanation of modal notions.

It is plausible to think that, had Quine and Davidson paid closer attention, and had they been willing to compromise their reluctance towards reference, we would have avoided quite a lot of discussion about issues and pseudo-problems such as the ontological status of possible worlds, trans-world identity and the like. Quine’s victory would have still be a victory, but he might have avoided it being Pyrrhic.

Perhaps Føllesdal was reluctant to raise these issues to his thesis advisor and other older distinguished philosophers from whom he had learned so much. More likely, we think, is that Føllesdal was utterly fascinated by what Quine, Davidson, and Dreben had to say to each other about the subtle differences and insightful similarities between Quine and Davidson’s approaches, and wanted their interests and interactions to guide the conversation. Why, given that Føllesdal was sitting there with them, did Quine and Davidson not bring up the extremely important contributions Føllesdal had made to the topics that interested them, and the threats to their own arguments and positions that these contributions presented? We don’t know.

Acknowledgements

We are grateful to the members of the Zoom group and, in particular, to Shannon Bain, Carlo Penco and Andrea Raimondi for their useful comments on previous drafts. We are particularly grateful to Benjamin Marschall and Andreas Føllesdal, for their invitation, and to Dagfinn Føllesdal, who has been a friend and a great inspiration for many years. The first two authors benefited from grants by the Spanish Government (PID2023-151480NB-I00 funded by MICINU/AEI/ 10.13039/501100011033 and by ERDF/UE) and the Basque Government (IT1612-22).