Necessity and Counterfactual Discourse

By James Walsh

The question “Is water necessarily H2O?” has a more complicated answer than may appear at first blush. To answer the question, one must first distinguish between conceptual and metaphysical necessity. By differentiating between these two types of necessity, it becomes clear that water is not necessarily H2O on a conceptual level. Whether water is necessarily H2O on a metaphysical level depends on the understanding of the word “water” on the part of the person who is judging whether water is metaphysically necessarily H2O. First I will expound upon the notion of conceptual necessity. Then I will evaluate questions of identity and necessity from a metaphysical perspective, which will involve an analysis of definite descriptions and rigid designations. Finally, I will present a positive view of necessity and identity in counterfactual discourse, which will depart from both conceptual and metaphysical necessity.

Conceptually necessary truths are those truths that are analytically true, that is, true in virtue of the content of the concepts. For example, the claim “John is tall” is not conceptually necessary whereas the claim “A square is a square” is conceptually necessary. It is conceptually necessary that a square is a square, because being a square is contained within the concept of being a square. This is not the case, however, for John and tallness, so John is not conceptually necessarily tall. A square not being a square is conceptually impossible, whereas John being short is conceptually possible, because the negation of shortness is not contained within the concept of John. This difference can be illustrated by conditionals.

(i)         Square(x) ⊃ Square(x)

(ii)        John(x) ⊃ Tall(x)

Conditional (i) is valid. That is, under no truth assignment to Square(x) could conditional (i) be false. However, if the value true is assigned to John(x) and the value false is assigned to Tall(x), then conditional (ii) is false. It is conceptually impossible that conditional (i) could be false, whereas it is possible to conceive of conditional (ii) being false. For this reason, it is conceptually necessarily that conditional (i) is true whereas it is not conceptually necessary that conditional (ii) is true.

If water is conceptually necessarily H2O, then the following conditional must be valid. That is, it must be true under any interpretation.

(iii) x=Water ⊃ x=H2O

One interpretation under which conditional (iii) is false is the assignment of truth to the antecedent and falsehood to the consequent. Is this truth-value assignment possible? At first glance it might not seem so. If something is water then it is H2O, as a matter of fact. However, the antecedent and consequent in this conditional are not about matters of fact. Rather, they are about concepts.

Consider the world in 1750, before the discovery that water is composed of two hydrogen atoms and one oxygen atom on the molecular level. Was it conceptually necessary then that water is H2O? I do not believe that it was conceptually necessary then that water and H2O are identical. Indeed, very few speakers of English even had the concept of H2O. For similar reasons, I do not believe that is conceptually necessary that water and H2O are identical today. I can distinguish between the concepts of the substance I encounter daily and the molecule composed of two hydrogen atoms and one oxygen atom. Perhaps this can be more clearly illustrated with the analogous example of Hesperus, the Evening Star, and Phosphorus, the Morning Star.

The ancients referred both to the Evening Star, the brightest body in the sky after sunset, and the Morning Star, the brightest body visible before sunrise. Eventually it was discovered that the Evening Star and the Morning Star are, in fact, both the planet Venus. Thus, the Evening Star and the Morning Star are, as a matter of fact, the same celestial body. Yet, they were conceived of as different bodies; the concepts “the Evening Star” and “the Morning Star” were clearly distinct before the discovery that the Evening Star is the Morning Star. The same holds for water and H2O. Though water is, as a matter of fact, H2O, it is not conceptually necessary that water is H2O, because their conceptual content differs. Thus, conditional (iii) can be rendered false by assigning truth to the antecedent and falsehood to the consequent.

One may still wish to assert that water is H2O as a matter of metaphysical necessity. To what does this amount? To evaluate metaphysical necessity, I must first understand what one means in saying that “water” is necessarily H2O. In other words, to what does the word “water” refer?

Saul Kripke addresses the problem of names and referents, writing that a referent’s name is fixed by an initial baptism and then later uses of the name are linked to the referent through a causal chain. Furthermore, names are rigid designators. That is, a name can be used to refer to its referent in counterfactual discourse. Conceptually possible counterfactual situations are often called possible worlds, and rigid designators designate across possible worlds. So, in the case of Hesperus and Phosphorus, one referent (the planet Venus) was baptized twice, and the rigid designators Hesperus and Phosphorus apply to the same referent in each possible world. Therefore, in every possible world, Hesperus is Phosphorus. Thus, Kripke believes, Hesperus is necessarily Phosphorus. Kripke’s argument can be formalized as follows.

(1)   X = Hesperus                                            [1]        Premise

(2)   X = Phosphorus                                        [2]        Premise

(3)   Hesperus = Phosphorus                             [1][2]   Transitivity of Identity

\  ☐ [Hesperus = Phosphorus]                       [1][2]   Necessity of Identity


Let’s assume for the time being that this argument is sound.[1] Kripke also offers an argument that definite descriptions (denoting phrases that refer to only one referent) are not rigid designators. For example, assume “Aristotle” refers to the definite description “the man who taught Alexander”. Then it is necessary that Aristotle was Alexander’s tutor. Yet, it is possible that Aristotle may never have taught Alexander, contradicting the previous statement. Thus, “Aristotle” is not equivalent to the definite description “the man who taught Alexander.” The argument can be formalized as follows (A = “Aristotle” and T = “the man who taught Alexander”).

(1)   A = T                                                         [1]        Assumption

(2)   ☐ [A = T]                                                  [1]        Necessity of Identity

(3)   ◊ ¬ [A = T]                                                [3]        Premise

(4)   ¬☐ [A = T]                                                [3]        Modal Operation

(5)   [A = T] ⊃ [☐ [A = T] & ¬☐ [A = T]]       [3]        Discharge [1]

\  ¬ [A = T]                                                   [3]        Reductio ad absurdum


Let’s also assume for the time being that this argument is sound. One must pay close attention to the meaning of the variables. The conclusion is not that Aristotle, as a matter of fact, was not Alexander’s tutor. The conclusion, rather, is that “Aristotle” is not equivalent to the definite description “the man who taught Alexander.” When one says “Aristotle” one is not referring to “the man who taught Alexander.” A defender of the definite description theory of names might object that the premise Kripke introduces in the third line is not true and, thus, the argument is not sound. Kripke defends this charge by pointing to the use of counterfactual antecedents like “suppose Aristotle had never gone into philosophy at all” (Kripke, 57). The common use of the name “Aristotle” in this way suggests that “Aristotle” is not equivalent to the definite description “the last great philosopher of Antiquity.” Similarly, one can wonder what would have happened if Aristotle had never tutored Alexander, implying that “Aristotle” is not equivalent to the definite description “the man who taught Alexander.” Thus, Kripke’s modal argument demonstrates that the definite description theory of names does not mirror the use of names in ordinary language. This linguistic claim is sufficient refutation of the definite description theory of names.

However, Kripke jumps from a linguistic claim to a metaphysical claim. Kripke not only states that the use of the word “Aristotle” as a rigid designator in counterfactual situations implies that “Aristotle” is not a definite description. Rather, Kripke also means that there is a possible world in which Aristotle died in his youth and never become Plato’s student and Alexander’s tutor. What is the nature of this metaphysical possibility? I believe that Kripke jumps from an innocent linguistic claim about “Aristotle” to a more dubious metaphysical claim about Aristotle in a possible world. The claim about “Aristotle” is that it can be used in counterfactual discourse. The claim about Aristotle is, if I have interpreted Kripke correctly, that, as a matter of fact, he could have acted differently than he did. I am more hesitant than Kripke to take this jump.

One reason I am hesitant to take this jump is because I am unsure of where to draw the line between possible and impossible counterfactual situations. There is an abundance of counterfactuals to which Kripke does not grant metaphysical possibility. For example, Kripke explicitly denies the counterfactual antecedent “If I were born of different parents” the status of metaphysical possibility. The same is true of “If I were a cat” and “If I were you.” Counterfactual statements often include these or equally problematic antecedents. Kripke writes that these are not possible, that is, metaphysically possible, because one could not be born of different parents and a human could not have been a cat. Why not? They are used in counterfactual statements. It seems that the problem is a need to specify what precisely is being rigidly designated.

Kripke responds by appealing to a notion of personal identity that could be consistent across possible worlds. The two biggest candidates in the philosophical literature for theories of personal identity are bodily continuity and psychological continuity.[2] Yet Kripke does not endorse these views. Indeed, Kripke believes it is metaphysically possible that one could have a different body than one does. Furthermore, Kripke believes that it is metaphysically possible that one could be psychologically different than one is. A possible motivation for Kripke’s rejection of these criteria for personal identity is the existence of many counterfactual statements that treat these criteria of personal identity as contingent (i.e. “If I had a different body” or “If I had amnesia”).

Kripke’s positive view of identity is essentialist. This holds for personal identity as well. For Kripke, the essential property that makes a person is that it develops from a particular sperm and egg. Kripke writes, “How could a person originating from different parents, from a totally different sperm and egg, be this very woman?” (Kripke, 113). Thus, Kripke can distinguish between mere counterfactual discourse about persons and metaphysical possibility about persons. Identical twins present an empirical counter-example to Kripke’s metaphysical claim, because identical twins develop from the same zygote but are not identical persons. A more charitable reading of Kripke could amend his view so that rigid designators refer to the same zygote after its final division, if indeed it does divide. However, one could still use counterfactual language that many ordinary English speakers would say is true despite not conforming to this essentialist model. Consider an identical twin’s statement to his twin, “If we were not identical twins, we would not look the same.” For Kripke the antecedent is not metaphysically possible, because his strict sense of rigid designation precludes it. However, since this counterfactual is true according to the standards of common sense, Kripke’s sense of rigid designation is too strict to accurately reflect meaningful counterfactual discourse. Thus, origin does not seem like a property that is essential true across possible worlds. It is unclear exactly what speakers are rigidly designating in counterfactual discourse about persons.

What is being rigidly designated when one says “water”? Hilary Putnam presents a famous thought experiment that speaks eloquently to the problem. Imagine a world, nearly identical to the actual world, which Putnam dubs Twin Earth. The only difference between Earth and Twin Earth (the inhabitants of which call their planet “Earth”) is that the liquid Twin Earthlings call “water,” which has all the properties and functions of the liquid Earthlings call “water”, is composed of XYZ instead of H2O. Putnam concludes that the inhabitants are not actually talking about the substance Earthlings rigidly designate “water,” and thus “‘meanings’ just ain’t in the head” (Putnam, 227).

Though Putnam’s thought experiment was originally an argument for semantic externalism, it can also be interpreted as an argument about the necessity of identity. Under this interpretation the argument is that “water” rigidly designates a particular substance when used on Earth and rigidly designates another substance when used on Twin Earth. Since the rigid designators preclude the possibility of “water” referring to the same thing when an Earthling and Twin Earthling speak, the identity of “water” is also necessary across possible worlds (Twin Earth can be considered a possible world for the purposes of this argument). This interpretation of Putnam’s argument can be formalized as follows.

(1)   Water = H2O                                             [1]        Premise

(2)   ¬ [H2O= T.E. Water]                                [2]        Premise

(3)   ¬ [Water = T.E. Water]                             [2]        Transitivity of Identity

\  ☐ ¬ [Water = T.E. Water]             [1][2]   Necessity of Identity


Though the argument is valid, it is less clear if the argument is sound. The premise introduced on the first line, that “water” designates H2O, is surely the most obvious target for a detractor. What are the grounds for believing that “water” rigidly designates H2O?

One essentialist theory is that one is referring to H2O when one says “water,” and that water is necessarily metaphysically H2O. However, one could be rigidly designating conceptual content when using the word “water.” Imagine that a person’s conceptual content when they consider both water and Twin Earth water is limited to certain properties of both (we can postulate that this person lives before the discovery that water on Earth is, as a matter of fact, H2O). In this case “water” does not refer to H2O, because the same conceptual content can exist for XYZ. This interpretation of the Twin Earth though experiment can be formalized as follows.

(1)   Water = substance with property P           [1]        Premise

(2)   T.E. Water = substance with property P   [2]        Premise

(3)   Water = T.E. Water                                   [1][2]   Transitivity of Identity

\  ☐ [Water = T.E. Water]                             [1][2]   Necessity of Identity

Considering the step from the third line to the conclusion, this is not an argument against the necessity of identity. Rather, it is a similar argument to Putnam’s but uses the word “water” to rigidly designate something other than that which Putnam designates. Ordinary speakers of English might disagree about what precisely is being rigidly designated in the Twin Earth example. Is there an answer as to which of these two options is correct?

There are many instances in which a speaker of English will defer to an authority about the essence of a substance. Putnam refers to this as the “division of linguistic labor” (Putnam, 227). Kripke gives the example of gold and fool’s gold. “[Fool’s gold] is not another kind of gold. It’s a completely different thing which to uninitiated person looks just like [gold]” (Kripke, 119). Furthermore, though the non-chemist may not be able to differentiate between gold and fool’s gold, he would defer to a chemist about which substance is which. This supports the notion of scientific essentialism, and is a point in favor of the position that “water” refers to H2O.

There are motivations for believing that something other than molecular structure is referred to when using the word “water” in counterfactual discourse, however. For example, if “water” refers to H2O, then is it the case that nobody in 1750 knew what “water” referred to? This seems to me a very peculiar conclusion. One does not have to be an expert in chemistry but, rather, an expert in everyday recognition to know what water is. Another example is that of jade. “Jade” refers to stones of the type Nephrite and Jadeite. There is no essential property of jade. One could claim that the essential property of jade is being either Nephrite or Jadeite. However, if we take this line, what is to prevent its use in the case of water? After all, water could be the disjunction of H2O and XYZ. Since there is only one type of water it is difficult to know whether English speakers would treat “water” like “jade” or like “gold.” Thus, even if names do rigidly designate an essential property, it is not always clear which property is the essential property.[3]

There are also instances in which one will insist on using a word a particular way despite discouragement from an authoritative figure. For example, English speakers use the word “demand” to refer to the number of goods that will be sought at a particular price. However, any economist will note that this is actually “the quantity demanded.” “Demand,” in economics jargon, refers to the set of quantities demanded for all prices. Few people, even after learning this distinction, stop using the word “demand” in this context. Indeed, phrases like “supply exceeded demand” trip of the tongues and pens of politicians and pundits on television and in the newspapers. For an economist, the recognized expert on the matter, the phrase “supply exceeded demand” is meaningless. Many economists concede that even though this usage is not proper in technical economics jargon, it is the ordinary commonsensical usage of the word.

There are other examples of people ignoring the experts in the linguistic division of labor. For example, though an expert on human anatomy might insist that the thumb is a digit but not a finger, ordinary English speakers may reject this. The same could be said of psychologists and the terms “paranoid,” “obsessive compulsive,” and “bipolar.” Though many people know that OCD has a different meaning for the experts, they may use it to describe their habit of regularly tidying up their bedrooms.

Thus, it is not always the case that words have an essentialist basis, like “jade.” Nor is it always the case that people defer to the experts in the linguistic division of labor, as is the case with the words “demand” and “bipolar.” One might very well use the rigid designator “water” to refer to a liquid with numerous properties regardless of its molecular structure. It seems strange to say that, should this person ever reach Twin Earth, she would incorrect in her usage of the word “water.” Rather, she is rigidly designating something other than what Kripke and Putnam are rigidly designating. One of the virtues of the Twin Earth thought experiment, I would argue, is that it demonstrates that names can be interpreted as designating different features of a substance. It is not immediately clear which of these interpretations is correct, but I am inclined to say that both methods of rigid designation are just methods of designation, neither correct nor incorrect.

There is another, perhaps greater, threat to Kripke’s view of metaphysical necessity and possibility. Imagine an elementary school student who is learning addition. She receives her math test back, unfortunately, with a failing grade. She looks through her work and discovers that she was wrong in thinking that 3+2=6. Had she correctly answered this problem she would have passed the test. She exclaims, “If 3+2 had equaled 6, then I would have passed my math test!”

Kripke would claim that it is not metaphysically possible that 3+2=6. That is – it is not true in any possible world that 3+2=6. Yet this counterfactual is problematic for Kripke’s view for a number of reasons. The first reason is that it could appear in ordinary discourse despite having an antecedent that is conceptually impossible. The second reason is that, though the antecedent is conceptually impossible, the common English speaker might say that the counterfactual statement is true. Thus, there can be valid counterfactual discourse without resort to the notion of possibility. Indeed, many (perhaps all) who would grant that the conditional “If 3+2=6, then I would have passed my math test!” is true do not believe that 3+2=6 is true in any possible world. Ordinary counterfactual discourse does not always coincide with the theory of possible worlds or metaphysical possibility and necessity, never mind conceptual possibility and necessity. Furthermore, it is important to remember that Kripke argues against the definite description theory of names by appealing to the use of ordinary counterfactuals. If Kripke’s view cannot accommodate ordinary counterfactuals, this would imply that Kripke’s view is also incorrect.

I will now briefly sketch a positive view of identity and necessity. My objective is to make the all of the following counterfactual conditionals acceptable.

(iv)             If I had overslept, then I would have been late for class.

(v)               If I had been born of different parents, then I would look different than I do.

(vi)             If I were a dog, then I would bark.

(vii)           If I were a tree, then I would be tall.

(viii)         If negation had distributed over conjunction, then I would have passed my logic exam.

I will start with statement (v). Suppose that a particular sperm and egg are being rigidly designated when using the word “I.” Then this counterfactual is confused, so this cannot be the meaning of “I”. There is precious little we could chose about a person as an essential quality, consistent across possible worlds, that will make both statements (v) and (vi) true. When we consider statement (vii) this becomes even more of a problem. So what is being rigidly designated? What is the common feature of “I” in statements (v), (vi), and (vii)?

The only thing in common is that they are the same “I.” There is a certain essence that is consistent. This essence – the property of something that makes it itself – is sometimes called haecceity.[4] Haecceity is independent; it does not supervene on anything and it is completely irreducible. Thus, one can emerge from a different zygote and still have the same haecceity, because haecceity is not reducible to origins. One can imagine oneself as an animal of a different species without loss of haecceity, because species is irrelevant to haecceity. Even consciousness and sentience are irrelevant to haecceity, because one can still say, “If I were a tree…” Statement (iv) is still fine on this reading; there is no loss of haecceity by having overslept.

What about statement (viii)? Negation does not, in fact, distribute over conjunction. Perhaps a situation in which it does is even conceptually impossible. But, even if we can’t imagine negation without its distributive properties, the haecceity of negation has nothing to do with its distributive properties. Haecceity just is, independently. So, without loss of haecceity, we can reason about situations in which negation distributes over conjunction.

There are two objections I anticipate. The first is that my solution does not account for the intuitive appeal to some statements like “If I had been born of different parents, then I would no longer be me.” An argument for the intuitive appeal of this statement should not rely on origin essentialism. Notice that this statement relies on a non-origin essentialist reading to even have a meaningful antecedent. Indeed, the origin essentialist cannot make sense of “I” if I am born of different parents. Perhaps this statement has some intuitive appeal because the word “me” in the consequent functions like a predicate. That is, claiming, “If I were a cheetah, then I wouldn’t be me,” is tantamount to claiming, “If I were a cheetah, then I wouldn’t have certain properties” or “If I were a cheetah, then I wouldn’t be quite the same as I actually am.” Suppose one argues against this solution by refusing to accept that “me” acts as a predicate here, but is rather a rigid designator identical to “I.” Then the same problems I sought to avoid resurface. For example, the statement “If I were a cheetah, then I would run faster than humans,” becomes incoherent. Yet ordinary speakers of English know what it means (indeed, they speak this way quite often).

The second objection I anticipate is that haecceity does not exist, and I have reduced identity to something non-existent. I embrace this objection. Haecceity does not exist. It is made up. We talk like it exists. We think like it exists. It just doesn’t. However, I am only trying to account for counterfactual speaking and reasoning. If that speaking and reasoning is all in virtue of something that does not exist, then so be it. As a matter of conceptual mapping, we require haecceity to evaluate some of the trickier counterfactuals I have brought up throughout this paper. Haecceity just happens not to exist.

Thus, counterfactual discourse hinges on something that is not out there in the world, something that does not exist. Where does this leave metaphysical necessity? If one wishes for metaphysical necessity to be tied to something in the world, like molecular structure or a particular zygote, then one’s metaphysical account of necessity will not coincide with the use of many counterfactual conditionals. If, on the other hand, one wishes to be guided by counterfactual conditionals like “If I were a T-Rex, then I would be a carnivore,” one must abandon the notion that metaphysical necessity is tied to some real properties. Perhaps some metaphysician does not care whether metaphysical necessity coincides with counterfactual speaking and reasoning, or whether metaphysical necessity is tied to anything real. Then this metaphysician must be more precise about what exactly metaphysical necessity amounts to.

[1] If this were an argument about conceptual necessity, then the move from the third line to the conclusion would be invalid. I provided an argument to this effect earlier.

[2] Even if one believes that bodily continuity or psychological continuity is sufficient for personal identity in actuality, this criterion seems irrelevant in counterfactual discourse as evidenced by statements that treat both as contingent.

[3] Kripke provides a similar example, though my interpretation of it diverges from Kripke’s intentions with it. Kripke argues that, though pain is correlated with C-fibers firing, there is the possibility of pain without C-fibers firing. Thus, pain is not identical to C-fibers firing. Here Kripke takes a phenomenal experience as the essence of pain, though a neuroscientist might claim that a C-fiber firing is essential. However, Kripke is not arguing against scientific essentialism. This demonstrates that it is not always clear which property is deemed essential.

[4] Thanks to my friend David Hefer for introducing me to this solution though, as will soon be explained, this solution is not without its problems.

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