Abstract
My task today is an unusual and not very pleasant one. I am not here to debate the adequacy of any philosophical thesis. Rather, my job is to assess claims involving credit and blame. According to Quentin Smith, the central doctrines of Naming and Necessity were developed by Ruth Marcus in her pioneering papers on quantified modal logic in the late 40’s, and in her paper, ‘Modalities and Intensional Languages’ in 1961.1 Smith maintains that Saul Kripke learned these doctrines from her, initially misunderstood them, and, when he later straightened things out, mistakenly took the doctrines to be his own. Finally, Kripke is supposed to have published them without properly citing her. The entire profession was allegedly fooled, despite the fact that Kripke and Marcus were among its most well known members, and their work was familiar to leading researchers in the field. For years nobody said anything. Now, more than 20 years later, Smith claims to be bringing the truth to light.
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Notes
Synthese, XIII, Dec. 1961, 303–322. This paper is reprinted in Ruth Barcan Marcus, Modalities, (New York and Oxford: Oxford University Press), 1993. Citations from the paper will be from Modalities.
R.C. Barcan (Marcus), ‘A Functional Calculus of First Order Based on Strict Implication’, Journal of Symbolic Logic, 11, 1946, 1–16. Also, R.C. Barcan (Marcus),’The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication’, The Journal of Symbolic Logic, 11, 1946, 115-8.
R.C. Barcan (Marcus), ‘The Identity of Individuals in a Strict Functional Calculus of Second Order’, The Journal of Symbolic Logic, 12, 1947, 12–15.
In ‘Modalities and Intensional Languages’, pages 9 and 10, Marcus refers to theorem 2.32* of her 1947 paper as, in effect, establishing the necessity of identity. (The symbol ‘ ’ is the (strict) identity predicate. The connective is strict equivalence, the terms are individual variables, and the theorem itself has the force of its universal closure.) Marcus derives this theorem in her quantified version of S4 from her theorems 2.23 and 1.104*. (The symbol ‘ m’ stands for the material identity predicate. Material identity and strict identity are defined predicates that turn out to be provably strictly equivalent in Marcus’ S4.) The point to note here is that Marcus’ derivation of the necessity of identity depends on a controversial principle about the iterability of the necessity operator, which is not something that the thesis itself intuitively requires. (The proof also utilizes the Barcan and converse Barcan formulas. See below.) If variables are treated as rigid designators — with respect to assignments — as in the now standard Kripke-style semantics for modal systems, the above version of the necessity of identity falls out automatically from the semantics without any special assumptions about the accessibility relation, or the corresponding axiomatic modal systems. In this connection, it is worth noting another theorem that Marcus refers to in ‘Modalities and Intensional Languages’ in her discussion of the necessity of identity. This is theorem 2.33* of her 1947 paper. This establishes the strict equivalence of Marcus’ two forms of identity. (Theorem 2.32*, and hence the S4 premise guaranteeing the iterability of the necessity operator, is used in the proof of this.) The theorem itself is closely related to the necessity of identity. This can be seen as follows: First, we use the definition of ‘ ’ (strict identity) to give the import of the theorem as (i) Next we apply the definition of strict implication to give us (ii). The combination of (ii) together with the second order Barcan formula and the second order converse Barcan formula yields (iii). Finally, we apply the definition of ‘ m’ (material identity) to get (iv). Although this might be taken to be a version of the necessity of identity, as before the proof relies on controversial modal principles — including the second order Barcan and converse Barcan formulas. These principles are not intuitively required by the necessity of identity itself, and are dispensable if variables are taken as rigid designators in the semantics of all the modal systems. (I am indebted to Saul Kripke for a discussion of the material in this paragraph, especially the role of the second order Barcan and converse Barcan formulas.) The second order Barcan and converse Barcan formulas also seem to be involved in the proof of theorem 2.23 which Marcus uses in her proofs of both theorem 2.32* and 2.33*. Note, the definitions of material identity and strict identity are (F)(Fx ⊃ Fy) and respectively. Given the two second order Barcan formulas, the formulas and are strictly equivalent, which establishes 2.23. Finally, it may be worth pointing out why the necessity of identity cannot be derived in the now familiar way in Marcus’ systems without the help of some controversial supplementary principles like those we have been appealing to. We may begin by attempting a derivation from theorem 2.4 of her quantified extension of S2. (i) (Theorem 2.4 of Barcan 1947) (ii) (From (i) and 2.2 of Barcan 1947) (iii) (From (ii) and 2.3 of Barcan 1947 Now all we need to establish is, and we will have the desired result. But establishing this is problematic. Suppose we proceed as follows: (v) Axiom Schemata 2, 3, and 5 of the first Barcan 1946 paper) (vi) (From (v) by universal generalization) (vii) x x (From (vi) by the definition of ‘ ’) If S2 had necessitation we could derive. But S2 does not have necessitation. Moreover, even if we could get, we would have to appeal to the converse Barcan formula to get the needed, which has the force of. In light of this we might try a different derivation. This time we start with Marcus’ theorem 2.17. (i) (Theorem 2.17 of Barcan 1947) (ii) (From (i) and 2.2 of Barcan 1947) (iii) (From (ii) and 2.3 of Barcan 1947) (iv) (v) (Axiom Schemata 2, 3, and 5 of the first Barcan 1946 paper) (vi) ((v) plus the definition of strict implication) (vii) (From (vi) by universal generalization) (viii) (From (vii) plus the second order Barcan formula) (xi) (From (viii) plus the definition of ‘ m’) (x) (From (iv) and (ix)) As far as I can tell, this is the closest one can get to an unproblematic derivation of a version of the necessity of identity in Marcus’ system. Although the derivation can be done in Marcus’ quantified version of S2, it uses “material identity” rather than “strict identity”, and, most importantly, it requires the second order Barcan formula.
Arthur Smullyan, review of W.V. Quine, “The problem of interpreting modal logic”. Quine’s paper appeared in The Journal of Symbolic Logic, 12, 1947, 43–48. Smullyan’s review appeared in The Journal of Symbolic Logic, 12, 1947, 139-141.
Arthur Smullyan, ‘Modality and Description’, The Journal of Symbolic Logic, 13, 1948, 31–37.
Frederic B. Fitch, ‘The Problem of the Morning Star and the Evening Star’, Philosophy of Science, 16, 1949, 137–141.
The Journal of Philosophy, Vol. XL, 1943, 113–127.
The Journal of Symbolic Logic, Vol. 12, 1947, 43–48.
In the 1947 article Quine gave a slightly different version of the argument, one which emphasized what he took to be the intimate connection between the logical content of objectual quantification and certain rules of inference — in particular existential generalization. We can reconstruct the basic idea as follows. (P1)a An occurrence of an objectual variable within a certain construction is bindable by a quantifier outside the construction only if existential generalization from that position is universally truth-preserving. (P2)a Existential generalization from the position of ‘x’ in a formula, (⋯x⋯), will be universally truth-preserving only if ‘x’ occupies a position which is transparent — only if for any pair α and β of coreferential singular terms the sentence, (⋯α⋯), that results from substituting α for, ‘x’, is true iff the sentence, (⋯β⋯), that results from substituting α for ‘x’, is true. (For suppose that this were not so. Suppose that for some pair α and β of coreferential singular terms the sentence, (⋯α⋯), is true whereas the sentence, (⋯β⋯), is false. In such a situation, both the sentence [α = β & (⋯α⋯)] and the sentence [(β= β& ~(⋯β⋯)] are true. But then if existential generalization is universally truth preseving, must both be true, which is impossible.) Combining these premises with (P3), plus the definitions of opacity and pure designation, produces the same results as above.
’Opacity’, The Philosophy of W.V. Quine, Hahn and Schilpp (eds.), (LaSalle Illinois, Open Court), 1986, 229–289.
’Quantification and Opacity’, Linguistics and Philosophy, 10, 1987, 77–100. See also, his’ some Remarks on Indiscernibility’, Canadian Journal of Philosophy, Supplementary volume 18, 1992, 167-178.
’Quantification and Leibniz’s Law’, Philosophical Review, vol. 96, 1987, 555–578.
The same holds for premise Pla of the argument in footnote 10.
And do not support universally truth-preserving existential generalization.
And do support existential generalization.
And do not support existential generalization.
Richard, ‘Quantification and Leibniz’s Law’; Kazmi,’ some Remarks on Indiscernibility’.
In addition, Smullyan explicitly maintained that existential generalization on a formula containing a modal operator is universally truth-preserving where names are involved, but fails to be so when the existentially generalized variable replaces a description rather than a name.
Alonzo Church, review of Frederic B. Fitch, ‘The problem of the Morning Star and the Evening Star’, The Journal of Symbolic Logic, 15, 1950, p. 63.
Point (vi) is explicit only in Marcus.
Page 12, in Modalities.
See pages 10 and 14-15.
’Discussion of the Paper of Ruth Marcus’, Synthese, 14, 1962, 132–143. Reprinted in Modalities.
Pages 33 and 34 of Modalities.
It is significant that Marcus responds to a straightforward question about the necessity of identities involving names (and their intersubstitutability in modal constructions) with remarks about epistemology and synonymy. This reinforces the impression given by the text of her article that she thought of the view of names as mere tags (and hence as being synonymous if coreferential) as being inseparable from, and even the ground for, her views of the behavior of names in modal constructions. This linking of the modal status of names with controversial claims about their meaning and epistemology marks a very important contrast between Marcus’ view and the view developed by Kripke in Naming and Necessity.
Marcus’ discussion of proper names occurs in the section of her paper devoted to answering Quine’s objections to quantifying-in. She begins her discussion by saying “The rebuttals are familiar and I will try to restate some of them”. [Page 10 in Modalities]. Moreover, in a very closely related paper, ‘Extensionality’, Mind, Vol. 59, 1960, pp. 55-62, Marcus briefly sketches a response to Quine’s Morning Star-Evening Star example which is largely the same as the one she gives in ‘Modalities and Intensional Languages’. The discussion in ‘Extensionality’ is prefaced by a footnote in which Marcus says that she is restating a point made by Fitch in his 1950 paper.
Moreover, Smith’s quote from Marcus on this point contains massive ellipsis, and gives a misleading picture of her discussion. Here is his quote. But to give a thing a proper name is different from giving a unique description ⋯ [An] identifying tag is a proper name of the thing⋯ This tag, a proper name, has no meaning. It simply tags. It is not strongly equatable with any of the singular descriptions of the thing. Here is the beginning of the passage quoted, without Smith’s first ellipsis. But to assign a thing a proper name is different from giving a thing a unique description. For suppose we took an inventory of all the entities countenanced as things by some particular culture through its own language, with its own set of names and equatable singular descriptions, and suppose that number were finite (this assumption is for the sake of simplifying the exposition). And suppose we randomized as many whole numbers as we needed for a one-to-one correspondence, and thereby tagged each thing. This identifying tag is a proper name of the thing. [my emphasis] (p. 11 of Modalities) Marcus says that this identifying tag — namely the number assigned to the object in our artificial, randomized assignment — is a proper name. Clearly it is not an example of an ordinary proper name. Rather, Marcus seems here to be illustrating the theoretical possibility that we, as theorists, might introduce certain elements as mere tags. The passage continues as follows: In taking our inventory we discovered that many of the entities countenanced as things by that language—culture complex already had proper names, although in many cases a singular description may have been used. This tag, a proper name, has no meaning. It simply tags. It is not strongly equatable with any of the singular descriptions of the thing ⋯ (pp. 11 and 12 of Modalities) What is Marcus referring to in this passage when she says “This tag, a proper name, has no meaning”? Is it to the numbers of our randomized assignment, which have just been called both tags and proper names two sentences back? Is it to proper names in the language of the culture we are describing? Or is it to both? My guess is that the reference is probably to both. But if it is to both, we are not given an argument for taking the two to be on a par.
Page 11 in Modalities.
See note 28.
I do not object here to the substance of Marcus’ position, which is close to my own. Rather, I am merely pointing out one reason why the modal argument seemed more persuasive, and was more widely accepted, when presented by Kripke.
See Naming and Necessity, Harvard University Press, Cambridge, Mass., 1980, pp. 61–62.
Such as Dummett’s objection that proper names can be taken to be equivalent to descriptions that always take wide scope over modal operators. See Dummett, Frege: Philosophy of Language, Harper and Row, New York, 1973, pp. 112–116.
This is an important feature of Kripke’s version of the modal argument that does not seem present in Marcus’ version. Both Kripke and Marcus use modal properties of names to distinguish them from descriptions. However, the way they establish the modal properties of names is quite different. Kripke provides examples in which we evaluate simple sentences containing proper names (but no modal operators) at alternative possible worlds (counterfactual circumstances). He uses these examples to show that the referent of a name at one world is the same as its referent at other worlds, and hence that names are rigid. It then follows that identities involving names are necessary if true, and that coreferential names are intersubstitutable in modal constructions. Marcus, on the other hand, seems to think that these modal properties of names somehow follow from the quantified version of the necessity of identity, either by itself or in conjunction with her controversial view that names are “mere tags”.
However, this contribution must be understood as subject to the qualification in footnote 4. An explicit semantic system in which variables are treated as rigid designators is given in Saul Kripke, ‘A Completeness Theorem in Modal Logic’, The Journal of Symbolic Logic, Vol. 24, Number 1, 1959, 1–14. (The paper was received by the journal in August of 1958.)
Ibid.
Journal of Philosophy, LXVIII, 1971, 187–202. This paper is reprinted in Modalities.
The passage quoted by Smith is taken from page 61 of Modalities. Two points are of interest here. First, at this time Marcus had no objection to characterizing proper names as rigid designators, even though she presumably did not think that in doing so she was “assimilating them to some descriptions”. Second, in the passage from which this quote was taken, Marcus continues to express some ambivalence regarding the question of the extent to which names, as ordinarily used, are rigid designators. Thus, she ends the paragraph from which the quote was taken by saying, “For those that are quick to argue that ordinary names cannot always be used in such a purely referential way, we can, in giving the interpretation, expand our lexicon to provide neutral, purely referential names where necessary”. (p. 61 Marcus’emphasis)
Page 12, Modalities.
Page 12, Modalities.
Page 12, Modalities.
Page 10, Modalities. The passage continues in a somewhat confusing way, with Marcus saying that therefore since (14) is “valid” (13) must be as well. She then adds that this was “precisely the import of my theorem [of the necessity of identity]”. Put aside that her theorem didn’t involve names at all. Surely we would now see her claims about (13) and (14) saying the same thing, and being jointly valid, as going well beyond the claim that they are necessarily equivalent. Of course, if — contrary to Smith’s thesis — Marcus was not carefully distinguishing necessity from logical validity, analyticity, and aprioricity, then her tendency in the article to slip from one to another is quite understandable.
Page 10 of Modalities.
Smith would have avoided this particular problem, while keeping somewhat closer to the passage in Marcus, had he attempted to construct an argument ruling out the possibility that some name α for Venus has, for some particular person, the sense of ‘the (actual) morning star’ while some name β has, for some person, the sense of ‘the (actual) evening star’. For example, consider the following: (P1) If the description theory is correct, and I semantically associate the name ‘Venus’ with the description ‘the (actual) evening star’, then I can know a priori the proposition I express by the sentence ‘Venus is the (actual) evening star, if there is such a thing’. (P2) If the description theory is correct, and you semantically associate the name ‘Venus’ with the description ‘the (actual) morning star’, then you can know a priori the proposition you express by the sentence ‘Venus is the (actual) morning star, if there is such a thing’. (C1) Thus, if the description theory is correct, then both the proposition that Venus is the (actual) evening star, if there is such a thing and the proposition that Venus is the (actual) morning star, if there is such a thing must be knowable a priori. Hence, if the description theory is correct, we can know a priori that the (actual) evening star is the (actual) morning star, if there are such things. (P3) But one cannot know this a priori. (C2) Therefore, the description theory is incorrect. Still, this argument is invalid. Conclusion (C1) does not follow from (P1) and (P2); it is simply false. According to the description theory if you and I semantically associate different descriptions with the name ‘Venus’ then the name has different senses for us. Because of this the proposition I express with the sentence Venus is the (actual) evening star is not the proposition you express by that sentence. Consequently, it would be correct for me to report, “I know a priori that Venus is the (actual) evening star, if there is such a thing, but I cannot know a priori that Venus is the (actual) morning star, if there is such a thing” while it would be correct for you to report the opposite. According to the description theory, there is no single interpretation of Venus is the (actual) evening star, if there is such a thing and Venus is the (actual) morning star, if there is such a thing according to which both are knowable a priori. Of course, the failure of this argument is not Marcus’ responsibility; for there is no such argument in her paper.
P2 could be questioned on the grounds that it assumes some sort of closure principle for propositions knowable apriori — e.g., if A, B, and C are knowable apriori, and D is a consequence of A, B, C, then D is knowable apriori. I am not endorsing such a closure principle, or even P2. Rather, I am trying to make the strongest argument one can, based on Marcus’ text, for the conclusion that the propositions that Hesperus is the evening star and Phosphorus is the morning star are not knowable apriori.
A case in point is Smith’s uncomprehending criticism of the following remark of the undergraduate Saul Kripke in the 1962 ‘Discussion of the Paper of Ruth Marcus’. The tags are the ‘essential’ denoting phrases for individuals, but empirical descriptions are not and thus we look to statements containing ‘tags’, not descriptions, to ascertain the essential properties of individuals. Thus, the assumption of a distinction between ‘names’ and ‘descriptions’ is equivalent to essentialism. [my emphasis] (page 34, Modalities) Smith follows Marcus, ‘A Backward Look at Quine’s Animadversions on Modalities’, reprinted in Modalities, 1993, 226-227, in seeing Kripke’s remark as attributing to Marcus the absurd view that it is essential property of an individual like Socrates that he was named’ socrates’ — i.e., the view that Socrates could not have existed without being named’ socrates’. Smith then takes this as evidence that Kripke misunderstood Marcus. But it is Smith (and Marcus) who have misunderstood. Kripke was not criticizing Marcus for holding the view that individuals could not have had different names. Rather, Kripke was showing how the doctrine that there is a class of singular terms which are rigid designators collides with Quine’s doctrine that even if de dicto necessity (in which the necessity operator is prefixed to a closed sentence) is accepted, de re necessity (in which we quantify into a modal context formed by prefixing the necessity operator to a formula containing a free variable) is illegitimate. Quine’s idea was that even if we could make sense of a statement being necessary, we cannot make sense of an object having a property essentially, or necessarily (which is what we express by quantifying in). According to Quine we cannot make sense of an object necessarily having a certain property independently of how it is designated or described because for any such object o and property P there will be different (closed, singular) terms t1 and t2 referring to o such that the sentences Necessarily t1 is P and Necessarily t2 is P differ in truth value. Kripke’s response (on behalf of Marcus) can be put in contemporary terms as follows: If names are rigid designators, and n is a name of o, then the de re claim that o has the property P necessarily is equivalent to the de dicto claim that the statement Pn is necessary. Since n refers to the same thing in all worlds, the de dicto claim is true iff o has the property P in every world — which is just what the de re claim says. Thus, if one grants the legitimacy of de dicto claims, and also recognizes the rigidity of names, one has to grant the legitimacy of de re. essentialist claims as well. Alternatively, if one insists (for whatever reason) that de re essentialist claims do not make sense, then one must insist that neither names, nor any other terms, can be rigid designators. In the discussion Kripke did not take a stand on which of these alternatives was correct, but was content to simply frame the issue between Marcus and Quine. (See page 35, Modalities)
For a discussion of the difference between rigidity and direct reference see David Kaplan, ‘Afterthoughts’, Themes from Kaplan, Almog, Perry, and Wettstein, eds. (University Press Oxford, New York and Oxford), 1989, 565–614.
Versions of this paper were read by Paul Benacerraf, Sarah Broadie, Fiona Cowie, Al Akhtar Kazmi, Mark Richard, Nathan Salmon, and Michael Thau. I would like to thank them for their helpful comments. In addition, I would like to thank Saul Kripke for a conversation about the material indicated in footnote 4, and Ruth Marcus for conversations about her views in ‘Modalities and Intensional Languages’.
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Soames, S. (1998). Revisionism about Reference: A Reply to Smith. In: Humphreys, P.W., Fetzer, J.H. (eds) The New Theory of Reference. Synthese Library, vol 270. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5250-1_2
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