Abstract
Expressions are used in a variety of ways. Two radically different ways in which the expression ‘nine’ can occur are illustrated by the paradigms:
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(1) Nine is greater than five,
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(2) Canines are larger than felines.
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Bibliography
R. B. Angell, Reasoning and Logic, New York 1963.
P. Benacerraf, ‘What Numbers Could Not Be’, Philosophical Review 74 (1965) 47–73.
R. Carnap, Meaning and Necessity, Chicago 1947, 2nd ed., 1956.
D. Carney and K. Scheer, Fundamentals of Logic, New York 1964.
A. Church,‘A Formulation of the Logic of Sense and Denotation’, in Structure, Method, and Meaning (ed. by P. Henle, M. Kallen, and S. K. Langer), New York 1951.
A. Church, ‘On Carnap’s Analysis of Statements of Assertion and Belief’, Analysis 10 (1949–50) 97–99.
A. Church, Review of Quine’s ‘Notes on Existence and Necessity’, Journal of Symbolic Logic 8 (1943) 45–47.
G. Frege, ‘On Sense and Reference’, originally published in Zeitschrift für Philosophie und philosophische Kritik 100 (1892) 25–50; translated in Translations from the Philosophical Writings of Gottlob Frege (ed. by P. Geach and M. Black ), Oxford 1960.
K. J. Hintikka, ‘Individuals, Possible Worlds, and Epistemic Logic’, Noûs 1 (1967) 33–62.
D. Kaplan, Foundations of Intensional Logic (Dissertation), University Micro-films, Ann Arbor 1964.
H. S. Leonard, An Introduction to Principles of Right Reason, New York 1957.
W. V. Quine, ‘Notes on Existence and Necessity’, The Journal of Philosophy 40 (1943) 113–127.
W. V. Quine, ‘Two Dogmas of Empiricism’, Philosophical Review 60 (1951) 20–43; reprinted in [15].
W. V. Quine, ‘Notes on the Theory of Reference’, in [15].
W. V. Quine, From a Logical Point of View, Cambridge, Mass., 1953, 2nd ed., 1961.
W. V. Quine, ‘Three Grades of Modal Involvement’, in Proceedings of the Xlth International Congress of Philosophy, Brussels, 1953y Vol. 14, pp. 65–81, Amsterdam; reprinted in [20].
W. V. Quine, ‘Quantifiers and Propositional Attitudes’, The Journal of Philosophy 53 (1956) 177–187; reprinted (minus 15 lines) in [20].
W. V. Quine, Word and Object, New York 1960.
W. V. Quine, ‘Reply to Professor Marcus’, Synthese 13 (1961) 323–330; reprinted in [20].
W. V. Quine, The Ways of Paradox and Other Essays, New York 1966.
P. F. Strawson, Individuals, London 1959.
A. Tarski, ‘The Concept of Truth in Formalized Languages’, originally published in Polish in Prace Towarzystwa Naukowego Warszawskiego, Wydzial III, no. 34 (1933), pp. vii + 116; translated in A. Tarski, Logic, Semantics, Metamathematics, Oxford 1956, pp. 152–278.
References
This paper is intended as a commentary on Quine’s ‘Quantifiers and Propositional Attitudes’. Quine’s article was first published in 1956 and I have been thinking about it ever since. Quine has not been idle while I have been thinking, but his subsequent writings do not seem to have repudiated any part of ‘Quantifiers and Propositional Attitudes’ which remains, to my mind, the best brief introduction to the field. The first half of my reflections was read to the Harvard Philosophy Colloquium in January 1966. Its writing was aided by conversations with Montgomery Furth. The present ending has been influenced by a number of different persons, most significantly by Saul Kripke and Charles Chastain. But they should not be held to blame for it. Furth, who also read the penultimate version, is responsible for any remaining deficiencies aside from Section IX about which he is skeptical. My research has been partially supported by N.S.F. Grant GP-7706.
The quotation is from Word and Object, p. 144, wherein the inspiration for ‘opaque’ is explicitly given. The assimilation of intermediate occurrences to accidental ones might fairly be said to represent a tendency on Quine’s part. The further evidence of Word and Object belies any simplistic characterization of Quine’s attitudes toward intermediate occurrences.
In ‘Three Grades of Modal Involvement’, p. 172 in [20] and other places. An intriguing suggestion for notational efficiency at no loss (or gain) to Quine’s theory is to take advantage of the fact that occurrences of variables within opaque contexts which are bindable from without are prohibited, and use the vacated forms as “a way of indicating, selectively and changeably, just what positions in the contained sentence are to shine through as referential on any particular occasion” (Word and Object, p. 199). We interpret, ‘Hegel believed that x is greater than five’ with bindable ‘x’, as ‘x is such that Hegel believed it to be greater than five’ which is modeled on (8). Similarly, ‘Hegel believed that x is greater than y’ is now read as, ‘x and y are such that Hegel believed the former to be greater than the latter’. (8) itself could be rendered as, ‘\(\exists \) x[x = nine & Hegel believed that x is greater than five]’, and still not be a logical consequence of (5).
The reader will recognize that I have incorporated, without reference, many themes upon which Quine has harped, and that I have not attempted to make my agreement with him explicit at each point at which it occurs. Suffice it to say that the agreements far outweigh the disagreements, and that in both the areas of agreement and of disagreement I have benefited greatly from his writings.
See especially the end of ‘Three Grades of Modal Involvement’. I am informed by scholarly sources that Aristotelian essentialism has its origin in ‘Two Dogmas of Empiricism’. It reappears significantly in ‘Reply to Professor Marcus’, where essential properties of numbers are discussed, and in Word and Object, p. 199, where essential properties of persons are discussed. I will later argue that the two cases are unlike.
In ‘A Formulation of the Logic of Sense and Denotation’.
See Meaning and Necessity, Section 9, for the discovery of the explicandum, and Section 40 for the discovery of the explicans.
See ‘On Sense and Reference’ pp. 58, 59 in Translations from the Philosophical Writings of Gottlob Frege.
The acute reader will have discerned a certain similarity in function, though not in foundation, between the Frege quotes and another familiar quotation device.
These parallels are exhibited at some length in my dissertation Foundations of Intensional Logic.
A drawback to this position is that the resulting correct applications of Leibniz’ Law are rather unexciting. More interesting intermediate entities can be obtained by taking what Carnap, in Meaning and Necessity calls ‘intensions’. Two expressions have the same intension, in this sense, if they are logically equivalent. Other interesting senses of ‘intension’ might be obtained by weakening the notion of logical equivalence to logical equivalence within sentential logic, intuitionistic logic, etc. Church suggests alternatives which might be understood along these lines.
I have approximately followed the notational devices used by Quine in ‘Quantifiers and Propositional Attitudes’. Neither of us recommend the notation for practical purposes, even with the theory as is. An alternative notation is suggested in note 3 above.
Also, see Word and Object, p. 211, for an implicit use of exportation.
The ‘nearly’ of ‘nearly analytic’ is accounted for by a small scruple regarding the logic of singular terms. If a language L containing the name ‘tyFy’ is extended to a metalanguage L’ containing the predicate ‘Δ’ for denotation-in-L and also containing the logical particles, including quotes, in their usual meaning, then I regard \([\exists xx = \iota yFy \to \Delta ('\iota yFy',\iota yFy)]\) as fully analytic in L’. My reasons for thinking so depend, in part, on my treatment of quotation names as standard names, for which see Section VIII below. I am being careful, because Quine suggests disagreement in an impatient footnote to ‘Notes on the Theory of Reference’ (I am grateful to Furth, who recalled the footnote.) I do not know whether our disagreement, if a fact, is over quotation or elsewhere. The whole question of analyticity is less than crucial to my line of argument.
For a recent expression see Word and Object, Section 41.
The same difficulty was noticed, independently, by John Wallace and reported in a private communication.
Quoted from the end of Quine’s ‘Reply to Professor Marcus’. I fully agree with Quine’s characterization of the case, though not with the misinterpretation of Church’s review of ‘Notes on Existence and Necessity’ from which Quine’s characterization springs.
See the discussion of what Carnap calls L-determinateindividual expressions in Meaning and Necessity, Section 18, and also Tarski’s discussion of what he calls structural descriptive names in ‘The Concept of Truth in Formalized Languages’, Section 1.
The latter wonder is not to be confused with an ontological anxiety concerning the nature of nine, which is more appropriately expressed by dropping the word ‘number* in the wonder description.
Benacerraf so concludes in ‘What Numbers Could Not Be’.
The present discussion of standard names is based on that in the more technical environment of my dissertation, pp. 55–57.
Given this understanding of Nec, it is interesting to note that on certain natural assumptions ‘Δn(α,y)’ is itself expressed by ‘Nec(\(\left| \!{\overline {\, {} \,}} \right. \)α = x\(\left. {\overline {\, {} \,}}\! \right| \), y)’.
Note that an attempt to identify the object perceived in terms of resemblance with the perception rather than in terms of the causal chain leading to the perception would seriously distort an account of misperception
The corresponding principle for determining who it is that a given proper name, as it is used by some speaker, names, was first brought to my attention by Saul Kripke. Kripke’s examples incorporated both the indirect path from person named to person naming and also the possible distortions of associated descriptions. The existence of a relatively large number of persons with the same proper name gives urgency to this problem even in mundane settings. In theoretical discussions it is usually claimed that such difficulties are settled by “context”. I have recently found at least vague recognition of the use of genetic factors to account for the connection between name and named in such diverse sources as Henry Leonard: “Probably for most of us there is little more than a vaguely felt willingness to mean… whatever the first assigners of the name intended by it.” (An Introduction to Principles of Right Reason, section 30.2), and P. F. Strawson: “[T]he identifying description… may include a reference to another’s reference to that particular… So one reference may borrow the credentials… from another; and that from another.” (Individuals, footnote 1, page 182). Though in neither case are genetic and descriptive features clearly distinguished. Kripke’s insights and those of Charles Chastain, who has especially emphasized the role of knowledge in order to establish the desired connection between name and named, are in large part responsible for the heavy emphasis I place on genetic factors.
Although it is useful for scholarly purposes to have a catalogue of such “fallacies” (such as that provided in Carney and Scheer, Fundamentals of Logic), the value of such discussions in improving the practical reasoning of rational beings seems to me some-what dubious. A sensitive discussion of a related form of argument occurs in Angell, Reasoning and Logic, especially pp. 422–423.
Such failures may also be due to self-deception, an inaccurate self-concept, but then the purported object does not exist at all.
Insofar as I understand Hintikka’s ‘Individuals, Possible Worlds, and Epistemic Logic’, the domain of values of the bound variables fluctuates with the placement of the bound occurrences of the variables. If, in a quantifier’s matrix, the occurrences of the variable bound to the quantifier fall only within uniterated epistemological contexts, then the variables range over possible(?) individuals “represented” by vivid names. If, on the other hand, no occurrences of the variable fall within epistemological (or other opaque) contexts, then the variables range over the usual actual individuals. And if the variable occurs both within and without an epistemological context, then the values of the variables are inner individuals which are also actual. Thus if Ralph believes in Santa Claus, and σ is Ralph’s vivid Santa Claus description, Hintikka would treat ‘\(\left| \!{\overline {\, {} \,}} \right. \)Ralph believes that σ = Santa Claus\(\left. {\overline {\, {} \,}}\! \right| \)’ as true and as implying ‘\(\exists \)x Ralph believes that x = Santa Claus’, but would treat’\(\exists \) x[x = Santa Claus & Ralph believes that x = Santa Claus]’ and presumably ‘\(\exists \)x[\(\exists \) yy = xRalph believes that x = Santa Claus]’ as false, and not as consequences of ‘\(\left| \!{\overline {\, {} \,}} \right. \)σ = Santa Claus & Ralph believes that σ = Santa Claus\(\left. {\overline {\, {} \,}}\! \right| \).
I disregard precognition explained by a reverse causal chain.
We might say in such cases that the name specifies its denotation, in the sense in which a set of specifications, though not generated by the object specified, is written with the intention that there is or will be an object so described.
One such weakened notion of representation is that expressed by ‘Ralph Bel (\(\left| \!{\overline {\, {} \,}} \right. \)α = x \(\left. {\overline {\, {} \,}}\! \right| \), y)’ analyzed as in (44) using our current R, which here, in contrast to the situation for ΔN (see reference 22 above), is not equivalent to ‘R(α, y, Ralph)’. Still this new notion of representation, when used in place of our current R in an analysis of the form of (44), leads to the same relational sense of belief.
Note especially the “secret identity” genre of children’s literature containing Superman, Batman, etc.
At least one author, Hintikka, has seemed unwilling to allow Ralph a belief about Ortcutt merely on the basis of Ralph’s few glimpses of Ortcutt skulking around the missile base. See his ‘Individuals, Possible Worlds, and Epistemic Logic’, footnote 13.
Another way out is to accept the fact that two names may represent the same person to Ralph though Ralph believes the non-identity, but to put an ad hoc restriction on exportation. For example to analyze (33) as: ‘\(\exists \)α[R(α, Ortcutt, Ralph) & Ralph B \(\left| \!{\overline {\, {} \,}} \right. \)α is a spy\(\left. {\overline {\, {} \,}}\! \right| \)] & ~ \(\exists \)α[R(α, Ortcutt, Ralph) & ~ Ralph B \(\left| \!{\overline {\, {} \,}} \right. \)α is a spy\(\left. {\overline {\, {} \,}}\! \right| \)]’. This prevents exportation where contradiction threatens. But again much that we would like to say is inexpressible in Quine’s nomenclature.
It should be noted that in Church’s ‘On Carnap’s Analysis of Statements of Assertion and Belief’ serious objections are raised to even the first step.
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Kaplan, D. (1969). Quantifying In1 . In: Davidson, D., Hintikka, J. (eds) Words and Objections. Synthese Library, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1709-1_14
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