Abstract
At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part of the misleading material mode of speech, and as such dismissed, rather than addressed, ontological problems. Central to the analysis in the present paper is the concept of an explication, which was seen by both Carnap and Quine as being of great philosophical importance. It will be shown that the concept of explication played a significant role in how each formulated their mature position on ontology. Both these final positions on ontology can also be seen as a evolving in reaction to Carnap’s flawed handling of ontological matters at the time of Syntax. Carnap, influenced by Tarski’s work on semantics, comes to believe that the concept of reference can be given an acceptable explication, and that by doing so we can see reference to abstract objects as unobjectionable. As a result, Carnap develops a position very different from the one presented in Syntax. Quine strongly rejected the instrumentalism of Syntax, and sought to give an explication of ontological questions that was language independent. This paper closes with a discussion of each’s understanding of the other’s position.
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Notes
- 1.
The present paper, although independent, is something of a sequel to my paper “On the Quinean-Analyticity of Mathematical Proposition” [17]. In my earlier paper I look at how the positions of Carnap and Quine on analyticity are related to their views on explication. In that paper I had to purposefully ignore their debate on ontology in order to focus on their views on analyticity. This paper is meant to do the opposite—analyticity will be considered only where it is necessary to consider it in order to understand their respective positions on ontology.
- 2.
In a footnote to §56 of Word & Object, Quine writes ‘It was indeed I, if I may reminisce, who in 1934 proposed ‘material mode’ to him as a translation of his German.’
- 3.
Sections with letters affixed to the numbers were prepared for the original German edition but not included for lack of space.
- 4.
For simplicity I am avoiding discussing relations and functions.
- 5.
Despite the 1963 publication date, most of the material for the Schilpp volume on Carnap was written in the mid-1950s. This is still, of course, much later than Syntax.
- 6.
Since what characterizes a coordinate language is that elements of the domain are picked out in some systematic way, there is no reason why we would be limited to countable domains. We might pick out the objects in some domain systematically using real numbers or ordinals for instance.
- 7.
[4] §39 discusses which theses of Syntax need to be altered in light of of developments in semantics. His general outlook here is that, on the whole, the various theses in Syntax, including discussions of the material mode of speech and of quasi-syntactic sentences “remain valid” but ought to be “supplemented by the corresponding semantical discussions”. This is an unstable position, given the material mode of speech is predicated on the elimination of the notion of reference, and the notion of quasi-syntactic depends on the obsolete notion of a syntax language.
- 8.
See [14] for an early argument to this effect.
- 9.
This would, then, have included the sections of Syntax prepared for the original German edition but not included for lack of space.
- 10.
Carnap does talk of explication as a two stage process. We begin by clarification of the explicandum, and then we provide the explicatum. But in the second stage we are in no way bound by what is identified in the first stage.
- 11.
Preprints of this paper were made available, and the paper was to be included in volume 9 of Erkenntnis, but the journal ceased publication before volume 9 was produced.
- 12.
[13] is an interesting review of this work of Quine’s. This work hints at the nominalist project, and Church already sees its demise. Church writes “Apparently it is hoped that an adequate formalized language may be devised in which all abstract nouns are syncategorematic, and the tenability of the nominalistic position thereby demonstrated.
It would seem, however, that such a demonstration of the tenability of the nominalistic position must be at the same time a demonstration of its extreme artificiality. In the opinion of the reviewer, the effect is only to emphasize the illusory character of the question whether abstract nouns really have designata. For the matter is relative, on the present showing, not only to the choice of a particular language, but also the choice as to which particular notation or notations in the language shall be regarded as denoting the existential quantification (the syntax of the language will ordinarily not determine the latter choice uniquely).”
- 13.
Of course, Quine does not think it worthwhile to go through a detailed study of how metaphysicians have used the term to show that this is in fact the case.
- 14.
Concerning Frege’s explication of number Carnap writes “Before Frege, nobody was able to give an exact account of the meanings of [arithmetical] words in non-arithmetical terms. By Frege’s explication of the numerical words, which I regard as one of the greatest philosophical achievements of the last century, the logical connection between these words and logical particles like “there is”, “not”, “or”, and “the same as” became completely clear for the first time. Therefore we have to say that in spite of practical skill in usage, people in general, and even mathematicians before Frege, were not completely clear about the meaning of numerical words.” [11, p. 935, my italics]
- 15.
If the metalanguage does not contain the object language, but contains a translation of the object language, this condition must be adjusted accordingly.
- 16.
There are differences, however, between Carnap and Frege’s definition. Carnap defines the numbers as classes of the second level. It is also worth noting that Carnap is now aware that the definitions depend on a standard interpretation of the higher level quantifiers.
- 17.
Quine, as is well known, makes a lot out of Carnap’s use of ‘analytic’ in the above quote. But Carnap could have equally used the term ‘provable’ here instead of ‘analytic’.
- 18.
Of course, one might say say that because of the need for a standard interpretation of higher order logic, one cannot be sure to have completely unambiguously defined the numbers. But whatever one’s views on higher order quantification, one cannot deny that, at least with impressive clarity, we can define such a system.
- 19.
According to an explication of our arithmetical vocabulary, and an explication of our semantic vocabulary as it applies to our system of arithmetic, numbers exist and numerical terms refer. Carnap does not take this position to amount to platonism. Platonism would involve asserting that numbers exist and numerical terms refer, in an unexplicated sense of ‘exist’ and ‘refers’ (technically, in giving an explication of our arithmetical vocabulary we do not explicate existence, but show the connection between logical notions like existential quantification and our arithmetical vocabulary—see Footnote 14).
- 20.
Howard Stein briefly makes a similar point about external questions being questions concerning the correctness of an explication (see [32] p. 280).
- 21.
Carnap discusses the axiom of infinity in §37e of [8]. Here he says that it can either be taken as a primitive sentence—an axiom, or taken as a rule in the meta-language that makes the assertion of the existence of infinitely many objects L-true. It is clear from here (and from [10] pp 47–48) that Carnap never had a definitive position on the axiom of infinity, but thought that under the proper interpretation it should count as analytic.
- 22.
For further discussion of Quine’s views on set theory and higher order logic see [31].
- 23.
That Quine, more than 20 years after the publication of Meaning & Necessity, still took Carnap to be defending a version of his thesis that philosophical confusion results from the use of universal words, is reason to suspect Quine never reread the published version to see how Carnap responded to his comments on the early draft.
References
Beth, E.W. 1963. Carnap’s views of the advantage of constructed language systems over natural language in the philosophy of science. In The philosophy of Rudolf Carnap, vol. XI of the library of living philosophers, ed. P.A. Schilpp, 469–502. LaSalle: Open Court.
Carnap, R. 1934/1937. The logical syntax of language. London: Routledge & Kegan Paul.
Carnap, R. 1939/1955. Foundations of logic and mathematics. In International encyclopaedia of unified science, ed. O. Neurath, R. Carnap, and C. Morris. Chicago: University of Chicago Press, combined ed.
Carnap, R. 1942. Introduction to semantics. Cambridge: Harvard University Press.
Carnap, R. 1945. The two concepts of probability: The problem of probability. Philosophy and Phenomenological Research 5(4): 513–532.
Carnap, R. 1947/1956. Meaning and necessity: A study in semantics and modal logic, 2nd ed. Chicago/London: University of Chicago Press.
Carnap, R. 1950. Logical foundations of probability. Chicago: University of Chicago Press.
Carnap, R. 1958. Introduction to symbolic logic and its applications. New York: Dover. Revised english translation ed.
Carnap, R. 1963a. E. W. Beth on constructed language systems. In The philosophy of Rudolf Carnap, vol. XI of library of living philosophers, ed. P.A. Schilpp, 927–932. La Salle: Open Court.
Carnap, R. 1963b. Intellectual autobiography. In The philosophy of Rudolf Carnap, vol. XI of library of living philosophers, ed. P.A. Schilpp, 927–932. La Salle: Open Court.
Carnap, R. 1963c. P. F. Strawson on linguistic naturalism. In The philosophy of Rudolf Carnap, vol. XI of library of living philosophers, ed. P.A. Schilpp, 933–940. La Salle: Open Court.
Carnap, R. 1963d. W.V. Quine on logical truth. In textitThe philosophy of Rudolf Carnap, vol. XI of library of living philosophers, ed. P.A. Schilpp, 915–922. La Salle: Open Court.
Church, A. 1939. Review of W.V.O. Quine’s ‘A logistical approach to the ontological problem’. The Journal of Symbolic Logic 4(4): 170.
Creath, R. 1990. The unimportance of semantics. In Proceedings of the 1990 biennial meeting of the philosophy of science association, East Lansing, vol. 2, ed. M.F.A. Fine and L. Wessels.
Goodman, N., and W.V. Quine. 1947. Steps toward a constructive nominalism. The Journal of Symbolic Logic 12(4): 105–22.
Lavers, G. 2004. Carnap, semantics and ontology. Erkenntnis 60(3): 295–316.
Lavers, G. 2012. On the Quinean-analyticity of mathematical propositions. Philosophical Studies 159(2): 299–319.
Lavers, G. 2015. Carnap on abstract and theoretical entities. Ontology after Carnap. Prepared for: ed. S. Blatti and S. Lapointe. Oxford: Oxford University Press.
Quine, W.V.O. 1939/1976. A logistical approach to the ontological problem. In The ways of paradox and other essays, 107–32. Cambridge: Harvard University Press.
Quine, W.V.O. 1951/1963. Two dogmas of empiricism. In From a logical point of view, 20–46. New York: Harper & Row.
Quine, W.V.O. 1951/1976. Carnap’s views on ontology. In The ways of paradox and other essays, 203–211. Cambridge: Harvard University Press.
Quine, W.V.O. 1960. Word and object. Cambridge: MIT.
Quine, W.V.O. 1963. Carnap and logical truth. In The philosophy of Rudolf Carnap, vol. xi of library of living philosophers, ed. P.A. Schilpp, 385–406. La Salle: Open Court.
Quine, W.V.O. 1966/1969. Existence and quantification. In Ontological relativity and other essays, 91–113. New York: Columbia University Press.
Quine, W.V.O. 1969a. Epistemology naturalized. In Ontological relativity and other essays, 69–90. New York: Columbia University Press.
Quine, W.V.O. 1969b. Ontological relativity. In Ontological relativity and other essays, 26–68. New York: Columbia University Press.
Quine, W.V.O. 1970/1976. Homage to Carnap. In The ways of paradox and other essays, 40–43. Cambridge: Harvard University Press. Revised and enlarged edition ed.
Quine, W.V.O. 1976. The ways of paradox. In The ways of paradox and other essays, 1–18. Cambridge: Harvard University Press.
Quine, W.V.O., and R. Carnap. 1990. Dear Carnap, Dear Van: The quine-carnap correspondence. Berkeley: University of California Press.
Quine, W.V.O., and J.S. Ullian. 1970/1978. The web of belief, 2nd ed. New York: Random House.
Shapiro, S. 1991. Foundations without foundationalism. Oxford: Oxford University Press.
Stein, H. 1992. Was Carnap entirely wrong after all? Synthese 93(1–2): 275–95.
Acknowledgements
“I would like to thank Eliot Michaelson for reading a draft of this paper and offering comments. I would also like to thank Richard Creath for helping on one particular point.”
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Lavers, G. (2015). Carnap, Quine, Quantification and Ontology. In: Torza, A. (eds) Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language. Synthese Library, vol 373. Springer, Cham. https://doi.org/10.1007/978-3-319-18362-6_13
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