Abstract
In the third chapter several ontological reductions and eliminations that Quine carried out were sketched. Attention was paid to the objects that survived the reductions, i.e. sets and physical objects, and to their criteria of identity. The notion ‘reduction’ itself was taken at face value. Quine, however, did not disregard the problems related to this notion. Ontological reduction is closely related to Quine’s famous and notorious tenet of ontological relativity or inscrutability of reference.’ The reader will have noted that for the ontological reductions in the third chapter the interchange of reductans and reductum is inconsequential. What is important is that objects can be clearly identified, or located in a structure, not what the objects are an Sich.
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Notes
In Quine 1990b, 6, Quine stated that there is no distinction between these two terms. In the title of the text the inscrutability is called an indeterminacy. In later texts Quine coined the new term “indeterminacy of reference”, see Quine 1994c, 495, or Quine 1995a, 73.
Quine’s ontological relativity and inscrutability of reference have been heavily discussed, see Douven 1999, Vergauwen 1999, Orenstein 1997; Nelson 1996; Reynolds 1994; Zabludowski 1989; Elder 1988; Welch 1984; Davidson 1984; Grünfeld 1981; Du Toit 1979; Cornman 1976; Loux & Solomon 1974; Teller 1973; Greenlee 1973; Thompson 1972; Field 1972; Thomason 1971. The themes dealt with in section 2–4 have received almost no attention.
The relativity of ontology to the provincial apparatus of individuation was earlier expressed in “Speaking of objects”, see Quine 1969a, 6. This text from 1957 was an intermediate presentation of his preparation of Quine 1960. A still earlier occurrence of the lingering ideas is in Quine 1953c, 105–107. Quine 1953c is a compilation of various texts written between 1939 and 1947.
Quine 1960, 29.
See Quine 1960, 68; Quine 1969a, 89.
Quine 1960, 51.
The indeterminacy of translation does not apply to grammar or syntax. In Quine 1960, 53; 73, it was already stated that the net output does not change if the linguist uses different grammatical categories. The grammarian’s task is to provide a recursive characterisation of the string of a language, and this is no real problem for the linguist. The linguist may come up with different syntactic structures, but the net output will remain unaltered. Nevertheless, some readers have misinterpreted Quine. Quine is more explicit in Quine 1990a, §19; Quine 1987c, 10, and in Quine 1990b, 5. The indeterminacy of translation of pronouns and other referential devices only involved the equation of certain foreign locutions to these devices. The difference will only be verbal or will involve the choice of one syntactical structure over another. Neither does the indeterminacy of translation extend to the logical connectives of propositional logic, i.e. negation, conjunction and alternation, see Quine 1960, 57; Quine 1969a, 103–104; Quine 1970a, 82; Quine 1990a, 82. The fact that a decision procedure exists is relevant here, see Quine 1960, 60. Moreover, if quantification is envisaged substitutionally, then there are “behavioral criteria of translation” for it, see Quine 1969a, 104–105.
In Quine 1960, ontology is relative to the English syntax. One could also consider the relativity of ontology to the syntax of the logic of quantification. Instead of looking at different languages, one considers different logical systems. In chapter 1.2 it was already pointed out that combinatorial logic has ontological commitment. Deviant logics have ontological commitment if their logical connectives can be translated into the connectives of standard quantificational logic. See Quine 1953c, 105: “the quantificational form is a convenient standard form in which to couch any theory. If we prefer another language form, for example, that of combinators, we can still bring our criterion of ontological commitment to bear in so far as we are content to accept appropriate systematic correlations between idioms of the aberrant language and the familiar language of quantification.”
Quine 1960, 53; see also o.c. 61; 80.
There may be problems with the notion of language, see Quine 1960, 214: “What are languages, and when do they count as identical or distinct?”; Quine 1969a, 142: “A trouble with the individuation a language is that it… has been given no satisfactory principle of individuation.” This problem will not directly be taken into account in this section. See also Cutrofello 1992.
In `The problem of meaning in linguistics“, Quine wrote that the perception of bodies is universal, see Quine 1953b, 61–62: ”What provides the lexicographer with an entering wedge is the fact that there are many basic features of men’s ways of conceptualizing their environment, of breaking the world down into things, which are common to all cultures.“
Quine 1969a, 35: “Reference itself proves behaviorally inscrutable.”
Quine 1969a, 29–35.
Quine 1969a, 30.
Quine 1969a, 30.
Quine 1969a, 33. Analytical hypotheses were introduced in Quine 1960, 68: “[The linguist] segments heard utterances into conveniently short recurrent parts, and thus compiles a list of native ”words“. Various of these he hypothetically equates to English words and phrases, in such a way as to conform [some given conditions]. Such are his analytical hypotheses,as I call them.”
Quine 1969a, 35–38.
See Quine 1960, 79.
Quine 1969a, 35.
Quine 1969a, 39.
Quine 1969a, 46.
Moreover, it is of no avail to suppose that each person has his own apparatus of individuation and his own ontology. This would be at odds with Quine’s demand that language is not private, see Quine 1969a, 47.
In Quine 1974, Quine wavered between the two views on the home language, see o.c., 8384.
Quine 1990b, 6. The passage is repeated in Quine 1990a, 51–52.
Quine’s views on reference and ontology are profoundly influenced by Tarski’s theory of truth. Quine portrays the theory in Quine 1953a, 130–138; Quine 1970a, chapter 3; Quine 1990a, §35.
Quine 1994c, 495. Also in Quine 1990a, 31–32; Quine 1995a, 72–73; Quine 1997, 573574, and Quine 1998, 31 only the proxy function argument is mentioned.
Reprinted in Quine 1966a, 212–220. Just before the introduction of proxy functions Quine added a footnote (fn 5) in which he said that he had repeated a lecture from 1954 until that point, but that the rest of the paper was new. The strategy was already explained in “The scope and language of science”, a text from 1954, see Quine 1966a, 243.
Quine 1966a, 217–218. In Quine 1981c, Quine stresses the fact that the proxy function should be expressible or defmable in the metalanguage. The proxy function is not necessarily a real function, but can be an ontologically neutral virtual functions, see Quine 1969a, 57; Quine 1981c, 234.
Quine 1966a, 219.
Ibid.
Quine 1969a, 58.
See Quine 1966a, 220.
The account of ontological relativity in Quine 1969b draws heavily on the idea of proxy functions. The argument appears more neatly in Quine 1981a, 19–20; Quine 1983b, 421; Quine 1984a; Quine 1985b, 171; Quine 1987b, 134–135; Quine 1990a, 31–33; Quine 1995a, 71–73, Quine 1995b, 258–260.
See Quine 1981a, 19; Quine 1983a, 500; Quine 1995a, 72. In Quine 1990a Quine writes that one can waive the condition, because one might want to treat expressions and their Gödel-numbers alike and assign them a single proxy, and at the same time make a distinction between the two in one’s global theory of things. In Quine’s basic strategy however the one-to-one restriction remains.
See Resnik 1996, 132: “We can summarize the logical heart of the argument from proxy functions in a familiar, and easy, theorem which states that any set of first-order sentences (with or without identity) that has a model (true interpretation) in one domain has a model in a domain of the same size. I like to call this the Same Size Theorem.” Resnik extends the use of the theorem to languages that are richer than first-order ones.
Quine 1969a, 57; see also Quine 1987a, 84; Quine 1990a, 32, Quine 1995a, 73.
See Quine 1981a, 16; Quine 1987b, 130; Quine 1995a, 73.
Quine 1990b, 6.
Quine 1981a, 19.
Quine 1995a, 71.
Quine 1990b, 6. Quine speaks of an illustration rather than of an argument. I have shown in the previous pages that there is indeed an argument for ontological relativity based on the indeterminacy of translation in Quine’s writings. Quine became less convinced that this was indeed a good argument, hence the phrase “illustrates”.
Quine 1969a, 48.
See Quine & Pivcevic 1988, 5: “At one stage, ontology seemed to me central to philosophy; what there is, and what being means. In later years I came to see that ontology, the positing of objects of one sort or another, is secondary to the relating of scientific theory to the stimulation of our sensory receptors.”
Early on Quine had recognised that ontology is dependent on the standard logic, and that standard logic can be given up. For example, his first logistics were even not yet expressed in this quantificational form. After having acquiesced in quantificational logic Quine was sceptical of deviant logics of which the ontological commitments were not clear, see Quine 1953c, 105; Quine 1970a, 80–94.
Quine 1990a, 36. See similar remarks in Quine 1969a, 24–25; Quine 1970a, 89.
See Quine 1995a, 74–75: “I conclude from it that what matters for any objects, concrete or abstract, is not what they are but what they contribute to our overall theory of the world as neutral nodes in its logical structure.”
There is some disagreement between modem structuralists whether this distinction should be maintained. Shapiro thinks there is a difference, see Shapiro 1997, 10: “Clearly, there is an intuitive difference between an object and a place in a structure — between an office and an officeholder.” For Resnik objects only exist as places in a structure, see Resnik 1997, 4–5: “Mathematical objects are featureless, abstract positions in a structure…”
Quine 1992, 8; for similar remarks see Quine 1969a, 44; Quine 1983a, 500; Quine 1987b, 137.
In Quine 1992, 9 there is a discussion of the relation between global structuralism and naturalism.
See Quine 1981a, 19.
Quine 1981a, 19.
Quine 1976a, 503.
Quine 1979a, 166.
See Quine 1979a, 166: “The physical-state predicates are the predicates of some specific lexicon, which I have only begun to imagine, and which physicists themselves are not ready to enumerate with conviction.”
Quine 1979a, 501.
Quine 1995a, 91.
Quine 1979a, 503.
Barrett & Gibson 1990, 161: “Among his hundreds of papers on logic, there is not one dealing with model theory. For instance, in set theory, Quine has concentrated on such things as different axiom systems, the role of existence assumptions, etc. He has not paid any attention to what might be called the model theory of set theory.”
See the next section.
Quine 1987a, 127.
See Quine 198la, 174: “Models afford consistency proofs; also they have heuristic value; but they do not constitute explication. Models, however clear they be in themselves, may leave us still at a loss for the primary, intented interpretation.”
Quine 1950a, 33.
Quine 1950a, 114–115. See also Quine 1970a, 51–53. Quine here explicitly places model theory within set theory.
See Quine 1963, 10, 14. In this work Quine mentions some result of model theory, namely the use of inner models, see o.c., 234, or nonstandard models, see o.c. 305. Furthermore, a similar definition of a model is given in Quine 1991 a, 225.
The word interpretation is used in a different sense, namely in the way Davidson uses the term, see Quine 1995a, 80–81. However, the word reinterpretation appears in the index and appears in the context of the proxy function argument.
Quine 1960, 273; Quine 1966a, 115–117; Quine 1987a, 63–67; Quine 1995a, 55.
Quine 1960, 273. Quine quoted Russell’s Mysticism and Logic and Other Essays.
Quine 1981a, 149.
See Quine 1981a, 151.
Quine 1981a, 150.
Quine 1974, 114.
This theme will be more fully elaborated in the first section of the next chapter.
Quine 1969a, 50.
Quine 1969a, 49. In Quine 1974, 44–45, Quine tries to immunise the problems related to pointing.
See Quine 1960, 255.
Quine 1969a, 48.
See Quine 1969a, 50: “In the language of the theory there are predicates by which to distinguish portions of this universe from other portions, and these predicates differ from one another purely in the roles they play in the laws of the theory.”
Quine 1969a, 51.
Quine 1969a, 68.
It is not sure that one could do any better than Quine has done. The regress of interpretations is not easily blocked. It is possible that one has to acquiesce in a counterintuitive end of the regress. In his recent work on philosophy of mathematics Shapiro uses a similar trick. The regress is ended by means of a “U-language”. This term was coined by Haskell Brooks Curry, see Shapiro 1997, 51: “the communicative language which is mutually understood by speaker and hearer. I shall call this language the U-language, i.e.; the language being used”.
Some inconveniences of the Löwenheim-Skolem theorem have been blown up to apocalyptic proportions by Putnam. For the most convincing paper see Putnam 1983.
Quine 1950a, 209.
Quine mentioned the constructive improvement of Hilbert and Bernays, see Quine 1950a, 211; Quine 1970a, 54. These authors have shown that for any consistent schema a true interpretation in the universe of integers can be found, and in the purely arithmetic vocabulary of elementary number theory.
Quine had ten years earlier, in 1954, already written the paper “Interpretations of sets of conditions”, in which he gave a proof of the theorem. The paper is reprinted in Quine 1966b, 205–211.
In his sermon at the end of “Is there a problem about substitutional quantification”, Kripke gives this criterion as an example of formal criteria without philosophical backing, see Kripke 1976, 411. Quine protests, see Quine 1981a, 175. See also Chihara 1973, 120–137.
Quine 1966a, 219. In Quine 1969a, 60–61, Quine is more explicit about this impossibility: “If the background theory assumes the axiom of choice and even provides a notation for a general selector operator, can we in these terms perhaps specify an actual proxy function embodying the Löwenheim-Skolem argument? The theorem is that all but a denumerable part of an ontology can be dropped and not missed. One could imagine that the proofs proceeds by partitioning the universe into denumerably many equivalence classes of indiscriminable objects; such that all but one member of each equivalence class can be dropped as superfluous; and one would then guess that where the axiom of choice enters the proof is in picking a survivor form each equivalence class. If this were so, then with the help of Hilbert’s selector notation we could indeed express a proxy function. But in fact the Löwenheim-Skolem proof has another structure. I see in the proof even of the strong Löwenheim-Skolem theorem no reason to suppose that a proxy function can be formulated anywhere that will map an indenumerable ontology, say the real numbers, into a denumerable one.”
Quine 1974, 114–115.
For an easy proof see Boolos & Jeffrey 1989, 151–152.
Quine 1974, 115.
The paper was first drafted in 1951 for Journal of Symbolic Logic, and was reprinted in Quine 1966b, 114–120. The paper begins with the Rosser’s result that in NF the axiom of infinity is equivalent to 00 Nn, for which there was not yet a proof in NF. This leaves open the option that NF can be strengthened by adding its negation. In NF all the natural numbers differ from the empty set, and yet the empty set is a member of the natural numbers. This was the m-inconsistency that triggered Quine’s discussion.
Quine 1966b, 117.
Quine 1966b, 118. This word “translation” is used. The paper antedates Word and Object by some years, but on the other hand Quine did not withdraw its conclusions and mentioned it in “Ontological relativity”, fn 16. One cannot conceive that indeterminacy of translation could apply to it without spoiling the argument.
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Decock, L. (2002). Ontological Relativity. In: Trading Ontology for Ideology. Synthese Library, vol 313. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3575-9_5
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