Abstract
This essay defends the neo-Quinean approach to ontology against the criticisms of two neo-Carnapians, Huw Price and Amie Thomasson.
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Notes
See Carnap (1950) and Quine (1951). An earlier version of Quine’s paper was presented at a meeting of the Philosophical Seminar of the University of Chicago in 1951, a meeting at which Carnap was also present. Both papers have been reprinted many times. They are reprinted together in Feigl et al. (1972, pp. 585–601).
For a discussion of the expressive advantages gained by having an unlimited supply of all-purpose third-person-singular pronouns at one’s disposal, see Van Inwagen (1998), pp. 238–240 in particular. This essay is reprinted in Van Inwagen (2001); the relevant passage is on pp. 19–21 in the reprinted version.
By a ‘volume’ we understand what is normally called a non-0 volume—thus, the volume of a point-mass, as we are using ‘volume’, is not “0” or “0 cubic centimeters” or “0 cubic light-years”; rather a point-mass does not have a volume (in the present sense) at all. My only purpose in giving ‘volume’ this non-standard sense is to simplify the statement of the argument.
Expressions like ‘the mass of x in grams’ are open terms. The validity of the inference of (5) from (3) and (4) is comparable to the validity of the inference of ‘\(\exists x x\) is bald’ from ‘\(\exists x\) (x is a woman & the father of x is bald)’. (I take “free logic” not to be “ordinary textbook quantifier logic.”)
Here’s a little exercise in X-phi. Give a statistically significant number of high-school physics teachers a true-false test. Include among the statements to be marked ‘T’ or ‘F’ the statement ‘The average density in grams per cubic centimeter of an object of non-0 volume is equal to its mass in grams divided by its volume in cubic centimeters’. I predict that that statement will be marked ‘T’ by every one of them.
See Van Inwagen (2009).
See Price, p. 332 and Thomasson, pp. 63–69.
Note that the second occurrence of ‘nine’ in (7) can be replaced by ‘the number nine’—unambiguously a noun phrase—salva grammatica and the first cannot.
Translated into “philosophers’ English,” the first of the two offset sentences would read, ‘It is true of at least one thing that it is such that the Admissions Committee has it members and nine is an odd number’.
Note that there is no number z such that (e.g.) \(5 = z \times 0\); therefore, ‘5 / 0’ is an improper description.
More exactly: if the expression ‘y / z’ in the sentence ‘\(\forall x\, \forall y \,\forall z (x=y / z \rightarrow x\) is a number)’ is replaced by ‘the w such that (w is a number & \(y =w \times z)\)’, the resulting sentence is an instance of a theorem of logic.
See Schiffer (1996).
Or perhaps for semantical reasons? I suppose that a philosopher might decline to use ‘proposition’ and ‘property’ on the ground that these words were meaningless; such a philosopher might compare ‘If snow is white, then snow has the property of being white’ to ‘If snow is white, then snow is variably counter-tessalated’ and ‘There are no properties’ to ‘There are no variable counter-tessalates’.
Schiffer is fully aware of the problem posed by the falsity of such sentences and proposes a solution to it. (See Part IV of Schiffer.) I would summarize his solution as follows: the principle to which this note is attached is—in its full generality—a rule of English, or is at any rate endorsed by the rules of English. Therefore, the rules of English imply a contradiction. When this fact has become known to us, we need respond to this discovery only by taking care not to apply the rules in those cases in which they lead to a contradiction. Thomasson is also aware of the problem. Her solution is (in effect; I have translated it into it a form that applies to the principle to which this note is attached) to restrict the range of the variable ‘A’ to terms denoting concrete objects and the range of the variable ‘F’ to predicates whose extensions comprise only concrete objects. Her solution is thus both more precise and more stringent than Schiffer’s. His solution implies the thesis that the sentence ‘If wisdom is a possible property, then wisdom has the property of being a possible property’ is analytic (it seems evident that that thesis does not imply a contradiction), and hers does not. Thomasson does not explain why she “draws the line” where she does: she does not explain why her restriction on the ranges of ‘A’ and ‘F’ should be regarded as a principled restriction. (See Thomasson, pp. 258 and 262.)
Note that ‘If the property of being non-self applicable exists and wisdom is non-self-applicable, then wisdom has the property of being non-self applicable’ is true.
See, for example, Sect. 2 (“Linguistic Frameworks”) of Carnap (1950). (In Feigl, Sellars, & Lehrer, pp. 586–590). See, particularly, the sub-section “The system of numbers” (pp. 587–588).
I concede that there would be more to specifying the framework than writing out a set of axioms. One would certainly have to say something about how to relate the objects so “introduced” to numerical adjectives, to the number-words that are used to state the results of counting and measuring: ‘There are five sheep in the field’, ‘The area of Manhattan is 87.46 square kilometers’...I take it to be Carnap’s position that a person introducing the “numbers” framework would say things that implied that sentences like ‘The number 5 = the number of sheep in the field if and only if there are five sheep in the field’ were analytic within the framework.
That is, denotes the object “introduced” by the framework-analyticity of sentences like, ‘The number 0 = the number of sheep in the field if and only if there are no sheep in the field’.
That is, in the language whose vocabulary is the vocabulary of the axioms. The language of the framework also includes empirical predicates and terms (see the previous two notes).
For all she is the Laplacian Reckoner, she is not an infinite being: even she were able to determine the truth-value of any individual term of the infinite sequence, ‘F(0)’, ‘F(1)’, ‘F(2)’, ...(and no finite being would be), she would be unable to complete the “supertask” of determining the truth-value of every such sentence.
For example: “As has been shown, if the framework axioms are consistent, then neither ‘\(\forall x\mathbf{F}x\)’ nor its negation be deduced from those axioms. ‘\(\forall x\mathbf{F}x\)’ is, on its intended interpretation, either a true or a false statement about the natural numbers. If a universal statement in the framework language is a false statement about the natural numbers on its intended interpretation, its negation can be deduced from the framework axioms if they are true on their intended interpretations—since, in that case, for some numeral \(n,\ulcorner \sim \mathbf{F}n \urcorner \) can be deduced from the axioms. Therefore, if the framework axioms true on their intended interpretation (and hence consistent), ‘\(\forall x\mathbf{F}x\)’ is, on its intended interpretation, a true statement about the natural numbers: every natural number has the property expressed on that interpretation by ‘F’.”
See note 21.
The Putnam of the “Quine-Putnam Indispensability Argument” is the Putnam of Putnam (1971). Putnam later disowned the philosophy of quantification presupposed by the argument.
Colyvan (2015). This reference is to a later version of the article than the one Price cites, but the formulation of the argument is the same in both versions.
See note 28.
Note that Price, in reminding his readers of the content of (C), uses the phrase ‘believe that there are mathematical entities’—as opposed to ‘have ontological commitment to mathematical entities’. I can see no significant difference in meaning between ‘believe that there are mathematical entities’ and ‘affirm the existence of mathematical entities’.
Of course the conclusion of the TYNQUA is ‘There are numbers’ and not ‘You ought to believe that there are numbers’—but let that go.
I won’t mention the “rules” again. As far as I can see, the “rules” are simply the rules of logic and are not the special property of scientists.
The quoted words are Quine’s—see Quine (1948, p. 10).
Obviously this cannot be a complete statement of a method to be followed in metaphysics or ontology. If for no other reason, it tells the reader nothing about how to recognize a logical consequence of some set of propositions we “bring to our study of metaphysics” as a metaphysical proposition.
I expect that “the internal standards of everyday life” are closely related to what Thomasson refers to as “the usual straightforward kinds of empirical checks.” (Thomasson, p. 37).
This claim for the paraphrase contains the germ of the way Norma would reply to the arguments of William P. Alston’s classic paper Alston (1958): a philosophical paraphrase of a sentence need not have the same meaning as that sentence.
At this point in Carnap’s text, there is a footnote citing p. 708 of Quine (1939).
Carnap (1947–1956, p. 43). This passage is quoted in part by Thomasson, p 74.
The medieval nominalists and realists, incidentally, would have classified ‘nominalismus’ and ‘realismus’ as names of positions in logic, not metaphysics. (And by ‘logic’ they meant something like what a present-day philosopher would call ‘philosophical semantics’. See Parsons (2014).) C. S. Lewis, writing in that tradition, has said “The word realism has one meaning in logic, where its opposite is nominalism, and another in metaphysics, where its opposite is idealism.” (Lewis 1961, p. 57)
Goodman and Quine (1947).
Quine later attempted to distance himself from this “position statement.” He came very close to saying, “I didn’t really mean it.” See the “black rubric” added to the entry for “Steps toward a Constructive Nominalism” in the bibliography of Quine (1953), pp. 173–174. (It is there that the phrase ‘its appealingly forthright opening sentence’ occurs.)
As Walter Raleigh (the twentieth-century critic, not the Elizabethan adventurer) said, “If you talk nonsense in Saxon you are found out at once; you have a competent judge in every hearer. But put it into Latin and the nonsense masquerades as profundity of abstract thought.” (I have often seen this statement quoted, but I am unable to supply a citation.) Well, ‘to on’ is Greek and ‘existentia’ is Latin, but those inconvenient facts don’t weaken the essential applicability of Raleigh’s point to Carnap’s choice of words. (And do we not have it on good authority that “the ontological question...can be put in three Anglo-Saxon monosyllables.”?)
Carnap (1947–1956, pp. 43–44).
Thomasson quotes a longer passage of which it is a part (Thomasson, p. 68), and has gone so far as to italicize the sentence ‘However, the concept of existence here has nothing to do with the ontological concept of existence or reality’; presumably, therefore, she attaches special importance to it. Immediately following her quotation of the passage, she speaks of “that (nonontological) concept of existence [that Carnap accepts]”.
That is to say, I endorse the positions (propositions) the sentences (8) and (9) express in the context of utterance/inscription called “the ontology room.” See van Inwagen (2014a).
I do not deny that many ontologists would reject the thesis that sentences like, e.g, ‘Universals exist’ or ‘Universals have real existence’ or ‘Universals really exist’ or ‘Universals are among the constituents of reality’ or ‘Whatever else the world may contain, it contains universals’ mean no more than (differ only in rhetorical force from) ‘It is not the case that everything is not a universal’. Well, being an ontologist does inoculate one against meta-ontological error or semantical illusion.
Goodman (1956, pp. 35–36).
Goodman, p. 36: “...the nominalist recognizes no distinction of entities without a distinction of content.”
I do not know how to define ‘metaphysical principle’. But I insist that a metaphysical principle need not employ some recondite “ontological concept of existence or reality.” Goodman’s Distinction Principle, for example, could be formulated this way: \(\forall x\,\forall y\, \sim \) (\(x \ne y \) & \(\sim x\) and y differ in content).
This principle is modeled on a principle affirmed by the Eleatic Stranger; see Sophist, 247E.
I do not claim in this section to have presented an adequate characterization of what it is for a philosopher to affirm a metaphysical thesis. I claim only to have presented a sufficient condition for a philosopher’s having affirmed a metaphysical thesis.
Sorensen (2007).
This is not meant to be an exhaustive list of the features I believe a good philosophical paraphrase should have.
A metaphysician might offer a false shadow-neutral sentence as a shadow-neutral paraphrase of ‘There are opaque objects that cast shadows’ but that proposition would not be a shadow-neutral paraphrase of the “everyday” sentence: the everyday sentence is a “good” shadow-sentence, and a shadow-neutral sentence is a shadow-neutral paraphrase of a “good” shadow-sentence only if it is true.
For a much more elaborate treatment of the questions discussed in this section, see van Inwagen (2014a).
I am grateful to Amie L. Thomasson and three referees for Synthese for extremely helpful comments on drafts of this paper.
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van Inwagen, P. The neo-Carnapians. Synthese 197, 7–32 (2020). https://doi.org/10.1007/s11229-016-1110-4
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DOI: https://doi.org/10.1007/s11229-016-1110-4