Remarks on Christopher Hill s Thought and World. Anil Gupta University of Pittsburgh

Transcription

1 Remarks on Christopher Hill s Thought and World Anil Gupta University of Pittsburgh One of Christopher Hill s aims in his new book is to bring about what he alls a marriage of 1 heaven and hell. Hill proposes a way of joining together ideas about the onept of truth that are 2 often seen to be in irreonilable onflit: deflationism and the orrespondene theory. Hill s proposal, I want to suggest, is one that orrespondene theorists an happily aept. It is the deflationists that are likely to resist it. But I do not see in this any argument against Hill s elegant proposal. Hill s proposal works, essentially, by assigning separate domains to the onfliting parties: there are two notions of truth, and one is to be allotted to the orrespondene theorists and the 3 other to the deflationists. Both notions pertain to propositions or in Hill s preferred terminology, whih I shall follow, thoughts. Thoughts, as Hill oneives of them, are objets of attitudes suh as belief and desire. More speifially, they are logially strutured entities and have onepts as their fundamental onstituents. Both notions of truth have thoughts as their domain of appliation, but the two arve out this domain in different ways. The notion allotted to the orrespondene theorist all it orrespondene truth or truth may be defined as follows: (C) An objet x is true iff there is a state of affairs y suh that y is atual and x semantially 1 Thought and World: An Austere Portrayal of Truth, Referene, and Semanti Correspondene (Cambridge: Cambridge University Press, 2002). All parenthetial referenes are to the pages of this book. 2 See Marian David, Correspondene and Disquotation: An Essay on the Nature of Truth (Oxford: Oxford University Press, 1994). 3 I am departing from Hill s exposition in speaking of the two notions of truth. Hill reognizes only one notion of truth, the one allotted below to the deflationists (fn. 2, 145-6). But Hill does talk about our two notions of truth-onditions (116), and the notion I allot to the orrespondene theorists an be defined using onepts that Hill thinks are legitimate and important.

2 orresponds to y. 4 If we take fats to be atual states of affairs, then (C) yields the familiar formulation of the orrespondene theory: a thought is true iff it semantially orresponds to a fat. I should stress that the onepts of semanti orrespondene and state of affairs used in (C) are not the ones that 5 deflationists an onstrut out of their minimal resoures. States of affairs, as Hill oneives of them, are built out of objets and properties. And semantial orrespondene is in general a substantial relationship between oneptual stuff and extraoneptual reality. Hill offers several arguments for the importane in our oneptual sheme of a substantial onept of state of affairs and of semanti orrespondene arguments that should please the orrespondene theorists. The orrespondene theorists have reasons to be pleased also with the notion of truth allotted to them. It will serve all the philosophial funtions that they might assign to it. For example, it will serve as the foundation of the realism/antirealism debates: the realist affirms that thoughts in an area of dispute (e.g., ethis) are truth-apt (i.e., truth-apt), while the antirealist denies it. For another example, the notion will serve in artiulating a truth-onditional (i.e., truth- onditional) aount of meaning and ontent. A final example: the notion an be used by the physialists to underwrite their attempts to understand language-world relations in physial terms. Sine words express onepts, there is a derived but substantial semantial relationship between words and the world. And nothing preludes physialistially inlined philosophers from exploring the physial basis of this relationship. Correspondene theorists have reasons, then, to be pleased with their allotment in Hill s proposed ompromise. 6 4 Note that (C) is superfiially similar to Hill s (CT), whih he rejets (39, 54-55). The differene between the two is that while (C) is merely a stipulative definition, (CT) is a laim. It affirms the equivalene of the two notions of truth. 5 See Paul Horwih, Truth, seond edition (Oxford: Clarendon Press, 1998), Chapter 7, and Crispin Wright, Truth and Objetivity (Cambridge MA: Harvard University Press, 1992), Chapter 1. 6 Hill shows that the onept of semanti orrespondene an be defined using his substitutional quantifiers and one non-logial notion, namely, the state of affairs that p. In one sense, then, what Hill is granting to the orrespondene theorists is quite minimal. Yet the notion granted them is powerful enough to serve all their inflationary ends. Christopher Hill s Thought and World Page 2

3 thus: The notion allotted to the deflationists all it deflationary truth or true d is defined (D) An objet x is true [stritly: true d] iff (Óp)(p and x = the thought that p). 7 Here Ó is, in Hill s terminology, an existential substitutional quantifier. Note that, unlike firstorder quantifiers, Ó binds variables in sentene positions. Hill s theory (46-52) yields the following relationships between the two notions of truth. Truth implies truth, but not onversely. However, on thoughts that semantially orrespond to d states of affairs, the onverse impliation holds also and the two notions oinide. Hill observes that (D) improves on the paradigmati deflationary theory, namely, Horwih s Minimalism. Minimalism takes truth to be impliitly defined by the totality of thoughts of the form (T): (T) The thought that p is true iff p. 8 Thus, aording to Minimalism, the impliit definition of truth has an infinity of axioms an infinity larger than the ardinality of any set. Yet, despite this abundane of axioms, the Minimalist definition is quite weak. It fails to imply generalizations about truth (e.g., that only thoughts are true and that modus ponens preserves truth). On the other hand, despite its dedutive weakness, the definition is ideologially heavy: its definientia ontain all the onepts. It appears, therefore, that the definition plaes unreasonable demands on what is needed for a full grasp of the onept 9 of truth. In ontrast, as Hill observes, the ideologial resoures invoked in the definiens of (D) 7 This definition and (C) also is meant to apply only to non-indexial thoughts. Hill develops an attrative theory of indexial thoughts, but our purposes do not require us to delve into it. 8 I am ignoring the problems reated by the paradoxes. 9 For a fuller presentation of these problems, see my Minimalism, Philosophial Perspetives 7 (1993), , and A Critique of Deflationism, Philosophial Topis 21 (1993), Christopher Hill s Thought and World Page 3

4 10 are modest. And (D) is logially stronger than Horwih s impliit definition. It implies all the instanes of (T) and at the same time yields the desired generalizations about truth. Hill s definition improves on Minimalism, then, in important ways. Still, the deflationists have reasons to be onerned about their allotment in Hill s ompromise. Let me indiate three suh onerns. As one would expet, all the onerns enter on Hill s substitutional quantifiers. First: Hill s definition is aeptable only if substitutional quantifiers are available independently of true. But is that so? Does English have independent means of expressing these quantifiers? Hill addresses this issue (24-7) and suggests that the expression so-and-so works as a sentential variable and it invariably happens that works as a universal substitutional quantifier, in at least some of their uses. Here is a slight variant of Hill s example: (1) It invariably happens that when Joe predits that so-and-so, it turns out that so-and-so. Hill seems to me to be right that so-and-so is working like a sentential variable here. (Note that so-and-so is quite versatile in English; it an oupy name and verb positions as well.) However, there an be reasonable doubt about the funtioning of It invariably happens that. It is plausible to read it as generalizing on the oasions on whih Joe issues preditions. (1) seems to be equivalent to Whenever Joe predits that so-and-so, it turns out that so-and-so. 11 If it is, then we do not have in (1) a lear instane of substitutional quantifiation. Hill gives other 10 Hill also offers a diret hallenge to the ideology objetion (64-74). I respond to Hill s hallenge in the postsript to the reprinting of A Critique of Deflationism in, Bradley Armour- Garb and J. C. Beall (eds.), Deflationary Truth (Chiago: Open Court), forthoming. 11 It may be objeted that (1) expresses a omplete thought, but on the proposed reading it ontains the parameter so-and-so. Response: It is ommon to express omplete universal thoughts using parameters. We find this in mathematis and also in ordinary disourse. An example is He who rides a tiger will find it hard to dismount. Note that this kind of use of parameters is insuffiient to express (D). Christopher Hill s Thought and World Page 4

5 examples but reasonable doubts an be raised about them also. 12 Seond: Even if English an express substitutional quantifiers, do these quantifiers really provide the foundations for the ommonsense onept of truth (25)? Perhaps substitutional quantifiation is to be explained in terms of the onept of truth. Or perhaps the two are interdependent. A natural way of explaining Ó is this: (ÓE) The thought expressed by (Óp)... p... is true iff one of its substitution instanes is true. But this explanation is unavailable if one uses substitutional quantifiers to define truth. How, then, are the substitutional quantifiers to be explained? Hill addresses this issue (17-22) and proposes that the quantifiers should be explained in terms of the rules of inferene governing them. Hill formulates the logial rules for the existential and universal substitutional quantifiers they are parallel to the rules governing the first-order quantifiers and he laims that these rules suffie to define the quantifiers Corresponding to names, there are in English (and other natural languages) the ategories of pronoun and ommon noun. Dorothy Grover, Hill, and others have noted that some expressions in English an be viewed as the sentential analogues of pronouns, i.e., as prosentenes. Question: Can some expressions in English be viewed as the sentential analogues of ommon nouns? In the Prosentential Theory of Grover, Joseph Camp, and Nuel Belnap, a prosentene suh as It is true an have a noun phrase (e.g., every statement ) as its anteedent. To make the parallel between pronouns and prosentenes omplete, it is desirable to have sentential analogues of ommon nouns. An easy way of obtaining suh analogues is to hold that statement is systematially ambiguous. In some of its uses it funtions as a ommon noun, but in some others as the sentential analogue of a ommon noun. But I am not sure that this idea an be made to fit the linguisti evidene. For the prosentential theory, see Grover s olletion of essays, A Prosentential Theory of Truth (Prineton: Prineton University Press, 1992). 13 It seems to me that Hill s rule of Universal Elimination should be liberalized to allow instantiation with open thoughts (with the usual restrition about the onflit of bound variables). The liberalization is needed to apture inferenes suh as Everything Barry believes is true, and Christopher Hill s Thought and World Page 5

6 It seems to me that the logial rules do not fix a determinate sense for Ó, or even one determinate enough to ensure that (D) defines a deflationary notion of truth. Suppose, for example, that we take truth to be the norm governing assertion. That is, we hold that only true thoughts should be affirmed and that valid inferenes are those that preserve truth. Suppose further that we introdue a quantifier Ó* with a semantis parallel to (ÓE) but with true interpreted as truth. Now the inferenes that are logially valid for Ó* are exatly the same as those that are valid for Ó. If we look simply at the patterns of logial inferenes governing Ó, we annot tell it apart from Ó*. For all we know, Ó means Ó*, with the onsequene that deflationary truth, as defined in (D), is no different from orrespondene truth. The deflationists may well worry that they are being given orrespondene truth in a shiny new logial wrapper. Third: Even if the two onerns above are alleviated, deflationists will likely remain dissatisfied. For Hill s definition (D) undermines one of their entral theses, namely, that truth performs a vital logial funtion. The point is learest with those deflationists who follow W. V. 14 Quine and maintain the primay of first-order logi. Quine observed that in first-order logi we an generalize diretly on name positions. For example, we an generalize on Fred in (2) Fred believes that something is blue, and something is blue, and obtain ( z )(z believes that something is blue, and something is blue). But we annot generalize diretly on sentene positions for example, the positions oupied by something is blue in (2). The following is not well-formed in first-order logi: (3) ( x)(fred believes that x, and x). everything Terry believes is true; hene, everything that Barry believes Terry believes is true. Parallel remarks apply to the rule of Existential Introdution. 14 The point holds also for the prosentential theory of truth. In this theory, truth is assigned to the logial ategory of prosentene and is entirely non-redundant. Christopher Hill s Thought and World Page 6

7 One the truth-prediate is available, however, we an in effet generalize on sentene positions using first-order variables. The intent of (3) an be expressed thus: ( x )(Fred believes x, and x is true). Truth, aording to Quine and his deflationist followers, performs an essential logial funtion. It enables us to generalize on sentene positions using nominal variables. In ontrast, the notion of truth allotted to the deflationists in Hill s ompromise is fully redundant. One substitutional quantifiers are available, it an be thrown away. Deflationists are likely to omplain of unfairness when they ompare their allotment with that of the orrespondene theorists. What is likely to arouse their ire is not their own meager allotment even the deflationists will reognize that they are deserving of it but the substantial allotment of their rivals. Hill s ompromise is not a brash deflationism, one that would interrupt the philosophial debates over realism and antirealism, or one that would ditate the form of a theory of meaning, or one that would try to derail physialisti investigations into word-world relationships. Hill s ompromise is a polite and well-onsidered view, one that makes strong laims and raises interesting questions, but one with whih only a brash deflationist will want to pik a quarrel I wish to thank Dr. José Martínez-Fernández for his helpful omments on this essay. Christopher Hill s Thought and World Page 7