PETER J. GRAHAM
BRANDOM ON SINGULAR TERMS (Received in revised form 15 April 1997)
A referentialist in the philosophy ...
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PETER J. GRAHAM
BRANDOM ON SINGULAR TERMS (Received in revised form 15 April 1997)
A referentialist in the philosophy of language explains inference in terms of reference and truth, and reference and truth in terms of wordworld or sentence-world relations. An inferentialist in the philosophy of language explains reference and truth in terms of inference. The inferentialist holds that singular terms, in particular, are those parts of speech that are governed by certain peculiar inferential commitments or inferential relations, by word-word or sentence-sentence relations. A natural question to either a referentialist or inferentialist is, Why should there be singular terms? Here I address the inferentialist answer to this question offered by Robert Brandom in the chapter of his recent book, Making it Explicit (Harvard UP: 1994), entitled “Substitution: What Are Singular Terms, and Why Are There Any?”1 According to Brandom’s overall conception of language, the role speech acts play is fundamental: the semantic properties of singular terms, predicates and other parts of speech derive their semantic properties from the semantic properties of sentences, which in turn derive their semantic properties from the speech acts they are used to perform (cf. chapter 2). Hence, by focusing on our practice of assertion in inference, we discover the semantic properties of sentences. In turn, the semantic properties of sentences should be given in terms of the substitutional inferential relations they bear to other sentences, and not, as the referentialist would do, in terms of the truth-values of sentences or the states of affairs and their component parts that sentences refer to or describe. Brandom argues, in transcendental fashion, that given his characterization of singular terms in substitution-inferential terms it follows that any language with negation or conditional expressions requires singular terms. I try to show that the argument fails.
Philosophical Studies 93: 247–264, 1999. c 1999 Kluwer Academic Publishers. Printed in the Netherlands.
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Brandom’s approach is interesting and important for it seeks to reverse the traditional order of explanation in philosophical thinking about language. Begin not with reference and truth as relations between words and sentences on the one hand and objects, properties, and states of affairs on the other and then explain inference, Brandom recommends, but rather begin with our substitution-inferential practices and then explain reference and truth. If the argument under discussion here fails then we should pause to question whether such an inversion in the order of explanation will succeed. That is, we should first question whether characterizing singular terms inferentially and not referentially is a satisfactory starting point, and then question the overall approach. The overall approach itself is interesting, for it purports to not only explain why there are singular terms, but also why there should be objects (cf. chapter 7). The paper begins by expositing Brandom’s substitution-inferential characterization of singular terms. The dialectical strategy of the bulk of the paper is to show that from within the largely inferentialist point of view Brandom’s argument fails. Only when discussing the argument’s failure do I oppose inferentialism to referentialism. SUBSTITUTIONAL SYNTAX
Brandom individuates the syntactic categories of linguistic expressions in terms of which substitutions of sentential and subsentential expressions preserve sentencehood (367–368). He distinguishes between being substituted in, being substituted for, being a substitutional variant of, and being a substitution frame, as syntactic categories of linguistic expressions (368). Singular terms, such as ‘Jaques Derrida’ and ‘The shortest spy’, are substituted-fors. Sentences are substituted-ins. Sentences that are substitutionally related to other sentences are substitutional variants. “Predicates”, Frege’s incomplete expressions, are substitutional frames. Consider, e.g., the sentences (1) and (2). (1) (2)
Benjamin Franklin walked. Bertrand Russell walked.
The relevant constituent expressions in the two sentences are ‘Benjamin Franklin’ and ‘Bertrand Russell’. If we produce (2) via
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substitution from (1), then ‘Bertrand Russell’ is substituted for the occurrence of ‘Benjamin Franklin’ in (1). ‘Bertrand Russell,’ which is “extracted” from some other sentence where it occurs, is “written over” ‘Benjamin Franklin’ to produce (2). What is substituted in is the entire sentence, and what is substituted for is a singular term. The sentences (1) and (2) are substitutional variants of one another. (1) is a variant of (2) because (2) can be derived from (1) by substituting ‘Bertrand Russell’ for ‘Benjamin Franklin’ in (1). Likewise for (2). This is the substitution process; substitutional frames are its result (368). Substitutional frames (sentence frames, expression frames) are what is common to a set of substitutional variants. The following three sentences are substitutional variants. (3) (4) (5)
If Bill Clinton walks, then Hilary Rodham talks. If Al Gore snores, then Hilary Rodham talks. If Bob Dole naps, then Hilary Rodham talks.
Since substitutional frames are the result of the substitution process, Brandom claims that “swapping” one substitution frame for another should not be thought of as substitution (369). The move from (1) to ‘Benjamin Franklin talked’ is the result of replacing ‘a walked’ for ‘a talked’.2
SUBSTITUTIONAL SEMANTICS
The preceding characterized the relevant notions from syntax in substitutional terms. Syntactically construed, singular terms are substituted-fors. However, semantically construed, singular terms are substituted-fors with a further property. The further property is explained in terms of substitution inferences. Substitution inferences relate substitutional (frame) variants as premise and conclusion. Consider an example inference involving a substitutional variant. (7) (8)
Benjamin Franklin invented bifocals. The first postmaster general of the United States invented bifocals.
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If we take (7) as a premise, and (8) as a conclusion, then we are inferring (8) on the basis of (7) via substituting ‘the first postmaster general of the United States’ for ‘Benjamin Franklin’. Assuming correct inferences preserve truth (or warranted assertibility of whatever), the inference from (7) to (8) is correct if Benjamin Franklin is the first postmaster general of the United States (370). The substitution inference materially involves the singular terms ‘Benjamin Franklin’ and ‘the first postmaster general of the United States’ (370). What is the semantic difference between singular terms (substituted-fors) and substitutional frames supposed to be? The difference is straightforward. “Substitutions for singular terms yield reversible inferences : : : Replacements of predicates need not yield reversible inferences” (371). Consider the substitution inference (9) to (10). (9) (10)
Benjamin Franklin founded the University of Pennsylvania. The first postmaster general of the United States founded the University of Pennsylvania.
The inference preserves correctness either way. That is, (9) entails (10) and (10) entails (9). Substitution inferences substituting singular terms that are materially involved are symmetric. Brandom defines singular terms as substituted-fors that are governed by symmetric inferential commitments (symmetric substitution rules, see below). Symmetry is the further property that turns substituted-fors into singular terms. Symmetry is not the case, however, for many predicates. The inference from (11) to (12) is not reversible. (12) is inferentially weaker than (11). That is, (11) entails everything that (12) entails, but (12) does not entail everything that (11) entails. (11) (12)
Kim is a bachelor. Kim is a male.
Substitution inferences replacing sentence frames that are materially involved are usually asymmetric (371).3
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Brandom encodes inferential relations into the content of a predicate. The inferential relation between ‘bachelor’ and ‘male’ is, as it were, “essential” to the content of the two words. The relationship between ‘bachelor’ and ‘male’ is made explicit in the universally quantified conditional, ‘all bachelors are males’.4 When the predicate or sentence frame is materially involved in the correctness of a substitution inference, the status preservingness of the inference depends upon the inferential relationship between the replacing predicate and the predicate replaced. The inferential relationship is made explicit by a universally quantified conditional linking the two predicates. Brandom refers to these conditional statements as ‘Simple Material Substitution-Inferential Commitments’ (SMSICs).5 Because that is too much to say in one breath, I will call them, in the case of frames, replacement rules. Replacement rules (usually) state asymmetric inferential relations. Brandom groups singular terms “: : : into equivalence classes by the good substitution inferences in which they are materially involved” (372). Brandom’s idea is simple. Just as certain inferential relations are encoded into the contents of predicates, so too certain inferential relations are encoded into the contents of singular terms. How does this work? Recall the relationship between ‘Benjamin Franklin’ and ‘the first postmaster general of the United States’. The relationship is made explicit in the identity statement, ‘Benjamin Franklin is (=) the first postmaster general of the United States’. Singular terms like ‘Benjamin Franklin’ are also materially involved in other substitution inferences that substitute other expressions for it, such as ‘the founder of the University of Pennsylvania’ or ‘the inventor of bifocals’. The set of such explicitly stated relationships is an equivalence class. It is this set or equivalence class that Brandom identifies as the content of a singular term. This set gives the Simple Material Substitution-Inferential Commitments (SMSICs) associated with a singular term. I will call this set the substitution rules for a singular term. Replacement rules and substitution rules are like inferential licenses. Given a premise that involves a frame or a singular term, the corresponding replacement rule for the frame or the substitution rule for the singular term will license certain substitution (replacement)
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inferences where the predicate or the singular term is materially involved, preserving correctness. There are some linguistic contexts, however, where substituting a singular term for another that it is related to by a substitution rule does not preserve correctness. Belief contexts, and maybe modal contexts, are good examples. Consequently it is appropriate to distinguish between those contexts where the substitution rules govern and where they do not. Brandom calls “primary” those contexts that permit substitution (replacement) inferences (371).
INFERENTIAL POLARITY
Brandom argues that any language with substituted-fors and negation or conditionals requires that symmetric and only symmetric substitution rules govern substituted-fors; asymmetric substitution rules and negation or conditionals are incompatible. That is, in an expressively rich language with negation and conditional expressions, if there are substituted-fors, those substituted-fors must be symmetrically related. Brandom’s strategy is to discover additional word-word relations, not special word-world relations, that force symmetric substitution rules for substituted-fors. In this section I explain some notions that are involved in the argument. Brandom’s reasoning essentially involves the claim that there must be primary contexts.6 Brandom’s argument as I reconstruct it is a reductio: if there were asymmetric substitution rules for substituted-fors and the language in which they are a part contains negation or conditional expressions, there would be no primary contexts. I focus throughout on the case of negation.7 The argument for the claim that if there were asymmetric substitution rules then there would be no primary contexts makes essential use of the notion of an inferentially complementary context. Brandom claims, rightly, that if a context is primary, then so too is its inferential complement. So if the inferential complement is not primary, then neither is the original. An inferentially complementary context reverses the inferential polarities of a context. Let me give an example involving negation. Take the sentence ‘Kim is a bachelor’ where ‘Kim’ has primary occurrence (‘a is a bachelor’ is a primary context). The sentence
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‘Kim is a bachelor’ entails, but is not entailed by, ‘Kim is a male’. Let us say ‘Kim is a bachelor’ is inferentially stronger than ‘Kim is a male’. Now add negation. First notice that ‘a is not a bachelor’ and ‘a is not a male’ are both primary contexts. Second notice that the sentence ‘Kim is not a bachelor’ does not entail the sentence ‘Kim is not a male’. After all, whoever Kim is, Kim may be a married man. But also note that the sentence ‘Kim is not a male’ does entail the sentence ‘Kim is not a bachelor’. What has happened? When we added negation the direction of inferential strength reversed. ‘a is not a male’ is inferentially stronger than ‘a is not a bachelor’. Negation, when added to a primary context, reverses the inferential strength – the polarity – of the frame in the context. Let us say that the frame ‘It is not the case that a is a bachelor’ or that the frame ‘a is not a bachelor’ is the negation-complement of ‘a is a bachelor’. If frame ‘F[ ]’ is inferentially stronger than frame ‘G[ ]’, then the negation-complement of frame ‘F[ ]’ is inferentially weaker than the negation-complement of frame ‘G[ ]’. Negationcomplements are inferential complements. Since the replacement rule ‘8x(Fx ! Gx)’ makes explicit that ‘F[ ]’ is inferentially stronger than ‘G[ ]’, the question arises as to how the rule is involved in inferences from the negation-complement of ‘G[ ]’, ‘G[ ]’, to the negation-complement of ‘F[ ]’, viz. ‘F[ ]’. That is, the rule tells you how to go from ‘a is F’ to ‘a is G’, but does it tell you what to do when you get to a sentence like ‘a is G’? You may think that it does not tell you what to do, because you may think the rule says something like “when you see an ‘F’, scratch it out and write in a ‘G’ ”. Then when you see an expression like ‘G[ ]’ the rule does not tell you what to do. But this would be a mistake. In fact, the rule does tell you what to do. That is because the replacement rule, like the frames it connects, has a “negation-complement”. The rule just is the claim that everything that is F is also G. That means if something is not G, then it is not F. The rule ‘8x(Fx ! Gx)’ is equivalent to the rule ‘8x(Gx ! Fx)’. So it is not the case that the rule does not tell you what to do when you get to a sentence like ‘G[ ]’. It tells you exactly what you can do: you can “scratch out” ‘G[ ]’ and “write in” a ‘F[ ]’.8
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THE ARGUMENT
Brandom’s argument takes the following form. If a language contains substituted-fors that are governed by asymmetric substitution rules, then the language cannot contain expressions like negation that invert inferential polarities; asymmetric substitution rules and negation are incompatible. So any language with negation and other inferential inverters must have its substituted-fors governed by symmetric substitution rules. He argues by reductio. Assume, then, that the substituted-fors of a language are governed by asymmetric substitution rules. If they are, then what appear to be obviously good substitution inferences involving negation will not be licensed by the substitution rule. (I go through an example in the next three paragraphs.) But if they are not so licensed, then the context in question is not a primary context. Since any context can be negated, it follows that there are no primary contexts. But there are primary contexts, hence it follows that substituted-fors cannot be governed by asymmetric substitution rules. This is Brandom’s answer to the question, Why should there be singular terms? The crucial premise is that asymmetric substitution rules do not license certain apparently good substitution inferences. Let us go through an example for the purpose of illustrating the reductio. Suppose the singular term ‘Alpha’ is related to the singular term ‘Beta’ asymmetrically, where ‘Alpha’ is inferentially stronger than ‘Beta’. The inference from ‘Alpha is F’ to ‘Beta is F’ is thus good, but the inference from ‘Beta is F’ to ‘Alpha is F’ is not. Now consider how the fact that negation reverses inferential polarities applies to the case of asymmetric substitution rules. If the inference from ‘Alpha is F’ to ‘Beta is F’ is good and the inference from ‘Beta is F’ to ‘Alpha is F’ is bad, then the inference from ‘It is not the case that Beta is F’ to ‘It is not the case that Alpha is F’ is good, but the inference from ‘It is not the case that Alpha is F’ to ‘It is not the case that Beta is F’ is bad. These are the facts that must be accounted for. But this, Brandom claims, cannot be done on the assumption that substituted-fors are governed by asymmetric substitution rules. According to the rule, you can substitute ‘Beta’ for ‘Alpha’, but you cannot (in general) substitute ‘Alpha’ for ‘Beta’. The rule only applies if ‘Alpha’ appears first, as it were. So, according to the rule, the inference from ‘It is not the case that Alpha is F’ to ‘It is not the
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case that Beta is F’ should be good. The problem for asymmetric substitution rules is that the inference is bad. Asymmetric substitution rules, then, get the wrong results. Since ‘It is not the case that Alpha is F’ is just as much a primary context as ‘Alpha is F’, the fact that negation is involved makes no difference to the applicability of the substitution rule. If the context is primary then the substitution rule applies regardless of whether the rule is symmetric or asymmetric. To repeat, if the inference from ‘Alpha is F’ to ‘Beta is F’ is a good inference, then inference from ‘Beta is not F’ to ‘Alpha is not F’ is just as good. And if ‘Beta is F’ to ‘Alpha is F’ is a bad inference, then the inference from ‘Alpha is not F’ to ‘Beta is not F’ is just as bad. But postulating asymmetric substitution rules for singular terms gets this wrong. The rule ‘Alpha > Beta’ fails to license the inference from ‘Beta is not F’ to ‘Alpha is not F’ and it fails to rule out the inference from ‘Alpha is not F’ to ‘Beta is not F’. So once negation is added to a language with singular terms and predicates, asymmetric substitution rules ruin an obvious pattern of good inference, the contrapositive. Asymmetric substitution rules entail that substitutional strength does not track inferential strength. So the postulation of asymmetric substitution rules is incompatible with the existence of negation in a language with primary contexts.9 Crudely, what drives the argument is the claim that if there were asymmetric substitution rules then an obvious pattern of good inference, the contrapositive, would not be “sanctioned”. Since the presence of negation introduces the contrapositive, the presence of asymmetric substitution rules would be incompatible with negation (or conditional expressions).
SEMANTIC RULES AND RE-WRITE RULES
So what, then, is wrong with Brandom’s argument?10 The argument conflates “re-write” rules of a certain sort with genuine replacement and substitution rules. Once we pull these two apart, we see that Brandom has shown that “re-write” rules are objectionable, but he has failed to undermine the real target, asymmetric substitution rules. There are at least two ways of taking the claim that singular terms are governed by asymmetric substitution rules. The first is to think of them as one-way re-write rules. The second is to think of them as
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one-way semantic substitution rules. One-way re-write rules work as follows. Consider the rule ‘a > b’. If you have a sentence of the form ‘Qa’ where ‘Q[ ]’ is a frame and ‘a’ is a singular term, then you can form a new sentence ‘Qb’ by rewriting ‘b’ for ‘a’, but not conversely. So, regardless of the frame (though the context must be primary), if ‘a’ occurs, then you can “scratch” it out and “write in” ‘b’. Re-writing is still conceived as a type of inference, but it ignores the nature of the frame that the singular term occurs in. For the rule to license the rewrite, the singular term need only occur in primary context, nevermind the polarity of the context. How do genuine one-way semantic substitution rules work? They work the way asymmetric replacement rules work for predicates. Just as ‘F[ ] >> G[ ]’ (see note 8) links ‘F[ ]’ and ‘G[ ]’ asymmetrically, so too does the rule ‘a >> b’ link the expressions ‘a’ and ‘b’ asymmetrically.11 This means that ‘a’ is inferentially stronger than ‘b’ in simple indicative sentences. That means if the sentence frame is of the garden variety ‘a is Tall’ then ‘a is Tall’ is inferentially stronger than ‘b is Tall’. The peculiar inferential properties of a context will turn out to matter here, unlike the case of “re-write” rules, for semantic substitution rules, as opposed to re-write rules, are sensitive to negation. So if the re-write rule predicts that the inference from ‘Fa’ to ‘Fb’ is a good inference (but not conversely), then it will incorrectly predict that the inference from ‘Fa’ to ‘Fb’ is a good inference (but not conversely). Here we see that the rewrite rule gets the wrong results. However, the substitution rule will predict that the inference from ‘Fa’ to ‘Fb’ is a good inference (but not conversely), and it will (correctly) predict that the inference from ‘Fb’ to ‘Fa’ is a good inference (but not conversely). Here we see that the semantic substitution rule gets the correct results. Crudely, the difference is that asymmetric semantic rules contrapose though asymmetric re-write rules do not. Brandom’s argument turns on thinking of the asymmetric rules governing singular terms that he is trying to show are incompatible with the presence of negation as semantic one-way re-write rules, and not as semantic one-way substitution rules. The mistake is simple. Brandom’s alleged target is the existence of semantic asymmetric substitution rules, not asymmetric re-write rules, and he only argues
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against the latter, and not, as he must, against the former. The reductio argument does not go through; the contrapositive is sanctioned.
BRANDOM’S REPLY
Brandom is aware of the possibility of understanding asymmetric substitution rules as I understand them here, as distinct from simple asymmetric re-write rules. He discusses their possibility in the second to last section of the chapter, entitled “Can the Substitutional Significance of the Occurrence of a Subsentential Expression Be Determined in Different Ways for Different Contexts?” (397) Brandom notes that if the suggestion that substituted-fors can be governed by asymmetric substitution rules as I conceive them can be made to work, then that would “be devastating for the overall argument that has been offered here” (398). He does not think, however, that it can. Brandom reasons against asymmetric substitution rules as follows. The general worry Brandom advances is the difficulty of determining the inferential polarity so as to determine whether an asymmetric rule applies or not. He begins by supposing that all logically atomic predicates are sorted into two classes according to their inferential polarity. (We could assume, instead, that they all have positive polarity. The point is that they have to have one or the other, but not both.) If P has a positive polarity, and the substitution rule linking a and b is ‘a >> b’, then the inference from Pa to Pb is good. If P has negative polarity, then the inference from Pb to Pa is good. Once negation and conditional embedding is introduced, changes in inferential polarity occur, as described above. Then we must track the inferential polarity of the predicates in the expression frame. We could do so by expressing “all the logical compounds in disjunctive normal form and [then] count the number of negations the term placeholder is within the scope of. If it is odd, the polarity of its proximal logically atomic frame is reversed by the whole context; if even, the original polarity is retained” (398). Brandom does not think this will do. He writes: Such a procedure will work as offered only if all predicates are one-place, including logically compound ones. If not, the polarity of a predicate can be different in different argument places. Thus Pa Pb will have opposite polarities for the two
!
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!
argument places – one in the antecedent and the other in the consequent. The two place predicate P P will not be sorted, then, into either polarity class by the procedure outlined above, and its inferential properties will accordingly not be determined by : : : the relation between a and b (398).
The argument here is clear. We must be able to sort predicates into one of two polarities. Since P can have negative polarity in the antecedent and positive polarity in the consequent of a conditional, the two-place predicate P ! P will have both polarities. But then we cannot sort the predicate by polarity. Hence the suggestion can only be made to work if all predicates are one-place. Brandom anticipates the right reply: do not sort predicates by their polarity, rather sort argument places. So, assuming that “the underlying frame P has positive polarity, in P ! P , the position will have negative polarity, and the position will have positive polarity” (399). So now the proposal is to sort one-place atomic predicates by their polarity, and then for two-place predicates take into consideration argument place. (We will discover below that we must also sort polarity by occurrences of arguments for compound one-place predicates.) This is consonant with the original description of the proposal. When P is embedded in an antecedent of a conditional, that is equivalent to falling within the scope of a negation. Then the polarity reverses from positive to negative. Brandom offers two objections to the proposal thus understood. First, “this proposal will still not determine what should be said about the inferential relations between Pa ! Pa and Pb ! Pb in the case where” a is inferentially stronger than b (399). His argument is straightforward. Pb ! Pb is either inferentially stronger or inferentially weaker than Pa ! Pa. But, claims Brandom, we cannot explain this on the assumption that a is inferentially stronger than b. For if we were to produce Pb ! Pb via substitution of b for a from Pa ! Pa, then Pb ! Pb should both be strengthened and weakened. That is because substituting for the term in the antecedent should inferentially strengthen the conditional, and substituting for the consequent should inferentially weaken the conditional (Cf. 399, 380–381). This argument is unsuccessful. First, in so far as it relies on the premise that we can produce Pb ! Pb from Pa ! Pa via substituting b for a, it goes wrong. That is because according to the rule, you can only derive Pa ! Pb via substitution, because the antecedent
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argument place has negative polarity and the consequent argument place has positive polarity. You cannot derive Pb ! Pb. The correct answer then is simple. Pa ! Pb is inferentially weaker than Pa ! Pa. Second, in so far as we are simply asked to compare the inferential strengths of Pa ! Pa and Pb ! Pb regardless of how the two conditionals came about, it is unclear whether Brandom’s claim that one has to be stronger than the other can be sustained. Why not suppose they have the same inferential strength? After all, taking into consideration just the rule, substitute b for a (viz. ‘a >> b’) you can only infer Pa ! Pb from Pa ! Pa and you can only infer Pa ! Pb from Pb ! Pb. Once asymmetric substitution rules are introduced, should results like this be surprising? Certainly they should not be ruled out absent further reasons for believing that they cannot have the same inferential strengths. And since other conditionals can have the same strength, it does not seem that such reasons will be forthcoming. Brandom’s second objection, he says, is “decisive”. He writes: One can take a sentence with two terms occurring in it at argument places of different polarities and form from it a one-place predicate or sentence frame: P Q, which can be represented as R. In this sentence frame, has both positive and negative polarity. This is fatal to the scheme suggested for keeping tack of polarities to permit projection of substitution-inferential properties in the face of asymmetrically significant substituted-for expressions (399).
!
The essential claim is that we can represent one-place predicates with two occurrences of the argument with one-place predicates with one occurrence of the argument. Since the two occurrences have different inferential polarities, the one occurrence would have both polarities. But that cannot be, so asymmetric substitution rules cannot apply to one-place predicates with two occurrences of the argument. The argument is question-begging. The proponent of asymmetric substitution rules will not allow the maneuver of representing a oneplace predicate with two (or more) occurrences of the argument with an expression with only one (or fewer) occurrence(s) of the argument (unless special care is taken in the formulation of the rules governing such representations such that the objection has no force, viz. devising special rules to accommodate the proposal). That is, there are restrictions governing when we can use a syntactically simpler expression to represent a more complex one. Though we can standardly represent ‘9x(Px ! Px)’ with an expression such as
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‘9xRx’, we cannot represent ‘9xPx ! 9yPy’ with ‘9xRx’. Why can we standardly represent Pa ! Qa as Ra? It has to do with our overall semantic theory. Since standard semantic theory does not assume asymmetric substitution rules, such a representation is generally acceptable. But when asymmetric substitution rules are introduced, it would be question-begging to assume that Ra could represent Pa ! Qa, for the different inferential polarities of the antecedent and the consequent of the compound predicate would not be tracked by the one occurrence of the argument in the atomic predicate. When the inferential polarity of an occurrence of an argument is not at issue, the representation of a one-place predicate with many occurrences of the argument with an expression with only one (or fewer) occurrences of the argument should be non-problematic. However, when the inferential polarity of an occurrence of an argument does matter, then just such a move is problematic. No wonder Brandom thinks this move is “decisive”; standard semantic theory simply assumes that there are no asymmetric substitution rules at play. What Brandom needs is an argument to the effect that given the incompatibility between representing Pa ! Qa as Ra and asymmetric substitution rules we should give up on asymmetric substitution rules. But what, other than convenience, could be a consideration in favor of such a form of representation that the inferentialist proponent of asymmetric substitution rules would not find question-begging?12 It does not seem, then, that Brandom has an argument, certainly not a conclusive argument, against the acceptability of asymmetric substitution rules. They may have their problems. It may be very difficult computationally to track inferential polarities. But then again, it may not. It may be very hard to devise a semantic theory, a model theory and a proof theory, that includes asymmetric substitution rules. But then again, it may not be any harder than developing a semantic theory that includes symmetric substitution rules. Even if, however, Brandom is correct and asymmetric substitution rules will not fly, it should be said that Brandom’s argument that asymmetric substitution rules wreck the contrapositive, that they are incompatible with the joint existence of negation (and other inferential inverters) and primary contexts, does not work against asymmetric substitution rules properly construed, i.e. as distinct from one-way rewrite rules. That is, when Brandom comes to discussing
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the real target, he does not argue that it founders on the presence of negation. If I am correct then Brandom’s efforts to show why there should be singular terms, why there should be symmetrically significant substituted-fors, were largely misplaced in an effort to show why there should not be one-way re-write rules. The possibility of asymmetric substitution rules, I conclude, is “devastating” to Brandom’s argument.
CONCLUSION
The issue driving this discussion is a certain fact about expressions such as ‘Tully’, ‘Benjamin Franklin’, and ‘The author of ‘On Denoting’ ’ in natural language. The fact is that they behave symmetrically in substitution inferences. The inferentialist encodes this fact into his account of singular terms. A referentialist, on the other hand, does not. Rather the referentialist explains this property in virtue of certain relations between singular terms and the world. According to the referentialist, the content of a singular term is (in part) its referent (in the case of names) or its denotation (in the case of definite descriptions), and the content is determined by extra-linguistic facts. The content in turn determines the correctness of substitution inferences. Since identity is symmetric, the content of a singular term will license symmetric substitution inferences. So, if we think that ‘Cicero’ and ‘Tully’ are co-referential, we will infer from ‘Cicero is F’ to ‘Tully is F’ and vice versa. It would be odd if we thought that Cicero is Tully, or that ‘Cicero’ and ‘Tully’ are co-referential, or that Benjamin Franklin was the first postmaster general of the United States, and we thought that ‘Cicero’ and ‘Tully’ or ‘Benjamin Franklin’ and ‘The first postmaster general of the United States’ were asymmetrically related substitutionally. So, on the referentialist picture, two expressions that refer to the same thing are symmetrically related because of the identity of the thing referred to. Or, better, two expressions that purport to refer to the same thing are symmetrically related because of the purported identity of the thing purportedly referred to. Word-world relations, or purported word-world relations, underwrite word-word relations. Crudely, we infer from ‘Tully is F’ to ‘Cicero is F’ because we think ‘Tully’ and ‘Cicero’ co-refer, and we correctly so infer because Tully is Cicero. Correctness of inference
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is explained by co-reference. Of course the referentialist owes us an answer to the question, Why should there be singular terms? But given an answer the referentialist can plausibly explain why there should by symmetric substitution inferences. Likewise, the inferentialist, if he can explain why there should be singular terms, will succeed without much ado in accounting for the correctness of symmetric substitution inferences. But in order to do that, of course, the inferentialist needs to explain why substitution rules governing substituted-fors per se should state symmetric inferential relations and not asymmetric ones. Though Brandom stipulates that singular terms are symmetrically linked substituted-fors, the theory should explain why this should be so. There is nothing in the idea of an inferential license that entails that the license should go two-way rather than one-way. Inferential licenses involving any kind of subsentential expression, by their very nature, could be one-way or two-way. So the question arises, given that singular terms are two-way, why should this be so? We can take, I think, Brandom’s “transcendental” argument as an answer to this question. They should be two-way because, once we introduce negation, they cannot be one-way. Showing that this is so is extremely important for Brandom, for his account of singular terms is the basis for his discussion of why there should be objects. Since I do not think the argument works, I am not moved to accept Brandom’s account of singular terms, and so I am inclined to doubt that he can account for why there are objects.13
NOTES 1
All parenthetical references are to Brandom. For “referentialism” Brandom uses the word “representationalism”, indicating that the position has its roots in Descartes. 2 Since my argument focuses on singular terms, I do not purport to correctly describe Brandom’s account of predicates. I find the relation on Brandom’s account between predicates (ordinarily conceived), such as ‘is a bachelor’ and ‘is tall’, and frames, such as ‘If John is tall then [ ] is friendly’, vexing. Frames do not seem to me to be the same thing as predicates, and do not, at least for Brandom, seem to be composed out of predicates, singular terms, other parts of speech, and logical vocabulary. (But see M. Dummett, Frege: Philosophy of Language (Cambridge: Harvard UP, 1973), chapter 2.) My account of what Brandom takes to be a predicate is here incomplete and may suffer from inaccuracies. It is clear, at
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least terminologically, that frames are not substituted-fors, for he thinks of frames as the result of the substitution process. 3 Philip Kremer pointed out a problem for this characterization of predicates in conversation. The synonyms ‘a is a bachelor’ and ‘a is an adult unmarried male’ are substitutable (replaceable) symmetrically. Does it then follow, on Brandom’s view, that synonyms are singular terms? 4 Though some of these might also be “material” or “synthetic” as in ‘All whales are mammals’ (cf. 94ff.). 5 I ignore here what counts as a “commitment” and why the notion is semantically important. 6 I ignore here why this should be so (cf. 365–366). 7 If natural language conditional expressions are correctly analyzed as material conditionals, which is what Brandom’s argument requires, viz. that conditional expressions are truth-functional, then the conditional p q can be understood as p or q. Hence Brandom’s point can be made in terms of negation (and disjunction) alone. 8 In what follows I will represent ‘ x(Fx Gx)’ as ‘F[ ] >> G[ ]’ to emphasize the fact that interpreting such a rule in an inferentialist semantics combined with asymmetric substitution rules may require special provisions. For example, the rule stated this way obviously presupposes that the singular term substituted for ‘x’ will be governed by symmetric substitution rules. If the terms substituted for ‘x’ are governed by asymmetric substitution rules, then further properties governing the rule must be defined. I avoid pursuing such technicalities here. 9 The argument appears on pages 378–381. It is restated, more in the fashion that it is presented here, on page 385. 10 Brandom discusses a number of other possible replies. For example, why not do without negation? Doesn’t the argument also apply to sentences? to predicates? etc. Cf. 381–399. 11 It is important not to represent the rule that links ‘a’ and ‘b’ as ‘ P(Pa Pb)’ for that way of representing the rule presupposes that argument occurrences do not have inferential polarities (see below “Brandom’s Reply”). 12 The anonymous reviewer suggested that at this point Brandom might claim that even though he has not provided a knock-down argument against asymmetric substitution rules (ASRs), he has provided grounds for doubting that they are coherent or conceivable from an inferentialist point of view. It does not seem, the reviewer suggested, that the peculiar semantic properties of positive and negative polarity assigned to occurrences of argument places can be made sense of from an inferentialist point of view, for it is difficult to conceive of the features of use, the particular substitution-inferential practice, that would generate or be explained by such properties. My reply to this suggestion is threefold. First, it amounts to conceding that the arguments of chapter 6 do not work on their own, which is all I have set out to show. Second, though this may be what Brandom would say in response to my discussion, it does not seem to be what he holds in the book. He does not seem to hold that inferentialism per se is incompatible with ASRs. Rather he seems to grant their possibility and then he goes on to argue that they are incompatible with certain other features of use that are in some way essential or “non-negotiable”. Third, it does not seem so strange to me that there could be speakers whose substitution-inferential practices were governed by ASRs. We would not interpret
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them with beliefs about objects, perhaps, but that does not mean that we could not make sense of their ontology or their practices. We can imagine the practices that would generate such properties, even though it may take some creative effort. 13 I am grateful to Philip Kremer for very helpful discussions and comments on previous drafts, to the anonymous reviewer for Philosophical Studies for very thoughtful comments on the penultimate draft, to Peter Kung for a discussion on the section entitled “Brandom’s Reply”, to Aldo Antonelli for discussion of some of the technical issues raised by the possibility of asymmetric substitution rules, and to Fred Dretske and Johan van Bentham for advice and encouragement.
Department of Philosophy Stanford University Stanford, CA 94305-2155 USA