Download brandomsingularterms..

1
BRANDOM, SINGULAR TERMS, AND THE SYNTAX-SEMANTICS INTERFACE
By the canonical order of semantic explanation one first uses a theory of reference as the core
part of an explanation of a truth, the theory of which is then part of an explanation of what
people do with language such as issue speech acts and infer. Robert Brandom (1994) seeks to
reverse this (following Michael Dummett (1993)) by reversing the usual order of explanation of
correct inference. Typically, inferences are good or bad depending upon whether they preserve
truth. Brandom, on the other hand, wants to characterize goodness or badness of inference in
terms of norms such as assertibility, commitment, and entitlement, and then use the resulting
model of inference to explain truth and reference.
But inference is a relation that holds between sets of sentences. How then can inference
explain the referential meaning of subsentential units such as the singular terms and predicates of
first order logic, or their natural language analogues? Since, according to Brandom, our very
concept of “object” is parasitic upon our mastery of linguistic units that purport to refer to them,
he desperately needs an account of the inferential behavior of singular terms that does not invoke
the fact that they refer to individual objects. And a sizable chunk of Making it Explicit is given
over to doing just this. But Brandom’s arguments have recently come in for sustained criticism.
Peter Graham (1999) undermines Brandom’s transcendental argument that any language with
negation and implication must include terms that are singular in Brandom’s sense. Jerry Fodor
and Ernie Lepore (2001) first claim that Brandom is confused about syntax and then argue that in
any case singular terms do not betray the kind of inferential patterns that Brandom alleges. Mark
McCullagh (2005) argues that even if Brandom can answer the Fodor/Lepore criticisms, the
project rises and falls with the inferentialist’s ability to distinguish between intensional and
2
extensional contexts. Since Graham sees little prospect for this, he is pessimistic about the
success of Brandom’s project.
In what follows I defend Brandom’s proposal from the Fodor/Lepore criticisms but then
show how the interplay of syntactic and semantic features of subsentential units gives rise to a
new, and I think unsolvable, problem for Brandom’s account. But while it is clear that Fodor,
Lepore, Graham, and McCullough take Brandom’s inferentialist project to rise and fall with his
analysis of singular terms, I will conclude by showing that this is not so. If one is more careful
about the division of labor between the linguist and philosophical theorist of meaning, then one
can be an inferentialist without subscribing to Brandom’s analysis of singular terms. However,
this examination does reveal another explanatory burden that Brandom has not confronted, what
sense to make of the referential apparatus of formal theories. Luckily for the inferentialist
though, this is the topic of an early paper Neil Tennant (1987), which contains a fascinating neoMaimonist construal of the relevant locutions that is available to the Brandomian inferentialist.
I. SYMMETRIC SUBSTITUTION
Brandom explains the meaning of substentential units in terms of “simple material substitutioninferential commitments” (SMICs), which are good inferences that involve substituting parts of
one sentence for one another. For example, the following SMIC involves what Brandom refers to
as “singular terms.”
Bill Clinton likes hamburgers.
The forty-second President of the United States likes hamburgers.
The following involves “predicates.”
Bill Clinton is happy.
3
Bill Clinton is in an emotional state.
Brandom holds that one can differentiate between these two kinds of substitutional inferences
without appealing to referential features of singular terms or predicates.
The SMICs that determine the material-inferential significance of the occurrence of
singular terms are symmetric: a commitment to the correctness of the inference that
results from substituting A’ for A is also a commitment to the correctness of the
inference that results from substituting A for A’. The set of SMICs that determine the
material-inferential significance of the occurrence of any predicate, by contrast,
include asymmetric ones. . . (Brandom 1994: 375)
Then Brandom uses this putative fact to explain other factors of singular terms, such as their
purported reference.
In one sense this should be completely non-problematic. Coextensive terms that pick out
individual objects should allow reflexive, symmetric, and transitive substitutions in extensional
contexts. For the non-inferentialists, this is because individual objects are self identical, and the
metaphysical nature of identity ensures that it is a reflexive, symmetric, and transitive relation.
But for Brandom, this is reversed. Following Kraut (1980), Brandom holds that what it is for us
to take identity to have these properties is for it to be the mirror of inferential patterns involving
singular terms. In this manner our very grasp of what it is to be an object is parasitic on our
mastery of linguistic inferences.
II. THE NATURE OF SYNTACTIC CATEGORIES
Brandom’s proposal requires a prior notion of syntactic categories, for what is available to be
substituted into in his SMICs are instances of syntactic categories. On his account,
4
[two strings] belong to the same syntactic or categorical category just in case no
well-formed sentence in which the one occurs can be turned into something that is
not a sentence merely by substituting the other for it (Brandom 1994: 367-68).
This then allows us to discern which categories are such that their sentential units are symmetric
in their substitution instances.
Fodor and Lepore reject this. After stating that the linguist needs to first have a grasp of
the notion of a syntactic category to then define the grammaticality of a sentence, Fodor and
Lepore write,
This is a point that Chomsky made with considerable effect against taxonomic
linguists some four decades ago; they too had thought that appeals to substitution in
sentences would ground a “discovery procedure” in terms of which ‘NP,’ ‘PRED’
and the like could be defined. As far as we know, however, nobody in linguistics
thinks that any more (Fodor and Lepore 2001: 474).
The fact that my own criticism of Brandom so centrally involves his account of syntactic
categories requires me to note that Fodor and Lepore are here being frightfully misleading about
the current state of syntax. That is, ninety-nine percent of the work in syntax consists in positing
structures and categories with the purpose of gauging the resulting theory in terms of Brandom’s
substitution test. This holds true even in the hyper neo-Chomskyan approaches (e.g. Radford
2009) that Fodor and Lepore misleadingly present as universal in contemporary syntax. The
patterns of Brandomian substitutions that all syntacticians take to be central to assessing rival
theories are what linguists refer to as “distributional data.”
It is also important to realize that there are thriving syntactic frameworks that reject the
Chomskyan arguments about the nature of categories to which Fodor and Lepore refer. All of the
5
non-transformational frameworks such as Head Driven Phrase Structure Grammar (Bender, Sag,
and Wasow 2003) and Categorial Grammar (Morrill 2010) are driven by the rejection of the way
syntactic categories and structures have been posited solely to do justice to Chomsky’s
innateness hypotheses, philosophically odd account of simplicity of theory, and related
arguments for the necessity of transformations. Instead, the focus is on getting the relevant
distributional data right, not overgenerating, and discerning a syntax that interfaces well with
morphology, semantics, and pragmatics.
To be sure, as McCullagh shows, there are non-interesting categories. Consider the fact
that,
in English the string ‘troact’ occurs only in the word “retroactive’ and the string
‘barbat’ occurs only in the word ‘rebarbative,’ the set {‘troact’, ‘barbat’} meets it
[Brandom’s criteria] as well: for each of this set’s members is always a
sentencehood-preserving substitute for any other (McCullagh 2005: 215-16).
So the interesting question is what else is necessary besides satisfaction of distributional tests for
positing syntactic categories (and either transformations or deeper lexical structure governed by
such categories). Chomskyans like Fodor and Lepore hold that what else is needed is consistency
with Chomsky’s innateness arguments and arguments about the nature of simplicity in science,
so that syntaxes for natural languages must be derivable from a universal grammar with a
minimal number of syntactic categories.
But linguists such as Johnson and Lappin (1998) and philosophers such as Sterelny
(2006) and Cowie (1999) reject Chomsky’s recent approach because they reject: (1) the manner
in which Chomskyans take innateness concerns to constrain syntax, (2) Chomsky’s
characterization of the way simplicity guides science, (3) the Chomskyan (e.g. Fodor and
6
Piattelli-Palmarini: 2010) rejection of evolutionary explanations, and (4) the resulting
imprecision and tendency to overgenerate of contemporary Chomskyan theories such as
Government and Binding and Minimalism. This last concern is the reason why nearly everybody
in computational linguistics utilizes non-transformational syntax such as HPSG, Tree Adjoining
Grammar, or Categorial Grammar.
For non-transformational syntactitians what differentiates interesting from noninteresting distribution classes is simply whether the substitution class in question does
explanatory work with respect to the other areas of linguistics. Morphology, semantics, and
pragmatics will contain no interesting generalizations involving the set {‘troact’, ‘barbat’}. So
we can either say it is not a syntactic category, or that it is an uninteresting one. But this is not a
difference that makes a difference in computation (P. Blackburn and J. Bos: 2005) and
semantics-friendly (S. Lappin: 1997) approaches to syntax. And it certainly does not provide any
ammunition against Brandom.
III. ASYMMETRIC SINGULAR TERMS
Fodor and Lepore (2001: 476) hit much closer to the mark when they note that in all cases where
the referent of one singular term is the part of another singular term’s referent, asymmetric
inferences are generated. It follows from “Part of Paris is burning” that “Part of France is
burning,” but the reverse inference is not good. Or consider “Father was at Magdalen” and
“Father was at Oxford.” The first entails the second, but not vice versa. But then since we live in
a universe where the objects to which singular terms apply are spatially nested, it follows that by
Brandom’s account there are no singular terms.
7
As McCullagh (2005: 194) notes, a charitable reading of Brandom suggests a way out of
this, as at one point Brandom states the issue in terms of whether members of syntactic classes,
“fail to be systematically asymmetrically substitution-inferentially significant in the way
predicates are (Brandom 1994: 388).” The issue of course is then how to characterize this
systematicity. Neither Brandom nor McCullagh are very clear here.
If, pace McCullagh, the inferentialist could somehow help herself to the distinction
between extensional and intensional contexts, then one could answer the Fodor/Lepore
argument. Consider the following definition, where a superscripted e denotes that the context is
extensional:
a and b are singular terms if, and only if,
(1) a and b are in the same syntactic category,
(2) ((Pe)(Pe[a]  Pe[b]) 
(Qe)(Qe[a]  Qe[b])).
This says that in every possible world where b has all of a’s properties, a also has all of b’s
properties. “Paris” and “the capital of France” are such that everything true of Paris is true of the
capital of France, and vice versa. Of course, at this point in the explanation Brandom cannot
appeal to truth in this manner. But for the inferentialist, the formula says that necessarily if b is
substitutable for in for a in all extensional propositions in which a occurs, then a is also
substitutable in for b in all extensional propositions in which b occurs. On either construal,
“Paris” and “part of France” do not satisfy the antecedent; some things are true of one that are
not true of the other (and vice versa).1
1
I should briefly note that one might opt for stating this in terms of a counterfactual conditional
as a necessary conditional, a move that might help deal with Kripke (1980) style counterfactuals
8
IV. THE PROBLEM
At this point one might be tempted to balk at Brandom’s characterization of definite descriptions
as singular terms because of the quantificational structure Russell (1905) revealed. This,
however, would be to misunderstand Brandom’s proposal. Nothing he says here requires him to
deny that the correct translation into a formal language would involve quantification. And the
nature of his enterprise requires him to treat Russellian definite descriptions as being in the same
category as proper names, for Brandom seeks to explain reference to individual objects entirely
in terms of a set of inferential patterns. Since we refer to objects with names and definite
descriptions, Brandom needs to find a unified inferential pattern that captures both. The
generalized asymmetry test above, restricted to extensional contexts, does this fine.
Of course this would all be illicit if the reason for grouping definite descriptions and
singular terms together was that they both purported to refer to individual objects. But this is
exactly why Brandom defines syntactic category in terms of syntactic distributional tests. For
Brandom, the fact that names and definite descriptions pass the same distributional tests ensures
that they are members of the same category, and then the fact that their substitutability in
inferences is symmetric in the generalized manner I showed above is part of an explanation of
what it is for them to refer to objects. If one notes that the substitutions are also reflexive and
transitive, this provides part of an explanation of what we are doing when we talk about objects.
such as Paris not being the capital of France. However, since that would require characterizing
closeness of possible worlds in this context, I will not explore the option here.
9
Unfortunately, it only takes a little examination of the relevant distributional data to
undermine this story. Yes, names like “Frank” and definite descriptions like “the dog” obey the
same syntactic distributional tests. But so do non-plural quantified noun phrases like the singular
indefinite descriptions “some dog” or “a dog” or the universally quantified phrase “every dog”
and “each dog.” But then Brandom would have to say that “every dog” is a singular term!
Consider indefinite descriptions (“a so and so”). While these are singular terms for
Brandom, since they satisfy the same distributional tests as definite descriptions, they fail
Brandom’s semantic substitution tests. “A small dog on Hearthstone Drive s” licenses “a small
mammal on Hearthstone Drive s,” for all s and in all possible worlds. But there are s in the
actual world such that “a small mammal on Hearthstone Drive s” does not license “A small
dog on Hearthstone Drive s.”
If we allow ourselves to ignore the full set of pragmatic/semantic insights of Discourse
Representation Theory2 (see Kadmon: 2001) we can simplify and say that “A dog is happy”
means that at least one dog is happy. But since that is consistent with several dogs being happy,
Brandom is not going to be able to characterize purported reference to individual objects in terms
of singular terms. And Brandom admits as much. He writes,
2
I mention Discourse Representation Theory because [citation deleted for anonymity] (p.c.)
has argued trenchantly that one possible response for might be be to invoke differences in
anaphoric behavior of singular terms as revealed in DRT. I will not go on to discuss this because:
(1) don’t have intuitions about how exactly this might go without smuggling in representational
facts of which Brandom can’t avail himself at this point in the explanation, and (2) as I will
show, nothing is lost and much is gained if the inferentialist uses my argument to abandon this
part of Brandom’s edifice.
10
The restriction to substitution instances is required because one may, for instance,
infer asymmetrically from the applicability of a singular term to the applicability of a
predicate: from “The inventor of bifocals is Benjamin Franklin” to “The inventor of
bifocals is an American.” These do not count as substitution inferences even in the
extended sense allowing replacement of frames, because they cross syntactic
categorical boundaries. (Brandom 2001: 215)
But “an American” and “Benjamin Franklin” do not cross syntactic boundaries for Brandom. For
Brandom takes satisfaction of grammaticality distributional tests to be sufficient for definition of
such boundaries. And it is at the very least very difficult to see what account of syntactic
grammaticality would group names and definite descriptions together in one category and
indefinite descriptions in another. For then one would have to find substitution instances of
indefinite descriptions for definite ones (or vice versa) that did not preserve syntactic well
formedness. But, syntactically, definite and indefinite descriptions are just quantified noun
phrases. One has to turn to the contribution to truth preserving inferences each make in order to
differentiate between the two of them. And this is precisely what Brandom’s order of explanation
prevents him from doing.
Brandom might bite the bullet and argue that definite descriptions are not singular terms.
After all, one can affix nouns and adjectives in front of names, for example, “Happy Gilmore,”
and one cannot do this for singular quantified noun-phrases (“Happy every dog”). But, in
addition to robbing Brandom’s account of singular terms of the ability to explain purported
reference of definite descriptions, the linguistic argument doesn’t really work. When we affix
adjectives or nouns in front of singular nouns we affect the presupposed domain of discourse,
11
allowing the possibility that there is more than one object with the name in question, such as
“Sad Gilmore.” In these contexts the original noun no longer purports to refer to one object.
V. NEIL TENNANT’S NEO-MAIMONIZM
A full discussion of this problematic would involve an explanation of how Montague became the
grandfather of generalized quantifier theory by using the typed lambda calculus to account for
the unified syntactic, and divergent semantic, behaviors of names and quantified noun phrases
(D. Dowty, R. Wall, and S. Peters 1980). Here it suffices to say that the natural language syntax
and syntax-semantics interface is recursive, and after lambda cancellation (in extensional
contexts) we get the familiar formulas of first order logic.
This suggests one possible direction for Brandom. Perhaps, the inferentialist should avail
herself of the work of linguists in the Montagovian tradition and, qua philosophers, focus on
characterizing the meaning of formulas in the reduced logic. Then perhaps one would not need to
characterize “singular term” as a category of natural language, just noting that the translations for
definite descriptions (λP[λQy[x[P(x)  x = y]  Q(y)]]) and names (λP[P(j)]) and indefinite
descriptions (λP[λQx[P(x)  Q(x)]]) get the required inferences right when attached to
predicates of the appropriate type. And as inferentialists, we just hold that the singular terms of
the resulting predicate logic are implicitly defined in terms of the explicit introduction and
elimination rules for the reduced logic. Assuming this is not theft over honest toil, the very
success of such an approach would be seem to be a hard blow for the Brandomian, rendering
much of the explanatory framework of Making it Explicit completely superfluous.
More problematic though, this seems like the perfect recipe for a kind of lazy naturalism
that seeks to replace philosophy of X with the science of X. If the only point of the theory of
12
meaning is to come up with the best empirically oriented theory of the inferential role of natural
language sentences, then this would be justified. But that is not the case. One should note that
one would be very surprise after reading the criticisms of Fodor, Lepore, and the others to read
Brandom’s two recent efforts: Between Saying and Doing (2008) and Reason in Philosophy
(2009). The applications of an inferentialist approach to meaning in those works covers an
amazing variety of traditional philosophy (e.g. the nature of autonomy, historicism, the
computational theory of mind, meta-ethics, the theory of modality, the nature of indexicals,
etc.);3 nowhere there does Brandom explicitly mention or implicitly presuppose his analysis of
singular terms.
And by briefly examining Brandom’s pragmatic account of the de dicto/de re scope
ambiguities in propositional attitudes we can show that Brandoms abandonment of his analysis
of singular terms is justified. There is nothing untoward about taking Brandom’s inferentialist
account of representational locutions to be about the correct formal translations isolated by the
linguist. Thus, the issue does not get settled by fiat once we defer to the linguist about syntactic
category, logical form, and lambda reductions of these logical forms.
Of course one is likely to object here that this is theft over honest toil. Isn’t the
Montagovian linguist only able to recrusively pair up natural language sentences with fomral
translations because she knows that th etwo share the same truth conditions? And for htat matter,
didn’t Montague himself design the referentialist possible worlds semantics for his intensional
logic?
From these questions, paired with Brandom’s failure to characterize singular terms, it is
clear that the inferentialist must provide an account of just what linguists (as well as
3
See [deleted for anonymous review] and [deleted for anonymous review].
13
mathematicians, philosophical logicians, and computer programmers) are doing with the
referential locutions that show up in their model theory for formal languages. But here is one
place where a Sellarsian inferentialist like Brandom can help herself to some of the philosophy
of logic developed in the Dummettian inferentialist tradition, in particular the neo-Maimonism of
Neil Tennant.
Va.
My goal here is extremely modest. I just want to show that if the inferentialist can help
herself to the formal translations of sentences that differentiate between de dicto and de re
readings of propositional attitude ascriptions, then nothing stops her from adopting Brandom’s
explanation of aboutness. The antecedent of this claim will be defended in Vb below.
We can start by considering these two readings of “John believes that a fish walks:”
de dicto- believe’(j,^x[fish’(x) & walk’(x)]
de re- x[fish’(x) & believe’(j,^walk’(x)]
Montague showed how each of these can be derived recursively from the syntactic derivations of
the natural language sentence.4 The de dicto reading states that John is in the belief relation to the
sense (denoted by the up carrot) of “a fish walks,” and the de re reading states that there is thing
that is a fish that is such that john is in the belief relation to the sense of that thing walking.
4
For these derivations, see (Dowty, Wall, and Peters 1981: 207-8). I should note here that I am
not saying that Montague’s quantifying out strategy to get the de re reading is linguistic gospel.
In fact, one could take a hint from Brandom’s analysis and try model the view that the syntaxsemantics interface only produces a de dicto reading, presenting the de re reading as derived
from the de dicto reading and pragmatic factors. If this could be modeled here, it would actually
have far reaching implications for a number of phenomena at the semantics/pragmatics border
that involve analogous scope distinctions (cf. Kadmon 2001).
14
Though Montague attempted to model the meaning of these sentences in his own possible worlds
framework, his true genius was in devising a syntax-semantics interface that managed to
recursively derive both form a recursive derivation of the corresponding natural language
sentences.5
It is somewhat strange that Brandom takes the inferentialist need to explain reference to
be discharged solely by an inferentialist constural of de dicto/de re ambiguities in propositional
attitude ascriptions. But the reason he thinks this is worth quoting a length.
Thus, in order to identify vocabulary in alien languages that means what ‘of’ and
‘about’ used in this sense do, one must find expressions of de re ascriptions of
propositional attitudes. It is these ascriptions that we use to say what we are talking
and thinking about. My strategy here is to address the question of how to understand
what is being expressed by representational vocabulary by asking how expressions
must be used in order to qualify as de re ascripitons of propositional attitudes. What
do they make explicit? What are we doing when we talk and think about what we are
talking and thinking about? This is a strategy for trying to understand intentionality
generally, from a pragmatist point of view (Brandom 2000: 169-170).
5
Perhaps the largest cultural misunderstanding between philosophy of language and linguistics
concerns this very point. Pilosophers of language who fixate on critiquing Montague’s possible
worlds analysis of content completely miss the actual nature of his monumental contribution to
formal semantics and computational linguistics. Montague is the Isaac Newton of these fields
entirely because of the manner in which his fragment provided the very first (in the whole history
of linguistics) proof of concept for an actual recursive syntax-semantics interface. See the
discussion in Lappin (1997).
15
For Brandom, the material inside the scope of the propositional attitude ascription is that which
is attributed to the bearer of the attitude, and the material outside the scope is that undertaken by
the person ascribing the attitude. This has a important normative twist.
The part of the content specification that appears within the de dicto ‘that’ claus is
limited to what, according to the ascriber, the one to whom the commitment is
ascribed would (or in a strong sense should) acknowledge a an expresion of what that
individual is comitted to. The part of the content specfication that appears within the
scope of the de re ‘of’ includes what according to the ascriber of the commitment
(but not necessarily according to the one to whom it is ascribed), is acknowledged as
an expression of what the target of the ascription is committed to. (This is what the
target should, according to the ascriber, acknowledge only in a much weaker sense of
‘should’ (Brandom 2000: 177-178).)
And the point of doing this is so that people can use their collateral commitments to extract
information from the belief of others’.
Extracting information from the remarks of others requires grasping what is
expressed when on offers de re characterizations of the contents of their beliefs-that
is, to be able to tell what their beliefs would be true of if they were true. It is to grasp
the representational content of their claims. The point I have been making is that
doing this is just mastering the social dimension of their inferential articulation
(Brandom 2000: 181-182).
If John believes that Cicero is a great orator, and we know that Cicero is Tully, then we can infer
that TUlly is such that John believes he is a great orator. Likewise we can differentiate what a
16
person is trying to do (shoot a deer) from what she will succeed in doing (shoot a cow) by
making de dicto attributions in the first case and de re attributions in the second.
As noted, I don’t seek to defend Brandom’s account here. From what I’ve said, it should
be clear that if Brandom can help himself to the formal translations above, then he can tell the
kind of story he wants to tell. So the important question is whether he can so help himself.
Vb.
Here is our problem. Applying Brandom’s explanation of de re attributions to sentences
of Montague’s Intensional Logic does not support an inferentialist account of meaning unless the
linguist can be fairly presented as (when discerning recursive pairings of natural language and
formal language sentences) isolating inferential roles in the first place. If the linguist has to
appeal to word/object referential relations in devising the translation procedures, then Brandom’s
explanation is a non-sequitur.
The inferentialist should reply that, just as distributional data is the evidence by which
syntactic theories are tested, correct inferences form the empirical evidence for semantic
theories. And surely this is true. The whole point of post Montague Grammar is that a formal
entailment relation is defined over the logic, such that the translations (α’,β’) of two natural
language sentences (α,β) are wrong if and only if the inferential relations between α’ and β’ are
the same as those between α’ and β’ as modelled by the logical theory of meaning for the formal
language.
This is correct, as far as it goes. And (in addition to having an actual recursive syntaxsemantics interface) the ability to define consequence rigorously over the logical language is the
reason all computational semantics rests on Montague’s shoulders. But sadly, for the
inferentialist these facts to not go far enough. For in standard post-Montagovian semantics the
inferential relations between the formal language sentences are defined using model theory,
17
where a set of sentences Γ entails α if and only if every model for all the sentences in Γ is also a
model of α. And models are defined in the familiar post-Tarskian way, with singular terms
denoting objects in a domain and predicates as characteristic functions of n-tuples in the domain.
But this then seems to leave the inferentialist completely bereft. IN order to get the
inferential role of sentences right, linguists must consider the truth conditions of formal language
translations of these sentences, truth conditions which constitutively involve reference. I
conjecture that this is in fact the reason that Brandom engaged into his ill fated foray into protolinguistics in the first place, because he thought that the inferentialist could not help herself to
results gained in this manner.
As far as I can tell, the inferentialist has only one out here, and that is to provide an
inferentialist account of what is going on when linguists, logicians, and computer scientists do
referential model theory. Strangely, given the ubiquity of appeals to reference in these fields, this
is a task at which Brandom never even hints. But luckily, in “On the Withering Away of Formal
Semantics” and elsewhere,6 Neil Tennant marshals a variety of proof theoretic results to do just
this.
6
In this paper I just focus on the material in “On the Withering Away. . .” to present the neo-
Maimonism that Brandom needs. A complete discussion would include Tennant’s (1997,
forthcoming) discussions of various proof theoretic requirements such as harmony and
conservative extension on any inferentialist account of logical operators. This material is also
desperately important for sustaining Brandom’s view that the function of logical operators serve
to make explicit inferential patterns that don’t involve those very operators. See [citatation
deleted for anonymity] for a brief discussion of the conservative extension requirement in this
context. Brandom’s own (2008) account of negation for propositional modal logic fails the
18
Tennant first notes that the usual division of labor in logic is to model provability with a
proof theoretic entailment relation (“single turnstile”: |-) and unprovability with a countermodel,
where the model theoretic entailment (“double turnstile”: |=) is shown to fail by the existence of
a model that makes true of the premises and makes false the purported conclusion. It is in this
way that finite beings are able to traverse logical space. If Γ entails α then there is a finite proof
of α from Γ (Γ |- α) and if Γ does not entail α then there is a countermodel making all of Γ true
and α false (Γ|≠α). In light of the inferentialist need to explain reference and truth in terms of
inference, and in light of the standard manner in which reference and truth are used to define
models, the inferentialist must provide some other account of what is going on when logical
consequence fails to hold.
Tennant’s proposal here is clear. Γ fails to entail α if, and only if, there is an intuitively
consistent set of sentences Π such that Π proves each member of Γ and Π proves α. Much of
Tennant’s original paper: (1) considers various reduction results in logic that in decidable cases
give us an effective procedure to discern the appropriate Π and that in undecidable cases in some
sense show that such a Π exists, and (2) shows how Gödel’s incompleteness results do not create
any special problems for the inferentialist who defines truth in terms of Tennant’s notion of
provability.7
For our purposes what is important is that Tennant takes his analysis of entailment failure
to be an inferentialist explanation of what is really going on when people engage in model
requirement, and the fact that he does not provide introduction and elimination rules makes it
impossible to pose the question of Harmony. Tennant (forthcoming) has the clearest explanation
of harmony in the literature.
7
On this very issue see [citation deleted for anonymity].
19
theory. For him, when one successfully constructs a model one is doing nothing more that
finding a set Π of consistent sentences that proves every member of Γ but also proves the
negation of α. Later, in his discussion of Gödel’s theorems, he writes,
The whole burden of ‘semantic insight’ in these two proofs of the incompleteness of
second order logic is borne by the claim that the second order induction axiom, via
the substitution instance above, ensures that only the standard natural numbers are in
the domain. But, as remarked earlier, this is perfectly comprehensible and
representable from a proof-theoretic point of view. One is simply applying induction.
That is a move governed by certain syntactic constraints. There is no mysterious
transcendent semantic intuition at work here, delivering itself of results beyond the
reach of formulable rules of proof (Tennant 1987: 317).
This is a strong claim to the effect that when one takes oneself to be manipulating the platonistic
structures treated by model theory to illustrate various forms of logical failure (unprovability,
incompleteness, usolvability, etc.) one is really doing the same sort of thing one did when one
proved things in the initial object langauge. All one is doing when one goes “metalinguistic” is
offering a new set of sentences (Π) that one takes to be intuitively consistent and proving things
with that new set.
I am not here trying to defend Tennant’s program, but rather just noting that Brandom’s
program rises and falls with it. First, Brandom has to say something about what mathemeticians,
computer scientists, linguists, and philosophical logicians are doing with representational model
theory, and it is not clear how an inferentialist could do this except via Tennant’s account.
Second, Tennant’s proposal answers the problem that arises from the collapse of Brandom’s
account of singular terms. We had proposed taking singular terms to be implicitly defined by the
20
introduction and elimination rules for the operators of logical languages. But this just pushed the
question back to how natural and logical languages are connected. But the most successful
attempt to do this in a rigorous manner (with a recursive natural language syntax and recursive
syntax-semantic interface) is post-Montague semantics, and Montague himself notoriously
regarded the logical language to be dispensable, since the recursive syntax-semantic interface
allows one to see the model theory as presenting models for natural language sentences. But,
again, if Tennant’s program is plausible, the inferentialist can help herself to the results of postMontague semantics without violating her inferentialist scruples.
VI.
FURTHER ISSUES
While our proposed outreach to what Brandom (2001) calls ‘Oxford inferentialism’ provides a
seed to solving his problem with singular terms, it also raises a plethora of other interesting
philosophical issue. First, if we follow Brandom’s practice of reading the post-Kantian German
Idealists in terms of some of these debates we see that both Brandom and Tennant need to
account for some version of Salomon Maimon’s infinite intellect. Second, work in the
Dummettian tradition entails that Brandom’s view that logical operators are merely explicative
(as opposed to ampliative) places requirements on accounts of logical operators that contradict
Brandom’s own account of propositional modal logic. And finally, saving Brandom from his
problems with singular terms does nothing to save his account from what many take to be its
deepest problem, a commitment to an evolutionarily implausible intractable gulf between the
sentience of humans who can use language and everyone else.
21
VIa.
Pittsburgh inferentialists are somewhat notorious for finding intellectual provenance in
the tradition of German Idealism (e.g Brandom 2008). Thus it is fascinating that Tennant’s view
is a modern restatement of the linchpin of Salomon Maimon’s post-Kantian idealism. Maimon’s
view that Kantian intuition was a picture of conceptual relations of the understanding came from
his deep analysis of how pictorial methods in geometric proof were in the process of being
replaced by proofs solely involving algebra (Buzaglo 2002). Given his continued adherence to
the Kantian inferentialist view of concepts, Maimon’s revived rationalist gift to the German
Idealists is incredibly similar to Tennant’s vision. I conjecture that it was the manner in which
this aspect of Maimonism influenced Fichte and Hegel (Beiser 1987, 2002) is part of what ends
up making Hegel such an inspiring figure for Brandom.
Interestingly, Tennant begins his paper with an extended meditation on the use of figures
in geometrical reasoning to show how his broader proposal is a species of the manner in which
algebraic reasoning replaced pictorial methods in mathematics. Though mathemeticians might
still use pictures as aids to our finite minds, they do not consider the propositions in question to
be proved, or to be shown unprovable from a given set of axioms, unless there is a demonstration
by proof of the species that Tennant describes. This too is an almost exact replica of what
Maimon means when he says that intuitions are mere pictures that are ultimately reducible to
concepts.
The strong similarities suggests
my issue
God’s intellect
naturalism stuff from review of 2008
22
VIb. Explication
Can be much clearer about Brandom’s philosophy of logic when talking about proof theory
VIc. Objects
Note that our view of singular terms as what is implicitly defined by provability relations does fit
well with Brandom’s definition of object?
A related possibility would be to try to explain reference in terms of a prior grasp of objects via
the practical, non-linguistic inferences we make involving objects. In analytical philosophy of
mind, teleosemantics (G. MacDonald and D. Papineau 2006) is in large part an attempt to do just
this. While this would not obviate most of Making it Explicit it would run directly afoul of
Brandom’s arguments that (2001) practical inferences are parasitic on linguaform theoretical
inferences and that (2009) non-linguistic animals are not different in kind from thermostats. In
continental philosophy, Heidegger’s emphasis on non-linguistic practical inferences makes him
the starting point for an object-oriented metaphysics (Harman 2002) and philosophy of mind
(Okrent 2007) that ends up rejecting Brandom on just these counts. This being said, I don’t think
this work is inconsistent with any of the three projects I am going to go on and discuss.
8
8
I’d like to thank [deleted for anonymous review].
23
References:
Beiser, F. 1987. The Fate of Reason: German Philosophy from Kant to Fichte. Cambridge:
Harvard University Press.
Beiser, F. 2002. German Idealism: The Struggle against Subjectivism, 1781-1801. Cambridge:
Harvard University Press.
Bender, E., I. Sag, and T. Wasow. 2003. Syntactic Theory. Stanford: CSLI Press.
Blackburn, P. and J. Bos. 2005. Representation and Inference for Natural Language: A First
Course in Computational Semantics. Stanford: CSLI Press.
Brandom, R. 1994. Making it Explicit: Reason, Representing, and Discursive Commitment.
Cambridge: Harvard University Press.
Brandom, R. 2001. Articulating Reasons: An Introduction to Inferentialism. Cambridge: Harvard
University Press.
Brandom, R. 2008. Between Saying and Doing: Towards Analytic Pragmatism. Oxford: Oxford
University Press.
Brandom, R. 2009. Reason in Philosophy: Animating Ideas. Cambridge: Harvard University
Press.
Buzaglo, M. 2002. Solomon Maimon: Monism, Skepticism, and Mathematics. Pittsburgh:
University of Pittsburgh Press.
Cowie, F. 1999. What’s Within: Nativism Reconsidered. Oxford: Oxford University Press.
Dowty, D., R. Wall, and S. Peters. 1980. Introduction to Montague Semantics. Dordrecht: D.
Reidel.
Dummett, M. 1993. The Logical Basis of Metaphysics. Cambridge: Harvard University Press.
24
Fodor, J. and E. Lepore. 2001. Brandom’s burdens: compositionality and inference. Philosophy
and Phenomenological Research 63, 465-81.
Fodor, J. and M. Piattelli-Palmarini. 2010. What Darwin Got Wrong. New York: Farrar, Straus,
and Giroux.
Godfrey-Smith, P. 2006. Mental Representation, Naturalism, and Teleosemantics. In
Teleosemantics, edited by G. MacDonald and D. Papineu, 42-68.
Graham, P. 1999. Brandom on singular terms. Philosophical Studies 93, 247-64.
Harman, G. 2002. Tool Being: Heidegger and the Metaphysics of Objects.
Johnson, D. and S. Lappin. 1998. Local Constraints vs. Economy. Stanford: CSLI Press.
Kraut, R. 1980. Indiscernibility and Ontology. Synthese 44: 113-35.
Kadmon, N. 2001. Formal Pragmatics: Semantics, Pragmatics, Presupposition, and Focus.
London: Blackwell.
Kripke, S. 1980. Naming and Necessity. Cambridge: Harvard University Press.
Lappin, S. 1997. The Handbook of Contemporary Semantic Theory. London: Wiley-Blackwell.
McCullagh, M. 2005. Inferentialism and singular reference. Canadian Journal of Philosophy 35,
183-220.
Morrill, G. 2010. Categorial Grammar: Logical Syntax, Semantics, and Processing. Oxford:
Oxford University Press.
Okrent, M. 2007. Rational Animals. Columbus: Ohio University Press.
Radford, A. 2009. Analysing English Sentences: A Minimalist Approach. Cambridge: Cambridge
University Press.
Russell, B. 1905. On denoting. Mind 14: 479-93.
Tennant, N. 1987. On the withering away of formal semantics. Mind and Language : 302-18.
25
Tennant, N. 1997. The Taming of the True. Oxford: Oxford University Press.
Tennant, N. forthcoming. *****************