=Paper=
{{Paper
|id=Vol-444/paper-6
|storemode=property
|title=Varieties of Analytic Pragmatisms
|pdfUrl=https://ceur-ws.org/Vol-444/paper06.pdf
|volume=Vol-444
}}
==Varieties of Analytic Pragmatisms==
https://ceur-ws.org/Vol-444/paper06.pdf
Varieties of Analytic Pragmatism
Danielle Macbeth
In his Locke Lectures Brandom proposes to extend what he calls the project of analysis to encompass
various relationships between meaning and use.1 As the traditional project of analysis sought to clarify
various logical relations between vocabularies—Russell’s theory of descriptions, for instance, showing how
sentences containing definite descriptions can be rewritten, ostensibly without any change in meaning, as
sentences containing only propositional functions and standard logical locutions—so Brandom’s extended
project seeks to clarify various pragmatically mediated semantic relations between vocabularies. A
vocabulary V1 is, for example, a pragmatic metavocabulary for another vocabulary V2 just if V1 enables
one to say what one must be able to do to count as saying the things V2 enables one to say. The point of the
exercise in both cases is to achieve what Brandom thinks of as algebraic understanding, “the sort of . . .
understanding characteristic of mature mathematized sciences” (pp. 212-3). Because the pragmatist critique
of the traditional project of analysis was precisely to deny that such understanding is appropriate to the case
of natural language, the very idea of an analytic pragmatism is called into question by that critique. What I
want to try to do here is to clarify the prospects for Brandom’s project, or at least something in the vicinity
of that project, through a comparison of it with what I will suggest we can think of as Kant’s analytic
pragmatism as developed by Peirce.
Much as Brandom situates himself relative to the standard project of analysis as it was challenged by
the later Wittgenstein’s pragmatism, so Kant situates himself relative to the dogmatism of Descartes’ new
algebra as challenged, so he thought, by Hume’s skeptical doubts. Because what is at issue in Kant’s case
would seem to be precisely the sort of algebraic understanding that Brandom esteems as “the very best sort
of understanding to have” (p. 214), it is worth briefly rehearsing both Descartes’ achievement in
mathematics and the skeptical challenge it engendered before turning to the version of analytic pragmatism
Kant developed in response to that challenge.
Before Descartes the paradigm of mathematics was Euclidean demonstration, a practice in which the
task is to find, that is, to construct, a diagram that provides a path from one’s starting point to some desired
conclusion. Because in this form of mathematics one achieves results by reasoning through a diagram,
seeing it now this way and now that in an ordered progression of steps, the diagram is itself the locus of
proof in this form of mathematics. Having an adequate diagram just is having a proof in ancient
mathematics. Descartes’ signal achievement was to show how to dispense with diagrams in mathematics,
bringing thereby a radically new level and sort of clarity to the subject.2
By way of illustration, consider the following problem: we are given a square AD and line BN; the task
is to prolong the side AC to E so that EF, laid off from E on EB, is equal to NB. Heraclides’ solution, as
given in Pappus’s Collection and reproduced in Descartes’ Geometry, is this diagram:3
1
Published, with an afterword, as Between Saying and Doing: Towards an Analytic Pragmatism (Oxford: Oxford
University Press, 2008).
2
See my “Viète, Descartes, and the Emergence of Modern Mathematics”, Graduate Faculty Philosophy Journal (2004)
25: 87-117.
3
All references to Descartes’ works are to the Adam-Tannery (AT) edition of the Oeuvres de Descartes (Vrin, Paris,
1964-76). The English translations used are The Geometry of Rene Descartes (G), trans. David Eugene Smith and
Marcia L. Latham (New York: Dover, 1954), and The Philosophical Writings of Descartes (CSM), in three volumes,
translated by John Cottingham, Robert Stoothoff, Dugald Murdoch, and in the case of the correspondence, Anthony
Kenny (Cambridge: Cambridge University Press, 1984-91).
That is, BD is extended to G, where DG = DN. Taking now the circle whose diameter is BG, it can be
shown (by a chain of reasoning through the diagram that need not concern us) that the point E that is
wanted is at the intersection of that circle and AC extended as needed. Already in the Regulae, Descartes
reports that such a practice of demonstrating through diagrams “did not seem to make it sufficiently clear to
my mind why these things should be so and how they were discovered” (AT X 375; CSM I 18). As he
remarks in his Geometry of this solution in particular, “those not familiar with this construction would not
be likely to discover it” (AT I 387; G 188). His own approach, we will see, is a methodical, stepwise
construction that eventuates in an equation the root of which solves the problem.
We know that BD equals CD because they are sides of one and the same square. Call that length, which
is given by the terms of the problem, a. Let c be the length EF, and take the length DF as that which is
sought, the unknown x. CF, then, is equal to a – x because, by compositionality, CF + FD = CD. Because
the triangles BDF and ECF are similar, we know that BF : DF :: EF : CF, that is, that a – x : c :: x : BF. So,
transforming this proportion into an equation, we know that BF = cx/(a – x). But because BDF is right at D,
we also know that BF2 = BD2 + FD2; that is, BF2 = a2 + x 2. Combining the two equations thus gives us
(cx/(a – x))2 = a 2 + x 2, which we can transform in a sequence of steps licensed by familiar algorithms of
algebra into the equation x4 – 2ax3 + (2a 2 – c 2)x2 – 2a 3x + a4 = 0. The root of this equation can then be
constructed and the problem is solved.
In solving this problem, Descartes appeals to four relationships that can be expressed both graphically
in a diagram and symbolically in the language of algebra: equality (of sides of a square), compositionality
(of lines from their parts), proportionality (of triangles), and the relationship that is expressed in the
Pythagorean theorem.4 And as we have just seen, the symbolic expression of these relations furthermore
enables one to combine the given information systematically into a single equation and thereby to solve the
problem without any need for the additional constructions that are involved in the Euclidean demonstration.
In Descartes’ geometry one does not need to discover the diagram that is the medium of Euclidean
demonstration but only to translate the given information into symbolic form and then combine it all into a
single solvable equation. It is just this that enables Descartes to claim that he has a method for the discovery
of truths in mathematics. Although there is no method by which to discover the diagram that is needed in a
Euclidean demonstration, once we conceive the problem symbolically—the diagram not as an iconic
display of objects of various sorts in relations but simply as a presentation of relations and proportions that
can equally well be expressed algebraically—Descartes can show us how combine the given information
symbolically into a single equation and thereby to solve the problem. As Poincaré would later remark,
“before Descartes, only luck or genius allowed one to solve a geometrical problem. After Descartes, one
has infallible rules to obtain the result; to be a geometer, it suffices to be patient . . .”.5 Translation of a
problem into a symbolic language the signs of which are everywhere governed by rules yields what we
might well think of as an algebraic understanding of that problem.
Descartes’ mathematics is systematic, algorithmic, and symbolic. It is in these respects quite unlike the
sort of diagrammatic demonstration one finds in Euclid. And yet, Descartes at first thought, mathematics
needs images. As he explains in the Regulae, mathematics needs images because the intellect reflecting in
the absence of an image can discover logical possibilities that are not real possibilities, that are shown to be
unreal by an image one forms: “even if the intellect attends solely and precisely to what the word denotes,
the imagination nonetheless ought to form a real idea of the thing, so that the intellect, when required, can
be directed towards the other features of the thing which are not conveyed by the term in question, so that it
may never injudiciously take these features to be excluded” (AT x 335; CSM i 61). For example, using the
intellect alone one might determine that extension is not body and on that basis mistakenly conclude that
there can be extension without body. Such a mistake is avoided, on the Regulae account, by one’s forming
a real idea of an extension in the imagination and discovering on that basis that it is impossible to form an
image of extension that is not also an image of body. The distinction between extension and body is only a
distinction of the intellect; there cannot actually be extension without body.6 That extension requires a body
4
I owe this observation to Kenneth Manders. See his “Euclid or Descartes?”, ms.
5
Henri Poincaré, Preface to his Oeuvre de Laguerre, vol. I, quoted in Manders, “Euclid or Descartes?”.
6
This is why Descartes thinks that there can be no vacuum: “The impossibility of a vacuum, in the philosophical sense
of that in which there is no substance whatsoever, is clear from the fact that there is no difference between the
extension of a space, or internal place, and the extension of a body. For a body’s being extended in length, breadth and
depth in itself warrants the conclusion that it is a substance, since it is a complete contradiction that a particular
extension should belong to nothing; and the same conclusion must be drawn with respect to a space that is supposed to
is not logically necessary, but as the imagination reveals it is necessary nonetheless. It is, as the point might
be put, not formally necessary but instead materially necessary.
According to Descartes’ early account the necessary non-logical relations that are needed in
mathematics, without which it would be paralyzed, are to be grounded in the faculty of imagination. When
Descartes came to realize that his new mathematical practice enabled him to discover truths even in cases
in which no corresponding image could be formed, he needed another account. What he came up with was
the idea that God creates these necessary but non-logical truths and implants in us the ideas by which to
discover them using only the pure intellect. By reflecting on our innate ideas of, for instance, substance,
duration, order, and even thinking itself, one can discover by reason alone both the essence and
fundamental laws of nature and the essence and fundamental laws of the mind, including the method by
which inquiry ought to be conducted. Mathematics in particular thus came to be seen as at once ampliative,
that is, a science within which to discover new and significant truths, and also strictly logical, that is, by
means of reason alone.7 The pure science of the intellect that Plato had first envisaged had finally been
realized.
Mathematical reasoning, according to Descartes, is at once deductive, each thing following of necessity
from what came before, and also ampliative. By reflecting on one’s God-given ideas and assenting only to
what is clear and distinct regarding them, that is, what is clearly necessary in them, whether or not logically
necessary, one discovers new truths. This, Kant would come to think, is sheer dogmatism. Although
logically necessary relations among concepts are unproblematic because grounded in the law of identity,
one cannot simply assume as given the non-logical necessary relations that are needed in mathematics.8 Of
course, if the existence of God could be proven, then one could perhaps talk of (divinely) implanted ideas;
but the existence of God cannot be proven and hence one cannot talk of such ideas.9 To talk of such ideas is
to appeal to nothing more than a brute Given, as unfounded as it is unquestionable. It is this rejection of any
Given, of the very idea of an indubitable foundation for our knowledge of necessary but non-logical
relations, that entitles Kant to be recognized as the first pragmatist. And because his pragmatism is
furthermore systematic, rigorous, and theoretical (in something like the way that the physical sciences are
theoretical), it deserves to be called the first analytic pragmatism.10
But as is invariably the case with pragmatism, Kant’s pragmatism can be interpreted in either of two
ways. The first, and less radical, way is to take the rejection of the Given to impair in some fundamental
way our capacity for knowledge of fully objective truth. On this interpretation, one leaves in place the need
for a foundation, if knowledge of fully objective truth is to be possible, all the while denying that that need
can be met. This is the pragmatism of James, Dewey, Rorty, and, we will see, Brandom. For all such
be a vacuum, namely that since there is extension in it, there must necessarily be substance in it as well” (AT VIII A
49; CSM I 229-230).
7
Of course it is not strictly logical in the Scholastic sense of logic, but it is, Descartes thinks, strictly logical in the true
sense of logic, in the kind of logic that provides the rules that govern the direction of the mind, “which teaches us to
direct our reason with a view to discovering the truths of which we are ignorant” (AT IX B 14; CSM I 186). Both
Locke and Leibniz similarly held that by logic alone (as they understood logic) one might extend one’s knowledge.
8
Thus Kant, unlike Descartes, limits what he calls general logic to what is, as we would say, formally necessary. It is,
he thinks, psychologistic to include among purely logical relations those that are necessary but not logically necessary.
As I argue below, necessary but not logically necessary relations are to be understood by appeal to the practices and
activities of the special sciences, mathematics and the natural sciences. The transcendental aesthetic and transcendental
logic serve to set out the necessary conditions of such practices and activities.
9
See Kant’s remarks in “On a discovery whereby any new critique of pure reason is to be made superfluous by an older
one” (AK 8:222).
10
That Kant’s philosophy is systematic and rigorous is obvious enough. That it is theoretical is indicated, on the one
hand, by the familiar contrast Kant draws between the practice of mathematics and that of philosophy, and on the other,
by the fact that he thinks that the philosopher must follow the practice of the physicist rather than the mathematician.
As is made clear in the B Preface, the philosopher, like the natural scientist, puts forth hypotheses and then tests them.
The Critique itself is such a test, and a very successful one Kant thinks. But he nonetheless cautions us in the Method
that “in its transcendental efforts . . . reason cannot look ahead so confidently [as in mathematics it can], as if the path
on which it has traveled leads quite directly to the goal, and it must not count so boldly on the premises that ground it
[as mathematics can] as if it were unnecessary for it frequently to look back and consider whether there might not be
errors in the progress of its inferences to be discovered that were overlooked in its principles and that make it necessary
either to determine them further or else to alter them entirely” (A735/B763-A736/B764). As we will see in more detail
below, natural science, unlike mathematics on Kant’s view, is constitutively self-correcting, and hence philosophy is as
well.
pragmatists there is a kind of bedrock, for instance, our language and interests, or our agreements, or our
social practices, that is to provide such foundations as there are for knowing, or at least our talk of
knowing. To read Kant as a pragmatist of this variety is to take the forms of sensibility and understanding
likewise to stand as surrogates for the foundation that is not otherwise to be had. So read Kant is, I think,
clearly guilty of psychologism.
The second, more radical and I think more insightful, response to the rejection of the Given is to see not
only that the Given is a myth but also that knowledge of fully objective truths does not require a Given, and
indeed, could not be helped by a Given insofar as what is Given is merely a kind of blind prejudice, merely,
as Peirce would say, what one is inclined to think. But if the Given, assuming there were one, could not
possibly provide a foundation for knowing then it must be the foundationalist picture itself that is a myth; it
must be that it is not the products of inquiry that are the key to knowing but instead the process, the
dynamic activity of inquiry, the actual practices and processes of science. This is the pragmatism of Peirce
and Sellars. To read Kant as such a pragmatist—and hence as a transcendental idealist not because of his
pragmatism (as on the first reading) but in spite of it—is to take the forms of sensibility and understanding
not as standing surrogate for some mythic foundation but instead as conditions of the possibility of the
activity of inquiry. I want very briefly to indicate how such a reading of Kant would go.
According to Kant the practices and processes of science involve two very different sorts of activities,
on the one hand, the constructive practices of mathematics and on the other, the theoretical, postulational,
and self-correcting practices of the empirical sciences. His key insight on the side of mathematics is that
although the new mathematical practice inaugurated by Descartes does not use images or Euclidean
diagrams, but instead symbols and equations, it is nonetheless essentially diagrammatic. Indeed, it is the
algebraic practice of successive writings and rewritings that first concretely displays the inherently
temporal and dynamic character of all mathematical practice, and so even of Euclidean demonstration,
which, one might think, essentially involves space for the drawing of the diagram but not time. Although
the inherently diagrammatic, spatial, character of reasoning in mathematics is best illustrated in Euclidean
geometry, its essentially temporal nature, the fact that it constitutively involves an organic process of
unfolding over time is better illustrated in Descartes’ algebra. This was Kant’s deepest insight: that it is not
the product but the process of mathematical proof, that is, the activity of constructing, that is the key to
understanding the nature and possibility of our knowledge of the necessary but non-logical relations in
mathematics; for it is this process that forges those necessary bonds among concepts that constitutes
knowledge in mathematics, that “[brings] forth the truth together with the proof” (A734/B762; cf. B15-16).
Space and time serve on this account not as a Given foundation but instead as the conditions of the
possibility of such constructive activity.
The practice of natural science is very different according to Kant. It achieves knowledge of its laws,
which like the truths of mathematics involve necessary but non-logical relations, not through constructions
but through postulation and experimentation: “reason, in order to be taught by nature, must approach nature
with its principles in one hand, according to which alone the agreement among appearances can count as
laws, and, in the other, the experiments thought in accordance with these principles” (Bxiii). On Kant’s
account, our inquiries into the nature of the empirical world become science properly speaking only when
we learn to approach nature not as a student awaiting instruction (in effect, a Given) but “like an appointed
judge who compels witnesses to answer the questions he puts to them” (ibid.). Empirical inquiry is in this
way constitutively self-correcting. And much as space and time are the preconditions of the constructive
activities of mathematics so, Kant argues, the pure concepts of the understanding, and in particular those
under the title of relation, are the precondition of self-correction in natural science.11
There are three sorts of judgments under the title of relation: categoricals, hypotheticals, and
disjunctives. That both categoricals and hypotheticals are needed if self-correction is to be possible is a
familiar theme from Sellars, and Brandom following him. Concepts must be inferentially related if
judgment, as opposed to mere classificatory behavior, is to be possible; and such relations, if they are to
provide grounds for judgments rather than merely causes of them, must themselves be available as the
contents of judgments. There can be categorical judgments that describe only if there are also hypothetical
ones.
11
The forms of judgment falling under the titles of quantity and quality are preconditions of all science, mathematics as
much as physics; only those under the title of relation (and modality, but these do not concern the content of judgment)
are peculiar to the practice of the natural, empirical sciences.
But although hypothetical judgments are necessary for judgment, they are not sufficient according to
Kant. One needs also the capacity to judge disjunctively. We can begin to understand why when we
consider the fact that not only do we correct our categorical judgments in light of our hypothetical
judgments, we also can correct our hypothetical judgments in light of our categorical judgments. That is,
any conflict between the two can be resolved either by giving up the relevant categorical judgment or by
giving up the hypothetical one. And in most cases of conflict it will be reasonably clear which makes more
sense. But there is no guarantee of this. In some cases it will seem that none of the conflicting claims can
reasonably be jettisoned. In such cases, what needs to be revised is not merely a categorical or a
hypothetical but one’s conception of what is possible, what makes sense at all.
The ancient problem of change provides a simple illustration of the point. Change is pervasive in our
lives, but before Aristotle it seemed that changes is impossible insofar as it cannot come from what is or
from what is not. We have an inconsistent triad: (1) there is change; (2) change cannot come from what is
(because it already is); (3) change cannot come from what is not (because nothing comes from what is not).
Each of the three claims taken alone seems compelling. That there is change seems manifest in experience;
and that nothing can come either from what is (because it already is) or from what is not (because nothing
comes from nothing) also seem to be obviously true. The conflict cannot be resolved, so it seems, by
rejecting any of our three claims.
Hume’s skeptical challenge is essentially similar. We have (we think) knowledge of causal relations.
Hume shows that this knowledge cannot be either a relation of ideas, known by reason alone (because it is
not logically necessary), or a matter of fact based on experience (because though not logically necessary, it
is nonetheless necessary). But surely, Hume thinks, such knowledge could only be based on the one or the
other. And the same is true of Kant’s antinomies. Indeed, antinomy is at the heart of the whole of Kant’s
critical enterprise insofar as the reality on which thought aims to bear both must rationally constrain
judgment, if judgment is to be rational at all, and cannot rationally constrain judgment insofar as reality has
Kant thinks no inherently normative significance.
In cases involving only categoricals and hypotheticals either experience contradicts some purported
inferential connection among concepts or some conceptual connection leads to a contradiction among
putative experiences. In the cases of concern here we end up contradicting ourselves insofar as none of the
available options seem to make any sense. We need, then, a third conception of judgment, and it must be
just the sort of disjunctive judgment Kant provides. Suppose that categorical and hypothetical judgments
were the only two forms of judgment involved in inquiry, that they were together sufficient to ground our
second thoughts. There would in that case be no guarantee that there would not be a stalemate between
them, that is, a case in which we find ourselves wanting to affirm that A and that not-B and that A entails
B. And yet there cannot be an irresolvable stalemate for reason. Although it would be dogmatism to assume
that we have already in hand the conceptual resources that are needed to understand reality as a whole, it
would be skepticism to deny that we can achieve such resources as are needed. To avoid dogmatism we
need to recognize that we may well find ourselves with an inconsistent triad that we simply do not know
how to resolve by the usual means; to avoid skepticism we need a third form of judgment enabling us to
express the difficulty in the form of a judgment and so reason about it. That third form of judgment is
precisely what Kant gives us, a disjunctive judgment of the form A is (B or C), where the sphere of
possibilities is exhaustive. By making our current understanding of all the possibilities explicit in this way,
we are at the same time put in a position to come to understand the new possibilities that will resolve our
difficulties. Kant’s table of the pure concepts of the understanding establishes in this way the preconditions
for our second thoughts and thereby the science of nature.
According to the reading just outlined, Kant’s pragmatism involves rejecting not only any Given but
also the whole foundationalist picture on which it depends. What is set in the place of the foundationalist
picture is the practice of scientific inquiry, specifically, the activity of construction in mathematics and of
hypothesis, experiment, and self-correction in natural science. Two developments in the sciences after Kant
would prove critical to the development of Peirce’s Kantian analytic pragmatism, first, the emergence over
the course of the nineteenth century of yet another form of mathematical practice according to which
theorems are to be proved by strictly deductive, logical reasoning from definitions alone, and also a new
sort of physics that does not merely use mathematics but to a surprising extent just is mathematics. For our
purposes it is the first of these, the new mathematical practice of deducing theorems on the basis of
definitions, that is of primary importance. What it shows is either that Kant was wrong about the
constructive nature of mathematics or that he was wrong about the non-constructive character of purely
logical reasoning. Most, including Brandom, assume that the first is correct; they jettison Kant’s philosophy
of mathematics while embracing his conception of logic as formal. Peirce argues that it is the second that is
correct, and he does so on the basis of his analyses of reasoning, analyses that, he claims, “surpass in
thoroughness all that has ever been done in print, whether in words or in symbols—all that De Morgan,
Dedekind, Schroeder, Peano, Russell, and others have ever done [notice that Frege is not mentioned],—to
such a degree as to remind one of the difference between a pencil sketch of a scene and a photograph of
it”.12 What these analyses reveal, according to Peirce, is that “all necessary reasoning . . . is mathematical
reasoning,” that it is diagrammatic (ibid.). It follows that a good logical notation, like a good mathematical
one, enables one to reason in the notation itself; just as on Kant’s own account of the notations of
mathematics, a good logical notation ought to enable one to exhibit logical relations in a way facilitating
the discovery of new truths. (I have argued elsewhere that Frege’s notation is good in just this sense.13) If,
now, we combine that insight with Kant’s insight into the practice of the natural sciences, in particular, his
insight into the role of self-correction in that practice, we thereby give up the last semblance of
foundationalism in mathematics. Although not the whole point, one constitutive role of axiomatizing,
rigorously defining, and deductively reasoning in mathematics, and indeed in logic as well, is to reveal
errors in our conceptions and to facilitate thereby the process of self-correction. It is just as Peirce says:
“one of the most wonderful features of reasoning” is the fact that “it not only corrects its conclusions, it
even corrects its premises”.14
For Peirce as for Kant “the data for the generalizations of logic are the special methods in the different
sciences”; “to penetrate these methods the logician has to study various sciences rather profoundly”.15 Their
analyses are undertaken in order to achieve an understanding of the actual practice of science, the striving
for truth. And because they are, the variety of analytic pragmatism Kant and Peirce espouse is quite unlike
that we find in Brandom’s Locke Lectures. First, and most obviously, Brandom develops and pursues his
version of analytic pragmatism not as a logician but as an analytic philosopher of language; his aim is not
so much to understand the practice of modern mathematics and the modern mathematical sciences as it is
to emulate these sciences in order to achieve thereby the sort of understanding that he thinks they achieve.
But there are other differences as well. I will consider three that relate to their various understandings of the
nature of algebraic understanding, and also a fourth that is more global and perhaps the most important of
all.
According to Brandom, algebraic understanding is the understanding that is achieved by “constructing
the conceptual contents expressed by a target vocabulary” and “it does that by exhibiting them as
complexes formed as the products of applying explicit algorithms to the conceptual contents expressed by a
base vocabulary” (p. 213). This, he thinks, is not merely a good thing but the “gold standard” of
understanding insofar as “it takes the issue of what one means . . . out of the hands, out from under the
authority, of the one making the claims. It establishes a fact of the matter about the inferential relations that
articulate the contents of the concepts expressed by the target vocabulary that swings free of the beliefs and
preferences of the concept user” (p. 214). The idea finds an echo in Peirce’s claim that “the very first lesson
that we have a right to demand that logic shall teach us is, how to make our ideas clear . . . to know what
we think, to be masters of our own meaning”.16 But for Peirce making one’s ideas clear, being master of
one’s own meaning, is not the intrinsic good that it is for Brandom. Whereas Brandom takes clarity, in
particular, conceptual clarity, to be a cardinal virtue, for Peirce such clarity is important primarily as a
means: to make one’s ideas clear is the first step on the way to improving them. Brandom does envisage a
use for clarity insofar as it more easily enables us to settle disputes as they arise; nowhere does he suggest
that such disputes might require us to revise and correct the ideas, however clear, with which we began.
A second, closely related difference is that Brandom’s account, unlike Peirce’s, is essentially static. For
Brandom algebraic understanding consists in being clear about some thing; his focus is on the products of
understanding. Peirce is concerned rather to understand the processes of understanding, and as we have
seen, this focus on the activity of inquiry is a direct consequence of his rejecting, with Kant, not only a
12
Charles Sanders Peirce, “The Three Normative Sciences” (1903), in The Essential Peirce: Selected Philosophical
Writings, II: 1893-1913, ed. N. Houser and C. Kloesel (Bloomington and Indianapolis: Indiana University Press, 1998),
p. 206.
13
See my Frege’s Logic (Cambridge, Mass.: Harvard University Press, 2005).
14
Charles Sanders Peirce, Reasoning and the Logic of Things: The Cambridge Conference Lectures of 1898, ed.
Kennth Laine Ketner (Cambridge, Mass.: Harvard University Press, 1992), p. 165.
15
Letter to Daniel C. Gilman quoted in the Introduction to The Essential Peirce: Selected Philosophical Writings, I:
1867-1893, ed. N. Houser and C. Kloesel (Bloomington and Indianapolis: Indiana University Press, 1992), p. xxix.
16
Charles Sanders Peirce, “How to Make Our Ideas Clear” (1878), in Essential Writings I, p. 126.
Given foundation but also the whole foundationalist conception of knowing. The difference between Peirce
and Brandom on this point is, furthermore, reflected in the notation each aspires to. Brandom’s diagrams
display various relationships that can obtain among vocabularies and practices-or-abilities. Like the
diagrams developed by Euler and Venn, Brandom’s diagrams utilize the two-dimensional space of the page
graphically to present relations. What Brandom’s graphs do not enable one to do is to reason in the
diagram. Of course one can, given a particular meaning-use diagram, draw inferences about the relations
depicted; what one does not, and cannot, do is draw those inferences graphically. And the reason one
cannot is that, as Kant’s study of mathematical practice led him to see, a notation within which to reason
must involve three levels of articulation: primitive signs, wholes of those signs in relation, which in some
way present the entities of interest, and finally wholes of these (intermediate) wholes of primitives.
Think, for instance, of calculation in Arabic numeration. The primitives are the ten digits and the
intermediate wholes are the numerals we form by concatenations of those primitives. These intermediate
wholes are then arranged in a particular way on the page depending on the calculation one wishes to
perform, say, addition or subtraction, multiplication or division. Having set up one’s numerals
appropriately, one then (perceptually) reconfigures the display in various ways: considering now one
primitive sign from one numeral and one from the other, one performs a calculation, writes the result in the
appropriate place, and goes on in a familiar stepwise fashion until the desired result is obtained. Similarly
in Euclidean geometry, there are, first, the primitives (points, lines, angles, and areas), then the wholes
composed of those primitives, that is, the familiar figures (circles, triangles, and so on) that make up the
subject matter of Euclidean geometry, and finally there are the diagrams themselves within which can be
discerned various intermediate wholes depending on how the diagram is regarded. I have argued elsewhere
that it is just this feature of Euclidean diagrams that enables them to constitute ampliative demonstrations.17
And it is true in general that the extraordinary power and fruitfulness of such notations as vehicles of
reasoning rests on just this feature. Because Brandom’s notation has only two levels of articulation, only
primitive parts and wholes of those parts, it is not and cannot be a medium of reasoning. Nor, of course, is
it intended to be. What matters for Brandom’s purposes is the display of relations, not any activity an
inquirer might engage in.
Perhaps it will be objected that Brandom does concern himself with activities and processes; after all,
his is a form of pragmatism. He is concerned with use as much as with meaning. The crucial question,
however, is how he is concerned with use. As Brandom reads Wittgenstein, that use underlies and so is
prior to meaning is shown by the fact that usage and consequently meaning can and does change (see p. 6).
Thus if we want to codify meaning, say, in order to create a dictionary, we must first look to how words are
actually used by (native) speakers of the language. As the point is developed in Making It Explicit, explicit
rules codifying meanings essentially depend, on pain of a vicious regress, on rules implicit in practice.18
The regress of interpretations is to be stopped by one’s implicit grasp of a rule as manifested in one’s
practice. As should be clear, this is the version of pragmatism that jettisons the mythic Given while keeping
in place the foundationalist picture overall. The need for a Given remains and is here met by appeal to
practices.
But one can also read Wittgenstein differently, as rejecting not only the Given but also the whole static
foundationalist picture on which it depends.19 Much as an animal is an instance of a form of life, where a
form of life is characterized by particular capacities, perceptual and motor, and a narrative of growth,
development, and characteristic behavior, so, on this reading, a person going by a signpost (say) is an
instance of a (now socially rather than biologically evolved) form of life characterized by various activities
and abilities, among them the ability to see and so to follow the way a signpost points. Much as mere stuff
can acquire, in the course of the evolutionary emergence of animals, the significance of food, that is, of
being (appropriately or normally) nourishing for an animal of a certain sort, so what is otherwise a mere
stuff can acquire, in the course of the social evolutionary emergence of rational animals, the significance of
being a reason for us. The signpost itself, in such a context, can tell us the way to go on. In place of the
foundationalist picture, we have on this reading the picture of a kind of animal with its characteristic
capacities and activities, as an instance of a form of life that is itself a narrative of birth, growth, and finally
17
See my “Diagrammatic Reasoning in Euclid’s Elements”, forthcoming.
18
Robert B. Brandom, Making It Explicit: Reasoning, Representing, and Discursive Commitment (Cambridge, Mass.:
Harvard University Press, 1994).
19
See John McDowell, “How Not to Read Philosophical Investigations: Brandom’s Wittgenstein”, reprinted in The
Engaged Intellect: Philosophical Essays (Cambridge, Mass.: Harvard University Press, 2009).
death. The activities of life itself, and in particular our own form of life as the rational animals we are, thus
play a constitutive role in this account that is altogether different from that they play on Brandom’s reading.
This difference between the two varieties of pragmatism it is possible to read into Wittgenstein is
further reflected in the fact that Brandom’s analytic pragmatism, by contrast with that of Peirce, inevitably
needs a given vocabulary that provides, in effect, the bricks and stones with which to build its structures.
As Brandom himself puts the point, “every context in which it [algebraic understanding] is available
contains an appeal to a base vocabulary whose use is not held in place algebraically, but depends on
another sort of practical mastery and understanding” (p. 215-6), one that Brandom thinks of as
hermeneutic. Because Brandom conceives analysis as a matter of constructing contents by “exhibiting them
as complexes formed as the products of applying explicit algorithms to the conceptual contents expressed
by a base vocabulary (treated for this purpose and relative to this construction, as simple)” (p. 213), he
simply must have some materials given at the outset. The task is that of conceptual engineering, of building
structures out of given materials. On a more Kantian and Peircean version of analytic pragmatism what
analysis reveals is not structure or form for an antecedently given content, but instead a dynamic, organic
process of intellectual inquiry and growth mediated, at least in many instances, by a symbolic, or as Peirce
would say, diagrammatic, language, one that is fully meaningful in its own right and has not two but three
levels of articulation.
There is, finally, a very striking difference in the overall orientation of Peirce and Brandom that is not, I
think, accidental to the varieties of analytic pragmatism they espouse. Because for Peirce the central
concern of the philosopher is actual scientific inquiry, which is first and foremost constitutively self-
correcting, Peirce’s first, and in a sense only, rule of reason is “that in order to learn you must desire to
learn and in so desiring not to be satisfied with what you already incline to think”.20 To learn, and so to be a
true scientist in Peirce’s sense, one must be devoted to “the pursuit of truth for truth’s sake”, where this
devotion is, Peirce thinks, a kind of existential commitment, “a mode of life”, “the devoted, well-
considered, life-pursuit of knowledge”.21 Peirce describes his own philosophical ideas as the fruits of just
such a life, as growing “out of a contrite fallibilism, combined with a high faith in the reality of knowledge,
and an intense desire to find things out”.22 Brandom’s orientation, inspired by the example of David Lewis,
is very different. On this approach “what philosophers should do is lay down a set of premises concerning
some topic of interest as clearly as possible, and extract consequences from them as rigorously as possible.
Having done that, one should lay down another, perhaps quite different set of premises, and extract
consequences from them as rigorously as possible” (p. 225). What Brandom finds “liberating and
exhilarating about this metaphilosophical attitude is that Lewis . . . didn’t care much what reasons one had
for starting with one set of premises rather than another. He was entirely open to, and indeed eager to, turn
his awe-inspiring intellect to following out the consequences of even the wackiest of claims” (p. 226). It is
in just this spirit that Brandom would have us take up his work in the Locke Lectures (ibid.). For Peirce,
although “there is no positive sin against logic in trying any theory which may come into our hands”,
nevertheless “it is better to be methodical in our investigations”23; and this is better because “the more
voraciously truth is desired at the outset, the shorter by centuries will the road to it be”.24 If one desires
truth above all else then Lewis cannot be one’s model.
Brandom’s variety of analytic pragmatism aims to extend the project of analysis that is exemplified in
such work as Russell’s theory of descriptions to embrace not only meanings but also use. Because
pragmatism, in particular the pragmatism of the later Wittgenstein, is for him simply the idea that there is
no Given foundation for meaning, his variety of analytic pragmatism is and must be limited to feats of
construction between bits of vocabulary. But perhaps a further step is needed as well. If, as I have argued,
the Given could not possibly found either meaning or truth and knowledge insofar as it would be utterly
unquestionable and hence merely what we are inclined to think (which is a matter for psychology, not
20
Reason and the Logic of Things, p. 178.
21
Charles Sanders Peirce, “The Century’s Great Men in Science” (1901), originally appearing in the New York Evening
Post, quoted in the Introduction to The Essential Peirce, II, pp. xxii-xxiii.
22
Charles Sanders Peirce, “Concerning the Author” (1897), in Philosophical Writings of Peirce, ed. Justus Buchler
(New York: Dover, 1955), p. 4.
23
Reasoning and the Logic of Things, p. 178.
24
Reasoning and the Logic of Things, p. 170.
philosophy), then it is the whole static foundationalist picture that must be given up, replaced with just the
focus on the activities of inquiry in the sciences that we find in Peirce and Kant.25
But although these two varieties of pragmatism are in this regard very different, they are nonetheless
alike in embracing the need for systematic theorizing in philosophy, in eschewing the sort of quietism that
Wittgenstein can seem to espouse. As the analytic pragmatism of Kant and Peirce furthermore shows, the
idea of an analytic pragmatism, which can easily seem oxymoronic, is not inherently problematic. Kant, the
first pragmatist, certainly did not eschew philosophical theorizing, the forming and testing of hypotheses,
and nor did Peirce; for both, such a “scientific”, and so inherently self-correcting, attitude is constitutive of
the practice of philosophy. Indeed, one could say that, for them, to be a pragmatist just is to be an analyst
insofar as the method of their variety of pragmatism is critique, the task of self-scrutiny that reason can and
must take up in the aftermath of dogmatism and the inevitable skepticism that follows it. Brandom’s variety
of analytic pragmatism is not so easily seen as a real and organic unity. It may well be that in the end his
variety is just as John McDowell has described it, the project of (in Brandom’s words) “perversely
transplanting perfectly healthy pragmatist organs into the rotting corpse of analytic philosophy” (p. 202). I
leave this question for others to decide.
25
As Sellars puts it, “science is rational, not because it has a foundation but because it is a self-correcting enterprise
which can put any claim in jeopardy, though not all at once.” Wilfrid Sellars, “Empiricism and the Philosophy of
Mind”, in Science, Perception and Reality (London: Routledge and Kegan Paul, 1963), §38, p. 170.