## 1. General Characterization of Carnap's Philosophy


### 1.1 Rational Reconstruction and Explication



Carnap differed fundamentally from the western philosophical tradition
in his conception of philosophy and his attitude toward philosophical
problems. These supposed problems, he thought, were largely artifacts
of our inadequate tools--they originate in confusions due to the
languages our species has evolved over millennia to deal with the
practical problems of a pre-scientific and pre-technological everyday
life. These primitive tools leave us unequipped even to express, let
alone to address, the traditional problems of philosophy coherently;
our inherited languages distort the picture too badly, and to see
things more adequately we need to devise new concepts and organize our
thoughts in less parochial categories. Just as we have devised new
concepts and vocabularies to find out about the world in systematic
scientific inquiry, so we have to leave behind our traditional ways of
articulating how everything fits together, how we should understand
our place in the world, and how we should shape our lives in
response.



So philosophical inquiry became, for Carnap, a kind of
"conceptual engineering" (see Creath 1990, Flocke
forthcoming-b) rather than a form of inquiry or search for knowledge.
It did not ask how things are, in Carnap's view, but rather
how--within the constraints of our available tools and the
knowledge available from the sciences--we *want* things to
be. This form of "voluntarism" (Jeffrey 1992) lies at the
basis of Carnap's philosophy from beginning to end.



Carnap applied this voluntaristic conceptual engineering in many
different ways to many different problems, at different levels and on
different scales. He applied it both within science and to larger
problems *about* science (e.g., scientific language), or about
the place of science in our lives. He applied it both to local
reconstructions or explications of particular concepts (e.g.,
confirmation), and more globally, to entire language frameworks (see
 section 1.2
 below). And he wanted the local and global to fit together; precise
definitions of explicated concepts were to be situated within such
larger frameworks.



The terminology evolved over the years. Carnap tended to think of his
first engineering projects as "rational reconstruction";
later he favored the term "explication". Both refer to the
reconstruction or replacement of particular terms or concepts within
our more primitive ordinary languages (or vestiges of them in
scientific languages) rather than to the design and development of
entire languages or language frameworks. There was a progressive
change of emphasis over the course of Carnap's career in the
goals and the scope of this reconstructive engineering. In the early
years Carnap (along with most of his colleagues in the 1920s Vienna
Circle) saw these engineering projects in much the same light as the
eighteenth-century *Encyclopedistes* and
nineteenth-century positivists had seen them. Ordinary language and
traditional concepts were to be *overcome*; they were to be
*replaced* by better and more scientific ones. Later,
Carnap's view became more pluralistic and dialectical (Stein
1992); he increasingly recognized the practical nature of conceptual
engineering and allowed more room for the standpoint of the language
user, as well as the differing priorities and value systems involved
in the choice of language frameworks or explications. Recently,
Carnap's idea of explication has attracted a good deal of
attention (Maher 2007; Kitcher 2008; Carus 2007a; Dutilh Novaes &
Reck 2017; Brun 2016; several papers in Wagner 2012), particularly
among authors seeking to define the proper role of the new
subdiscipline of experimental philosophy (Justus 2012; Shepherd &
Justus 2015; Schupbach 2017) or of the methodology of mathematical
philosophy (Leitgeb 2013). More details are to be found in the
supplement on
 Methodology.
 (For more on conceptual engineering more generally, see, e.g.,
Cappelen 2018.)


### 1.2 Frameworks



Explications or rational reconstructions were envisaged by Carnap as
situated (where possible) in larger linguistic or conceptual
frameworks, constructed object languages with a hierarchy of
metalanguages in which to define and explore truth, analyticity,
synonymity, designation and other semantic resources of the object
language, and of the object language with respect to its
extra-linguistic environment.



Frameworks always involve logical consequence relation(s), their
definition(s) of what follows from what logically. But this need not
always mean that frameworks have purely logical object languages that
are then provided with empirical interpretations. Other modes of
inference employed in existing scientific disciplines, including
conceptual inference, experimental procedures, and the reasoning from
these, can also be reconstructed in or by frameworks. Carnap continued
to hope that all of them could, eventually, be understood in more
straightforwardly logical terms, but he realized that this was a
long-term program and not immediately on the horizon. In particular,
the framework could also come equipped with an inductive logic, where
the deductive consequence relation for the object language is
augmented by a numerical degree-of-confirmation assignment that
satisfies the axioms of probability. In any case, Carnapian language
or framework go beyond what we now mean by a formal language: they do
not just involve a syntactic vocabulary and syntactic formation rules.
From the modern logical point of view, a Carnapian framework is close
to a logic or a formal theory (but perhaps with an interpretation),
while from the philosophy of science point of view, a Carnapian
framework is meant to reconstruct the conceptual and inferential
presuppositions of a scientific theory rather than a scientific theory
itself.



Carnap's earliest attempts to develop frameworks, which sought
to encompass the conceptual resources of all empirical knowledge, can
be found in *Der logische Aufbau der Welt* (1928a, *The
Logical Construction of the World*), commonly referred to as the
*Aufbau*, its abbreviated original German title. Carnap there
focused on sketching a phenomenalist framework in which scientific
concepts could be constructed from pure observation. The idea was to
have a single framework relative to which any scientific sentence
whatsoever (other than purely logical or mathematical ones) could be
judged to be cashable or not cashable in empirical, observational
terms. However, as Carnap soon realized, the framework failed to
address theoretical scientific concepts, disposition concepts, or
probabilistic concepts, among much else.



The frameworks on which Carnap worked after this were less specific to
particular epistemological problems, and more abstract and general. In
his view, the specification of a framework was a prerequisite for any
rational reconstruction of rational discourse whatsoever. As we will
discuss in more detail below, his *Logische Syntax der Sprache*
(1934, translated as *The Logical Syntax of Language*, 1937,
hereafter LSS) worked out two different frameworks for mathematics
(and physics) and developed a corresponding account of philosophy as
the logical syntax of the language of science. Soon after, Carnap
followed Alfred Tarski in making the basic concept of
"truth" language-relative; and in 1950 he applied the same
idea more explicitly to the basic concept of "existence".
It only made sense to speak of something "existing"
relative to a framework (i.e., one could only speak of
"existence" as *internal* to a framework), he said,
not in any general sense (*external* to any framework
whatever). This deflationary conception of truth and existence (and
many other previously metaphysical concepts) again reflects
Carnap's resistance to the suggestive traps set by ordinary
language and the philosophical tradition that has been too ready to
fall into these traps.



In his later work, Carnap extended his construction of semantic
frameworks by developing frameworks in which probabilistic relations
play a central role, including eventually frameworks for rational
decision and action (decision theory). The specific details of
Carnap's various linguistic frameworks are discussed in the
following supplements:
 *Aufbau* (Section 1),
 *Logical Syntax of Language*,
 Semantics,
 The Reconstruction of Scientific Theories, and
 Inductive Logic.


### 1.3 Pluralism and Tolerance



Carnap differed from the philosophical tradition not only in his
suspicion of ordinary language and its potentially misleading
"philosophical" artifacts, and in his engineering impulse
to replace our inherited languages by better-constructed and more
precise constructed linguistic frameworks, but also in his
increasingly pronounced pluralism among frameworks. In the
*Aufbau*, Carnap had already discussed the availability of
different frameworks (phenomenalist, physicalist, and more), and how
they were more or less suitable for different purposes (see the
supplement on
 *Aufbau*).
 But these frameworks still differed only in the choice of non-logical
primitives and in the definition of non-primitive terms--the
frameworks were still based on the same syntactic formation rules and
on one and the same logical system. As far as the explicit endorsement
of syntactic and logical pluralism and tolerance is concerned, the
turning point came in 1932, while Carnap was writing his book (now
often considered his masterpiece) *Logical Syntax of Language*.
The starting point of that book, as we will see in more detail in
 section 4
 below, had been strongly motivated by the search for a single
standard language of science. But this was now combined with
Carnap's new idea that, for philosophical statements
*about* science, the standard of communicative acceptability
should not (as in Wittgenstein's *Tractatus*) be that it
have *meaning* (that it picture some state of affairs), but
that it be translatable into the "formal mode of speech".
His criterion for the scientific (non-metaphysical) status of a
philosophical statement, that is, had shifted from the reducibility of
a sentence to "atomic" observation sentences to its
expressibility as a statement solely about linguistic artifacts
(rather than about the supposed things and processes they refer to).
But Carnap had still thought, until late 1932, that a single standard
language for logical syntax could be found, and had invested a lot of
time in devising such a language system. At that point, however, two
sets of controversies attracted attention: the so-called
"protocol sentence debate" about the correct form of
observation sentences (and by implication, the role of observation in
science), and the dispute about the foundations of mathematics among
the three schools of logicism, intuitionism, and formalism. Both these
controversies came to seem to Carnap, after years of involvement in
each of them, to stumble over artifacts of inherited language just
like the old philosophical problems the Vienna Circle thought it had
swept away. He came to regard the different positions in these debates
not as potentially "right" or "correct" (or
"wrong" or "incorrect") but as different
proposals for language frameworks in which to frame the questions,
different ways of articulating the problems surrounding empirical
evidence and the nature of mathematics, respectively. And it seemed to
him that these proposals were mostly not mutually exclusive; on the
contrary, he came to think that many different alternative languages
should be pursued and developed to see how well they perform in
different contexts. He saw them as motivated by different needs and
requirements, perhaps by different ultimate values, and he thought the
discussion of values should not be confused with the study and
development of the language frameworks themselves: "in
logic", he famously wrote in the *Syntax* (LSS:
SS17), "there are no morals".



This new pluralism undermined the initial premise of the
*Syntax* book on which he was working then, but Carnap
nonetheless took it on board. The language he had initially been
intending to propose as the single standard language of science was
now used simply as an example, and to be sure that it wasn't
taken too prescriptively Carnap also developed another language
(Dr.-Seuss-like, he called them "Language I" and
"Language II"), and stressed that both were acceptable,
though each had its strengths and weaknesses for different purposes.
The new linguistic pluralism was stated as the



> 
> 
> *principle of tolerance: we are not in the business of setting up
> prohibitions but of arriving at conventions*... *In logic
> there are no morals*. Everyone is welcome to set up his logic,
> i.e., his form of language, as he pleases. If he wants to discuss it
> with us, though, he needs to state his intentions clearly, and give
> syntactical specifications rather than philosophical debates. (LSS:
> SS17)
> 
> 
> 



This principle would remain a permanent, indeed the dominant,
component of Carnap's philosophy for the rest of his career. For
more details on Carnapian tolerance, see the supplement
 Tolerance, Metaphysics, and Meta-Ontology (Sections 1 and 2).


### 1.4 Metaphysics



Why, under this pluralism, should some statements and expressions
still be excluded, as *not* having any content, as *not*
conveying anything but as being just empty verbiage that purports to
say something significant? Why, that is, should
"metaphysics" still be excluded, as Carnap notoriously
insisted? Surely the metaphysician is as free as anyone else to choose
her language?



These questions take us back to the engineering ethos described in
 section 1.1
 above, about explication and rational reconstruction. Language
choice, for Carnap, was not an end in itself but was rather in the
service of freeing ourselves from the distorted perspective on the
world imposed on us by our inherited natural languages. These
languages had not evolved to optimize the transparent representation
of knowledge, but for very different, primitive practical purposes.
For the pursuit of knowledge, and insight into the human condition in
the light of that knowledge, better languages are needed. What makes a
language "better"? In principle Carnap leaves that open.
Everyone has their own values about what they want languages to do for
them, and will choose accordingly. But Carnap's own values were
those of the Enlightenment. His value hierarchy placed the value of
escaping from the complacent, passive acceptance of authority, or of
traditional or folk ideas--and finding something objectively
better--near the top. The replacement of knowledge accepted
passively from authority or tradition by objective knowledge was his
goal just as it had been the goal of the
*Encyclopedistes*. And by "objective"
knowledge, Carnap meant essentially scientific and practical
knowledge, just as they did.



This did not mean a rejection of the humanistic tradition, or of
dimensions to values other than the scientific and
engineering-oriented. Carnap took entirely for granted (so deeply that
he hardly ever bothered to make it explicit) that literature, art, and
music shaped people's values and were closely connected with
them. But these were for individuals to negotiate. Since his
experience of the First World War, he had realized that the German
intelligentsia's political indifference, its overindulgence in
humanistic individual values, had been partly to blame for the war. He
had resolved, therefore, to attend more to the framework that all
humans shared, and that formed the basis for their social and
political cohabitation. Objective knowledge was, to him as to the
Enlightenment, at the core of this shared framework. Practical
(especially political) decisions should be *informed* ones,
arrived at in the light of the best possible knowledge about the
available choices and their consequences.



Metaphysics was, in his view, a distraction from this program.
Metaphysics was a kind of failed art form masquerading as knowledge,
so it was both fake art *and* fake knowledge. Unlike a logical
or mathematical proof or the confirmation of a scientific theory,
metaphysical proposals are unable to command widespread agreement;
even the criteria by which they should be judged are often in
dispute.



On the other hand, all of Carnap's repeated attempts, over
several decades, to give a precise delineation--to explicate the
distinction--between scientific (or meaningful or communicatively
adequate) statements and metaphysical (non-scientific, non-meaningful)
ones failed. He therefore became more liberal and less exacting about
what was to be regarded as metaphysical. He was willing to allow that
many metaphysical theories of past philosophers (he cites Aristotle,
Leibniz, Kant, Peirce, and Whitehead, among others) could be regarded
as useful steps toward the construction of "the most general
frameworks containing categorial concepts which are fundamental for
the representation of all knowledge", and moreover that he
himself regarded this task as among "the most important problems
of philosophy" (Carnap 1963b: 862). See the supplement
 Tolerance, Metaphysics, and Meta-Ontology (Section 2 and 3)
 for further detail.


### 1.5 Verification and Confirmation



Carnap's life-long quest to explicate the distinction between
statements that genuinely convey something and empty verbiage that
only purports to say something (metaphysics) began with
Wittgenstein's *Tractatus*, the Vienna Circle's
provisional starting point. The Circle interpreted Wittgenstein as
requiring what Carnap later called a "molecular" language,
by which he meant a language that permitted only finitely restricted
quantification. This posed an obvious problem in that scientific
theories, the very paradigm of what the Circle regarded as proper
(non-metaphysical) knowledge, nearly all contain unrestricted
universal quantifiers and thus range, in principle, over an infinite
number of instances. As Carnap already acknowledged in his first
writings on the subject, well before Popper appeared on the scene,
this meant that theories could not, strictly speaking, be verified;
they could only be confirmed up to a certain confidence level, or
disconfirmed (e.g., Carnap 1926: 7-9).



As we will see in
 section 5
 below, this and related problems constituted a large part of the
Circle's agenda during the late 1920s and early 1930s. The
important thing to keep in mind through all this is that "the
verification principle" in its crude form was never advocated by
Carnap or any other major figure in the Circle. (More detail on this
in the supplement on
 The Reconstruction of Scientific Theories (Section 1).)
 In the *Aufbau*, Carnap had, it is true, worked out a
finitist, "molecular" phenomenalist language and advocated
the epistemological benefits of reconstructing scientific concepts on
its basis. During this period, he was attracted to a form of radical
positivism that played down theories as mere auxiliary devices for the
prediction of observations. The observations that confirm theories, in
this view, was really all there was to science, in what amounted to a
kind of instrumentalism about theories, as it would later be
called.



But soon afterwards, in his *Logical Syntax*, and more
explicitly when he published "Testability and Meaning" in
1936-37, Carnap decisively distanced himself from such
doctrines. In the light of the new principle of tolerance, the
obsession with just one standard language form seemed unnecessarily
"absolutist" and rigid. In "Testability and
Meaning" it is stressed that many different language forms are
possible in science and should be investigated, and that none is
"correct" or uniquely acceptable for the purposes of
scientific confirmation. The point is to devise languages that meet
certain goals of inquiry better than others, in the awareness that
some languages may be better for the pursuit of one goal, while other
languages are preferable for other goals. This is perhaps the first
fully explicit expression of the engineering ethos described in
section 1.1 above.



This period also marks a return to the recognition that radical
positivism of the "molecular" or *Tractatus* sort
hardly does justice to actual science--so Carnap returns now to
science as it actually is done rather than an idealized, purely
factual science. This meant, once again, an acceptance that
theoretical vocabulary needed to be accounted for in one's
conception of science. Another kind of concept characteristic of
actually practiced science that gets special attention in
"Testability and Meaning" is disposition concepts (e.g.,
"soluble" or "refrangible"; more on
disposition concepts in the supplement
 The Reconstruction of Scientific Theories (Section 2)).
 Probabilistic concepts would soon come into focus as well as a
significant preoccupation.


### 1.6 Theory Reconstruction and Inductive Logic



From this period, then, Carnap once again focused on scientific
theories, and on theoretical languages as not fully reducible to
empirical observation sentences. While he had given up the effort to
*reduce* theories to observations, he remained preoccupied with
the complementary problems of how a theory can be *confirmed*
by observations, and how the empirical *content* of a theory
can be determined. Both of these problems were articulated, and seen
as interrelated, in "Testability and Meaning", but
thereafter they took separate paths. The first of these problems was
central to Carnap's preoccupation with inductive logic from
about 1942, though he was never able to develop it to the point where
it could be applied to the confirmation of *theoretical*
sentences (as opposed to mere empirical generalizations). The second
problem was the focus of significant attention to the nature of
theoretical languages and the degree to which theories are constrained
by evidence, as well as the problem how to identify the analytic and
synthetic parts of a theoretical hypothesis or a theory, i.e., to
distinguish what components of it come with the language framework in
which it is expressed, and what components contain actual information
about the world. See sections
 8.1
 and
 8.3
 below on Carnap's further pursuit of both problems and his
controversies and interactions with Popper, Hempel, and others on
these issues. The supplement
 The Reconstruction of Scientific Theories (Sections 3 and 4)
 deals in more detail with Carnap's distinction between
observation language and theoretical language in science, and with
Carnap's reconstruction of scientific theories and theoretical
terms by means of Ramsey sentences and related logical resources.



His own primary attention during the later years of his career was to
inductive logic, where he began by distinguishing two fundamentally
different explicanda of the concept "probability": (i) the
idea of probability as *relative frequency* of some occurrence
in a series of events or in a population, which he regarded as a
legitimate and entirely empirical matter. He contrasted it with (ii)
probability understood as an *epistemic* measure of our
certainty or uncertainty about the empirical truth or adequacy of a
statement. The latter was Carnap's focus; at the outset he
worked out a structural and logical conception of epistemic
probability, influenced by Waismann and Keynes, as further explained
in the supplement
 Inductive Logic,
 and progressed over the years toward a more "personalist"
view, though never giving up the logical conception entirely. He
worked closely with various students and associates on these problems,
especially Richard Jeffrey, Yehoshua Bar-Hillel, and John Kemeny. See
 section 8.2
 below, see the supplement
 Inductive Logic
 for the details of his structural account of probability, and see the
supplement
 Methodology (Section 1)
 for his probabilistic explication(s) of inductive confirmation. Ray
J. Solomonoff's work on universal inductive inference was also
triggered by Carnap's inductive logic. (Solomonoff studied with
Carnap in Chicago. See Sterkenburg 2018 for a discussion and
evaluation.)


### 1.7 Structuralism



Another strand of Carnap's indifference to ontology was his
lifelong focus on *structures* as the main objects of
knowledge. Even as early as 1922, Carnap had thought that mathematics,
correctly understood, is not so much the study of quantity and number
as the study of structures; Kant's dictum that something is
scientific just insofar as it is mathematical was now superseded, he
thought, by his new dictum that something is scientific just insofar
as it is *structural* (Carnap 1922b: p. cl[r], translated and
quoted in Carus 2007a: 163). And if the object of our knowledge is not
the particular or the qualitative but the structural, then, as Hermann
Weyl had said, "A science can determine its subject matter only
up to an isomorphic representation".



> 
> 
> In particular, it is altogether indifferent toward the
> "essence" of its objects of study...It is mysticism
> to expect of scientific knowledge that it reveal--to
> acquaintance--a deeper essence than that openly available to
> acquaintance. The conception of isomorphism pinpoints the
> unquestionable and ineluctable limit to knowledge. (Weyl 1926: 22
> [1947: 25-26])
> 
> 
> 



Weyl speaks here in the language of axiomatic systems and their
structurally identical--isomorphic--models, a language
largely articulated at the beginning of the twentieth century by David
Hilbert. But Hilbert had only made more precise the notions of
structuralism that went further back and had animated a great deal of
nineteenth-century mathematics (see Schiemer 2013), culminating in the
group-theoretic (algebraic) understanding of the new non-Euclidean
geometries and Felix Klein's celebrated "Erlanger
Programm" for the unification of geometry by this means, which
also inspired the early Bertrand Russell. Russell himself, and before
him Gottlob Frege and Richard Dedekind, had given
"top-down" definitions of structural concepts by means of
higher-order logical quantifiers (as in Frege's 1879 famous
definition of the ancestral of a relation in his
*Begriffsschrift*, or in Dedekind's 1888 definition of
simply infinite system in his *Was sind und was sollen die
Zahlen?*, or in Whitehead and Russell's 1910-1913
*Principia Mathematica*), all of which influenced Carnap
significantly. An equally important influence, at about the same time
as Klein, was the epistemological structuralism of Hermann von
Helmholtz. Carnap was clearly inspired by these ideas, not only in his
earliest work, but all through his career, even into his work on
probability and induction, as we will see below
 (section 8).



Carnap is best known, though, for his application of structuralism
first to epistemology, in the *Aufbau*, and then to mathematics
itself, in the *Syntax* and later work, as well as to
mathematically formulated scientific theories. The frameworks
discussed in section 1.2 above were always structural ones, in which
Carnap invariably abstracted from the actual instantiation of the
structures in question in actual languages or conceptual systems, with
the result that even some of his closest allies and associates
misunderstood him, including (among others) Russell, Neurath, Popper,
and Quine (see
 sections 3
 through 8 below for details). The articulation of these structural
frameworks is discussed in the supplements
 *Aufbau*,
 *Logical Syntax of Language*,
 Semantics,
 and
 Reconstruction of Scientific Theories.



Carnap's structuralism about mathematics also points forward, in
its anticipation, for instance, of Tarski's structural
delimitation of logic modeled on the Erlanger Programm (Tarski 1986,
Sher 1991), and has recently been seen as a precursor of a new form of
mathematical structuralism based on homotopy type theory in its
emphasis on invariance (Awodey 2017).



From the *Aufbau* (see the supplement
 *Aufbau* (Section 2)
 on Carnap's early structuralism) to his mature reconstruction
of scientific theories (see the supplement
 The Reconstruction of Scientific Theories (Section 6)
 on Carnap's later structuralism), Carnap sought to articulate
an innovative type of *conceptual* or *linguistic*
structuralism about science that is metaphysically neutral and which
resembles modern versions of structuralism about mathematics: the
cognitive content of what can be asserted precisely and meaningfully
in science can be reconstructed as a structural constraint on
empirical content, and one should aim at such structural
reconstructions as they enhance the objectivity of science. While
structural properties are expressed using logical concepts usually
discussed in the context of *deductive* logic, Carnap's
later work on *inductive* logic considers probability measures
that are logical or structural in the analogous sense, i.e., where
probabilities remain invariant under isomorphisms. This
"inductive structuralism" is discussed in supplement
 Inductive Logic.


### 1.8 Values



Carnap is not generally known for his (very sparse) publications about
values, but what he did publish is sufficient (in conjunction with
recently published texts) to yield a fairly accurate insight into his
thinking, which turns out to be sufficiently original to have
significant potential for further development. Carnap's main
publication on values is the final (and longest) chapter of his
replies to critics in the Schilpp volume (the Reply to Kaplan, Carnap
1963b). On the basis of this text, Carnap has generally been
classified simply as an (ethical) non-cognitivist. And there is a
close resemblance between Carnap's proposed logic of normative
statements ("optatives", Carnap calls them) and that of
Richard Hare (1954) published at about the time Carnap's reply
was written (though it was not published until 1963). The term
"non-cognitivist" to describe the view that normative
statements cannot be true or false (and that therefore no
"ought" can be derived from an "is", as Hume
had put it), was, in fact, proposed by Carnap--one of his more
widely-accepted (if low-profile) coinages.



However, it had been assumed that since Carnap required a framework to
be in place for any kind of rational discourse to be possible, the
choice of frameworks itself must be simply a matter of personal whim,
at the level of Hume's declaration that there is no rational
argument for me to prefer the relief of a pain in my little toe to the
prevention of some world-engulfing catastrophe. This problem of the
irrationality of framework choice (George 2012) or--put another
way--the supposed infinite regress in the selection of
meta-frameworks for the choice of framework (Richardson 2007;
Steinberger 2016; Carus 2017) has been discussed recently from various
angles. It is a special case, in the way Carnap is still usually seen,
of the supposedly more general impossibility, for Carnap, of bringing
reason to bear on normative choices, since in his view all reasoning
seems to presuppose internality to a framework.



But from an interpretive viewpoint, this was clearly an unsatisfactory
position, since Carnap had in fact from his earliest days used
reasoning to argue for normative positions, and continued to do so all
his life. So there seemed to be a tension, at such a basic level that
one would surely think Carnap must or should have been aware of it. In
fact, there is no tension, as it turns out that Carnap (at least in
his later years and probably for much of his career) held a
quasi-Kantian view whereby the logical reasoning we employ in
mathematics, logic, and science (including inductive logic and
decision theory) is conceived as subordinate to (and narrower in scope
than) a purely normative form of reasoning--in Kantian terms,
*Verstand* (understanding) is subordinate to (and narrower
than) *Vernunft* (reason). So at least it appears from a
recently published fragmentary draft Carnap wrote in 1958 of a
continuation of or sequel to the reply to Kaplan about values that had
appeared in the Schilpp volume (Carnap 2017); see the supplement
 Tolerance, Metaphysics, and Meta-Ontology
 for further discussion.



More recent forms of normative non-cognitivism have recast their
doctrines somewhat to describe them as "expressivist"
(Blackburn 1993; Gibbard 1990). From this starting point Huw Price
(1988) has sought to generalize expressivism to include not only
normative language but other kinds as well. In some more recent
expositions of this proposed globalized expressivism or
"functional pluralism" (Price 1997; see also Creath 1994
on the sense on which Carnap's view can be called
"functionalist"), he invokes Carnap's conception of
mathematics as the exemplar on which he proposes to model his approach
to all sectors of language; he calls this the "Carnap
thesis", and assigns it fundamental importance in the
development of a new "global expressivism" as he also
calls his position (Price 2013, 2018). In view of the discussion
above, it would seem that Carnap himself had already generalized his
functionalist "Carnap thesis" regarding mathematics to at
least values and possibly also to other sectors of language (Carus
2018; Price 2018). This is also consistent with the new-found interest
in Carnap's "inferentialism" (Peregrin 2011,
forthcoming; Chalmers 2012), discussed further in
 section 5
 below. Perhaps, in some respects, current philosophy is beginning to
catch up to Carnap.



(General surveys of Carnap's work can be found in, e.g., Mormann
2000, Friedman and Creath 2007.)


## 2. Toward the *Aufbau*


### 2.1 Beginnings



Carnap was born on 18 May 1891 in the small town of Ronsdorf, now part
of Wuppertal, an industrial city near the Ruhr area of northwestern
Germany. His mother was a schoolteacher, and her father, Friedrich
Wilhelm Dorpfeld (1824-93), had been a leading educator and
educational thinker in the Herbartian tradition. Carnap was
home-schooled by his mother until secondary school, and brought up
religious, but the emphasis was on the ethical, rather than the
doctrinal, dimensions of religious life. As a result, Carnap said, he
had no crisis of conscience when he later abandoned any belief in God
or the supernatural. In 1908 the family moved to Jena, into the house
of another famous relative, Carnap's maternal uncle Wilhelm
Dorpfeld (son of Friedrich Wilhelm), a well-known and highly
influential archaeologist. Carnap made trips to Greece with his uncle
during this time. He subsequently finished secondary school in Jena
and enrolled in the university there, studying philosophy, physics,
and mathematics, vaguely intending to become a high-school science
teacher.



At the University of Jena he soon encountered the "Sera
Circle", an offshoot of the Youth Movement that swept Germany in
the years before World War I. He became enthralled with the idea, as
he later said, that social forms and behavioral standards did not have
to be assimilated uncritically from the surrounding society, or from
tradition, but could be freely invented. The "voluntarism"
that suffuses every phase of his later philosophical career (Jeffrey
1992) seems to have had its origins here. He became not only an
enthusiastic participant in the Youth Movement but also a leader,
representing the Jena branch at the climactic national meeting of
local Youth Movement groups at the Hoher Meissner in 1913 (Werner
2003).



Carnap's first exposure to logic came from an obscure and
reclusive professor of mathematics at Jena, Gottlob Frege. Carnap was
so fascinated that he took every course Frege offered (including two
courses on Frege's Begriffsschrift and a course on Logic in
Mathematics). His resulting shorthand notes are sufficiently detailed
to permit a reconstruction of Frege's response after the system
of the *Grundgesetze* had been undermined by Russell's
paradox (Reck & Awodey 2005). It would be another decade, though,
before Carnap came to see Frege's logic as the key to a new way
of doing philosophy. Carnap also studied with neo-Kantians and
*Lebensphilosophen*, including Bruno Bauch (whose course on
Kant's First Critique left a lasting impression), Herman Nohl (a
student of Dilthey) and--while in Freiburg for a
semester--Heinrich Rickert, whose lectures Carnap was
particularly enthusiastic about.



The war interrupted this development. Carnap and his Youth Movement
friends, though hardly enthralled, felt they could not shirk their
duty to serve. Carnap spent most of 1914-17 at the front (first
the eastern, then the western), and took part in some of the bloodiest
engagements. In 1917 he was wounded, awarded the Iron Cross, and spent
the remainder of the war at a radio research facility in Berlin. He
also became politically active: he joined the (by then anti-war)
Independent Socialist Party, circulated excerpts from the world press,
mostly critical of the German government, to friends with his comments
(Werner 2015), and participated in the transformation of the Youth
Movement (or parts of it) into a political force. He teamed up with
Karl Bittel, another Youth Movement leader, to start the underground
*Political Circular*, a newsletter for university Youth
Movement adherents that appeared irregularly during the months
immediately preceding the German Revolution of 1918. In the first
issue, Carnap reviewed two books on proposals for worldwide political
union (Carnap 1918a). He also prepared for publication a much longer
and more detailed analysis of the entire political situation following
Germany's military defeat, but the Revolution occurred just as
it was to be published, and it never appeared. (See the editors'
introduction to Carnap 2019; it has now been published, along with
other early Carnap manuscripts, in Dambock, Sandner, & Werner
forthcoming.)



Carnap's newfound political orientation was a non-Marxist
libertarian socialism of a kind represented by Gustav Landauer
(1870-1919), a writer much admired by both Bittel and Carnap
(Carnap 1919: 124, as described in Carus 2007a: 59). What is most
striking about Carnap's unpublished analysis of the German
situation after the defeat, though, is how *un*political it
remains, in any literal sense. He certainly deplores the unwillingness
of educated Germans to dirty their hands with politics, and urges a
fundamental change in attitude, balancing the exclusive German
emphasis on the contemplative life with greater involvement in the
active life. However, what Carnap calls "politics" in this
analysis is "everything... that has some connection with
the public social life of people"--which, as he makes quite
explicit, includes practically all human activities, including some
very ivory-tower ones. Indeed, the key to his advocacy of greater
"political involvement" is that he assigns intellectual
work a central and indispensable role in arriving at the "form
of community [*Gemeinschaftsgestalt*]" that could serve
to coordinate the vast and heterogeneous multitude of tasks and jobs
that have "some connection with the public social life of
people". Only by virtue of such a "form of
community" can we hope to remove this otherwise anarchic hive of
activities "from the realm of chaotic whim and subordinate them
to goal-oriented reason" ["*der choatischen
Willkur zu entziehen und der zielbewussten Vernunft zu
unterwerfen*"] (Carnap 1918b: 17-18, translated and
quoted in Carus 2007a: 63).


### 2.2 *Der Raum*



For Carnap the basis for "goal-oriented reason" could only
be a comprehensive system of knowledge, and this exhortation to remove
the design of our system of the sciences "from the realm of
chaotic whim", and to "subordinate" it to
"goal-oriented reason" reverberates throughout his early
philosophical papers (e.g., Carnap 1923: 107), which have now been
published together with English translations in Carnap (2019). In the
editors' introduction to this new edition it is argued that this
program was not just a momentary response to a particular crisis, but
continued to inform the architectonic of Carnap's philosophy
throughout its development. This is hardly disputed with respect to
the immediately following stages of Carnap's career, addressing
the nature and design of the system of knowledge--his
dissertation on philosophical problems of space and geometry, *Der
Raum* (1922a) and other early papers. *Der Raum*
[*Space*] prefigures later works in its effort to disentangle
various meanings of the word "space" and to show that
philosophical confusion had resulted from the failure to distinguish
them clearly. In this case, Carnap distinguishes "formal",
"intuitive", and "physical" space. The first
was a purely logical or set-theoretic construction of space; the
second was built up from a version of Hilbert's axioms
restricted to a local, subjective space; the third was the space of
physics. In each case, by separate arguments, Carnap reaches the
conclusion that the space we must assume as the precondition for any
knowledge is not Euclidean space, as Kant had argued (and some
Kantians such as Natorp were still arguing), nor even any metric
space, but topological space of arbitrarily many dimensions. While
this represents a form of (neo-)Kantianism Carnap would soon leave
behind, it was tempered by the critical role of the "factual
basis [*Tatbestand*]" in deciding among mathematically
possible kinds of physical space. The factual basis was determined
only up to the topological relations among its elements;
Carnap's residual Kantianism is expressed in the topologically
"necessary form" (not reaching to metrical relations) our
perception imposes on its elements (see Heis 2011 on the neo-Kantian
background in the philosophy of geometry).


### 2.3 The *Aufbau* Program



A series of notes taken during this period exhibit Carnap's
preoccupation with the question how the system of knowledge could,
unlike the proposals of Diderot and d'Alembert in the
*Encyclopedie* and those in its wake such as
Comte's and Ostwald's (1914a, 1914b), be unified
*deductively*, as Leibniz--and Frege--had envisaged
(on Ostwald as a starting point for Carnap during this period, see
Dahms 2016). What especially preoccupied the young Carnap was the
challenge of giving the system empiricist underpinnings, i.e., finding
deductive relations between sense perceptions and the abstract
concepts of the advanced sciences. For a year or two he struggled with
this problem without success, until finally, in early 1922, just
before the publication of *Der Raum*, Carnap read Bertrand
Russell's *Our Knowledge of the External World* (1914).
Here he found his answer--the concepts were to be derived not by
*analysis* of experience, and deduction from the resulting
elements, but by *construction*, using a "principle of
abstraction" (Russell 1914a: 44-45; see also Pincock
2002). Experiences could be gathered into equivalence classes, and for
purposes of constructing a "real" world, each such class
can be regarded as a concept, defined by its extension. Immediate,
momentary experience--the basis for knowledge among positivists,
phenomenologists, as well as fictionalists such as the German
philosopher Hans Vaihinger--need not be transcended in such a
construction. The hitherto insurmountable problem of forcing the fluid
character of lived experience into the straitjacket of deductive
relations disappears.



This move also overcame another traditional positivist and
phenomenological obstacle to Carnap's project of a Leibnizian,
deductive system of knowledge, formulated most drastically by Hans
Vaihinger (who influenced Carnap in this regard): the
"chaos" of subjective experience, as we immediately
experience it, has no structure whatever. Nothing is really
"given" but the undifferentiated chaos itself. No
distinguishable "elements" present themselves as naturally
isolable from it or as inherently available, without externally
imposed fictions. Russell's principle of abstraction--his
method of substituting "logical constructions for inferred
entities" (such as qualities)--solved this problem, but
with the addition of a small but indispensable contribution from
phenomenology. What enabled Carnap to obtain the elements he sought
*without* isolating identifiable elements within the
undifferentiated "chaos" was a single act of
phenomenological discernment: a partition of the entire
"chaos" into just two sectors, which he called the
"living" and "dead" components of experience.
This one distinction allowed Carnap to arrange experiences into a
temporal sequence ("dead" experience is past;
"living" experience present), making it possible to
identify holistic temporal cross-sections of experience, in which the
total experience of a given specious present remains intact as a
momentary whole. This chronological sequence of experiential
time-slices now gave Carnap the basic framework he needed for
identifying qualities as cross-temporal equivalence classes of
discernable persistences across series of adjacent specious presents.
These holistic time-slices did not need to be *analysed*.
Qualities and qualitative relations could, rather, be
*constructed* as something like equivalence classes of
sufficiently "similar" persistences across a series of
adjacent time-slices (up to any desired degree of precision in
"similarity"). The result was that what empiricists such
as Hume or Mach had always hoped to achieve by "analysis of the
sensations" could be achieved *without* analysis. Carnap
called it "quasianalysis" (which is explained in more
detail in the supplement
 Methodology (Section 3)).
 Physical objects could be constructed as connected classes of
qualities, and from objects the path to a "reality" seemed
clear.



In this early stage of what became the *Aufbau* project, Carnap
still followed Vaihinger in distinguishing sharply between the direct,
genuine, first-hand knowledge of the "chaos" and the
fictive, constructed nature of "reality". But he put the
boundary between them in a different place. This was because
Husserl's phenomenology offered an escape route from
Vaihinger's completely undifferentiated chaos. It yielded
certain distinctions *within* the chaos (e.g., between
"living" and "dead" experience) that could
claim a degree of objectivity. These distinctions, Carnap then
thought, were *not* fictional, but actually extended the range
of what could be genuinely *known*, even without fictions, just
from the chaos itself. So Carnap's boundary between the
immediately known *primary world* (of sensory
"chaos" plus a minimal, phenomenologically extrapolated
structure) and a fictive *secondary world* of
"reality" included more in the "primary"
sector than Vaihinger's. Carnap thought he could show on
phenomenological grounds that the primary world is two-dimensional in
all sense modalities (Carnap 1924). So the boundary between the fixed
primary world and the freely choosable secondary worlds
("realities") was located at the ascent from two to three
dimensions. Within the primary world, the construction proceeded
entirely by explicit definition, beginning from the qualities obtained
by quasianalysis. Secondary worlds, by contrast, are not uniquely
determined. The construction of a secondary world proceeds, rather, by
optimizing its fit to whichever fictions are chosen to guide the
construction, subject to the constraint of the (fixed) primary
world.



Carnap remained as radically pragmatist about the choice among
fictions to guide this ascent as Vaihinger; the choice of fictions was
entirely practical and purpose-relative. (For more on
Vaihinger's account of fictions, see, e.g., Chapter 1 of Appiah
2017.) To obtain the *scientific* secondary world, Carnap
maintained, we need only two fictions, corresponding roughly to
Kant's categories of cause and substance: a principle of
induction (or uniformity of nature) and a principle of
"continuity" (as Mach had called it), requiring certain
clusters of perceptions, such as those grouped into a "physical
object", to remain constant, under certain conditions, while we
are not perceiving them.



Sometime during 1924, the *Aufbau* project changed course
drastically, and arrived at essentially its later published form
(Carus 2016). The phenomenological approach to the basis was dropped;
a fixed "primary world" was no longer to be distinguished
by phenomenological intimation from the various "secondary
worlds" built upon it. Russell's "construction
principle", as Carnap called it, came to dominate the project,
and would become the book's epigraph:



> 
> 
> The supreme maxim in scientific philosophizing is this: Wherever
> possible, logical constructions are to be substituted for inferred
> entities. (B. Russell 1914a: 155)
> 
> 
> 



So now the two-dimensionality of perceptual space, for instance, is no
longer obtainable from phenomenological discernment, but becomes as
much a logical construction as everything else (*Aufbau*:
SSSS89, 117, 124). And in a talk Carnap gave about the
*Aufbau* project in Vienna in January 1925, we find a new
guiding principle: "Overcoming subjectivity" (Carnap
1925a, 1925b, as quoted in Carus 2007a: 168; 2016).


### 2.4 Vienna and Wittgenstein



After completing the *Aufbau* first draft in late 1925, along
these new lines, Carnap left for Vienna, where he became a lecturer
[*Privatdozent*] and submitted the *Aufbau* manuscript
to Moritz Schlick as his *Habilitationsschrift*. He immediately
became an active participant in Schlick's weekly Circle, which
was embarking just then on yet another careful re-reading of
Wittgenstein's *Tractatus*. This group would soon (due to
Otto Neurath's effective propaganda) become known to the world
as the "Vienna Circle", the fount of a new
(anti-)philosophy known as "logical positivism"--a
term Carnap never liked.



Like others in the Vienna Circle, Carnap saw the *Tractatus* as
a basis for solving the perennial problem of accommodating the truths
of logic and mathematics to empiricism. Wittgenstein was no
empiricist, but his characterization of logical truth as a pure
artifact of representation, empty of empirical significance, gave the
Vienna Circle what they needed. Their logicism extended
Wittgenstein's truth-functional conception of logic to the whole
of mathematics, and their empiricism interpreted Wittgenstein's
atomic sentences as sense perceptions, along the lines of the
*Elementarerlebnisse* at the basis of Carnap's
*Aufbau*. This version of Wittgenstein made mathematics
consistent with empiricism. However, its weaknesses were obvious even
to the Circle: First, from the empiricist perspective of the Vienna
Circle, Wittgenstein's truth-functional conception of logic
seemed to require finitism; even the most abstract theories of physics
could then employ only restricted, finitary quantification rather than
unrestricted quantification over a potentially infinite number of
observations ( *Aufbau*: SS180; Carnap 1936-37:
SS23). And second, Wittgenstein's exclusion of
"elucidations" (meta-sentences about the object sentences
framed in the language of science) was not only paradoxical (it made
all statement and discussion of logical principles meaningless) but
seemed at odds with recent developments in the foundations of
mathematics, especially Hilbert's metamathematics, and the
brilliant use made of this approach by Skolem, Tarski, and by one of
Carnap's own students, Kurt Godel. (In turn,
Godel's arithmetization of syntax and his incompleteness
theorems would have an enormous impact on Carnap's *Logical
Syntax of Language* just a few years later--see the
supplement on
 *Logical Syntax of Language*
 for more details.)



Carnap set to work, after his arrival in Vienna, to solve these two
problems. He embarked on a major project to explore "general
axiomatics", in which he sought to show that Hilbertian
axiomatics could be accommodated within the Wittgensteinian
representational framework--i.e., he sought to show that the
Hilbertian "method of bifurcation" (into metalanguage and
object language), while mathematically useful, could ultimately be
reduced to a Wittgensteinian single language. The immediate goal was
to prove a fundamental completeness theorem, purporting to show that a
consistent axiom system is categorical just in case it is decidable
(Awodey & Carus 2001). After three years of concentrated work on
this project (a substantial manuscript of several hundred pages
survives in Carnap's papers), Alfred Tarski convinced him that
this theorem was defective, and that Carnap's attempt to work
within a single language failed to capture the metamathematical
concepts fully (but see Schiemer 2013). And late in 1930, Godel
actually showed that an important special case of Carnap's
theorem was false: second-order arithmetic, though categorical, is not
decidable. This famous result put an end to Carnap's project of
fusing Hilbert and Wittgenstein.


## 3. The *Aufbau*


### 3.1 Main Point and Motivation of the *Aufbau*



As we saw in
 section 2
 above, the *Aufbau* project began as a continuation of the
encyclopedic ambitions of the Enlightenment, in response to the
catastrophe of the war and the hopes inspired by the German
revolution--only that in contrast to the eighteenth-century
*Encyclopedistes*, and to similar projects since then,
Carnap conceived the idea of a system of knowledge as a
*deductive* system, under the influence of his teacher
Frege.



By the time of the book's publication the emphasis had shifted,
but the idea of bringing all concepts into a single deductive system
survives. In a lecture given to a general audience in Vienna in 1929,
Carnap explains the point of his book by telling a dialectical story
of human history as a struggle between "critical
intellect" and "imagination". At first imagination
ruled the day, but then in antiquity, critical intellect made a
discovery that enabled it to put strict limits on imagination's
claims:



> 
> 
> That is the discovery of *one* [single] *comprehensive
> space*. All things are in space; any two things are always
> spatially related to each other. So there is also a path from me to
> any [given] thing.
> 
> 
> 



So existence claims could now be subjected to a simple test:



> 
> 
> *Every thing is accessible*. If someone now claims that a thing
> of a particular kind exists, I can demand of him that he show me the
> path from me to the claimed thing.
> 
> 
> 



Imagination responds by relocating its gods and gremlins to remote or
inaccessible locations, but as humankind explores more of the earth,
this stops working. So imagination "goes for a really radical
option; it evacuates its creations to the non-spatial, the
'trans-spatial'", which is plausible since we quite
legitimately refer to things that are not physical objects, so not
locatable in space. Feelings, mental images, and thoughts, for
instance, are non-spatial. So instead of situating its gods in a
physical location such as Mount Olympus, Carnap explained,



> 
> 
> the putative God was removed from space into the realm of the spirits.
> God was regarded now as a *spiritual being without a body.*
> 
> 
> 



But people starting noticing "that something isn't quite
right with that sort of claim, that there is something rather odd,
something problematic about it". So imagination went further and
replaced theology with metaphysics.



> 
> 
> Here the concept of God no longer has anything physical or anything
> physically rooted about it... The flight from the grasp of
> critical reason with its spatial system appears to have been
> completely successful.
> 
> 
> 



But critical intellect now has an answer: the *Aufbau*
system--"now a system is discovered that comprehends not
just [corporeal] things, but everything thinkable, all concepts,
whether thing-like or not". This system is the natural successor
and generalization, in Carnap's dialectical drama, of physically
all-encompassing space:



> 
> 
> In space all things have spatial relations to each other, and there
> has to be a path of access from me to each thing. In the same way, on
> the basis of the concept-system, an all-comprehending conceptual
> space, so to speak, all concepts have relations to each other (in this
> case logical, conceptual relations). And here there has to be a
> connecting path to each concept from the contents of my experience,
> e.g., from my perceptions. Everything of which I can speak has to be
> traceable back to things experienced by me. All knowledge I can have
> relates either to my own feelings, mental images, thoughts, etc. or
> can be derived from my perceptions...
> 
> 
> 



Though Carnap had redesigned the system in 1924 to dispense with the
phenomenological development of the "primary world" from
which the "realities" or "secondary worlds" of
science and everyday reality were constructed, it could be said that
he adopted Husserl's method of "bracketing" the
supposed external reality to which our subjective world appears to
refer--and that he adopted it more radically and strictly than
Husserl himself. For Carnap bracketed not just the external reality
but also the internal subjectivity, leaving only the bare logical
structure of the constitution system unbracketed (Carus 2016).


### 3.2 Significant Aspects of the Published *Aufbau*



In the published *Aufbau* this abstemious bracketing policy is
applied very strictly. Carnap adopts a principle of extensionality
that does not exclude the use of intensional languages in auxiliary
roles, but denies them any ultimate significance. Fregean
"Sinn" (sense) is specifically excluded as merely
psychological (SS44), having only "epistemic value"
but not "logical value" (SS50), which is limited to
the extensional meaning of an expression. Each step in the spelled-out
constitution of the subjective ("autopsychological") world
is explained not only in logical symbols but also in a simple
paraphrase, then in "realistic language" (as ordinarily
used in science) and finally in a language of "fictive
construction". But Carnap makes clear that this is solely for
convenience and to make the steps more transparent to readers. The
four languages may differ not only in form but in their
"Sinn", their epistemic value (the different mental images
they elicit), he says, though their logical value is always identical
and is expressed most neutrally and clearly in the symbolic language
(SS95); for more detail, see the supplement
 *Aufbau*.



Behind this radical extensionalism lies precisely the new strictness
with which Carnap applied the Husserlian "bracketing"
strategy in 1924--ironically just at the time he abandoned the
phenomenological development of the constitutional basis. (More
details on Carnap's extensionalism are to be found in the
supplement
 Semantics (Section 2).)
 The most direct expression of this was a more thoroughgoing and
self-conscious rejection of ontology. In the final chapter of the
*Aufbau*, which addresses some philosophical problems to which
the constitutional system can be applied, the overriding theme is the
irrelevance of ontological questions to the actual constitutional
system (Friedman 2007). And in the same year as the *Aufbau*
Carnap published a pamphlet on *Pseudo-problems in Philosophy*
(Carnap 1928b) in which the "problem of realism" is the
most prominent example of such pseudo-problems.



The actual detailed construction of the autopsychological realm
occupies only a small part of the book. The first sections focus
largely on what Carnap would later call "clarification of the
explicandum" (see
 section 1.1
 above). Carnap considers various options for the choice of *basic
elements* (the elements or building blocks of which everything is
to be constructed) and *basic relations* (the relations between
and among these building blocks that is to effect the construction).
The radicalism of Carnap's push for simplification is expressed
by his choice of only a *single* kind of basic elements,
"elementary experiences", and a *single* basic
relation, "recollection of similarity". The elementary
experiences were not isolated "sense data" of traditional
empiricism (the isolated pitch and timbre of momentary sounds or
colored points of the visual field that we find in Hume or Mach), but
holistic time slices of total experience, from which nothing has yet
been abstracted; Carnap was here attempting to do justice to the
psychology courses he had taken as an undergraduate, where he had
learned about the new directions taken in *Gestalt* psychology
by Kohler, Koffka, and others. By quasianalysis, an abstraction
technique formalizing Russell's "principle of
abstraction", (see the supplement
 Methodology (Section 3))
 the similarities among these time-slices could retrospectively be
grouped (by repeated application of the basic relation, recollection
of similarity) into something like equivalence classes of, say, a
certain color or a certain smell that were sufficiently similar. By
this means Carnap constructs the subjective cognitive world of a
single mind in some detail, up to the point where, on that basis, a
three-dimensional objective world of space-time can be constructed
(see the supplement
 *Aufbau* (Section 2)
 for more detail concerning some of these constructions).



At this crucial point of the *Aufbau*
(SSSS125-7), the ascent from two to three dimensions,
where Carnap stops spelling out the steps in detail, he also suspends
the explicit definition applied up to there, and instead resorts to an
informally described optimization approach, whereby certain fairly
obvious desiderata (continuity of motions, temporal continuity of
objects and processes, etc.) are to be maximized subject to certain
(again fairly obvious) constraints (see the supplement
 *Aufbau* (Section 3)
 for further details). The construction of the physical realm and the
further realms on its basis (the heteropsychological, social,
cultural, and value realms) are sketched very sparsely. The book ends
with a final section discussing some philosophical consequences of the
constitution system, addressing (though only obliquely, and hardly by
name) both phenomenology and various forms of realism.


### 3.3 Later Discussion of the *Aufbau*



When the book was published in 1928, it was widely discussed and,
along with Wittgenstein's *Tractatus*, became one of the
classic texts of the Vienna Circle. Its effect was amplified in the
English-speaking world by A.J. Ayer's acknowledgement of Carnap
as the philosopher to whom he "owe[s] most" in his
best-selling *Language, Truth, and Logic* (Ayer 1936), which
was understood as an accessible summary exposition of the supposed
phenomenalism of the *Aufbau*, but misrepresented the book
quite seriously. This misrepresentation contributed to the later
neglect of the book among Anglo-American philosophers, which even the
sophisticated discussion, critique, and further development by Nelson
Goodman (1951) or the belated English translation (1967) could hardly
budge. It also allowed many preconceptions about the book to continue
circulating almost through the end of the twentieth century.



Only toward the end of that century did a revaluation set in,
initiated by Michael Friedman, who took issue, in a series of papers
(later collected in Friedman 1999), with the entire English-speaking
tradition (going back to Ayer) of seeing the *Aufbau* as a
phenomenalist project of reducing all knowledge to sense impressions
on the model of Hume or Mach. Instead, Friedman pointed out, we should
see it in the context of its neo-Kantian origins. From that
perspective, the *Aufbau* is better understood as seeking a new
basis of scientific objectivity--achieving objective knowledge
despite the subjective starting point of individual perception, and
the structuralism discussed above
 (section 3.2).
 On the basis of Friedman's discussions, many others have since
contributed to the revaluation of the *Aufbau* (Richardson
1998; Mormann 2000; Pincock 2005, 2009; the papers collected in
Dambock 2016.)



This new interpretive interest in the *Aufbau* and its
philosophical context has also led to renewed efforts to reconstruct
the *Aufbau*'s constitution system with new tools.
Goodman's 1951 critique of quasianalysis has finally found
responses and repairs from Mormann (1994, 1997, 2009) and Leitgeb
(2007); Leitgeb (2011) goes further and argues that if the goals of
the *Aufbau* strategy are limited in certain ways,
Goodman's and Quine's critiques no longer apply (see the
supplement
 *Aufbau* (Sections 3 and 4)).
 Chalmers (2012) suggests a much more drastic *rationalistic*
revision of the *Aufbau*; where Carnap thought it would be
possible, in principle, to derive all true scientific sentences
whatsoever from basic true sentences in an "empiricistically
acceptable" constitution system just by means of the
system's definitions, Chalmers drops any empiricist ambitions
and replaces the role of definitions by that of *a priori*
knowledge, including *synthetic a priori* knowledge (whose
existence Carnap of course denied).


## 4. The Road to *Syntax*



The Wittgensteinian program favored by the Vienna Circle
 (section 2.4
 above) had collapsed in 1930. But Carnap soon recovered, and during a
sleepless night on 21 January 1931, conceived of an entirely new basis
for the Vienna Circle's characteristic doctrines (Awodey &
Carus 2009). Instead of trying to fuse Hilbert and Wittgenstein,
Carnap now dropped Wittgenstein altogether and pursued a Hilbertian
approach. "Meaning" was no longer rooted in the
correspondence between configurations of elementary facts and their
linguistic representations. In fact, meaning was banished altogether,
at least in our statements *about* the language of science (our
metalinguistic "elucidations" such as those in the
*Tractatus* itself or the *Aufbau*). The scientific
language itself had empirical meaning, but how this was to be
understood became a matter of dispute (the famous
"protocol-sentence debate") within the Vienna Circle (the
sentences recording observations were called
*Protokollsatze* by the Circle, which became
"protocol sentences" in English). This brought about
a split in the Circle between a more realistic "right
wing" (who adhered to something closer to Wittgenstein's
picture theory and held that once a state of affairs was
"registered [*konstatiert*]" by an observer there
could be no further doubt) and the "left wing" who
followed Carnap in his new reference-avoiding syntax program (see
Uebel 2007 on this debate). In any case our elucidations of the object
language remain, in the new syntax framework, entirely within the
linguistic realm; we are talking always and only about language. In
logical syntax, we should be careful not to talk about
"facts" or "things" but instead only about
sentences or thing-names. We should restrict ourselves in principle to
the "formal mode of speech" (sentences and names),
employing the "material mode of speech" (facts and things)
only for convenience, and when we are sure we can translate it into
the formal mode. The (meta-)mathematical methods of Hilbert, Tarski,
and Godel were, in other words, to be extended to the whole of
knowledge.



Carnap's immediate task was to create a canonical language for
the formal mode of speech. Taking his cue from Hilbert's
metamathematics, he began by stripping this language down to bare
bones, eliminating all problematic assumptions. It would consist
simply of strings of dots on a page, and the basic laws of arithmetic
would arise unambiguously in the metalanguage from the immediately
evident patterns of dots (e.g., the commutative law from the
perceptibly equivalent number of dots counted from the left and from
the right). Carnap soon found he could not express certain essential
concepts in this limited language, and turned instead to a more usual
axiomatized arithmetic. This also had the advantage that, by using
Godel's new trick of arithmetizing syntax, Carnap could now
more easily express the syntax of the language (i.e., its logic) in
the language itself. So the syntactic metalanguage collapses into the
object language, and there is, as before, only a single language. The
canonical language for the formal mode of speech seemed within his
grasp.



This idea also gave Carnap a new route to the elimination of
metaphysics, superseding the Wittgensteinian strategy with its meaning
criterion. The new criterion dispensed with meaning. It required that
any statement either be at the object level (straightforwardly
factual) or translatable into the formal mode of speech--i.e.,
into the canonical language or an equivalent. Carnap assumed that his
canonical language, once fully worked out, could express the entire
language of physics, as well as containing its own metalanguage. Since
the Vienna Circle's "unity of science" program held
that all knowledge was expressible in the language of physics, Carnap
proposed his canonical language as a *universal language* for
all knowledge (Carnap 1932b). Another way of expressing the new
criterion, then, was that any acceptable statement must be phrased in
the language of physics. The new idea of January 1931 flowed into
Carnap's discussions with Neurath and others to produce the new
doctrine of physicalism (Uebel 2007, 2018).



But the demands on the "correct" language for the formal
mode of speech were exorbitant. Carnap had originally wanted to keep
it weak and uncontroversial, but it had to be capable of expressing
all the mathematics needed for physics. On the other hand, its
arithmetized syntax had to be capable of expressing the basic concept
of "analytic truth", or it would be impossible to
determine when a formal-mode statement "holds". Before
1930, it had been assumed that provability was the standard of
mathematical truth, but now Godel had shown that for each
consistent and recursively axiomatized system that included enough
arithmetic, some true sentences are not provable in the system. So a
different criterion was needed, but one that would still--like
provability--pick out the logically true sentences solely by
means of the formation and transformation rules of the language.
Carnap did attempt such a criterion for "analyticity" in
the first draft of his syntax book (entitled *Metalogic*),
written in late 1931 and the spring of 1932. He sent the typescript to
Godel, who pointed out that the new criterion was defective. In
fact, he added, it is *impossible* to define analyticity or
logical truth in *any* metalanguage that can be faithfully
represented in the object language (e.g., by arithmetization); this is
now familiar to us as Tarski's theorem on the indefinability of
truth. So Carnap's single-language approach fails after all
(Awodey & Carus 2007, 2009).



And without the single canonical language containing its own
metalanguage, there is no longer any reason to regard any particular
metalanguage as more "suitable" or "natural"
than any other. One option may turn out to be more *useful*
than another for particular purposes, but this is no reason to
privilege it as uniquely "correct" (or canonical). With
Godel's assistance, Carnap developed a new definition of
analyticity, but it hardly seemed to matter any more; the *language
relativity* of any definition of truth or analyticity moved to the
center of attention. The disputes about protocol sentences within the
Vienna Circle merged in Carnap's mind with the disputes among
intuitionists, logicists, and formalists in the philosophy of
mathematics.



All these disputes, he realized in the autumn of 1932, concerned the
question of how to set up a language, which has no right or wrong
answers. One could only try out different ways, and see which ones
worked better. This new attitude, which first appeared in
Carnap's reply to Neurath about protocol sentences (Carnap
1932b), received its definitive statement in the "principle of
tolerance" quoted in *1c.* above, enunciated in the
*Logical Syntax of Language* (LSS: SS17). In this
principle, the voluntarist and utopian convictions of his youth,
partially submerged during the *Aufbau* period, finally found
adequate *philosophical* expression. He spent the remainder of
his career absorbing the consequences of this breakthrough, and
working on a vast number of language projects within the new freedom
it afforded.


## 5. *Logical Syntax of Language*



The *Syntax* is probably Carnap's best-known book, and
has attracted much of the renewed attention to Carnap in recent years.
At the time of its publication, the Vienna Circle was disintegrating,
its members were fleeing from political persecution, and philosophical
communication was disrupted. Its English translation, published 1937,
lacked context and was almost uniformly misunderstood by nearly
everyone, with the partial exception of Quine, whose later work in
logic, the philosophy of logic, and logic-based philosophy was
inspired by--though sometimes opposed to--the *Logical
Syntax*. Through Quine, some of Carnap's ideas eventually
also found their way into the logic education of many philosophy
departments in the US. On the other hand, what Quine understood, as is
evident from his 1934 Harvard Lectures, immediately after the
book's publication (reprinted in Creath 1990), was the *first
draft* of the *Logical Syntax*, in which the principle of
tolerance was still absent. So even *his* comprehension of the
*Syntax* was partial and one-sided (Creath 1987, Friedman
2006). In any case, the book was widely assumed to have been
superseded by the time the translation appeared, now that Carnap had
meanwhile embraced semantics and dropped his insistence on the
"formal mode of speech" (above,
 section 1.3).
 Only recently, therefore, has the *Syntax* come to be
appreciated in its full radicalism.



In this recent work, the principle of tolerance has attracted the most
attention. Previously, the rejection of meaning and insistence on the
formal, rather than the material, mode of speech had been in the
foreground since, after all, the entire philosophical Part V of the
book had been devoted to it, and Quine had reinforced that emphasis.
It is fair to say that the principle of tolerance taken by
itself--unlike the notion of analyticity or theses of
conventionalism (see the supplement
 Carnap vs Quine on the Analytic-Synthetic Distinction)--was
 hardly discussed before its present, belated reception in the Carnap
literature. It is a new idea on the philosophical scene today, whose
consequences are still being digested.



It certainly has lost none of its explosive revolutionary force as a
radical program for philosophy (Creath 2009), and this is what has
most divided commentators. Like most revolutionary ideas, it has
encountered steadfast and vocal resistance. Most commentators have
been concerned to limit the scope of the principle of tolerance, to
dilute it or trivialize it, while the appreciative minority has mostly
remained defensive. Much of the literature, therefore, is devoted to
clarification and the correction of misunderstandings (e.g., Goldfarb
& Ricketts 1992; Ricketts 1994; Goldfarb 1995), rather than
positive explorations of the principle of tolerance and its
consequences (with a few exceptions: Carus 2017, Kitcher 2008, Creath
2009, Kutz, Mossakowski, and Lucke 2010, Justus 2012). Thus the
remainder of this section will, after a brief exposition of the
book's contents, focus on these recent discussions and
clarifications. Carnap's principle of tolerance is discussed in
more detail in section 1 of the supplement
 Tolerance, Metaphysics, and Meta-Ontology,
 and the *Logical Syntax* more generally in the supplement
 *Logical Syntax of Language*.


### 5.1 Brief Exposition of *Logical Syntax*



The stated aim of the book is to show that logic is syntactical, i.e.,
that it consists in formal theories of linguistic symbols--a
theory is "formal", Carnap says (LSS [1937: 1]) when



> 
> 
> no reference is made in it to either the meaning of the symbols (e.g.,
> the words) or to the sense of the expressions (e.g., the sentences),
> but simply and solely to the kinds and order of the symbols from which
> the expressions are constructed.
> 
> 
> 



The idea had of course been suggested by Hilbert's "method
of bifurcation [*Methode der Zweiteilung*]" as Carnap had
called it, distinguishing a meta-mathematics with concrete meaning, on
the one hand, from mathematics proper, on the other, which was to be
regarded as purely formal, and the formal properties of which (e.g.,
consistency) Hilbert had aimed to study and prove in
meta-mathematics--a method which Carnap sought to extend from
mathematics to the whole of knowledge. The "chief motivation for
my development of the syntactical method", Carnap later wrote,
was this:



> 
> 
> In our discussions in the Vienna Circle it had turned out that any
> attempt at formulating more precisely the philosophical problems in
> which we were interested ended up with problems of the logical
> analysis of language. Since in our view the issue in philosophical
> problems concerned the language, not the world, these problems should
> be formulated, not in the object language, but in the metalanguage.
> Therefore it seemed to me that the development of a suitable
> metalanguage would essentially contribute toward greater clarity in
> the formulation of philosophical problems and greater fruitfulness in
> their discussions. (Carnap 1963a: 55)
> 
> 
> 



That the main concepts of deductive logic ("e.g., provability,
derivability from given premises, logical independence, etc".)
are purely syntactical was argued primarily by showing how they could
be defined in two exemplary languages without reference to the
meanings of any terms. Language I is a form of primitive recursive
arithmetic, and was intended to exemplify a constructivist kind of
language, while Language II contains classical mathematics. (In modern
terminology, both of these "languages" are really
theories.) Of the book's five parts, the first three are taken
up with the development of these two languages. In part IV, Carnap
goes beyond the treatment of specific languages to sketch a template
for "general syntax"; he tries to give a framework for the
syntactical development or description of any language whatever. He
abstracts from the syntactical categories of the particular language
under consideration, and does not even assume he is given its set of
variables, the distinction between its logical and descriptive
vocabulary, its negation symbol, or any other syntactic property.
Instead, all these sets and concepts are to be defined solely from the
transformation (inference) rules of the language (see
SS46-47); Carnap is developing here what we would now call a
version of "proof-theoretic semantics" or "logical
inferentialism" (see the supplement
 *Logical Syntax of Language*
 for further details). Throughout all parts of the *Logical
Syntax*, Carnap distinguishes between the "d-terms"
specifiable this way (derivable, proof, demonstrable, refutable,
decidable) from the "c-terms" (consequence, valid,
contravalid, determinate, incompatible, content, synonymous). Though
both are considered to be "syntactic" terms by Carnap, the
c-terms seem closer to what we would now call "semantic".
This raises the question, for the modern reader, what Carnap actually
means by "syntactic" (or "formal") here; and
it turns out (as Carnap himself later recognized) that
"syntax" includes much of what he would later call
"semantics". Indeed we find (Wagner 2009: 22) that
languages I and II are not actually "formal" in our sense
at all; they are interpreted languages. While the syntactic method, as
Carnap here conceives of it, requires that the interpretations be
disregarded, a particular fixed interpretation implicitly remains in
place. Carnap often refers to the import of some syntactic result or
attribute "in material interpretation [*bei inhaltlicher
Deutung*]" (e.g., LSS: 30), and the material interpretation
sometimes slips in to play a role in the argument. Accordingly, Tarski
(1936 [2002]: SS2) characterizes Carnap's definition of
consequence for Language II in the *Logical Syntax* as
*semantic*, acknowledges that "The first attempt at the
formulation of a precise definition for the proper concept of
following comes from R. Carnap" (in the *Logical
Syntax*), and regards his own model-theoretic definition of
logical consequence as essentially equivalent to Carnap's
(though applicable to a broader range of formalized languages than
just to Language-II-like languages; see the supplement
 *Logical Syntax of Language*).
 This character of the *Logical Syntax* as a transitional work
between syntax and semantics raises many subtle interpretative and
historical issues that require distillation of the actual argument
from the (often newly-invented) terminology in which it is embedded.
Fortunately, Pierre Wagner's (2009) excellent handbook on the
*Logical Syntax* provides the reader with a guide.



For all the technical apparatus, Carnap later acknowledged that
"the investigation of philosophical problems was originally the
main reason for the development of syntax" (Carnap 1963a: 55),
and the final Part V of the book is devoted to these. The focus,
however, is on the "syntax" idea itself, not on the other
main idea, the principle of tolerance. There is a simple reason for
this: Part V was almost entirely written before Carnap arrived at the
principle of tolerance in late 1932, and when the book went to the
publisher it had to be cut (the definition of
"analyticity" for Language II (SS 34d), for instance,
was not even included in the original book, only in the 1937 English
translation). And Part V is devoted to a sustained argument for
sticking to the "formal mode of speech" and avoiding the
"material mode of speech" unless it is translatable into
the formal mode. So it is hardly surprising that philosophers (see for
instance Wolenski 2003) took this to be the book's main
philosophical point and thought Carnap had left it behind after the
embrace of semantics in 1935.


### 5.2 Recent Discussion and Commentary



Much of the recent discussion surrounding the *Syntax*,
especially the principle of tolerance, was inspired by
Godel's critique of Carnap, unpublished until 1995, that
was originally intended for the Schilpp (1963) volume on Carnap in the
*Library of Living Philosophers*. Godel withdrew his
paper, but six successive drafts of it were found in his
*Nachlass*, of which several have now been published
(Godel 1995). It appears, from its title ("Is Mathematics
Syntax of Language?") and much of the exposition, to focus
specifically on the "syntax" thesis, or more generally on
the "linguistic" accounts of the foundations of
mathematics deriving from Wittgenstein's *Tractatus*
(Goldfarb 1995: 325). However, Godel himself understood that
Carnap had meanwhile left behind that view (in its *Logical
Syntax* form), and recent commentary has focused on the principle
of tolerance (see section 1 of the supplement
 Tolerance, Metaphysics, and Meta-Ontology
 for the details of Godel's criticism).



Carnap's early-1930s syntactical method of avoiding reference
for terms in the philosophical metalanguage has recently been
identified as the first self-consciously worked-out program of what is
now often called "inferentialism" (Peregrin forthcoming),
a different form of which is especially championed by Robert Brandom
(1994, 2000), and has been found attractive by others (e.g., Price
2013). Though Carnap's inferentialism had different motivations
from Brandom's program of "reference explained away"
(Brandom 1984), there is clearly at least an analogous strategy at
work. While Carnap himself left the syntax program in its original
form behind when he went on to incorporate semantics into his overall
program for scientific languages, the syntax episode with its
explicitly inferentialist agenda is now viewed by some (e.g., Chalmers
2012, Peregrin forthcoming) an important innovation in its own right.
Some of these commentators thus regard Carnap's later embrace of
semantics as a step backwards. That had also been the view of Neurath
at the time (Uebel 2007, Mormann 1999, Carus 2019), and of Quine and
others later (e.g., Goldfarb & Ricketts 1992; Ricketts 1996;
Goldfarb 1997). These criticisms are at least partly due to a
perception that Carnap *returned* to a substantive conception
of meaning such as the Wittgensteinian one he had dropped in 1931, but
actually his conception of reference and meaning remained minimalist
and schematic, much to the frustration of, e.g., Russell (1940; see
Pincock 2007), who sought a substantive account of the intrinsic
nature of reference (see the supplement
 Semantics
 for further discussion).


## 6. Semantics and Modality


### 6.1 From Syntax to Semantics



Carnap had moved to Prague in late 1931, where he became a full
professor at the German University, and wrote both drafts of the
*Logical Syntax of Language*. The published book had tried to
fuse the three major ideas of 1931-2. First, in January 1931,
had come the rejection of Wittgenstein's picture theory of
meaning and its replacement by Hilbert's sharp distinction
between a language (a calculus, a purely formal symbol system) and its
interpretation, with the requirement that a language be entirely
specified by explicit rules. Closely bound up with this was the second
idea, the insistence on the "formal mode of speech" and
the avoidance of talk of meaning in the metalanguage. And third, late
in 1932, had come the principle of tolerance: no language is
definitive or "correct", there is no logical
"reality" for a language to "correspond to".
But within a year of the book's publication, the second idea had
been dropped; Carnap incorporated Tarski's new semantical
accounts of designation and truth, and extended his view of language
accordingly. The first and third ideas, however, survived for the rest
of Carnap's career. What did not survive was the overreaction
against "meaning" that accompanied the original insight of
January 1931--the exclusive emphasis on the "formal mode of
speech" in meta-discourse. In distinguishing between a language
and its interpretation, Carnap's first response had been to
restrict extra-linguistic interpretation to the object language (and
there to one particular--physicalistic--interpretation) and
dispense with it entirely in the "elucidatory"
metalanguage. But this restriction was loosened when Tarski convinced
him in 1935 that interpretation could be completely specified by
explicit rules governing satisfaction, designation, and truth.



By this time, the storm clouds gathering in Europe were obvious for
all to see, and like many of the Vienna Circle, Carnap sought an
appointment in North America. In 1936 he landed at the University of
Chicago, where he would stay for nearly twenty years, longer than he
spent anywhere else. While he felt personally and intellectually
comfortable in the United States, his written prose was never as
elegant or forceful in English as it had been in German, and his
publications were mostly quite technical. The larger context of his
philosophy was of course unknown to most colleagues and students, and
remained obscure to the larger public. This decontextualization of
logical empiricism was reinforced by political factors. As new
immigrants, Carnap and his Vienna Circle friends felt vulnerable in
the United States, and many of them, having previously supported
socialist causes in Europe, were kept under observation by the FBI,
including Carnap himself (Reisch 2005). It was thus in their interest
to play down the larger significance of their philosophical
preoccupations, and to pose as narrow specialists in technical
subjects.



Carnap's first major publication in English, soon after his
arrival in the United States, was "Testability and
Meaning" (1936-37), discussed in
 sections 1.5-6
 above, the first in a series of attempts to explicate
"empirical content" or "empirical
reducibility" more loosely than the strict reducibility
envisaged in the *Aufbau*. By the late 1930s, Carnap was
willing to countenance a theoretical language whose primitive terms
are not constructed bottom-up from observation sentences at all but
entirely top-down, "floating in the air, so to speak" so
that these basic theoretical terms can have "only an
*indirect interpretation*, which is incomplete in a certain
sense" (Carnap 1939: 65). With these steps, Carnap began his
return to a consideration of the theoretical language, which he had
left behind during the Vienna years. But his main focus, after
"Testability and Meaning", was the semantic framework
itself. In the slim volume on *Foundations of Logic and
Mathematics* for the Encyclopedia of Unified Science (1939), the
tripartite classification of linguistic theory into syntax, semantics,
and pragmatics was first laid out. A five-volume series of *Studies
in Semantics* was projected, of which the first two volumes,
*Introduction to Semantics* and *Formalization of Logic*
were published in 1942-3. Carnap then pursued a long-standing
interest in modal logic and intensional languages, and published
"Modalities and Quantification" in 1946, *Meaning and
Necessity* in 1947. More details on Carnap's work in
semantics can be found in the supplement
 Semantics.



Carnap had embraced semantics in 1935 because Tarski had convinced him
that designation and truth could be described and discussed in an
entirely schematic and objective way, free from any psychological,
subjective, or epistemological entanglements or commitments (Carnap
1936). As we have seen, the return to a schematic form of
"meaning" led many to regard *Logical Syntax* as
outdated. Carnap himself (e.g., 1942: SS39) was careful to deny
this, but probably didn't emphasize enough that the return of
"meaning" did not mean a return to an *explanatory*
conception of meaning like Russell's multiple relation theory of
belief or Wittgenstein's picture theory. This abstract and
schematic approach to meaning disturbed many empiricists, giving them
the impression that Carnap had no interest in what actually underlay
meaning, i.e., wherein the relation between predicate and property
(cf. Wilson 1982) actually consists. As B. Russell (1940: 314)
complained, for instance, Carnap ignored "certain prior
questions to be considered" before "the relation of
empirical knowledge to non-linguistic occurrences" could be
"properly understood". But these "prior
questions" were just the ones Carnap had put aside in 1931
(Pincock 2007). In this respect there is a seamless continuity in
Carnap's "minimalism" with respect to language; even
with the embrace of semantics in 1935, these questions remained
absent, and only began to make a rather shadowy reappearance with
Carnap's (1939) addition of *pragmatics* (the study of
language in use) to his conception of language. Semantics abstracts
from use and focuses only on the expressions themselves and their
designata, while syntax abstracts from designata as well (1939:
3-4; 1942: 9).



In Carnap's work after 1935, it is important to distinguish
between two different parts of the semantic enterprise. On the one
hand, there are the repeated attempts to pin down the inferential
relations between observation-statements and more general ones
*within* the general framework of semantics. In this work,
meaning and reference are considered particularly as they concern the
empirical content (or meaning) of general statements, whether
empirical generalizations or theories of more universal scope. This
includes "Testability and Meaning" (Carnap 1936-37),
the later work on the theoretical language (Carnap 1956a, 1959a), and
much of the work on inductive logic (see
 section 8
 below). On the other hand, there is the construction of the semantic
framework itself, its logical delineation and development; even if
this was in principle to serve the first purpose, it became in effect
a distinct project. This includes the *Studies in Semantics*,
the modal logic systems (Carnap 1946), and the later version of his
logic textbook, *Einfuhrung in die symbolische Logik*
(Carnap 1968b). We discuss this second component in
 section 6.2,
 immediately following, and the first component in
 section 8
 below.


### 6.2 Carnap's New Priorities



There are two main changes leading from the linguistic frameworks of
the *Logical Syntax* to the "semantic systems" of
*Meaning and Necessity*: Carnap took the semantic turn,
allowing for a relation of reference or designation; and beyond that
he allowed for intensional operators which he supplied with a new
intensional semantics.



From *Foundations of Logic and Mathematics* (1939) (and
*Introduction to Semantics*, 1942) Carnap had taken up
Tarski's conception of semantic truth. The principle of
tolerance in the *Logical Syntax* remained intact, but in the
following refined form: the syntactic rules of formation can be chosen
freely; if the syntactical rules of transformation (derivation,
inference) are determined prior to the semantic rules, they may be
determined freely as well, but the semantic rules will have to be
selected such that the transformation rules are sound with respect to
them; *vice versa*, if the semantic rules are chosen prior to
the transformation rules, the former may be determined freely, in
which case the latter will need to match the former by being sound
with respect to them (see, e.g., section 12 of Carnap 1939).
Completely new questions arose, e.g., whether the rules of inference
of classical propositional logic would determine the semantics of the
standard logical connectives *uniquely* (given certain
constraints): this novel type of categoricity question was answered in
the *negative* by Carnap (1943). (In recent years, this part of
Carnap's work has sparked a lively debate: see, e.g.,
Raatikainen 2008, Murzi & Hjortland 2009.) Semantics became just
as important in Carnap's work for the construction of formal
languages as syntax had been in the *Logical Syntax*.



Secondly, Carnap extended Tarski's extensional semantics by a
new intensional one, in which the truth values of sentences with
operators creating intensional contexts (such as a sentential operator
for necessity) can also be determined compositionally. Carnap's
invention of what would become "possible worlds
semantics," which he showed one could spell out in an
extensional metalanguage, had a decisive influence on the development
of modal logic and intensional semantics. Even though there are
significant differences between modern "Kripke semantics"
(which is rightly associated with Saul Kripke's work),
Carnap's intensional semantics is still a possible worlds
semantics in the sense that it evaluates formulas at possible worlds
("state-descriptions" in Carnap's terminology), and
the semantic rule for Carnap's operator '*N*'
for (logical) necessity invokes universal quantification over worlds:
\(N(A)\) holds in state-description *s* if and only if
*A* holds in every state-description (see SS41 of
*Meaning and Necessity*; the differences and similarities to
Kripke semantics are explained in detail in the supplement
 Semantics (Section 1)).
 On the side of theoretical linguistics, Richard Montague's
later intensional semantics for natural language built on
Carnap's semantics (see Partee 2011).



As discussed in the supplement
 Semantics (Section 2),
 he partially weakened his early radical thesis of extensionality by
the time of *Meaning and Necessity*.


### 6.3 Intensional Semantics



The languages to which Tarski's semantics applied were
extensional; Carnap's semantics extends Tarski's by
assigning compositionally to each singular term, each predicate, and
each sentence *both* an intension *and* an extension.
The intension of an expression explicates what we understand when we
understand it, and Carnap's treatment of this is again
"minimalist" in the sense that nothing subjective or
psychological is involved; "understanding" is entirely
schematic, i.e., determined solely by semantic rules. The extension of
an expression at a state-description is determined by applying the
semantic rules (or the expression's intension) to the
state-description. In the words of David Lewis (1970: 23):



> 
> 
> The plan to construe intensions as extension-determining functions
> originated with Carnap... Accordingly, let us call such functions
> Carnapian intensions.
> 
> 
> 



A state-description (an idea that derives from the
"Spielraume" in Wittgenstein's
*Tractatus*, and more distantly from Leibniz's idea of
possible worlds) is simply a set *X* of sentences for which the
following is the case: for each atomic sentence in the object
language, either the sentence or its negation is a member of
*X*, but not both; and *X* only includes atomic
sentences or negations of atomic sentences. One state-description
describes the "actual state of the universe" (Carnap 1947:
SS2), and how a linguistic expression is evaluated at that
state-description recovers the Tarskian extension of the expression.
Intensions are assigned to linguistic expressions by evaluating them
at *arbitrary* state-descriptions.



According to Carnap's setup, two sentences *A* and
*B* have the same intension if and only if the equivalence \(A
\leftrightarrow B\) is *L*-true. A sentence is *L*-true
(logically true) just in case it holds in in every state-description.
For Carnap this definition of *L*-truth explicates the informal
idea that a sentence is logically true if it is true in virtue of
semantic rules alone without reference to empirical facts. Later,
Carnap introduced the idea of "meaning postulates" that
could restrict the range of state-descriptions (Carnap 1952) and
adopted Quine's terminology by which only those sentences are
"logically true" whose truth is evident from the logical
particles alone, while the larger class of sentences true in all
state-descriptions are called "analytic".



Carnap (1946, 1947) worked out an intensional semantics for necessity
and possibility operators for different example languages, and for the
modal logic S5 that C.I. Lewis (1944) had previously discussed (see
the supplement
 Semantics (Section 1)
 for the details). He also started exploring areas that are presently
of special interest, such as "hyperintensional" semantics
(see, e.g., Yablo 2014): In the context of addressing the paradox of
analysis, he found that a stronger or finer-grained notion of synonymy
was needed than identity of intension, i.e., *L*-equivalence,
and he defined a relation called "intensionally isomorphic
to" for that purpose. In response to critiques by Benson Mates
and Leonard Linsky (1949), who pointed out instances of apparent
synonymity that were not intensionally isomorphic by Carnap's
definition, Carnap replied that this just showed that the
ordinary-language conception of "synonymity" is vague, and
that actually it conceals a number, perhaps a range, of explicanda;
for certain purposes, he agreed, a still stronger (or finer-grained)
conception of intensionality (and thus synonymity) might be required
(Carnap 1949).



Alonzo Church used Carnap's concept of intensional isomorphism
in his reconstruction of Frege's notions of sense and reference,
"A formulation of the logic of sense and denotation"
(Church 1951), and later also addressed a critique to Carnap directly
(Church 1954), to which Carnap (1954b) replied. John Myhill (1958) in
a critique of Church's reconstruction, re-discovered a paradox
first spelled out by Russell in Appendix B of *Principles* that
raises precisely the same issue about individuating intensions, and
since then the study of Russellian intensional logic, and
finer-grained versions of intensional identity, has continued (Church
1976, 1985; Linsky 1988; Anderson 1989; Cantini 2004; Deutsch
2014).



Carnap argues in *Meaning and Necessity* (especially SS30)
that his method of extension and intension is an improvement over
Frege's method of reference and sense, because it preserves the
extension and intension of a linguistic expression across contexts
(i.e., regardless of whether they are extensional or intensional
contexts), while Frege's method does not. Before Michael
Dummett's work on Frege, Carnap's detailed critical
engagement with Frege's theory of sense and reference in this
book probably did more to establish Frege as a classic of analytic
philosophy than any other single impulse. Not only Church, but many
others were inspired not only to reconstruct Frege's original
view in a more rigorous way, but to do so in the light of
Carnap's challenge and his critique of those views from a modern
point of view. Carnap's intensional semantics is discussed in
more detail in the supplement
 Semantics (Section 1).


## 7. Quine and "Empiricism, Semantics, and Ontology"



The best-known aspect of Carnap's reflections on semantics,
however, concern his various controversies with Quine, which addressed
a broad range of issues, two of which have aroused particular
interest: ontology and "the" analytic-synthetic
distinction. For many years after Quine launched his critique of
Carnap, in the 1950s, it was widely agreed that Quine had
"won", and for several decades his paper "Two Dogmas
of Empiricism" (Quine 1951) became perhaps the best-known and
most widely cited paper in all analytic philosophy. However, since the
revival of Carnap studies in the 1980s and 90s, the picture looks
rather different, and if there is a mainstream opinion on the
Carnap-Quine debates now, it would probably be something like the
position articulated in a series of papers by Richard Creath (1987,
1990, 1991, 1994, 2007, 2009) to the effect that Quine at least
partially misunderstood Carnap and that the two philosophers were
largely talking past each other (while of course trying hard not
to).



With respect to reductionism (the second dogma of empiricism in
Quine's 1951), Quine rightly criticized the viability of
Carnap's radical reductionism in the
*Aufbau*--which, however, Carnap himself gave up soon
after the *Aufbau*'s publication. It is much less clear
whether Quine is right to attribute a weaker form of reductionism to
the later Carnap, as Carnap regards the confirmation of scientific
hypotheses to be holistic and theory-relative from the *Logic
Syntax* at the latest. This is discussed in more detail in the
supplement
 The Reconstruction of Scientific Theories (Section 1).



The other "dogma of empiricism" that Quine discerned in
Carnap was his adherence to "the" analytic-synthetic
distinction. Unlike Quine, though, Carnap was not primarily interested
in defining analyticity for natural language, but rather in the
construction of linguistic frameworks for which a coherent notion of
analyticity could be defined in precise terms. Nor did Carnap imagine
that there was a single unique such distinction; he thought rather
that any such distinction had to be language-relative and himself
constructed precise definitions of analyticity for a number of
linguistic frameworks with different applications. True, Carnap also
attempted in *Syntax* to give a *general* definition of
"analytic" that would apply to *all* languages, but
did not think even at the time that he had succeeded. He went on
trying to find one, but never seriously proposed a solution. So
Quine's criticism of Carnap's lack of definition of
'analytic-in-language-L' with *variable*
'L' was definitely sound, but it ran in open doors, as
Carnap had never claimed to have supplied such a definition even to
his own satisfaction. It is a matter of ongoing debate, though,
whether Quine's concerns somehow undermined Carnap's
definitions of analyticity for *particular* formal frameworks
and whether these constructed and language-relative notions of
analyticity (the existence of which was of course acknowledged by
Quine) satisfied the conceptual role that Carnap ascribed to them. In
any case, Carnap himself did not think that every language had to have
analytic sentences. Most sophisticated language frameworks, especially
those equipped for scientific statements, would need them, since the
analytic sentences are just those that "come with" the
framework (by being provable by the rules of the framework without
further assumptions), but it is possible, Carnap thought, to design a
language that has no analytic sentences. (In terms of a modern
analogy: there are systems of non-classical logic, such as
three-valued Strong-Kleene logic, which include an interesting and
well-defined logical consequence relation, but where the set of
logically true statements is empty.) He did not think this worth
pursuing, though, since to him it was obvious that such a language
would not be scientifically useful. He often cited Einstein's
(1921) insistence that without Hilbert's strict distinction
between physical geometry and mathematical "purely
axiomatic" geometry (the latter of which was regarded as
analytic by Carnap), Einstein could never have formulated the theory
of relativity.



The debate between Carnap and Quine about analytic and synthetic has
produced a flood of commentary, which is still being added to (see,
e.g., Juhl & Loomis 2010 or Ebbs 2017 for recent discussions,
Proust 1986 [1989] for a broader historical perspective). The main
points of the controversy, the main commentators, and Carnap's
own view of the matter are discussed in more detail in
 Carnap vs Quine on the Analytic-Synthetic Distinction.



On the subject of ontology, Quine criticized Carnap's use of
quantifiers over intensional entities in Carnap's intensional
semantics. Closely related criticisms were voiced by many others,
especially including Carnap's own former Vienna colleague Otto
Neurath and the Oxford philosopher Gilbert Ryle, whose review of
*Meaning and Necessity* (Ryle 1949) was perhaps the nastiest
and most vituperative review ever written of anything Carnap wrote.
Carnap responded (calmly) with his well-known paper "Empiricism,
Semantics, and Ontology" (1950a), in which he distinguished
between two understandings of "existence" attributions,
internal and external. *Internal* ones are framework-relative;
they specify a language framework before claiming or denying or
questioning the existence of a thing. *External* existence
claims or questions lack such a relativization to a framework. For
Carnap only internal questions make sense, if you take them literally.
Thus "are there infinitely many numbers?" makes sense if
you relativize it to a framework such as, for instance,
Zermelo-Frankel set theory--which has an axiom of infinity, so
the answer is (trivially) yes. But without such a relativization the
question makes no sense to Carnap--unless, that is, you
reinterpret it as a *practical* (normative) question of
deciding among frameworks or explications. All of this applies, in
particular, to the quantification over abstract entities in a
framework for semantics, such as intensional semantics. In turn, Quine
rejected Carnap's internal/external distinction, which for Quine
relied on the analytic/synthetic distinction, as accepting a framework
would consist in accepting the sentences that are analytic in the
framework. Whether the ontological internal/external distinction needs
to build on the semantic analytic/synthetic distinction has itself
become a topic in recent philosophical work on metaphysical
deflationism about existence questions, which takes Carnap's
metaontological views as its historical starting point (see, e.g.,
Thomasson 2014; see the supplement
 Tolerance, Metaphysics, and Meta-Ontology (Sections 2 and 3)
 for further discussion).


## 8. Inductive Logic and the Re-Emergence of the Theoretical Language


### 8.1 Confirmation



Carnap's first sketch of a linguistic framework (that of the
*Aufbau*) envisaged complete reducibility of all concepts by
explicit definition, at least in principle. By the time of
"Testability and Meaning" (1936-37), as we saw
above, Carnap had conceded that such definitional reducibility is not
always possible, and suggested various forms of incomplete
reducibility that, while not employing only explicit definitions, at
least required of empirically meaningful sentences a clear grounding
in observation. He considers verifiability as a criterion for
empirical content or meaning, and rejects it for essentially the same
reason as he had a decade previously (in Carnap 1926: 7-9). He
also considers Popper's falsifiability criterion, and rejects it
because only sentences of a very particular logical form are
falsifiable at all (such as, e.g., "all swans are white").
Indeed, most scientific theories (all theories that use limit
concepts, for instance) have to be stated using unbounded multiple
mixed quantifiers, e.g., "for all *x* there is a
*y* such that \((\ldots x \ldots y\ldots)\)", and there
are instances of such sentences which can neither be verified *nor
falsified* by a single observational counter-instance. In
particular, to falsify such a statement there would have to be a
counter-instance *x* to falsify an unbounded existentially
quantified (empirical) sentence, which (as Popper himself
acknowledged) is not generally possible. So in these cases, typical of
theoretical science, falsifiability has no advantage over
verifiability. (For a more precise discussion of falsifiability, see
Schurz & Dorn 1988.)



Carnap therefore opts neither for verification nor for falsification,
but for a form of *partial* verification that he calls
"confirmation":



> 
> 
> If in the continued series of such testing experiments no negative
> instance is found but the number of positive instances increases, then
> our confidence in the law will grow step by step. Thus, instead of
> verification, we may speak of gradually increasing
> *confirmation* of the law. (TM1: 425)
> 
> 
> 



The acceptance or rejection of a scientific hypothesis becomes
partially a practical matter, and to some degree a matter of
convention. Carnap speaks in this connection of the "degree of
confirmation" but means this not in a quantitative but merely
"topological" (what he would later call
"comparative") sense. He specifically rejects
Reichenbach's proposal to equate degree of confirmation to
"the degree of probability in the strict sense which this
concept has in the calculus of probability, i.e., as the limit of
relative frequency" (TM1: 427). Five years later Carnap would
realize that the probability calculus could be given a different,
epistemic interpretation as had been done historically by Bayes,
Laplace, Pearson, and Keynes, and was now continued by Harold
Jeffreys--and he would make that interpretation the basis of his
remaining life's work of developing *quantitative*
explications of "degree of confirmation". (For more
details on Carnap's work on confirmation and inductive logic,
see the supplement
 Inductive Logic.)


### 8.2 Inductive Logic



Why did Carnap decide to change directions so radically, at the age of
52? This is unusual in a philosopher, especially as in Carnap's
case it involved reading his way into a whole new field of inquiry, as
well as learning a whole new branch of mathematics. We know that the
idea of a "degree of confirmation" had interested him
since at least the time of "Testability and Meaning". At
this time, as we saw in
 section 8.1
 above, he thought it could be defined only comparatively, since he
rejected Reichenbach's conflation of truth-value with frequency
as well as his identification of relative frequency and confirmation
(Carnap 1935b, 1936-37). And it had been the accepted wisdom in
the Vienna Circle that the classical (epistemic) interpretation of
probability had been entirely superseded by the frequency
interpretation, partly because the latter relied on Laplace's
much-criticized principle of indifference, which they classified as
metaphysical. Even Keynes (1921) had given insufficiently clear
arguments and his axioms were defective, they thought, but there was
interest in Wittgenstein's logical (purely analytic) conception
of probability, suggested in the *Tractatus*, and developed in
more detail by Waismann (1930).



Then in 1937, right after "Testability and Meaning",
Carnap was sent the typescript of Reichenbach's *Experience
and Prediction* for evaluation by the University of Chicago Press.
In a long letter to Reichenbach he takes him to task for exaggerating
the drawbacks of what Reichenbach chastises as the "disparity
conception" of probability, whereby the "weight" (or
"degree of confirmation" as Carnap also calls it) and
probability (understood as relative frequency) are two separate
(disparate) things. Reichenbach had gone so far in his submitted
draft, apparently, as to claim that the disparity conception was not
only the root of all philosophical error, but a form of metaphysics.
Carnap says that he himself is not sure what side he is on regarding
the disparity conception (and there is no reason to doubt this, in
1937, as far as we know), but he thinks both its acceptance and its
rejection are perfectly compatible with empiricism, and advises
Reichenbach to tone down his rhetoric.



Though he was open-minded about the "disparity conception"
during this period, it was only in the spring of 1941, according to
Carnap's autobiography, that he "began to reconsider the
whole problem of probability" (1963a: 72). He re-read
Keynes's book more carefully, and found it very enlightening
(ibid.). He began to develop a new conception of confirmation,
influenced by both Waismann and Keynes:



> 
> 
> But I tried a new approach. I believed that the logical concept of
> probability should supply an exact quantitative explication of a
> concept which is basic in the methodology of empirical science, viz.
> the concept of the confirmation of a hypothesis. (1963a: 72)
> 
> 
> 



The starting point of Carnap's new inductive logic was, first of
all, precisely Reichenbach's "disparity
conception"--i.e., to distinguish very clearly between two
different explicata of the ordinary-language word
"probability". One was relative frequency, which is an
empirical matter, and was held up as the *only* acceptable
interpretation of the Kolmogorov probability calculus by frequentists
such as von Mises, Reichenbach, and (classically) Ronald Fisher. The
other was epistemic probability, which Keynes and Harold Jeffreys held
to be the *only* acceptable interpretation. Carnap called them
"probability2" and
"probability1" respectively, and set about
clearing the ground for an explication of the latter, without casting
any doubt on the legitimacy of "probability2"
as an empirical tool. This distinction was the main focus of
Carnap's first article on inductive logic (Carnap 1945a).



The conception he developed in his next article (Carnap 1945b) was
indeed logical in the Wittgenstein-Waismann sense, in that the
relation between observation sentences and hypothesis was purely
logical and analytic. To achieve this, a relativized principle of
indifference was needed; unlike that of Laplace or Keynes,
Carnap's was entirely language-relative (framework-relative); it
was no longer a quasi-metaphysical assertion about the nature of
distributions, let alone about the statistical nature of the world,
but a matter of constitutive definition. As in any other area of
knowledge, Carnap thought it essential to define the framework before
making assertions, so that we are all on the same page. (This logical
or "structural" conception of probability and the
relativized principle of indifference are explained in concrete detail
in the supplement
 Inductive Logic.)
 This means that the value of a confirmation measure as applied to a
hypothesis and the evidence for or against it is an analytical
consequence (in the chosen language framework) of the logical and
inductive method given by the framework.



In 1950, Carnap published what would be longest book of his career by
far, the *Logical Foundations of Probability*, into which he
worked these two papers (much expanded) and several others, and also
went into great detail to bring a number of perspectives to bear on
the clarification of the explicanda of "probability" and
"confirmation" (both in the sense of
probability1). He also goes into detail to discuss ways of
arriving at axioms, and to motivate the choices he ends up with. In
the course of these clarifications he addresses a number of
philosophical issues surrounding induction, confirmation, and
scientific inference. A simpler exposition than Carnap himself gave of
his inductive logic project was given later by Kemeny (1963). See the
supplement
 Inductive Logic
 for further details.



Carnap's inductive logic encountered a wide range of criticisms,
e.g., that of Hilary Putnam, whose philosophical development had been
strongly influenced by regular meetings with Carnap at Princeton in
the 1950s. Putnam criticized the general idea of an algorithmic
account of the inductive confirmation of scientific hypothesis by
evidence (as exemplified by the special confirmation measure \(c^\*\)
that is described in the appendix of Carnap 1950b), while at the same
time laying the foundations of what would become *formal learning
theory* (see Putnam 1963 and the concluding section of the
supplement
 Inductive Logic).
 But perhaps the biggest obstacle to a better and more widespread
understanding of Carnap's inductive logic was the memorable
caricature of Carnap's whole enterprise by Karl Popper in his
attacks on Carnap during the 1950s and 1960s (e.g., Popper 1963).
These were so convincing that the philosophical public retained only
the caricature and hardly bothered to consult the original. In other
words, the same pattern repeated itself that we have already seen with
respect to the Quine-Carnap controversies of the 1950s and 60s
 (section 7
 above)--for a long time, the general philosophical public
retained only one side of the debate, influenced mainly by
Quine's (and then Popper's) superior rhetorical skills, as
a result of which both Quine and Popper were much more widely read
than Carnap (though Quine's proximity to traditional American
pragmatism surely also played a role). The difference between these
cases is that Popper, unlike Quine, actually misrepresented
Carnap's position quite blatantly, as Carnap's supporters
(e.g., Bar-Hillel 1955, 1956; Kemeny 1955, 1963) were quick to point
out. (Michalos 1971 gives a well-informed, brief, but balanced survey
of the Popper-Carnap controversy.)



Statisticians (and statistically literate philosophers) have been
quicker to acknowledge not only the continuity between Carnap's
inductive logic and the present-day renaissance of Bayesian
statistical inference, but Carnap's role in bringing epistemic
probability back from the dead and ensuring that it was taken
seriously again (e.g., Leblanc 1962; Skyrms 1996; Zabell 2007, 2011).
Many of the standard features of current Bayesianism were first
formulated in Carnap's *Logical Foundations* and in his
subsequent work. Carnap went on working on inductive logic for another
20 years after *Logical Foundations*; his final statement (the
"Basic System"), in which prior probabilities depended on
geometrical "quality space" features of the given
framework, appeared after his death in two long installments, edited
by his friend and associate Richard Jeffrey (Carnap 1971a, 1980; for
an extensive discussion of the "Basic System", see
Hilpinen 1973, Sznajder 2017). His later work appeared to move in a
more "personalist" direction (though see Sznajder 2018),
but Carnap continued to insist that the prior probability from which a
statistical inference proceeds be motivated rationally (by
considerations of symmetry) and *not* be merely subjective;
here he stuck to his original idea of the relation between evidence
and hypothesis being purely analytic and thus framework-relative.
Though this distinguishes his standpoint from current subjective
Bayesians, there are and have been many other kinds of Bayesians that
are reasonably close to Carnap's views, including
"objective" Bayesians (e.g., Jaynes 1968, J. Williamson
2010). (For more on Carnap's relation to current Bayesianism and
various discussions of it today, see the supplement
 Inductive Logic.)
 As one prominent Bayesian pointed out in 1971, one can distinguish at
least 46,656 possible varieties of Bayesians (Good 1971), and Zabell
(a later prominent Bayesian) thinks Carnap would surely qualify for
inclusion among these. Zabell also cites a characteristically
conciliatory passage from Carnap's posthumous "Basic
System" that sums up Carnap's appraisal of the
situation:



> 
> 
> I think there need not be a controversy between the objectivist point
> of view and the subjectivist or personalist point of view. Both have a
> legitimate place in the context of our work, that is, the construction
> of a set of rules for determining probability values with respect to
> possible evidence. At each step in the construction, a choice is to be
> made; the choice is not completely free but is restricted by certain
> boundaries. Basically there is merely a difference in attitude or
> emphasis between the subjectivist tendency to emphasize the existing
> freedom of choice, and the objectivist tendency to stress the
> existence of limitations. (Carnap 1980: 119, quoted by Zabell 2007:
> 294)
> 
> 
> 


### 8.3 Return to the Theoretical Language



As we saw in
 section 6.1,
 by the late 1930s Carnap had returned to a consideration of
theoretical languages whose primitive terms are not constructed
bottom-up from observation sentences at all but entirely top-down,
"floating in the air, so to speak" so that these basic
theoretical terms can have "only an *indirect
interpretation*, which is incomplete in a certain sense"
(Carnap 1939: 65). In Carnap's mind, the question of
confirmation of theories and the question of the empirical content of
theories were directly and inseparably connected, as they had been in
"Testability and Meaning". In this subsequent work on
these two questions, however, they were pursued separately, and for
all of Carnap's efforts, the two strands could not be joined up.
His inductive logic was never able to assign a degree of confirmation
other than zero to unrestricted universally quantified theories, which
was obviously a defect of the theory and was seized upon by Popper as
discrediting the entire enterprise (e.g., Popper 1963). Carnap's
own way around the problem was to argue that scientists often regard
the degree by which a piece of evidence *E* confirms a
universal law hypothesis \(\forall x P(x)\) to be given by the degree
to which *E* confirms an "arbitrary" instance of
the law \(P(a)\), where *a* is an individual constant that does
not occur in *E*: see Carnap (1945b: SS14). Later authors
tried to repair the defect in alternative ways, with varying degrees
of success; see the supplement
 Inductive Logic.
 On the other hand, though Carnap's work on the empirical
content of sentences in a theoretical language often discusses the
relations between observational language and theoretical language, he
was never quite able to spell out a criterion for empirically
meaningful sentences in the theoretical language that did not fall
prey to fairly straightforward criticism (e.g., Kaplan 1975). The
grand design of connecting up the projects of explicating confirmation
and of reconstructing scientific theoretical language remained a
distant goal.



We have already surveyed the inductive-logic side in the previous
 section 8.2.
 On the theoretical-language side, Carnap's first major paper
was "The methodological character of theoretical concepts"
(Carnap 1956a), followed by "Observation language and
theoretical language" (Carnap 1958) and "Theoretical
concepts in science" (1959a). Carnap also touches on theoretical
languages in several parts of the Schilpp volume (1963).
*Philosophical Foundations of Physics* (1966), finally, is a
redaction by Martin Gardner of a class Carnap gave at UCLA in the late
1950s, presented as an introductory textbook in the philosophy of
science. Among other things, it gives a lucid summary of
Carnap's mature views on the reconstruction of scientific
theories. See the supplement
 The Reconstruction of Scientific Theories (Sections 3-5)
 for details and criticism.



One common misunderstanding of Carnap's work on the theoretical
language is an extension of the above-discussed misunderstandings of
the *Aufbau*
 (section 3
 above). The *Aufbau* was traditionally perceived as an
exercise in providing phenomenalist or empiricist foundations for
scientific sentences. Therefore, it was assumed, the later work on
both inductive logic and the theoretical language must be motivated by
the aim of providing empiricist foundations for scientific sentences,
to distinguish them from non-scientific, i.e., metaphysical sentences.
This was certainly Popper's view, for instance, and largely
Quine's, but they were not alone; it was widespread until the
1990s, when the new and more careful scholarship about logical
empiricism began to take hold.



It is true, of course, that in Carnap's later work on scientific
theories and theoretical languages, he distinguishes between a
theoretical language and an observation language, and studied the
relations between them. What is often overlooked, though, is that even
in the *Aufbau* (and even in the earliest proto-*Aufbau*
manuscripts) Carnap was very clear that what we are to take as
"the given" is not inherently fixed or given *by
nature* (as Aristotle would have put it), but something we have to
*decide on*, something we have to specify provisionally in our
chosen form of rational reconstruction. Later Carnap became even
clearer that what we choose to regard as "observation
sentences" is purpose-relative and can't be decided once
for all contexts, in the abstract. As early as "Testability and
Meaning" (TM1: SS16) Carnap was saying that "there can
be several and even mutually exclusive bases" for confirmation
by observation. And in later work on the theoretical language this
pluralism is extended; in "The methodological character of
theoretical concepts" he merely enumerates various possible
requirements of different kinds and strengths that might be imposed on
the observation language.



In Carnap's view, the choice of the theoretical language depends
on the purpose. The boundary between "observational" and
"theoretical" terms, likewise, is relative to the language
chosen and not fixed by nature:



> 
> 
> no sharp boundary separates the *O*-terms from the
> *T*-terms. The choice of an exact dividing line is somewhat
> arbitrary. From a practical point of view, however, the distinction is
> usually evident. (Carnap 1966: 258)
> 
> 
> 



Observational terms are assumed to be fully interpreted; their
specification comes with an explicit link to observation (precisely
defined in some way), while theoretical terms are specified
axiomatically and are, in the first instance, uninterpreted or only
mathematically interpreted formulas. These formulas can then be
endowed with physical (or chemical, or biological, or social)
interpretations by means of correspondence rules, which logically
relate observation terms and theoretical terms.



Carnap's views on the theoretical language during this period
developed in response to critiques and commentaries from (as well as
personal correspondence with) C.G. Hempel (1945, 1958, 1963). One
response to these interactions was Carnap's adoption of an idea
first suggested by Frank Ramsey (1929) for the purpose of separating
the theoretical from the empirical content of a theory; this idea
first appeared in print in (the original German version of)
Carnap's paper "Observation language and theoretical
language" (1958). (This procedure is explained in detail in the
supplement
 The Reconstruction of Scientific Theories (Sections 4-6).)
 The idea was that a theory could essentially be stated in such a way
that all the theoretical terms in it are eliminated, i.e., it could be
stated solely in terms of its "empirical residue". But
Carnap's goal in adopting this method was not to suggest that
the theoretical language was eliminable, that theoretical terms could
or should be eliminated (as some versions of traditional empiricism
might have liked). The point was rather to understand the empirical
content of theoretical claims, and its logical function within
theories. This leads to many complications, which are still very much
under discussion (e.g., Demopoulos 2007, Friedman 2011, Schurz
2005).



The Ramsey approach was adopted, following Carnap, by others, notably
David Lewis (1970), who put it to a rather different, more
metaphysical use that was later adopted by Frank Jackson and other
advocates of the "Canberra Plan" of conceptual analysis.
This was also Chalmers's (2012) point of departure, in his more
metaphysical adaptation of the *Aufbau*, mentioned above
 (section 3).
 See the supplement
 The Reconstruction of Scientific Theories (Section 4).


## 9. Final Years and Legacy



In 1951, Herbert Feigl approached Paul Schilpp, the editor of the
*Library of Living Philosophers*, about doing a volume not on a
particular philosopher, but on logical empiricism as a movement.
Carnap and Reichenbach were to be in the foreground, as representative
figures for the movement as a whole. Schilpp was sufficiently
interested that he persisted with the idea even after
Reichenbach's sudden death in 1953; the volume was now to be
focused on Carnap alone. Carnap invested a great deal of time in the
project. He took the task of writing an autobiography seriously,
reviewing many of his old papers, including his extensive diaries, in
preparation for it. The resulting autobiography was much too long, and
had to be cut by a third before publication. (The cut portions are
available at the Young Research Library, University of California at
Los Angeles, Special Collections, Collection 1029 (Rudolf Carnap), Box
2, CM3, mostly in folder marked "M-A5"; extensive
quotations and references can be found in Carus 2007a.)



Unfortunately, publication was delayed by a series of mishaps, and
when the book finally appeared in 1963, logical empiricism was no
longer at the forefront of interest. Analytic philosophers had largely
been swayed by Quine's critique of Carnap over the past decade,
and philosophers of science were captivated by Thomas Kuhn's
book *The Structure of Scientific Revolutions*, published the
year before in the International Encyclopedia of Unified Science,
co-edited by Carnap. Logical empiricism no longer inspired passions,
either for or against; it seemed to belong to the past. Carnap saw in
the anti-war and student movements of the 1960s an American version of
the Youth Movement that had played such an important role in his own
development half a century earlier, but insofar as the students of the
1960s were interested in philosophy, it was not in logical empiricism.
A few weeks before his death, Carnap prepared a report for an American
Philosophical Association committee about his meeting in the summer of
1970 with some philosophers imprisoned in Mexico. It illustrates his
continued interest in social and political matters and in his fellow
philosophers, and appeared posthumously, in December of that year, in
the *Journal of Philosophy*. When Carnap died in Los Angeles in
1970, the philosophical world at large (as opposed to the major
figures whose views he had shaped, such as Quine, Goodman, Putnam,
Jeffrey, or Stein) had lost interest in him. But half a century later,
it is fair to say that Carnap's work is as much in the
foreground of philosophical discussion as it has ever been.


## 10. List of Supplements


* Supplement A: *Aufbau*
* Supplement B: Carnap versus Quine on the Analytic-Synthetic Distinction
* Supplement C: Inductive Logic
* Supplement D: Methodology
* Supplement E: Reconstruction of Scientific Theories
* Supplement F: Semantics
* Supplement G: *Logical Syntax of Language* (LSS)
* Supplement H: Tolerance, Metaphysics, and Meta-Ontology