## 1. Mapping the Movement



The term 'logical empiricism' has no very precise
boundaries and still less that distinguishes it from 'logical
positivism'. It is therefore hard to map. 'Logical
empiricism' here includes three groups: (1) the Vienna Circle,
here taken broadly to include those who were part of various private
discussion groups, especially that around Moritz Schlick, and also the
members of the more public Ernst Mach Society (Verein Ernst Mach), (2)
the smaller, but perhaps more influential Berlin Society for Empirical
Philosophy (later called the Berlin Society for Scientific
Philosophy), and (3) those influenced by or who interacted with
members of the first two groups and shared an intellectual kinship
with them. Besides Vienna and Berlin, there were important centers of
the movement in England, France, Scandinavia, at several universities
in the U.S., and even China. This characterization includes thinkers
who disagreed with doctrines espoused by members of the original
groups and even some who defined themselves in opposition to the
movement. This results in a vague boundary, but it suffices to
identify a movement in which a large number of able philosophers
self-consciously participated and to distinguish logical empiricism
from other movements.



It does not, however, distinguish logical empiricism from logical
positivism, and it is doubtful that any principled such boundary can
be drawn along doctrinal or sociological lines (Uebel 2013). Usually
when distinctions are drawn, 'logical empiricism' is the
wider term. Members of the Berlin group never used the term
'positivism' about themselves, but did use it concerning
some unnamed Viennese in stressing their differences from the latter.
In any case, these differences, even if real, were smaller than the
differences within the Vienna Circle on one hand or within the Berlin
group on the other. 'Positivist' is a term usually applied
by opponents of various doctrines. It was used by some of the Viennese
logical empiricists about themselves but generally with caution and in
stressing the differences between their own views and those of the
19th century positivists. The one philosopher who would
have unhesitatingly described himself as (having been) a logical
positivist was A.J. Ayer.



Another way of mapping the boundaries of logical empiricism is to list
the specific philosophers who were centrally or peripherally part of
it. This included many of the most important philosophers of the
mid-twentieth century. Hans Hahn, Moritz Schlick, Rudolf Carnap, and
Otto Neurath were leaders of the Vienna Circle, and Kurt Godel
regularly attended its meetings. The list of its members, visitors,
and interlocutors is staggering, including A.J. Ayer, Herbert Feigl,
Philipp Frank, Hans Hahn, Carl Hempel, Karl Menger, Richard von Mises,
Ernest Nagel, Karl Popper, W.V. Quine, Frank Ramsay, Hans Reichenbach,
Alfred Tarski, Friedrich Waismann, and Ludwig Wittgenstein, among many
others. Not all of these would admit to being part of the logical
empiricist movement, of course, but a case can be made that all
contributed to it. The Berlin Society for Empirical (or Scientific)
Philosophy was, as stated, smaller but perhaps more influential. Led
by Hans Reichenbach, it included Kurt Grelling, Walter Dubislav, Kurt
Lewin, Richard von Mises, Paul Oppenheim, and others. Hempel took his
doctorate in Berlin, working with Reichenbach until the latter was
forced to leave in 1933. Hempel also spent time in Vienna and Prague.
Of course, among the foremost associates of the Berlin Society was
Albert Einstein, who was also in Berlin also until 1933.



There was also an important group of logicians in Warsaw of which
Alfred Tarski is the best known. Tarski interacted significantly with
the logical empiricists in Vienna, Berlin, and the U.S., but it is
more reasonable to classify the Polish logicians as an allied group
rather than include them within the logical empiricist movement.



Because of the catastrophic dislocations of Europe in the 1930s, the
main focus of the logical empiricism moved from central Europe to
America by the close of that decade. *Erkenntnis*, the main
journal of the movement, which had been edited by Reichenbach and
Carnap, ceased publication by 1940. In 1930 Feigl moved to the U.S.,
and Carnap moved to Chicago in 1936. Hempel came to Chicago and Menger
to Notre Dame in 1937. The ensuing years witnessed a massive exodus to
America from central Europe. Reichenbach arrived in the U.S. in 1938
after five years in Turkey. Also in 1938 Gustav Bergmann and Philipp
Frank emigrated. Edgar Zilsel came in 1939. Alfred Tarski was on a
visit to the U.S. when Poland was invaded in 1939, and so he stayed.
And by 1940 Richard von Mises was also in America.



In the U.S., these exiles were joined by the Americans Nelson Goodman,
Charles Morris, W.V. Quine, Ernest Nagel, and, after the war, by
Reichenbach's UCLA students Hilary Putnam and Wesley Salmon.
Adolf Grunbaum can also be considered as clearly in the
Reichenbach lineage. And Wilfrid Sellars was, in his early years, a
close associate of Feigl. The American incarnation of the logical
empiricist movement enjoyed generally good relations with the American
pragmatists, not only because many of the logical empiricists had a
strong pragmatist component to their philosophy, but also because the
pragmatists and logical empiricists shared a common concern for
empirical methodology in the service of social reform.
Institutionally, the movement was represented in most major American
universities, and such journals as *Philosophy of Science*
(with Carnap and Feigl on the Editorial Board and Reichenbach and
Schlick on the Advisory Board) and *Philosophical Studies*
(founded and edited for many years by Feigl and Sellars) provided
ample outlet for their publications. In addition, the Inter-Scientific
Discussion Group was founded by Philipp Frank at Harvard. That grew
into the Institute for the Unity of Science, called by some the Vienna
Circle in exile. Meanwhile in Chicago the *Encyclopedia of Unified
Science* was established with Neurath, Carnap, and Morris as its
editors.



But even from late 30s onward the movement was hardly limited to
America. Ayer remained in England. Wittgenstein returned to Cambridge
in 1929, but with regular visits to Vienna, including those on which
he discussed issues surrounding a strong version of verificationism
with Schlick and Waismann. Popper fled to New Zealand in 1937, and in
1946 moved to the London School of Economics. Neurath fled from Vienna
to the Hague and then again in 1940 to England, where he remained till
his death in 1945. Friedrich Waismann went to England in 1937. In 1939
Rose Rand, a less well-known member of the Vienna Circle, fled to
England and then in 1954 emigrated once more to the U.S. There were
like-minded thinkers in Scandinavia (such as Jorgen
Jorgensen, Eino Kaila, and Arne Naess) and as far away as
Argentina (H.A. Lindemann) and China (Tscha Hung).



It is impossible to say when logical empiricism ceased to be
sufficiently cohesive to be identifiable as a continuing movement.
Certainly by 1960 a great many philosophers, including many who had
earlier clearly been part of the movement, were identifying themselves
in opposition to what they took to be logical empiricism. And some
members simply changed their minds or pursued different projects.
Logical empiricism probably never commanded the assent of the majority
of philosophers in either Europe or America, and by 1970 the movement
was pretty clearly over--though with lasting influence whether
recognized or not. In the 1980s there was a resurgence of historical
interest in logical empiricism. That historical interest continues to
clear away many of the caricatures and misconceptions about the
logical empiricists. Among the major results of this work is the
recognition of the tremendous variety and subtlety of views
represented within the movement and the fact that many of the
arguments later deployed by critics of logical empiricism had been
pioneered by the logical empiricists themselves.



Given the emphasis on science and its technical apparatus, social
renewal, clarity and rationality of belief, functionality, and above
all the palpable sense of doing philosophy in an importantly new way,
it is reasonable to associate logical empiricism with other forms of
European modernism in the 1920s and 30s, such as Neue Sachlichkeit in
art and the Bauhaus in architecture and design, and with mid-century
modernism as well as with political liberalism, from the New Deal to
the Great Society in the United States. There have been recognizably
modernist developments in various fields including philosophy for
centuries.


## 2. Background



With a movement as large and complex as logical empiricism a great
many factors went into raising the questions it would address, making
them seem urgent, and making it seem as though the intellectual
resources it would need to address these questions were either at hand
or could be developed.



One long-term process with profound implications was the steady
departure of the various sciences from philosophy to form autonomous
disciplines. By early in the twentieth century mathematics, physics,
chemistry, biology, and the social sciences were all pursued
professionally and independently from philosophy. And psychology was
just separating from philosophy. Yes, there were polymaths who could
and did pursue a science and philosophy professionally. Those were
increasingly rare, though single-discipline scientists did from time
to time make philosophic-seeming pronouncements. But they did so from
outside the field. This pattern of steady departures raised the
pressing question: What sort of thing remained behind? Once
mathematics and the empirical sciences all left, what was left for
philosophy?



The nature of philosophy was always a vexed philosophic question, but
now it was particularly insistent. Surely there was no domain of
empirical facts that philosophy could call its own. All that real
estate had been parceled out. One answer available at the time that
logical empiricism flourished was that the genuinely philosophic
remainder after the departure of the sciences is somehow deeper than
the empirical sciences and gets at matters, perhaps cultural ones,
that are more profound and important than anything that empirical
science even can address. This is either because on this conception
philosophy has a mode of access or "evidence" that the
empirical sciences do not and cannot have, or because the very idea of
fidelity to evidence and punctilious argument is somehow
small-minded.



The logical empiricists found this answer unappealing. Indeed, this
conception of philosophy is precisely what Carnap means by
'metaphysics'. (As a consequence, what Carnap meant by
that word is different from what late twentieth and early twenty-first
century philosophers generally mean in describing their own work as
analytic metaphysics.) The logical empiricists were eager to conceive
of their enterprise as scientific and to engage in philosophy only
insofar as it was also scientific. This science need not be empirical
and need not include all that was traditional in philosophy that had
not been incorporated into the independent sciences. The decision to
be scientific can hardly be the end of the story. It requires rather
better and more detailed answers to questions about what scientific
methods are, how the mathematical (and other apparently non-empirical
sciences) fit together with the empirical ones, and what, more
precisely, philosophy's role was.



A second series of developments that raised questions for logical
empiricism to address were developments in the sciences themselves,
especially the rise of non-Euclidean geometries in mathematics and the
establishment of relativity theory in physics. These posed a serious
challenge to what would otherwise be an attractive scientific
philosophy, namely some version of Kantianism. Kant had recognized
that the best of modern science was often mathematical in character
and had labored to integrate both geometry and arithmetic into our
empirical picture of the world. He had held that we could not
represent the world except as a Euclidean structure and hence
Euclidean geometry was, a priori, a permanent feature of any future
physics. The demonstration that non-Euclidean pure geometrical
structures were as consistent as Euclidean ones and that spaces can
indeed be represented as a non-Euclidean manifolds was one half of the
problem. The other half came when Einstein argued convincingly that
physical space was best described as a non-Euclidean manifold of
non-constant curvature. Plainly Euclidean geometry could not be
guaranteed a future physics. Modern mathematical logic also posed a
problem for other Kantian claims, but not in the same wrenching
way.



Many logical empiricists started out as neo-Kantians: Reichenbach,
Carnap, Schlick, and even Hempel (until he studied with Reichenbach,
who by that time had revised his view). The difficulties with geometry
and relativity certainly do not refute all forms of neo-Kantianism,
but the difficulties are quite real nonetheless. The need is to
understand how mathematics can be integrated into what is otherwise an
empirical enterprise, i.e., physics, chemistry, biology, etc.
Addressing this need was to be a major part of the logical empiricist
program.



The background of logical empiricism described so far has been
confined to the academic world, but events outside that domain shaped
the movement as well. World War I was an unmitigated disaster for
central Europe, followed by economic turmoil in the 20s and political
upheavals of the 30s. It is hard to exaggerate these changes.
Monarchies that had stood for centuries disappeared overnight and
their empires disintegrated. This level of political convulsion had
not been seen since the French Revolution, and that earlier upheaval
was comparatively confined. Cultural changes were equally profound,
and these were reflected by radical departures in the arts such as
painting, music, and architecture, and even more importantly in new
modes of living.



The logical empiricists were no mere bystanders. They, or at least the
main leaders of the movement, were politically and culturally engaged.
Even more important, this engagement was accompanied by the conviction
that their cultures were incapable of the necessary reform and renewal
because people were in effect enslaved by unscientific, metaphysical
ways of thinking. Such ways of thinking might be exemplified in
theology, in the racial hatreds of the day, in conceptions of
property, and in traditional ideas about the "proper"
roles of men and women in society. So to articulate a
"scientific world conception" and to defend it against
metaphysics was not just to express an academic position in the narrow
sense. It was a political act as well; it was to strike a blow for the
liberation of the mind. To articulate scientific methods and a
scientific conception of philosophy was the essential first step in
the reform of society and in the emancipation of humankind (Carnap
1958/2017, Creath 2009, Uebel 2012.



If all of this sounds like something out of the 18th
century Enlightenment, the analogy was not lost on the logical
empiricists themselves. Andre Carus has argued that this is
exactly what Carnap had in mind by "explication" (Carus
2007). Neurath frequently drew parallels between the logical
empiricists' anti-metaphysical program and the earlier
Enlightenment ambitions. Certainly Kant had inveighed against the
metaphysics of his time, and the anti-metaphysical tradition remained
strong within the scientific community through the 19th
century.



The point so far was not to ask whether the logical empiricists were
right in any of this. That question will come up later. So far the
issue has been only to see the motivations that the logical
empiricists had--and from their point of view--for
addressing certain questions and for thinking that answers to those
questions were urgently needed. None of this, however, says why the
logical empiricists thought they had or could have the means to answer
these questions. To that we now turn.



Since Newton the most paradigmatic examples of empirical science were
those claims, usually quantitative ones, that were properly inferred
from or appropriately confirmed by experience. Speaking very
informally, these are the ones that we have good reason to believe or
at least better reason to believe than the available alternatives. The
problem, of course, is to specify the form of proper inferences, the
form of an appropriate confirmation relation, and/or the structure of
good reasons. The task is daunting, but logic in a suitably broad
sense seems to be the right tool. Still speaking informally, logic
seems to give us the structure of (good) reasoning. There are other
conceptions of logic, of course, but this is a standard one and pretty
well describes what the movement needed.



If logic was the tool that was wanted, it was newly ready for service.
The progress of modern mathematical logic from Bolzano through Russell
and beyond was truly impressive. Arguably, it could now express all
parts of classical mathematics. Besides the first order predicate
calculus one would need either set theory or higher order logic, but
these were recent developments as well. Logic, like the empirical
sciences, was progressive and could be approached cooperatively by
more than one investigator. In *Our Knowledge of the External
World* (1914) Russell had even positioned logic as *the*
locus of scientific method in philosophy. It is small wonder then that
those who were looking for something scientific in what was left of
philosophy turned to logic. Wittgenstein's no-content theory of
logic in the *Tractatus* (1921/1922) was tantalizingly
suggestive about how mathematics could be integrated into an overall
empirical theory of the world. Wittgenstein also expressed a radical
verificationism in the early 1930s in his conversations with Schlick,
Waismann, and other members of the Vienna Circle. Many of the logical
empiricists in turn could see in some version of that verificationism
the ideal tool with which to carry out their anti-metaphysical
program. There was, naturally, much left to accomplish, but even with
Godel's results one could expect that further impressive
strides in logic could be made. Indeed, much was accomplished even if
the perfect account of scientific reasoning proved elusive. Perfection
is elusive in all the sciences, but that is no reason for despair.


## 3. Some Major Participants in the Movement



The logical empiricist movement is the sum of the interwoven
trajectories of its members, so one way of describing that movement is
to trace those various trajectories. To do so in detail for all those
involved would take rather longer than the movement lasted. That would
be inappropriate for one entry in an encyclopedia, especially one in
which entries for many of the members will appear independently. The
thumbnail sketches of the work of some representative figures below
show the breadth and international character of the movement. While
the list is long, it covers only a small fraction of those involved
and leaves out many important thinkers.



A.J. Ayer (1910-1989)
An English philosopher in the tradition of British empiricism,
Ayer visited the Vienna Circle in 1932-33. His book
*Language, Truth, and Logic* (1936) was a best seller after
World War II and represents logical positivism to many English
speakers.
Gustav Bergmann (1906-1987)
Born and trained in Vienna, Bergmann spent almost all of his
career at the University of Iowa. He was a philosopher of
science, mathematician, and metaphysician, who in his early years
joined in the Vienna Circle. But as his career progressed, his
ideas increasingly diverged from other members of the logical
empiricist movement.
Rudolf Carnap (1891-1970)
German by birth, he taught in Vienna, Prague, Chicago, and Los
Angeles. He was one of the leaders of the Vienna Circle and of logical
empiricism, especially of those within the movement whose formulations
were more liberal, e.g., with respect to the criterion of
verification. He defended logical and methodological pluralism and
worked to develop an epistemic approach to probability.
Walter Dubislav (1895-1937)
A German logician and philosopher of science, Dubislav was one of
the founders, with Reichenbach and Grelling, of the Berlin Society of
Empirical (later Scientific) Philosophy.
Herbert Feigl (1902-1988)
Born in what is now the Czech Republic, Feigl studied in Vienna
with Schlick and Hahn. He emigrated to the U.S. before most other
logical empiricists would do so. He taught at the Universities of Iowa
and Minnesota and founded both *Philosophical Studies*, with
Wilfrid Sellars, and the Minnesota Center for the Philosophy of
Science. He is best known for his work on the mind-body problem.
Philipp Frank (1884-1966)
This Viennese physicist and philosopher of science taught at
Vienna, Prague, and Harvard. He was part of a discussion group with
Hahn, Neurath, and others that preceded the Vienna Circle. At Harvard
he founded the Inter-Scientific Discussion Group that developed into
the Institute for the Unity of Science. He was also one of the
founders of the Boston Colloquium in the Philosophy of Science.
Kurt Godel (1906-1978)
Born in what is now Slovakia, Godel took his doctorate under
Hahn in Vienna, studying with Carnap and Schlick as well. He also
regularly attended Vienna Circle meetings and taught in Vienna. The
bulk of his career was spent at the Institute for Advanced Study at
Princeton. He is best known for his spectacular incompleteness
theorems, and his Platonist orientation toward mathematics. Though a
participant in the logical empiricist movement during the Vienna
years, Godel thought that Carnap's approach to mathematics
could be refuted. The alleged proof (Godel 1995) was not
published in Godel's lifetime and remains
controversial.
Kurt Grelling (1886-1942)
Grelling was born in Berlin and took his doctorate in
Gottingen under Hilbert. With Leonard Nelson he developed a
famous semantic paradox that bears their names. He was one of the
founders of the Berlin Society for Empirical (later Scientific)
Philosophy. Grelling died in the Holocaust because for bureaucratic
and political reasons news of an academic appointment in the U.S.
reached him too late.
Adolf Grunbaum (1923-2018)
Grunbaum moved from his native Germany as a teenager, studied
under Hempel at Yale, and spent the bulk of his career at the
University of Pittsburgh, where he founded the Center for Philosophy
of Science. The major themes of his work have been philosophy of space
and time, rationality, and psychoanalysis.
Hans Hahn (1879-1934)
Hahn, a distinguished mathematician, took his doctorate in his
native Vienna in 1902 and began teaching there in 1905. He was part of
a group with Frank, Neurath and others that discussed logical and
methodological issues prior to World War I. After teaching at
Czernowitz (now in Ukraine) and Bonn he was given a chair in
mathematics at Vienna in 1921. He was instrumental in bringing Schlick
there in 1922 and so was called by Frank "the actual founder of
the Vienna Circle" (Stadler 1997/2001, 642). His most famous
student was Godel.
Olaf Helmer (1910-2011)
Helmer took a doctorate in his native Berlin under Reichenbach and
a second doctorate under Susan Stebbing in London. He collaborated
with other logically minded philosophers. Indeed, the team of Hempel,
Helmer, and Oppenheim became known as "H2O".
The bulk of his career was spent at the Rand Corporation.
Carl G. Hempel (1905-1997)
Born just north of Berlin, Hempel studied at both Gottingen
and Berlin. Most of his doctoral work was completed under Reichenbach
when the latter was forced to leave Germany. Hempel taught at a number
of American universities, most famously at Princeton and the
University of Pittsburgh. He was the doctor father of many prominent
philosophers of science, and his work focused on confirmation,
explanation, and concept formation.
Richard Jeffrey (1926-2002)
This American logician and philosopher of science earned an MA
with Carnap (with whom he later collaborated) and a PhD with Hempel
(with whom he was for many years a colleague and close friend at
Princeton). He developed Jeffrey conditionalization (see below) and
defended probabilism.
Kurt Lewin (1890-1947)
Born in what is now Poland, Lewin took his doctorate in Berlin in
1916. He lectured there in both philosophy and psychology until 1933
when he emigrated to the U.S. via England. Thereafter he taught at a
number of American universities including Cornell, Iowa, MIT, and
Duke. Credited with founding modern social psychology, he laid the
foundations for what is now called sensitivity training as a way to
combat religious and racial prejudices.
Richard von Mises (1883-1953)
Born in what is now Ukraine, Richard von Mises is the brother of
the economic and political theorist Ludwig von Mises. Richard was a
polymath who ranged over fields as diverse as mathematics,
aerodynamics, philosophy, and Rilke's poetry. He finished his
doctorate in Vienna. He was simultaneously active in Berlin, where he
was one of the developers of the frequency theory of probability along
with Reichenbach, and in Vienna, where he participated in various
discussion groups that constituted the Vienna Circle. Eventually it
was necessary to escape, first to Turkey, and eventually to MIT and
Harvard.
Charles W. Morris (1901-1979)
Morris was an American pragmatist and philosopher of language at
the University of Chicago when Carnap arrived there. These two,
together with Neurath until the latter's death, were the chief
editors of the *Encyclopedia of Unified Science*. After Carnap
left Chicago, Morris moved to the University of Florida.
Otto Neurath (1882-1945)
This Austrian philosopher of science and sociologist took his
doctorate in political science in Berlin. A member of the First Vienna
Circle and a leader of the "left" wing of the Vienna
Circle, he was also politically active. He was a significant museum
director, and as part of this developed the ISOTYPE picture language.
His main philosophic themes were physicalism, anti-metaphysics, and
the unity of science. He was the Editor-in-Chief of the
*Encyclopedia of Unified Science* until his death. Eventually
he fled to the Netherlands and from there to England.
Paul Oppenheim (1885-1977)
A successful industrialist and heir to a substantial fortune,
Oppenheim was trained in his native Germany in chemistry and
philosophy. He was a close friend of Einstein, and helped to initiate
the Berlin Society for Empirical Philosophy. Oppenheim collaborated
with many important logicians and philosophers of science both in
Europe and the U.S. He also helped many to escape Nazi oppression, and
continued to help in a variety of ways even after he settled in
Princeton in 1939.
Karl Popper (1902-1994)
Born in Vienna and with a doctorate there, Popper was intensely
engaged in discussions with members of the Vienna Circle. His main
philosophical work, *The Logic of Scientific Discovery*
(1935/1959), appeared in a series edited by Schlick and P. Frank. He
did not however, regularly attend meetings of the Vienna Circle and
generally considered himself an outsider. Later he claimed to have
"killed" logical positivism. From Austria Popper escaped
to New Zealand and eventually to the London School of Economics, where
he was knighted for his political writings.
Hilary Putnam (1926-2016)
This American philosopher of science, mathematics, mind and
language earned his doctorate under Reichenbach at UCLA and
subsequently taught at Princeton, MIT, and Harvard. He was originally
a metaphysical realist, but then argued forcefully against it. He has
continued the pragmatist tradition and been politically active,
especially in the 1960s and 70s.
W.V.O. Quine (1908-2000)
Born in the U.S., Quine took his doctorate and spent his entire
career at Harvard. In 1932-33 he visited the Vienna Circle and
then Carnap and Warsaw. For the next six years, he said, he was a
disciple of Carnap's and even after they began to disagree,
Carnap set the agenda. Eventually they clashed over analyticity,
modality, and intensional contexts generally. Many similarities of
view with Neurath are apparent, especially on the issues of holism,
underdetermination, and naturalism in epistemology.
Hans Reichenbach (1891-1953)
Reichenbach was born in Hamburg and, after immersing himself in
mathematics, physics, and philosophy, took his doctorate in Erlangen,
Germany. He was a founder and the leader for the Berlin Society for
Empirical (later Scientific) Philosophy. In 1933 he was forced to
leave Berlin. He went to Turkey and then in 1938 to UCLA. Among his
many students were Hempel, Putnam, and W. Salmon, and so almost all
philosophy of science in the U.S. can trace its academic lineage to
Reichenbach. Though interested in social and educational reform, he
worked primarily in philosophy of physics. He developed and defended a
frequency theory of probability, and emphasized both scientific
realism and the importance of causality and causal laws.
Wesley Salmon (1925-2001)
Salmon was born in Detroit and, after an initial interest in
theology, earned his PhD under Reichenbach at UCLA. He taught at a
number of universities including Brown, Indiana, Arizona, and
Pittsburgh. His interests centered on causality and explanation, and
his statistical relevance model of explanation can be thought of as
addressing and in large measure resolving the problem of the single
case in frequency theories of probability.
Moritz Schlick (1882-1936)
Schlick was born in Berlin and eventually took his doctorate there
in mathematical physics under Max Planck. He taught at a number of
German universities before he was, at the instigation of Hans Hahn,
called to the Chair in the Philosophy of the Inductive Sciences at
Vienna, a chair that was previously held by Boltzmann and Mach.
Schlick was one of the first philosophers to write about
Einstein's relativity theory. He was close to Wittgenstein and
one of the conduits for the latter's strict verificationism. His
work ranges from space and time to general epistemology and ethics. In
1936 he was assassinated on the steps of the university by a deranged
student.
Wilfrid Sellars (1912-1989)
Wilfrid Sellars was the son of well-known philosopher, Roy Wood
Sellars. Wilfrid studied at Buffalo, Oxford, and Harvard before
teaching at Iowa, Minnesota, Yale, and Pittsburgh. He was a close
associate and collaborator with Feigl at Minnesota. (In 1947 he
declared himself a logical empiricist and much later said that he and
Feigl were for years discrete parts of a single entity.) He defended
scientific realism, pragmatism, and naturalism, and his philosophy of
language drew heavily on Carnap's *Logical Syntax*
(1934/1937).
Alfred Tarski (1901-1983)
Born and educated in Warsaw, Tarski earned his doctorate under
Lesniewski. He happened to be visiting the U.S. when Poland was
invaded and so avoided the fate of so many of his colleagues. He
taught at the University of California at Berkeley for more than 30
years. While it is unclear whether he should be counted as a logical
empiricist, he visited the Vienna Circle and hosted its members in
Warsaw, and his "The Concept of Truth in Formalized
Languages" (1936/1956) was very influential on Carnap and on the
development of semantics among the logical empiricists generally.
Friedrich Waismann (1896-1959)
Waismann was born in Vienna and earned his doctorate there under
the direction of Schlick in 1936. From 1926 to 1933 he held
discussions with Wittgenstein, generally in the company of Schlick,
but also sometimes Carnap or Feigl. Waismann kept detailed minutes of
these conversations. At one point he and Wittgenstein contemplated a
joint book, but Wittgenstein later changed his mind. Besides the
printed text of the *Tractatus* these conversations were the
main conduit of Wittgenstein's ideas into the Vienna Circle. In
1937 Waismann was able to emigrate to England. After a couple of years
at Cambridge, where he was shunned by Wittgenstein, he moved to
Oxford, where he taught until his death.
Ludwig Wittgenstein (1889-1951)
Born into an immensely wealthy Viennese family, Wittgenstein
studied at Cambridge from 1911, where he formed friendships with
Russell, Keynes, and Moore. His *Tractatus
Logico-Philosophicus* (1921/1922), which among other things tries
to show that logic has no content, was enormously influential on many
logical empiricists. Wittgenstein continued to spend much of his time
in Austria working variously as an elementary school teacher, a
gardener, and as an architect of a house for his sister in Vienna.
While there he held influential discussions with Schlick, Waismann,
and others. From 1930 he held teaching posts at Cambridge and
increasingly distanced himself from the logical empiricists. His later
work focused on ordinary language and inspired many other philosophers
as well.

## 4. Issues



It is not possible in an essay of this scope to trace all the issues
that the logical empiricists addressed or even to treat any one of
them with completeness. What is possible is to highlight some salient
issues, clear away some misconceptions about them, and sketch a bit
how those issues were developed over time. The first is a related set
of concerns: empiricism, verificationism, and anti-metaphysics. The
second is the logical empiricists' treatment of logic and
mathematics as analytic. Third is the related issues of the unity of
science and reduction. And finally, comes the issue of probability.
Given what has already been said, the reader should be aware that none
of the doctrines discussed below was shared by all members of the
logical empiricist movement.


### 4.1 Empiricism, Verificationism, and Anti-metaphysics



Since antiquity the idea that natural science rests importantly on
experience has been non-controversial. The only real questions about
the sources of scientific knowledge are: Are there parts of science
that do not rest on experience or rest also on something other than
experience? If so what account can we give of those parts? And to the
extent that science does rest on experience how can we know that it
does? There is another question about science related to these, though
not strictly about the sources of science, and that is: Why, in making
claims about the world, should we be scientific as opposed to, say,
mystical? The difficulty is that any scientific answer to this last
question would reasonably be thought to beg the very question it
purports to address.



Long before the twentieth century the prevailing opinion was that
Euclidean geometry, standard mathematics, and logic did not rest on
experience in any obvious way. They were largely presupposed in our
empirical work, and it was difficult to see what if anything might
disconfirm them. Geometry was a special case and might be handled in
different ways that we shall not discuss here. That leaves logic and
mathematics.



If Frege and Russell were right, then mathematics could be thought of
as expressing no more than logical truths and handled in whatever way
logic was to be treated. For Frege both mathematics and logic were
analytic, but that, even if true, does not provide the needed answers.
Wittgenstein's no-content theory of logic suggested that all of
the real claims, the ones that had genuine content, could be
appropriately supported by experience, and the logical and hence
mathematical claims had no content to support. This seemed to open the
way for a thoroughgoing empiricism in which the logical and
mathematical fit in with the ordinary claims of physics and biology in
a harmonious way. The next subsection about analyticity discusses the
question of whether the needed distinctions can be drawn.



In developing his theory of types Russell said in effect that some
expressions that seem to be sentences in fact say nothing at all. This
is because, despite appearances, they are not grammatically well
formed. Wittgenstein found this suggestive. In the *Tractatus*
he suggested that much else was nonsense as well including traditional
metaphysics and supposed claims about the "higher". When
in late 1929 Wittgenstein proposed (Waismann 1967/1979), in
conversations with Schlick and Waismann, a strict verificationism as a
basis for identifying the legitimate parts of discourse, this seemed
to the logical empiricists to be a very attractive tool for setting
aside the unscientific parts of philosophy.



This does not mean, however, that all logical empiricists or even all
members of the Vienna Circle accepted the strict verificationist view
that in order to be meaningful a claim must be implied by a finite
number of observation sentences. Even though those observation
sentences need not be true, this view had the drawback that so-called
laws of nature would not be meaningful on this criterion. Schlick was
prepared to bite the bullet and hold that laws were not statements at
all but principles of inference. Others were not prepared to go so far
and sought more liberal formulations. This more liberal or
"left" wing of the Vienna Circle included Carnap, Philipp
Frank, Hahn, and Neurath. Carnap does not seem to have been a strict
verificationist even in the *Aufbau* (1928/1967).



Over the years a great many different formulations of verificationist
principles ensued. Most of them came to a bad end rather quickly, and
this is sometimes taken as a convincing argument that any form of
verificationism is utterly misguided. Perhaps, but we should be
cautious. There are undoubtedly many different features joined in any
one of the proposals, and even a sequence of failures may not show
where to place the blame. The central idea behind verificationism is
linking some sort of meaningfulness with (in principle) confirmation,
at least for synthetic sentences. The actual formulations embodied not
only such a link but various particular accounts of confirmation as
well. Now confirmation is a complex matter, and it is unlikely that we
shall have the final satisfactory account any time soon. This should
not persuade us, however, that there are no satisfactory accounts of
confirmation any more than our current lack of the final physics
should convince us that there are no physical facts of the matter. So
even a string of failures in formulating verificationist principles
may mean no more than that the embedded accounts of confirmation are
too simple but the link between meaningfulness and confirmation is
nevertheless sound.



Even if we set this caution aside, there may be parts of a
persistently employed strategy that lead to persistent failure. These
parts and failures might be avoidable. To see how this may be so we
will compare what is perhaps the most famous formulation of the
verificationist principle, in Ayer 1936, with a later one, in Carnap
1956. A.J. Ayer had visited the Vienna Circle from late 1932 on into
1933, returning home for the summer term. While in Vienna he attended
meetings of the Circle and overlapped for five weeks with Quine.
Neither Carnap nor Neurath were there at the time, so the left wing of
the Circle was not fully represented. When Ayer returned to England he
published *Language, Truth, and Logic* in 1936. Even
immediately it was widely discussed, and after the war sales were
spectacular. For many in England this book was the epitome of logical
positivism and remains so.



Ayer was careful to restrict his criterion of meaningfulness to
synthetic sentences and to demand only in principle confirmation. And
the formulation seems very natural: Confirmation is a feature that
applies to sentences (or groups of them) and not to sub-sentential
parts, and for an empiricist the content that a synthetic sentence has
would be empirical content. So it would seem that to have empirical
content a sentence, *A*, should either directly imply some
observational sentence or add to the observational content of some
other sentence, *B*. That is, the conjunction of *A* and
*B* should imply some observational sentence not implied by
*B* alone. This formulation may be natural, but it is also
fatally flawed. It would declare any sentence whatsoever as
meaningful: For any sentence *A* and any observation sentence
*O*, *A* would be meaningful because it could be
conjoined to *A* [?] *O*. The latter would not in
general imply *O*, but the conjunction would.



Other more elaborate formulations followed along the same lines, and
other more elaborate counterexamples appeared just as fast. Hempel
reviewed the situation twice within about a year (Hempel 1950 and
1951). First he concluded that it was a lively and promising line of
research and later concluded that it was not promising at all. In
retrospect it may be that the problems arise because we were led by
the fact that confirmation is a feature that applies to whole
sentences into thinking that the level at which to apply the criterion
was the level of whole sentences. Now a sentence with meaningless
parts might well pass some test especially if the test involves its
being combined with other sentences that can have meaningless parts.
So one way to avoid this difficulty is to try to find a formulation
that applies the test at the level of basic expressions, those that
can be thought of as "not having parts" so to speak.



This is the strategy that Carnap employed in "The Methodological
Character of Theoretical Concepts" (1956). Observational terms
are assumed to have empirical content. Logical terms are assumed to
have none. And all defined terms are assumed to be replaced by their
definitions. If for some basic, non-logical term there is a sentence
that contains that term as its only non-logical element and if that
sentence implies some observation sentence, then that sentence has
empirical content and so does its only non-logical term. If we have
established that each term from some set, *K*, is empirically
significant we might test still further terms by seeing whether those
further terms can add to what is sayable with terms from *K*.
Carnap's actual definition is quite complicated, but it does
seem to avoid the difficulties of its predecessors. It also allows an
account of why those predecessors ran into trouble, viz., that they
applied at the level of whole sentences (naturally enough) rather than
to elementary terms.



Not long after Carnap's definition was published David Kaplan
devised what seemed to be counterexamples. They became fairly well
known, but they were not published until 1975. Shortly thereafter it
was shown (Creath 1976) that either Carnap's definition is not
open to the counterexamples as presented or it can be patched in a
very natural way so that it avoids them. This does not show that there
are no counterexamples or that there are no other features of the
definition to which one might object. But it does show that the
situation is not as dire as Hempel supposed in 1951.



We need to address another issue in considering verificationism, the
persistent criticism that it is self-undercutting. The argument for
this claim goes like this: The principle claims that every meaningful
sentence is either analytic or verifiable. Well, the principle itself
is surely not analytic; we understand the meanings of the words in it
perfectly well because we understand our own language. And we still do
not think it true, so it cannot be true in virtue of meaning. And it
is not verifiable either (whatever we choose 'verifiable'
to mean).



This sounds more compelling than it is. Ayer understood the principle
to be a definition, defining a technical term, 'meaning'.
If so, then the sentence expressing the principle would indeed be
analytic. So the self-undercutting charge strictly fails. But so
construed and with nothing else said about it, the principle would not
have the same punch as before. Why should a metaphysician care whether
his or her utterances lack some technical feature?



Carnap explicitly takes up the "self-undercutting" charge
against verifiability in *Philosophy and Logical Syntax*
(1935), and he is not interested in introducing a new technical term,
'meaning', or in denying this new technical property to
unverifiable sentences. Carnap is careful to distinguish the language
for which the verifiability principle is given from the meta-language
in which we talk about that language. This meta-language would be the
language in which the principle would be expressed. This may seem to
offer another strategy against the "self-undercutting"
charge because the principle applies to a different language than that
in which it is expressed. This is not Carnap's strategy. Carnap
fully understands that if the general verificationist strategy is
followed, there will also be a verificationist principle expressed in
the meta-meta-language governing the meta-language.



Carnap's real defense of the principle was achieved by changing
the nature of the discussion. By 1934 Carnap had introduced an
important new element into his philosophy called the Principle of
Tolerance. Tolerance is a radical idea. There is no uniquely correct
logic (1934/1937 xiv-xv). Empiricism is a convention (Carnap,
1936/1937 33). Perhaps more precisely each of the various versions of
empiricism (including some sort of verificationism) is best understood
as a proposal for structuring the language of science. Before
tolerance, both empiricism and verificationism are announced as if
they are simply correct. Correspondingly, what Carnap called
metaphysics was then treated as though it were, as a matter of brute
fact, unintelligible. But what is announced thus dogmatically can be
rejected equally dogmatically. Once tolerance is in place, alternative
philosophic positions, including metaphysical ones, are construed as
alternative proposals for structuring the language of science. No
theoretical argument or evidence can show that one of the proposed
languages is the uniquely correct one. Nor can theoretical arguments
or evidence show that it is false. Neither proposals nor languages are
the sort of thing to be true or false. Instead, proposals call for
practical decisions and practical arguments rather than for
theoretical reasons or evidence. Carnap believes that there are indeed
very good practical reasons for adopting the proposal of
verificationism, for choosing a language of science in which all
substantive (synthetic) claims can, at least in principle, be brought
before the court of public experience. The reason is that if we do not
require this, the result is "wearisome controversies" that
there is no hope of resolving. That, he thinks, is the sad history of
attempts to get beyond science, and it is just too painful.



If the proposals constituting some version of verificationism are
adopted, then in the language thus constituted it will be analytically
true that there are no synthetic sentences that are both unverifiable
and meaningful. The notion of meaning here is not some new technical
invention. Rather, 'meaning' is used in something like the
ordinary sense. No grammatically well-formed sentence of this new
language violates the verifiability principle. And the principle
itself is completely safe. Thought of in this way the verifiability
principle does not describe natural language; it is not intended to.
It is intended to reform language to make it a more useful tool for
the purposes of science. Carnap is under no illusion that natural
languages are free from what seem to be metaphysical commitments. Nor
is he under the illusion that defenders of the sort of metaphysics he
targets will readily step up to the challenge of presenting precise
rules of grammar and inference. There is no weakening of his defense
of empiricism, but it is put on a somewhat different footing.



It is important to emphasize that Carnap's Principle of Tolerance
introduces a new conception of philosophy with far-ranging
implications beyond those just discussed concerning verification. The
idea that philosophy is concerned with language and its analysis was
not new. What is novel is the idea that what had been seen as
philosophical claims were better understood as proposals for
structuring the language of science. Since these languages and
the concepts they contained were to be thought of as tools, none of
which was uniquely correct, the choice among the alternatives was a
practical decision about usefulness for certain purposes rather than a
theoretical question. Philosophy still has important work to do: It
can analyze existing concepts. And since many existing concepts are
vague, it can also make them more precise in a variety of ways through
explication. Philosophy can also investigate wholly new concepts. In
all this, philosophy explores the consequences of structuring the
language of science in this way or that. It becomes, thus, a kind of
conceptual engineering. Conceptual analysis, explication,
construction, and engineering continue to be fruitful ideas in
philosophy, though it is not always understood how much of this was
initiated or shaped by Carnap and other logical empiricists.


### 4.2 Analyticity



Logic, mathematics, and mathematical geometry had traditionally seemed
to be confirmationally "different". Indeed it is hard to
indicate any conditions under which any parts of them would be
disconfirmed. Leibniz had called them truths of reason. Hume said that
they represented relations of ideas. Kant had held that the truths in
these areas were a priori. Mathematics and geometry were not analytic
for Kant, but logic was. Kant had two criteria of analyticity,
apparently thinking them equivalent. First, in subject-predicate
sentences, an analytic sentence is one in which the concept of the
predicate is contained in that of the subject. Second, an analytic
sentence is one whose denial is self-contradictory. This seems to
include not only the sentences whose surface logical form would be of
the required sort but also those that can be got from such logical
truths by making substitutions that were conceptually equivalent. The
more modern rough analog of this is to say that the analytic sentences
are those that are true in virtue of logic and definition.



Frege certainly developed logic beyond that which was available to
Kant, but he did not think of himself as changing the analytic status
of it. Logic is after all the only avenue we have for giving meaning
to the notion of (logical) contradiction. Of course Frege also
attempted to reduce mathematics to logic (including both first and
second order logic), and insofar as that reduction was successful it
would have implied that mathematics was analytic as well. Frege said
little of geometry, but for him it was synthetic a priori.



Carnap had not only studied with Frege, but like many of the logical
empiricists he had started out as a neo-Kantian as well. So especially
in view of Russell's relatively more successful attempt at
reducing mathematics to logic, it was perhaps natural that Carnap
would consider both mathematics and logic as analytic. Geometry could
be handled in several different ways that we will not discuss here.
But from fairly early on there was widespread agreement among the
logical empiricists that there was no synthetic a priori, and that
logic and mathematics and perhaps much else that seemed impervious to
empirical disconfirmation should be thought of as analytic. The point
of drawing the analytic-synthetic distinction, then, is not to divide
the body of scientific truths or to divide philosophy from science,
but to show how to integrate them into a natural scientific whole.
Along the way the distinction clarifies which inferences are to be
taken as legitimate and which are not. If, as Carnap and Neurath were,
you are impressed by Duhemian arguments to the effect that generally
claims must be combined in order to test them, the analytic-synthetic
distinction allows you to clarify which combinations of claims are
testable.



If analytic, a sentence is true in virtue of the conventions of
language. In saying that, however, we must pause to confront two
widespread confusions. First, Quine alleges (1963, 385f) that the
notion of analyticity was developed and purports to explain for both
Kant and Carnap how certainty is possible. In fact certainty has
little or nothing to do with analyticity for the leading logical
empiricists. In saying that such claims are based on convention they
were explicitly calling attention to the revisability of conventions
and the sentences that owed their meanings to those conventions.
Second, nowadays any talk of convention is likely to prompt the
response: "But that cannot be! No proposition can be made true
by our conventions or decisions." Unless it is a proposition
about conventions, this second sentence of the response is true. But
it is also completely irrelevant. Analyticity applies to
*sentences* rather than propositions. Our conventions and
decisions can and do affect what expressions mean and thus what
sentences mean. Once the meaning is specified, it may well be that any
sentence that has this meaning would be true even if, for example, the
point masses of the universe were arranged quite otherwise than they
in fact are. These are the analytic sentences. No claim is being made
that meaning causes anything or that convention *makes*
anything true. The "making" image here is out of place. It
is just that in these cases the truth value of the sentence may well
be functionally dependent on meaning alone. If it is, then in this
special sense, truth value depends on meaning, and that depends on
convention. Other sentences whose meanings are specified might well be
true or false depending on how things in the external world, so to
speak, are arranged. In this other category of sentence the truth
value is not functionally dependent on meaning alone. They are the
synthetic sentences. Now this puts matters extremely informally. But
at least the nature of the confusions over certainty and convention
should be clear.



In the *Logical Syntax of Language* (1934/1937) Carnap defined
'analytic' in a new way in order to circumvent
Godel's incompleteness results. The method used was to
distinguish between a derivation relation (the relation that holds
between some premises and what can be got from them in a finite number
of steps) and a consequence relation. The latter is an essentially
semantic relation that holds between some premises and some other
claim such that on all valuations under which the premises are all
true, so is that other claim. This definition bears a stronger
resemblance to Tarski's account in (Tarski 1936b/1956). In any
case, Carnap is able to show that for any sentence of pure mathematics
either it or its negation is a consequence of the null set of
premises. This leaves Godel's results completely intact as
they concerned what is provable, that is, derivable from the null set
of premises or from any one consistent axiomatization of mathematical
truths.



As noted above, another innovation of *Logical Syntax* is the
Principle of Tolerance. While it reflects a long-standing attitude on
Carnap's part, the principle itself is new. Later Carnap was to
say that the Principle of Tolerance was "perhaps better called
the principle of conventionality" (Carnap 1942, 247), that is,
the conventionality of linguistic forms. Tolerance stabilizes the
verification principle as well as Carnap's empiricism, and it
reinforces the idea that the analytic-synthetic distinction is always
relative to a particular language (Creath 2009).



In the late 1950s Carnap began exploring (1963a and 1966) how a notion
of analyticity might be developed for novel theoretical terms where
the theories in which those terms are embedded are presented by means
of a system of postulates. It is not clear that the account he
developed was intended to supersede his earlier account. In any case
Carnap's suggestion is as follows (where for convenience terms
are used autonomously): Let *T* be the totality of theoretical
postulates, and *C* be the totality of mixed sentences (the
sentences of the theory containing both antecedent and novel terms).
Also let *R*(*TC*) be the Ramsey sentence for
*TC*, that is, the result of replacing each of the
non-observational terms in *TC* with predicate variables and
closing that open sentence with corresponding existential quantifiers.
*R*(*TC*) [?] *TC* can, Carnap says, be thought
of as the analytic sentence for the theory, that is, a sentence that
gives to the theoretical terms of *TC* their meaning. Over the
last decade, this idea of Carnap's has provoked considerable
discussion that has not yet been resolved. Whatever worries there may
be concerning this part of Carnap's view, they are distinct from
the more famous concerns raised by Quine.



Quine began having doubts about analyticity about 1940, though he
seems not to have been firmly committed against it until later. In any
case his doubts were not published until 1951 in his famous paper
"Two Dogmas of Empiricism". Quine's readers have
understood his arguments in many different ways. The most general form
of his complaint is that 'analytic' so far lacks the
appropriate tie to observational criteria that Carnap's own
account of theoretical terms in empirical science would demand. More
specifically, where there has been an attempt at such a general
criterion it has resulted in either a "drastic failure as tended
to admit all or no sentences as analytic, or there has been a
circularity" (Quine 1963, 404) of a kind that defines
'analytic' in terms that themselves lack the appropriate
empirical criteria and so can be accounted for only by appeal to
analyticity itself.



This complaint falls far short, as Quine well understood, of a proof
that Carnap's appeal to analyticity was doomed. First, it relies
on the demand that theoretical terms must satisfy some empirical
significance criterion. Many people at the time, including some who
followed Quine in rejecting analyticity, also rejected any general
empirical significance demand for theoretical terms. Second, one could
accept the demand for theoretical terms in physics or chemistry and
deny, as Carnap did, that the demand applied to his own work. This is
because Carnap saw himself as working in an area within
metamathematics rather than in empirical linguistics. Third, Quine did
not pretend to have considered all of the possibilities for the
explication of analyticity. And so it may be possible to meet
Quine's demands to the extent that they are legitimate. Fourth
and finally, Quine seems in *Roots of Reference* (1974) to have
provided an explication for 'analytic' that meets his
demand for empirical/behavioral criteria without inducing either the
drastic failure or the circularity envisioned above.



There is another somewhat independent thrust to Quine's campaign
against analyticity. In the last section of "Two Dogmas"
(1951) Quine gives an extremely attractive sketch for an alternative
epistemology that apparently makes no appeal to analyticity. Insofar
as that sketch can be filled out successfully it would constitute a
dispensability argument against analyticity. Whether it can be thus
filled out, however, remains to be seen.



Quine's other provocative theses, including especially his
claims about the indeterminacy of translation, while relevant to his
assessment of analyticity, would carry us too far afield to consider
their ramifications here. As with most topics in philosophy there is
no uniform agreement in the literature as to whether the notion of
analyticity is or can be made sufficiently clear for use in scientific
philosophy. Nor is there such agreement that Quine's
epistemological sketch can be satisfactorily filled out. Both
approaches have their defenders and their detractors. But between them
they seem to be the most promising avenues for integrating the
logic-mathematical part of science with the more straightforwardly
empirical parts. Since Carnap is and Quine can be argued to be within
the logical empiricist tradition, this progress toward such
unification can be counted as part of the legacy of the movement.


### 4.3 Unity of Science and Reduction



The commitment of some of the logical empiricists to the unity of
science has been in recent years often discussed but less often
understood. One hears in conversation that it was a sort of rearguard
action designed to preserve as much as possible of a phenomenalist
version of ontological reduction. One reads in print that it can be
refuted by the obvious fact that the various sciences have quite
distinct theoretical vocabularies (Suppes 1978). Both reactions are
misplaced.



It was the left wing of the Vienna Circle, and above all Otto Neurath,
that championed the unity of science. They also promoted physicalism,
anti-foundationalism, and a generally naturalistic viewpoint. A main
focus of their activities from the late 30s was *The Encyclopedia
of Unified Science* edited by Neurath in Europe and Carnap and
Charles Morris in Chicago. A great many philosophers of many different
persuasions participated in that project. The project may have been
unified science, but they did not have a completely unified view of
what that project was. Here we will discuss the Neurath and Carnap
versions of it to see what their central concerns were.



Neurath seems to have had two primary motivations to advance under the
banner of the unity of science. First, he was concerned that there be
no a priori methodological cleavage between the natural and the social
sciences. On the social scientific side he was concerned that these
sciences not condone some private, mysterious mode of insight
(empathy) whose results could not be checked against more ordinary
public observation. Such a methodology would be a harbor for
metaphysics. On the natural scientific side, he was concerned to point
out that, for Duhemian and other reasons, the situation is much
messier than is sometimes supposed, and so invidious comparisons by
natural scientists at the expense of social science were
unwarranted.



Second, because Neurath was socially and politically engaged he was
concerned that the various sciences be connected in such a way that
they could be used *together* to solve complex human and social
problems. For this, considerable overlap of vocabulary was needed, and
this he called a "universal jargon".



In recent years it is sometimes claimed that Neurath meant by the
unity of science what some contemporary philosophers have defended as
the disunity of science. One cannot rule this claim out a priori. But
the often substantial differences among the current defenses of
disunity make evaluating this claim difficult. It is fair to say,
however, that Neurath was suspicious of grand hypotheses, familiar
since the 19th century to derive all of chemistry, biology,
psychology, and the social sciences (in that order) from a few basic
principles of physics. It is unclear whether this stems from a general
opposition to system building, since he was eager to develop
inferential connections among the various sciences. Perhaps this is
better expressed as an opposition to *speculative* system
building and to the idea that there is only one way of systematizing
our science than to systematicity as such.



Carnap's position on unity is different from Neurath's,
but they overlap. Carnap distinguished the unity of the language of
science from the unity of the laws of science. He wanted to defend the
former and to say what would be required for the latter. As far as the
unity of the language of science, Carnap did in the *Aufbau*
try to initiate a program for defining all of scientific concepts on
the basis of a very small number of basic concepts, perhaps only one
basic concept. That does afford a certain conceptual economy, but it
is now generally held by Carnap scholars (see especially Friedman 1987
and Richardson 1998) that ontological reduction and reduction to a
phenomenalist basis was far from his motive. Carnap explicitly
acknowledged that another system of definitions, one with a
physicalist basis, might also be possible. Instead of ontological
economy and a phenomenal basis, Carnap's project seems to have
been the more Kantian one of indicating how semantic intersubjectivity
is possible: How can it be that, even though I have only my own
experiences and you have only yours, we can nevertheless share a
common body of concepts? The answer is given in terms of shared
inferential structure and identifying any given concept with a unique
place within that shared overall structure. This is a highly holistic
conception of concepts and it depends on thinking of the body of
scientific commitments as a whole, as a unity.



The *Aufbau* was largely drafted before Carnap joined the
Vienna Circle. Once there and under some influence from Neurath,
Carnap campaigned more insistently for physicalism and for the unity
of science. They seemed often to be two sides of the same coin. From
1933 onward there was a succession of monograph series with
'Unified Science' in the title. Until his death in 1945,
Neurath was in each case the main editor and Carnap either the
associate editor or one of the associate editors. *The
International Encyclopedia of Unified Science*, begun in 1938 is
undoubtedly the most famous of these. Carnap's own essay on this
topic "Logical Foundations of the Unity of Science" (1938)
was printed as part of the very first number in the encyclopedia.



The dates here are relevant because by the time of this essay Carnap
had already decided (Carnap 1936-37) that theoretical terms
could not in general be given explicit definitions in the observation
language even though the observation reports were already in a
physicalist vocabulary. The partially defined theoretical terms could
not be eliminated. This seems to have caused Carnap no consternation
at all, and it never seems to have occurred to him that there was any
conflict whatever between this result and the unity of science. This
is because by this point the elimination of concepts was not the point
of the exercise; their inferential and evidential integration was.



In the 1936-37 article, "Testability and Meaning"
Carnap called the partial definitions themselves "reduction
sentences" and the system of definitions of theoretical terms,
both partial and complete, as a reduction of the theoretical terms to
the observational basis. Plainly he means by the word
'reduction' something other than what we currently mean,
not that there is anything univocal about current uses of the word. By
'reduction' of vocabulary *A* to vocabulary
*B* Carnap means the specification of the inferential relations
that would allow us to say what sentences or combinations of sentences
in *A* would count as evidence for sentences in *B*.



This is also the key to what Carnap means by the unity of the language
of science. The language of science is unified, no matter how
different and exotic its various technical vocabularies may be, when
each of its terms is reduced to (can be tested in) a common public
observation vocabulary. The call for the unity of the language of
science, then, amounts to no more than the demand that the various
claims of the separate sciences should be publicly testable in a
common observation language. Controversies will of course arise as to
what the observational vocabulary should be and what are the
acceptable forms of linkage. Carnap's demand for unity in the
language of science abstracts from those controversies to concentrate
on the goal of public testability. That does not seem to be an
unreasonable demand.



The unity of the language of science so far discussed is quite a
different issue from the unity of the laws of science. And
Carnap's attitudes toward them are quite different. The latter
issue concerns the extent to which the laws of one special science can
be inferred from those of another. Carnap tries to articulate what
would be involved in such a unification, but he nowhere says that such
a unity is either possible or mandatory. Finding any sort of
inferential connections among sets of laws would be welcome of course.
But the question of how much unity there is, if any, among the various
sciences is an empirical question that philosophers are ill equipped
to answer. Philosophers should not make pronouncements, especially in
advance of having putative laws in hand, either that scientific laws
are unified or that they are not. A certain modest deference to the
empirical facts that philosophers generally do not have, again, does
not seem unreasonable.



Taking unity as a working hypothesis, as some philosophers have done,
amounts to *looking for* inferential and nomological
connections among various sets of laws, but not to the assertion that
such connection will be found. Even if we accept the idea that such
connections would be welcome if found, the question of whether one
should spend significant effort in looking for them is not thereby
answered. That would be a difficult and delicate practical question of
how to apportion one's research effort that for the purposes of
this essay we must set aside.


### 4.4 Probability



There are two broad approaches to probability represented in logical
empiricism. One of these, the so-called frequentist approach, has an
extensive 19th century history and was further developed
from about 1920 onward by Richard von Mises and Hans Reichenbach. The
other is the epistemic approach to probability. This goes back at
least to Laplace at the end of the 18th century. In the
20th century Rudolf Carnap, who explored what he called
logical probability, and Frank Ramsey and Richard Jeffrey whose
accounts can be distinguished from Carnap's and are often called
subjective probability, all defended the epistemic approach. While
Ramsey visited the Vienna Circle he was not much influenced by its
members on these matters. By contrast, Jeffrey studied and later
collaborated with Carnap but also made significant contributions of
his own.



It is natural to begin thinking about probabilities with a simple
mathematical account that takes as its point of departure various
games of chance involving cards, dice, or coins. Bettors have long
noted that some outcomes are much more likely than others. In this
context it is convenient to take the probability of a kind of outcome
to be the ratio of such outcomes to all possible outcomes. Usually for
reasons of symmetry in the physical set up, the possible outcomes are
assumed to be equally likely. Where that assumption happens to be true
or nearly so the empirical results of, say, a great many throws of a
pair of dice tends to be close to what the simple mathematical account
would suggest. Conversely, where the outcomes deviate from the
expected ratios, bettors begin to suspect that the dice, coins, and
cards (or the manipulations of them) are not all that they seem. The
suspicion is that the outcomes are not equally likely and that the
simple mathematical account does not apply.



These facts suggest both two limitations of the simple account and the
beginnings of a way around them. The first limitation is that the
account applies only where the outcomes can be partitioned into
alternatives that are equally likely. This is not the case when dice
are loaded or in such real world cases as radioactive decay or weather
forecasting. A second limitation is that the account, in describing
the possible outcomes as equally likely, implicitly appeals to the
very probability notion for which clarification was sought. The
realization that we can sometimes discover the falsehood of the
assumption of equal likelihood and make a much more reasonable
estimate of probability by making a large number of trials is very
suggestive. And from his dissertation onward Reichenbach worked out a
variety of imagined physical models that could guide ones thinking
about probability in useful ways. The result is what is often called
the frequency theory of probability (or sometimes the statistical
frequency theory or the limit frequency theory).



Even a perfectly fair coin in an odd number of flips will never result
in exactly the same number of heads and of tails. When the coin is
fair and the number of flips is even, an outcome perfectly balanced
between heads and tails is not guaranteed either. So, even on the
assumption that the probability of the coin's coming up heads
does not change over the course of the trials, we need to be cautious.
A larger number of flips might make us more confident that the ratio
we have seen is close to the "actual" value, but there is
no finite number of flips after which we can say that the observed
ratio is exactly right. We will never make an infinite number of flips
either, and in actual cases a large finite number of flips might so
erode the coin as to bias the coin and discredit the result.
Notwithstanding these limitations on an actual series of trials one
can imagine an infinite series of trials and define a notion of
probability with respect to it. This raises its own difficulty, namely
that ratios are not defined for infinite collections. They would be
defined, however, for any finite initial segment of such an infinite
series, thus giving a sequence of ratios. If this sequence of ratios
settles down on a limit, the probability of the coin showing a head
given that it has been flipped can be defined as the limit of the
ratio of heads to total flips as the number of flips goes to
infinity.



While probability thus defined has a somewhat counterfactual
character, that is not an obvious defect. Moreover, this notion of
probability applies perfectly well to biased coins and loaded dice, as
well as to radioactive decay. On the surface at least it also seem to
avoid using the notion of probability in its own definition, and in
these respects it seems to be an important improvement over the simple
mathematical model with which we began. The definition locates the
probability objectively "out in nature" so to speak, and
this comports well with Reichenbach's scientific realism.



A problem that remained troublesome concerns the fact that one often
wants to assign probabilities to particular events, events that in the
nature of things cannot be repeated in all their particularity. Thus
it is unclear how a frequency theory of probability is to be applied
to such individual cases. This is often called the problem of the
single case. It is a little difficult to assess how serious this is,
because in actual practice we often have no difficulty in making
probability assignments to single cases. Suppose we are interested in
the probability of rain tomorrow. Tomorrow will never be repeated, and
we want to estimate the probability now. What we do is to look back
through the records to find days relevantly like today and determine
in what fraction of those cases those days were followed by rainy days
and use that as our estimate. Even if we are comfortable with this
practice, however, it is another matter to say why this should give us
a reasonable estimate of the value of the limit involved in a
logically impossible infinite sequence. This problem of the single
case was much discussed, and Wesley Salmon made progress in dealing
with it. Indeed, Salmon's account of statistical explanation can
be viewed as a substantial mitigation of the problem of the single
case (W. Salmon 1970).



There are residual difficulties in making estimates of the
probabilities on the basis of finite evidence. The problem is that
even when we are assured that the sequence of ratios has a limit, we
have no a priori grounds for saying how close the current ratio is to
that limit. We can boldly estimate the limit by means of the so-called
"straight rule". This just takes the most recent ratio as
the desired estimate. This is a good practical solution where the
number of trials is already high, but this does not really say why the
estimate should be good, how good it is supposed to be, or how many
trials would be high enough. In addition, the straight rule can yield
counterintuitive results where the number of trials is small.



Though there are these issues outstanding, frequency theories define a
concept of probability indispensable for quantum theories and for a
wide variety of other applications in the natural and social sciences.
It was not the only concept of probability to be developed by the
logical empiricist tradition. The primary other such concept was the
epistemic conception of probability. We will begin with Carnap and
then move to those who developed a subjectivist account.



Carnap is addressing a different issue than was addressed by von Mises
and Reichenbach. Instead of focusing on physical phenomena and ratios
within them, Carnap focuses on arguments and takes as his point of
departure the widespread conviction that some arguments are stronger,
in varying degrees, than others, even for the same conclusion.
Similarly some bodies of evidence can give us more reason to believe a
given conclusion than would another body of evidence. Carnap sets as
his task the development of a quantitative concept of probability that
will clarify and explicate these widespread convictions. Such a
quantitative concept would be an extraordinarily useful tool, and it
would be a useful successor to our ordinary, somewhat scattered
notions of confirmation and induction.



Carnap approaches the problem by first considering extremely limited
artificial languages and trying to find a confirmation function that
will work for that. If he succeeds he would then try to develop an
account that would work for a broader and richer range of languages.
In this his approach is like that of a physicist developing a physical
theory for the highly artificial situation of a billiard table or air
track and then broadening the theory to deal with a wider range of
cases. In Carnap's case, however, it is somewhat unclear what
success would be in an artificial language very much unlike our own.
In any case, Carnap is not trying to describe our linguistic habits
but to clarify or even to replace them with something more useful.



As early as *Logical Syntax* (Carnap 1934/1937,
244/316-17) Carnap had suggested that Wittgenstein's
remarks in the *Tractatus* about ranges (*Tractatus*,
4.463) might be a starting point for thinking about probability. By
1945 Carnap also distinguished the two approaches described here,
insisting that they were not competitors but were attempting to
explicate two different concepts of probability. One need not choose
one as the only concept; both concepts were useful. Reichenbach, by
contrast, never conceded that both concepts were needed and insisted
that his frequency notion could serve all epistemic purposes for which
any notion of probability is needed.



Carnap's general strategy was first to identify a broad class of
confirmation functions, as subjectivists Ramsay and de Finetti were
also to do, and then find a natural way of limiting this class still
further. The confirmation functions have to meet some basic
mathematical conditions. The axioms that state these conditions
partially define a function, and this function can be interpreted in a
number of ways. Carnap himself lists three in Carnap 1950. In (1955),
John Kemeny (one of Carnap's collaborators and later a
co-inventor of BASIC programming language and still later president of
Dartmouth College) gave an argument that persuaded Carnap that it was
more fruitful to think of the function as indicating fair betting
quotients rather than evidential support. This took Carnap even closer
in conception to the work of such subjectivists as Ramsey and de
Finetti. Indeed, the discussion of fair betting quotients, and related
issues of Dutch book arguments had been initiated by de Finetti.



In *Logical Foundations of Probability* (1950) Carnap had
discussed Bayes' theorem and promised to expand the discussion
in a second volume. Carnap's interest in Bayesianism grew, but
that second volume never materialized, quite possibly because rapid
development of the field was still under way at the time of
Carnap's death. As his work proceeded Carnap tended to explain
probabilities by reference to events and propositions rather than
speak overtly about sentences. A similar change appears in the rest of
Carnap's work as well. It is not clear, however, whether this
amounts to a major change of view or a change in what he sees as the
most felicitous mode of expression. As the years progressed Carnap
tended to see the remaining differences between himself and his
subjectivist co-workers as chiefly differences in emphasis. In any
case the subjectivist tradition is now dominant in philosophical
discussions of probability (Zabell 2007, 293). Richard Jeffrey, whose
own work arose out of logical empiricism, carried on that tradition
for 35 years after Carnap's death. Jeffrey himself made major
contributions including a principle for updating ones beliefs when the
evidence one learns is not certain. The world knows this principle as
"Jeffrey conditionalization"; he called it simply
"probability kinematics".



Popper's view of probability, his propensity theory, differs
from either of the two approaches discussed above. Unlike the
epistemic approach of Carnap and others, Popper was not trying to
clarify inductive relations because he did not believe that there are
inductive inferences. Theories can be corroborated by their passing
severe tests, but they are not thereby inductively confirmed or made
more probable. For a discussion of whether there are any significant
similarities between Popper's idea of corroboration and the
ideas of inductive confirmation that he rejects, see (Salmon 1967,
1968).



Propensities are thought of as tendencies of a physical event or state
to produce another event or state. Because propensities are to be
features of external events and not, to use Hume's phrase,
relations of ideas, the propensity theory and the
statistical-frequency theory are sometimes grouped together as
accounts of chance. Popper has specifically applied propensities to
single non-repeatable events (1957), and that suggests that the
concept of propensity does not involve any essential reference to long
sequences of events. Popper has also taken propensities as producing
outcomes with a certain limit frequency (1959). This does suggest a
rather closer tie to the statistical frequency approach. Later
philosophers developed both sorts of propensity theories, single-case
theories and long-run theories. (Gillies 2000) And like other
approaches to probability and induction all these views remain
controversial. While we will not discuss the relative merits of the
various approaches further, those who are interested in Popper's
views in this area should look at the many papers on probability,
induction, confirmation, and corroboration, and Popper's
replies, in *The Philosophy of Karl Popper* (Schilpp 1974).


## 5. Impact



In 1967 John Passmore reported that: "Logical positivism, then,
is dead, or as dead as a philosophical movement ever becomes."
(1967, 57) Earlier in the same article he had equated logical
positivism with logical empiricism, so presumably that was dead too.
At that time few would have disagreed with Passmore, even though
Carnap was still alive and active. But in speaking of this movement
Passmore was referring not to a movement but to specific doctrines,
and his interpretation of them was much influenced by Ayer. Even so,
Passmore conceded that the movement had left a legacy and that
"the spirit which inspired the Vienna circle" persisted.
It still does.



Part of the movement's legacy lies in contemporary philosophy of
science. In the US nearly all philosophers of science can trace their
academic lineages to Reichenbach. Most were either his students or
students of his students and so on. His scientific realism inspired a
generation of philosophers, even those clearly outside the movement.
Even the reaction against various forms of realism that have appeared
in recent decades have roots in the logical empiricist movement.
Moreover, philosophers of science are expected to know a great deal of
the science about which they philosophize and to be cautious in
telling practicing scientists what concepts they may or may not use.
In these respects and others contemporary philosophers promote a kind
of naturalism, and by so doing they follow both the precept and the
example of the logical empiricists.



There are other issues where the legacy of logical empiricism is still
visible. Two different approaches to probability are still under
discussion. One of them explores the objective chances of external
events; this investigation follows in the tradition of the frequency
theory of Reichenbach and von Mises. The second approach has an
epistemic conception of probability as exemplified by Carnap. S.L.
Zabell summarizes the current situation as follows:



> 
> But although the technical contributions of Carnap and his school
> remain of considerable interest today, Carnap's most lasting
> influence was more subtle but also more important: he largely shaped
> the way current philosophy views the nature and role of probability,
> in particular its widespread acceptance of the Bayesian paradigm (as,
> for example, in Earman, 1992; Howson and Urbach, 1993; and Jeffrey,
> 2004). (Zabell 2007, 294)
> 



There is also a continuing concern for how the various sciences fit
together. Some have scouted theoretical unification and others a more
pluralistic model, just as the logical empiricists did. There was for
a while a vogue for the disunity of science. Some even said that their
conception of the disunity of science is just what Neurath meant by
the unity of science. Parts of the discussion were intended as
challenges to logical empiricism, but often the arguments used were
pioneered by the logical empiricists themselves.



For the 30 years after Passmore's report metaphysics became ever
more visible in philosophy. It was a diverse development, but in the
self-conceptions of many of its most prominent practitioners there was
no attempt to shun science or logic or to think that metaphysics had
access to facts that were deeper than or beyond those that a proper
science could reach. So the metaphysics that blossomed was not
necessarily of the sort that Carnap, Neurath, Reichenbach, and others
combated. Finally, in contemporary meta-philosophy variously logical
empiricist ideas on ontology (Blatti and Lapointe 2016), explication
(Kitcher 2008, and Carus 2007), and philosophy as conceptual
engineering (Creath 1990, Chalmers 2020, and Haslanger 2000) continue
to be of interest.



Even in its heyday many philosophers who on either doctrinal or
sociological grounds can be grouped with the logical empiricists did
not see themselves that way. We should not expect philosophers today
to identify with the movement either. Each generation finds its place
by emphasizing its differences from what has gone before. But the
spirit of the movement still has its adherents. There are many who
value clarity and who want to understand the methodology of science,
its structure, and its prospects. There are many who want to find a
natural home within a broad conception of science for conceptual
innovation, for logic and mathematics, and for their own study of
methodology. And importantly there are those who see in science a
prospect for intellectual and social reform and who see in their own
study of science some hope for freeing us all from the merely habitual
ways of thinking "by which we are now possessed" (Kuhn
1962, 1). These are the motives that define the movement called
logical empiricism. As Twain might have said, the reports of its death
are greatly exaggerated.