Logical empiricism is a philosophic movement rather than a set ofdoctrines, and it flourished in the 1920s and 30s in several centersin Europe and in the 40s and 50s in the United States. It had severaldifferent leaders whose views changed considerably over time.Moreover, these thinkers differed from one another, often sharply.Because logical empiricism is here construed as a movement rather thanas doctrine, there is probably no important position that all logicalempiricists shared—including, surprisingly enough, empiricism.And while most participants in the movement were empiricists of oneform or another, they disagreed on what the best form of empiricismwas and on the cognitive status of empiricism. What held the grouptogether was a common concern for scientific methodology and theimportant role that science could play in reshaping society. Withinthat scientific methodology the logical empiricists wanted to find anatural and important role for logic and mathematics and to find anunderstanding of philosophy according to which it was part of thescientific enterprise.

The following discussion of logical empiricism is organized under fiveheadings:

• 1. Mapping the Movement
• 2. Background
• 3. Some Major Participants in the Movement
• 4. Issues
  • 4.1 Empiricism, Verificationism, and Anti-metaphysics
  • 4.2 Analyticity
  • 4.3 Unity of Science and Reduction
  • 4.4 Probability
• 5. Impact
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Mapping the Movement

The term ‘logical empiricism’ has no very preciseboundaries and still less that distinguishes it from ‘logicalpositivism’. It is therefore hard to map. ‘Logicalempiricism’ here includes three groups: (1) the Vienna Circle,here taken broadly to include those who were part of various privatediscussion groups, especially that around Moritz Schlick, and also themembers of the more public Ernst Mach Society (Verein Ernst Mach), (2)the smaller, but perhaps more influential Berlin Society for EmpiricalPhilosophy (later called the Berlin Society for ScientificPhilosophy), and (3) those influenced by or who interacted withmembers of the first two groups and shared an intellectual kinshipwith them. Besides Vienna and Berlin, there were important centers ofthe movement in England, France, Scandinavia, at several universitiesin the U.S., and even China. This characterization includes thinkerswho disagreed with doctrines espoused by members of the originalgroups and even some who defined themselves in opposition to themovement. This results in a vague boundary, but it suffices toidentify a movement in which a large number of able philosophersself-consciously participated and to distinguish logical empiricismfrom other movements.

It does not, however, distinguish logical empiricism from logicalpositivism, and it is doubtful that any principled such boundary canbe drawn along doctrinal or sociological lines (Uebel 2013). Usuallywhen distinctions are drawn, ‘logical empiricism’ is thewider term. Members of the Berlin group never used the term‘positivism’ about themselves, but did use it concerningsome unnamed Viennese in stressing their differences from the latter.In any case, these differences, even if real, were smaller than thedifferences within the Vienna Circle on one hand or within the Berlingroup on the other. ‘Positivist’ is a term usually appliedby opponents of various doctrines. It was used by some of the Vienneselogical empiricists about themselves but generally with caution and instressing the differences between their own views and those of the19^th century positivists. The one philosopher who wouldhave unhesitatingly described himself as (having been) a logicalpositivist was A.J. Ayer.

Another way of mapping the boundaries of logical empiricism is to listthe specific philosophers who were centrally or peripherally part ofit. This included many of the most important philosophers of themid-twentieth century. Hans Hahn, Moritz Schlick, Rudolf Carnap, andOtto Neurath were leaders of the Vienna Circle, and Kurt Gödelregularly 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 manyothers. Not all of these would admit to being part of the logicalempiricist movement, of course, but a case can be made that allcontributed to it. The Berlin Society for Empirical (or Scientific)Philosophy was, as stated, smaller but perhaps more influential. Ledby Hans Reichenbach, it included Kurt Grelling, Walter Dubislav, KurtLewin, Richard von Mises, Paul Oppenheim, and others. Hempel took hisdoctorate in Berlin, working with Reichenbach until the latter wasforced to leave in 1933. Hempel also spent time in Vienna and Prague.Of course, among the foremost associates of the Berlin Society wasAlbert Einstein, who was also in Berlin also until 1933.

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

Because of the catastrophic dislocations of Europe in the 1930s, themain focus of the logical empiricism moved from central Europe toAmerica by the close of that decade.Erkenntnis, the mainjournal of the movement, which had been edited by Reichenbach andCarnap, ceased publication by 1940. In 1930 Feigl moved to the U.S.,and Carnap moved to Chicago in 1936. Hempel came to Chicago and Mengerto Notre Dame in 1937. The ensuing years witnessed a massive exodus toAmerica from central Europe. Reichenbach arrived in the U.S. in 1938after five years in Turkey. Also in 1938 Gustav Bergmann and PhilippFrank emigrated. Edgar Zilsel came in 1939. Alfred Tarski was on avisit 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, byReichenbach’s UCLA students Hilary Putnam and Wesley Salmon.Adolf Grünbaum can also be considered as clearly in theReichenbach lineage. And Wilfrid Sellars was, in his early years, aclose associate of Feigl. The American incarnation of the logicalempiricist movement enjoyed generally good relations with the Americanpragmatists, not only because many of the logical empiricists had astrong pragmatist component to their philosophy, but also because thepragmatists and logical empiricists shared a common concern forempirical methodology in the service of social reform.Institutionally, the movement was represented in most major Americanuniversities, and such journals asPhilosophy of Science(with Carnap and Feigl on the Editorial Board and Reichenbach andSchlick on the Advisory Board) andPhilosophical Studies(founded and edited for many years by Feigl and Sellars) providedample outlet for their publications. In addition, the Inter-ScientificDiscussion Group was founded by Philipp Frank at Harvard. That grewinto the Institute for the Unity of Science, called by some the ViennaCircle in exile. Meanwhile in Chicago theEncyclopedia of UnifiedScience was established with Neurath, Carnap, and Morris as itseditors.

But even from late 30s onward the movement was hardly limited toAmerica. Ayer remained in England. Wittgenstein returned to Cambridgein 1929, but with regular visits to Vienna, including those on whichhe discussed issues surrounding a strong version of verificationismwith Schlick and Waismann. Popper fled to New Zealand in 1937, and in1946 moved to the London School of Economics. Neurath fled from Viennato the Hague and then again in 1940 to England, where he remained tillhis death in 1945. Friedrich Waismann went to England in 1937. In 1939Rose Rand, a less well-known member of the Vienna Circle, fled toEngland and then in 1954 emigrated once more to the U.S. There werelike-minded thinkers in Scandinavia (such as JørgenJørgensen, Eino Kaila, and Arne Naess) and as far away asArgentina (H.A. Lindemann) and China (Tscha Hung).

It is impossible to say when logical empiricism ceased to besufficiently cohesive to be identifiable as a continuing movement.Certainly by 1960 a great many philosophers, including many who hadearlier clearly been part of the movement, were identifying themselvesin opposition to what they took to be logical empiricism. And somemembers simply changed their minds or pursued different projects.Logical empiricism probably never commanded the assent of the majorityof philosophers in either Europe or America, and by 1970 the movementwas pretty clearly over—though with lasting influence whetherrecognized or not. In the 1980s there was a resurgence of historicalinterest in logical empiricism. That historical interest continues toclear away many of the caricatures and misconceptions about thelogical empiricists. Among the major results of this work is therecognition of the tremendous variety and subtlety of viewsrepresented within the movement and the fact that many of thearguments later deployed by critics of logical empiricism had beenpioneered by the logical empiricists themselves.

Given the emphasis on science and its technical apparatus, socialrenewal, clarity and rationality of belief, functionality, and aboveall the palpable sense of doing philosophy in an importantly new way,it is reasonable to associate logical empiricism with other forms ofEuropean modernism in the 1920s and 30s, such as Neue Sachlichkeit inart and the Bauhaus in architecture and design, and with mid-centurymodernism as well as with political liberalism, from the New Deal tothe Great Society in the United States. There have been recognizablymodernist developments in various fields including philosophy forcenturies.

2. Background

With a movement as large and complex as logical empiricism a greatmany factors went into raising the questions it would address, makingthem seem urgent, and making it seem as though the intellectualresources it would need to address these questions were either at handor could be developed.

One long-term process with profound implications was the steadydeparture of the various sciences from philosophy to form autonomousdisciplines. By early in the twentieth century mathematics, physics,chemistry, biology, and the social sciences were all pursuedprofessionally and independently from philosophy. And psychology wasjust separating from philosophy. Yes, there were polymaths who couldand did pursue a science and philosophy professionally. Those wereincreasingly rare, though single-discipline scientists did from timeto time make philosophic-seeming pronouncements. But they did so fromoutside the field. This pattern of steady departures raised thepressing question: What sort of thing remained behind? Oncemathematics and the empirical sciences all left, what was left forphilosophy?

The nature of philosophy was always a vexed philosophic question, butnow it was particularly insistent. Surely there was no domain ofempirical facts that philosophy could call its own. All that realestate had been parceled out. One answer available at the time thatlogical empiricism flourished was that the genuinely philosophicremainder after the departure of the sciences is somehow deeper thanthe empirical sciences and gets at matters, perhaps cultural ones,that are more profound and important than anything that empiricalscience even can address. This is either because on this conceptionphilosophy has a mode of access or “evidence” that theempirical sciences do not and cannot have, or because the very idea offidelity to evidence and punctilious argument is somehowsmall-minded.

The logical empiricists found this answer unappealing. Indeed, thisconception of philosophy is precisely what Carnap means by‘metaphysics’. (As a consequence, what Carnap meant bythat word is different from what late twentieth and early twenty-firstcentury philosophers generally mean in describing their own work asanalytic metaphysics.) The logical empiricists were eager to conceiveof their enterprise as scientific and to engage in philosophy onlyinsofar as it was also scientific. This science need not be empiricaland need not include all that was traditional in philosophy that hadnot been incorporated into the independent sciences. The decision tobe scientific can hardly be the end of the story. It requires ratherbetter and more detailed answers to questions about what scientificmethods are, how the mathematical (and other apparently non-empiricalsciences) fit together with the empirical ones, and what, moreprecisely, philosophy’s role was.

A second series of developments that raised questions for logicalempiricism to address were developments in the sciences themselves,especially the rise of non-Euclidean geometries in mathematics and theestablishment of relativity theory in physics. These posed a seriouschallenge to what would otherwise be an attractive scientificphilosophy, namely some version of Kantianism. Kant had recognizedthat the best of modern science was often mathematical in characterand had labored to integrate both geometry and arithmetic into ourempirical picture of the world. He had held that we could notrepresent the world except as a Euclidean structure and henceEuclidean geometry was, a priori, a permanent feature of any futurephysics. The demonstration that non-Euclidean pure geometricalstructures were as consistent as Euclidean ones and that spaces canindeed be represented as a non-Euclidean manifolds was one half of theproblem. The other half came when Einstein argued convincingly thatphysical space was best described as a non-Euclidean manifold ofnon-constant curvature. Plainly Euclidean geometry could not beguaranteed a future physics. Modern mathematical logic also posed aproblem for other Kantian claims, but not in the same wrenchingway.

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 geometryand relativity certainly do not refute all forms of neo-Kantianism,but the difficulties are quite real nonetheless. The need is tounderstand how mathematics can be integrated into what is otherwise anempirical enterprise, i.e., physics, chemistry, biology, etc.Addressing this need was to be a major part of the logical empiricistprogram.

The background of logical empiricism described so far has beenconfined to the academic world, but events outside that domain shapedthe movement as well. World War I was an unmitigated disaster forcentral Europe, followed by economic turmoil in the 20s and politicalupheavals of the 30s. It is hard to exaggerate these changes.Monarchies that had stood for centuries disappeared overnight andtheir empires disintegrated. This level of political convulsion hadnot been seen since the French Revolution, and that earlier upheavalwas comparatively confined. Cultural changes were equally profound,and these were reflected by radical departures in the arts such aspainting, music, and architecture, and even more importantly in newmodes of living.

The logical empiricists were no mere bystanders. They, or at least themain leaders of the movement, were politically and culturally engaged.Even more important, this engagement was accompanied by the convictionthat their cultures were incapable of the necessary reform and renewalbecause people were in effect enslaved by unscientific, metaphysicalways of thinking. Such ways of thinking might be exemplified intheology, in the racial hatreds of the day, in conceptions ofproperty, 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 againstmetaphysics was not just to express an academic position in the narrowsense. It was a political act as well; it was to strike a blow for theliberation of the mind. To articulate scientific methods and ascientific conception of philosophy was the essential first step inthe reform of society and in the emancipation of humankind (Carnap1958/2017, Creath 2009, Uebel 2012.

If all of this sounds like something out of the 18^thcentury Enlightenment, the analogy was not lost on the logicalempiricists themselves. André Carus has argued that this isexactly what Carnap had in mind by “explication” (Carus2007). Neurath frequently drew parallels between the logicalempiricists’ anti-metaphysical program and the earlierEnlightenment ambitions. Certainly Kant had inveighed against themetaphysics of his time, and the anti-metaphysical tradition remainedstrong within the scientific community through the 19^thcentury.

The point so far was not to ask whether the logical empiricists wereright in any of this. That question will come up later. So far theissue has been only to see the motivations that the logicalempiricists had—and from their point of view—foraddressing certain questions and for thinking that answers to thosequestions were urgently needed. None of this, however, says why thelogical empiricists thought they had or could have the means to answerthese questions. To that we now turn.

Since Newton the most paradigmatic examples of empirical science werethose claims, usually quantitative ones, that were properly inferredfrom or appropriately confirmed by experience. Speaking veryinformally, these are the ones that we have good reason to believe orat least better reason to believe than the available alternatives. Theproblem, of course, is to specify the form of proper inferences, theform of an appropriate confirmation relation, and/or the structure ofgood reasons. The task is daunting, but logic in a suitably broadsense seems to be the right tool. Still speaking informally, logicseems to give us the structure of (good) reasoning. There are otherconceptions of logic, of course, but this is a standard one and prettywell 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 Russelland beyond was truly impressive. Arguably, it could now express allparts of classical mathematics. Besides the first order predicatecalculus one would need either set theory or higher order logic, butthese were recent developments as well. Logic, like the empiricalsciences, was progressive and could be approached cooperatively bymore than one investigator. InOur Knowledge of the ExternalWorld (1914) Russell had even positioned logic asthelocus of scientific method in philosophy. It is small wonder then thatthose who were looking for something scientific in what was left ofphilosophy turned to logic. Wittgenstein’s no-content theory oflogic in theTractatus (1921/1922) was tantalizinglysuggestive about how mathematics could be integrated into an overallempirical theory of the world. Wittgenstein also expressed a radicalverificationism in the early 1930s in his conversations with Schlick,Waismann, and other members of the Vienna Circle. Many of the logicalempiricists in turn could see in some version of that verificationismthe ideal tool with which to carry out their anti-metaphysicalprogram. There was, naturally, much left to accomplish, but even withGödel’s results one could expect that further impressivestrides in logic could be made. Indeed, much was accomplished even ifthe perfect account of scientific reasoning proved elusive. Perfectionis 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 interwoventrajectories of its members, so one way of describing that movement isto trace those various trajectories. To do so in detail for all thoseinvolved would take rather longer than the movement lasted. That wouldbe inappropriate for one entry in an encyclopedia, especially one inwhich entries for many of the members will appear independently. Thethumbnail sketches of the work of some representative figures belowshow the breadth and international character of the movement. Whilethe list is long, it covers only a small fraction of those involvedand 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 bookLanguage, Truth, and Logic (1936) was a best seller afterWorld War II and represents logical positivism to many Englishspeakers.

Gustav Bergmann (1906–1987)

Born and trained in Vienna, Bergmann spent almost all of hiscareer at the University of Iowa. He was a philosopher ofscience, mathematician, and metaphysician, who in his early yearsjoined in the Vienna Circle. But as his career progressed, hisideas increasingly diverged from other members of the logicalempiricist movement.

Rudolf Carnap (1891–1970)

German by birth, he taught in Vienna, Prague, Chicago, and LosAngeles. He was one of the leaders of the Vienna Circle and of logicalempiricism, especially of those within the movement whose formulationswere more liberal, e.g., with respect to the criterion ofverification. He defended logical and methodological pluralism andworked to develop an epistemic approach to probability.

Walter Dubislav (1895–1937)

A German logician and philosopher of science, Dubislav was one ofthe founders, with Reichenbach and Grelling, of the Berlin Society ofEmpirical (later Scientific) Philosophy.

Herbert Feigl (1902–1988)

Born in what is now the Czech Republic, Feigl studied in Viennawith Schlick and Hahn. He emigrated to the U.S. before most otherlogical empiricists would do so. He taught at the Universities of Iowaand Minnesota and founded bothPhilosophical Studies, withWilfrid Sellars, and the Minnesota Center for the Philosophy ofScience. He is best known for his work on the mind-body problem.

Philipp Frank (1884–1966)

This Viennese physicist and philosopher of science taught atVienna, Prague, and Harvard. He was part of a discussion group withHahn, Neurath, and others that preceded the Vienna Circle. At Harvardhe founded the Inter-Scientific Discussion Group that developed intothe Institute for the Unity of Science. He was also one of thefounders of the Boston Colloquium in the Philosophy of Science.

Kurt Gödel (1906–1978)

Born in what is now Slovakia, Gödel took his doctorate underHahn in Vienna, studying with Carnap and Schlick as well. He alsoregularly attended Vienna Circle meetings and taught in Vienna. Thebulk of his career was spent at the Institute for Advanced Study atPrinceton. He is best known for his spectacular incompletenesstheorems, and his Platonist orientation toward mathematics. Though aparticipant in the logical empiricist movement during the Viennayears, Gödel thought that Carnap’s approach to mathematicscould be refuted. The alleged proof (Gödel 1995) was notpublished in Gödel’s lifetime and remainscontroversial.

Kurt Grelling (1886–1942)

Grelling was born in Berlin and took his doctorate inGöttingen under Hilbert. With Leonard Nelson he developed afamous semantic paradox that bears their names. He was one of thefounders of the Berlin Society for Empirical (later Scientific)Philosophy. Grelling died in the Holocaust because for bureaucraticand political reasons news of an academic appointment in the U.S.reached him too late.

Adolf Grünbaum (1923–2018)

Grünbaum moved from his native Germany as a teenager, studiedunder Hempel at Yale, and spent the bulk of his career at theUniversity of Pittsburgh, where he founded the Center for Philosophyof Science. The major themes of his work have been philosophy of spaceand time, rationality, and psychoanalysis.

Hans Hahn (1879–1934)

Hahn, a distinguished mathematician, took his doctorate in hisnative Vienna in 1902 and began teaching there in 1905. He was part ofa group with Frank, Neurath and others that discussed logical andmethodological issues prior to World War I. After teaching atCzernowitz (now in Ukraine) and Bonn he was given a chair inmathematics at Vienna in 1921. He was instrumental in bringing Schlickthere in 1922 and so was called by Frank “the actual founder ofthe Vienna Circle” (Stadler 1997/2001, 642). His most famousstudent was Gödel.

Olaf Helmer (1910–2011)

Helmer took a doctorate in his native Berlin under Reichenbach anda second doctorate under Susan Stebbing in London. He collaboratedwith 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 Göttingenand Berlin. Most of his doctoral work was completed under Reichenbachwhen the latter was forced to leave Germany. Hempel taught at a numberof American universities, most famously at Princeton and theUniversity of Pittsburgh. He was the doctor father of many prominentphilosophers 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 MAwith Carnap (with whom he later collaborated) and a PhD with Hempel(with whom he was for many years a colleague and close friend atPrinceton). He developed Jeffrey conditionalization (see below) anddefended probabilism.

Kurt Lewin (1890–1947)

Born in what is now Poland, Lewin took his doctorate in Berlin in1916. He lectured there in both philosophy and psychology until 1933when he emigrated to the U.S. via England. Thereafter he taught at anumber of American universities including Cornell, Iowa, MIT, andDuke. Credited with founding modern social psychology, he laid thefoundations for what is now called sensitivity training as a way tocombat religious and racial prejudices.

Richard von Mises (1883–1953)

Born in what is now Ukraine, Richard von Mises is the brother ofthe economic and political theorist Ludwig von Mises. Richard was apolymath who ranged over fields as diverse as mathematics,aerodynamics, philosophy, and Rilke’s poetry. He finished hisdoctorate in Vienna. He was simultaneously active in Berlin, where hewas one of the developers of the frequency theory of probability alongwith Reichenbach, and in Vienna, where he participated in variousdiscussion groups that constituted the Vienna Circle. Eventually itwas necessary to escape, first to Turkey, and eventually to MIT andHarvard.

Charles W. Morris (1901–1979)

Morris was an American pragmatist and philosopher of language atthe University of Chicago when Carnap arrived there. These two,together with Neurath until the latter’s death, were the chiefeditors of theEncyclopedia of Unified Science. After Carnapleft Chicago, Morris moved to the University of Florida.

Otto Neurath (1882–1945)

This Austrian philosopher of science and sociologist took hisdoctorate in political science in Berlin. A member of the First ViennaCircle and a leader of the “left” wing of the ViennaCircle, he was also politically active. He was a significant museumdirector, and as part of this developed the ISOTYPE picture language.His main philosophic themes were physicalism, anti-metaphysics, andthe unity of science. He was the Editor-in-Chief of theEncyclopedia of Unified Science until his death. Eventuallyhe 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 andphilosophy. He was a close friend of Einstein, and helped to initiatethe Berlin Society for Empirical Philosophy. Oppenheim collaboratedwith many important logicians and philosophers of science both inEurope and the U.S. He also helped many to escape Nazi oppression, andcontinued to help in a variety of ways even after he settled inPrinceton in 1939.

Karl Popper (1902–1994)

Born in Vienna and with a doctorate there, Popper was intenselyengaged in discussions with members of the Vienna Circle. His mainphilosophical work,The Logic of Scientific Discovery(1935/1959), appeared in a series edited by Schlick and P. Frank. Hedid not however, regularly attend meetings of the Vienna Circle andgenerally considered himself an outsider. Later he claimed to have“killed” logical positivism. From Austria Popper escapedto New Zealand and eventually to the London School of Economics, wherehe was knighted for his political writings.

Hilary Putnam (1926–2016)

This American philosopher of science, mathematics, mind andlanguage earned his doctorate under Reichenbach at UCLA andsubsequently taught at Princeton, MIT, and Harvard. He was originallya metaphysical realist, but then argued forcefully against it. He hascontinued 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 entirecareer at Harvard. In 1932–33 he visited the Vienna Circle andthen Carnap and Warsaw. For the next six years, he said, he was adisciple 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 ofview 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 inmathematics, physics, and philosophy, took his doctorate in Erlangen,Germany. He was a founder and the leader for the Berlin Society forEmpirical (later Scientific) Philosophy. In 1933 he was forced toleave Berlin. He went to Turkey and then in 1938 to UCLA. Among hismany students were Hempel, Putnam, and W. Salmon, and so almost allphilosophy of science in the U.S. can trace its academic lineage toReichenbach. Though interested in social and educational reform, heworked primarily in philosophy of physics. He developed and defended afrequency theory of probability, and emphasized both scientificrealism and the importance of causality and causal laws.

Wesley Salmon (1925–2001)

Salmon was born in Detroit and, after an initial interest intheology, earned his PhD under Reichenbach at UCLA. He taught at anumber of universities including Brown, Indiana, Arizona, andPittsburgh. His interests centered on causality and explanation, andhis statistical relevance model of explanation can be thought of asaddressing and in large measure resolving the problem of the singlecase in frequency theories of probability.

Moritz Schlick (1882–1936)

Schlick was born in Berlin and eventually took his doctorate therein mathematical physics under Max Planck. He taught at a number ofGerman universities before he was, at the instigation of Hans Hahn,called to the Chair in the Philosophy of the Inductive Sciences atVienna, a chair that was previously held by Boltzmann and Mach.Schlick was one of the first philosophers to write aboutEinstein’s relativity theory. He was close to Wittgenstein andone of the conduits for the latter’s strict verificationism. Hiswork ranges from space and time to general epistemology and ethics. In1936 he was assassinated on the steps of the university by a derangedstudent.

Wilfrid Sellars (1912–1989)

Wilfrid Sellars was the son of well-known philosopher, Roy WoodSellars. Wilfrid studied at Buffalo, Oxford, and Harvard beforeteaching at Iowa, Minnesota, Yale, and Pittsburgh. He was a closeassociate and collaborator with Feigl at Minnesota. (In 1947 hedeclared himself a logical empiricist and much later said that he andFeigl were for years discrete parts of a single entity.) He defendedscientific realism, pragmatism, and naturalism, and his philosophy oflanguage drew heavily on Carnap’sLogical Syntax(1934/1937).

Alfred Tarski (1901–1983)

Born and educated in Warsaw, Tarski earned his doctorate underLesniewski. He happened to be visiting the U.S. when Poland wasinvaded and so avoided the fate of so many of his colleagues. Hetaught at the University of California at Berkeley for more than 30years. While it is unclear whether he should be counted as a logicalempiricist, he visited the Vienna Circle and hosted its members inWarsaw, and his “The Concept of Truth in FormalizedLanguages” (1936/1956) was very influential on Carnap and on thedevelopment of semantics among the logical empiricists generally.

Friedrich Waismann (1896–1959)

Waismann was born in Vienna and earned his doctorate there underthe direction of Schlick in 1936. From 1926 to 1933 he helddiscussions with Wittgenstein, generally in the company of Schlick,but also sometimes Carnap or Feigl. Waismann kept detailed minutes ofthese conversations. At one point he and Wittgenstein contemplated ajoint book, but Wittgenstein later changed his mind. Besides theprinted text of theTractatus these conversations were themain conduit of Wittgenstein’s ideas into the Vienna Circle. In1937 Waismann was able to emigrate to England. After a couple of yearsat Cambridge, where he was shunned by Wittgenstein, he moved toOxford, where he taught until his death.

Ludwig Wittgenstein (1889–1951)

Born into an immensely wealthy Viennese family, Wittgensteinstudied at Cambridge from 1911, where he formed friendships withRussell, Keynes, and Moore. HisTractatusLogico-Philosophicus (1921/1922), which among other things triesto show that logic has no content, was enormously influential on manylogical empiricists. Wittgenstein continued to spend much of his timein Austria working variously as an elementary school teacher, agardener, 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 andincreasingly distanced himself from the logical empiricists. His laterwork focused on ordinary language and inspired many other philosophersas well.

4. Issues

It is not possible in an essay of this scope to trace all the issuesthat the logical empiricists addressed or even to treat any one ofthem with completeness. What is possible is to highlight some salientissues, clear away some misconceptions about them, and sketch a bithow those issues were developed over time. The first is a related setof concerns: empiricism, verificationism, and anti-metaphysics. Thesecond is the logical empiricists’ treatment of logic andmathematics as analytic. Third is the related issues of the unity ofscience and reduction. And finally, comes the issue of probability.Given what has already been said, the reader should be aware that noneof the doctrines discussed below was shared by all members of thelogical empiricist movement.

4.1 Empiricism, Verificationism, and Anti-metaphysics

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

Long before the twentieth century the prevailing opinion was thatEuclidean geometry, standard mathematics, and logic did not rest onexperience in any obvious way. They were largely presupposed in ourempirical work, and it was difficult to see what if anything mightdisconfirm them. Geometry was a special case and might be handled indifferent ways that we shall not discuss here. That leaves logic andmathematics.

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

In developing his theory of types Russell said in effect that someexpressions that seem to be sentences in fact say nothing at all. Thisis because, despite appearances, they are not grammatically wellformed. Wittgenstein found this suggestive. In theTractatushe suggested that much else was nonsense as well including traditionalmetaphysics and supposed claims about the “higher”. Whenin late 1929 Wittgenstein proposed (Waismann 1967/1979), inconversations with Schlick and Waismann, a strict verificationism as abasis for identifying the legitimate parts of discourse, this seemedto the logical empiricists to be a very attractive tool for settingaside the unscientific parts of philosophy.

This does not mean, however, that all logical empiricists or even allmembers of the Vienna Circle accepted the strict verificationist viewthat in order to be meaningful a claim must be implied by a finitenumber of observation sentences. Even though those observationsentences need not be true, this view had the drawback that so-calledlaws of nature would not be meaningful on this criterion. Schlick wasprepared to bite the bullet and hold that laws were not statements atall but principles of inference. Others were not prepared to go so farand sought more liberal formulations. This more liberal or“left” wing of the Vienna Circle included Carnap, PhilippFrank, Hahn, and Neurath. Carnap does not seem to have been a strictverificationist even in theAufbau (1928/1967).

Over the years a great many different formulations of verificationistprinciples ensued. Most of them came to a bad end rather quickly, andthis is sometimes taken as a convincing argument that any form ofverificationism is utterly misguided. Perhaps, but we should becautious. There are undoubtedly many different features joined in anyone of the proposals, and even a sequence of failures may not showwhere to place the blame. The central idea behind verificationism islinking some sort of meaningfulness with (in principle) confirmation,at least for synthetic sentences. The actual formulations embodied notonly such a link but various particular accounts of confirmation aswell. Now confirmation is a complex matter, and it is unlikely that weshall have the final satisfactory account any time soon. This shouldnot persuade us, however, that there are no satisfactory accounts ofconfirmation any more than our current lack of the final physicsshould convince us that there are no physical facts of the matter. Soeven a string of failures in formulating verificationist principlesmay mean no more than that the embedded accounts of confirmation aretoo simple but the link between meaningfulness and confirmation isnevertheless sound.

Even if we set this caution aside, there may be parts of apersistently employed strategy that lead to persistent failure. Theseparts and failures might be avoidable. To see how this may be so wewill compare what is perhaps the most famous formulation of theverificationist principle, in Ayer 1936, with a later one, in Carnap1956. A.J. Ayer had visited the Vienna Circle from late 1932 on into1933, returning home for the summer term. While in Vienna he attendedmeetings of the Circle and overlapped for five weeks with Quine.Neither Carnap nor Neurath were there at the time, so the left wing ofthe Circle was not fully represented. When Ayer returned to England hepublishedLanguage, Truth, and Logic in 1936. Evenimmediately it was widely discussed, and after the war sales werespectacular. For many in England this book was the epitome of logicalpositivism and remains so.

Ayer was careful to restrict his criterion of meaningfulness tosynthetic sentences and to demand only in principle confirmation. Andthe formulation seems very natural: Confirmation is a feature thatapplies to sentences (or groups of them) and not to sub-sententialparts, and for an empiricist the content that a synthetic sentence haswould be empirical content. So it would seem that to have empiricalcontent a sentence,A, should either directly imply someobservational sentence or add to the observational content of someother sentence,B. That is, the conjunction ofA andB should imply some observational sentence not implied byB alone. This formulation may be natural, but it is alsofatally flawed. It would declare any sentence whatsoever asmeaningful: For any sentenceA and any observation sentenceO,A would be meaningful because it could beconjoined toA ⊃O. The latter would not ingeneral implyO, but the conjunction would.

Other more elaborate formulations followed along the same lines, andother more elaborate counterexamples appeared just as fast. Hempelreviewed the situation twice within about a year (Hempel 1950 and1951). First he concluded that it was a lively and promising line ofresearch and later concluded that it was not promising at all. Inretrospect it may be that the problems arise because we were led bythe fact that confirmation is a feature that applies to wholesentences into thinking that the level at which to apply the criterionwas the level of whole sentences. Now a sentence with meaninglessparts might well pass some test especially if the test involves itsbeing combined with other sentences that can have meaningless parts.So one way to avoid this difficulty is to try to find a formulationthat applies the test at the level of basic expressions, those thatcan be thought of as “not having parts” so to speak.

This is the strategy that Carnap employed in “The MethodologicalCharacter of Theoretical Concepts” (1956). Observational termsare assumed to have empirical content. Logical terms are assumed tohave none. And all defined terms are assumed to be replaced by theirdefinitions. If for some basic, non-logical term there is a sentencethat contains that term as its only non-logical element and if thatsentence implies some observation sentence, then that sentence hasempirical content and so does its only non-logical term. If we haveestablished that each term from some set,K, is empiricallysignificant we might test still further terms by seeing whether thosefurther terms can add to what is sayable with terms fromK.Carnap’s actual definition is quite complicated, but it doesseem to avoid the difficulties of its predecessors. It also allows anaccount of why those predecessors ran into trouble, viz., that theyapplied at the level of whole sentences (naturally enough) rather thanto elementary terms.

Not long after Carnap’s definition was published David Kaplandevised what seemed to be counterexamples. They became fairly wellknown, but they were not published until 1975. Shortly thereafter itwas shown (Creath 1976) that either Carnap’s definition is notopen to the counterexamples as presented or it can be patched in avery natural way so that it avoids them. This does not show that thereare no counterexamples or that there are no other features of thedefinition to which one might object. But it does show that thesituation is not as dire as Hempel supposed in 1951.

We need to address another issue in considering verificationism, thepersistent criticism that it is self-undercutting. The argument forthis claim goes like this: The principle claims that every meaningfulsentence is either analytic or verifiable. Well, the principle itselfis surely not analytic; we understand the meanings of the words in itperfectly well because we understand our own language. And we still donot think it true, so it cannot be true in virtue of meaning. And itis not verifiable either (whatever we choose ‘verifiable’to mean).

This sounds more compelling than it is. Ayer understood the principleto be a definition, defining a technical term, ‘meaning’.If so, then the sentence expressing the principle would indeed beanalytic. So the self-undercutting charge strictly fails. But soconstrued and with nothing else said about it, the principle would nothave the same punch as before. Why should a metaphysician care whetherhis or her utterances lack some technical feature?

Carnap explicitly takes up the “self-undercutting” chargeagainst verifiability inPhilosophy and Logical Syntax(1935), and he is not interested in introducing a new technical term,‘meaning’, or in denying this new technical property tounverifiable sentences. Carnap is careful to distinguish the languagefor which the verifiability principle is given from the meta-languagein which we talk about that language. This meta-language would be thelanguage in which the principle would be expressed. This may seem tooffer another strategy against the “self-undercutting”charge because the principle applies to a different language than thatin which it is expressed. This is not Carnap’s strategy. Carnapfully understands that if the general verificationist strategy isfollowed, there will also be a verificationist principle expressed inthe meta-meta-language governing the meta-language.

Carnap’s real defense of the principle was achieved by changingthe nature of the discussion. By 1934 Carnap had introduced animportant new element into his philosophy called the Principle ofTolerance. Tolerance is a radical idea. There is no uniquely correctlogic (1934/1937 xiv–xv). Empiricism is a convention (Carnap,1936/1937 33). Perhaps more precisely each of the various versions ofempiricism (including some sort of verificationism) is best understoodas a proposal for structuring the language of science. Beforetolerance, both empiricism and verificationism are announced as ifthey are simply correct. Correspondingly, what Carnap calledmetaphysics was then treated as though it were, as a matter of brutefact, unintelligible. But what is announced thus dogmatically can berejected equally dogmatically. Once tolerance is in place, alternativephilosophic positions, including metaphysical ones, are construed asalternative proposals for structuring the language of science. Notheoretical argument or evidence can show that one of the proposedlanguages is the uniquely correct one. Nor can theoretical argumentsor evidence show that it is false. Neither proposals nor languages arethe sort of thing to be true or false. Instead, proposals call forpractical decisions and practical arguments rather than fortheoretical reasons or evidence. Carnap believes that there are indeedvery good practical reasons for adopting the proposal ofverificationism, for choosing a language of science in which allsubstantive (synthetic) claims can, at least in principle, be broughtbefore the court of public experience. The reason is that if we do notrequire this, the result is “wearisome controversies” thatthere is no hope of resolving. That, he thinks, is the sad history ofattempts to get beyond science, and it is just too painful.

If the proposals constituting some version of verificationism areadopted, then in the language thus constituted it will be analyticallytrue that there are no synthetic sentences that are both unverifiableand meaningful. The notion of meaning here is not some new technicalinvention. Rather, ‘meaning’ is used in something like theordinary sense. No grammatically well-formed sentence of this newlanguage violates the verifiability principle. And the principleitself is completely safe. Thought of in this way the verifiabilityprinciple does not describe natural language; it is not intended to.It is intended to reform language to make it a more useful tool forthe purposes of science. Carnap is under no illusion that naturallanguages are free from what seem to be metaphysical commitments. Noris he under the illusion that defenders of the sort of metaphysics hetargets will readily step up to the challenge of presenting preciserules of grammar and inference. There is no weakening of his defenseof empiricism, but it is put on a somewhat different footing.

It is important to emphasize that Carnap’s Principle of Toleranceintroduces a new conception of philosophy with far-rangingimplications beyond those just discussed concerning verification. Theidea that philosophy is concerned with language and its analysis wasnot new. What is novel is the idea that what had been seen asphilosophical claims were better understood as proposals forstructuring the language of science. Since these languages andthe concepts they contained were to be thought of as tools, none ofwhich was uniquely correct, the choice among the alternatives was apractical decision about usefulness for certain purposes rather than atheoretical question. Philosophy still has important work to do: Itcan analyze existing concepts. And since many existing concepts arevague, it can also make them more precise in a variety of ways throughexplication. Philosophy can also investigate wholly new concepts. Inall this, philosophy explores the consequences of structuring thelanguage of science in this way or that. It becomes, thus, a kind ofconceptual engineering. Conceptual analysis, explication,construction, and engineering continue to be fruitful ideas inphilosophy, though it is not always understood how much of this wasinitiated or shaped by Carnap and other logical empiricists.

4.2 Analyticity

Logic, mathematics, and mathematical geometry had traditionally seemedto be confirmationally “different”. Indeed it is hard toindicate any conditions under which any parts of them would bedisconfirmed. Leibniz had called them truths of reason. Hume said thatthey represented relations of ideas. Kant had held that the truths inthese areas were a priori. Mathematics and geometry were not analyticfor Kant, but logic was. Kant had two criteria of analyticity,apparently thinking them equivalent. First, in subject-predicatesentences, an analytic sentence is one in which the concept of thepredicate is contained in that of the subject. Second, an analyticsentence is one whose denial is self-contradictory. This seems toinclude not only the sentences whose surface logical form would be ofthe required sort but also those that can be got from such logicaltruths by making substitutions that were conceptually equivalent. Themore modern rough analog of this is to say that the analytic sentencesare those that are true in virtue of logic and definition.

Frege certainly developed logic beyond that which was available toKant, but he did not think of himself as changing the analytic statusof it. Logic is after all the only avenue we have for giving meaningto the notion of (logical) contradiction. Of course Frege alsoattempted to reduce mathematics to logic (including both first andsecond order logic), and insofar as that reduction was successful itwould have implied that mathematics was analytic as well. Frege saidlittle of geometry, but for him it was synthetic a priori.

Carnap had not only studied with Frege, but like many of the logicalempiricists he had started out as a neo-Kantian as well. So especiallyin view of Russell’s relatively more successful attempt atreducing mathematics to logic, it was perhaps natural that Carnapwould consider both mathematics and logic as analytic. Geometry couldbe handled in several different ways that we will not discuss here.But from fairly early on there was widespread agreement among thelogical empiricists that there was no synthetic a priori, and thatlogic and mathematics and perhaps much else that seemed impervious toempirical disconfirmation should be thought of as analytic. The pointof drawing the analytic-synthetic distinction, then, is not to dividethe 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 betaken as legitimate and which are not. If, as Carnap and Neurath were,you are impressed by Duhemian arguments to the effect that generallyclaims must be combined in order to test them, the analytic-syntheticdistinction allows you to clarify which combinations of claims aretestable.

If analytic, a sentence is true in virtue of the conventions oflanguage. In saying that, however, we must pause to confront twowidespread confusions. First, Quine alleges (1963, 385f) that thenotion of analyticity was developed and purports to explain for bothKant and Carnap how certainty is possible. In fact certainty haslittle or nothing to do with analyticity for the leading logicalempiricists. In saying that such claims are based on convention theywere explicitly calling attention to the revisability of conventionsand the sentences that owed their meanings to those conventions.Second, nowadays any talk of convention is likely to prompt theresponse: “But that cannot be! No proposition can be made trueby our conventions or decisions.” Unless it is a propositionabout conventions, this second sentence of the response is true. Butit is also completely irrelevant. Analyticity applies tosentences rather than propositions. Our conventions anddecisions can and do affect what expressions mean and thus whatsentences mean. Once the meaning is specified, it may well be that anysentence that has this meaning would be true even if, for example, thepoint masses of the universe were arranged quite otherwise than theyin fact are. These are the analytic sentences. No claim is being madethat meaning causes anything or that conventionmakesanything true. The “making” image here is out of place. Itis just that in these cases the truth value of the sentence may wellbe functionally dependent on meaning alone. If it is, then in thisspecial sense, truth value depends on meaning, and that depends onconvention. Other sentences whose meanings are specified might well betrue or false depending on how things in the external world, so tospeak, are arranged. In this other category of sentence the truthvalue is not functionally dependent on meaning alone. They are thesynthetic sentences. Now this puts matters extremely informally. Butat least the nature of the confusions over certainty and conventionshould be clear.

In theLogical Syntax of Language (1934/1937) Carnap defined‘analytic’ in a new way in order to circumventGödel’s incompleteness results. The method used was todistinguish between a derivation relation (the relation that holdsbetween some premises and what can be got from them in a finite numberof steps) and a consequence relation. The latter is an essentiallysemantic relation that holds between some premises and some otherclaim such that on all valuations under which the premises are alltrue, so is that other claim. This definition bears a strongerresemblance to Tarski’s account in (Tarski 1936b/1956). In anycase, Carnap is able to show that for any sentence of pure mathematicseither it or its negation is a consequence of the null set ofpremises. This leaves Gödel’s results completely intact asthey concerned what is provable, that is, derivable from the null setof premises or from any one consistent axiomatization of mathematicaltruths.

As noted above, another innovation ofLogical Syntax is thePrinciple of Tolerance. While it reflects a long-standing attitude onCarnap’s part, the principle itself is new. Later Carnap was tosay that the Principle of Tolerance was “perhaps better calledthe principle of conventionality” (Carnap 1942, 247), that is,the conventionality of linguistic forms. Tolerance stabilizes theverification principle as well as Carnap’s empiricism, and itreinforces the idea that the analytic-synthetic distinction is alwaysrelative to a particular language (Creath 2009).

In the late 1950s Carnap began exploring (1963a and 1966) how a notionof analyticity might be developed for novel theoretical terms wherethe theories in which those terms are embedded are presented by meansof a system of postulates. It is not clear that the account hedeveloped was intended to supersede his earlier account. In any caseCarnap’s suggestion is as follows (where for convenience termsare used autonomously): LetT be the totality of theoreticalpostulates, andC be the totality of mixed sentences (thesentences of the theory containing both antecedent and novel terms).Also letR(TC) be the Ramsey sentence forTC, that is, the result of replacing each of thenon-observational terms inTC with predicate variables andclosing that open sentence with corresponding existential quantifiers.R(TC) ⊃TC can, Carnap says, be thoughtof as the analytic sentence for the theory, that is, a sentence thatgives to the theoretical terms ofTC their meaning. Over thelast decade, this idea of Carnap’s has provoked considerablediscussion that has not yet been resolved. Whatever worries there maybe concerning this part of Carnap’s view, they are distinct fromthe more famous concerns raised by Quine.

Quine began having doubts about analyticity about 1940, though heseems not to have been firmly committed against it until later. In anycase his doubts were not published until 1951 in his famous paper“Two Dogmas of Empiricism”. Quine’s readers haveunderstood his arguments in many different ways. The most general formof his complaint is that ‘analytic’ so far lacks theappropriate tie to observational criteria that Carnap’s ownaccount of theoretical terms in empirical science would demand. Morespecifically, where there has been an attempt at such a generalcriterion it has resulted in either a “drastic failure as tendedto admit all or no sentences as analytic, or there has been acircularity” (Quine 1963, 404) of a kind that defines‘analytic’ in terms that themselves lack the appropriateempirical criteria and so can be accounted for only by appeal toanalyticity itself.

This complaint falls far short, as Quine well understood, of a proofthat Carnap’s appeal to analyticity was doomed. First, it relieson the demand that theoretical terms must satisfy some empiricalsignificance criterion. Many people at the time, including some whofollowed Quine in rejecting analyticity, also rejected any generalempirical significance demand for theoretical terms. Second, one couldaccept the demand for theoretical terms in physics or chemistry anddeny, as Carnap did, that the demand applied to his own work. This isbecause Carnap saw himself as working in an area withinmetamathematics rather than in empirical linguistics. Third, Quine didnot pretend to have considered all of the possibilities for theexplication of analyticity. And so it may be possible to meetQuine’s demands to the extent that they are legitimate. Fourthand finally, Quine seems inRoots of Reference (1974) to haveprovided an explication for ‘analytic’ that meets hisdemand for empirical/behavioral criteria without inducing either thedrastic failure or the circularity envisioned above.

There is another somewhat independent thrust to Quine’s campaignagainst analyticity. In the last section of “Two Dogmas”(1951) Quine gives an extremely attractive sketch for an alternativeepistemology that apparently makes no appeal to analyticity. Insofaras that sketch can be filled out successfully it would constitute adispensability argument against analyticity. Whether it can be thusfilled out, however, remains to be seen.

Quine’s other provocative theses, including especially hisclaims about the indeterminacy of translation, while relevant to hisassessment of analyticity, would carry us too far afield to considertheir ramifications here. As with most topics in philosophy there isno uniform agreement in the literature as to whether the notion ofanalyticity is or can be made sufficiently clear for use in scientificphilosophy. Nor is there such agreement that Quine’sepistemological sketch can be satisfactorily filled out. Bothapproaches have their defenders and their detractors. But between themthey seem to be the most promising avenues for integrating thelogic-mathematical part of science with the more straightforwardlyempirical parts. Since Carnap is and Quine can be argued to be withinthe logical empiricist tradition, this progress toward suchunification 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 ofscience has been in recent years often discussed but less oftenunderstood. One hears in conversation that it was a sort of rearguardaction designed to preserve as much as possible of a phenomenalistversion of ontological reduction. One reads in print that it can berefuted by the obvious fact that the various sciences have quitedistinct theoretical vocabularies (Suppes 1978). Both reactions aremisplaced.

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 mainfocus of their activities from the late 30s wasThe Encyclopediaof Unified Science edited by Neurath in Europe and Carnap andCharles Morris in Chicago. A great many philosophers of many differentpersuasions participated in that project. The project may have beenunified science, but they did not have a completely unified view ofwhat that project was. Here we will discuss the Neurath and Carnapversions of it to see what their central concerns were.

Neurath seems to have had two primary motivations to advance under thebanner of the unity of science. First, he was concerned that there beno a priori methodological cleavage between the natural and the socialsciences. On the social scientific side he was concerned that thesesciences not condone some private, mysterious mode of insight(empathy) whose results could not be checked against more ordinarypublic observation. Such a methodology would be a harbor formetaphysics. On the natural scientific side, he was concerned to pointout that, for Duhemian and other reasons, the situation is muchmessier than is sometimes supposed, and so invidious comparisons bynatural scientists at the expense of social science wereunwarranted.

Second, because Neurath was socially and politically engaged he wasconcerned that the various sciences be connected in such a way thatthey could be usedtogether to solve complex human and socialproblems. For this, considerable overlap of vocabulary was needed, andthis he called a “universal jargon”.

In recent years it is sometimes claimed that Neurath meant by theunity of science what some contemporary philosophers have defended asthe disunity of science. One cannot rule this claim out a priori. Butthe often substantial differences among the current defenses ofdisunity make evaluating this claim difficult. It is fair to say,however, that Neurath was suspicious of grand hypotheses, familiarsince the 19^th century to derive all of chemistry, biology,psychology, and the social sciences (in that order) from a few basicprinciples of physics. It is unclear whether this stems from a generalopposition to system building, since he was eager to developinferential connections among the various sciences. Perhaps this isbetter expressed as an opposition tospeculative systembuilding and to the idea that there is only one way of systematizingour 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 ofscience from the unity of the laws of science. He wanted to defend theformer and to say what would be required for the latter. As far as theunity of the language of science, Carnap did in theAufbautry to initiate a program for defining all of scientific concepts onthe basis of a very small number of basic concepts, perhaps only onebasic concept. That does afford a certain conceptual economy, but itis now generally held by Carnap scholars (see especially Friedman 1987and Richardson 1998) that ontological reduction and reduction to aphenomenalist basis was far from his motive. Carnap explicitlyacknowledged that another system of definitions, one with aphysicalist basis, might also be possible. Instead of ontologicaleconomy and a phenomenal basis, Carnap’s project seems to havebeen the more Kantian one of indicating how semantic intersubjectivityis possible: How can it be that, even though I have only my ownexperiences and you have only yours, we can nevertheless share acommon body of concepts? The answer is given in terms of sharedinferential structure and identifying any given concept with a uniqueplace within that shared overall structure. This is a highly holisticconception of concepts and it depends on thinking of the body ofscientific commitments as a whole, as a unity.

TheAufbau was largely drafted before Carnap joined theVienna Circle. Once there and under some influence from Neurath,Carnap campaigned more insistently for physicalism and for the unityof science. They seemed often to be two sides of the same coin. From1933 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 theassociate editor or one of the associate editors.TheInternational Encyclopedia of Unified Science, begun in 1938 isundoubtedly the most famous of these. Carnap’s own essay on thistopic “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 Carnaphad already decided (Carnap 1936–37) that theoretical termscould not in general be given explicit definitions in the observationlanguage even though the observation reports were already in aphysicalist vocabulary. The partially defined theoretical terms couldnot be eliminated. This seems to have caused Carnap no consternationat all, and it never seems to have occurred to him that there was anyconflict whatever between this result and the unity of science. Thisis because by this point the elimination of concepts was not the pointof the exercise; their inferential and evidential integration was.

In the 1936–37 article, “Testability and Meaning”Carnap called the partial definitions themselves “reductionsentences” and the system of definitions of theoretical terms,both partial and complete, as a reduction of the theoretical terms tothe 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 vocabularyA to vocabularyB Carnap means the specification of the inferential relationsthat would allow us to say what sentences or combinations of sentencesinA would count as evidence for sentences inB.

This is also the key to what Carnap means by the unity of the languageof science. The language of science is unified, no matter howdifferent and exotic its various technical vocabularies may be, wheneach of its terms is reduced to (can be tested in) a common publicobservation vocabulary. The call for the unity of the language ofscience, then, amounts to no more than the demand that the variousclaims of the separate sciences should be publicly testable in acommon observation language. Controversies will of course arise as towhat the observational vocabulary should be and what are theacceptable forms of linkage. Carnap’s demand for unity in thelanguage of science abstracts from those controversies to concentrateon the goal of public testability. That does not seem to be anunreasonable demand.

The unity of the language of science so far discussed is quite adifferent issue from the unity of the laws of science. AndCarnap’s attitudes toward them are quite different. The latterissue concerns the extent to which the laws of one special science canbe inferred from those of another. Carnap tries to articulate whatwould be involved in such a unification, but he nowhere says that sucha unity is either possible or mandatory. Finding any sort ofinferential connections among sets of laws would be welcome of course.But the question of how much unity there is, if any, among the varioussciences is an empirical question that philosophers are ill equippedto answer. Philosophers should not make pronouncements, especially inadvance of having putative laws in hand, either that scientific lawsare unified or that they are not. A certain modest deference to theempirical facts that philosophers generally do not have, again, doesnot seem unreasonable.

Taking unity as a working hypothesis, as some philosophers have done,amounts tolooking for inferential and nomologicalconnections among various sets of laws, but not to the assertion thatsuch connection will be found. Even if we accept the idea that suchconnections would be welcome if found, the question of whether oneshould spend significant effort in looking for them is not therebyanswered. That would be a difficult and delicate practical question ofhow to apportion one’s research effort that for the purposes ofthis essay we must set aside.

4.4 Probability

There are two broad approaches to probability represented in logicalempiricism. One of these, the so-called frequentist approach, has anextensive 19^th century history and was further developedfrom about 1920 onward by Richard von Mises and Hans Reichenbach. Theother is the epistemic approach to probability. This goes back atleast to Laplace at the end of the 18^th century. In the20^th century Rudolf Carnap, who explored what he calledlogical probability, and Frank Ramsey and Richard Jeffrey whoseaccounts can be distinguished from Carnap’s and are often calledsubjective probability, all defended the epistemic approach. WhileRamsey visited the Vienna Circle he was not much influenced by itsmembers on these matters. By contrast, Jeffrey studied and latercollaborated with Carnap but also made significant contributions ofhis own.

It is natural to begin thinking about probabilities with a simplemathematical account that takes as its point of departure variousgames of chance involving cards, dice, or coins. Bettors have longnoted that some outcomes are much more likely than others. In thiscontext it is convenient to take the probability of a kind of outcometo be the ratio of such outcomes to all possible outcomes. Usually forreasons of symmetry in the physical set up, the possible outcomes areassumed to be equally likely. Where that assumption happens to be trueor nearly so the empirical results of, say, a great many throws of apair of dice tends to be close to what the simple mathematical accountwould suggest. Conversely, where the outcomes deviate from theexpected ratios, bettors begin to suspect that the dice, coins, andcards (or the manipulations of them) are not all that they seem. Thesuspicion is that the outcomes are not equally likely and that thesimple mathematical account does not apply.

These facts suggest both two limitations of the simple account and thebeginnings of a way around them. The first limitation is that theaccount applies only where the outcomes can be partitioned intoalternatives that are equally likely. This is not the case when diceare loaded or in such real world cases as radioactive decay or weatherforecasting. A second limitation is that the account, in describingthe possible outcomes as equally likely, implicitly appeals to thevery probability notion for which clarification was sought. Therealization that we can sometimes discover the falsehood of theassumption of equal likelihood and make a much more reasonableestimate of probability by making a large number of trials is verysuggestive. And from his dissertation onward Reichenbach worked out avariety of imagined physical models that could guide ones thinkingabout probability in useful ways. The result is what is often calledthe frequency theory of probability (or sometimes the statisticalfrequency theory or the limit frequency theory).

Even a perfectly fair coin in an odd number of flips will never resultin exactly the same number of heads and of tails. When the coin isfair and the number of flips is even, an outcome perfectly balancedbetween heads and tails is not guaranteed either. So, even on theassumption that the probability of the coin’s coming up headsdoes 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 ratiowe have seen is close to the “actual” value, but there isno finite number of flips after which we can say that the observedratio is exactly right. We will never make an infinite number of flipseither, and in actual cases a large finite number of flips might soerode the coin as to bias the coin and discredit the result.Notwithstanding these limitations on an actual series of trials onecan imagine an infinite series of trials and define a notion ofprobability with respect to it. This raises its own difficulty, namelythat ratios are not defined for infinite collections. They would bedefined, however, for any finite initial segment of such an infiniteseries, thus giving a sequence of ratios. If this sequence of ratiossettles down on a limit, the probability of the coin showing a headgiven that it has been flipped can be defined as the limit of theratio of heads to total flips as the number of flips goes toinfinity.

While probability thus defined has a somewhat counterfactualcharacter, that is not an obvious defect. Moreover, this notion ofprobability applies perfectly well to biased coins and loaded dice, aswell as to radioactive decay. On the surface at least it also seem toavoid using the notion of probability in its own definition, and inthese respects it seems to be an important improvement over the simplemathematical model with which we began. The definition locates theprobability objectively “out in nature” so to speak, andthis comports well with Reichenbach’s scientific realism.

A problem that remained troublesome concerns the fact that one oftenwants to assign probabilities to particular events, events that in thenature of things cannot be repeated in all their particularity. Thusit is unclear how a frequency theory of probability is to be appliedto such individual cases. This is often called the problem of thesingle case. It is a little difficult to assess how serious this is,because in actual practice we often have no difficulty in makingprobability assignments to single cases. Suppose we are interested inthe probability of rain tomorrow. Tomorrow will never be repeated, andwe want to estimate the probability now. What we do is to look backthrough the records to find days relevantly like today and determinein what fraction of those cases those days were followed by rainy daysand use that as our estimate. Even if we are comfortable with thispractice, however, it is another matter to say why this should give usa reasonable estimate of the value of the limit involved in alogically impossible infinite sequence. This problem of the singlecase was much discussed, and Wesley Salmon made progress in dealingwith it. Indeed, Salmon’s account of statistical explanation canbe viewed as a substantial mitigation of the problem of the singlecase (W. Salmon 1970).

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

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

Carnap is addressing a different issue than was addressed by von Misesand Reichenbach. Instead of focusing on physical phenomena and ratioswithin them, Carnap focuses on arguments and takes as his point ofdeparture 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 agiven conclusion than would another body of evidence. Carnap sets ashis task the development of a quantitative concept of probability thatwill clarify and explicate these widespread convictions. Such aquantitative concept would be an extraordinarily useful tool, and itwould be a useful successor to our ordinary, somewhat scatterednotions of confirmation and induction.

Carnap approaches the problem by first considering extremely limitedartificial languages and trying to find a confirmation function thatwill work for that. If he succeeds he would then try to develop anaccount that would work for a broader and richer range of languages.In this his approach is like that of a physicist developing a physicaltheory for the highly artificial situation of a billiard table or airtrack and then broadening the theory to deal with a wider range ofcases. In Carnap’s case, however, it is somewhat unclear whatsuccess would be in an artificial language very much unlike our own.In any case, Carnap is not trying to describe our linguistic habitsbut to clarify or even to replace them with something more useful.

As early asLogical Syntax (Carnap 1934/1937,244/316–17) Carnap had suggested that Wittgenstein’sremarks in theTractatus about ranges (Tractatus,4.463) might be a starting point for thinking about probability. By1945 Carnap also distinguished the two approaches described here,insisting that they were not competitors but were attempting toexplicate two different concepts of probability. One need not chooseone as the only concept; both concepts were useful. Reichenbach, bycontrast, never conceded that both concepts were needed and insistedthat his frequency notion could serve all epistemic purposes for whichany notion of probability is needed.

Carnap’s general strategy was first to identify a broad class ofconfirmation functions, as subjectivists Ramsay and de Finetti werealso to do, and then find a natural way of limiting this class stillfurther. The confirmation functions have to meet some basicmathematical conditions. The axioms that state these conditionspartially define a function, and this function can be interpreted in anumber of ways. Carnap himself lists three in Carnap 1950. In (1955),John Kemeny (one of Carnap’s collaborators and later aco-inventor of BASIC programming language and still later president ofDartmouth College) gave an argument that persuaded Carnap that it wasmore fruitful to think of the function as indicating fair bettingquotients rather than evidential support. This took Carnap even closerin conception to the work of such subjectivists as Ramsey and deFinetti. Indeed, the discussion of fair betting quotients, and relatedissues of Dutch book arguments had been initiated by de Finetti.

InLogical Foundations of Probability (1950) Carnap haddiscussed Bayes’ theorem and promised to expand the discussionin a second volume. Carnap’s interest in Bayesianism grew, butthat second volume never materialized, quite possibly because rapiddevelopment of the field was still under way at the time ofCarnap’s death. As his work proceeded Carnap tended to explainprobabilities by reference to events and propositions rather thanspeak overtly about sentences. A similar change appears in the rest ofCarnap’s work as well. It is not clear, however, whether thisamounts to a major change of view or a change in what he sees as themost felicitous mode of expression. As the years progressed Carnaptended to see the remaining differences between himself and hissubjectivist co-workers as chiefly differences in emphasis. In anycase the subjectivist tradition is now dominant in philosophicaldiscussions of probability (Zabell 2007, 293). Richard Jeffrey, whoseown work arose out of logical empiricism, carried on that traditionfor 35 years after Carnap’s death. Jeffrey himself made majorcontributions including a principle for updating ones beliefs when theevidence 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, differsfrom either of the two approaches discussed above. Unlike theepistemic approach of Carnap and others, Popper was not trying toclarify inductive relations because he did not believe that there areinductive inferences. Theories can be corroborated by their passingsevere tests, but they are not thereby inductively confirmed or mademore probable. For a discussion of whether there are any significantsimilarities between Popper’s idea of corroboration and theideas of inductive confirmation that he rejects, see (Salmon 1967,1968).

Propensities are thought of as tendencies of a physical event or stateto produce another event or state. Because propensities are to befeatures of external events and not, to use Hume’s phrase,relations of ideas, the propensity theory and thestatistical-frequency theory are sometimes grouped together asaccounts of chance. Popper has specifically applied propensities tosingle non-repeatable events (1957), and that suggests that theconcept of propensity does not involve any essential reference to longsequences of events. Popper has also taken propensities as producingoutcomes with a certain limit frequency (1959). This does suggest arather closer tie to the statistical frequency approach. Laterphilosophers developed both sorts of propensity theories, single-casetheories and long-run theories. (Gillies 2000) And like otherapproaches to probability and induction all these views remaincontroversial. While we will not discuss the relative merits of thevarious approaches further, those who are interested in Popper’sviews in this area should look at the many papers on probability,induction, confirmation, and corroboration, and Popper’sreplies, inThe 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 logicalpositivism with logical empiricism, so presumably that was dead too.At that time few would have disagreed with Passmore, even thoughCarnap was still alive and active. But in speaking of this movementPassmore 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 ofscience. In the US nearly all philosophers of science can trace theiracademic lineages to Reichenbach. Most were either his students orstudents of his students and so on. His scientific realism inspired ageneration of philosophers, even those clearly outside the movement.Even the reaction against various forms of realism that have appearedin recent decades have roots in the logical empiricist movement.Moreover, philosophers of science are expected to know a great deal ofthe science about which they philosophize and to be cautious intelling practicing scientists what concepts they may or may not use.In these respects and others contemporary philosophers promote a kindof naturalism, and by so doing they follow both the precept and theexample of the logical empiricists.

There are other issues where the legacy of logical empiricism is stillvisible. Two different approaches to probability are still underdiscussion. One of them explores the objective chances of externalevents; this investigation follows in the tradition of the frequencytheory of Reichenbach and von Mises. The second approach has anepistemic 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 schoolremain of considerable interest today, Carnap’s most lastinginfluence was more subtle but also more important: he largely shapedthe 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 fittogether. Some have scouted theoretical unification and others a morepluralistic model, just as the logical empiricists did. There was fora while a vogue for the disunity of science. Some even said that theirconception of the disunity of science is just what Neurath meant bythe unity of science. Parts of the discussion were intended aschallenges to logical empiricism, but often the arguments used werepioneered by the logical empiricists themselves.

For the 30 years after Passmore’s report metaphysics became evermore visible in philosophy. It was a diverse development, but in theself-conceptions of many of its most prominent practitioners there wasno attempt to shun science or logic or to think that metaphysics hadaccess to facts that were deeper than or beyond those that a properscience could reach. So the metaphysics that blossomed was notnecessarily of the sort that Carnap, Neurath, Reichenbach, and otherscombated. Finally, in contemporary meta-philosophy variously logicalempiricist ideas on ontology (Blatti and Lapointe 2016), explication(Kitcher 2008, and Carus 2007), and philosophy as conceptualengineering (Creath 1990, Chalmers 2020, and Haslanger 2000) continueto be of interest.

Even in its heyday many philosophers who on either doctrinal orsociological grounds can be grouped with the logical empiricists didnot see themselves that way. We should not expect philosophers todayto identify with the movement either. Each generation finds its placeby emphasizing its differences from what has gone before. But thespirit of the movement still has its adherents. There are many whovalue clarity and who want to understand the methodology of science,its structure, and its prospects. There are many who want to find anatural home within a broad conception of science for conceptualinnovation, for logic and mathematics, and for their own study ofmethodology. And importantly there are those who see in science aprospect for intellectual and social reform and who see in their ownstudy of science some hope for freeing us all from the merely habitualways of thinking “by which we are now possessed” (Kuhn1962, 1). These are the motives that define the movement calledlogical empiricism. As Twain might have said, the reports of its deathare greatly exaggerated.

Bibliography

Cited Literature

• Ayer, A.J., 1936,Language Truth, and Logic, London:Gollancz.
• Blatti, S. and S. Lapointe (eds.), 2016,Ontology AfterCarnap, Oxford: Oxford University Press.
• Carnap, R., 1928/1967,Der logische Aufbau der Welt,translated by R.A. George asThe Logical Structure of theWorld, Berkeley: University of California Press.
• –––, 1934/1937,Logische Syntax derSprache, translated by A. Smeaton asThe Logical Syntax ofLanguage, London: Kegan Paul, Trench, Trubner & Co.
• –––, 1935,Philosophy and LogicalSyntax, London: Kegan Paul, Trench, Trubner, & Co.
• –––, 1936–37, “Testability andMeaning”,Philosophy of Science, 3: 419–71, 4:1–40.
• –––, 1938, “Logical Foundations of theUnity of Science”,International Encyclopedia of UnifiedScience (Volume 1, Number 1), Chicago: University of ChicagoPress, 42–62.
• –––, 1942,Introduction to Semantics,Cambridge, MA: Harvard University Press.
• –––, 1950,Logical Foundations ofProbability, Chicago: University of Chicago Press.
• –––, 1958 [2017], “Value Concepts”,transcribed and translated by A. Carus,Synthese 194:185–94. [Original manuscriptavailable online]
• –––, 1963a, “Carl G. Hempel on ScientificTheories”, inThe Philosophy of Rudolf Carnap, P.A.Schilpp (ed.), LaSalle, IL: Open Court, 958–66.
• –––, 1963b, “K.R. Popper on Probabilityand Induction”, inThe Philosophy of Rudolf Carnap,P.A. Schilpp (ed.), LaSalle, IL: Open Court, 995–998.
• –––, 1966,Philosophical Foundations ofPhysics, M. Gardner (ed.), New York: Basic Books.
• Carus, A.W., 2007,Carnap and Twentieth-CenturyThought: Explication as Enlightenment, Cambridge:Cambridge University Press.
• Chalmers, D., 2020, “What is Conceptual Engineering andShould It to Be?”,Inquiry, published online 16 September 2020. doi:10.1080/0020174X.2020.1817141
• Creath, R., 1976, “On Kaplan on Carnap onSignificance”,Philosophical Studies, 30:393–400.
• –––, 1990, “Introduction”, inDear Carnap,Dear Van: The Quine-Carnap Correspondence and Related Work, R.Creath (ed.), Los Angeles: University of California Press,1–43.
• –––, 2009, “The Gentle Strength ofTolerance:The Logical Syntax of Language and Carnap’sPhilosophical Programme”, inCarnap’s Logical Syntaxof Language, P. Wagner (ed.), Houndsmills, Basingstoke, UK:Palgrave Macmillan, 203–214.
• Earman, J., 1992,Bayes or Bust: A Critical Examination ofBayesian Confirmation Theory, Cambridge, MA: MIT Press.
• Friedman, M., 1987, “Carnap’sAufbauReconsidered”,Noûs, 21: 521–45.
• Gillies, D., 2000, “Varieties of Propensity”,British Journal for the Philosophy of Science, 51:807–835.
• Gödel, K., 1995, “Is Mathematics Syntax ofLanguage?” in K. Gödel,Collected Works (Volume3), S. Fefferman, et al. (eds.), Oxford: Oxford University Press,334–362.
• Haslanger, S. 2000, “Gender and Race (What Are They? What Do WeWant Them to Be?”,Noûs, 34: 31–55.
• Hempel, C.G., 1950, “Problems and Changes in the EmpiricistCriterion of Meaning”,Revue International dePhilosophie, 11: 41–63.
• –––, 1951, “The Concept of CognitiveSignificance: A Reconsideration”,Proceedings of theAmerican Academy of Arts and Sciences, 80: 61–77.
• Howson, C. and Urbach, P., 1993,Scientific Reasoning: TheBayesian Approach, LaSalle, IL: Open Court.
• –––, 2004,Subjective Probability: The RealThing, Cambridge: Cambridge University Press.
• Kaplan, D., 1975, “Significance and Analyticity: A Commenton Some Recent Proposals of Carnap”, inRudolf Carnap,Logical Empiricist, J. Hintikka (ed.), Dordrecht, Boston: Reidel,87–94.
• Kemeny, J., 1955, “Fair Bets and InductiveProbabilities”,Journal of Symbolic Logic, 20:263–73.
• Kitcher, Philip. 2008, “Carnap and the Caterpillar”,Philosophical Topics, 36: 111–27.
• Kuhn, T., 1962,The Structure of Scientific Revolutions,International Encyclopedia of Unified Science (Volume II,Number 2), Chicago: University of Chicago Press.
• Passmore, J., 1967, “Logical Positivism”,TheEncyclopedia of Philosophy (Volume 5), P. Edwards (ed.), NewYork: Macmillan, 52–57.
• Popper, K., 1935/1959,Logik der Forschung, translated bythe author asThe Logic of Scientific Discovery, New York:Basic Books.
• –––, 1957, “The Propensity Interpretationof the Calculus of Probability”, S. Körner (ed.),TheColston Papers, 9: 65–70.
• –––, 1959, “The Propensity Interpretationof Probability”,British Journal for the Philosophy ofScience, 10: 25–42.
• Quine, W.V., 1951, “Two Dogmas of Empiricism”,Philosophical Review, 60: 20–43.
• –––, 1963, “Carnap and LogicalTruth”, inThe Philosophy of Rudolf Carnap, P. Schilpp(ed.), LaSalle, IL: Open Court, 385–406.
• –––, 1974,The Roots of Reference,LaSalle, IL: Open Court.
• Reichenbach, H., 1916/2008,Der Begriff der Wahrscheinlichkeitfür die mathematische Darstellung der Wirklichkeit, editedand translated by F. Eberhardt and C. Glymour asThe Concept ofProbability in the Mathematical Representation of Reality,LaSalle, IL: Open Court.
• –––, 1938,Experience and Prediction: AnAnalysis of the Foundations and the Structure of Knowledge,Chicago: University of Chicago Press.
• Richardson, A., 1998,Carnap’s Construction of theWorld: The Aufbauand the Emergence of LogicalEmpiricism, Cambridge: Cambridge University Press.
• Russell, B., 1914,Our Knowledge of the External World as aField for Scientific Method in Philosophy, LaSalle, IL: OpenCourt.
• Salmon, W., 1967,The Foundations of ScientificInference, Pittsburgh: University of Pittsburgh Press.
• –––, 1968, “The Justification of InductiveRules of Inference”, inThe Problem of Inductive Logic,I. Lakatos (ed.), Amsterdam: North-Holland, 24–43.
• –––, 1970, “StatisticalExplanation”, inNature and Function of ScientificTheories, R. Colodny (ed.), Pittsburgh: University of PittsburghPress, 173–231.
• Schilpp, P. (ed.), 1974,The Philosophy of Karl Popper,LaSalle, IL: Open Court.
• Suppes, P., 1978, “The Plurality of Science”, inPSA 1978: Proceedings of the 1978 Biennial Meeting of thePhilosophy of Science Association (Volume 2), P. Asquith and I.Hacking (eds.), East Lansing, MI: Philosophy of Science Association,3–16.
• Tarski, A., 1936a/1956, “Der Wahrheitsbegriff in denformalisierten Sprachen”, translated by J.H. Woodger as“The Concept of Truth in Formalized Languages” inLogic, Semantics, Metamathematics, by A. Tarski, Oxford:Clarendon Press, 152–278.
• –––, 1936b/1956, “Über den Begriffden logischen Folgerung”, translated by J.H. Woodger as“On the Concept of Logical Consequence”, inLogic,Semantics, Metamathematics, by A. Tarski, Oxford: ClarendonPress, 409–20.
• Uebel, T., 2012, “Carnap, Philosophy, and ‘Politics inits Broadest Sense’”, inCarnap and the Legacy ofLogical Empiricism, R. Creath (ed.), Vienna: Springer,133–145.
• –––, 2013, “Logical Positivism –Logical Empiricism: What’s in a Name?”,Perspectivesof Science, 21: 58–99.
• Waismann, F., 1967/1979,Wittgenstein und der WienerKreis, translated by J. Schulte and B. McGinnis asWittgenstein and the Vienna Circle, Oxford: BasilBlackwell.
• Wittgenstein, L., 1921/1922,Logische-PhilosophischeAbhandlung, translated by C.K. Ogden asTractatusLogico-Philosophicus, London: Routledge & Kegan Paul.
• Zabell, S. L., 2007, “Carnap on Probability andInduction”, inThe Cambridge Companion to Carnap, M.Friedman and R. Creath (eds.), Cambridge: Cambridge University Press,273–294.

Other Selected Literature

• Awodey, S. and A. W. Carus, 2004, “How Carnap Could HaveReplied to Gödel”, in S. Awodey and C. Klein (eds.),Carnap Brought Home: The View From Jena, LaSalle, IL: OpenCourt, 203–223.
• Cartwright, N. , J. Cat, L. Fleck, and T. Übel, 1996,Otto Neurath: Philosophy Between Science and Politics,Cambridge: Cambridge University Press.
• Carnap, R. 2019,The Collected Works of Rudolf Carnap, Vol. 1,Early Writings, A. Carus et al. (eds.), Oxford: Oxford UniversityPress.
• Creath, R. 1990,Dear Carnap, Dear Van: The Quine-CarnapCorrespondence and Related Work, R. Creath (ed.), Los Angeles:University of California Press.
• Friedman, M., 1987, “Carnap’sAufbauReconsidered”,Noûs, 21: 521–45.
• –––, 1999,Reconsidering LogicalPositivism, Cambridge: Cambridge University Press.
• –––, 2000,A Parting of the Ways: Carnap,Cassirer, and Heidegger, LaSalle, IL: Open Court.
• Friedman, M. and R. Creath (eds.), 2007,The CambridgeCompanion to Carnap, Cambridge: Cambridge University Press.
• Frost-Arnold, G., 2013,Carnap, Tarski, and Quine at Harvard:Conversations of Logic, Mathematics, and Science, Chicago: OpenCourt.
• Hintikka, J. (ed.), 1962,Logic and Language: StudiesDedicated to Professor Rudolf Carnap on the Occasion of His SeventiethBirthday, Dordrecht: Reidel.
• ––– (ed.), 1975,Rudolf Carnap, LogicalEmpiricist: Materials and Perspectives, Dordrecht: Reidel.
• Howson, C., 1973, “Must the Logical Probability of Laws beZero?”British Journal for Philosophy of Science, 24:153–163.
• Jeffrey, R., 1975, “Probability and Falsification: Critiqueof the Popper Program”,Synthese, 30:95–117.
• –––, 2004,Subjective Probability: The RealThing, Cambridge: Cambridge University Press.
• Mancosu, P., “Harvard 1940–41: Tarski, Carnap, andQuine on a Finitistic Language of Mathematics for Science”,History and Philosophy of Logic, 26: 327–57.
• Miller, D., 1997, “Sir Karl Raimund Popper, CH, FBA”,Biographical Memoirs of Fellows of the Royal Society ofLondon, 43: 367–409.
• Parrini, P., W. Salmon, and M. Salmon (eds.), 2003,LogicalEmpiricism: Historical and Contemporary Perspectives, Pittsburgh:University of Pittsburgh Press.
• Rescher, N. (ed.), 1985,The Heritage of LogicalPositivism, Lanham, MD: University Presses of America.
• Rescher, N., 2006, “The Berlin School of Logical Empiricismand Its Legacy”,Erkenntnis, 64: 281–304.
• Richardson, A., 1998,Carnap’s Construction of theWorld: The Aufbauand the Emergence of LogicalEmpiricism, Cambridge: Cambridge University Press.
• Richardson, A. and Übel, T. (eds.), 2007,The CambridgeCompanion to Logical Empiricism, New York: Cambridge UniversityPress.
• Salmon, W. and G. Wolters (eds.), 1994,Language, Logic, andthe Structure of Scientific Theories: The Carnap-ReichenbachCentennial, Pittsburgh: University of Pittsburgh Press, andKonstanz, Germany: University of Konstanz Press.
• Sarkar, S., (ed.), 1992,Synthese: Carnap: A CentenaryReappraisal, 93(1–2).
• Schilpp, P. (ed.), 1963,The Philosophy of Rudolf Carnap,LaSalle, IL: Open Court.
• Spohn, W. (ed.), 1991,Erkenntnis: Special Volume in Honor ofRudolf Carnap and Hans Reichenbach, 35(1–3).
• Stadler, F., 1997/2001,Studien zum Wiener Kreis: Entwicklungund Wirkung des Logischen Empiricismus im Kontext, translated byC. Nielsen, et al. asThe Vienna Circle: Studies in the Origins,Development and Influence of Logical Empiricism, Vienna:Springer.
• Übel, T., 2007,Empiricism at the Crossroads: The ViennaCircle’s Protocol-Sentence Debate Revisited, LaSalle, IL:Open Court.
• Zabell, S. L., 1996, “Confirming UniversalGeneralizations”,Erkenntnis, 45: 267–283.

Academic Tools

	How to cite this entry.
	Preview the PDF version of this entry at theFriends of the SEP Society.
	Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO).
	Enhanced bibliography for this entryatPhilPapers, with links to its database.

Other Internet Resources

• Rudolf Carnap, maintained by Douglas Marshall (University of Minnesota).
• Institute Vienna Circle, Society for the Advancement of the Scientific World Conception,Vienna.
• Willard Van Orman Quine, maintained by Douglas Boynton Quine.
• Archives of Scientific Philosophy, Special Collections Department, University Library System, Universityof Pittsburgh.
• Vienna Circle Foundation, to promote studies of the work of members of the Vienna Circle and toprotect the Vienna Circle Archive, Amsterdam (this webpage is archivedat the Internet Archive).

Related Entries

Ayer, Alfred Jules |Carnap, Rudolf |Gödel, Kurt |Hempel, Carl |Neurath, Otto |Popper, Karl |Quine, Willard Van Orman |Reichenbach, Hans |Sellars, Wilfrid |Tarski, Alfred |Vienna Circle