Editing Logical positivism (section)

==Principles==

===Verification and Confirmation===

{{Main|Verificationism}}

====Verifiability Criterion of Meaning====

According to the [[verificationism|verifiability criterion of meaning]], a statement is ''cognitively meaningful'' only if it is either verifiable by [[observation|empirical observation]] or is an [[analytic proposition|analytic truth]] (i.e. true by virtue of its own [[semantics|meaning]] or its own [[syntax|logical form]]).<ref>{{cite journal |last=Hempel |first=Carl G |title=Problems and changes in the empiricist criterion of meaning |journal=Revue Internationale de Philosophie |year=1950 |volume=41 |pages=41–63}}</ref> ''[[meaning (philosophy of language)|Cognitive meaningfulness]]'' was defined variably: possessing [[truth value]]; or corresponding to a possible state of affairs; or intelligible or understandable as are scientific statements. Other types of meaning—for instance, emotive, expressive or figurative—were dismissed from further review.<ref>Various different views are discussed in Ayer's ''Language, Truth, and Logic'', Schlick's "Positivism and realism" (reprinted in {{harvnb|Sarkar|1996}} and {{harvnb|Ayer|1959}}) and Carnap's ''Philosophy and Logical Syntax''.</ref>

[[Metaphysics]], [[theology]], as well as much of [[ethics]] and [[aesthetics]] failed this criterion, and so were found cognitively meaningless and only ''emotively meaningful'' (though, notably, Schlick considered ethical and aesthetic statements cognitively meaningful).<ref>{{cite journal |last=Allen |first=Barry |year=2007 |title=Turning back the linguistic turn in the theory of knowledge |journal=[[Thesis Eleven]] |volume=89 |issue=1 |pages=6–22 |doi=10.1177/0725513607076129 |s2cid=145778455 |quote=In his famous novel ''[[Nineteen Eighty-Four]]'' [[George Orwell]] gave a nice (if for us ironical) explanation of the boon Carnap expects from the logical reform of grammar. Right-thinking [[Ingsoc]] party members are as offended as Carnap by the unruliness of language. It's a scandal that grammar allows such pseudo-statements as 'It is the right of the people to alter or abolish Government' ([[Thomas Jefferson|Jefferson]]), or 'Das Nichts nichtet' ([[Martin Heidegger|Heidegger]]). Language as it is makes no objection to such statements, and to Carnap, as to the Party, that's a sore defect. [[Newspeak]], a reformed grammar under development at the [[Ministry of Truth]], will do what Carnap wants philosophical grammar to do.}}</ref><ref>{{cite book |last=Schlick |first=Moritz |url=https://books.google.com/books?id=LTOaM0X6e6cC&q=%22The+future+of+philosophy%22 |chapter=The future Of philosophy |title=The Linguistic Turn |editor=Richard Rorty |location=Chicago |publisher=University of Chicago Press |year=1992 |pages=43–53}}</ref> Ethics and aesthetics were considered subjective preferences, while theology and metaphysics contained "pseudostatements" that were neither true nor false. Thus, logical positivism indirectly asserted [[Hume's law]], the principle that [[fact|factual]] statements cannot justify [[axiology|evaluative]] statements, and that the two are separated by an unbridgeable gap. [[A. J. Ayer]]'s ''[[Language, Truth and Logic]]'' (1936) presented an extreme version of this principle—the [[emotivism|boo/hooray doctrine]]—whereby all evaluative judgments are merely emotional reactions.<ref name=Ayer1>{{cite book |last=Ayer |first=A.J |title=Language, Truth, and Meaning |year=1936 |pages=2,63-77}}</ref>

====Revisions to the criterion====

Logical positivists in the Vienna Circle recognised quickly that the verifiability criterion was too restrictive.<ref name=sep-hempel/> Specifically, [[universal generalization|universal statement]]s were noted to be empirically unverifiable, rendering vital domains of science and [[reason]], such as [[hypothesis|scientific hypothesis]], ''cognitively meaningless'' under verificationism. This would pose significant problems for the logical positivist program, absent revisions to its criterion of meaning.<ref>{{cite encyclopedia |author=John Vicker |editor=Edward N. Zalta |year=2011 |title=The problem of induction |encyclopedia=The Stanford Encyclopedia of Philosophy |edition=Fall 2011 |url=https://plato.stanford.edu/archives/fall2011/entries/induction-problem/#VerCon |quote=This initial formulation of the criterion was soon seen to be too strong; it counted as meaningless not only metaphysical statements but also statements that are clearly empirically meaningful, such as that all copper conducts electricity and, indeed, any [[universal generalization|universally quantified statement]] of infinite scope, as well as statements that were at the time beyond the reach of experience for technical, and not conceptual, reasons, such as that there are mountains on the back side of the moon. |access-date=24 August 2012}}</ref>

In his 1936 and 1937 papers, ''Testability and Meaning'', [[Rudolf Carnap|Carnap]] proposed ''confirmation'' in place of verification, determining that, though universal laws cannot be verified, they can be confirmed.<ref name=Sarkar2005/> Carnap employed abundant logical and mathematical tools to research an [[inductive reasoning|inductive logic]] that would account for probability according to ''degrees of confirmation''. However, he was never able to formulate a model. In Carnap's inductive logic, a universal law's degree of confirmation was always zero.<ref name=IEP-Carnap>{{cite encyclopedia |last=Murzi |first=Mauro |url=https://www.iep.utm.edu/carnap |title=Rudolf Carnap (1891–1970) |encyclopedia=Internet Encyclopedia of Philosophy |year=2001}}</ref> The formulation of what eventually came to be called the "criterion of cognitive significance", stemming from this research, took three decades (Hempel 1950, Carnap 1956, Carnap 1961).<ref name=Sarkar2005/> [[Carl Hempel]], who became a prominent critic of the logical positivist movement, elucidated the [[paradox of the ravens|paradox of confirmation]].<ref>{{cite encyclopedia |last=Crupi |first=Vincenzo |title=Confirmation |year=2021 |url=https://plato.stanford.edu/archives/spr2021/entries/confirmation/ |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |access-date=2023-07-10 |edition=Spring 2021}}</ref>

In his 1936 book, ''Language, Truth and Logic'', [[A. J. Ayer]] distinguished ''strong'' and ''weak'' verification. He stipulated that, "A proposition is said to be verifiable, in the strong sense of the term, if, and only if, its truth could be conclusively established by experience", but is verifiable in the weak sense "if it is possible for experience to render it probable". He would add that, "no proposition, other than a [[Tautology (logic)|tautology]], can possibly be anything more than a probable [[hypothesis]]". Thus, he would conclude that all are open to weak verification.<ref>{{harvnb|Ayer|1936}} pp. 50–51</ref>

===Analytic-synthetic distinction===

{{Main|Analytic-synthetic distinction}}

In [[justification (epistemology)|theories of justification]], ''[[A priori knowledge|a priori]]'' statements are those that can be known independently of [[observation]], contrasting with ''[[a posteriori]]'' statements, which are dependent on observation. Statements may also be categorised into ''[[analytic-synthetic distinction|analytic]]'' and ''[[analytic-synthetic distinction|synthetic]]'': Analytic statements are true by virtue of their own [[semantics|meaning]] or their own [[syntax|logical form]], therefore are [[tautology (logic)|tautologies]] that are true by [[logical truth|necessity]] but uninformative about the world. Synthetic statements, in comparison, are [[contingency (philosophy)|contingent]] propositions that refer to a state of facts concerning the world.<ref>{{cite encyclopedia |last=Rey |first=Georges |title=The Analytic/Synthetic Distinction |date=2023 |url=https://plato.stanford.edu/archives/spr2023/entries/analytic-synthetic/ |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |access-date=2023-07-10 |edition=Spring 2023 |publisher=Metaphysics Research Lab, Stanford University |editor2-last=Nodelman |editor2-first=Uri}}</ref><ref>{{cite encyclopedia |title=Quine, Willard Van Orman: Analytic/Synthetic Distinction |encyclopedia=Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/quine-an/ |access-date=2023-07-10}}</ref>

[[David Hume]] proposed an unambiguous distinction between analytic and synthetic, categorising knowledge exclusively as either "relations of ideas" (which are ''a priori'', analytic and [[abstract and concrete|abstract]]) or "matters of fact and real existence" (''a posteriori'', synthetic and [[abstract and concrete|concrete]]), a classification referred to as [[Hume's fork]].<ref name=Flew>{{cite book |last=Flew |first=Antony |title=A Dictionary of Philosophy |url=https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA156 |edition=2nd |year=1984 |publisher=St. Martin's Press |location=New York |isbn=978-0-312-20923-0 |page=156}}</ref><ref>{{cite book |last=Mitchell |first=Helen Buss |title=Roots of Wisdom: A Tapestry of Philosophical Traditions |url=https://books.google.com/books?id=P6o0OUzwmSAC&pg=PA249 |year=2010 |publisher=Cengage Learning |isbn=978-0-495-80896-1 |pages=249–50}}</ref> [[Immanuel Kant]] identified a further category of knowledge: [[synthetic a priori|Synthetic ''a priori'']] statements, which are informative about the world, but known without observation. This principle is encapsulated in Kant's [[transcendental idealism]], which attributes the mind a constructive role in [[phenomena]] whereby [[Rationalism#Intuition-deduction thesis|intuitive]] truths—including synthetic ''a priori'' conceptions of [[space]] and [[time]]—function as an interpretative filter for an observer's experience of the world.<ref>{{cite encyclopedia |last=Rohlf |first=Michael |title=Immanuel Kant |year=2010 |url=https://plato.stanford.edu/entries/kant/#TraIde |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |access-date=2025-02-02 |edition=Summer 2024 |publisher=Metaphysics Research Lab, Stanford University}}</ref> His thesis would serve to rescue [[Newton's law of universal gravitation]] from Hume's [[problem of induction]] by determining [[uniformitarianism|uniformity of nature]] to be in the category of ''a priori'' knowledge.<ref>{{cite encyclopedia |last1=De Pierris |first1=Graciela |last2=Friedman |first2=Michael |title=Kant and Hume on Causality |year=2008 |url=https://plato.stanford.edu/entries/kant-hume-causality/ |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |access-date=2025-02-02 |edition=Summer 2024 |publisher=Metaphysics Research Lab, Stanford University}}</ref>

The Vienna Circle rejected Kant's conception of synthetic ''a priori'' knowledge given its incompatibility with the [[verificationism|verifiability criterion]].<ref>{{harvnb|Uebel|2008}} 2.3</ref> Yet, they adopted the Kantian position of defining mathematics and logic—ordinarily considered synthetic truths—as ''a priori''.<ref>{{cite book |title=Early Analytic Philosophy: Frege, Russell, Wittgenstein |editor1=William W. Tait |editor2=Leonard Linsky |editor2-link=Leonard Linsky |author=Michael Friedman |chapter=Carnap and Wittgenstein's ''Tractatus'' |page=29 |chapter-url=https://books.google.com/books?id=eNA_TdDTNkMC&pg=PA29 |isbn=978-0812693447 |year=1997 |publisher=Open Court Publishing}}</ref> [[Rudolf Carnap|Carnap]]'s solution to this discrepancy would be to reinterpret logical truths as tautologies, redefining logic as analytic, building upon theoretical foundations established in [[Ludwig Wittgenstein|Wittgenstein]]'s ''Tractatus''. Mathematics, in turn, would be reduced to logic through the [[Logical Positivism#Logicism|logicist approach]] proposed by [[Gottlob Frege]]. In effect, Carnap's reconstruction of analyticity expounded Hume's fork, affirming its analytic-synthetic distinction. This would be critically important in rendering the verification principle compatible with mathematics and logic.<ref>{{cite book |title=Realistic Rationalism |author=Jerrold J. Katz |chapter-url=https://books.google.com/books?id=szCaXDdhID8C&pg=PA69 |page=69 |chapter=The epistemic challenge to antirealism |isbn=978-0262263290 |year=2000 |publisher=MIT Press}}</ref>

===Observation-theory distinction===

{{See also|Ramsey sentence}}

[[Rudolf Carnap|Carnap]] devoted much of his career to the cornerstone [[doctrine]] of ''rational reconstruction'', whereby scientific theories can be formalised into [[predicate logic]] and the components of a theory categorised into ''[[Ramsey sentence|observation terms]]'' and ''[[Ramsey sentence|theoretical terms]]''.<ref name="sep-recon">{{cite encyclopedia |first1=Hannes |last1=Leitgeb |first2=André |last2=Carus |year=2020 |title=Supplement to "Rudolf Carnap": E. The Reconstruction of Scientific Theories |encyclopedia=The Stanford Encyclopedia of Philosophy |url=https://plato.stanford.edu/entries/carnap/reconstruct-sci-theories.html |access-date=2025-02-04 }}</ref> Observation terms are specified by direct observation and thus assumed to have fixed empirical definitions, whereas theoretical terms refer to the [[unobservable]]s of a theory, including [[abstract and concrete|abstract]] conceptions such as [[formula|mathematical formulas]]. The two categories of [[primitive notion|primitive terms]] would be interconnected in meaning via a [[deductive reasoning|deductive]] interpretative framework, referred to as ''correspondence rules''.<ref name=carnap-win>{{cite journal |first=John A. |last=Winnie |title=The Implicit Definition of Theoretical Terms |journal=J. Phil. Sci. |volume=18 |year=1967 |pages=223-229 }}</ref>

Early in his research, Carnap postulated that correspondence rules could be used to define theoretical terms from observation terms, contending that scientific knowledge could be unified by [[reductionism|reducing]] theoretical laws to "protocol sentences" grounded in observable facts. He would soon abandon this model of reconstruction, suggesting instead that theoretical terms could be defined implicitly by the [[axioms]] of a theory. Furthermore, that observation terms could, in some cases, garner meaning from theoretical terms via correspondence rules.<ref name="carnap-lt">{{cite book |first=Sebastian |last=Lutz |editor1=S. Lutz |editor2=A.T. Tuboly |chapter=Two Constants in Carnap’s View on Scientific Theories |year=2021 |doi=10.4324/9780429429835 |title=Logical Empiricism and the Physical Sciences |publisher=Routledge |pages=354-378}}</ref> Here, definition is said to be 'implicit' in that the axioms serve to exclude those interpretations that falsify the theory. Thus, axioms define theoretical terms indirectly by restricting the set of possible interpretations to those that are true interpretations.<ref name=carnap-win/>

By reconstructing the [[semantics]] of scientific language, Carnap's thesis builds upon earlier research in the reconstruction of [[syntax]], referring to [[Bertrand Russell]]'s [[logical atomism]]—the view that statements in [[natural language]] can be converted to standardised subunits of meaning assembled via a [[logical syntax]].<ref>{{cite book |last=Russell |first=Bertrand |chapter=The Philosophy of Logical Atomism [1918] |date=1988 |title=The Collected Papers of Bertrand Russell, Volume 8 |pages=157–244 |doi=10.4324/9781003557036-20 |location=London |publisher=Routledge |isbn=978-1-003-55703-6 |editor=John G Slater}}</ref> Rational reconstruction is sometimes referred to as the ''[[received view]]'' or ''syntactic view of theories'' in the context of subsequent work by [[Carl Hempel]], [[Ernest Nagel]] and [[Herbert Feigl]].<ref name=sep-recon/>

===Logicism===

By [[reductionism|reducing]] mathematics to logic, [[Bertrand Russell]] sought to convert the mathematical formulas of [[physics]] to [[symbolic logic]]. [[Gottlob Frege]] began this program of [[logicism]], continuing it with Russell, but eventually lost interest. Russell then continued it with [[Alfred North Whitehead]] in their ''[[Principia Mathematica]]'', inspiring some of the more mathematical logical positivists, such as [[Hans Hahn (mathematician)|Hans Hahn]] and [[Rudolf Carnap]].<ref name=Hintikka>{{cite book |last=Hintikka |first=Jaako |chapter=Logicism |title=Philosophy of Mathematics |editor1=Andrew D Irvine |publisher=North Holland |location=Burlington MA |year=2009 |url=https://books.google.com/books?id=mbn35b2ghgkC&pg=PA283 |pages=283–84}}</ref>

Carnap's early anti-metaphysical works employed Russell's [[type theory|theory of types]].<ref>{{cite journal |last=Schlick |first=Moritz |year=1932 |title=The elimination of metaphysics through logical analysis of language |journal=Erkenntnis |volume=2 |issue=1 |pages=1-31 |doi=10.1007/BF01886406}} Reprinted in {{cite book |title=Logical Positivism |last=Ayer |first=Alfred Jules |pages=60-81 |year=1959 |location=New York |publisher=Free Press}}</ref> Like Russell, Carnap envisioned a universal language that could reconstruct mathematics and thereby encode physics. Yet [[Kurt Gödel]]'s [[incompleteness theorem]] showed this to be impossible, except in trivial cases, and [[Alfred Tarski]]'s [[undefinability theorem]] finally undermined all hopes of reducing mathematics to logic. Thus, a universal language failed to stem from Carnap's 1934 work ''Logische Syntax der Sprache'' (''Logical Syntax of Language''). Still, some logical positivists, including [[Carl Hempel]], continued support of logicism.<ref name=Hintikka/>