Editing Logical positivism (section)

===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>