---
title: "Logical positivism"
chunk: 3/5
source: "https://en.wikipedia.org/wiki/Logical_positivism"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:39:44.646869+00:00"
instance: "kb-cron"
---

In theories of justification, 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 and synthetic: Analytic statements are true by virtue of their own meaning or their own logical form, therefore are tautologies that are true by necessity but uninformative about the world. Synthetic statements, in comparison, are contingent propositions that refer to a state of facts concerning the world.
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) or "matters of fact and real existence" (a posteriori, synthetic and concrete), a classification referred to as Hume's fork. Immanuel Kant identified a further category of knowledge: 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 intuitive truths—including synthetic a priori conceptions of space and time—function as an interpretative filter for an observer's experience of the world. His thesis would serve to rescue Newton's law of universal gravitation from Hume's problem of induction by determining uniformity of nature to be in the category of a priori knowledge.
The Vienna Circle rejected Kant's conception of synthetic a priori knowledge given its incompatibility with the verifiability criterion. Yet, they adopted the Kantian position of defining mathematics and logic—ordinarily considered synthetic truths—as a priori. Carnap's solution to this discrepancy would be to reinterpret logical truths as tautologies, redefining logic as analytic, building upon theoretical foundations established in Wittgenstein's Tractatus. Mathematics, in turn, would be reduced to logic through the 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.

=== Observation-theory distinction ===

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 observation terms and theoretical terms. Observation terms are specified by direct observation and thus assumed to have fixed empirical definitions, whereas theoretical terms refer to the unobservables of a theory, including abstract conceptions such as mathematical formulas. The two categories of primitive terms would be interconnected in meaning via a deductive interpretative framework, referred to as correspondence rules.
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 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. 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.
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. 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.

=== Logicism ===
By 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 and Rudolf Carnap.
Carnap's early anti-metaphysical works employed Russell's theory of types. 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.

== Philosophy of science ==
The logical positivist movement shed much of its revolutionary zeal following the defeat of Nazism and the decline of rival philosophies that sought radical reform, notably Marburg neo-Kantianism, Husserlian phenomenology and Heidegger's existential hermeneutics. Hosted in the climate of American pragmatism and common sense empiricism, its proponents no longer crusaded to revise traditional philosophy into a radical scientific philosophy, but became respectable members of a new philosophical subdiscipline, philosophy of science. Receiving support from Ernest Nagel, they were especially influential in the social sciences.

=== Scientific explanation ===