PhilSci-L01: Introduction and Logical Empiricism

In short

What makes a statement meaningful, and what makes a body of statements science?

The logical positivists of the Vienna Circle: a statement means something only if it is true or false by logic alone (like mathematics) or could in principle be checked by observation. Everything else that pretends to describe the world, above all traditional metaphysics, is not false but literally meaningless. Science is the body of statements that pass this test, tied to observation by logic.

The test turned out to be hard to state and too demanding for real science, so the movement softened into logical empiricism. Its picture of a scientific theory, a set of sentences linked to observation by rules, was later challenged by the view that a theory is a family of models.

On the mock exam this is Q1 (10 marks): the verifiability criterion of meaning and its significance for demarcation.

What separates science from everything else?

Physics, astrology and theology all make claims about the world. What sets science apart? This is the problem of demarcation: where the line between science and non-science runs. The Vienna Circle answered it with a theory of meaning, and their main target was metaphysics (the study of the nature of things or of being: space and time, causation, free will, mind and matter). Popper’s rival answer is in L01b.

The background: experience, reason and Kant

Two old answers in epistemology (the study of knowledge) set up the whole story.

Rationalism (Plato, Descartes, Spinoza, Leibniz): reason alone can give real knowledge of the world. Mathematics is the model: axioms, deduction, and the certainty and necessity rationalists seek.

Empiricism (Aristotle, Locke, Berkeley, Hume, and today Bas van Fraassen, met again in L05): experience is the fundamental source of knowledge about the world. Induction (generalising from observed cases) is central, and empirical knowledge is contingent and fallible.

These are positions about knowledge. Positions about what exists are a separate question: realism about objects (things exist independently of minds), idealism (objects depend in some way on mind or experience), realism about ideas (universals, general properties such as “redness”, exist independently of minds), nominalism (only individual things exist; general terms are just names). Keep the two questions apart, because the answers combine freely: Berkeley was an empiricist and an idealist, and a nominalist can be a realist about physical objects.

Immanuel Kant (late 18th century) tried to combine rationalism and empiricism. The content of knowledge comes from experience, but some conditions of knowledge are a priori (known independently of experience): space, time and basic concepts such as causation are not learned from experience; they are the conditions under which we can experience anything at all. His key claim is that some judgements are synthetic a priori:

• Synthetic: it extends knowledge, rather than unpacking what a concept already contains.
• A priori: its justification does not come from particular experiences.

Kant’s star example was Euclidean geometry: it tells us about real space, yet we know it without experiment. The logical positivists built their position by rejecting this.

The new tools: modern logic and modern physics

Around 1900 two developments made a new kind of empiricism look possible.

Logic. Gottlob Frege built modern first-order logic (variables, the quantifiers $\forall$ “for all” and $\exists$ “there exists”, predicates, rules of inference) and founded the philosophy of language. Alfred North Whitehead and Bertrand Russell tried to derive all of mathematics from logic. Ludwig Wittgenstein studied how language relates to reality. The lesson the positivists drew from all three: logic is tautological, true by form alone and adding no content about the world. This is what later lets them treat mathematics as empty of factual content too.

Physics. Relativity and quantum mechanics overturned what had looked like certain knowledge. General relativity also undid Kant’s example: a non-Euclidean geometry is true of our world, so Euclid’s geometry was no synthetic a priori truth.

The Vienna Circle

The Vienna Circle (1924 to 1938) was a group of scientifically minded philosophers founded by Moritz Schlick and Otto Neurath, with Rudolf Carnap as its central figure; the logician Kurt Gödel took part. Its early, aggressive phase is called logical positivism; the later, moderate phase is logical empiricism.

Their targets were the grand, obscure systems of German philosophy after Kant: G. W. F. Hegel and, in their own time, Martin Heidegger (a philosopher of being, often grouped with the existentialists). Against these they stood for Enlightenment values: reason, clarity, internationalism. Their programme combined empiricism with modern logic: legitimate knowledge is either empirically grounded or logically or mathematically necessary, and philosophy’s job is to clarify the language of science, never to compete with it.

Science, for them, is everyday reasoning made rigorous, aimed at predicting patterns in experience; philosophy studies its logical structure and leaves its history and psychology to others. Kuhn attacks exactly this separation, turning the field from justifying science to asking how science actually works (L02).

The Circle broke up in the 1930s. Schlick was murdered by a former student in 1936, Carnap had already left Austria, and the annexation of Austria by Nazi Germany in 1938 scattered the rest. Many ended up in the United States, where the movement softened.

Meaningful statements: analytic or verifiable

The positivists’ theory of language rests on two ideas.

First, the analytic-synthetic distinction. This is Kant’s distinction, restated in terms of language. An analytic statement is true or false by its meaning alone: “all bachelors are unmarried”. A synthetic statement is true or false because of its meaning and how the world is: “all bachelors are bald”. Analytic truths are necessary, but only because they are empty: they say nothing about the world.

The positivists claimed that all of logic and mathematics is analytic: it records how we have decided to use symbols, and does not describe the world. So, against Kant, there is no synthetic a priori: whatever we know independently of experience is analytic. Geometry shows how this works. Pure geometry is analytic: it only describes possible systems of points and lines. Which of those systems fits our space is an empirical question, and relativity says it is a non-Euclidean one.

Second, the verifiability criterion of meaning. It applies to every statement that claims to say something about the world. To understand such a statement is to know what observation would show it true or false; if no possible observation could bear on it, it says nothing.

Two clarifications keep this from being misread:

• In principle, not in practice. “There are mountains on the far side of the moon” (a standard example from outside the course readings) was meaningful before anyone could fly there: we knew what observation would settle it. Observation counts in a broad sense: any kind of sensory experience.
• Strict or weak. Read strictly, “verifiable” means conclusively provable by observation. That would make universal laws meaningless, since no finite number of observations proves “all metals expand when heated”. So the criterion came to be read weakly (outside the readings: early Schlick did want conclusive verification): there must be possible observations that count for or against the statement. Peter Godfrey-Smith, author of the week 1 reading “Logic Plus Empiricism”, notes that “testability” would have been the better word.

The verifiability criterion of meaning

A statement is meaningful (scientific) if it is verifiable: its truth can in principle be determined through observation or experiment.

“The meaning of a statement is its method of verification.”

Together with analytic statements, these are the only meaningful statements. The force is in the “only”: anything else is a pseudo-statement.

The criterion was a weapon. Science and everyday talk pass it. Poetry fails it harmlessly, since it never claimed to state facts. What fails harmfully is language that claims to state facts and does not: most traditional philosophy, much of ethics, and theology.

How a word gets its meaning: reduction to observation

Early Carnap saw philosophy as the logical analysis of language, done syntactically: he studied the forms of sentences and rules of deduction (syntax: the formal rules of a language, with meaning left out), and left meanings to psychology. A formal theory of meaning, semantics, only arrived in the late 1930s with Alfred Tarski. So Carnap had to explain meaning through logical relations between sentences.

He applies the criterion to single words. To fix what a word means, take the simplest sentence it can appear in, its elementary sentence: for “stone”, that is ”$x$ is a stone”. Then answer four questions about that sentence $S$:

1. What sentences is $S$ deducible from, and what is deducible from $S$?
2. Under what conditions is $S$ true, and under what conditions false?
3. How is $S$ to be verified?
4. What is the meaning of $S$?

For Carnap these are four formulations of one question. All factual language ultimately rests on observation sentences (also called protocol sentences: reports of what is observed). So to know how a sentence is logically linked to observation sentences is to know its truth conditions, its method of verification and its meaning. A word is meaningful when the sentences it can occur in are reducible to observation sentences.

Arthropods

”$x$ is an arthropod” is deducible from, and implies, the sentences ”$x$ is an animal”, ”$x$ has a segmented body”, ”$x$ has jointed legs”. Each of these can be checked by looking. That fixes the meaning of “arthropod”: a technical word reduced to observable conditions.

Carnap’s made-up word shows the other side. Someone says some things are “teavy” and others are not, but there are no empirical signs of teavyness; which things are teavy is an eternal secret. Then “teavy” means nothing. Images and feelings its user associates with it do not give it meaning.

An obvious objection: are deduction, truth, verification and meaning really one thing? Deduction is about logical consequence, truth about how the world is, verification about evidence, meaning about what an expression says. Equating them needs strong assumptions. Carnap himself pulled meaning apart from verification after Tarski, and Quine’s holism later attacked the link between meaning and testing (both below).

The weapon at work: metaphysics as pseudo-statements

The showcase is Carnap’s essay “The Elimination of Metaphysics Through Logical Analysis of Language” (1932). Earlier critics called metaphysics false or pointless; Carnap’s charge is stronger: meaningless in the strictest sense. A pointless question or a false, even self-contradictory, statement still has meaning; only meaningful sentences can be true or false. A pseudo-statement is a string of words that looks like a statement but does not make one at all.

Pseudo-statements arise in two ways.

Words with no criterion of application, like “teavy”: no observable conditions say when the word applies. “God” has a clear meaning in mythology (beings on Olympus, observable in principle); in metaphysics it is stripped of any reference to experience and given no new meaning. The same goes for “the Absolute”, “the Unconditioned”, “the thing in itself” (Kant’s world as it is apart from our experience), “absolute spirit”.

Meaningful words combined in a way logical syntax does not allow. Carnap calls this a type confusion: grammar lets you form the sentence, but it cannot be translated into a logically correct form. A typical case is applying a predicate meant for things to “being” or “existence” itself. His target sentence comes from Heidegger’s 1929 lecture What Is Metaphysics?:

"Das Nichts selbst nichtet": "The Nothing itself noths"

The sentence treats “nothing” first as the name of a thing (the Nothing) and then as a verb (it noths). In modern logic “nothing” is neither. “Nothing is $P$” means $\neg \exists xP(x)$ “it is not the case that there is an $x$ that is $P$“. No object called Nothing appears, so there is nothing that could do any nothing-ing. The sentence is grammatical, but it expresses no proposition. It is not false; it says nothing.

Likewise “something is $P$” is $\exists xP(x)$: existence is expressed by the quantifier, and is not an activity a thing performs. So Descartes’s “I think, therefore I am” needs no metaphysical “I” or ego: “I think” means only “there is something that thinks”, $\exists x\text{Thinks}(x)$.

Why, then, have so many brilliant people written metaphysics? Carnap: it has content, just not theoretical content. It expresses an attitude towards life, which art does better: metaphysicians are “musicians without musical ability”, dressing an attitude up as a theory as if truth were at stake.

The Carnap-Heidegger clash also marks the split between analytic philosophy (logic first) and continental philosophy (fundamental philosophical insight first). Alan Richardson, a historian of philosophy, summarising Michael Friedman, traces “the fundamental cleavage in 20th-century philosophy” to this dispute.

What this means for demarcation

Every meaningful statement is analytic or verifiable, and science consists of verifiable statements (plus logic and mathematics). So the line between science and non-science becomes a line between meaningful and meaningless factual claims.

Significance for demarcation

The criterion solves the problem of demarcation: theories whose statements are not verifiable consist of pseudo-statements and are pseudo-science. They seem to say something (like metaphysics), but they are literally meaningless.

So pseudo-science and metaphysics are excluded without anyone having to show them false: they never get as far as being true or false.

Popper, who knew the Circle but was never a member, drew the line differently. “Testability” turns up on both sides, but the jobs differ. For the positivists, a statement with no possible evidence for or against it is meaningless. Popper’s falsifiability separates science from non-science and says nothing about meaning: for him metaphysics can be meaningful, important, and the seed of later science. His further point, that no observations can ever verify a universal law, hits only the strict reading; against the weak reading the real difference is what the line separates. The full contrast is in L01b, under “Not science does not mean nonsense”.

What is a scientific theory? Sentences

The logical empiricists’ answer is the syntactic conception, also called the Received View. A theory is a collection of sentences in a formal logical language, made of three parts:

1. Axioms: the theoretical starting points, read as basic laws.
2. Derived sentences: everything deduced from the axioms by the rules of the language.
3. Correspondence rules: rules linking theoretical terms to observational terms.

It is called syntactic because it treats a theory as a formal system: a vocabulary plus rules for building and deducing sentences.

The key distinction is between observational terms (“red”, “pointer reading”) and theoretical terms (“atom”, “electron”). Theoretical terms are not directly observable, but they are meaningful because the correspondence rules connect them to the empirical world. An observation sentence contains only observational terms.

axioms (basic theoretical laws)
        |  deduction
        v
derived theoretical sentences
        |  correspondence rules
        v
observation sentences <-- tested

Kinetic theory and the ideal gas law

Axioms. Gases are systems of molecules in motion. Energy and momentum are conserved. Molecules are elastic and obey Newtonian mechanics.

Correspondence rules. Pressure $P$ is the mean force (per unit area) with which molecules hit the walls of the container. Absolute temperature $T$ is proportional to the mean kinetic energy of the molecules: $kT=\frac{2}{3}⟨\frac{1}{2}m{v}^2⟩$ where $k$ is Boltzmann’s constant, $m$ the mass of a molecule, $v$ its speed, and $⟨\cdot ⟩$ the average over all molecules.

Derivation. From the axioms plus the pressure rule, kinetic theory gives $PV=\frac{2}{3}N⟨\frac{1}{2}m{v}^2⟩$ with $V$ the volume and $N$ the number of molecules. Substituting the temperature rule turns the bracket into $\frac{3}{2}kT$ and gives the empirical Boyle-Charles ideal gas law: $PV=NkT$

Unobservable molecules, linked by rules to observable pressure, volume and temperature, yield a law you can check in a lab.

This was a normative ideal: a rigorous standard for evaluating scientific knowledge and progress. It was not an attempt to describe what goes on in a laboratory.

What went wrong with verificationism

It was hard to state. The criterion had to be demanding enough to exclude metaphysics and liberal enough to admit all of science, and every version failed one way or the other. The strict reading excludes universal laws, as we saw; the weak reading lets metaphysics in. “Metals expand when heated and the Absolute Spirit is perfect” now counts as testable: a metal that does not expand refutes the whole conjunction (if $A$ is false, $A\wedge B$ is false). Each patch opened a new hole.

It seems to undermine itself. A standard objection, from outside the course readings: the criterion itself is neither analytic nor verifiable by observation, so by its own standard it looks meaningless. (Defenders treat it as a proposal, not a factual claim.)

Theoretical terms resisted reduction. The first hope, translating all factual talk into talk about sensations, was soon dropped as too extreme. Observation sentences came to be about ordinary observable objects instead. Even so, sentences with words like “electron” or “gene” could not be turned into observation sentences one by one.

Testing is holistic. The American philosopher W. V. O. Quine argued in “Two Dogmas of Empiricism” that no single statement can be tested on its own. A prediction follows only from a hypothesis plus assumptions about instruments and conditions, so a failure says something in the bundle is false, not what. This is the Duhem-Quine thesis (the physicist Pierre Duhem had made the point earlier), covered in L03. If statements cannot be tested one at a time, and meaning is method of testing, they do not have meanings one at a time either. Quine calls this target “reductionism”: the dogma that each statement has its own set of confirming experiences. The positivists had in fact accepted holism about testing, but their criterion still attached observations to each sentence separately.

The analytic-synthetic distinction itself. Quine also argued that no sharp line between analytic and synthetic statements can be drawn: in his “web of belief”, even statements that look analytic could be revised in response to experience. That attacked the other pillar of the theory of language.

From outside the movement, Popper offered falsifiability as a rival criterion, one that demarcates science without judging meaning (L01b), and Kuhn’s history of science (L02) challenged the idea that theory change could be captured by logic at all.

The softening: logical empiricism

Carnap changed his view. In the 1930s, under the influence of the logicians Gödel (a fellow Circle member) and Tarski, he:

• stopped identifying meaning with verification: meaning is not just verification. In logical empiricism generally, talk of verification gave way to confirmation, which comes in degrees: evidence makes a statement more or less well supported, and inductive logic was meant to measure how much. The weak reading only asked whether such evidence is possible at all.
• accepted a full semantics, the theory of meaning he had earlier left to psychology: theoretical terms receive an interpretation of their own, instead of being mere shorthand for observations.
• weakened the correspondence rules to allow partial interpretation: a theoretical term gets part of its meaning from observation and the rest from its place in the theory. This is much closer to a realist view of science.

This is the final version of the Received View: still sentences plus correspondence rules, now with partially interpreted terms. (“Semantics” here means a theory of meaning; it is a different thing from the semantic conception of theories in the next section.)

He kept his rejection of metaphysics, but it lost force: once theoretical terms are interpreted as standing for electrons and fields, he cannot avoid ontology, the question of what exists. As Richardson puts it, “the move to semantics blunts the force of Carnap’s diagnosis of metaphysics as confusion.”

Godfrey-Smith sums up the later movement: meaning became holistic, a theory connecting to observation as a whole, and the analytic-synthetic distinction was kept but treated as questionable. Whether theories describe only patterns in what we observe, or hidden structure behind it, became the question of scientific realism (L05).

What is a scientific theory? Models

The semantic conception starts from three objections to the syntactic one:

1. Axiomatisation. Many scientific theories have never been axiomatised, and perhaps never will be.
2. Language dependence. One theory can be written in several equivalent ways. Identifying the theory with one of them seems wrong.
3. Models. Scientists actually work with models, and models often carry a theory’s content better than a list of sentences.

Its slogan: a scientific theory is a collection of models. A model here is a structure defined in mathematics or set theory (a vector space is an example of such a structure) that represents a possible system. It is called semantic because, in logic, a model is what gives sentences their truth: a structure in which they come out true.

Two senses of “model” are easily confused:

• Iconic or representational model: a concrete representation that captures features of its target, such as a mechanical model of the solar system. It is structurally similar, ideally isomorphic, to what it models (there is a one-to-one mapping between parts and relations that preserves structure).
• Mathematical or logical model: a structure that makes the sentences of a theory true. This is the main sense the semantic conception uses: it specifies the class of structures directly, and a model applies to a real system when the system has (approximately) that structure.

Kinetic theory as models

A gas of $N$ molecules in a region $C\subseteq {\mathbb{R}}^3$ of volume $V$ is modelled by points in phase space: ${\Gamma }_N=C^N\times {\mathbb{R}}^{3N}\subseteq {\mathbb{R}}^{6N}$ $C^N$ holds the positions of the $N$ molecules, ${\mathbb{R}}^{3N}$ their momenta: three of each per molecule, $6N$ coordinates in all. Laws of motion and collision say how the point moves. Statistical mechanics links these micro-models to thermodynamics: $V$ is fixed by the container, $P$ comes from average momentum transfer to the walls, $T$ from the equilibrium distribution of molecular energies. Under the idealisations, the models satisfy $PV=NkT$. The theory is this class of structures.

	Syntactic	Semantic
A theory is	Set of sentences	Class of models
Emphasis	Axioms, derivation	How structures apply to systems
Link to the world	Correspondence rules	Model fits target system
Typical tool	Formal logic	Set theory, mathematics

Does the difference survive?

The philosopher Hans Halvorson argued against the semantic view; his 2013 paper is titled “The Semantic View, If Plausible, Is Syntactic”. The philosopher of science Lutz concludes the debate does “not capture any significant differences”, and Frigg gives the balanced verdict: the syntactic view is too restrictive if it allows only formal sentences, since science needs models and natural language, while the semantic view still needs a language to specify its structures. On these readings the two collapse into each other, or are complementary descriptions of the same practice.

What to be able to write

• The verifiability criterion in the key’s words, “the meaning of a statement is its method of verification”, and its weak reading.
• The other kind of meaningful statement: analytic (logic and mathematics), true by form, empty of factual content. No synthetic a priori.
• Demarcation: unverifiable statements are pseudo-statements, so theories made of them are pseudo-science, literally meaningless (stronger than false).
• One example ready: arthropod reduction, or “The Nothing itself noths” against $\neg \exists xP(x)$.
• Carnap’s two sources of pseudo-statements (no criterion of application; type confusion) and metaphysics as an attitude towards life.
• One sentence of contrast with Popper: falsifiability sorts science from non-science, not meaning from nonsense.
• Problems for the programme: hard to formulate, apparently self-undermining, theoretical terms, Quine’s holism and attack on analyticity. How it softened: confirmation, Carnap’s move to semantics, partial interpretation.
• The syntactic conception (axioms, derived sentences, correspondence rules) with kinetic theory; the semantic conception’s three objections and slogan; whether the difference survives.

The full model answer for mock Q1 is the first exam question below.

Exam questions

Mock exam Q1: "Explain briefly the verifiability criterion of meaning, and its significance for the problem of demarcation." (10 points, half a page)

Key points: Meaningful (scientific) if verifiable in principle by observation or experiment; meaning of a statement is its method of verification; unverifiable statements are pseudo-statements; theories made of them are pseudo-science; pseudo-science (like metaphysics) seems to say something but is literally meaningless.

Follow the official key:

1. The criterion. A statement is meaningful (scientific) if it is verifiable: its truth can in principle be determined through observation or experiment. Slogan: “the meaning of a statement is its method of verification”.
2. The other kind of meaningful statement. Analytic statements (logic and mathematics), true in virtue of form, saying nothing about the world.
3. Demarcation. Theories whose statements are not verifiable are made of pseudo-statements, so they are pseudo-science: they seem to say something (like metaphysics), but they are literally meaningless.
4. An example. Not in the key, but have one ready: the arthropod reduction, or Heidegger’s “The Nothing itself noths” against $\neg \exists xP(x)$.

Contrast worth one sentence: Popper’s falsifiability separates science from non-science without calling non-science meaningless.

A half-page answer: The verifiability criterion of meaning, the central principle of the Vienna Circle and early Carnap, says that a statement about the world is meaningful only if it is verifiable: its truth can in principle be determined through observation or experiment. In the slogan, the meaning of a statement is its method of verification. (Verifiable is meant in principle and weakly: there must be possible evidence for or against, since conclusive proof would make universal laws meaningless.) The only other meaningful statements are analytic ones, those of logic and mathematics, which are true by their form and say nothing about the world. For Carnap a word is meaningful if the sentences it occurs in reduce to observation sentences: ”$x$ is an arthropod” is fixed by ”$x$ is an animal, $x$ has a segmented body, $x$ has jointed legs”. Its significance for demarcation is that it turns the line between science and non-science into a line between meaningful and meaningless. Statements that are neither verifiable nor analytic are pseudo-statements: grammatical, and seeming to say something, but literally meaningless. Metaphysics is the main target: Heidegger’s “The Nothing itself noths” treats “nothing” as a name and a verb, whereas logically “nothing is $P$” is just $\neg \exists xP(x)$, so the sentence expresses no proposition. Pseudo-science and metaphysics are thus excluded as meaningless rather than false. Popper, by contrast, demarcates science by falsifiability and allows non-science to be meaningful.

Explain Carnap's diagnosis of Heidegger's "Das Nichts selbst nichtet". What exactly is wrong with it, and what does Carnap conclude?

Key points: “Nothing” treated as a name and a verb; logically “nothing is $P$” is $\neg \exists xP(x)$; type confusion not translatable into logical form; meaningless pseudo-statement rather than false; metaphysics expresses an attitude to life.

• The sentence treats “nothing” as a name of a thing and then as a verb. In modern logic it is neither. “Nothing is $P$” is $\neg \exists xP(x)$: it is not the case that some $x$ is $P$. There is no object called Nothing that could do anything.
• This is a type confusion: grammar allows the sentence, but it cannot be translated into a logically correct form. (The other source of pseudo-statements is words with no criterion of application, like “God” in metaphysics or “the Absolute”.)
• Conclusion: the sentence is not false but meaningless, a pseudo-statement: it does not even reach the level where truth and falsity apply. Metaphysics has no theoretical content; it expresses an attitude towards life, which art does better (“musicians without musical ability”).

How was the early logical positivist programme challenged, and how did later logical empiricism differ from it?

Key points: Verifiability hard to formulate (strict reading kills laws, weak reading lets metaphysics in); self-undermining objection; theoretical terms not reducible; Quine’s holism and attack on the analytic-synthetic distinction; verification gives way to graded confirmation, Carnap’s move to semantics and partial interpretation, rejection of metaphysics kept but weakened.

• Formulation: the criterion had to exclude metaphysics and include all of science. Read strictly (conclusive verification) it makes universal laws meaningless; read weakly (possible evidence for or against) it lets in “metals expand when heated and the Absolute Spirit is perfect”, testable through its first half.
• Self-undermining (standard objection from outside the readings): the criterion is neither analytic nor verifiable.
• Theoretical terms like “electron” could not be translated into observation sentences.
• Quine: statements face experience only as a whole (Duhem-Quine), so they cannot be tested or given meaning one at a time; and there is no sharp analytic-synthetic line.
• External: Popper’s falsifiability, a rival criterion of science that does not judge meaning; Kuhn’s history.
• Later logical empiricism: verification gave way to confirmation, which comes in degrees. Carnap, under the influence of Gödel and Tarski, stopped identifying meaning with verification, accepted a full semantics and partial interpretation of theoretical terms (closer to realism): the final version of the Received View. Meaning became holistic, a term’s meaning coming partly from its place in the theory. He kept the rejection of metaphysics, but it lost force because a full semantics cannot avoid ontology.

Describe the syntactic conception of scientific theories (the received view) and illustrate it with kinetic theory.

Key points: Theory as sentences in a formal logical language; axioms, derived sentences, correspondence rules; theoretical vs observational terms; kinetic theory: rules for $P$ and $T$ turn the derived equation into $PV=NkT$; normative ideal.

• A theory is a collection of sentences in a formal logical language: (1) axioms, read as basic laws; (2) derived sentences, obtained by formal deduction; (3) correspondence rules linking theoretical terms to observational terms.
• Essential: the split between theoretical terms (atom, electron: not directly observable) and observational terms. Theoretical terms are meaningful because correspondence rules link them to the empirical world.
• Kinetic theory. Axioms: gases are molecules in motion; energy and momentum are conserved; molecules are elastic and Newtonian. Correspondence rules: pressure is the mean force (per unit area) of molecules on the walls; $kT=\frac{2}{3}⟨\frac{1}{2}m{v}^2⟩$. Derivation from the axioms plus the pressure rule: $PV=\frac{2}{3}N⟨\frac{1}{2}m{v}^2⟩$, and substituting gives the ideal gas law $PV=NkT$.
• It is a normative ideal: a rigorous standard for evaluating scientific knowledge. It was not an attempt to describe what labs actually do.

Compare the syntactic and semantic conceptions of theories. Why was the semantic view proposed, and does the distinction survive?

Key points: Syntactic: sentences plus correspondence rules; semantic: class of mathematical models; motivations: no axiomatization, multiple formulations, models in practice; Halvorson, Lutz, Frigg: views collapse or are complementary.

• Syntactic: theory = set of sentences (axioms, derivations, correspondence rules), tied to observation by a vocabulary distinction.
• Semantic: theory = a class of mathematical models representing possible systems; the emphasis is on how the structures apply to physical systems.
• Motivations for the semantic view: (1) many theories are not axiomatized; (2) one theory has several equivalent formulations, so identifying it with one is wrong; (3) scientists actually work with models.
• Does it survive? Halvorson argues against the semantic view (“The Semantic View, If Plausible, Is Syntactic”). Lutz: the debate does not capture any significant differences. Frigg: syntactic is too restrictive (science needs models and natural language), semantic also needs a language to specify structures. So they collapse into each other or are complementary.

Flashcards

What did Kant claim about synthetic a priori judgements?

That they exist: they extend knowledge yet are justified independently of experience, e.g. Euclidean geometry.

Why did the logical positivists deny that there is synthetic a priori knowledge?

Everything knowable a priori, including logic and mathematics, is analytic and empty of factual content.

How did relativity count against Kant's view of geometry, for the logical positivists?

A non-Euclidean geometry is true of our world, so Euclid was not synthetic a priori.

What is the difference between logical positivism and logical empiricism?

Logical positivism: the early, aggressive phase. Logical empiricism: the later, moderate phase.

What is the difference between an analytic and a synthetic statement?

Analytic: true or false by meaning alone. Synthetic: by meaning and how the world is.

Which two kinds of statement are meaningful for early Carnap?

Analytic statements (logic, mathematics) and empirically verifiable statements.

What does the verifiability criterion of meaning say?

A statement is meaningful only if its truth can in principle be determined by observation or experiment.

Which principle is summed up as "the meaning of a statement is its method of verification"?

The verifiability criterion of meaning (verificationism).

Why was the verifiability criterion read weakly, as possible evidence for or against?

Read strictly, as conclusive proof, it would make universal laws meaningless.

How does the verifiability criterion solve the demarcation problem?

Unverifiable statements are pseudo-statements, so theories built from them are pseudo-science.

Does verificationism call metaphysical statements false or meaningless?

Literally meaningless: they seem to say something but make no statement at all.

What is the difference between what a lack of possible evidence means for the positivists and for Popper?

Positivists: the statement is meaningless. Popper: it may be meaningful, just not scientific.

When is a word meaningful, for early Carnap?

When the sentences it can occur in are reducible to observation sentences.

What does Carnap's made-up word "teavy" show?

A word with no empirical criterion of application is meaningless, whatever images its user associates with it.

What are the two ways a pseudo-statement arises, for Carnap?

Words with no criterion of application, or meaningful words combined against logical syntax.

Why is Heidegger's "The Nothing itself noths" a pseudo-statement for Carnap?

It treats “nothing” as a name and as a verb; in modern logic it is neither.

What does metaphysics express, according to Carnap?

An attitude towards life, which art expresses better: metaphysicians are “musicians without musical ability”.

Why does "metals expand when heated and the Absolute Spirit is perfect" trouble verificationism?

Under the weak reading it is testable through its first half, so metaphysics slips in.

Why is the verifiability criterion said to undermine itself?

It is neither analytic nor verifiable, so by its own standard it looks meaningless.

Which two ideas of logical positivism did Quine attack?

Testing statements one at a time (holism instead), and a sharp analytic-synthetic distinction.

Why does holism about testing threaten the verifiability theory of meaning?

If statements are tested only as a whole, they cannot each have their own method of verification.

What did Carnap give up under the influence of Gödel and Tarski in the 1930s?

The identification of meaning with verification; he accepted a full semantics for theoretical terms.

What did Carnap's partial interpretation of theoretical terms replace?

The demand that theoretical terms be fully reduced to observations.

Did partial interpretation move Carnap towards or away from realism?

Towards realism: theoretical terms get meaning beyond observation.

What replaced verification in later logical empiricism?

Confirmation: evidence supports or undermines a statement by degrees, rather than verifying it.

Why did Carnap's rejection of metaphysics lose force after his move to semantics?

A full semantics cannot avoid ontology, so the line between theory and metaphysics blurs.

What is a scientific theory on the syntactic conception?

A collection of sentences in a formal logical language.

What are the three components of a theory on the syntactic conception?

Axioms, derived sentences, correspondence rules.

How do theoretical terms like "electron" get meaning on the syntactic conception?

Through correspondence rules tying them to observational vocabulary.

What is the syntactic conception of theories also called?

The Received View of theories.

Is the syntactic conception a description of laboratory practice?

No, a normative ideal: a rigorous standard for evaluating scientific knowledge.

How does kinetic theory illustrate the syntactic conception?

Correspondence rules link theoretical terms (mean molecular kinetic energy) to observables (temperature), so unobservable molecules yield the testable ideal gas law.

What is a scientific theory on the semantic conception?

A class of mathematical models representing possible systems.

What three criticisms motivate the semantic conception?

Many theories are not axiomatized; one theory has several equivalent formulations; scientists work with models.

What is the difference between an iconic and a mathematical model?

Iconic: a concrete representation similar to its target. Mathematical: a structure that makes a theory’s sentences true.

What does Halvorson argue about the semantic view?

The semantic view, if plausible, is syntactic.

Why does Frigg think neither conception of theories wins outright?

Syntactic is too restrictive (science needs models, natural language); semantic also needs a language to specify structures.

Does the syntactic/semantic distinction survive, on the recent debate?

Arguably not: the two collapse into each other or are complementary.

Links

• Course: Course overview
• Same week: PhilSci-L01b - Popper and Lakatos for Popper’s falsifiability criterion, the main alternative to verificationism
• Next: PhilSci-L02 - Kuhn on Scientific Practice for the historical critique of the received view
• Related: PhilSci-L03 - Under-determination for Quine’s holism and the attack on the analytic-synthetic distinction; PhilSci-L05 - Scientific Realism and its Critiques for the theory-observation distinction and realism about theoretical terms
• Week 1 readings: Carnap, “The Elimination of Metaphysics Through Logical Analysis of Language” (1932; trans. Arthur Pap in Ayer (ed.), Logical Positivism, 1959, abridged; on Canvas). Godfrey-Smith, Theory and Reality (2003), chapter 2, “Logic Plus Empiricism” (on Canvas).
• Background readings from the lecture: R. N. Giere and A. W. Richardson (eds.), Origins of Logical Empiricism, Minnesota Studies in the Philosophy of Science XVI (1996): Richardson, “Introduction: Origins of Logical Empiricism” (source of the “blunts the force” line, summarising Thomas Ricketts, and of the “fundamental cleavage” line, summarising Friedman); M. Friedman, “Overcoming Metaphysics: Carnap and Heidegger”; P. Galison, “Constructing Modernism: The Cultural Location of Aufbau”.
• Further reading: Stanford Encyclopedia of Philosophy, Logical Empiricism and Vienna Circle. F. Suppe (1974), The Structure of Scientific Theories. R. Frigg (2022), Models and Theories. Feigl, “The ‘Orthodox’ View of Theories” (1970), for the network-and-soil picture of the received view.