Logical Empiricism

BACKGROUND

Philosophy in the nineteenth century was dominated by German Idealism and Romanticism concerning things like “the absolute”, “becoming” and “the will”.

Logical Positivism originated in the 1920s in the Vienna and Berlin Circles, criticising metaphysics and any theories or theoretical terms not related to experience as meaningless nonsense e.g. ‘God exists’, ‘Every effect has a cause’, vital forces.

Emboldened by advances in logic and amid European social upheaval, the Logical Positivists sought to clearly articulate the scientific method and a scientific conception of philosophy.

Basic commitments of Logical Positivism:

1- Science is the only intellectually respectable form of enquiry.
2- All truths are either: (a) analytic, a priori and necessary, in other words, tautological, or (b) synthetic, a posteriori and contingent.
3- Knowledge is either purely formal and analytic (e.g., mathematics and logic), or it is a kind of empirical science.
4- The purpose of philosophy is to explicate the structure or logic of science. Philosophy is really the epistemology of science and analysing concepts.
5- Logic is to be used to express precisely the relationships between concepts
6- The Verifiability Criterion of Meaning:
A statement is meaningful iff it is either analytic or empirically verifiable
7- The Verification Principle:
The meaning of a non-tautological statement is the method by which it can be shown to be true by experience (i.e. its ‘method of verification’)

Verificationism is the conjunction of commitments 6 & 7.

The Logical Positivism movement developed over three decades into Logical Empiricism, spanning topics in the unity of science, confirmation, explanation, probability and more.
We will focus on Ayer’s evolution of the Verification Principle.
We generally think that the observations we make are able to justify some expectations or predictions about observations we have not yet made, as well as general claims that go beyond the observed.
For example, the observation that bread of a certain appearance has thus far been nourishing seems to justify the expectation that the next similar piece of bread I eat will also be nourishing, as well as the claim that bread of this sort is generally nourishing.
Such inferences from the observed to the unobserved, or to general laws, are known as inductive inferences.

OBSERVATION STATEMENTS

The criterion of verifiability says that a sentence is meaningful iff it has some relation to observation. Historically, the form that formulations of this criterion took was to settle on a class of observation sentences, and then to claim that all and only sentences which bear a certain specified relation to these sentences will count as meaningful.

There were then two tasks to be accomplished:
(i) saying what an observation sentence is
and
(ii) spelling out the required relationship between meaningful sentences and observation sentences.

One main issue regarding (i) is whether the observation sentences are thought of as claims about sense data, or as claims about material objects. Intuitively it is hard to see how material object statements could count as observation sentences if one buys a sense datum theory of perception (as Ayer and many of the other logical positivists did); but if one takes sense datum statements as the observation statements, then one runs the danger of making the material object statements of, e.g., science come out meaningless.

This is not a result that Ayer and the other logical positivists were prepared to accept; in their view, scientific and common sense claims made on the basis of sensory experience were the paradigm cases of meaningful utterances, and the question was whether other claims of philosophy should also be categorized as meaningful.

In what follows we’ll abstract away from the nature of observation sentences; we can take them loosely to include both sense datum statements and the material object statements corresponding to them, and focus instead on the relationship between a sentences which are not observation statements in either sense and observation required for the former to be meaningful.

Verifiability in practice:

Statements that could be verified “if we took enough trouble”
eg All the cars in the parking lot have four wheels; This raven is black

Verifiability in principle:

Statements that cannot be verified due to practical considerations, but which we know what kind of observations would verify them.

Eg There are craters on Pluto; Some dinosaurs were green etc

“All ravens are black right now” — Verifiable in principle?
“All ravens have always been, and will always be, black” — Verifiable in principle?

STRONG VERIFIABILITY

Ayer discusses attempts to define meaningfulness in terms of what he calls strong verifiability — expanded here to conclusive verification or conclusive falsification defined as:

S is conclusively verifiable := some set O of observation statements entails S
S is conclusively falsifiable := some set O of observation statements entails ¬S

4.1 Conclusive verifiability

A natural first attempt at defining meaningfulness in terms of strong verification is to say that a sentence is meaningful iff it is conclusively verifiable.

As Ayer notes, there is a problem with this view:

“. . . if we accept conclusive verifiability as our criterion of significance, as some positivists have proposed, our argument will prove too much. Consider, for example, the case of general propositions of law — such propositions, namely, as “arsenic is poisonous”; “all men are mortal”; “a body tends to expand when it is heated.” It is of the very nature of these propositions that their truth cannot be established with certainty by any finite series of observations.” (37)

Ayer’s point here is a general one and it shows that universally quantified claims are not conclusively verifiable. Because these claims are nonetheless meaningful, the suggested criterion of meaning is not a good one.

4.2 Conclusive falsifiability

A second attempt is to say that a sentence is meaningful iff it is conclusively falsifiable or, as Ayer puts it, “definitively confutable.”

Ayer responds to this suggestion by claiming that no generalization can either be conclusively verified or falsified by experience, since an observation statement can only contradict a generalization with the help of other supporting propositions.

But this is not obvious; and anyway there is a simpler argument against the equation of meaningfulness with conclusive falsifiability.

Just as universal generalizations are not conclusively verifiable, existential generalizations are not conclusively falsifiable. E.g., ‘There is at least one red swan.” It seems that no finite set of observation sentences can entail that this is false, for just the same reason that no finite set of observation sentences can entail that the universal generalization “All swans are non-red” is true.

4.3 Conclusive verifiability or falsifiability

This result suggests an obvious way of extending our first two attempts to define meaningfulness in terms of strong verification: we can claim that a sentence is meaningful iff it is either conclusively verifiable or conclusively falsifiable. This seems to deal with simple universal generalizations, since they are conclusively falsifiable, and with simple existential generalizations, since they are conclusively verifiable.

This seems to run into the following three problems:

4.3.1 Mixed quantification

There is still a problem in dealing with sentences which contain both universal and existential quantification, like:

‘For every question, there is an answer’

which may be formalized as:
∀x (x is a question → ∃y (y is an answer to x))

We know that this claim is not conclusively verifiable, for the same reason as ‘All swans are white’ is not conclusively verifiable: no finite set of observation statements entails the truth of a claim about all the questions.

So if it is to be meaningful, it had better be conclusively falsifiable. But it isn’t. To conclusively falsify a claim is to be able to derive its negation from a finite set of observation statements. In this case, we’d have to be able to derive:

¬∀x (x is a question → ∃y (y is an answer to x))
which is equivalent to

∃x ¬ (x is a question → ∃y (y is an answer to x))
equivalent to

∃x (x is a question & ¬ ∃y (y is an answer to x))
equivalent to

∃x (x is a question & ∀y ¬ (y is an answer to x))

So for our original sentence to be conclusively falsifiable, we have to be able to derive the above from some set of observation sentences. But we can’t: to derive this from a set of observation sentences, we’d have to be able to derive from such a set the universal claim that there is some question such that every answer fails to be an answer to that question. But we can no more derive this from a set of observation sentences than we can derive “All swans are white” from such a claim.
The problem here stems from the fact that conclusive falsifiability of a sentence is just conclusive verifiability of its negation, and if a sentence contains both existential and universal quantification in the above way, then both it and its negation will be universal claims.
So the claim that a sentence is meaningful iff it is either conclusively falsifiable or conclusively verifiable entails that all sentences of mixed quantification like the above are meaningless. But again, the positivists were not willing to accept this result.

4.3.2 ‘Most’ and other quantifiers

Another problem stems from certain quantifiers other than the universal and existential quantifiers, like ‘most.’ Consider, e.g,

Most ravens are black.

How would you go about trying to either conclusively verify or falsify this sentence on the basis of observation sentences?

One plausible idea: we could conclusively verify this sentence, it seems, if we could add to the list of observation sentences a general claim like ‘These are all the ravens.’ This general claim is conclusively falsifiable, and hence meaningful. So one wants to formulate a more general criterion, which gives a step-by-step analysis of meaningfulness, along the following lines:

S is meaningful iff either it or its negation are entailed by a set of sentences containing only observation sentences, sentences which are conclusively verifiable or falsifiable, and other sentences already qualified as meaningful by this test.

This resembles the test that Ayer eventually suggests.
But this kind of stepwise definition in terms of strong verification is challenged by a third problem

4.3.3 Statements about unobservables

Consider, for example, claims about electrons. Electrons are not directly observable; rather, they are postulated to explain phenomena which are observable. But just because the postulation of electrons explains observable phenomena, it does not follow that claims about electrons may be derived from observation sentences. But the positivists were, for good reason, reluctant to consign claims about electrons to the same category as metaphysical claims like “The Absolute is lazy.”

WEAK VERIFIABILITY

Ayer suggests a new approach:

“Accordingly, we fall back on the weaker sense of verification. We say that the question that must be asked about any putative statement of fact is not “Would any observations make its truth or falsehood logically certain?” but simply, “Would any observations be relevant to the determination of its truth or falsehood?” And it is only if a negative answer is given to this second question that we conclude that the statement under consideration is nonsensical.”

This move from focusing on what can be derived from observation claims to focusing on what observation claims might be relevant marks an important shift between two different ways of thinking about the criterion of verifiability.

But as Ayer notes, we need to be a bit more specific than this in formulating a weak criterion of verifiability. He gives two precise ways of formulating the basic intuition here

5.1 Ayer’s first definition

Ayer gave the following account of verifiability in the first edition (1936) of Language, Truth and Logic:

“Let us call a proposition which records an actual or possible observation an
experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.”

We can formulate this as follows:

S is meaningful iff there is some set of sentences S*and some observation sentence O such that
(i) O follows from S together with S*
AND
(ii) O does not follow from S* alone.

While this formula is fairly abstract, there is a simple and plausible thought behind it.

Ayer’s idea was that, given the failure of strong verification analyses of meaningfulness, verifiability cannot amount to equivalence or entailment relations between a sentence and some set of observation sentences; rather, what we want is a clear way of stating the thought that a sentence, even if not equivalent to a set of observation sentences, makes some difference to what is observable. This is what Ayer’s definition tries to capture.
It says, plausibly, that a sentence has empirical consequences, and hence is meaningful, if adding it to some stock of propositions changes which observation sentences follow from that stock of propositions.
This definition seems to do well with the cases which proved problematic above. Let’s examine them:

5.1.1 Sentences of mixed quantification eg. ‘Every liquid has a boiling point’

Consider the sentence ‘x is a liquid.’ By itself, it does not follow from this that ‘x has a boiling point’ is true. But it does follow from this sentence along with our example sentence that ‘x has a boiling point’ is true. So we get the good result that sentences like this one can be meaningful.

5.1.2 Other quantified sentence, eg. ‘Most apples are red’

Consider the sentence ‘These five items are all the apples.’ From this, it does not follow that ‘Three of these items are red’. But it does follow if we add the premise ‘Most apples are red’. Hence the latter claim qualifies as meaningful.

5.1.3 Statements about unobservables eg. ‘x is composed primarily of H2O molecules’

To see how this might work, note that we can have conditionals connecting claims about unobservables with observation statements. For example, consider ‘If a substance is composed primarily of H2O molecules, then it will boil at 100°C.’ From this, it does not follow that for some specified x, ‘x will boil at 100°C.’ But it does follow if we add a statement about unobservables: ‘x is composed primarily of H2O molecules’; hence we can count this statement, correctly, as meaningful by Ayer’s new criterion.

5.1.4 Restrictions on S*

There is, however, a problem implicit in the way that we just handled the case of statements about unobservables which is devastating to Ayer’s definition. This was pointed out by Isaiah Berlin. The problem is, intuitively, that when we go to decide whether a given sentence S is meaningful, we try to find some proposition or set of propositions S* such that, when we add S to S*, we can derive some observation sentence not derivable from S* alone; but there are no restrictions at all put on what S* can be.

The result is that we can derive from Ayer’s first definition the unwanted result that every sentence is verifiable, and hence meaningful. Consider the sentence:

‘The absolute is lazy’

Is there any sentence which, combined with this sentence, entails an observation sentence it does not entail by itself? The conditional sentence ‘If the absolute is lazy, then this is red’ is such a sentence.
In general for any sentence S, we can prove that S is meaningful by deriving from it together with the conditional S → O the observation sentence O.

5.2 Ayer’s second definition

Accordingly, in the second edition of the book (1946), Ayer gave a new account of the principle of verifiability. His aim was to stick with the spirit of his 1936 definition, while placing restrictions on the class of ‘supplementary propositions’ which could be used to derive an observation statement from a given sentence.

To this end, he distinguished between direct and indirect verifiability

Sentence S is Directly Verifiable :=
(i) S is an observation statement
OR
(ii) S entails in conjunction with a set of observation statements O* some observation statement O not entailed by O* alone.

Sentence S is Indirectly Verifiable :=
(i) S entails in conjunction with a set S* of statements some observation statement O not entailed by S* alone
AND
(ii) There is no statement in S* which is not either (a) directly verifiable, (b) analytic, or © capable of being independently shown to be indirectly verifiable.

The central claim of the theory is then:

A sentence is meaningful iff it is either directly or indirectly verifiable.

5.2.1 Hempel’s objection

Hempel’s objection stated in his “The Empiricist Criterion of Meaning” assumes the following two plausible claims:

(H1) A sentence is meaningful iff it is true or false.
(H2) For any sentence S, S is true iff ¬S is false.

Now take any true meaningful sentence (it can be an observation sentence, or not) like ‘This is red.’ Consider the conjunction

‘This is red and the Absolute is lazy’

This sentence must be meaningful, since it entails the observation sentence ‘This is red.’ So by (H1) it must be either true or false.

Suppose first that the sentence is true. Then it follows that ‘The Absolute is lazy’ must be true as well, since the truth of a conjunction entails the truth of its conjuncts. But then by (H1), it must be meaningful.

Suppose then that the sentence is false. Then by (H2), its negation must be true; and if both ‘Not (This is red and the Absolute is lazy)’ and ‘This is red’ are true, we know that ‘Not (The Absolute is lazy)’ must be true. But then we know by (H2) again that its negation ‘The Absolute is lazy’ must be false. But then it follows from (H1) that ‘The Absolute is lazy’ is meaningful.

So again a formulation of the principle of verifiability leads to the result that all sentences are meaningful.

How might Ayer respond to this argument? Is it plausible to deny (H2)?

5.2.2 Church’s objection

In his review of the second edition of Language, Truth, & Logic, Alonzo Church provided an argument for the same conclusion which made do with less substantial assumptions than 1 and 2.
Assume the following:

There are at least three observation sentences p, q, r, none of which entail either of the others.

Now we can take any sentence s — even a nonsense sentence like ‘The Absolute is lazy’ — and form the following complex sentence:

(1) (¬p & q) ∨ (r & ¬s)

Now note that sentence (1) counts as directly verifiable.
[Proof: p is an observation sentence; the conjunction of sentence (1) with p entails r; and r is an observation sentence which, by hypothesis, is not entailed by p alone.]

q is either entailed by sentence (1), or it is not. Either way, s will end up counting as meaningful.

Suppose first that q is not entailed by (1). Then, since q is entailed by the combination of (1) and s, and (1) is directly verifiable, s counts as indirectly verifiable.

Suppose now that q is entailed by (1) alone. Then q must be entailed by both of its disjuncts; in particular it must be entailed by its right-hand disjunct, which we label as sentence (2):

(2) r & ¬s

If (2) entails q, then the negation of s must be directly verifiable.
[Proof: if (2) entails q, then the conjunction of ¬s with r entails q; but q is not, by hypothesis, entailed by r alone.]

But since the negation of a directly verifiable statement is always indirectly verifiable, and hence meaningful, it follows that if q is entailed by (1), then s must be indirectly verifiable, and hence meaningful.
So whether or not q is entailed by (1), s is counted as meaningful — again, no matter what it is.

Bibliography

Hempel, Problems and Changes in the Empiricist Criterion of Meaning
Soames, Philosophical Analysis in the 20th Century Vol.1 via Jeff Speaks
Ladyman, Understanding Philosophy of Science
https://plato.stanford.edu/entries/logical-empiricism/