A Historical Introduction to the
Philosophy of Science
Ch. 12: Logical Reconstructionist Philosophy of Science
The following is a summary of the twelfth chapter of John Losee's book, A Historical Introduction to the Philosophy of Science (fourth edition), with some ancillary notes.
Philosophers discussed in this chapter: Percy Williams Bridgman (1882–1961); Carl Hempel (1905–97); Ernest Nagel (1901–87)
A Hierarchy of Language Levels
(p. 159) From the 1940s, philosophers of science sought to take Campbell's lead in reconstructing science as built on the foundations of a logical axiomatic system. They concerned themselves only with the logic of justification and not with the context of discovery.
(pp. 159–60) The logical reconstructionists identified four levels in the language of scientists, from apex to base:

Theories – laws are theorems in deductive systems

Laws – Invariant/statistical relations between concepts

Values of concepts – values assigned to scientific concepts

Primary experimental data – observational statements about readings
The logical reconstructionists concluded that:

Each level interprets the level below.

Predictive power increases from base to apex.

Principal division is between the bottom three observational levels and the theoretical/nonobservable level at the top.

Statements at the observational levels are test cases for theoretical statements.
Operationalism
(p. 160) Drawing on Einstein's analysis of simultaneity of two events, Bridgman argued that scientific concepts (third level) only gain significance by being linked to operations that assign them specific values.
(p. 161) For Bridgman, operational definitions link concepts (third level) to primary experimental data (fourth level) via the logical operational schema:
(x) [Ox ⊃ (Cx ≡ Rx)]
'For all operations performed, this particular concept applies only if this result occurs.'
[LA: the logical notation is:
(x) for all x (where x is a variable)
⊃ conditional (if ... then)
≡ bicondional (if and only if)
O, C, R predicates]
E.g., for all objects brought near a neutral electroscope, the object is electrically charged if and only if the leaves of the electroscope diverge.
Bridgman allowed some theoretical concepts even though the operations to determine their value were 'paper and pencil' calculations using a mathematical theory (e.g., 'stress').
(p. 162) Bridgman recognized two limitations of his operationalism:

impossibility of specifying all the circumstances required for an operation (e.g., for gas pressure, specifying sunspot activity is irrelevant)

of necessity, some operations remain unanalyzed (e.g., for measuring relative weight, not necessary to specify operations for making beam balances)
(pp. 162–3) For Bridgman, decisions to consider particular operations unanalysed by the scientific community are provisional only. All operations are, in principle, further analyzable.
The Deductive Pattern of Explanation
(p. 163) Hempel and Oppenheim saw scientific explanation as a logical deduction of a description of a phenomenon from general laws in conjunction with statements of antecedent conditions (e.g., Why does an oar appear bent in water?).
Logical reconstructionists used this pattern of deduction to:
 explain a value of a scientific concept (third level) by reference to a law (second level); and
 confirm a law (third level) by reference to the value of a scientific concept (second level)
(p. 164) Antecedent conditions include both boundary conditions and initial conditions.
Two examples:

explanation of the expansion of a heated balloon using GayLussac's Law
[LA: V = volume; T = absolute temperature] 
explanation of the dominance a species of finch on an offshore island
(p. 165) For Hempel and Oppenheim, for a successful deductive explanation:
 the conditional premise must be a true law
 statements about initial and boundary conditions must be true
Hempel and Oppenheim allowed for some explanations to be statistical/inductive (e.g., probability of a patient recovering from an infection).
Nomic v. Accidental Generalizations
(p. 166) Logical reconstructionists accepted Hume's skepticism about the necessary nature of scientific laws.
But Hume's analysis using constant conjunction fails to distinguish lawlike universals from accidental universals (e.g., Losee's synchronous ticking of two pendulum clocks).
Two problems for Hume's 'constant conjunction' account of scientific laws:

Genuine scientific laws (but not accidental generalizations) support counterfactual conditional statements.

Some scientific laws refer to nonexistent idealized entities.
(pp. 166–7) Braithwaite solved the problems by pointing out that genuine scientific laws (and not accidental generalizations) are deduced from higherlevel hypotheses, evidence for which is independent from the evidence for the lower level law (e.g., barium flame colour deduced from postulates of atomic theory).
(p. 167) Nagel supported Hume's account of scientific laws by distinguishing four characteristics of genuine laws:

Laws are not made true simply by virtue of the entity referenced not existing.

The scope of prediction of a law is not restricted.

Entities referred to in laws are not restricted to existing in particular times or places.

Laws are mutually and indirectly supported by other laws within the same axiomatic system.
The Confirmation of Scientific Hypotheses
(pp. 167–8) Hempel proposed three phases in the logical confirmation of a scientific theory:

collect experimental results

analyze whether the experimental results confirm a hypothesis

decide whether the hypothesis is true in light of the results
Phase 2 is the problem of how to confirm a theory as true for which Hempel thought the solution lay in the application of formal logic.
(p. 168) The raven paradox shows how both a black shoe (∼Ra ⋅ Ba) and a white glove (∼Ra ⋅ ∼Ba), counterintuitively, logically support the scientific law: 'All ravens are black'.
[LA: Note that Losee's third listed proposition is inadvertently missing the universal quantifier (x).]
[LA: the logical notation is:
∼ negation (not ...)
∨ disjunction (or ...)
⋅ conjunction (... and ...)
a constant (this shoe; this glove)
R raven
B black]
(p. 169) Hempel sought to dismiss the raven paradox by rejecting our common intuitions about confirmation of laws. He maintained that:

'All ravens are black' is about all objects in the universe (for all objects, if it is a raven, then it is black); and

Our background knowledge about ravens includes there being many more nonblack objects than ravens (hence, greater chance of disconfirmation if we focus on ravens)
(p. 170) Carnap's project of quantitatively measuring the degree of theory confirmation sought to:

develop an artificial language of measurement

use probability theory to assign degrees of confirmation

show how the calculated values align with our intuitions
Counterintuitively, Carnap's mathematical function for degree of confirmation rendered universal conditionals with infinitely many possible instances with a probability of zero.
Carnap's controversial solution was to redirect from confirmation of a universal generalization over large numbers to confirmation of the next observed instance of the generalization.
The Structure of Scientific Theories
(p. 171) The logical reconstructionists continued Campbell's 'hypothesisplusdictionary' analysis of the relationship between axiomatic theories and observation statements.
(p. 172) Hempel likened the relationship to that of a safety net (axioms) supported by rods from below (observation statements), with not every knot (undefined theoretical term) in the net separately supported by a rod.
[LA: Note that the diagram in the text incorrectly links observations with undefined terms. According to Campbell, the links are only to defined terms.]
To the question about what is a sufficient amount of support for a theory, Hempel looked to a theory of confirmation. He conceded in 1952 that finding such a theory is a future project.
Braithwaite and Koertge see the empirical significance of a theory as seeping upwards from observation statements to the defined and undefined terms in the axiom system.
Theory Replacement: Growth by Incorporation
(pp. 172–3) The logical reconstructionists noted in the history of science increasing explanatory breadth through 'growth by incorporation' of lowerlevel laws.
(p. 173) Nagel identified two types of incorporation/reduction:

homogeneous reduction – incorporated and incorporating theories substantially use the same concepts (e.g., Galileo's law of falling bodies incorporated into Newtonian mechanics)

heterogeneous reduction – incorporated and incorporating theories use different concepts, where incorporating theory refers to microstructure of objects (e.g., classical thermodynamics incorporated into statistical mechanics)
For Nagel, the formal and nonformal conditions for heterogeneous reduction are:

connectability – theoretical terms in the reduced theory are linked to terms in the reducing theory

derivability – experimental laws in the reduced theory are deducible from the reducing theory

empirical support – evidence supporting the theoretical assumptions of the reducing theory are in addition to that supporting the reduced theory

fertility – theoretical assumptions of the reducing theory suggest further development of the reduced theory
(p. 174) Bohr likened the absorption of lowerlevel theories into those at a more general level as an expanding nest of Chinese boxes that illustrate his Correspondence Postulate.
Bohr, and later Agassi, articulated the extension of the Correspondence Postulate as criteria for the successful absorption of one theory by its successor. For one theory to succeed another, the new theory must:

have greater testable content than its predecessor; and

be in asymptotic agreement with its predecessor where its predecessor succeeded
Questions to Consider:

How successful is Bridgman's operationalism at avoiding the necessity of providing an analysis for every aspect of an operation used in an experiment?

Did Braithwaite successfully distinguish genuine scientific laws that support counterfactuals from accidental generalizations?

Do you think the raven paradox is a defeater for Hempel's view of theory confirmation?

How important do you think is growth by incorporation to the progress of science?