Very Incomplete Notes for
An Introduction to the Philosophy of Science 
by Rudolf Carnap

Laws of science are statements expressing regularity. Laws can be universal
or statistical.  (3) 

Question in philosophy of science: How do we go from singular statements or
facts to universal statements or laws?  By observing regularities. (5)

What good are laws?  They are used to explain facts already known and to
predict facts not yet known. (6)

Deductive logic can be used to infer unknown facts from unversal laws, but
the logic of probability must be used from statistical laws. (19)

The most we can say of inductive conclusions is that the conclusion has a
certain degree of probability. Because we can only make finitely many
observations, we can never arrive at complete verification of a law.  Laws
are not verified, but rather falsified or confirmed. (21)

According to Reichenbach and Mises, the concept of probability should be
based on the limit of a relative frequency in an infinite series of
observations. (27)

According to Keynes, Jeffreys, and Carnap, probability refers not to a
frequency but a logical relation.  In some cases, probabilities can be
assigned. (31)

Both statistical and logical probability may occur together in the same
chain of reasoning. (39)

There are two ways of obtaining observations: passively as onlookers
(astronomy) or actively via the experimental method.  Using the experimental
method (especially for quantitative concepts), we determine relevant
factors, devise an experiment, and aim to find laws that connect all the
relevant magnitudes measured. (42)

The concepts of science may be divided into three groups: classificatory,
comparative, and quantitative. (51)

Rules for the process of measuring: define comparison, equality, zero, unit,
and scale. (64)

Carnap sees Hume's analysis of causality as a reject of necessity in
causality.  So single cause can be singled out as the cause.  Processes, not
things, cause events. (190)

Causal relation means predictability. (192)

To say that event B is caused by event A is to say that there are certain
laws in nature from which event B can be logically deduced when combined
with event A. (194)

Some empiricists hold that laws are merely universal conditional statements. 
Others (against Hume) believe laws imply necessity, that things could not be
otherwise. (198)

Claims about causes and effects are claims about instances of general laws.
(204)

Laws, as opposed to accidental universal statements, support
counterfactuals. (210)

A statement is causally true if it is a logical consequence of basic laws.
(214)

Determinism (Newtonian, Laplacian) is the thesis tht causal structure is so
strong that given a complete description of the world at one instant in
time, any event in he past or future can be calculated.  Quantum mechanics
goes the other extreme; the causal structure is not deterministic but
probabilistic (seemingly random).  Neither view is incompatible with free
will. (217)

Empirical laws can be confirmed directly by empirical observations. 
Theoretical (or hypothetical) laws refer to unobservable entitites, such as
molecules, atoms, electrons, protons, and electromagnetic fields. (227)

Theoretical laws are more general than emprical laws.  Theoretical laws
cannot be arrived at simply be generalizing empirical laws.  Theoretical
laws are related to empirical laws in a way somewhat analogous to the way
empirical laws are related to single facts.  Theoretical laws help explain
empirical laws already formulated and permit the derivation of new empirical
laws.  Theoretical laws start not with generalizations but with hypotheses. 
A hypothesis is tested by testing empirical laws which are derived from the
hypohtesis.  (230)

Theories from which more laws empirical laws can be derived are more
general, stronger theories.  Theories make it possible to derive/predict new
empirical laws which can be confirmed.  This is the supreme value of new
theories. (231)

It is an oversimplification to say that empirical laws are derived
(directly) from theoretical laws, because theoretical laws contain
theoretical terms whereasempirical laws contain only observable ones. 
Correspondence rules are needed to translate between nonobservables and
observables. Correspondence rules don't define theoretical terms in terms of
observable terms; they define observable terms in terms of theoretical ones.
(233)

Theories are underlying principles which unify hundreds of (otherwise
seemingly-unrelated) empirical laws.  Example's include Maxwell's equations
explaining electrical, magnetic, optical, radio waves, and X-rays laws and
Newton's physics unifying celestial and terresrial mechanics.  (244)

The history of science is that of creativity and visions.  Democritus
postulated atoms before there was any confirmation, Mendel postulated genes,
Newton postulated gravity, etc.  In all these cases, it's not that the
answer was so difficult to give, but that no one had asked the question.
(246)

According to Quine, analytic truths of the observational (rather than logical) language cannot
be understood until the meanings of all of their descriptive terms are
understood.  "No bachelors are married" isn't logically analytic, but is
analytic once we understand the meaning of 'bachelor'.  Can a sharp
distinction be made between analytic and synthetic statements?  Carnap
thinks so; Quine doesn't. (259)

Whatever sort of causality there is in the world is best expressed by the
laws of science. (277)

Deterministic laws say that under certain conditions certain things will be
the case.  Statistical laws state probability distributions rather than
certainties. Until recently, no one imagined that statistical laws indicated
an absence of determinism; rather, they indicated a current lack of
knowledge/precision which could be improved. (278)

The nondeterministic character of quantum mechanics rest on Heisenberg's
uncertainty principle (for certain pairs of magnitudes such as position and
momentum, it is impossible to measure both at the same instant with high
precision.  Quantum theory is fundamentally indeterministic in that it
supplies probabilities, not definite predictions, for the reults of
measurements.  The causality and structure of laws in physics is now very
different from in Newtonian physics.  This is leading to changes in the
language of physics. (286)