PHIL 460 Oct. 3
Theories as sentences
From logical empiricism through the 1980s
Universal sentences or statements (laws, generalizations)
Singular sentences or statements (observation reports)
Then the relationship between what is observed or experienced and a theory
is a logical relationship (valid or invalid, inductively strong or weak)
And all the theories of science are comprised of statements that are either
analytic (definitions, mathematics, and logic) or synthetic (the empirical
sciences)
“Where neither confirmation nor refutation is possible, science is not
concerned,” Ernst Mach.
Distinguishing between “the context of discovery” and “the context of
justification”
Possible definitions of a theory
Any set of sentences (including sets with one member) whose members are
declarative sentences
A set of sentences (including sets with one member) that constitutes an
explanation
A set of sentences (including sets with one member) that constitutes an
explanation and yields one or more predictions
A set of sentences that constitutes an explanation and yields predictions
about unobservable events, objects, forces, and so forth.
A set of sentences that includes laws
A set of sentences that began as a hypothesis (or group thereof) and has been
tested and/or confirmed to a sufficient degree
Explanation
To explain some phenomenon P is to subsume it under a law or set of
laws and a set of initial conditions
To explain some phenomenon P is to provide an answer to a “why?”
question that is such that both it and the answer are acceptable for a given
purpose/to a given community
Causation
Humean: “We say “A is the cause of B when B is always preceded by A”
(there are no known counter-examples) – in other words, cause just is
“constant conjunction”
Counterfactual: “If it had been the case that A, then it would have been the
case that B” iff there is an auxiliary set S of true statements consistent with
the antecedent A such that the members of S, when conjoined with A, entail
the consequent B.
One problem with counterfactuals:
P  Q is false iff P is true and Q is false
Laws, explanation, and prediction
Universal statements
All A’s are B’s
(x) (Ax  Bx) or ~(x) (Ax & ~Bx)
E: The water in my car radiator is frozen
L: All things being equal, relatively pure water freezes at 32 degrees
C: My car radiator contains relatively pure water and it was below 32
degrees last night.
E: The water in my car radiator will freeze tonight if I don’t add anti-freeze
L: the same
C: The relatively pure water in my radiator and the predicted temperature
Justification: how to distinguish between good theories and bad (as
importantly, how to judge one good theory better than another good
theory)?
Rosso: with ‘good’ understood as “it is reasonable to believe that the
theory is true”
Alternative: with ‘good understood as “it is reasonable to pursue the
theory”
Theoretical virtues as criteria for evaluating a theory … because we
cannot assess a theory’s “correspondence” to that it seeks to explain – we
cannot assess its accuracy?
Features of a theory we are able to evaluate and that are relevant to “its
likely truth” OR its promise and acceptability in guiding research
Internal: Truth-conducive? Pragmatic? Aesthetic? Psychological?
Entrenchment (conservatism or consistency with other accepted theories)
Explanatory cooperation (explanatory of other theories)
Testability
Generality
Simplicity
External:
Explanation (explanatory power)
Testing and confirmation (predictive success)
Empirical accuracy
PHIL 460 Oct. 5
Key topics:
Logic of confirmation
Critique of “narrow” inductivism
Alternative: “sophisticated” inductivism
Auxiliary hypotheses
Crucial tests
Ad hoc hypotheses
Empirical content and testability
Argument forms
Material conditionals: P  Q
P is the antecedent; Q is the consequent;  is the logical operator
P Q P Q
TT
T
TF
F
FT
T
FF
T
An argument is valid iff it is not possible for the premises to be true and the
conclusion false.
An argument is invalid iff it is not valid.
Valid argument form:
Invalid argument form:
Modus tollens
Denying the antecedent
PQ
~Q
-------~P
PQ
~P
------~Q
Valid argument form:
Invalid argument form:
Modus ponens
Affirming the consequent
PQ
P
------Q
PQ
Q
------P
If you studied, you did well in the course.
You did well in the course.
-----------------------------------------------You studied.
If you studied, you did well in the course.
You didn’t study.
-------------------------------------------------You did not do well in the course.
Auxiliary hypotheses:
H

I
If the earth is moving, then we will observe stellar parallax.
Not I
We do not observe stellar parallax.
-----------------------------------------------------------------------------Not H (the earth is not moving)
A: the stars are close enough that parallax would be observable by the naked
eye.
Ad hoc hypotheses:
Galileo: Looking through the telescope one can see that the moon’s surface
is not a perfect sphere, but earthlike – with mountains, valleys, and craters.
His opponents: It is a perfect sphere; there is crystalline invisible to us that is
filling in the craters, etc.
Galileo: Okay, you’re right. There is invisible crystalline, but it’s actually on
top of the mountains making them higher than they appear. (Game, set,
match)
Crucial tests: what is being tested?
H1  E1 but H2  E2
If the result is E2, we have shown (can conclude) ~H1
T  (H  E)