Theory



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

|T T | T |

|T F | F |

|F T | T |

|F F | 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 P ( Q

~Q ~P

-------- -------

~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)

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