3.1 (The Mother of All Problems, the Problem of Confirmation)

-> a.k.a. The Problem of the Confirmation of Theories

• How can observations confirm a scientific theory?

• What connection between observation and a theory makes the observation evidence for the theory?

Logical empiricists wanted to develop a logical theory of evidence and confirmation that treated confirmation as an abstract relation between sentences.

• Problem of Induction: Why should we expect past observations to hold in the future?

  • Similar, but not identical, to the Problem of Confirmation

David Hume, an inductive skeptic who claimed induction has no rational basis, in 1739 asked, “What reason do we have for thinking that the future will resemble the past?”

3.2 (Induction, Deduction, Confirmation, and Explanatory Inference)

Support for a theory ≠ Proving a theory
-> Logical empiricists believed evidence can support one theory over another, but evidence can never prove it because there’s always room for error.

Types of Inference:

1. Inductive Logic: Inferring to a generalization based on a set of previously observed cases.

2. Projection: Inferring to a prediction about the next case of something based on a set of previously observed cases.

3. Deductive Logic: Inferring to a particular case based on a generalization.

   • A theory of patterns of argument that transmit truth with certainty.

   • A conclusion in an argument is deductively valid (logically consistent) if it follows from the premises of the argument.

4. Explanatory Inference: Inferring to a hypothesis about a structure or process that would explain the data.

   • a.k.a. abductive inference, theoretical induction, explanatory induction, theoretical inference, inference to the best explanation

Logical Empiricist Theory of Confirmation:

• Emphasized logical analysis: The relationships between the statements that make up a scientific theory + the statements that describe observations = observations supporting theory

• Aimed for generalization: Scientific discovery should establish generalizations by forming and testing them via observations of objects and occurrences.

  • Inferences from observations that support a generalization are always non-deductive.

• Oversimplification: Used simplified and artificial cases rather than cases from real science.

  • Wanted to strip the Problem of Confirmation down to its bare essentials, which they saw in formal logic.

Hypothetico-deductivism: A theory of confirmation that posits that hypotheses in science are confirmed when their logical consequences turn out to be true -> a theory is confirmed when a true statement about observables can be derived from it.

3.3 (The Ravens Problem)

How is it that repeated observations of black ravens can confirm the generalization that all ravens are black?

Hempel’s View:

Logical equivalence: What we have when two sentences say the same thing in different terms.
* If H is logically equivalent to H* then it’s impossible for H to be true but H* to be false, or vice versa.
* Problems with logical equivalence:
* All ravens are black -> all non-black things are not ravens
* Anything that confirms one will confirm the other

Good’s View:

An observation may or may not confirm a hypothesis depending on other factors and preexisting knowledge and assumptions that the observer possesses. The relevance of an observation to a hypothesis isn’t a simple matter of the content of the two statements – it depends on other assumptions as well.

Good’s View Expanded Upon:

Whether or nor an observation confirms a hypothesis depends on the order in which you learn about the properties of the subject in question. There is only confirmation when the observations arise during a genuine test that has the potential to disconfirm as well as confirm.

Godfrey-Smith’s View:

We can only understand confirmation and evidence by taking into account the procedures involved in generating data.

Wason Selection Task Experiment in psychology: Which masks do you have to remove to know whether it’s true that if there is a circle on the left of a card, there’s a circle on the right as well?

• Many people make logical errors in certain circumstances regardless of intelligence or education level.

• Same structure as the Ravens problem

• Not all observations of cases that fit a hypothesis are useful as tests.

3.4 (Goodman’s “New Riddle of Induction”)

Goodman wanted to show that there can’t be a purely formal theory of confirmation.

• The deductive validity of arguments depends only on the form or pattern of the argument, not the content -> major feature of deductive logic

• Two inductive arguments can have the same form, but one of them can be good while the other is bad, so form is not what determines whether an inductive argument is good or bad

  • Thus, there can be no purely formal theory of induction and confirmation.

  • Whether an induction is good or bad depends on what language we treat as our starting point

• A good theory of induction should include a restriction on the terms that occur in inductive arguments (green vs grue emerald example).

1. One line under an argument means it’s supposed to be deductively valid.

2. Two lines under an argument means it’s not supposed to be deductively valid.

Goodman’s Problem encapsulates within it several distinct hard methodological issues in science:

1. Curve-fitting problem in data science

2. Natural kind problem - a collection unified by real similarity as opposed to stipulation or convention. How do you get the right categories for prediction and extrapolation?

   • Important in sciences the deal with complex networks of similarities and differences across the cases they try to generalize about