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Chapter 3

# PHIL 2180 Chapter Notes - Chapter 3: Rudolf Carnap, Deductive Reasoning, Inductive Reasoning

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**preview**shows half of the first page. to view the full**1 pages of the document.**Chapter3: Induction and Confirmation

Problem of Induction: Question of whether inductive reasoning leads to knowledge understood in the classic

philosophical sense. What reason do we have for thinking that the future will resemble the past?

David Hume: Scottish empiricist in the 18th century who constructed and believed in the problem of induction.

Problem of Confirmation: Notion that evidence (data, premises) can affect the credibility of hypotheses

(theories, conclusions). Does observational evidence provide support for a scientific theory?

Logical empiricists wanted a theory of evidence or “theory of confirmation” that would cover the problem of

confirmation. They believed all evidence derives from observation.

Deductive Logic: Well understood and less controversial kind of logic. If the “premises” of the argument are

true, the conclusion is guaranteed to be true. If it has false “premises,” the conclusion may be false.

Empiricists believed that the key idea was that science aims at formulating and testing generalisations.

Inductive Logic: The use of premises that seek to supply strong evidence for (not absolute proof of) the truth of

the conclusion. Categorized as all good arguments that are not deductive.

Abductive Inferences/Logic: An explanatory inference. Conclusion to the best explanation.

Projection: Inferring from a number of observed cases to arrive at a prediction about the next case, not to

generalize about all cases.

Logical Empiricists Approach to Non-Deductive Inference:

1. Formulate and inductive logic that looked as much as possible like deductive logic. Carl Hempel.

2. Apply the mathematical theory of probability:

Reasoning written as a ratio of the number of favorable outcomes to the number of possible

outcomes.

Rudolf Carnap used probability theory to understand confirmation.

Hypothetico-Deductivism: Testing hypotheses and determining whether their logical consequences are

consistent with observed data.

Logical Equivalence: When two sentences say the same thing in different terms.

The Ravens Problem:

“All ravens are black.”

Is logically equivalent to…

“All nonblack things are not ravens.”

So, if you observe a white shoe, the theory is proved as the logical equivalent is true, therefore the

original must also be true, even though not all ravens are black.

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