Chapter 2 Scientific Reasoning

Deduction and Induction Hume’s Problem

Inference to the Best Explanation (IBE) Probably and Induction

Deduction and Induction

• Logician make an important distinction between deductive and inductive patterns of reasoning.

• Deductive inference/reasoning has the following property: P and C have good relation.

• Inductive inference/reasoning : P and C have no relation.• Deductive is a much safer activity than inductive.• Scientists used inductive reasoning whenever they move

from limited data to a more general conclusion.

1st statement the premises of 2nd statement inference (P)3rd statement - the conclusion (C)

Hume’s Problem

Hume’s Problem

• David Hume (18th century Scottish philosopher, 1711-1776) argued that the use of induction can’t be rationally justified at all. We use induction all the time, in everyday life and in science, but he insisted this was just a matter of brute animal habit.

• Whenever we make inductive inferences, we seem to presuppose what he called ‘Uniformity of Nature’ (UN).

• UN is not always true. A ‘non-uniform’ universe is conceivable, it follows that we can’t strictly prove the truth of UN.

• If we could prove that UN is true, then the non-uniform universe would be a logical impossibility.

• Hume concludes that our confidence in induction is just blind faith – it admits of no rational justification whatever.

• If Hume is right about his opinion, the foundations on which science is built do not look quite as solid as we might have hoped. This puzzling state of affairs is known as Hume’s problem of induction.

• Peter Strawson respond to Hume’s problem: Induction is one of the standards we use to decide whether claims about the world are justified.

• Frank Ramsey, a Cambridge philosopher from the 1920s, said that to ask for a justification of induction was ‘to cry for the moon’.

Hume’s Problem

Inference to the Best

Explanation (IBE)

• Some philosopher describe IBE as a type of inductive inference to mean ‘any inference which is not a deductive’.

• ‘inductive inference’ is reserved for inferences from examined to unexamined instances of a given kind. So, IBE & inductive inference are them two different type of non-deductive inference.

• Scientist frequently use IBE, e.g. Charles Darwin in the theory of evolution, and Einstein’s famous work on Brownian motion.

Inference to the Best Explanation (IBE)

• Whether IBE or ordinary induction is a more fundamental pattern of inference?

• Gilbert Harman has argued that IBE is more fundamental, ordinary induction is ultimately dependent on IBE.

• Other said that IBE itself parasitic on ordinary induction.

• If we want to use IBE, we need someway of deciding which of the competing hypothesis provides the best explanations of the data – the simplest or the most parsimonious one.

Inference to the Best Explanation (IBE)

Probably and

Induction

• The concept of probability is philosophically puzzling.• The word ‘probability’ seems to have more than one

meaning.• The frequently interpretation of probability: it equates

probabilities with proportions or frequencies.• A statements probability is the measure of the

strength of evidence in its favor.• Most statistician would in fact favour the frequency

interpretation but the problem of how to interpret probability, like most philosophical problems, can’t be resolved mathematically.

Probably and Induction

• Philosophers of science are interested in probability for 2 main reasons:

• 1st is that in many branches of science (especially physics and biology) we found laws and theory that are formulated using the notion of probability, e.g.: the theory known as Mendelian genetics.

• 2nd is the hope that it might shed some light on inductive inference.

Probably and Induction

• There are 2 types of interpretation of probability: subjective and logical.

• The subjective interpretation of probability implies that there are no objective facts about probability, independently of what people believe.

• e.g.: Brazil will win the World cup.• The logical interpretation of probability holds that a

statement is objectively true or false, relative to a specified body of evidence.

• e.g.: 1 to 10 of all Englishwomen live to the age of 100• The logical interpretation of probability hold more promise of

a satisfactory response to Hume, than the subjective.• Unfortunately, most people today believe that the logical

interpretation of probability faces very serious, probably insuperable, difficulties.

Probably and Induction