BP Psychology and Science

Chapter 4: Deriving theories from the facts: induction

Logic: concerned with the deduction of statements from other, given, statements. It is concerned with what follows from what

Example 1:

1. All books on philosophy are boring.

2. This book is a book on philosophy.

3. This book is boring.

(1) and (2) are the premises and (3) is the conclusion. It is evident, I take it, that if (1) and (2) are true then (3) is bound to be true. It is not possible for (3) to be false once it is given that (1) and (2) are true. To assert (1) and (2) as true and to deny (3) is to contradict oneself. This is the key feature of a logically valid deduction. If the premises are true then the conclusion must be true. Logic is truth preserving.

Example 2:

1. Many books on philosophy are boring.

2. This book is a book on philosophy.

3. This book is boring.

• In this example, (3) does not follow of necessity from (1) and (2). Even if (1) and (2) are true, then this book might yet turn out to be one of the minority of books on philosophy that are not boring. Accepting (1) and (2) as true and holding (3) to be false does not involve a contradiction. The argument is invalid.

Example 3:

1. All cats have five legs.

2. Sputnik is my cat.

3. Sputnik has five legs.

• This is a perfectly valid deduction. If (1) and (2) are true then (3) must be true. It so happens that, in this example (1) and (3) are false. But this does not affect the fact that the argument is valid.

Scientific knowledge cannot be derived from the facts if ‘derive’ is interpreted as ‘logically deduce’

Example:

Premises:

1. Metal x1 expanded when heated on occasion t1.

2. Metal x2 expanded when heated on occasion t2.

n. Metal xn expanded when heated on occasion tn.

Conclusion:

All metals expand when heated.

• This is not a logically valid argument. It lacks the basic features of such an argument. It is simply not the case that if the statements constituting the premises are true then the conclusion must be true.
• Arguments of this kind, which proceed from a finite number of specific facts to a general conclusion, are called inductive arguments, as distinct from logical, deductive arguments.

If an inductive inference from observable facts to laws is to be justified, then the following conditions must be satisfied:

1. The number of observations forming the basis of a generalisation must be large.

2. The observations must be repeated under a wide variety of conditions.

3. No accepted observation statement should conflict with the derived law.

The principle of induction: if a large number of As have been observed under a wide variety of conditions, and if all those As without exception possess the property B, then all As have the property B.

Problems with induction:

• The demand for large numbers of observations -‘large’ is vague
• What counts as a significant variation in circumstances?
• One attempt to avoid the problem of induction involves weakening the demand that scientific knowledge be proven true, and resting content with the claim that scientific claims can be shown to be probably true in the light of the evidence.

Valid logical argument:

1. Fairly pure water freezes at about 0°C (if given sufficient time).

2. My car radiator contains fairly pure water.

3. If the temperature falls well below 0°C, the water in my car radiator will freeze (if given sufficient time).

• Here we have an example of a valid logical argument to deduce the prediction 3 from the scientific knowledge contained in premise 1. If 1 and 2 are true, 3 must be true. However, the truth of 1, 2 or 3 is not established by this or any other deduction. For the inductivist the source of scientific truth is experience not logic.

The general form of all scientific explanations and predictions can be summarised thus:

1. Laws and theories

2. Initial conditions

3. Predictions and explanations

We have been unable to give a precise specification of induction in a way that will help distinguish a justifiable generalisation from the facts from a hasty or rash one, a formidable task given nature’s capacity to surprise, epitomised in the discovery that supercooled liquids can flow uphill

Resources:

What is This Thing Called Science 4^th Edition (CHALMERS)