Epistemology

Tihamér Margitay – Péter Hartl

3. Induction

The growth of our knowledge

Instead of trying to give responses to scepticism, we are going to examine these kind of questions:

What are the sources of our knowledge?

What is the basis of our knowledge?

Sources: Perception, memory, inference, (testimony)

How can we acquire knowledge?

How can we extend our knowledge?

Inference: The things we already know provide reasons in favour of other beliefs.

We have beliefs about the future events or unobserved events, facts.

Inferences in everyday life

Inductive generalisations:We experienced that some roses are stingers, then we

conclude that all roses are stingers.

My XY cd player has broken down. My friend's cd player is the same modell, and his player doesn't work properly either. Therefore the XY cd players are rubbishy.

We had seen that some foreign tourists were ripped off in restaurants in Budapest, so we concluded that the foreign tourists would be ripped off in Budapest.

We saw three swans. All of these swans were white, so we conclude that all swans are white.

Inductive generalisation

(Enumerative inductive generalisation)1. The 1. observed individual with property A had a property B.

2. The 2. observed individual with property A had a property B.

….

Therefore: The individuals with property A usually have property B. (Most of A’s are B’s.)

Or: All A’s are B’s.

Other form:All observed A were B.

Therefore: Most of the A’s are B’s.

Or: All A are B.

Inference from individuals to individuals

All observed camels were ungulates.This animal is a camel.Therefore: This is an ungulate animal.

All observed A were B.a is ATherefore: a is B.

Deductive and inductive inferences

Deductive inference: the premises are claimed to support the conclusion in a such way that it is impossible for the premises to be true and conclusion is false.

All movie stars are extroverts.

Elizabeth Taylor was a movie star.

Therefore, Elizabeth Taylor was extrovert.

Inductive inference: the premises are claimed to support the conclusion in a such way that it is improbable that the premises are true and conclusion is false.

All dinosaur bones discovered until this day have been at least 65 million years old.

Therefore: (it is probable that) The dinosaurs have extincted 65 million years ago.

Strong and weak inductions

There are strong and weak inductive inferences.

Stong induction: it is improbable the premises are true and the conclusion is false.

Weak induction: the conclusion does not follow probably from the premises.

To evaluate an inductive inference we must have previous knowledge about the world.

Form and matter:

All deductive inferences have a logical scheme. When we analyse this logical scheme we are able to determine whether it is a valid argument.

The strongness of inductive inference is based on what is the inference is about. Appealing to only the form we are not able to distinguish strong and weak inferences from each other.

Strong and weak inferences

In the past the sun has rised in every day.Therefore the sun will rise tomorrow.-strong

In the past I have never been to Bratislava.Therefore, I won't be to Bratislava tomorrow.-weak

Induction in science

In science we are based on (strong) inductive inferences:The physicist establishes the mass of the electron in

such a way that he measures the mass of a smaller group of the electrons, and from this makes generalizations that the mass of all of the electrons in the universe is this much.

What is basis of induction?

Strong inductive inferences

The reliability of inductive inferences is based on what kind of individuals and properties we make the inductive generalisation about.

All observed camels were ungulates.

Therefore: All camels are ungulate animals.

This is strong inference, given the premise, the conclusion is probably true.

Since we have a good reason to think that the „ungulate” is typical property of the species.

This property is typical for all individuals of the species. There are no differences among the individuals regarding this property.

Therefore: it is highly probable that all camels are ungulate animals.

Inductive inference

Induction is usually an automatic thinking.

Each of us has to think about new experiences in terms of old experiences.

Induction is necessary in order to learn new things about the world. (baby learning the language)

But it's very easy for us to stop with the generalisations, to accept them without examining them further.

Overgeneralisation

A common mistake is overgeneralisation.We conclude a too general conclusion based on a

few observed cases and we ignore the differences between the individuals.

Example: Many people have stereotypes.

Based on a few experiences they conclude that all black people /all asian people are …

Overgeneralisation

Or: If I've done poorly on essay exams in the past, when I find out that I have to take an essay exam my automatic thought may be:

"I do poorly on essay exams."

I am generalising from one or two experiences of a certain kind to all experiences of a certain kind.

But of course there are significant differences between people or written exams.

Statistical inferences

Statistical inferences80 % of the population of Hungary agree with

death penalty.18 % of the students of BME are religious.Public opinion polls show that 45 % of USA

citizens will vote for the democrats. (These examples are fictitious.)

Statistical inferences

We would like to know that what kind of properties the things possess which belong to a certain group.

Statistical inference is based on analysing a sample.We select a sample from the population and we make

generalisations based on the observation of the sample

We have found that the a certain proportion of the sample possesses a certain characteristic).

Then we conclude that the group as a whole (the population) possesses the same proportion of the characteristic.

Statistical inference

Form:

N percent of the observed A’s were B.Therefore: N percent of all A’s are B.

Statistical syllogism:

A proportion Q of population P has attribute A.An individual X is a member of P.Therefore: There is a probability which corresponds to Q

that X has A property.

Evaluating inductive inferences

In everday life and in science we encounter statistical inferences.

Commercial: 80 % of the Hungarian dentists recommend Snow White toothpaste.

Science: Statistical evidence gives justification that a certain medicine is probably effective.

These stastical inferences are reliable (strong indutive reasoning), when the sample is representative.

Representativity of the sampleIn 1936 before the presidential election a public opinion poll

was made in the US.

Ten millions (!) of ballot papers were sent by post.

The citizens were randomly selected from phone directories and car registers.

Two million answers have arrived.

Based on these answers the republican Alf Landon's victory with 57 to 43 percent was forecasted.

But the democrat Roosvelt has made a 61% overwhelming victory.

What caused the mistake?

Representativity of the sampleProblem: the sample was not representative (it was biased).

The proportion of republicans in the sample was much greater than the proportion in the whole population.

Because: The names were chosen from the telephone books and car registers only. In the 1930 years the car-owners and telephone-owners were wealthier than the average.

More of the rich people were republican voters.

Therefore Landon's supporters have a greater chance to get into the sample than Roosevelt's voters.

Representativity of the sampleWe call a sample representative regarding a characteristic

F, when the proporton of F among in the sample corresponds with the proportion of F in the whole population.

The selected sample needs to be random. All individuals of the population have (theoretically) an equal chance to get into the sample.

The representativity depends on the size of sample, although merely the size of the sample does not make the sample representative.

Requirement of randomnessThe requirement that a sample be randomly selected

sometimes can be taken for granted.

Example: When a doctor takes a blood sample to test for blood sugar, there is no need to take a little bit from the finger, a little from the arm and a little from the leg.

Because blood is a circulating fluid, it can be assumed that it is homogenous in regard to blood sugar.

But when the population consists of discrete units, the requirement of randomness must be given more attention.

Hume's problem of inductionThe statements which are based on induction are not and

cannot be justified. The reliability of induction cannot be justified.

We conclude from observed cases to unobserved cases.

But I only have reason to believe that my experiences make the concluson of inductive inference probable, if I have reason to believe that events which I have not observed are similar to events which I have observed.

But this claim „the unobserved things are / will be similar to the observed things” cannot be justified unless we presuppose inductive inferences are reliable.

Hume's problem of induction

The inductive inferences are based on the claim: „The unobserved things are /will be similar to the observed cases.”

We belive that the nature is uniform. (Example: The mass of the electron is the same independently from the time and location of the electron.), therefore the inductive inference can be justified.

But how do we know that? When I appeal to the uniformity of past experience, it begs the question. Experience itself has not given to me reason the unobserved will resemble the observed, because when we argue for this claim we appeal to an inductive inference.

(The unobserved things are similar to the observed cases, because in the past the things which we had already observed resembled things which we have observed later.)

Begging the question (Petitio principii)

Hume: The possible justification of the inductive inferences is question begging, therefore inductive claims can not be justified. Therefore we have no sufficient reasons to believe in induction.

Question begging: Arguer creates the illusion that premises provide adequate support for the conclusion by leaving out a key premise, by restating the conclusion as a premise, or by reasoning in a circle.

One of the premises depend on the truth of the conclusion.

Examples

1. Capital punishment is justified for the crimes of murder and kidnapping because it is quite legitimate and appropriate that someone be put to death for having committed such hateful and inhuman acts.

2. (Circular reasoning): Ford Motor Company clearly produces the finest cars in the United States. We know they produce the finest cars because they have the best design engineers.

This is true because they can afford to pay them more than other manufacturers. Obviously they can afford to pay them more because they produce the finest cars in the United States.

These arguments are clearly fallacious.

Hume' problem of induction

The problem is NOT that I might be wrong or I have been wrong about conclusion of inductive inferences.

The problem is NOT the probability of the inductive inferences.

The problem is: the belief that our inductive inferences which are based on experience give us reliable knowledge about the unobserved things can not be justified. Therefore believing in induction is irrational.

But: What does 'justification' and 'rational' mean here?

Is the justification circular?

This „circularity” is not vicious. This is not a fallacious argument (unlike the former two examples):

Inductive reasoning has proved reliable in the past. Therefore inductive reasoning is generally reliable.

It is not circular, it would be circular if the argument need the premise „(in the future) inductive reasoning is reliable”.

It is not a deductive argument. It would be circular, if it was interpreted as a deductive argument. But the argument is a good inductive argument.

The inductive inferences work, and this is enough.

We don't need a non-circular, deductively valid (sound) argument to give reasons to believe in inductive inferences.

Justification and meta-justification

The justification of induction might be circular, but this is not a problem.

We don't need a further justification.

If our inductive reasonings are reliable (they usually lead to true conclusions), then we can appeal to them.

We don't need to have justified beliefs about that we have justified beliefs. If our beliefs are justified, that's enough.

And our inductive inferences work, and we have empirical corroboration that they work.

(Additionally: from an evolutionary perspective we have an explanation why does induction work.)

Rationality in everyday life

Hume: Because the induction cannot be justified, therefore believing claims based on induction are irrational. (We believe that because we have instincts, habits, inclinations to them.)

But Hume uses the notion of rationality in a very restricted sense. But actually we use 'rational' in a different sense.

On the contrary: we think that it would be irrational to doubt about that: „the Sun will rise tomorrow.”

It is possible that the Sun won't rise, still it is rational to believe that it will.

Rational ≠ justifiable by an inference!

Why should we accept Hume's conception of rationality?

Inference to the best explanation

Harman: Inductions are inferences to the best explanation.

All observed A’s were B’s.

The best explanation to this fact is that all A’s are B’s.

Therefore All A's are B's

There is no circularity in here. It's an explanation why the induction is reliable.

Sceptic doesn't have an explanation why the inductive inferences work (or why they worked in the past).

There are laws in the nature, which are invariable, and the best scientific theories refer to these laws, and this is the best explanation of why the inductive inferences really work.

The induction is reliable, because in the world there are in fact universal and invariable laws.

Hypothetical reasoning

Explanations are used in everday life and in science.

Example: You get in your car, turn the key, but the car fails to start. Why?

Perhaps the spark plugs are dirty, or the ignition coil is shorted, or the fuel pump is broken. Or perhaps someone sabotaged the car overnight.

These conjectures are hypotheses, and the reasoning used to produce them is hypothetical reasoning.

Hypothetical reasoning

Examples: An attorney suggests hypotheses to the jury when arguing about the motive for a crime.

A doctor hypothesizes about the cause of a disease.

The Ptolemaic and Copernican theories about the Sun and the planets are hypotheses which provide explanations to the observations, and suggest specific questions to be answered through controlled experiments.

Because of the lack of direct observation we need explanations.

The evidence is not sufficient to indicate what exactly is going on.

Hypotheses are constructed to make sense of the situation and to direct future action.