Critical Thinking Slide 10

CRITICAL THINKING & PRACTICAL REASONING

Session 10 – INDUCTIVE REASONING IN THE SCIENCES & EVERYDAY LIFE( PART 1)

Session Overview
•This session is dedicated to inductive reasoning ( as found in the sciences and everyday life). It is to enable students know the methods of scientific or empirical research- how data are presented and conclusions drawn. And the quality of reasoning contained in scientific or empirical claims.
•Goals and Objectives
At the end of the session, the student will
1. Will be able to distinguish between verifiable and confirmable statements.
2. Types of hypothesis.
3. Account for the predictive power of hypotheses.

Session Outline
The key topics to be covered in the session are as follows:
•Topic One: INDUCTIVE REASONING
•Topic Two : CONTRASTING VERIFIABLE AND CONFIRMABLE STATEMENTS.
(a). Verifiable statement(particular statement)
(b). Confirmable statement(general statement)
•Topic Three: THE TYPES OF HYPOTHESIS
(a). law-like Hypothesis.
(b). Statistical Hypothesis.
•Topic Four: PREDICTIVE POWER OF HYPOTHESES

Topic One
INDUCTIVE REASONING

WHAT IS IT.
•In session 8 we discussed the two types of arguments; “deductive” and “inductive”. In this session we look at inductive argument again.
•We defined inductive argument as an argument where the premises provide good reasons or evidence to support the probability of the conclusion being true and thus it is possible for the premises to be true and the conclusion to be false without any contradiction (unlike a deductive argument).
• The premises of inductive argument are treated as evidence, data, or observation reports or research findings that support the conclusion.

• The quality and quantity or how good the evidence provided by the premises are will determine the degree of probability of the conclusion being true, believable or acceptable.
•Examples:
(1). For the past twenty years of my life it has been raining every Friday. Tomorrow is Friday. Therefore, tomorrow it will rain.

(2). For the past three weeks it has been raining every Friday.
Tomorrow is Friday. So tomorrow, it will rain.

(3). Every Friday it rains. Every Fs is Rs
Tomorrow is Friday. = Tomorrow is F
So, tomorrow it will rain. So, Tomorrow is R.

•If we look at the above examples, E.g1 and E.g2 are inductive arguments because it is possible for the conclusion to be false even when the premises are true. However based on the evidence provided in the premises the conclusion of E.g1 is more likely to be true than that of E.g2. this is because an evidence of “raining on every Friday for the past twenty years” is stronger than an evidence of “raining on every Friday for the past three weeks”. So E.g1 is a good inductive reasoning whilst E.g2 is weak inductive reasoning. In fact the probability of the conclusion of E.g2 being false is higher than that of E.g1 but both examples are inductive.

•However, if we look at E.g3, we realize that it is not possible for the conclusion to be false when we assume the premises to be true, so E.g3 is a valid DEDUCTIVE argument and for that matter has the LOGICAL STRUCTURE or PATTERN of MODUS PONENS.
•This means that an inductive argument does not provide the structure or pattern of logical proof like MODUS PONENS, MODUS TOLLENS, HYPOTHETICAL SYLLOGISM AND DISJUNCTIVE SYLLOGISM as it is in the case of deductive argument.(refer to session 9)
• But rather it’s premises provide evidence that confirms the likelihood or degree of probability of the conclusion being True. There is no certainty with inductive reasoning. This is because no matter how good the evidence or reasons are, it is still possible for the conclusion drawn to turn out to be false.

Topic Two
CONTRASTING VERIFIABLE STATEMENT AND CONFIRMABLE STATEMENT

What are verifiable statements and confirmable statements
•Because we treat the premises of inductive arguments as evidence or observation reports out which conclusions are drawn, the statements that make up inductive arguments from the premises to the conclusion are understood or examined in terms of verifiable statements and confirmable statements
•VERIFIABLE STATEMENTS are the same as PARTICULAR STATEMENTS. They are also called evidence, data, test results, observation reports or research findings.
•They are called verifiable statements because as particular statements their reference classes are finite. That is the subject is fixed or countable.

We can know the total number of the subject and because of that we can always cross check to determine whether they are true or false.
•Examples:
1. Next week Friday it will rain.
2. The students in this class are from the distance education school.
3. Accra is filthy.
•All the above examples can be determined to be true or false. For instance, in E.g1, we wait to see if it will rain next week Friday. In E.g2, we can get the students in that particular class and inquire if they are all from distance education school.

We can also embark on a survey in Accra to see whether there no filth can be found in any part of Accra, because the statement refers to only one city ( Accra).
• Thus when it comes to verifiable statements, because their reference classes or subjects are finite(particular statements), a test or an experiment or observation can be done to establish directly in one, two or few times, to determine whether they are true or false.
•We therefore define verifiable statement as a statement that is directly testable through experience because its reference class or subject is finite(countable).
•NB: All verifiable statements are particular statements.

•CONFIRMABLE STATEMENTS on the other hand are the same as GENERAL STATEMENTS. They are also call hypotheses.
•EXAMPLES:
1. Every Friday it rains.
2. All students are from distance education school.
3. Some taxi drivers in Accra can speak Chinese.
4. Some students cheat in exams.
5. All snakes are poisonous.
•All the above statements are CONFIRMABLE STATEMENTS because their reference classes or subjects are infinite(uncountable) .

Because their subjects are uncountable we cannot test or observe directly to determine fully whether they are true or false.
•For instance, there are uncountable number of Fridays. So we cannot get access empirically to all Fridays to determine if it rains on each Friday. So the best we can do is monitor all the Fridays for a period to see if it rained or will rain. However that will not exhaust all the Fridays that E.g1 refers to. Thus even if it rains on all the Fridays for the period of 10years, in the 11th, 12th, or 13th year it is possible that it will not rain on one particular Friday and that will make the statement, “every Friday it rains” false. The same for E.g2 & E.g5.

•If we take the E.g3, we realize that the reference class “some taxi drivers in Accra” is infinite as well, because if we do a survey we might gather a sample of 50 taxi drivers, but there could be others who can also speak Chinese but we might not include them in our sample so in effect the actual reference class may be more than 50. They may be 100, 200, 1000, etc. So here again we cannot get the total reference class so we only select just a sample to test the statement and that sample will not exhaust the reference class of the statement in E.g3 on page 14. The same analysis can be done on the E.g4 as well.
•Thus CONFIRMABLE statements are testable indirectly because their reference class are infinite. That is the subject is limitless in number to ascertain or count them all.

•We only gather a sample or evidence to test them, however what ever may be the results of our observation or sample or evidence, we project to be the result of the confirmable statement.
•Thus confirmable statements are testable indirectly based on the results of verifiable statements.
•We therefore define confirmable statement as statements that are indirectly testable through experience because their reference classes or subjects are infinite(countable).
•NB: All confirmable statements are general statements and they are also called hypotheses.

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