Logic: The Art of Thinking

Lesson

Induction

 
 
 

An induction is an invalid argument in which the premises may all be true and the conclusion false at the same time. An inductive argument does not provide certainty for the truth of thge conclusion.

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Types of Induction

I. Enumerative Generalization 

II. Inductive analogy 

CRITERIA with which to evaluate the inductions

1. Number of observed cases (premises)

2. Positive analogy between the observed cases (premises) and the unobserved case (conclusion )

3. Negative analogy amongst the observed cases

4. Relevance

5. Strength of conclusion relative to the premises

III. Eliminative Induction also known as causal reasoning

Mill's Methods

1. Agreement

2. Disagreement

3. Joint Method of Agreement and Disagreement

4. Concomitant Variations

5. Residues

IV. Statistical Induction

V. All others

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Inductive Arguments rely upon the principle of induction or the assumption of the Uniformity of Nature.

 

a,b,c,d have property P and Q x has a,b,c,d

a,b,c, have property R y has a,b,c

_____________________________ _______________

.. d will have property R .. y will have d

 

 

SCIENCE

 

Scientific Method may be considered as the critique of argument in light of evidence according to the cannons of Logic . Thus it is a paradigm of critical thinking.

 

Problem

 

Doubt

 

Inquiry---1. Abduction- Hypothesis Formation (working hypothesis)

2. Deduction-Consequences of hypothesis (observation statements)

3. Induction-Testing-gathering eveidence-continuous process

continues until falsifying instances are found.

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The greater the effort to test and to falsify the greater the probability that the hypothesis is true in the absence of counter evidence or falsifying instances.

 

Evaluation of Hypotheses

Criteria Other Criteria

 

1. Relevance Psychological

2. Testability Reliigious

3. Compatability Aesthetic

4. Predictive-explanatory power Economic

5. Simplicity

 

Logic of Falsification Verification

 

H > O VALID H > O INVALID

-O modus tollens O fallacy

----------- --------------- affirming antecedent

.. - H .. H

 

Crucial Experiment Auxillary Hypotheses

 

H v H H & A & A & A.... > O

H > O - O

H > O ------------------------

O v O .. -(H & A & A & A...)

- O ------------------------

------------------ .. -H v -A v -A v -A v ...

..- H

------------------

.. H

 

 

 
 
 
 

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