KNOWLEDGE AND LANGUAGE:
INDUCTION AND DEDUCTION
Needs provocative exploratory paragraph here positing squeaky clean formal logic as an emergent artifact of the messiness of language!
It is essential that TOK students appreciate the difference between deduction and induction. Experience has shown that even the strongest students, who can often parrot the definitions, are initially confused when questioned using real cases. I find it worth teaching deduction and induction from scratch using an interactive lecture presentation before proceeding to the class activities
DEDUCTION: LOOKING AT SYLLOGISMS
Aristotelian logic hinges on deduction. Deduction is reasoning from the general to the particular. As in the oft repeated syllogism:
1. All men are mortal
2. Socrates is a man
3. Socrates is mortal
A deductive argument can provide logical certainty without providing useful information about the real world. For this reason sound deductions are recognized as “valid” rather than “true.” If any of the original premises are incorrect or absurd, the conclusion of the syllogism may be worthless despite its inescapable, internal logical consistency.
1. All women are mortal
2. Socrates is a woman
3. Socrates is mortal
1. All goats have six legs
2. Socrates is a goat
3. Socrates has six legs
INDUCTION AND CONTINUITY
The world exhibits underlying order and continuity. Our knowledge of this seems partially a priori and partially the product of discovery by trial and error. For instance there is evidence to suggest that infants expect objects to fall down and know in advance that objects increasing in size are getting closer.
PRIMACY OF INDUCTION?
Predictability is the assumption underlying inductive reasoning, whereby we generalize from a set of particular instances. If deduction is reasoning from the general to the specific; then induction is arriving at the general from the specific. There is disjoint with this reversal. The logic is broken. Induction may be inextricable from how we encounter a more or less uniform world, but we must concede that inductive reasoning is psychological rather than strictly logical. Why?
Every time I see a swan it is white...
I conclude that all swans are white
CLASS ACTIVITY I: APPLYING INDUCTIVE
AND DEDUCTIVE REASONING TO SOME REAL DATA
Allow students to work in pairs. Provide the graph of the relationships between body mass and maximum lifespan in birds and mammals and the guiding questions. Printable pdf.
Encourage students to read closely the annotation that explains the red and blue graphs and animal silhouettes. Students with French or Spanish will almost certainly work out from etymology that volant means flying. Allow a timed 12 minutes to answer the guiding questions. Remind students that intention here is to differentiate between deduction and induction; not to learn intriguing facts about animal lifespans.
1. What is the general relationship between body mass and longevity. Did you decide this by deduction or induction?
2. Generally how does a flying vs. a non-flying lifestyle make a difference to the general relationship between body mass and longevity. Did you decide this by deduction or induction?
3. Mark boldly on your graph where you estimate the following animals would appear:
A. Grizzly bear
C. Etruscan pygmy shrew (weighing only 1.3 grams)
E. Homo sapiens
Be precise: did you make each of your five decisions by deduction, induction or a combination of both? What were some of the interesting details that arose during your discussion.
CLASS ACTIVITY II: FALSIFICATION
AS THE DEMARCATION OF SCIENCE
After calling on students to report back their findings on the animal lifespan activity, quickly challenge them more profoundly with the following Knowledge Question:
If science is so dependent on induction—a psychological rather than logical process—does the whole edifice of science have no solid foundation? Is this an unsurmountable problem?
Finally, show students the BBC How can I know anything at all? animation exploring Karl Popper's response to the unsettling problem of induction in the sciences. The animation is succinct, and worth showing at least twice.
Follow up with a lively whole class consolidation discussion; referring back to the induction as a shaky foundation for science Knowledge Question and emphasizing the importance of assimilating valuable new TOK vocabulary like: conjecture, refutation, falsification, demarcation and pseudoscience.