Socrates nearly always features in syllogism examples, and for good reason. He was willing to die by hemlock poisoning rather than be banished from his beloved Athens for the crime of fostering subversive critical thinking in the public arena. He claimed no original knowledge and left no writings of his own. His wisdom lives on because his life and work were championed in the works of Plato. Socrates declares (in Plato's Theaetetus: 150) that “god constrains me to serve as midwife, but has debarred me from giving birth.”  Socrates' maieutic method (mid-wife-as-opposed-to-didact) is, of course, the watchword for effective, constructivist TOK teaching!

Socrates nearly always features in syllogism examples, and for good reason. He was willing to die by hemlock poisoning rather than be banished from his beloved Athens for the crime of fostering subversive critical thinking in the public arena. He claimed no original knowledge and left no writings of his own. His wisdom lives on because his life and work were championed in the works of Plato. Socrates declares (in Plato's Theaetetus: 150) that “god constrains me to serve as midwife, but has debarred me from giving birth.” 

Socrates' maieutic method (mid-wife-as-opposed-to-didact) is, of course, the watchword for effective, constructivist TOK teaching!

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

A large ample size of white Swannery denizens

A large ample size of white Swannery denizens


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

Cygnus atratus: a large black waterbird from Australia

Cygnus atratus: a large black waterbird from Australia

Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white.
— Karl Popper (1959: 4) The Logic of Scientific Discovery. London: Hutchinson


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
B. Mole
C. Etruscan pygmy shrew (weighing only 1.3 grams)
D. Pelican
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.

Relationships between body mass and maximum lifespan in birds and mammals. Silhouettes highlight a selection of species with much longer or shorter lifespans than expected given their body size. These species are (A) Myotis brandtii, Brandt's bat; (B) Heterocephalus glaber, naked mole rat; (C) Vultur gryphus, Andean condor; (D) Loxodonta Africana, African elephant; (E) Dromaius novaehollandiae, emu; (F) Dorcopsulus macleayi, Papuan forest-wallaby; (G) Ceryle rudis, pied kingfisher and (H) Myosorex varius, forest shrew. Blue points and line represent volant birds and mammals. Red points and line represent non-volant birds and mammals. Blue triangles represent bat species and red triangles represent non-volant bird species.  Healy, K et al. (2014) Ecology and mode-of-life explain lifespan variation in birds and mammals, Proceedings of the Royal Society B, DOI: 10.1098/rspb.2014.0298

Relationships between body mass and maximum lifespan in birds and mammals.

Silhouettes highlight a selection of species with much longer or shorter lifespans than expected given their body size. These species are (A) Myotis brandtii, Brandt's bat; (B) Heterocephalus glaber, naked mole rat; (C) Vultur gryphus, Andean condor; (D) Loxodonta Africana, African elephant; (E) Dromaius novaehollandiae, emu; (F) Dorcopsulus macleayi, Papuan forest-wallaby; (G) Ceryle rudis, pied kingfisher and (H) Myosorex varius, forest shrew.

Blue points and line represent volant birds and mammals. Red points and line represent non-volant birds and mammals. Blue triangles represent bat species and red triangles represent non-volant bird species. 

Healy, K et al. (2014) Ecology and mode-of-life explain lifespan variation in birds and mammals, Proceedings of the Royal Society BDOI: 10.1098/rspb.2014.0298

 

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.

The sun will rise tomorrow...            1. How could you arrive at this conclusion by induction?           2. How could you arrive at this conclusion by deduction?

The sun will rise tomorrow... 

          1. How could you arrive at this conclusion by induction?
          2. How could you arrive at this conclusion by deduction?

As for Adler, I was much impressed by a personal experience. Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analyzing in terms of his theory of inferiority feelings, Although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. “Because of my thousandfold experience,” he replied; whereupon I could not help saying: “And with this new case, I suppose, your experience has become thousand-and-one-fold.”
— Karl Popper talking about Adler's pseudoscientific "individual psychology" theory that was so vague it worked for every case and was irrefutable. In Karl Popper, Conjectures and Refutations, Routledge, London