Ages 13+
Concepts & Flawed Reasoning

Ages 13+
Concepts & Flawed Reasoning

Case Study 1

The Concepts of Intension and Extension

Beginning at around 13, students can begin formalizing their reasoning using intensional definitions. These formal definitions, which are internal to concepts themselves, rather than drawn from experience, can open up new avenues for reasoning and lead to new kinds of arguments. 

Consider the following scenario:

During a presidential election campaign, 14-year-old Lea defends a candidate who, in her eyes, is the only one worth voting for. She explains her candidate’s platform to her friends around the table at lunch in the school cafeteria and says how she wishes she already had the right to vote and that she begged her parents to vote on her behalf. 

Lea’s arguments seem to have convinced her friends, but Anna, sitting at one end of the table, interjects: ″Who cares? As my parents say, all presidents are liars! I’m never going to vote.”

The other girls and boys present agree loudly. A surprised Lea tries to think of a comeback, but can’t think of what to say.

The bell rings. Everyone gets up to go back to class.

When she gets home after school, Lea tells her mother about the scene at lunch and asks her opinion: ″What would you have said to Anna?”

If you were Lea’s mother, how would you have replied? How can you use reason to respond to Anna’s argument, which seems to be an argument from authority?

There are two ways to determine whether all presidents are liars or not:

  1. Extensional method: Research the history of presidential elections, and compare the promises made by candidates to their actions after being elected. This method will allow you to determine whether all presidents over the course of history have lied. Perhaps they all have lied. But even in this case, Anna’s argument would be valid but only up to the present day, since one cannot predict the future and, therefore, what a new president will do. Perhaps Lea could then defend her favored candidate by arguing that, once elected, he or she will be different.

  2. Intensional method: Research political science and show that the electoral system and certain institutions pressure candidates to lie in order to get elected and that this is considered the “rules of the game.” If this can be demonstrated, it would be a valid pattern for the past and the future. In this hypothesis, Anna’s argument will be valid for the present and the future (so long as the same institutions remain in effect). Notice, however, that this method gives Lea an opportunity for more subtle reasoning. All presidents may end up making false promises or misleading the public on certain points, but we can distinguish between deliberate, malicious lies and those that arise from the pressures of the office. This would allow her to poke holes in Anna’s rationale for not voting, since certain candidates may still be more honest than others.