Reason and imagination

Activity 1 - What role does reason play in the natural sciences?

Conceptual understanding: The validity of inductive reason is often related to the amount of evidence.

Time: 15 min.
Task: Consider the following questions:

Which is the correct final square?
How do you know?
What kind of reason is this - inductive or deductive?
How does this relate to the production of knowledge in the natural sciences.
Look at the data points below, how might the pattern (line of best fit) change as more data points are included in the set? What difficultly does this suggest about inductive reasoning?

Source

Activity 2 - What if...?

Conceptual understanding: Imagination is used to design submicroscopic models that might help explain the macroscopic world.

Time: 15 min.
Background info: Ernest Rutherford model of the atom (see Brian Cox explain it this video) was formed using the results of his famous gold foil experiment. Each feature of his model is supported by observations and empirical data:

As almost all the positive alpha particles passed through the gold foil so he suggested that most of the atom must be empty space.
Occasionally, the positive alpha particles were deflected or reflected so he suggested that there must be a small dense area of positive charge in the atom (the nucleus).
The negative electrons suggested by Thomson's plum pudding model did not seem to impact Rutherford's experiment so he suggested they are orbiting the nucleus in some manner.

Task: Suggest models of the atom that he might have proposed if he had seen the following observations: Perhaps assume that your only prior knowledge is:

Electrons existing as particles.
Gold foil is charge-neutral..

There are no incorrect answers here as long as you can explain how the evidence supports your model.

Observation set A

All the alpha particles are reflected back towards the radiation source.

Observation set B

Half of the alpha particles are reflected/deflected and half pass through.

Observation set C

Some alpha particles remain inside the gold foil and do not pass through, nor get reflected.

Activity 3 - Invalid deductive reason

Conceptual understanding: A conclusion can be limited by invalid deductive reason.

Background info: The information below outlines what deductive reason is and an example of a flaw. Deductive reason is the application of a general rule (premise 1) to a specific case (premise 2) to reach a conclusion. In the example (below left), although the two premises are true, the logic applied in invalid - in reality, other animals can also have beaks. We can demonstrate this clearly using a Venn diagram (below right).

Task: Watch this clip from The Simpson. In this video, Homer uses deductive reason to reach an invalid conclusion about his idea of a Bear Patrol (in a town which didn't have any bears to begin with!).

Premise 1: The is a Bear Patrol in the town.
Premise 2: There are no bears present in the town.
Conclusion: The Bear Patrol must keep the bears out of the town.

a. Given that both premises are true, can you identify the flaw in his logic?

b. Outline Lisa's example of invalid logic in the same structure as above.

c. Use Venn diagrams to demonstrate the flaw in the logic applied.