RUME 27
2025
Alexandria, Virginia
How do Mathematicians Explain Conditionals? Diagrams and Explanations for ‘if P(x) then Q(x)’ and ‘P(x)⇒Q(x)’
Page: 989
At the introduction to proof, Venn or Euler diagrams are commonly used to illustrate concepts in logic. Standard diagrams show 𝑃(𝑥) ∧ 𝑄(𝑥) as the intersection of truth sets for 𝑃(𝑥) and 𝑄(𝑥), and 𝑃(𝑥) ∨ 𝑄(𝑥) as their union. But textbooks rarely include a diagram for the conditional, and those that do use a diagram that differs from the standard form. Does this reflect typical mathematicians’ thinking? What do they draw when asked for a diagram to represent the conditional, and does this depend upon sentence formulation? This preliminary report describes a pilot study in which mathematicians and mathematics PhD students were asked to draw a diagram and provide a short accompanying explanation for either ‘if 𝑃(𝑥) then 𝑄(𝑥)’ or ‘𝑃(𝑥) ⇒ 𝑄(𝑥)’. Results show that they all draw essentially the same diagram, representing a true universal conditional. I illustrate variety in the provided explanations.