§5 Meta-Reflection and Practice

Why do we bother with formal logic? As we saw in the previous chapters, our minds are prone to passion and bias. Logic acts as the external “scaffolding” that keeps our beliefs upright. By moving beyond “gut feelings” and into formal structures, we move closer to being what Russ Payne calls a Reasonable Person.

Formal logic is primarily structured around two pillars: deduction and induction. While deductive reasoning provides the logical support for mathematics, artificial intelligence, and computer science, it is induction that provides most of what is known about the empirical workings of the world. Deductive structures provide conclusive support, but inductive reasoning allows us to reason “beyond the evidence”—inferring from what is already known to conclusions about what those bits of information suggest is probably true about unobserved cases.

We must generalize to survive; without generalizing from past experience, we would not know that fire burns or how to navigate daily challenges. A Reasonable Person recognizes that while induction involves probability rather than absolute certainty, it is the tool used for progress in science, medical experiments, and the law. By using formal patterns such as statistical syllogisms or arguments by analogy, we can ensure our conclusions are well-supported and avoid the pitfalls of hasty generalizations. As reasonable people often agree, the strength of an analogy or a statistical sample depends on careful deliberation and the identification of relevant similarities and dissimilarities.

PRACTICE: Argument Evaluation

Instructions: For each example, identify if the argument is Deductive or Inductive.

• If it is Deductive, determine if it is Valid or Invalid. If valid, is it Sound?

• If it is Inductive, determine if it is Strong or Weak. If strong, is it Cogent?

1. The Medical Analogy “Clinical trials showed that this new medication effectively reduced blood pressure in 95% of the test subjects. You have a similar medical profile to the participants in that trial. Therefore, this medication will likely reduce your blood pressure.”

Assessment: Inductive. Strong (based on the 95% success rate). Cogent (assuming the trial data is true).

2. The Logical Chain “If you live in Seattle, then you live in Washington State. You do not live in Washington State. Therefore, you do not live in Seattle.”

Assessment: Deductive. Valid (Modus Tollens form). Sound (assuming the geography is accurate).

3. The Hasty Generalization “I met two philosophy professors yesterday and both of them were wearing turtlenecks. Therefore, all philosophy professors wear turtlenecks.”

Assessment: Inductive. Weak (the sample size is too small to support a universal conclusion).

4. The Valid “Nonsense” “All trees are made of marshmallows. All things made of marshmallows are edible. Therefore, all trees are edible.”

Assessment: Deductive. Valid (the structure is perfect). Unsound (the premises are factually false).

5. The Categorical Error “If it is a diamond, it is a hard stone. This stone is hard. Therefore, this stone is a diamond.”

Assessment: Deductive. Invalid (Fallacy of Affirming the Consequent—many other stones, like sapphire or quartz, are also hard).

6. The Statistical Prediction “Most students at Green River College use the campus library. Marcus is a student at Green River College. Therefore, Marcus uses the library.”

Assessment: Inductive. Strong (the word ‘most’ provides probability). Cogent (if the majority of students actually do use the library).