Logic Toolkit: Quick Reference

Argument Forms at a Glance

Deductive (certainty): If premises are true and form is valid, conclusion must be true. Valid forms: modus ponens (If A then B; A; therefore B), modus tollens (If A then B; not B; therefore not A). Invalid forms: affirming the consequent (If A then B; B; therefore A), denying the antecedent (If A then B; not A; therefore not B).

Inductive (probability): Conclusion is probable based on evidence. Types: generalization (specific to general), analogy (similar cases), causal reasoning (correlation to causation). Strength depends on evidence quantity, quality, and representativeness.

Key distinctions: Valid = conclusion follows from premises. Sound = valid + true premises. Strong = inductive argument with well-supported conclusion. Cogent = strong + true premises.

Fallacy Quick Reference

Relevance fallacies: Ad hominem (attack the person), straw man (misrepresent the argument), red herring (change the subject), appeal to authority (cite non-expert), appeal to emotion (substitute feeling for evidence).

Weak induction fallacies: Hasty generalization (too little evidence), false cause (correlation as causation), slippery slope (unsupported chain of consequences), weak analogy (insufficient similarity).

Presumption fallacies: False dilemma (only two options presented), begging the question (conclusion assumed in premise), loaded question (contested assumption embedded), circular reasoning (premise and conclusion say the same thing).

Worked Example: Running the Toolkit on One Argument

Watch the whole toolkit applied to a single claim: "Every dictator I can name rose to power during an economic crisis, so economic crises cause dictatorships."

Step 1 - Name the form. This is inductive (a generalization from cases), not deductive. So we judge it by strength, not validity.

Step 2 - Test the inference. It reasons from a handful of remembered cases to a universal causal claim. That is the pattern of a hasty generalization, and the leap from correlation to cause is false cause.

Step 3 - Look for the missing set. The examples are the cases that fit; crises that produced no dictator (many democracies weathered the 1930s and 2008) are invisible to the reasoner. This is selection/survivorship bias.

Step 4 - Rebuild it honestly. A defensible version would read: "Severe economic crises raise the probability of democratic breakdown, conditional on weak institutions - as comparative studies of interwar Europe suggest." Note how the honest version adds a probability, a condition, and a source. That is the difference between a slogan and an argument.