Logic and puzzles

Claims that can be tested for truth

An argument needs more than a persuasive speaker or an agreeable conclusion. These courses ask what is being claimed, which premises support it, and whether the conclusion follows. Some questions concern the structure of a statement; others concern the quality of the evidence offered in a discussion. Keeping those questions separate helps when a conclusion happens to be true but the argument for it is poor. The examples move between symbolic reasoning and ordinary disagreements without treating a label as a substitute for an explanation.

Truth values before disputed arguments

Start with Statements and truth. It distinguishes statements with truth values from other kinds of sentence, then introduces and, or and not. Conditionals and the contrapositive lead into truth tables, validity and soundness, and syllogisms. This provides a way to inspect an argument without first deciding whether you like its subject or its conclusion.

Then read Fallacies. The course covers straw man, ad hominem, hasty generalization, slippery slope, false dilemma, circular reasoning and appeal to authority. Each deserves more than a name to memorize. Ask which claim was changed, which relevant evidence is missing, or which link in a proposed chain of consequences still needs support. Return to the original argument before deciding that a criticism applies.

Write out the rows instead of guessing

The truth-table unit includes runnable JavaScript that prints the truth values of a conditional. Compare its output with a table you have filled in yourself. Work through the possible values of the premises and look for a case where they are true but the conclusion is false. In a discussion, try an equally explicit record: write the original claim, the offered reason and the conclusion on separate lines. This makes a switch of subject or an unsupported step easier to identify than a quick exchange of labels.

Criticism that addresses the actual reason

A straw man can turn “some” into “all” or “reduce” into “ban”. A false dilemma leaves out alternatives, including positions between the two offered choices. For a generalization, count the cases and ask how they were selected, not just how memorable the story is. When someone cites an authority, ask whether the person has expertise in the relevant field and whether other experts agree. The course does not teach that every use of an expert is automatically an error.

Validity and soundness also answer different questions: the first concerns whether the conclusion follows, while soundness additionally requires true premises. Practice explaining that difference in words before moving on. Recognizing a fallacy should help repair an argument or clarify a disagreement, rather than merely provide a way to dismiss the person speaking.