A Priori vs A Posteriori Worksheet: 12 Examples with Answers
Label twelve scenarios by the person's stated basis for a belief, then compare your reasoning with an explained answer.
Read, apply, check
Work with examples, make your reasons visible, and compare your answer with an explanation. Try a worksheet before opening its solutions; use the print options for a class or study group.
Label twelve scenarios by the person's stated basis for a belief, then compare your reasoning with an explained answer.
Mark premises and conclusions, test guarantees with counterexamples and compare sample-based estimates in twelve explained arguments.
Separate logical validity from premise truth in ten original cases, a two-step diagram and a four-row truth table with explained answers.
Read if and only-if arrows, classify conditions and repair definitions in twelve original problems with explained answers and a diagram.
Read Meditation II with an original argument map, an observation-and-judgment table, objections and eight explained reading checks.
Reconstruct Hume’s dilemma with an original map, everyday cases, two conditional coin models, response comparisons and eight explained reading checks.
A mean relative to us is the appropriate response in the circumstances, judged by reason. It is not always the numerical midpoint, not whatever an individual prefers and not a command to compromise between every pair of actions.
The exception is a very specific one: a person with extensive color experience might form the idea of a particular shade never previously seen. Hume is not imagining someone with no experience of color inventing it from nothing. The passage challenges an unrestricted claim that every simple idea must copy a corresponding prior impression.
Epicurus argues that being dead cannot be an evil for us because good and bad require awareness, and death ends awareness. The argument depends on that account of harm. Separate it from questions about the experience of dying, another person’s grief and the loss of a possible future.
Epicurus first divides desires into natural and empty kinds, then divides natural desires into necessary and unnecessary kinds. A need with a point of satisfaction differs from an endless expectation of wealth or fame as a guarantee of security. To classify a case, examine what is wanted, why it is wanted and what would count as enough.
Pleasure can be good without making every pleasant action worth choosing. Epicurus asks what follows: an immediate pleasure may bring greater later annoyance, while a present difficulty may lead to a better result. A worked comparison shows why changed circumstances can change the choice.
Epicurus distinguishes necessity, chance and our own agency, then separates wisely judged action from a merely fortunate result. Read those claims in the letter before bringing in later discussions of the atomic swerve. An unpredictable event alone does not explain a person’s reasons or control.
Epictetus separates our use of choice from external conditions and results. His bath example preserves two aims: carrying out the activity and responding appropriately when it is obstructed. Learn how that distinction keeps preparation meaningful without promising a guaranteed outcome.
Epictetus asks readers to examine the judgment added to an event and to pause before hasty assent. Read the distinction between an occurrence, its appearance and its evaluation, then assess the strong ethical claim without mistaking it for a denial of bodily injury.
Epictetus’s actor metaphor separates receiving a role from performing it. His duties passage adds attention to relationships and care for others. Learn what these passages explain, and why a role label alone does not settle every conflict or justify ancient obedience as a universal modern rule.
A different witness for each object is weaker than one witness shared by all. Complete two-object matrices show the distinction and the valid direction.
Negating every object has some partner requires one object with no partner. Follow the conversion and compare a failed row with a single false cell.
Use a conditional for every P is Q and a conjunction for some P is Q. Complete domain models expose the common swaps and the empty-P case.
Exactly one requires a P witness and identity-based uniqueness. Compare zero, one and two P objects, then check why two names need not mean two objects.
Identify each variable occurrence and its nearest binder. An assignment table, safe renaming and a capture counterexample make scope visible.
Universal introduction needs an arbitrary name with the right dependencies. Compare an invalid particular-premise inference with complete licensed proofs.
An existential witness is temporary, not an identified named object. A complete seven-line proof shows how to discharge the witness and preserve only the name-free conclusion.
Russell’s outer denial can hold when no unique P exists; the inner denial still requires one. Compare four complete models and make the chosen analysis explicit.
Choose a logic question, from translation and finite models to complete truth tables and audited natural-deduction proofs.
Build an eight-row table from distinct letters and subformulas, then audit the final conditional column and a parentheses counterexample.
Find and verify a countervaluation, preserve forced values, repair a failed trial and distinguish a rejected branch from an exhaustive validity result.
Check one common valuation, compare all pairwise witnesses, and separate inconsistency-driven validity from the truth of a conclusion.
Derive a nested conditional with exact block ranges, then diagnose an endpoint at the wrong level and an illegal closed-line export.
Prove a shared conclusion in two sibling cases, check every range and reject one-case or mismatched-endpoint shortcuts.
Choose assumptions from the goal, distinguish ¬I from classical IP, and audit two full proofs with exact contradiction and discharge steps.
Prove both directions of a compound equivalence, audit six nested block ranges and check the resulting biconditional on all four rows.