Practice worksheet
A Priori vs A Posteriori Worksheet: 12 Examples with Answers
The important question is not when someone learned a claim, but what supports their belief now. Work through these twelve scenarios before opening the answers. Some examples deliberately leave information out: recognizing that gap is part of the exercise.
How to use the worksheet
For each scenario, label the stated basis of justification: A for a priori, P for a posteriori, or U when the scenario does not tell you enough. Then write one sentence identifying the support. A label without a reason does not show that you have understood the distinction.
In this worksheet, a priori justification is justification that does not depend on experiential evidence for the claim being considered. A posteriori justification depends on experience: observation, measurement, testimony, or evidence about events in the world. These are introductory working explanations. Philosophers disagree about the precise scope of experience, the status of intellectual intuitions and whether some apparently a priori justification can be defeated.
Do the first four cases on your own. Compare your reasons with a partner before moving to the more difficult cases. For independent study, open each answer only after writing your explanation. A teacher can print the questions without the solutions and use the full version during discussion.
Ask three questions before choosing a label
- What is the exact claim? Separate a mathematical result, a conditional statement and a claim about a particular event.
- What is the person relying on? Look for a calculation, an argument from stated meanings, an observation, a report, or a measurement.
- Would that stated support need information about the world? Do not replace the described method with another method the person could have used.
Learning the words from a teacher is different from using the teacher's testimony as your present evidence for the truth of a statement. Likewise, a proposition that can be proved mathematically might actually be believed by a particular person because a calculator displayed it. The distinction can concern a person's route to justification, not simply a permanent sticker attached to a sentence.
Twelve scenarios: decide before opening the answers
The scenarios specify how a person reaches a judgment unless the missing information is the point of the case. Treat stipulated definitions and formal assumptions as given. These are original teaching examples, not reports about real students.
Case 1
A class defines a hexagon as a polygon with six sides. Ari concludes that a hexagon has six sides by attending to that definition, without inspecting a drawing.
Show answer and explanation for case 1
A — on the stated conceptual basis.
The support is the stipulated definition. Ari does not need to count the sides of a particular object to establish what the defined term means. This does not establish that any hexagons exist in the room. A claim that a particular drawing is a hexagon would involve checking the drawing.
Case 2
Bea believes the café opens at 8 a.m. because its current opening-hours notice says so. She has not reasoned from a definition of café.
Show answer and explanation for case 2
P — testimony about a particular business.
The notice supplies information about the world. Understanding its words is necessary, but understanding alone does not determine this café's opening time. The notice could be outdated, so experiential support is not automatically conclusive or reliable. Whether Bea has knowledge is a further question.
Case 3
Cai checks 17 + 25 = 42 by breaking 25 into 20 and 5 and applying the rules of arithmetic. Cai does not consult a device or count a collection of physical objects.
Show answer and explanation for case 3
A — arithmetic reasoning as described.
The justification comes from a calculation using understood arithmetic rules. The case does not require empirical evidence that these particular objects total 42. Being able to make mistakes while calculating does not by itself turn arithmetic reasoning into a posteriori justification.
Case 4
Dev believes 17 + 25 = 42 solely because a calculator displayed 42. Dev cannot check the calculation and is relying on what the device reports.
Show answer and explanation for case 4
P — for Dev's stated route to belief.
The proposition is the same as in case 3, but the described support differs. Dev relies on an observed display and assumptions about the device's operation. The proposition is capable of an a priori proof; this does not mean that every person who believes it has performed or understood that proof.
Case 5
Eli says, 'I know that 125 − 25 = 100.' The scenario does not say whether Eli calculated it, read a worked solution, or trusted someone else's answer.
Show answer and explanation for case 5
U — the actual basis is not specified.
You can identify a possible a priori route, but you cannot infer which route Eli used. Asking for the missing reason is better than guessing. This is why the exercise asks about the stated justification rather than demanding that every proposition receive one universal label.
Case 6
Fran concludes that the meeting room contains twelve chairs after counting the chairs in that room this morning.
Show answer and explanation for case 6
P — observation and counting of a particular collection.
Arithmetic helps Fran count correctly, but the claim that these chairs are in this room depends on observation. Mathematical tools can occur inside an empirically supported inquiry. Their presence does not make the whole claim independent of experience.
Case 7
For this exercise, 'scarlet' is stipulated to name a color. Gia concludes that anything scarlet is colored by using that stipulation, without checking whether there are any scarlet objects.
Show answer and explanation for case 7
A — within the stated conceptual setting.
The stipulation supplies the relevant relation between the terms. The conclusion is conditional on that meaning. It is not a claim that scarlet objects exist nearby, that a particular object is scarlet, or that color categories are beyond philosophical debate.
Case 8
Han believes there is a scarlet folder on the desk because Han looks at the desk and sees one there.
Show answer and explanation for case 8
P — perception of a particular object.
Compare case 7. Understanding the color term does not tell Han which objects are on the desk. Lighting or a misleading appearance could affect the observation. The type of support and the quality of that support are separate matters.
Case 9
Imani reasons that if a report is accurate and it says a bridge is closed, then the bridge is closed. Imani is assessing that conditional inference, not asserting that this particular report is accurate.
Show answer and explanation for case 9
A — reasoning about the stated conditional.
The point is the relation between the assumptions and the conclusion. Establishing that the actual report is accurate would require further evidence, as would establishing that the bridge is currently closed. Do not silently add those empirical claims to the question.
Case 10
Jules tests three samples of a metal, observes expansion when they are heated, and concludes that the metal generally expands under those conditions.
Show answer and explanation for case 10
P — experimental evidence.
The inference relies on measurements and observations. The three tests may not justify an unrestricted universal claim; sample quality, conditions and other evidence matter. A posteriori identifies the kind of support, not a guarantee that the inference is strong enough for knowledge.
Case 11
Within a specified Euclidean geometry system, Kai derives a theorem from the given axioms and accepted rules of inference. Kai is not measuring a triangular object outdoors.
Show answer and explanation for case 11
A — for the formal derivation as described.
The proof proceeds within the specified assumptions. Whether a physical surface is adequately represented by Euclidean geometry is another question and can involve empirical investigation. Always preserve the mathematical setting instead of treating an ideal theorem and a measurement as the same claim.
Case 12
Lina remembers seeing rain outside yesterday and believes that it rained at that place yesterday. Lina now relies on that memory, rather than on a definition of rain.
Show answer and explanation for case 12
P — remembered experience.
The supporting event is perceptual experience, even though Lina is not looking outside now. Memory can preserve experiential support; it does not turn an event claim into a priori knowledge merely because it happens in the mind. Whether the memory is accurate is a separate question.
Compare the method, not just the subject
| Cases | What stays the same or looks similar? | What changes? |
|---|---|---|
| 3 and 4 | The arithmetic proposition | Understood calculation versus reliance on a device |
| 7 and 8 | Vocabulary about scarlet objects | A conceptual relation versus a claim that an object is present |
| 9 and an actual bridge report | An inference about a report | The conditional reasoning versus evidence that its assumptions hold |
These pairs explain why a keyword shortcut is unreliable. 'Math' does not settle how a person actually knows a result. 'Looking inward' does not settle whether a belief depends on earlier observation. A logical inference can be a priori in its form while an argument's factual premises require a posteriori support.
Four mistakes to avoid
A priori does not simply mean known before birth. Innateness concerns origin or possession; a priori justification concerns a kind of support. A person can learn concepts and later reason with them without checking a particular event.
A posteriori does not mean certain because it was observed. A measurement can be faulty and a report can be wrong. Reliability and strength still need evaluation.
Necessary is not a replacement label for a priori. Necessity concerns whether a claim could have been otherwise, while this worksheet concerns the basis of justification. The philosophical debates connecting the two distinctions are more complicated than a two-column vocabulary test.
Analytic is not automatically the same distinction. Analyticity is generally discussed in relation to meaning; the a priori/a posteriori distinction concerns justification or knowledge. Case 1 uses a stipulated definition as an uncomplicated starting point, not as proof that every possible account of these concepts agrees.
Teaching notes and a useful way to assess answers
Ask learners to circle the phrase that supplies the support before they select a category. Award credit for identifying that support and preserving the scope of the claim. For case 5, the useful response is to request the missing method; marking U is not avoiding the philosophical question.
If a learner disputes case 4, ask them to distinguish 'there is an a priori proof available' from 'Dev's present justification comes from that proof.' If they dispute case 11, ask whether they mean the formal theorem or the claim that an actual object fits its model. These disagreements can make the lesson better when the exact proposition is kept visible.
For an extension, have each learner rewrite one scenario so that the same proposition receives a different stated route to justification. They should explain what changed and avoid inventing new certainty. There is no need to present the score as a measure of intelligence or philosophical ability: the purpose is to practice identifying reasons.
Sources and further reading
- Stanford Encyclopedia of Philosophy: A Priori Justification and KnowledgeWorking distinction, experience, defeasibility and philosophical disagreements.
- Stanford Encyclopedia of Philosophy: Rationalism vs. EmpiricismReason, experience and the distinction from innate knowledge.
- Internet Encyclopedia of Philosophy: A Priori and A PosterioriThe difference from analytic/synthetic, necessity and the roles of experience and testimony.