IB Theory of Knowledge 3.7 Counter-pressure That Does Not Cancel: Four Shapes Notes

3.7 Counter-pressure that does not cancel: four shapes

Counter-argument that leaves the position untouched

1. An opposing paragraph adds little if it states a rival view and then repeats the original claim without answering the challenge. Explain why the rival changes your position, or why your position survives it.
2. The Excellent band, 9–10, includes "clear awareness and evaluation of different points of view". Awareness identifies another view; evaluation weighs its reasons and what follows from accepting or rejecting it.
3. Compare your claim before and after the opposing paragraph. It may become narrower, better supported or unchanged for a reason you can now explain. A changed word alone tells you little about the quality of that reasoning.
4. Here are four useful ways to test a claim: limit where it applies, offer a competing explanation, examine the cost of accepting it, or test a counterexample. These are options, not an exhaustive list or a required essay structure.
5. Knowledge questions admit plausible competing answers. If you can see only one, investigate what someone could reasonably dispute about its evidence, assumptions or implications.
6. You may conclude that a tension remains unresolved. Explain why the competing views survive scrutiny and what would help you decide between them.

Shape one: the limiting condition

1. In this shape the rival reading is right inside a range, and your job is to state the range. The claim survives, smaller and more defensible than the one you started with.
2. Take a claim that a proof settles a question for good. Non-Euclidean geometries, developed by Lobachevsky and Bolyai in the nineteenth century, replaced Euclid's parallel postulate with a different starting point.
3. A valid proof establishes what follows from the axioms and rules of inference being used. It does not by itself show that those axioms are the right ones for describing a physical situation. The original claim needs that distinction.
4. The shape fails when the limit is drawn so tightly that nothing could contradict the claim any more. That is retreat wearing the clothes of precision, and a reader can see it because the narrowed claim is no longer contestable.
5. State the condition under which the claim holds, then explain what happens when the condition is absent. A limit is useful only if it changes what you can conclude about a case.
6. This approach can help with titles asking to what extent, or containing words such as always or never. Check whether the title calls for limits, exceptions or a judgment of degree.

Shape two: the competing explanation

1. Here the rival accounts for the same evidence through a different mechanism. You may need evidence that distinguishes the mechanisms, rather than more observations that fit both.
2. In the 1854 cholera outbreak in Soho, John Snow argued that the disease travelled in water from a pump on Broad Street, while the prevailing account had it travelling through bad air. Both accounts had the same deaths to explain.
3. Compare what each explanation accounts for and what each leaves unexplained. If the rival does better on part of the evidence, consider whether that narrows your claim or gives you reason to reject it.
4. The commonest failure is a preference dressed as an argument. Calling your explanation the more scientific one states which explanation you like, and a reader who prefers the other has been given no reason to move.
5. This is a problem of underdetermination: the evidence available so far may support more than one explanation. Ask whether further evidence could distinguish them and what additional assumptions each requires.
6. The shape suits titles about method, interpretation or evidence, because each of those turns on how a conclusion was reached rather than on what the conclusion says.

Shape three: the cost of the position

1. In this shape nobody refutes you. Accepting your claim means giving something up, and the pressure is the price rather than a counterexample. Arguing that the price is worth paying is stronger than pretending there is no price.
2. Suppose you require an event itself to be repeated before accepting knowledge about it. That would exclude claims about singular historical events, even where several sources support them. Distinguish repeating an event from independently checking the evidence for it.
3. Say what accepting the standard would exclude, why someone might resist that loss, and whether the loss is justified. You may end by defending, revising or rejecting the standard.
4. This approach needs a position specific enough to have consequences. A qualified claim can still exclude evidence or impose a cost; identify what follows from accepting it.
5. A cost needs weighing. Explain why it is acceptable, or revise the claim if the loss outweighs what the proposed standard gains.
6. This approach can help with titles proposing a standard or asking what we should do. Consider both the knowledge the standard supports and what it excludes.

Shape four: the case that nearly breaks it

1. A strong counterexample tests the reach of a general claim. Explain why it is a serious challenge before considering whether the claim survives.
2. Take a claim that mathematical proof gives knowledge a person can check unaided. In 1976 Kenneth Appel and Wolfgang Haken announced a proof of the four colour theorem that relied partly on computer-assisted checking. Much of the proof was also written and checked by humans.
3. Represent the counterexample accurately. A weakened version may leave your argument unanswered by the strongest evidence against it.
4. Then say what is left. Either the claim narrows, to proof giving checkable knowledge where the checking stays at human scale, or the claim changes, to checking that can be distributed across people and machines.
5. If the case defeats your position, revise the position. Evaluation can lead you to reject a claim you originally intended to defend.
6. This approach can help with titles about certainty and reliability by testing which claims survive a difficult case.

Choosing a shape that fits the title

1. Choose an approach after examining your cases. A title may admit several kinds of challenge, and one case may raise more than one.
2. Try a constructed practice question: To what extent does the reliability of a method matter more than the results it produces? Discuss with reference to two areas of knowledge. One approach is to ask under which conditions reliable methods deserve priority. A competing explanation or an ethical cost might also be relevant.
3. Develop the challenges your argument needs within the 1,600-word limit. A catalogue of objections leaves less room to examine any of them.
4. You may use the same kind of challenge in both areas of knowledge if their methods or evidence give it different consequences. Do not force a difference merely to vary the layout.
5. Choose a rival view with reasons worth considering. Explain what makes it difficult to dismiss and how your argument answers it.

When an opposing paragraph changes the subject

1. An opposing paragraph can change the subject without testing the original claim. Check what follows 'on the other hand': does the new point bear on the argument you were making?
2. Two columns of opposed assertions leave the reader to do the evaluation. Explain why each view is plausible and how the evidence affects your judgment.
3. A rival view needs reasons. If you write 'some people think', identify a relevant source where one exists, or make clear that you are considering a possible objection and explain its grounds.
4. 'It could be argued' can introduce a hypothetical objection, but it does not supply the argument. State the reasons someone would have for holding that view.
5. Ask what the paragraph tests and whether it helps answer the title. A point can be useful without fitting one of the four approaches above.