Valid, sound, and why your opinion of the conclusion gets in the way

Here's an argument you could have heard from a neighbour this week. Every flat in this building that's had damp has had its windows painted shut. Your windows are painted shut. So you're going to get damp.

Most people nod along. The premises sound right, the conclusion sounds like the kind of thing that happens, and the whole thing has the rhythm of reasoning. Now hold the shape and change the words. Every cat is a mammal. Your dog is a mammal. So your dog is a cat.

Same skeleton. The second version is obviously broken, and that means the first one was broken too. Nothing about the damp argument guaranteed its conclusion; it just had a conclusion you were ready to believe. Telling those two things apart, the quality of the link and your opinion of the conclusion, is the whole of this lesson, and it turns out to be harder than it sounds, for reasons psychologists measured in 1983.

Lesson 1 gave you the six-step check and filled in the first three: find the conclusion, find the premises, supply what's missing. This lesson fills in step 4 for one kind of argument, the kind that claims to guarantee its conclusion. And it explains why step 6, consult your opinion of the conclusion, comes last and not first.

What "valid" means, and what it doesn't

Take the cat argument and ask one question: could both premises be true and the conclusion still be false? Yes. Every cat is a mammal, your dog is a mammal, and your dog is not a cat. That is a possible situation (in fact it's the actual one), and it's enough to sink the argument.

That question is the definition. In the words of forall x, the open logic textbook we lean on throughout this course: "An argument is valid if and only if the conclusion is a consequence of the premises. An argument is invalid if and only if it is not valid, i.e., it has a counterexample."¹ A counterexample is a possible case in which every premise is true and the conclusion is false. Find one and the argument is invalid. Show that none can exist and it's valid.

Notice what the definition is about. It's about the link between premises and conclusion, and nothing else. It is not about whether the premises are true, not about whether the conclusion is true, and not about whether the argument is any good. forall x puts it bluntly: "validity is not about the actual truth or falsity of the sentences in the argument ... It is often said that logic doesn't care about feelings. Actually, it doesn't care about facts, either."¹

That sentence offends people the first time they read it. Surely an argument with a false premise is a bad argument? It might be. But "bad" is a bigger word than "invalid". Validity is one specific property, and it's worth keeping narrow, because it's the property you can check without knowing anything about the world.

Worked example: the shape is what's valid

Stay with the fish. Write it in standard form, the way lesson 1 taught you.

1. All fish fly.
2. All whales are fish.
--------------------------
C: All whales fly.

Two false premises, a false conclusion, and a valid argument. Now swap the content and keep the shape.

1. All mammals breathe air.
2. All whales are mammals.
------------------------------
C: All whales breathe air.

Two true premises, a true conclusion, and the same valid argument. The letters underneath are identical: all A are B, all C are A, so all C are B. What made the first argument valid wasn't anything about fish. It was the shape, and the shape is shared.

This is the mechanism behind the counterexample method. A valid form is a shape that can't take you from truth to falsehood, whatever you pour into it. So to test a shape, you keep it and pour in content that makes the premises obviously true and the conclusion obviously false. If you can, the shape doesn't guarantee anything, and neither did the argument you started with. If every attempt fails because the conclusion keeps coming out true, you're starting to see why the shape holds.

One piece of housekeeping before you use this, because the words matter. A counterexample, as defined above, is a possible case: a way things could be in which every premise is true and the conclusion is false. The swap is a technique for finding one. When you pour cats and dogs into a shape, you build a parallel argument whose premises are actually true and whose conclusion is actually false, and the real world is then exactly the case the shape was supposed to rule out. Logicians call this move refutation by logical analogy. Two routes, one target: sometimes you can describe the case directly (the flat next door has painted-shut windows and a bone-dry wall), and sometimes belief gets in the way and swapping the content is how you see past it. Either way, what you produce is a counterexample in the one sense this course uses: a possible case with true premises and a false conclusion.

Try it on the damp argument from the opening. Its shape is: all A are B (every damp flat has painted-shut windows); this C is B (your flat has painted-shut windows); so this C is A (your flat is damp). The cat-and-dog version made the premises true and the conclusion false. So the shape is invalid, and the damp argument is invalid, however plausible the conclusion. Your neighbour might still be right about the damp. Their argument didn't show it.

The four cells, and the one that's empty

Once you separate validity from truth, there's a small table you should be able to draw from memory. Down the side, the argument is valid or invalid. Along the top, the premises are all true or at least one is false. Every combination can occur except one.

Valid, all premises true. Then the conclusion is true; that's what validity means. Whales breathe air.

Valid, a false premise. The conclusion might be false (all fish fly, all whales are fish, so all whales fly) or, by luck, true (all fish fly, all sparrows are fish, so all sparrows fly). A valid form with a false premise guarantees nothing about the conclusion either way.

Invalid, all premises true. The conclusion might be true (every cat is a mammal, my neighbour's tabby is a mammal, so the tabby is a cat) or false (every cat is a mammal, my dog is a mammal, so my dog is a cat). The premises being true doesn't help, because the link doesn't hold.

Invalid, a false premise. Anything goes.

The empty cell is: valid, all premises true, conclusion false. That combination cannot exist. Rarity has nothing to do with it; "valid" rules it out by definition. Knachel's open textbook states validity three ways in a row to make exactly this point: an argument is valid when "its premises guarantee its conclusion", when "IF its premises are true, then its conclusion must also be true", and when "it is impossible for its premises to be true and its conclusion false".² Those are three descriptions of one empty cell, and it's the piece of this lesson I'd ask you to memorise rather than reconstruct.

The table has a use that's easy to miss. If you know an argument is valid and you know its conclusion is false, you've learned something about the premises without reading them: at least one of them is false. That's the shape of a very old style of argument called reductio, and it's the shape of every "if that were true, then this would follow, and it doesn't" you have ever made.

Sound: the word for what you actually wanted

Validity by itself doesn't get you anywhere. A valid argument with a false premise is a perfectly built bridge starting from the wrong bank. What you want is an argument that's valid and has true premises. That is called sound. Again from forall x: "an argument is sound if and only if it is both valid and all of its premises are true."¹

A sound argument guarantees its conclusion, which is a stronger thing than making it likely. If someone shows you a sound argument for a conclusion you dislike, the conclusion is true and your dislike is the thing that has to move. That's a strong claim, and it's exactly why "sound" is a high bar: you have to establish validity, which logic can do, and the truth of every premise, which logic can't.

Here's the line from forall x that runs through this whole course. To rebut an argument, "you can show that (one or more of) the premises are not true, or you can show that the argument is not valid. Logic, however, will only help you with the latter!"¹ Logic tests the link. Whether the premises are true is a question about the world, and it needs evidence, which is the business of other courses (statistics, science, history) and of lesson 7's acceptability condition here. What this lesson gives you is the half of the job you can do at your desk.

A myth worth clearing away

You may have been taught that deduction goes from the general to the particular and induction goes from the particular to the general. It's in a lot of school notes, and it's wrong. The Internet Encyclopedia of Philosophy's survey of this distinction takes the proposal up directly, in the form that deductive arguments "begin with a 'general' or 'universal' premise and move to a less general conclusion" while inductive ones "begin with 'particular', 'specific', or 'individual' premises and move to a more general conclusion", and rejects it as "much too crude for drawing a categorical distinction", facing "prima facie plausible exceptions" it can't absorb.³

The real difference is what the premises are claimed to do. Van Cleave's open textbook puts it in one pair of sentences: a deductive argument is one "whose conclusion is supposed to follow from its premises with absolute certainty", and an inductive argument is one "whose conclusion is supposed to follow from its premises with a high level of probability".² Direction of travel has nothing to do with it.

Two examples make this stick. "All humans are mortal; Socrates is human; so Socrates is mortal" is deductive and runs general to particular, which fits the myth. But "this coin came up heads a thousand times, so the next toss will probably be heads" is inductive and runs particular to particular. And "Ana and Ben are the only two people in the choir; Ana is forty; Ben is forty; so everyone in the choir is forty" runs particular to general and is deductive: if those premises are true the conclusion cannot be false.

Why does it matter? Because the two kinds get different tests. For a deductive argument, one counterexample is fatal, and "valid" is all or nothing. For an inductive argument, a counterexample is just a data point, and the question is how strong the support is, which is lesson 5. If you sort by direction, you'll run the wrong test on a quarter of what you meet.

Worked example with a gap: building a counterexample

Here's the method, done once for you and then handed over. Take this shape:

1. All A are B.
2. Some B are C.
-------------------
C: Some A are C.

It looks reasonable. A sits inside B, and C overlaps B, so surely C reaches A? Let's try to break it. The rule: pick everyday classes for A, B and C that make both premises obviously true and the conclusion obviously false.

First attempt: A = cats, B = mammals, C = pets. All cats are mammals, true. Some mammals are pets, true. Some cats are pets. True. This substitution isn't a counterexample; the conclusion came out true. That doesn't mean the argument is valid. It means this particular content didn't expose the gap. Both premises can be true in ways that leave the conclusion true, and the question is whether they can be true in a way that leaves it false.

Now you try. Keep A = cats and B = mammals. Find a C that overlaps mammals but has no cats in it at all. Write it down before you go on.

Two things to notice about the method. First, the content you use to break a shape has nothing to do with the content of the argument you're testing. You're testing the skeleton, so you want the most familiar flesh you can find: cats, dogs, mammals, whales, squares and rectangles. Familiar content makes truth and falsehood obvious, which is the point.

Second, a failed attempt proves nothing, and a successful one proves everything. If you try three substitutions and each leaves the conclusion true, you haven't shown validity, only that you haven't found the hole yet. Proving a shape valid takes a different tool (lesson 4 gives you the Venn method for exactly this family), and the asymmetry is real: one counterexample settles invalidity, no number of confirming cases settles validity.

Where it goes wrong in practice: belief bias

Everything so far you could learn from a textbook. Here is the part the textbooks were slower to admit. Even people who understand the definition of validity, who've been told to judge logic and nothing else, judge the conclusion instead.

In 1983 Jonathan Evans, Julie Barston and Paul Pollard at Plymouth Polytechnic in England ran three experiments on syllogisms, the two-premise arguments this lesson has been using.⁴ The design was clever. Every argument was one of four kinds: valid with a believable conclusion, valid with an unbelievable one, invalid with a believable one, invalid with an unbelievable one. Undergraduates were told to treat each as a logic problem and to accept a conclusion only if it necessarily followed from the premises.⁵

Evans's own examples, from a later review he wrote of this work, are worth reading slowly, because you'll feel the pull.⁵

Valid, believable: "No police dogs are vicious. Some highly trained dogs are vicious. Therefore, some highly trained dogs are not police dogs."

Valid, unbelievable: "No nutritional things are inexpensive. Some vitamin tablets are inexpensive. Therefore, some vitamin tablets are not nutritional."

Invalid, believable: "No addictive things are inexpensive. Some cigarettes are inexpensive. Therefore, some addictive things are not cigarettes."

Invalid, unbelievable: "No millionaires are hard workers. Some rich people are hard workers. Therefore, some millionaires are not rich people."

Look at the last two. They have exactly the same shape. Both are invalid; from "no A are B, some C are B" what actually follows is "some C are not A" (some cigarettes are not addictive; some rich people are not millionaires), and the conclusion offered runs the other way. You can build the counterexample for the cigarettes one yourself: imagine the only addictive things in the world are cigarettes, all of them expensive, and there are also some cheap cigarettes that aren't addictive. Both premises true; "some addictive things are not cigarettes" false.

Those two figures are the pattern in miniature. The paper's abstract reports "substantial belief biases" alongside "equally substantial effects of logic", and one consistent interaction: "belief bias was more marked on invalid than on valid syllogisms."⁴ In other words, people did respond to logic, valid arguments were accepted more than invalid ones, but a believable conclusion could carry an invalid argument most of the way to acceptance, while an unbelievable conclusion made even a valid argument harder to accept. In the second experiment, with sixty-four students, subjects were correct 87% of the time when logic and belief pointed the same way and 48% of the time when they conflicted.⁴ Where the two disagreed, judgement fell to a coin toss.

I want to be precise about what you're allowed to conclude. The people in these studies were intelligent adults who had been told, in writing, to judge the logic. They were not careless. They were doing what minds do.

Why the mind does this

The honest answer has two layers: what is well established, and what is still argued about.

What's established is the pattern itself. It has been replicated many times, including by Evans's group with the same materials, and it's larger on invalid arguments.⁴⁶ The mechanism the outline of this course uses, and which Evans and his colleagues proposed as one account, goes like this. Checking a conclusion against what you already believe is fast; you do it before you've finished reading. Checking whether the premises force the conclusion is slow; you have to build the situation the premises describe and look for a way the conclusion fails. If the fast check comes back "yes, that's true", many people stop there. If it comes back "no, that's absurd", they go looking for the flaw, and find it. Evans's group called this selective scrutiny: the conclusion is scanned for believability first, and the premises get real attention mainly when the conclusion fails that scan.⁶

The verbal protocols from the 1983 study fit that picture. The abstract describes them as, in some cases, "rationalizations for prejudiced decisions" and, in others, "a genuine process of premise to conclusion reasoning".⁴ Some subjects had decided and were explaining afterwards; some were reasoning. And in Evans's later account of the protocols, subjects who focused first on the conclusion were more open to belief, while those who started from the premises reasoned better.⁶ Where you look first matters.

What's unsettled is the deeper story, and the disagreement is sharper than a footnote. Evans's own team offered a second account alongside selective scrutiny, on which people reason first and fall back on belief when the logic feels inconclusive.⁶ Karl Christoph Klauer and his colleagues reanalysed twenty-two studies in 2000, concluded the standard accept-or-reject data are too sparse to tell those accounts apart, and proposed their own.⁷ And in 2010 Chad Dube, Caren Rotello and Evan Heit mounted the strongest challenge of all. Using methods built to separate accuracy from willingness to say yes, borrowed from the study of memory, they argue that belief doesn't degrade reasoning at all: you scrutinise a believable argument just as hard as an unbelievable one, and what belief shifts is your threshold for saying "follows", so you accept the same quality of evidence more readily.⁸ That isn't a quibble about wording. If they're right, the fast-check story above is wrong, and the classic experiments were measuring a response habit rather than a reasoning failure. What would settle it is more data of the kind their method demands: designs that trace accuracy and willingness separately, such as confidence-rating curves or forced choices between matched arguments, rather than lone accept-or-reject counts. So far each camp claims those results for its own side, and I'm not going to pretend it's resolved.

Here's the ground every account shares, and it's all the practical advice needs: a conclusion you already believe is more likely to get your yes, whether or not the argument earned it. Maybe you check less, as Evans's group read it. Maybe you check just as hard and say yes more easily, as Dube, Rotello and Heit read it. Either way, an invalid argument for something you believe will get past you more often than an invalid argument for something you doubt, and the defence in the next section works under both stories, because it doesn't ask you to check harder. It asks you to check in a fixed order, before your opinion of the conclusion gets a vote.

The fix is an order of operations

You can't switch belief bias off. What you can do is stop your first reaction to the conclusion from being the last word. That's what step 6 of the check is for, and why it's step 6 and not step 1.

When you meet an argument, especially one whose conclusion you have feelings about:

1. Find the conclusion.
2. Find the premises.
3. Supply what's missing.
4. Test the link. For a deductive argument, that means asking: could every premise be true and the conclusion still false? Try to build the case.
5. Test the premises. Are they true, or acceptable on the evidence you have?
6. Only now ask whether you believe the conclusion, and let steps 4 and 5 tell you what to do with that belief.

The order matters more than any single step. If you skip to 6, you'll do 4 badly, and you'll do it worst on the arguments that flatter you. If you force yourself through 4 first, you'll catch the cigarettes argument even though you agree with it, because "could the premises be true and this false?" has an answer that doesn't depend on what you think of cigarettes.

One habit that helps: when the conclusion is one you like, swap the content for something neutral before you judge the shape. That's what the cat-and-dog version of the damp argument did in the first paragraph. You couldn't feel the flaw with damp in the sentences; you could feel it instantly with cats. The shape hadn't changed. Your feelings had gone quiet.

What people get wrong

"Valid means true." Validity is a property of the link. "All fish fly, all whales are fish, so all whales fly" is valid and everything in it is false. If you catch yourself saying "that's not valid, it's not even true", you've merged two questions that need to stay apart.

"Valid means good." A valid argument with a false premise establishes nothing. The word you want for "good" in the deductive case is sound, and sound is a much harder thing to show.

"A false conclusion means the argument is invalid." No. A false conclusion plus a valid form tells you a premise is false. The whales-fly argument is valid, false conclusion and all. What a false conclusion rules out is soundness, not validity.

"Logic tells you what's true." It tells you what follows from what. In forall x's words, logic helps you show an argument is invalid but not that a premise is false.¹ If someone says "logically, X", they've either shown that X follows from premises you'll have to check separately, or they've said nothing.

"Deduction goes general to particular." Covered above. The distinction is what the premises claim to do, and the direction test fails on ordinary examples running both ways.³

"I understood the definition, so I'm immune." The subjects in 1983 had the definition in the instructions. Understanding validity and applying it under the pull of a believable conclusion are two different skills, and only the second one protects you.

Practice

Sort each of the six arguments below into one of the four cells: valid or invalid, premises all true or at least one false. For every invalid one, give a counterexample: describe a possible case in which every premise is true and the conclusion is false. Describe the case directly where you can see it; where you can't, keep the shape, swap the content, and let the parallel argument show you the case. Do the work on paper before you open the answers.

1. All squares are rectangles. All rectangles have four sides. So all squares have four sides.
2. All squares are rectangles. Some rectangles are not squares. So some squares are not rectangles.
3. No insects have eight legs. All spiders have eight legs. So no spiders are insects.
4. All birds can fly. Penguins are birds. So penguins can fly.
5. Every apple in this bowl is green. The fruit in my hand came from this bowl and is green. So the fruit in my hand is an apple.
6. Anyone who can vote here is over eighteen. Maya is over eighteen. So Maya can vote here.

One more from lesson 1, as a spaced review. "I left the party early because the last train was at eleven." Argument or explanation? It's an explanation: the leaving is taken as given and the sentence says why. Now: "You should leave the party early, because the last train is at eleven." That "because" introduces a premise, and this is an argument with a missing premise in brackets: [If you miss the last train, you'll have no way home]. Same word, opposite job, which is why the indicator words are hints and not rules.

Connections

This lesson fills in step 4 of the check for deductive arguments. Lesson 3 gives you the four conditional shapes worth memorising (if-then, and its cousins) and the two invalid look-alikes that fool almost everyone; you'll recognise argument (6) above when you get there. Lesson 4 gives you a pencil-and-paper method for all/no/some arguments like the ones in this lesson, so you can prove a shape valid rather than just failing to break it.

Lesson 5 opens the other kind of link, where the premises only claim to make the conclusion probable, and where a counterexample weakens rather than kills. Belief bias comes back in lesson 9 as motivated reasoning, the same fast conclusion-check running on the news, and the symmetry note above becomes a checklist.

Go deeper

• forall x: Calgary, Part I (chapters 1 to 3), free at forallx.openlogicproject.org. Twenty pages on arguments, validity, and the other logical notions, written plainly by logicians. Parts II and III give you truth tables, the formal version of the counterexample method, if you want the symbols.
• Van Cleave, Introduction to Logic and Critical Thinking (2nd ed., CC BY 4.0), sections 1.6 to 1.8. Validity, soundness and the deductive/inductive distinction in about six pages, free, with exercises. The natural next thing to read after this lesson.
• Knachel, Fundamental Methods of Logic (CC BY 4.0), section 1.4, the same ground stated a different way. Reading one idea in two writers’ words is a cheap way to find out whether you actually have it.
• The Internet Encyclopedia of Philosophy on deductive and inductive arguments, if you want to see how unsettled the distinction gets once you push on it. Section 9 is where the general-to-particular proposal is taken apart. Harder than the rest of this list, and worth it.
• Evans, "In two minds: dual-process accounts of reasoning", Trends in Cognitive Sciences 7(10), 2003, 454 to 459. A short, readable review by the lead author of the 1983 study, with the belief-bias effect in a box and the Wason task, which lesson 3 covers, in another.
• Evans, Barston and Pollard, "On the conflict between logic and belief in syllogistic reasoning", Memory & Cognition 11(3), 1983, 295 to 306. The original paper. It's readable, and the verbal protocols in the discussion are worth the effort.

Sources

1. Magnus, P. D., Button, T., Trueman, R., Zach, R. et al., forall x: Calgary (Fall 2025 edition, CC BY 4.0), chapter 2. Definitions of valid, invalid and counterexample; "validity is not about the actual truth or falsity of the sentences in the argument ... It is often said that logic doesn't care about feelings. Actually, it doesn't care about facts, either"; definition of sound as valid with all premises true; rebutting an argument by attacking a premise or the link, and "Logic, however, will only help you with the latter!"
2. Two open textbooks, both CC BY 4.0, both read on LibreTexts at draft time. Knachel, M., Fundamental Methods of Logic (University of Wisconsin-Milwaukee), section 1.4: validity stated three ways ("its premises guarantee its conclusion"; "IF its premises are true, then its conclusion must also be true"; "it is impossible for its premises to be true and its conclusion false"), and an argument is sound "just in case (i) it’s valid, AND (ii) its premises are in fact true". https://human.libretexts.org/Bookshelves/Philosophy/Logic_and_Reasoning/Fundamental_Methods_of_Logic_(Knachel)/01%3A_The_Basics_of_Logical_Analysis/1.04%3A_Deductive_and_Inductive_Arguments Van Cleave, M., Introduction to Logic and Critical Thinking, 2nd ed., sections 1.6 to 1.8: a deductive argument’s conclusion is "supposed to follow from its premises with absolute certainty", an inductive argument’s "with a high level of probability"; a sound argument is "a valid argument that has all true premises"; "whereas strong inductive arguments are defeasible, valid deductive arguments aren’t". https://human.libretexts.org/Bookshelves/Philosophy/Logic_and_Reasoning/Introduction_to_Logic_and_Critical_Thinking_2e_(van_Cleave)/01%3A_Reconstructing_and_Analyzing_Arguments/1.06%3A_Validity
3. Internet Encyclopedia of Philosophy, "Deductive and Inductive Arguments", section 9. States the general-to-particular proposal in the form quoted here and rejects it as "much too crude for drawing a categorical distinction", one facing "prima facie plausible exceptions" it cannot absorb. https://iep.utm.edu/deductive-inductive-arguments/
4. Evans, J. St. B. T., Barston, J. L. & Pollard, P., "On the conflict between logic and belief in syllogistic reasoning", Memory & Cognition 11(3), 1983, 295 to 306. Plymouth Polytechnic. Three experiments; abstract: "Substantial belief biases were observed despite controls for possible conversions of the premises. Equally substantial effects of logic were observed despite controls for two possible response biases. A consistent interaction between belief and logic was also recorded; belief bias was more marked on invalid than on valid syllogisms." Protocols "interpreted in some cases as providing rationalizations for prejudiced decisions and, in other cases, as reflecting a genuine process of premise to conclusion reasoning." Experiment 2 (64 undergraduates, paid volunteers): "Overall, subjects were correct 87% of the time when logic accorded with belief and 48% of the time when it did not" (p. 300, read from the paper).
5. Evans, J. St. B. T., "In two minds: dual-process accounts of reasoning", Trends in Cognitive Sciences 7(10), 2003, 454 to 459, Box 1. The four example syllogisms (police dogs; vitamin tablets; cigarettes; millionaires) as the four cells of the 1983 design; participants instructed to endorse only conclusions that necessarily follow; "intelligent adult populations (undergraduate students) are consistently influenced by the prior believability of the conclusion"; "more belief-bias on invalid arguments".
6. Lambell, N. J., Evans, J. St. B. T. & Handley, S. J., "Belief bias, logical reasoning and presentation order on the syllogistic evaluation task", Proceedings of the Cognitive Science Society (read from the eScholarship PDF). Restates the 1983 results with the same materials: "71% of participants across three experiments erroneously endorsed" the invalid believable conclusion, and "only 10% of participants across three experiments erroneously endorse" the invalid unbelievable one. Describes the selective scrutiny model (believability of the conclusion scanned first) and the misinterpreted necessity model, and reports from the 1983 protocols that subjects who focused first on the conclusion were more susceptible to belief while those who focused on the premises reasoned better. Their own replication used materials "identical to those employed by Evans et al. (1983)".
7. Klauer, K. C., Musch, J. & Naumer, B., "On belief bias in syllogistic reasoning", Psychological Review 107(4), 2000, 852 to 884 (abstract). A model-based meta-analysis of 22 studies found the standard acceptance data "structurally too sparse" to discriminate between accounts of belief bias.
8. Dube, C., Rotello, C. M. & Heit, E., "Assessing the belief bias effect with ROCs: It's a response bias effect", Psychological Review 117(3), 2010, 831 to 863 (abstract and title). Argues, from ROC analyses that separate accuracy from response criterion, that belief bias in these tasks is a shift in willingness to accept, not a change in reasoning accuracy: people do not reason worse on believable conclusions, they are readier to say yes. The strongest form of the dissenting view; presented in the lesson as a live, unresolved challenge.