Reality and Belief

Ask someone how they know the sun will rise tomorrow and you get a shrug, because the question sounds like a trick. Ask how they know they are not dreaming and the shrug turns into something warier. Both are requests for exactly the same thing, and the fact that they feel so different is the first evidence that the word "know" is carrying more than it looks.

This course spends fifteen lessons on three questions people argue about badly: what is actually real, whether there is a God, and whether we are anything special. None of them can be argued about well until the standard for a good answer is fixed, and that is the job of this lesson. It is the least dramatic in the course and the one the other fourteen lean on.

What a claim to know contains

Knowing is not the same as believing, because a belief can be false and knowledge cannot. If you believed the meeting was at three and it was at four, you did not know it was at three. You were wrong. So truth is one condition, and it is a condition about the world rather than about you.

A true belief is not enough either. Someone who backs a horse because its name reminds them of a childhood dog, and wins, held a true belief and knew nothing. They were lucky. So something has to connect the believing to the truth, and the traditional name for that something is justification: a reason, evidence, a reliable route by which the belief arrived.

Together these give the analysis that held the field for two thousand years. You know that p when

1. p is true,
2. you believe that p,
3. you are justified in believing that p.

It is usually credited to Plato, though the credit is loose. In the Theaetetus, written around 369 BC, Socrates puts up the proposal that knowledge is true judgement with an account, takes it seriously for several pages, and then rejects it without finding anything to put in its place. The dialogue ends in failure, which is worth knowing: the analysis is not handed down as doctrine, it is the best surviving candidate from an argument that Plato thought he had lost.

The Meno gives the better image. True opinions, Socrates says, are like the statues of Daedalus, which were reputed to run away in the night unless somebody tied them down, and what ties an opinion down is working out the reason for it. Justification is a tether. An untethered true belief is not worthless, it is just liable to be gone in the morning.

Notice what each condition does on its own, because the sceptical arguments in the next lesson go after them one at a time. Truth is a fact about the world. Belief is a fact about you. Justification is the relation between the two, and it is the only one of the three you can inspect from where you are sitting. That asymmetry is the entire opening through which scepticism gets in.

Example. Three people each say "there is milk in the fridge". The first checked an hour ago and there is. The second has not looked but always buys milk on Tuesdays, and today is Tuesday, and there is milk. The third insists there is milk because they feel there is, and there is. Which of them knows?

The first clearly does: true, believed, and justified by the right sort of route. The third clearly does not, because the belief is true and nothing connects it to the truth, which is the horse and the childhood dog again. The second is the interesting one and the honest answer is that it depends on how good the Tuesday habit is. If they have bought milk every Tuesday for ten years, the inference is a decent one and most people would grant knowledge. If they have done it twice, it is a guess wearing a reason. Justification is not a switch, it comes in degrees, and the analysis above hides that by writing condition three as though it were yes or no.

Now you. A doctor reads a scan and concludes the patient has a fracture. The scan is genuine, the reading is competent, the patient does have a fracture. Later it emerges the scan was mislabelled and belongs to a different patient, who also has a fracture in the same place. Did the doctor know?

Three pages that broke it

In June 1963 Edmund Gettier published a paper in Analysis, volume 23, running from page 121 to page 123. It was three pages long, it was his only significant publication, and it ended the two thousand year consensus.

His first case. Smith and Jones have both applied for a job. The company president has told Smith that Jones will get it. Smith has also counted the coins in Jones's pocket and found ten. Smith therefore has strong evidence for

the man who will get the job has ten coins in his pocket

and believes it on that basis. As it happens, Smith gets the job, and, unknown to him, Smith has ten coins in his own pocket. The belief is true. It is believed. It is justified, by the president's word and a count. And it is plainly not knowledge, because Smith is right about a proposition that turns out to be about himself for reasons that had nothing to do with him.

Bertrand Russell had constructed the same shape fifteen years earlier, in Human Knowledge: Its Scope and Limits (1948), with a cleaner example that is now the standard teaching case. A clock on the wall stopped exactly twenty four hours ago. You glance at it at precisely the moment it is right, read the time off it, and form a true belief about the hour, justified by the ordinary and normally excellent practice of looking at clocks. You do not know the time. You would have said the same thing a minute earlier and been wrong.

The common structure is this: justification that does not reach through to the truth, so that the belief is true by accident. That matters because ruling out accident was supposed to be justification's entire job. The third condition was added precisely to exclude the horse named after the dog, and Gettier's cases show that it does not exclude it, it only makes the luck harder to see.

Example. Someone owns a car and you have seen them driving it for years, so you believe "somebody in this office owns a car". In fact they sold it last week and are driving a hire car, but a new colleague you have never spoken to owns one. Is this a Gettier case, and what makes the answer yes or no?

Yes, and the diagnostic is the same as before. The belief is true, believed, and justified. But the justification runs through a false intermediate claim, that your colleague still owns a car, while the truth of your belief rests on a completely separate fact you know nothing about. Take away the new colleague and your evidence is untouched while your belief becomes false, which shows the evidence was never tracking the thing that made it true. That test, asking whether the belief could have been false with the evidence unchanged, is the most useful thing to carry away from this section.

Now you. A stopped clock is on the wall. You know it is stopped, but you also know it stopped at exactly 6:00 and you have independent reason to think it is now within a minute or so of six. You look, read 6:00, and believe it is about six. It is. Is this a Gettier case?

Sixty years of repairs

The obvious first patch was to require that your reasoning contain no false step. Michael Clark proposed it within months, in 1963, and it handles both of Gettier's cases, since Smith's inference runs through the falsehood that Jones will get the job. It fails on cases built without any false step, which were duly built.

Reliabilism, developed by Alvin Goldman from 1967, drops justification as a matter of having reasons and requires instead that the belief be produced by a process that mostly yields truths. Robert Nozick proposed sensitivity in Philosophical Explanations (1981): you know only if, had p been false, you would not have believed it. Ernest Sosa preferred safety: you know only if you could not easily have believed p falsely. Timothy Williamson, in Knowledge and Its Limits (2000), took the more radical line that the whole project is misconceived, that knowledge is not built out of belief plus extras but is a basic state in its own right.

Sixty years on there is no agreed analysis of knowledge. That sounds like a failure and for the purposes of this course it is not, because nothing later depends on having a definition. What the course needs is the three parts, the recognition that luck defeats knowledge, and the safety test. Those survive every version of the dispute.

Knowing is not being certain

Here is the distinction the next three lessons live on, and it is the one most often collapsed in ordinary argument.

Certainty is a maximum. To be certain of p is for there to be no possibility whatever that you are wrong. Descartes, in the Meditations of 1641, went looking for beliefs with that property, on the reasonable-sounding ground that a house built on anything less could fall down. He found almost nothing, and the next lesson follows him into that hole.

Knowledge, on almost every modern account, demands much less. Fallibilism is the position that you can know that p while it remains possible that you are wrong about p. You know your own name, and you could conceivably have been swapped at birth. You know you had breakfast, and you could conceivably be misremembering. Requiring certainty for knowledge does not make knowledge more rigorous, it makes the word useless, since on that standard almost nothing outside mathematics and your own current experience is ever known by anyone.

Why this matters so much: the sceptical arguments coming in the next lesson are excellent at establishing that you cannot be certain. If knowledge required certainty, that would be the end of the matter and the course could stop at lesson two. Because it does not, the sceptic has further work to do, and watching exactly how that further work is attempted is what lessons two to four are about.

Example. A friend says: "You can't be one hundred percent sure the external world exists. So you don't really know it does. So believing in it is just faith, like religion." Where does this go wrong?

At the second step, and the error is an equivocation on "really know". The first claim is true and almost nobody disputes it. The second slides from an absence of certainty to an absence of knowledge, which only follows if knowledge requires certainty, and that premise is never stated because stating it would reveal how implausible it is. The third step compounds it by treating everything short of certainty as equally unsupported, which throws away the entire difference between a belief with overwhelming evidence and one with none. Lesson five is about how to grade that difference properly, and lesson twelve returns to this exact move, because it is the commonest bad argument in debates about God, deployed by both sides.

Now you. A second friend replies: "Fine, but if you admit you might be wrong about the external world, you have to admit you might be wrong about anything, and then no belief is better than any other." What has been assumed?

The standard an argument has to meet

One paragraph of housekeeping, because the rest of the course is arguments and they are all judged the same way. An argument is valid when its premises cannot all be true while its conclusion is false, and sound when it is valid and its premises are in fact true. Validity is about shape and is settled without leaving your chair; soundness needs the world. The practical consequence, which the logic course develops and this one simply uses, is that if you find an argument valid and you reject its conclusion, you are obliged to name a premise you deny. "I do not find it convincing" is not a move. Every major dispute in this course, including the existence of God and whether we are alone, can be laid out as one valid argument with three or four premises, and each position is a choice about which premise to give up. The final lesson does that explicitly.

What philosophers actually think

The 2020 PhilPapers Survey, run by David Bourget and David Chalmers, asked close to 1800 professional philosophers where they stood on a long list of questions. On the external world, 79.5 percent accepted or leaned towards non-skeptical realism, 6.6 percent towards idealism, and 5.4 percent towards skepticism, with the rest choosing something else. The proportions in the 2009 round were close to the same.

Two things follow. First, scepticism is not a live position among people who spend their careers on this, which is worth knowing before spending a lesson on it. Second, and more important, that is not an argument, and you should not take it as one. The reason to read the next lesson is that the sceptical arguments are genuinely hard to answer, and the interesting question is not whether professionals believe the conclusion but what exactly they think is wrong with the reasoning. Four out of five philosophers rejecting a conclusion while still teaching the argument every year is a signal that the argument is doing something useful.

The three conditions are now on the table, along with the fact that the third one leaks, and the distinction between knowing and being certain. The next lesson takes the strongest arguments ever built for the claim that condition three never holds for anything outside your own head, and states them at full strength before laying a finger on them.

The sceptical arguments have a bad reputation, mostly earned by the way they are usually presented. Somebody says you cannot prove you are not dreaming, everybody agrees that is interesting, and the conversation moves on without anyone having stated an argument. This lesson states three, at full strength, and does not answer any of them. The answering is lesson four.

Take the standard from lesson one seriously while reading. These arguments are all valid. If you reject the conclusion, you owe a premise.

The dream argument

Descartes opens the Meditations on First Philosophy (1641) with it, though the observation is much older and appears in Zhuangzi in the fourth century BC, where a man dreams he is a butterfly and wakes unsure which way round it goes.

Descartes' version is tighter than the folklore. He does not claim you might be dreaming right now and leave it there. He argues:

1. There is no mark by which waking experience can be told from dreaming experience with certainty.
2. If there is no such mark, then any belief you hold on the basis of experience might be a belief formed while dreaming.
3. A belief formed while dreaming, about the world outside you, is not knowledge.
4. So no belief you hold on the basis of experience is knowledge.

Premise 1 is the one people attack, usually by saying dreams are incoherent, or that you can read text in waking life and not in dreams, or that pinching works. These replies share a defect: each cites a feature of dreams noticed while awake. To use the feature you would have to know you were awake when you noticed it, which is what is in question. The reply is not obviously wrong, but it is circular in a way that needs argument rather than assertion.

The more effective objection runs at premise 3, and it is worth seeing now because the same move works elsewhere. Dreaming is parasitic. You dream of houses and horses and your mother, and those concepts came from somewhere. A mind that had only ever dreamed would have nothing to dream about. So the dream argument, pushed all the way, may undercut itself: universal dreaming is not a coherent hypothesis. This does not save any particular belief, since tonight's dream can still be wrong about everything, but it limits the damage.

Example. Someone says: "I know I am awake because I just did a reality check. I looked at my hand, looked away, looked back, and it was the same." What premise is this aimed at, and does it hit?

It is aimed at premise 1, offering stability of perception as the mark that distinguishes waking from dreaming. It does not hit, for the circularity reason above: the claim that hands are unstable in dreams is something learned while apparently awake, and lucid dreamers report perfectly stable hands. But notice the shape of the failure, because it recurs throughout the course. The test is not useless, it is just useless against this argument, since the argument has already put in question the very body of experience the test appeals to. A test that assumes what is in dispute cannot settle the dispute.

Now you. A second person says: "The dream argument proves too much. If I cannot tell dreaming from waking, then I cannot tell whether I am dreaming the argument, so I have no reason to accept its conclusion either." Is that a good objection?

The evil demon

Descartes escalates in the same work. Suppose not a natural lapse of judgement but a deceiver of the utmost power and cunning, who devotes all his energy to misleading you. The sky, the earth, your body, and the memory of yesterday are all produced in you by the demon. What survives?

Very little, and the little that survives is the famous part. You cannot be deceived about your own existence while being deceived, since deception requires a subject. Cogito, ergo sum is not a syllogism so much as a performance: the act of doubting establishes the doubter. It is worth being precise about what it delivers, because it is routinely oversold. It gives you a thinking thing, existing now. It does not give you a body, a past, a world, or the identity of the thinker with the person whose name you sign.

It is also worth noticing what the demon hypothesis costs its user. A deceiver of unlimited power and unlimited malice is a large thing to posit, and lesson nine asks what a hypothesis has to do to earn its keep. Descartes does not need the demon to be plausible, only possible, but that concession is doing real work and a reader should mark it now: the sceptic is running on bare possibility, and the strongest reply in lesson four is that bare possibility is cheap.

The demon is stronger than the dream in two ways. It reaches memory, so the argument about dreaming being parasitic on waking experience no longer applies: the demon could have manufactured the concepts. And it reaches reasoning, since a sufficiently powerful deceiver could make invalid inferences feel valid. That second reach is what makes the demon genuinely alarming rather than merely striking.

Example. A student says the cogito proves too little to be interesting, since knowing that something is thinking gets you nowhere. Is that fair?

Half fair, and the half that is wrong matters. It is true that the foundation is very thin, and the attempt to build outward from it, via an argument that a perfect God would not permit systematic deception, is the least admired part of the Meditations. But the cogito is not really a premise to reason from, it is an existence proof: it shows the sceptical argument has a floor, that not everything can be doubted at once. That matters for the shape of the debate, because a scepticism with no fixed point consumes itself, while one with a fixed point is a position that can be argued with. The student is right that the floor is low and wrong that a floor is worthless.

Now you. Both the dream and the demon conclude that you cannot trust your experience. Why is the demon the stronger argument?

The brain in a vat

The modern restatement, from Hilary Putnam in Reason, Truth and History (1981), removes the theology. You are a brain in a vat of nutrients, wired to a computer that feeds you exactly the experiences you are having now. Everything seems as it does. Nothing you could check would come out differently.

Its usual form is not the four-step argument above but a shorter and sharper one built on a principle from logic:

1. You do not know you are not a brain in a vat.
2. If you know you have hands, and you know that having hands entails not being a brain in a vat, then you know you are not a brain in a vat.
3. So you do not know you have hands.

Step 2 is an application of closure: knowledge is closed under known entailment, meaning that if you know p, and you know p entails q, then you are in a position to know q. Closure looks almost undeniable. It is what licenses ordinary reasoning: knowing the train leaves at six and knowing that entails it does not leave at seven, you know it does not leave at seven. Denying it has a cost that lesson four takes seriously.

Premise 1 looks undeniable too, since the vat scenario is constructed to be indistinguishable from the inside. So the argument is valid, both premises are plausible, and the conclusion is that you do not know the most obvious thing about yourself. That is the sceptical problem in its cleanest modern form, and it is why the vat rather than the demon is what contemporary epistemology argues about.

Putnam himself thought the hypothesis self-refuting, by an argument about what words refer to: a brain that had only ever been in a vat could not mean by "vat" what we mean, since its word never contacted any vats, so its sentence "I am a brain in a vat" could not be true. The argument is ingenious and contested, and it only touches lifelong vat-dwellers, not someone envatted last Tuesday.

Example. Someone objects: "The vat story is unscientific. We have no such computers, no such surgery, and no reason to think anyone is doing this." Does the objection work?

No, and seeing why is important. The sceptic is not claiming the scenario is likely, or actual, or even physically achievable. The argument needs only that it is possible and that you cannot rule it out from the inside. Premise 1 says you do not know it is false, and improbability is not knowledge of falsehood: you do not know you will not be struck by lightning today, though it is very unlikely. The objection would matter if the argument were an inference to the best explanation, which is exactly the form lesson four uses against it. Here it misses.

Now you. Compare the three arguments. Which of the three conditions from lesson one does each attack, and do they all attack the same one?

Why these are not silly

Two features make the sceptical arguments worth a lesson rather than a joke.

First, nobody has produced an answer that all sides accept, and the attempts are the history of modern epistemology. Descartes tried to argue from a non-deceiving God, which most readers find circular. Kant tried to argue that the very possibility of experience presupposes an objective world. Moore held up his hands. Putnam used the theory of reference. Every one of these is a serious position with serious critics, and lesson four takes the best of them.

Second, the arguments are not idle. Their structure is reused wherever someone claims a hypothesis cannot be ruled out and concludes that you therefore know nothing about the matter, which is a move made constantly in arguments about God, about consciousness, and about whether the universe is fine-tuned. Recognising the shape here makes it recognisable later, and lesson nine gives the criterion for when it is legitimate.

What the arguments share is that they trade on a gap between experience and its causes. You have the experiences. The claim that a world outside causes them is an inference, and lesson four's most promising reply argues that it is a very good inference, which requires the machinery of lesson five. Before that, the version of this argument that is currently taken most seriously, and most often misreported, is the one where the deceiver is not a demon but ourselves.

Of all the arguments in this course, this is the one most people have heard and the one most people have heard wrong. The popular version is "we are probably living in a simulation, and a philosopher proved it". That is not the conclusion, it is not close to the conclusion, and the gap between the two is a useful lesson in reading an argument for what it says.

What the argument actually claims

Nick Bostrom published "Are You Living in a Computer Simulation?" in Philosophical Quarterly in 2003. Its conclusion is that at least one of the following three propositions is true:

1. The human species is very likely to go extinct before reaching a posthuman stage of technological maturity.
2. Any posthuman civilisation is extremely unlikely to run a significant number of simulations of its evolutionary history.
3. We are almost certainly living in a computer simulation.

That is a disjunction. It says one of these holds, and it does not say which. Bostrom's own stated view has been that we should distribute our belief roughly evenly across the three, which is the opposite of a claim that the third is true.

The reasoning behind it is short. Suppose a civilisation reaches the point where it can run detailed simulations of conscious beings at low cost. Suppose some such civilisations choose to run simulations of their own ancestors, which is the kind of thing curious and wealthy societies do. Then the number of simulated observers with experiences like ours vastly exceeds the number of original ones, because the originals are one civilisation and the simulations are many. If you have no way of telling which kind you are, you should think you are probably of the more numerous kind.

Each of the three propositions is a way of blocking that conclusion. The first blocks it by denying anyone gets the technology. The second blocks it by denying anyone uses it. The third accepts it.

Example. A friend says: "Bostrom calculated the probability we are simulated at over 99 percent." What has gone wrong?

Two things. The argument produces no such number and produces no unconditional probability at all. What it produces is a conditional: if the first two propositions are false, then the third follows, because the counting argument goes through. Turning that into an unconditional figure requires you to supply your own confidence that civilisations survive and that survivors simulate, and neither of those is something Bostrom claims to know. The friend has taken the last horn of a trilemma and reported it as the conclusion of the whole thing, which is the standard misreading. Note the general shape, since it comes back in lesson ten: a conditional result presented as a categorical one is the commonest way a careful argument gets inflated in transmission.

Now you. Which of the three propositions does a committed techno-optimist who also thinks simulating conscious beings is morally monstrous end up accepting?

The assumption that carries the weight

The argument needs one substantial premise that is easy to miss: substrate independence, the thesis that consciousness depends on the structure of a computation rather than on what the computation runs on. If a mind is what a certain pattern of information processing does, then implementing that pattern in silicon produces a mind, and simulated people are people.

If substrate independence is false, the argument collapses at once. A simulation would then contain no observers, only very good models of observers, and there would be nobody inside it wondering whether they were simulated. The counting argument needs simulated minds to count.

This is why lesson eight, on consciousness, is not a detour. The simulation argument is a hostage of the hard problem: it is only as strong as the claim that running the right program is sufficient for experience. Bostrom is explicit that he assumes this, and the assumption is not a small one. A large minority of philosophers of mind reject it.

There is also a quieter assumption in the counting step. It says that if most observers with your evidence are simulated, you should believe you are probably simulated. That is an indifference principle, and it is the same kind of reasoning that lesson thirteen examines under the name of anthropic reasoning, where it produces the Doomsday argument and a good deal of trouble. Whether the principle is sound is genuinely open, and anyone who accepts it here should be prepared to accept its consequences there.

There is a third assumption, less often noticed, about cost. The counting argument needs simulations to be cheap relative to the resources of a mature civilisation, since a civilisation that could afford three ancestor simulations would not swamp the original population. Bostrom estimates the computational requirements and argues they are modest for a civilisation with planetary-scale computing. The estimate depends on a further claim, that the simulation need not be run at full physical fidelity: it can model minds in detail and fill in the rest of the universe on demand, rendering the distant galaxy only when somebody points a telescope at it. That is a plausible engineering shortcut and it introduces a vulnerability, since a world built that way might behave oddly under sufficiently careful observation, which is what the testing proposals below are looking for.

Example. Suppose it turns out that consciousness requires specific biochemistry and cannot be implemented in silicon at all. Which of the three propositions does that establish?

None of them, and that is the point worth taking away. Substrate independence is not one of the three horns, it is a premise of the argument that generates them. If it fails, the trilemma never gets stated: there is no counting argument, because ancestor simulations contain no observers to count, and the question of which proposition is true does not arise. A reader who rejects substrate independence is not choosing horn one or horn two, they are declining the whole argument. Confusing a premise with a disjunct is easy here because horn two also concerns simulations not happening, but the two positions are quite different: horn two says nobody runs them, while rejecting substrate independence says running them would not produce anybody.

Now you. A defender replies that even if biological consciousness were required, a sufficiently advanced civilisation could grow biological brains in vats and feed them a simulated world, so the argument survives. Does it?

What would count as evidence

The scientific press periodically reports that physicists have found a way to test the hypothesis. It is worth being clear about what such tests could and could not do.

Proposals usually look for artefacts of discretisation: a smallest length, a cutoff in the spectrum of high energy cosmic rays, a lattice structure that would betray a simulation running on a grid. One much-discussed paper by Beane, Davoudi and Savage (2012) worked out what signatures a lattice quantum chromodynamics simulation of our universe would leave.

The trouble is asymmetric. A positive result would be striking but not decisive, since a discrete universe is a live physical hypothesis in its own right and needs no simulator. A negative result shows only that we are not in a simulation of that particular design, and the space of designs is unbounded. A simulator with any competence would not leave detectable seams, and a simulator with the resources to run our world can presumably patch the parts we look at closely.

That last consideration is the interesting one, and lesson nine takes it up properly. A hypothesis that can absorb any observation whatever is in trouble, not because it is false but because its flexibility means no observation supports it either. The simulation hypothesis is unusually good at absorbing observations, and its defenders often treat that as a strength. It is a weakness, and saying exactly why is the business of lesson nine.

Example. Someone argues: "The universe is made of quantised fields, spacetime may be discrete at the Planck scale, and quantum mechanics has an observer-dependent flavour. That is what a simulation would look like." What is wrong with the inference?

It treats features that are equally well explained by physics being as it is as though they were predictions of the simulation hypothesis specifically. To count as evidence, an observation must be more likely if the hypothesis is true than if it is false, which is the machinery of lesson five. Quantisation is exactly what you would expect from a quantum field theory whether or not anyone is simulating it, so it does not discriminate. The observer-dependence point is worse, since it rests on a popular misreading of measurement in quantum mechanics that does not require anything mental. Notice that the argument would have been made in the same tone had the universe turned out continuous, with continuity cited as evidence of unlimited computational resources.

Now you. Suppose the argument's counting step is granted, along with substrate independence. Does it follow that the world around you is unreal?

Why it belongs in this course

Three reasons, none of which is that the conclusion is likely.

First, it is the clearest available case of a valid argument with a surprising conclusion, where the work of responding is choosing a premise. Everyone who has an opinion about it has, whether or not they realise it, accepted one of the three propositions.

Second, it shows how much a single hidden assumption can carry. Substrate independence is stated in one sentence in Bostrom's paper and everything depends on it.

Third, it is the best illustration in the course of the difference between a claim you cannot rule out and a claim you have reason to believe. You cannot rule this one out. That fact alone gives it nothing, and the reason it gives it nothing is the subject of lesson five.

The sceptical arguments are now on the table in their classical and modern forms, stated at full strength and unanswered. The next lesson answers them, or rather surveys the four serious attempts and prices each one.

The vat argument from lesson two is valid and both its premises are plausible, so a reply has to deny one of them. There are exactly two places to stand, and the interesting fact about the literature is that every major answer of the last century occupies one or the other, usually while insisting it is doing something more subtle.

Recall the argument. You do not know you are not a brain in a vat. If you know you have hands, then since having hands entails not being a vat brain, you know you are not a vat brain. Therefore you do not know you have hands.

Moore: deny the first premise

G. E. Moore gave the British Academy lecture "Proof of an External World" in 1939. He held up one hand, said "here is one hand", held up the other, said "and here is another", and declared the existence of external objects proved.

Read as a rebuttal this is a joke, and it has been received as one by generations of students. Read as what it is, it is a serious argument about the direction of inference. Moore is not claiming to refute the sceptic's reasoning. He is observing that the sceptic's argument and his own share a form, and differ only in which end you start from.

The sceptic runs: I do not know I am not a vat brain, therefore I do not know I have hands. Moore runs it backwards: I know I have hands, therefore I know I am not a vat brain. Both are valid. Both use the closure principle. They cannot both be sound, and the question is which premise is better supported.

Put that way, Moore has a real case. How confident are you that you have hands? Extremely. How confident are you in the epistemological principle that indistinguishable scenarios cannot be ruled out? Rather less, on reflection, since it is an abstract claim in a contested field. Moore's point is that when a valid argument runs from premises you find less certain to a conclusion you find less credible than the denial of those premises, the rational move is to run it the other way. A proof is only as good as its most doubtful premise, and here that is not the hand.

The cost is that this feels like refusing to engage, and in a sense it is. Moore offers no account of how you know you have hands in the face of the vat possibility. He says you do know it, more surely than you know any philosophical premise, and that this is enough.

Example. Someone objects that Moore is begging the question, since the existence of his hand is exactly what the sceptic doubts. Is the objection right?

It is the standard objection and it is weaker than it sounds. Begging the question means assuming your conclusion as a premise, and every argument does assume its premises: the charge only bites if the premise has no support independent of the conclusion. Moore's premise does have such support, namely that it is among the most secure beliefs anyone has. The sceptic's premise likewise has support, namely the indistinguishability of the scenarios. So both arguments assume something, neither assumes its own conclusion outright, and the dispute is about which premise survives comparison. The objection misdescribes a standoff as a fallacy, which is a common way of dressing up a preference as a logical point.

Now you. The sceptic replies to Moore: "You cannot claim to know you have hands, because if you were a vat brain you would say exactly the same thing with the same confidence." Does this rebut him?

Deny closure

The second place to stand is premise two. Fred Dretske argued in 1970, and Robert Nozick in Philosophical Explanations (1981), that knowledge simply is not closed under known entailment.

Nozick's machinery is sensitivity: you know p only if, had p been false, you would not have believed it. Test it on the two beliefs. Had you not had hands, would you believe you did? No, you would have noticed. So the hand belief is sensitive and counts as knowledge. Had you been a vat brain, would you believe you were not? Yes, necessarily, since that is how the scenario is built. So that belief is not sensitive and does not count. Closure fails, because one belief passes the test and something it entails does not.

This is elegant and the price is high. It licenses saying: I know I have hands, and I do not know I am not a handless brain in a vat. Keith DeRose named these abominable conjunctions, and the name stuck because almost everyone finds them intolerable to assert. Worse, closure is what licenses ordinary deductive reasoning, and a theory that permits knowledge to evaporate across a valid inference has given up something structural to save something local.

Shift the standard

The third reply, developed by DeRose and by David Lewis in "Elusive Knowledge" (1996), says both parties are right because "know" does not express one fixed relation.

On contextualism, how much a speaker must rule out to count as knowing varies with the conversation. In ordinary contexts the vat possibility is not in play and "I know I have hands" is true. In an epistemology seminar, where the possibility has been raised and made salient, the standards rise, and "I do not know I have hands" is also true. The two sentences do not contradict each other any more than "Francisco is tall" said of a jockey and of a basketball player.

The attraction is that it explains the data: why scepticism is compelling while you are reading about it and evaporates when you stand up. The cost is that it makes a metaphysical-sounding dispute into a fact about English. Many find that deflationary in a way that does not fit how the argument feels, and there is a technical worry that the sceptic can simply insist on the high standard and ask whether you know, in that sense, and the answer is still no.

Example. A contextualist and a Nozickian are both told: "In the seminar you said you do not know you have hands, and in the corridor you said you do. One of those is false." How does each answer?

The contextualist says neither is false, because the word changed its meaning between the two rooms, exactly as "flat" does when applied to a table and to Kansas. The Nozickian cannot say that, since for them "know" is univocal and the answer is fixed: you do know you have hands, in every context, and you never know you are not a vat brain, in any context. So the Nozickian is committed to the abominable conjunction being literally true everywhere, while the contextualist avoids it by denying that both conjuncts are ever assertable at once. That is the real division between the two replies, and it shows they are not variants of one idea.

Now you. Which premise of the vat argument does contextualism deny?

Explain the experience

The fourth reply, and the one this course will lean on, treats the question as an ordinary problem of inference. It goes back to Bertrand Russell in The Problems of Philosophy (1912) and was developed carefully by Jonathan Vogel in 1990.

You have experiences. Two hypotheses explain them: an external world of persisting objects, or a vat and a machine. Both predict your experience equally well, since that is how the vat was built. So they cannot be separated by prediction. They can be separated on the other virtues a hypothesis is judged by, and the real world hypothesis wins on almost all of them. It explains why experience is coherent across senses, why objects behave lawfully when unobserved, why other people report what you would expect, and why the world is so often inconvenient. The vat hypothesis explains none of this by itself: it has to add, for each regularity, that the machine was programmed to produce it. Every regularity is a separate stipulation.

The cost is that this is not a proof and does not pretend to be. It concludes that the external world is the better explanation, not that the vat is impossible. If you demand certainty, it gives you nothing. Lesson one is what makes this acceptable: knowledge does not require certainty, so a conclusion that is merely far better supported than its rival is exactly what knowledge is made of.

Example. A sceptic answers Vogel: "Your objection is that the vat hypothesis needs extra stipulations. But I can state mine in one sentence. The machine simulates a world exactly like the one you believe in. That is simpler than your version, not more complicated, since I get all your physics for free and add one vat." What is wrong with the reply?

It smuggles the complexity into the phrase "a world exactly like the one you believe in", which is not a simple specification but a pointer to the entire content of the rival hypothesis. Unpacked, the vat theory contains all of the real world theory as a description of what the machine computes, plus a vat, plus a machine, plus whoever built it. Length of sentence is not what parsimony measures, and lesson nine makes this precise. Notice the reply is a good one in the sense that it forces the defender to say what simplicity actually means, and that anybody using parsimony as a weapon in the God lessons will need an answer ready.

Now you. Of the four replies, which are compatible with each other?

That reply needs a way of saying what "better supported" means, precisely enough to use in harder cases where the answer is not obvious. That is the next lesson, and it is the tool the second half of this course runs on.

Everything from here on is a contest between hypotheses that nobody can settle by looking. Did the universe have a cause? Is the fine structure of physics surprising? Is the silence of the sky evidence that we are alone? These cannot be argued with the tools of lesson one alone, because the answer is never that one side knows and the other does not. What is needed is a way of saying how much a piece of evidence should move you, and that is this lesson.

The probability course develops this properly. Here we need three ideas and one formula.

Belief comes in degrees

The first move is to stop treating belief as a switch. You do not merely believe or disbelieve that it will rain tomorrow, you have some level of confidence, and you act on it by carrying an umbrella or not. Philosophers call that level a credence, a number between 0 and 1.

This matters because most bad arguments in the rest of the course exploit the binary picture. "You cannot prove there is no God, so atheism is faith too" works only if belief has two settings. Once you allow degrees, the reply is easy: the claim is not that the probability is zero, it is that it is low, and a low credence is a different thing from a high one even though neither is certainty. Lesson one killed the certainty confusion; this kills its more resilient cousin.

The second move is to notice that a credence has to start somewhere before the evidence arrives. That starting point is the prior, and it is where most real disagreement lives. Two people who agree completely about the evidence can end up far apart because they began far apart, and pretending otherwise produces arguments that go nowhere for hours.

Example. A test for a disease is 99 percent accurate in both directions. The disease affects 1 person in 10,000. You test positive. How worried should you be?

Much less than the number suggests. Imagine a million people. About 100 have the disease and 99 of them test positive. The other 999,900 are healthy, and 1 percent of them, about 9,999, test positive anyway. So roughly 10,098 people test positive and about 99 of them are ill: just under 1 percent. The test is excellent and you are still very probably fine, because the prior was so low that even strong evidence cannot drag it far. This is the single most useful pattern in the lesson. When someone presents evidence for a claim that starts out very improbable, the evidence has to be extraordinarily discriminating to make the claim likely, and "the test is 99 percent accurate" is nowhere near enough.

Now you. Someone replies that the calculation is a trick, because your particular test came back positive and the other 999,999 people are irrelevant to your case. Where does this go wrong?

Bayes in one example

The formula that makes this exact is Bayes' theorem. Write $P(H)$ for your prior in a hypothesis, $P(E|H)$ for how likely the evidence is if the hypothesis is true, and $P(E)$ for how likely the evidence is overall. Then

Read it as an instruction rather than an equation. Your new confidence is your old confidence, multiplied by how well the hypothesis predicted what you saw, divided by how likely that observation was anyway.

The last part is what people forget, and it is the whole game. Evidence that any hypothesis would have predicted is worthless, because the denominator is as large as the numerator and nothing moves. Evidence is only evidence to the extent that it was more expected on one hypothesis than on its rivals.

That gives the practical test, and it is worth memorising because the rest of the course uses it constantly. Do not ask whether the evidence fits the hypothesis. Ask how much more likely the evidence is if the hypothesis is true than if it is false. That ratio, the likelihood ratio, is the strength of the evidence, and everything else is presentation.

Example. An advocate says the fine structure of physics is evidence for design, because a designed universe would certainly permit life. Apply the test.

The claim gives you the numerator, that $P(E|H)$ is high: if there is a designer who wants life, a life-permitting universe is very likely. It says nothing about the denominator, and the denominator is where the argument lives. To make this evidence you must also say that a life-permitting universe is unlikely otherwise, and defending that requires a view about how physical constants could have been, which is a hard and contested question rather than an obvious one. The argument as stated is incomplete rather than wrong, and lesson ten takes up the missing half. What the test does immediately is show you exactly which half is missing, which is why it is worth having before meeting the argument in its full dress.

Now you. A different advocate argues that the universe is not evidence for design, because whatever the constants had been, someone would have found them remarkable. Is that a good reply?

Why unfalsifiable claims get nothing

Now a consequence that will do a lot of work later.

Suppose someone offers a hypothesis so flexible that it accommodates any observation whatever. Whatever happens, the theory can explain it afterwards. People usually treat this as a strength, and say the theory has never been refuted.

Apply the test. If the hypothesis predicts every possible observation equally, then $P(E|H)$ is the same for all E, and the likelihood ratio against any rival is 1. No observation discriminates. The theory is never refuted and never confirmed either, and these are the same fact rather than two facts. Its survival is not a track record, it is an artefact of its shape.

This is the precise version of the point Karl Popper made with falsifiability, and the Bayesian form is more useful, since it comes in degrees rather than being a pass or fail. A theory can be a little bit accommodating and lose a little bit of confirming power. Lesson nine takes this further and applies it to whole pictures of reality.

Example. Two people argue about a claimed psychic. The psychic performs well under casual conditions and poorly under controlled ones. The believer says the laboratory atmosphere of scepticism disrupts the ability. What is wrong with that move, in the language of this lesson?

It converts a discriminating experiment into a non-discriminating one after the result is known. Before the test, the psychic hypothesis predicted success and the fraud hypothesis predicted failure, so the likelihood ratio was large and the experiment was worth running. The rescue adds a clause saying failure is also expected, which makes both outcomes compatible with the hypothesis and drives the ratio to 1. Notice the timing is the offence rather than the content: if the disruption claim had been stated in advance, with a specification of what counts as a disruptive atmosphere, it would have been a testable refinement. Added afterwards, it converts a theory that could have earned support into one that cannot. Lesson nine calls this ad hoc rescue.

Now you. A friend says: "The simulation hypothesis is unfalsifiable, so it is unscientific, so it is false." Which step is wrong?

What this does not give you

Two honest limitations, since the machinery is often oversold.

It does not supply priors. Bayes tells you how to update, not where to begin, and in the arguments ahead the priors are frequently the whole dispute. Someone who assigns a very low prior to any supernatural claim and someone who assigns a moderate one will read the same evidence and reach different places, both correctly by their own lights. What the framework does is make that disagreement visible and locate it, which is more than most arguments about God ever manage.

It also does not make the numbers real. Nobody has a well-defined credence in the existence of a deity to three decimal places, and writing one down does not create one. The value of the apparatus in a subject like this is qualitative: it tells you which direction the evidence pushes, roughly how hard, and when a piece of evidence is doing nothing at all. That is enough to settle a surprising number of arguments.

The tools are now in place. Before using them on the hardest questions, one more preparation is needed, because the errors in lessons ten to fourteen are not mainly errors of logic. They are errors of perspective, made by a particular kind of animal reasoning about its own importance.

Everything so far has been about arguments. This lesson is about the arguer, because the questions coming up are ones where people reason worse than usual in ways that are known, measured and specific. Knowing the failure modes in advance is worth more here than another technique, since the arguments in lessons ten to fourteen are not hard to follow. They are hard to assess without flinching.

None of what follows is an argument against any conclusion. Pointing out that someone has a motive to believe something is not a refutation, and treating it as one is itself a standard error with a name, the genetic fallacy. The use of this lesson is diagnostic: it tells you where to check your own work.

Putting ourselves at the centre

Anthropocentrism is the habit of taking human concerns, scale and categories as the natural frame for describing everything. It is not a moral failing, it is the default setting of a creature that evolved to model other creatures of roughly its own size and speed.

Its signature is the question that smuggles in its own answer. "What is the purpose of the universe?" presupposes that universes are the kind of thing that have purposes, which is what would need showing. "Why is the universe so finely tuned for life?" presupposes tuning, which is the conclusion of the argument in lesson ten rather than a datum it starts from. The trick is not that these questions are forbidden, it is that they are not neutral, and answering them as posed concedes the contested part before the argument begins.

A related habit is treating rarity as significance. Life is rare in the universe as far as we can see, and rarity feels like it must mean something. It need not. Gold is rare and means nothing; a particular arrangement of pebbles on a beach is unique and means nothing.

Thinking we are unusual

The false uniqueness effect is the measured tendency to underestimate how many other people share our abilities and desirable traits, while overestimating how many share our failings. It was named by Suls and Wan in the 1980s and sits alongside the better-known better-than-average effect, where most people in a group rate themselves above the median of that group.

The classic demonstration is Ola Svenson's 1981 study of drivers, in which a large majority rated themselves in the top half for both safety and skill. The precise proportions have been argued over since, and the effect is weaker for skills that are easy to check and stronger for vague traits, but the basic finding has survived four decades.

The relevance here is not about driving. It is that a species reasoning about whether it is special, in a universe it cannot compare itself to, is running exactly the procedure this effect distorts. That does not settle whether we are special. It says the intuition of specialness is not evidence, because we would have it either way.

Example. Someone argues: "Human consciousness is unlike anything else we know of in the universe, which suggests it is not the sort of thing that just happens." Identify what is doing the work.

Two things, neither of them the stated premise. First, "anything else we know of" covers a sample of one planet, so the comparison class is not the universe but the small part of it we have inspected, and the claim is true and uninformative in the way that "this is the tallest mountain in my garden" is. Second, the move from "unlike anything else" to "not the sort of thing that just happens" needs the assumption that unusual things require special explanation, which is anthropocentrism doing exactly what it does. Notice what a good version of this argument would look like: it would have to say what the relevant reference class is and why consciousness is improbable within it, which is the structure lesson ten demands of the design argument.

Now you. A cosmologist says the universe is not fine-tuned for life, because it is almost entirely vacuum at a few degrees above absolute zero and hostile to us everywhere we have looked. Is this a good reply to the fine-tuning argument?

Seeing agents everywhere

Humans detect agency on very little evidence. The cost asymmetry explains why: mistaking a rock for a predator wastes a moment, mistaking a predator for a rock is fatal, so selection tunes the detector to fire early. Justin Barrett named the result a hyperactive agency detection device, and Fritz Heider and Marianne Simmel had demonstrated the phenomenon as early as 1944, when subjects shown an animation of two triangles and a circle moving about a rectangle spontaneously described a story of bullying and escape. Almost nobody describes the shapes.

The consequence for this course is that the intuition that something was done on purpose is cheap. It arrives unbidden for weather, for machinery, for the behaviour of markets, and for the universe. That does not mean nothing is done on purpose. It means the feeling carries very little evidential weight on its own, in exactly the sense of lesson five: a mind that produces the feeling in response to purposeless triangles produces it whether or not there is an agent, so the likelihood ratio is near 1.

Example. A believer objects: "You have explained why I might see agency where there is none. You have not explained away the cases where there is agency, and by your reasoning I should doubt that my friend has a mind, since the same detector reports it." Is the objection fair?

Fair as stated and answerable. The detector firing is indeed poor evidence on its own, and belief that your friend has a mind does not rest on it: it rests on a large body of independent support, that your friend is built as you are, behaves as you do, reports what you would report, and is the product of the same process that produced you with your mind. The detector supplies a hypothesis and the rest of the evidence confirms it. The point about the universe is that the second half is exactly what is missing, so the detector is carrying the whole load. That is the honest form of the argument, and notice it concedes something real: the bias shows the intuition is worthless by itself, not that agency is absent.

Now you. Why is the Heider and Simmel result stronger evidence about human psychology than the observation that people once believed thunder was thrown by a god?

Wanting the answer

Motivated reasoning is the finding that people evaluate evidence differently depending on whether they like the conclusion. Ziva Kunda's 1990 review established the standard framing: we do not simply believe what we want, we search harder for flaws in unwelcome evidence and accept congenial evidence with less scrutiny, and the process feels like ordinary thinking from the inside.

This is the one bias in the lesson that is symmetric and personal. Both the person who wants there to be a God and the person who wants there not to be one are subject to it, and so is the person who wants to be the sort of person who has no stake. The practical defence is not to try to want nothing, which does not work, but to notice which conclusion would be convenient and apply extra scrutiny there.

Selection effects

The subtlest item on the list, and the most important for lessons thirteen and fourteen. A selection effect arises when the process that produced your sample is correlated with what you are measuring, so the sample misrepresents the population no matter how large it is.

The statistics course tells the standard story: the Literary Digest poll of 1936 gathered 2.4 million responses, an enormous sample, and got the presidential election wrong by 17.8 points, because the lists it drew from and the people who chose to reply were not representative. Size does not fix a selection effect, it only makes you more confident in the wrong answer.

Abraham Wald's wartime work on aircraft is the cleanest illustration. Asked where to add armour based on the damage on returning bombers, he pointed out that the sample consisted only of aircraft that returned, so the places with no damage on the survivors were precisely the places where damage was fatal. Reading the data the obvious way gets the answer exactly backwards.

Hold on to the structure. The question is never only what you observed, it is what the process of observing could possibly have shown you. That question, asked about our own existence, is the anthropic principle of lesson thirteen.

Example. Someone notices that every planet we have studied closely enough to know its history has produced intelligent life, and concludes that intelligence is probably common. What is wrong?

The sample is one, and worse, it was selected by the very property being measured, since we could only be studying our own history from the inside if intelligence had arisen here. A planet where it did not arise has nobody to do the studying. So the observation was guaranteed in advance regardless of whether intelligence is common or vanishingly rare, which by the test of lesson five makes it worth nothing: the likelihood ratio is 1. This is Wald's bombers with the survivors reduced to a single aircraft, and it is the core difficulty in every argument about how likely life is.

Now you. A colleague says these biases are a reason to distrust religious belief specifically, since agency detection and motivated reasoning explain it. Is that a sound use of the lesson?

The equipment is now assembled: a standard for knowledge, the sceptical challenge and the best answers to it, a way of weighing evidence, and a list of the ways this particular animal goes wrong. The rest of the course applies it. The first application is the oldest question of the three, which is what the world is made of.

Scepticism asked whether you are entitled to believe in an external world. This lesson asks a different question that is constantly confused with it: what the world is, assuming there is one. A sceptic says you cannot know the table is there. An idealist says the table is there and is made of something other than what you assumed. These are not the same position and they have almost nothing to do with each other.

Three positions

Realism about the external world holds that physical objects exist and have their properties independently of any mind. The table would be there, with its shape and mass, if every observer vanished. This is what almost everyone believes before being asked and what 79.5 percent of philosophers endorsed in the survey cited in lesson one.

Idealism holds that what exists is minds and their contents, and that physical objects are constituted by experience rather than causing it. The table is real, is public, and will hurt if you walk into it, and it is not made of mind-independent stuff.

Phenomenalism is the more cautious descendant, associated with John Stuart Mill, who defined matter as the permanent possibility of sensation. Statements about tables are analysed as statements about what would be experienced under various conditions. The table in the empty room is not a thing sitting there unobserved, it is the truth that anyone who walked in would see one.

The difference from scepticism is worth restating because it is where most readers go wrong. All three positions agree that you can know perfectly well there is a table. They disagree about what that knowledge is knowledge of.

Why the question is not silly

The usual first reaction is that idealism is obviously false and that anyone can refute it by kicking something, which is what Samuel Johnson did in 1763 when Boswell reported Berkeley's view: he kicked a large stone and said "I refute it thus".

Johnson's kick refutes nothing, and seeing why is the beginning of taking the question seriously. Berkeley's claim was never that stones are insubstantial or that you can walk through them. He held that stones are exactly as hard, as public and as kickable as everyone thinks, and that this hardness consists in a regular structure of experience rather than in mind-independent matter. The kick produces precisely the sensation Berkeley predicts. It discriminates between the hypotheses not at all, which by lesson five means it is not evidence.

The serious route in is the one Locke opened and Berkeley closed. Locke, in the Essay Concerning Human Understanding (1690), distinguished primary qualities, which objects have in themselves, from secondary qualities, which are powers to produce sensations in us. Shape, size, motion and solidity are primary. Colour, sound, taste and warmth are secondary: the redness is not in the apple, it is in you, and what is in the apple is a surface that reflects certain wavelengths.

Galileo had said much the same in Il Saggiatore (1623), and the distinction survives in modern physics, which describes the world in terms that never mention how anything looks.

Example. A friend says the primary and secondary quality distinction shows that science has already proved idealism, since it turns out colour is in the mind. What has gone wrong?

The distinction does the opposite. It removes colour from the object and leaves shape, mass and motion firmly in it, which is a realist conclusion: the world is not as it appears, and it is still there, having properties of its own. The friend has taken the demotion of one class of properties as though it were the demotion of all of them. Notice that this is exactly the step Berkeley did take, deliberately and with an argument, which is what makes him interesting: he agreed with Locke about colour and then asked why shape should be treated differently. The friend is helping themselves to Berkeley's conclusion without Berkeley's reasoning.

Now you. Why does the fact that physics describes the world without mentioning appearances not settle the question in the realist's favour?

Berkeley's argument

George Berkeley published A Treatise Concerning the Principles of Human Knowledge in 1710. His slogan is esse est percipi, to be is to be perceived, and his case has two parts.

The first attacks Locke directly. If secondary qualities are mind-dependent because they vary with the observer, then so are primary ones. Put one hand in hot water and one in cold, then both in tepid: the same water feels warm and cool, which is the standard argument about temperature. But size varies with distance, shape varies with angle, and motion varies with the observer's own motion. Whatever argument demotes colour demotes shape. Locke has drawn a line he cannot defend.

The second is the master argument, and it is the one worth sitting with. Berkeley challenges you to conceive of a tree existing unperceived. You try, and you form a mental image of a tree in an empty forest. But in doing so you are conceiving of it, so there is a mind in the picture after all, namely yours. Berkeley concludes that the very attempt to think of something unperceived defeats itself.

Nearly everyone senses that something is wrong here, and saying what takes care. The standard diagnosis is that Berkeley conflates the object of thought with the act of thinking. When I imagine an unperceived tree, the tree I imagine is unperceived even though my imagining is a perception. Compare: I can think about a thought I am not having, and there is no contradiction, because the thought I am thinking about is not the thought I am thinking with. The argument trades on a use and mention confusion.

That diagnosis is now standard and it does not rescue realism by itself, since it defeats one argument for idealism rather than establishing that matter exists. Berkeley's first argument, against Locke's line, remains and is harder.

Example. Take Berkeley's first argument seriously. Water at one temperature feels warm to a cold hand and cool to a hot one, so warmth is in the observer. A coin looks round from above and elliptical from an angle, so shape is in the observer too. What can the realist say?

That the two cases are not parallel, and the difference is that the variation in shape is systematic and predictable from the geometry of the viewing position, while the variation in warmth is not predictable from anything about the water. Knowing the coin is round plus the angle, you can compute the ellipse; knowing the water is at 30 degrees, you cannot compute whether it feels warm without also knowing the hand. So shape supports a single objective assignment that explains every appearance, and temperature does not. That is a real reply and it concedes Berkeley something: the line between primary and secondary is not where Locke drew it by listing qualities, it is drawn by which properties admit of an observer-independent assignment that predicts the observations.

Now you. Does the reply above survive relativity, where length and duration genuinely depend on the observer's motion?

Where this leaves us

Berkeley had an answer to the obvious objection, which is what happens to the furniture when nobody is in the room. His answer was God, who perceives everything continuously, which is why the world is stable and public rather than flickering in and out as people enter and leave. That is a serious move within his system and it makes idealism dependent on the arguments of lessons ten and eleven, which is a heavy dependency.

Phenomenalism tried to keep the idealism without the deity, and ran into a technical problem it never solved: analysing "there is a table in the empty room" into claims about what would be experienced requires specifying the conditions of observation, and those specifications keep having to mention physical objects, such as an observer with working eyes standing in a lit room. The analysis presupposes what it was supposed to eliminate.

So the realist is in decent shape, not because idealism is absurd but because its best versions either need God or cannot be stated without circularity. That is a conclusion reached by weighing rather than by kicking, which is the whole point.

Example. Someone says: "If the simulation hypothesis were true, idealism would be true, since everything would be information in a computer rather than matter." Is that right?

No, and the confusion is instructive. A simulation is run on a computer, which is a physical object in some world, so the simulated table is constituted by physical states of that machine rather than by anyone's experience. That is a claim about what matter is made of at bottom, not a claim that matter is mental, and it is closest to a realism with an unexpected inventory. It would become idealism only if the computer itself were held to be mental, which requires a separate argument. Notice that this repeats the distinction the lesson opened with: changing the story about the substrate is not the same as denying there is a substrate.

Now you. Which of the three positions is most threatened if consciousness turns out to be entirely explicable in physical terms?

This lesson is about consciousness and not about free will. Whether your choices are determined and whether your experiences are physical are separate questions with separate literatures, and the free-will course handles the first. Running them together is the standard undergraduate error: a determinist can think experience is irreducible, and a libertarian can be a strict physicalist.

The reason consciousness appears in this course is structural. Idealism in lesson seven needs minds to be fundamental. The simulation argument in lesson three needs minds to be implementable in silicon. One argument for God in lesson ten treats consciousness as something physics cannot deliver. All three are hostage to what is settled here, which is why the question cannot be skipped.

The easy problems and the hard one

David Chalmers drew the distinction in 1995 and the vocabulary stuck. The easy problems are explaining the functions: how the brain discriminates stimuli, integrates information, reports its own states, controls behaviour, attends, remembers. They are called easy not because they are simple, since they are the work of neuroscience for the next century, but because we know what a solution would look like. You specify a mechanism that performs the function, and when the mechanism is found the problem is over.

The hard problem is why any of that is accompanied by experience. There is something it is like to see red, and it is not obvious that any account of wavelength discrimination explains why the process is accompanied by that rather than by nothing at all. The worry is that you could give a complete functional story and the question would remain open.

Thomas Nagel set the problem up in "What Is It Like to Be a Bat?" (1974). Bats navigate by echolocation, we know a great deal about how, and none of it tells us what the bat's experience is like from the inside. Nagel's point was not that bat consciousness is mysterious in a way ours is not, but that objective description systematically leaves out the subjective character of experience, and that this is a general feature rather than a gap in current knowledge.

Example. Someone says the hard problem is a failure of imagination, and that vitalism looked just as hard until biochemistry explained life. Is the parallel good?

It is the best objection in the area and it is not decisive. The parallel is real: vitalists insisted that no arrangement of chemistry could produce life, and they were wrong, and the explanation worked by showing that being alive just is a set of functions performed. The disanalogy is what "life" turned out to mean. Every phenomenon vitalists pointed at, metabolism, reproduction, growth, was functional, so explaining the functions explained the thing. The hard problem is defined by the claim that experience is not exhausted by function, so the same move does not obviously apply. Whether that claim is true is the dispute; the vitalism parallel assumes it is false rather than showing it. Notice both sides can state this cleanly, which is a sign of a real disagreement rather than a confusion.

Now you. Why does the hard problem, if genuine, cause trouble for the simulation argument of lesson three?

Three arguments for a gap

The claim that physics cannot deliver consciousness rests on three arguments, all from the 1970s and 1980s, all still argued about.

The knowledge argument, from Frank Jackson in 1982. Mary is a brilliant scientist who has lived her whole life in a black and white room and has learned every physical fact about colour vision: wavelengths, cone responses, the complete neuroscience. She is released and sees a ripe tomato. Does she learn something? The intuition is that she does, that she learns what red looks like. If she knew all the physical facts and still learned something, there are non-physical facts.

The conceivability argument, from Chalmers. A philosophical zombie is a being physically identical to you, atom for atom, which has no experience at all: the lights are off inside. If such a being is coherently conceivable, then experience does not follow logically from the physical facts, and physicalism, which says the physical facts fix everything, is false.

The explanatory gap, from Joseph Levine in 1983. This is the weakest and most robust of the three. Even granting physicalism, there is a gap in our understanding: we cannot see why the physical story entails the experiential one, in the way we can see why the molecular story entails that water is a liquid at room temperature. Levine's claim is about explanation rather than metaphysics, which is what makes it hard to dismiss.

The standard replies are worth knowing. Against Mary: she gains an ability or a new way of representing an old fact rather than a new fact. Against zombies: conceivability is a poor guide to possibility, and the apparent coherence of a zombie may reflect how we think about experience rather than how experience is. Against the gap: it may be a permanent limitation of creatures like us rather than evidence about the world, a position called mysterianism and associated with Colin McGinn.

Example. Mary leaves her room, sees the tomato, and says "so that is what red looks like". A physicalist replies that she has gained an ability rather than a fact. What would settle which is right?

Almost nothing observable, and that is the honest answer. Both sides predict exactly the same behaviour from Mary: the surprise, the sentence, the new capacity to recognise red on sight. The dispute is over how to describe what happened, and by the standard of lesson five two hypotheses that predict identical observations are not separated by those observations. That does not make the question empty, since the descriptions have different consequences elsewhere, notably for whether a complete physics would be a complete account of the world. But it explains why forty years of argument has not converged, and it tells you what to be suspicious of: anyone claiming that a neuroscience result has settled the knowledge argument has almost certainly mistaken a claim about mechanism for a claim about completeness.

Now you. Chalmers says zombies are conceivable, so physicalism is false. Where exactly does an opponent break the argument?

The positions

Physicalism holds that experience is physical, either identical to brain states or realised by them. Its burden is the three arguments above.

Dualism holds that experience is a further ingredient. Its burden is causal: if experience is non-physical yet makes you say "I am conscious", it must affect the physical world, and physics as we have it has no room for an extra cause. Property dualism, which keeps one substance and two kinds of property, is the usual modern form and inherits a weaker version of the same problem.

Panpsychism holds that experience is a fundamental feature of matter, present in simple form everywhere and combining into complex forms in brains. It is not the view that electrons have opinions. It takes seriously Russell's point from lesson seven, that physics describes structure and leaves intrinsic nature open, and proposes that the intrinsic nature is experiential. Its burden is the combination problem: nobody can say how simple experiences add up to a single unified one.

Illusionism, defended by Keith Frankish and in a different form by Daniel Dennett, holds that the hard problem is an artefact of introspection, which misrepresents our own states as having properties they lack. There is no experience of the sort the hard problem is about, and what needs explaining is why we are so convinced there is. Its burden is that it appears to deny the one thing nobody can doubt, though its defenders reply that it denies only a theory about that thing.

Example. A friend argues: "Consciousness cannot be physical, and the only remaining explanation is God, so the hard problem is evidence for theism." Evaluate the inference.

Two failures. First, "the only remaining explanation" ignores three live alternatives just listed, since panpsychism, property dualism and illusionism are all non-theistic and all compatible with the hard problem being genuine. An argument from elimination has to eliminate. Second, and by the machinery of lesson five, theism must make consciousness more likely than its rivals do for this to count as evidence, and it is not clear that it does: a deity might create zombies, or minds of some other design, and no one has specified what a deity makes probable here. What survives is much weaker and still worth saying: if consciousness is not physical, a purely physicalist picture of reality is incomplete, which is a real result and not a theistic one.

Now you. Which position in this lesson is most congenial to idealism from lesson seven, and does it rescue it?

Lessons seven and eight left several pictures of reality standing, none of which can be separated from the others by observation. Lessons ten to fourteen will do the same on a larger scale. So the question has to be faced directly: when no experiment discriminates, is there any rational ground for preferring one picture to another, or is it taste?

There is ground, and this lesson says what it is. The criteria are three, and each of them is regularly misused.

Parsimony, properly stated

Ockham's razor is usually quoted as "the simplest explanation is usually right", which is both unattributable to William of Ockham and false as stated. The simplest explanation of the motion of the planets is that they go in circles, and they do not.

The defensible version is about what a hypothesis posits rather than how it sounds: do not multiply entities beyond necessity. A theory that explains the data using fewer independent assumptions, fewer kinds of thing, and fewer free parameters is preferable to one that explains the same data with more.

Two refinements matter. First, the count is of kinds rather than of individuals. A theory positing a trillion electrons is not less parsimonious than one positing three, since electrons are one kind; a theory positing electrons and ectoplasm posits two. Second, what counts is not the length of the sentence but the content of the commitment, which is why the sceptic's one-line rescue in lesson four failed. "A machine simulates a world exactly like the one you believe in" is short and contains the whole of the rival theory inside it.

There is a real justification underneath, not merely an aesthetic preference. Every free parameter a theory contains is a dial that can be set after the fact, and a theory with enough dials can fit any data whatever. Fitting data you have already seen is easy; predicting data you have not is hard, and the dials are what make the difference. This is the same fact that lesson five expressed as a likelihood ratio, and it is why parsimony is not a matter of taste.

Example. Two accounts of a noise in the attic: mice, or a poltergeist that behaves exactly as mice would. Both fit. Why prefer mice, in the terms above?

Because the poltergeist theory posits a new kind of thing, and posits it with no independent support, while mice are a kind already known to exist and known to make that noise. It also has a free parameter doing suspicious work: the clause "behaves exactly as mice would" was not predicted by anything in the poltergeist hypothesis, it was fitted to the observation after the fact, and the same hypothesis could have been fitted to any other noise. Notice this is not the claim that poltergeists are impossible, which would be a stronger and unsupported claim. It is that the theory earns nothing from the evidence because it was shaped to match it, so your credence should stay at whatever the prior was, and the prior for a new kind of entity is low precisely because kinds are what parsimony counts.

Now you. Does parsimony favour atheism over theism, as it is often said to?

Explanatory power

The second criterion is how much a hypothesis explains, and there is a precise test hiding inside the vague word.

A hypothesis explains an observation to the extent that the observation would have been expected given the hypothesis and surprising without it. That is the likelihood ratio again, and it means explanatory power is not a matter of how satisfying the story feels. A story can feel enormously explanatory and have no power at all, if it would have felt equally explanatory whatever had happened.

The test to apply is: what does this hypothesis forbid? A hypothesis that forbids nothing explains nothing. If you cannot say what observation would have been incompatible with it, then no observation counts in its favour.

This is where the criterion bites on the pictures from lesson seven. Idealism, panpsychism and physicalism predict all the same observations, which means none of them derives support from observation. The argument between them has to be conducted entirely on parsimony and coherence, and anyone claiming that the evidence favours their side has misunderstood the situation.

Example. A physicalist says the success of neuroscience is evidence for physicalism, since we keep finding neural correlates for mental states. Does that work?

Not as stated, because the rivals predict the correlates too. Property dualism holds that mental properties depend systematically on physical ones, so it expects exactly the correlations neuroscience finds. Panpsychism expects them. Even idealism can accommodate them, as regularities in experience. Since every position predicted the finding, the finding discriminates between none of them, and by the test above it has no explanatory power with respect to this dispute. What would discriminate is something no experiment has offered: a demonstration that the physical account is complete, that nothing is left over once the correlates are mapped, and completeness is not the sort of thing a correlation can establish. The physicalist has a good case, and it is made of parsimony rather than of data.

Now you. What observation, if any, would be incompatible with physicalism about the mind?

The cost of being unrefutable

The third criterion follows from the second and deserves its own name because it is so often inverted.

Consider Last Thursdayism: the universe was created last Thursday, complete with fossils, memories, half-finished books, and light already in transit from distant galaxies. It is consistent with every observation anyone will ever make. No experiment can touch it.

Nobody believes it, and the reason is instructive. It is not that it has been refuted, because it cannot be. It is that its immunity is manufactured. Every piece of evidence for an old universe is handled by an extra clause saying that the evidence was created in place, and each clause is added specifically to neutralise a specific observation. The theory has one assumption for every fact, which is the maximum possible violation of parsimony, and it forbids nothing, which is the maximum possible absence of explanatory power.

Now the important part. A criterion that kills Last Thursdayism must also be applied to hypotheses you may like better. The same structure appears in a God who is responsible for everything but forbids nothing, in a simulation whose operators patch anything we examine closely, and in a multiverse invoked to explain fine-tuning, which lesson thirteen examines. Each is a case where flexibility is offered as strength, and in each the flexibility is what removes the evidential support.

The rule to carry forward is this: an explanation that would have accommodated the opposite observation equally well has explained nothing. Applying it evenhandedly is most of what it means to think clearly about the next five lessons.

Example. A defender says: "God's reasons are beyond human understanding, which is why we cannot predict what a created world would look like." What does this cost the argument?

It costs the design argument its evidence. If we cannot say what a created world would look like, then we cannot say a life-permitting universe was more expected on theism than without it, and the numerator of lesson five's ratio is undefined. The move is a perfectly reasonable thing for a theist to say in response to the problem of evil, where it is called sceptical theism and appears in lesson eleven, and that is exactly the difficulty: it cannot be used in one lesson and withdrawn in the other. A hypothesis that is inscrutable enough to absorb the suffering in the world is inscrutable enough to absorb the fine-tuning as well. Consistency here is the single most useful discipline in the philosophy of religion, and it constrains both sides.

Now you. Does this lesson show the multiverse is an illegitimate response to fine-tuning?

There is a way of presenting these arguments that makes them look foolish, and a way that makes them look compelling, and both are available for all five. This lesson uses neither. Each argument is set out in the form its best defenders give it, its valid structure is displayed, and then the single premise doing the work is identified, because that is where any real disagreement has to be.

Before starting, one thing to keep from lesson six. The intuition that the universe was made on purpose arrives free, in everyone, for reasons that have nothing to do with whether it is true. So the feeling that these arguments are obviously right, and the feeling that they are obviously silly, are both worth discounting.

The cosmological arguments

Two versions, often confused.

The Kalam argument, revived by William Lane Craig from medieval Islamic sources:

1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. So the universe has a cause.

It is valid. Premise 2 is the one most discussed, usually by appeal to Big Bang cosmology, and it is weaker than it looks: the standard model describes the universe expanding from a hot dense state 13.8 billion years ago, and says nothing about whether that state was the beginning of existence. The singularity is where the theory breaks down rather than where time starts, and several live proposals have no beginning at all.

But premise 1 is where the real difficulty is, and it is easy to miss. Every case of causation we know is a case of rearrangement: things that begin to exist within the universe begin from pre-existing material, in time, under physical law. The premise generalises from that to the universe itself, which began, if it began, without pre-existing material and without a prior time for the causing to happen in. The inductive base does not obviously cover the case.

The contingency argument, from Leibniz, is stronger because it avoids all of this:

1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause.
2. The universe exists.
3. So the universe has an explanation.
4. If the universe has an external cause, that cause is a necessary being.

Premise 1 is the Principle of Sufficient Reason, and it is the load-bearing claim. Denying it means accepting a brute fact, something that exists with no explanation at all. Many philosophers accept exactly that, and the theist's reply is that accepting a brute universe while refusing a necessary being is arbitrary. The atheist's reply is that a necessary being is itself a brute fact with a nicer name. This is a genuine impasse and it is much more interesting than the Kalam.

Example. A critic answers the Kalam with "then what caused God?" Is that a good objection?

Not to the argument as stated, and understanding why is worth more than the objection. Premise 1 says whatever begins to exist has a cause, and the conclusion is a cause that did not begin, so no inconsistency arises: the argument is not "everything has a cause" and has not been made to except itself. The objection lands only if premise 1 is reformulated as the universal claim, which the defender never made. What survives is a better question, why an uncaused eternal deity is more acceptable than an uncaused eternal universe, and that is the contingency argument's territory. Notice how a popular objection can be both very common and aimed at a version of the argument nobody defends.

Now you. The Kalam concludes that the universe has a cause. How much further is it to the God of any actual religion?

Design and fine-tuning

The argument from biological design is the one everybody knows, from William Paley's Natural Theology (1802) and the watch found on a heath. It is also the one case in intellectual history where an argument of this shape was decisively answered, and that is why it matters here.

Paley's reasoning was good. The eye is an intricate arrangement of parts serving a function, the only known source of such arrangements was design, so a designer was the best explanation. Darwin supplied a second source, and the evolution course sets out the argument: heritable variation plus differential survival produces functional complexity with no foresight. The design inference was not refuted by philosophy but by the discovery of an alternative mechanism.

The lesson to carry is about inference rather than biology. "I cannot think of another explanation" is a fact about you, and Paley, who was neither careless nor stupid, was in exactly that position and was wrong. That should discipline how much weight anyone puts on the same move today.

Fine-tuning is the surviving version, and it is not about biology. Certain constants in physics appear to lie in narrow ranges outside which no complex structure would form. If the cosmological constant were substantially larger, the universe would expand too quickly for galaxies. Change the relative strength of the fundamental forces and stars do not burn or carbon does not form. The claimed narrowness varies wildly between authors and some of the famous numbers are disputed, but the phenomenon is taken seriously by working cosmologists, which the biological argument no longer is.

Stated in the machinery of lesson five: the observation E is a life-permitting universe. The claim is that $P(E)$ given a designer is high, and given no designer is tiny, so E strongly favours design.

Three replies. First, nobody knows the space of possible constants or its probability measure, so the "tiny" is asserted rather than computed. Second, a multiverse makes some life-permitting universe unsurprising, and lesson nine argued this is not automatically ad hoc. Third, and most important, the observation is selected: we could not have observed a universe that forbade observers. Lesson thirteen takes that up in full, because it is the objection that does the work.

Example. A defender of fine-tuning objects that the selection point is a non-explanation: of course we could only observe a life-permitting universe, but that does not explain why there is one. Is the objection right?

It is right that the selection point does not explain why, and wrong that this matters. The design argument is an evidential argument: it claims that the observation raises the probability of design. The selection reply attacks that claim rather than offering a rival explanation, by pointing out that the observation was guaranteed given that anyone is observing at all, so by lesson five its likelihood ratio is 1 and it cannot raise anything. Compare the firing squad: surviving twelve marksmen who all miss does call for explanation, which is why the analogy is popular, but the disanalogy is that you could have observed the alternative in the firing squad case, since surviving with a wound or hearing the shots is possible, and nobody observes a universe without observers. Whether the disanalogy holds is argued in lesson thirteen; here the shape of the disagreement is the thing to see.

Now you. Why does the reply above leave the contingency argument untouched?

The ontological argument

Anselm, in the Proslogion of 1078, argued from the concept alone: God is that than which nothing greater can be conceived; a being that exists is greater than one that does not; so if God existed only in the understanding, a greater could be conceived, which is a contradiction.

It has been reformulated many times, most influentially by Alvin Plantinga using modal logic: if it is possible that a maximally great being exists, then it exists. Validity here is not in doubt given the modal system chosen, and the entire question is whether the possibility premise is true, which turns out to be as hard as the original question.

Almost nobody is persuaded by it, including most theists, and Gaunilo pointed out within Anselm's lifetime that the same form appears to prove a greatest conceivable island. Its interest is as a test case for the machinery of this course: an argument can be valid, its premises can be hard to refute, and it can still fail to move anybody, which should prompt the question of what exactly is wrong. The usual answer, from Kant, is that existence is not a property that makes a thing greater.

Example. Apply the test from lesson nine to the fine-tuning argument: what does the design hypothesis forbid?

Very little, as stated, and that is its weakness rather than the narrowness of the constants. A designer might have made a universe with different physics and sustained life by other means, or made a small universe with one world rather than a vast and mostly empty one, or made life common rather than apparently rare. Since the hypothesis as usually offered does not tell us which, it fails to predict much, and a hypothesis that predicts little confirms weakly even when the observation fits. The way to strengthen the argument is to specify the designer's aims in advance and then check, which is what the more careful defenders attempt. The way to weaken it is to appeal to inscrutable purposes, which lesson nine showed cannot be done here and then withdrawn in lesson eleven.

Now you. Which of the five arguments is least damaged by the objections in this lesson, and why?

The arguments against the existence of God are fewer than the arguments for, and one of them is much stronger than the rest. This lesson gives that one most of its space.

A note on scope, which is the first thing careful writers on this subject establish. None of these arguments touches a deistic first cause or the necessary being of the contingency argument. They are aimed at a specific and much richer claim: that there exists a being who is omnipotent, omniscient and perfectly good. That claim is what most believers hold and it is what has content enough to be argued with, and the reader should notice that an atheist who defeats it has not defeated everything in lesson ten.

The problem of evil

The oldest statement is attributed to Epicurus and survives in Lactantius. Its modern form has two versions that need separating, because they fail and succeed differently.

The logical problem, pressed by J. L. Mackie in 1955, claims a flat contradiction:

1. God is omnipotent, omniscient and perfectly good.
2. An omnipotent being could prevent any evil; an omniscient being knows of it; a perfectly good being would want to.
3. Evil exists.
4. So no such God exists.

For this to work, premises 1 and 3 must be strictly inconsistent, and that is a strong claim. It fails if there is any possible reason a good being might have for permitting evil, even one nobody has thought of.

Alvin Plantinga's free will defence, developed through the 1970s, supplies one. If free will is a great good, and genuine freedom entails the possibility of choosing wrongly, then a world containing free agents who sometimes choose evil may be better than a world of automata. Even an omnipotent being cannot make someone freely choose the good, since a caused choice is not free in the relevant sense.

The defence is widely accepted as settling the logical problem, and it is worth being precise about what that means. Plantinga did not argue that this is God's actual reason. He argued that it is possibly a reason, which is all that is needed to break a claim of strict contradiction. It is a minimal result and it is a real one.

It also costs something. It commits the theist to a libertarian account of free will, the position the free-will course sets out and which a majority of philosophers reject. And it addresses only moral evil, leaving earthquakes, childhood cancers and the suffering of animals for hundreds of millions of years before any human chose anything.

Example. Someone replies that natural evil is caused by the free choices of fallen angels, so the free will defence covers it after all. Evaluate the move using lesson nine.

It is logically available and it is expensive in exactly the way lesson nine described. The hypothesis was introduced to neutralise a specific observation, has no independent support, and forbids nothing, so it is an ad hoc rescue of the Last Thursday kind. Note carefully what that does and does not show. It does not show the claim is false, and against the logical problem it works, since the logical problem needs strict inconsistency and a merely possible scenario defeats it. What it cannot do is help with the evidential problem below, because there the question is how probable the observations are, and a hypothesis manufactured to fit them contributes no probability. The same move therefore succeeds against one version and fails against the other, which is why the two must be kept apart.

Now you. Why does the free will defence not help with the 200 million years of animal suffering before humans existed?

The evidential problem

The version that survives. William Rowe stated it in 1979 and it does not claim contradiction at all, which is what makes it hard.

1. There exist instances of intense suffering which an omnipotent, omniscient being could have prevented without thereby losing some greater good or permitting some equally bad or worse evil.
2. A perfectly good being would prevent any such suffering.
3. So no such being exists.

Rowe's illustration is a fawn burned in a forest fire started by lightning, which dies in agony over several days, unseen. The claim is not that no reason could exist. It is that we have looked, and the hypothesis that there is a justifying reason for each such case is not what we would expect, given the sheer quantity and distribution of suffering.

This is an argument of exactly the kind lesson five described. It concedes that theism is not refuted and claims that the observations are much more probable on atheism than on theism, so they lower the probability of theism.

The main reply is sceptical theism: we are not in a position to judge what reasons an omniscient being might have, so our failure to find one is weak evidence that there is none, in the way that a novice's failure to see the point of a grandmaster's move is weak evidence that it is pointless.

The reply is powerful and it has a price, which lesson nine already named. A theism inscrutable enough to absorb the evidence of suffering is inscrutable enough to absorb the evidence of fine-tuning, and someone who uses this defence here should not appeal to what a good creator would plausibly do in lesson ten. There is a further cost that troubles many theists more: if we cannot judge what a good being would permit, our moral reasoning about what to prevent is undermined too.

Example. Rowe's argument needs premise 1, that some suffering has no justifying reason. A critic says nobody can know that. Does the argument collapse?

Not quite, and the repair is the interesting part. Rowe himself distinguished the claim that there is no justifying reason from the claim that we can see none, and rested the argument on an inference from the second to the first. That inference is legitimate when we would expect to see a reason if there were one, and illegitimate otherwise, which is exactly where sceptical theism attacks. So the argument does not collapse, it becomes conditional on a judgement about our epistemic position, and both sides can state their side of it clearly. Stephen Wykstra pressed the sceptical case in 1984 and Rowe accepted the reformulation, which is an unusually clean example of a philosophical dispute narrowing to one identifiable question rather than dissolving into vagueness.

Now you. Does the evidential problem of evil work against the deistic first cause of lesson ten?

Divine hiddenness

A distinct argument, developed by J. L. Schellenberg from 1993.

1. If a perfectly loving God exists, then any person capable of a relationship with God, and not resisting it, would be in a position to believe God exists.
2. There are people who are capable, not resisting, and do not believe.
3. So no perfectly loving God exists.

The argument's strength is premise 2, which is empirical and hard to deny: there have been sincere seekers who wanted to believe and could not, and vast populations who never encountered the claim. The usual reply targets premise 1, arguing that hiddenness serves some good, such as preserving the freedom to respond or producing a better kind of faith. Notice that these replies have the same structure as the responses to evil, and inherit the same difficulty about what can be known of divine purposes.

Incoherence arguments

Finally, a family of arguments claiming the divine attributes are internally inconsistent. Can an omnipotent being create a stone too heavy to lift? Can omniscience coexist with freedom? Can a being outside time act at a moment?

These are the weakest arguments in the lesson, and it is worth saying so plainly. Each has a standard reply, usually a refinement of the attribute: omnipotence is the power to do anything logically possible, which dissolves the stone; foreknowledge is treated in the free-will course, where the scope error in the argument is diagnosed exactly. A defender can absorb these with definitions, and the definitions are not obviously ad hoc, since they were largely in place before the objections.

Example. An atheist says the problem of evil disproves God. A theist says the free will defence answers the problem of evil. Both are overstating. What is the accurate statement?

That the free will defence answers the logical problem and not the evidential one. The logical problem claimed a strict contradiction and no longer stands, which most philosophers on both sides accept. The evidential problem claims that the quantity and distribution of suffering is much more expected if there is no God, and that argument is alive, contested, and unaffected by Plantinga's result. So the atheist is overstating by saying "disproves", since evidential arguments do not disprove, and the theist is overstating by treating a reply to one version as a reply to both. Notice that getting this right requires no position on the underlying question, only attention to what each argument claims.

Now you. A theist argues that atheists cannot call anything evil without an objective standard, so the problem of evil refutes itself. Does it?

More heat is generated by the words in this lesson than by any argument in the course. Almost all of it comes from three confusions, and once they are cleared the remaining disagreements are substantive and much smaller.

Two things "atheist" means

Consider two people. The first says: there is no God. The second says: I have no belief that there is a God, and I do not claim to know there is not.

These are different mental states and they carry different burdens. The first is a claim about the world and needs defending like any other. The second is a report of where someone's credence sits and needs no defence of the same kind, though it can still be criticised as unreasonable given the evidence.

The literature usually calls the first positive or strong atheism and the second negative or weak atheism, and the everyday word covers both. That would be harmless except that arguments are constantly conducted with one party using one sense and the other party attacking the other.

Notice how lesson five makes the distinction precise, and better than the labels do. Belief is not a switch, it is a credence. The positive atheist has a credence near 0. The negative atheist has one that is merely low, or has declined to form one. The theist has one that is high. There is no sharp line, and the ordinary vocabulary pretends there is.

Example. A theist says: "Atheism is a belief system too, and it takes just as much faith, because you cannot prove God does not exist." Untangle it.

Three separate errors. First, it trades on the ambiguity: negative atheism is the absence of a belief, and an absence is not a belief system, though positive atheism is a position and the charge partly lands there. Second, "you cannot prove" invokes the certainty standard that lesson one disposed of: almost nothing is provable in that sense, including the existence of other people, and holding a well-supported low credence is not faith. Third, it assumes that two positions equally short of proof are equally supported, which is the flattening from lesson one again and is exactly what lesson five exists to refute. What survives is a fair point worth conceding: someone who asserts confidently that no god of any description exists has taken on a burden, and should be asked to carry it.

Now you. A negative atheist says they need no arguments at all, since they merely lack a belief and the burden is entirely on the theist. Is that right?

Agnosticism is a claim about evidence

The second confusion is treating agnosticism as a refusal to answer, or as a polite midpoint between two rude extremes.

T. H. Huxley coined the word in 1869, and he meant something specific and demanding. Agnosticism for Huxley was a principle of method: do not profess certainty in conclusions that are not demonstrated or demonstrable. It is the application of a standard, not an avoidance of one.

So agnosticism is itself a claim, namely that the evidence does not settle the question, and that claim can be right or wrong. Someone who says the evidence is balanced is asserting something about the arguments of lessons ten and eleven, and can be shown to have misjudged them.

This also explains why agnosticism and atheism are not alternatives on a single line. They answer different questions. Atheism is about what you believe; agnosticism is about what you claim to know. A person can be an agnostic atheist, holding no belief in a god while claiming no knowledge either way, and that is the commonest position among nonbelievers who have thought about it. Agnostic theism is likewise available and has a long religious tradition behind it.

Burden of proof

The third confusion. "You cannot prove a negative" is false, and it is a pity it is so often said, because a real principle sits underneath.

Negatives are provable all the time: there is no prime number between 24 and 28, there is no elephant in this room. What is hard is proving a negative about something whose absence would leave no trace, and that is the actual asymmetry.

Bertrand Russell made the point in 1952 with a china teapot orbiting the sun between Earth and Mars, too small for any telescope to detect. Nobody could disprove it. The insistence that it must therefore be taken seriously would be absurd, and the reason is lesson nine's: the hypothesis was constructed to be evidentially inert. Its unfalsifiability earns it nothing.

The precise statement is that the burden falls on whoever proposes an entity, and that a hypothesis designed to be undetectable cannot draw support from its own undetectability. This cuts against careless atheism too, since "there is definitely nothing beyond the physical" is also a claim about a vast domain.

Example. Is the God hypothesis relevantly like Russell's teapot?

In one respect and not in another, and the honest answer says both. It is like the teapot in that a sufficiently inscrutable deity is undetectable by construction, and lesson nine showed that such a hypothesis cannot draw support from evidence. It is unlike the teapot in that nobody has ever offered an argument for the teapot, whereas there are arguments for theism with long histories and serious defenders, and lesson ten set out five of them. The teapot analogy is therefore a good answer to "you cannot disprove it, so you should be neutral" and a poor answer to the contingency argument, which does not rest on undetectability at all. Using it against the second is the mirror of the theist using inscrutability in lesson eleven and plausibility in lesson ten: a move that works in one place deployed where it does not fit.

Now you. Why is "extraordinary claims require extraordinary evidence" a consequence of lesson five rather than a separate principle?

The positive stance

None of this says what to do on a Sunday, and secular humanism is the attempt to answer that without a deity: an ethics grounded in human welfare and reason, a commitment to inquiry, and the view that meaning is made rather than received.

The standard objection is old and deserves a real answer. Without God, it is said, there is no foundation for morality, so the atheist has no right to call anything wrong.

The ethics course sets out the reply in full, and the compressed version is Plato's. In the Euthyphro, Socrates asks whether the pious is loved by the gods because it is pious, or pious because the gods love it. Both horns hurt the objection. If God commands the good because it is good, then goodness is independent of God and the atheist can have it. If things are good merely because God commands them, then goodness is arbitrary, and had the command been to torture children that would have been good, which almost every believer denies.

The upshot is not that theism cannot ground ethics, since sophisticated answers exist, most of which identify God with the good rather than treating goodness as a command. It is that the simple version of the objection fails, and that moral realism without God is a live position defended by many philosophers who are not atheists.

Meaning is the other half. The humanist claim is that a meaningful life consists in relationships, work, understanding and care, and that these are not made hollow by being finite. Whether that is satisfying is not a question a course can settle. Whether it is coherent is, and it is.

Example. Someone says the low rate of theism among professional philosophers shows the arguments for God fail. What is wrong with the inference, and what does survive?

It is an appeal to authority, and lesson one already flagged the shape when reporting the same kind of number about scepticism: a majority of experts is not an argument, and this majority could be explained by selection into the profession or by shared assumptions rather than by the arguments. What survives is still worth having. Expert opinion is evidence about where the arguments lead, weaker than the arguments themselves but not nothing, in the way that a surgeon's judgement is evidence without being a proof. The right use is as a check on your own reading: if you find an argument in lesson ten overwhelming and most specialists do not, that is a reason to reread rather than to conclude they are fools.

Now you. Which of the positions in this lesson is available to someone persuaded by the contingency argument of lesson ten but also by the evidential problem of evil in lesson eleven?

Two principles pull in opposite directions in modern cosmology, and almost every confused argument about our place in the universe comes from applying one where the other belongs.

The first says we are nothing special, so what we observe is typical. The second says our observations are filtered by the requirement that we exist to make them, so what we observe is guaranteed to be atypical in specific ways. Both are right, in their places, and knowing which is which is the skill this lesson teaches.

The Copernican principle and what it actually rests on

The the-scientific-revolution course tells the history. What Copernicus did in 1543 was not to demonstrate that the Earth moves, which he could not do, but to show that a heliocentric model accounted for the retrograde motion of the planets in a natural way rather than by adding machinery. The Earth lost its central place as a by-product.

The generalisation came much later and is due largely to Hermann Bondi in the 1950s. The Copernican principle holds that we do not occupy a privileged position in the universe. It has been extraordinarily fruitful: the Sun turned out to be an ordinary star, the galaxy an ordinary galaxy, the chemistry ordinary chemistry.

It is worth being clear that this is an assumption and not a discovery, and that it can fail. It was assumed that our epoch was typical, and then in 1998 the acceleration of the expansion was measured and it turned out that we live in an unusual period, after matter domination and before the universe empties out. The principle is a good default that has earned its keep, not a law.

Example. Someone argues that since the Copernican principle has been right every time, we should assume Earth is a typical planet and life is therefore common. Is that a legitimate use?

No, and the reason is the one that carries the whole lesson. The Copernican principle applies to properties that were not involved in selecting your vantage point, and it fails for properties that were. Our position in the galaxy was not selected by our being observers, so assuming it typical is reasonable. Being on a planet that has produced observers was selected by exactly that, since there is nobody on the others to make the inference. So the very fact that makes Earth a candidate for the argument also disqualifies it from the principle. This is Wald's bombers from lesson six, transposed: the sample is not the planets, it is the planets with someone on them to look.

Now you. The acceleration discovery showed our epoch is atypical. Does that refute the Copernican principle?

Anthropic reasoning

Brandon Carter introduced the term in 1973, and the idea is simpler than its reputation. The weak anthropic principle says that what we observe must be compatible with our existence as observers.

Stated that way it sounds trivial. Its force is that it removes the need to explain certain apparent coincidences, because the selection effect already accounts for them.

Carter's original example remains the clearest. Robert Dicke had pointed out in 1961 that the age of the universe is suspiciously close to the lifetime of a typical star, which looks like a coincidence demanding explanation. It is not. Observers made of carbon need at least one generation of stars to have lived and died to produce the carbon, and they need the universe not to have run out of active stars, so any observer anywhere will find themselves in that window. The coincidence is a consequence of who is doing the observing.

Now apply it to fine-tuning from lesson ten. The fact that the constants permit life looked like it needed explaining. If there is only one universe with one set of constants, it still does. If there are many, with varied constants, then observers arise only in the rare life-permitting ones and every observer finds their constants congenial, exactly as every lottery winner finds they won. On that picture the observation predicts nothing and supports nothing, and the likelihood ratio is 1.

This is why the fine-tuning argument and the multiverse are so tightly coupled. The theist's reply, and it is a serious one, is that the multiverse is being invoked to do a job. Lesson nine gave the test: the leading multiverse proposals were motivated independently, by eternal inflation and by the string landscape, which is what saves them from being ad hoc. Whether they are true is a question for physics and is unsettled.

Example. A critic says anthropic reasoning explains nothing, because "we observe X because otherwise we would not be here" is a tautology. Is that fair?

It is fair as a description and wrong as a criticism, and separating the two is the point. The principle is close to a tautology, and that is precisely its power: it is not offered as a causal explanation of why the constants have their values, it is offered as a reason why the values need no further explanation. Those are different jobs. Compare a simpler case. Asking why every fish you caught with a net of two inch mesh is longer than two inches does not call for a theory of fish growth, it calls for a look at the net. The anthropic principle is the look at the net. It leaves the deeper question of why there is a lake entirely open, and anyone who offers it as an answer to that question has overreached.

Now you. The fishing net analogy needs something to be true of the lake. What?

The Doomsday argument

Now the cautionary tale, because anthropic reasoning is easy to overextend and here is what happens when it is.

The argument, developed by Brandon Carter and John Leslie and refined by Richard Gott, runs like this. You are a human being, and you can number yourself in the sequence of all humans who will ever live. Roughly 100 billion have lived so far. If you assume you are a random sample from all humans who will ever exist, then you are probably not in the first tiny fraction of them. But if humanity goes on to colonise the galaxy and produce a hundred trillion people, you would be in the first thousandth, which is improbable. So a long future is unlikely, and extinction is probably nearer than we think.

The argument is valid and its conclusion is absurd, so a premise must go. Which one is genuinely contested, and the candidates are worth knowing because they are the same premises the simulation argument used.

The usual objection targets the self-sampling assumption, the claim that you should reason as if you were a random sample from some reference class. It is unclear what the reference class is: all humans, all mammals, all conscious beings, all observers? The answer changes the conclusion and nothing determines it. A second objection is that the argument would have worked at any point in history, and would have told a Roman that the future was short, which it was not. A third is that it confuses your existence, which is not a random draw, with a sample drawn by someone.

The honest position is that nobody has produced a fully satisfying diagnosis, which is why the argument is still discussed. What it establishes for our purposes is negative and important: indifference reasoning over observers, applied casually, generates conclusions nobody accepts. Anyone who accepted the counting step of the simulation argument in lesson three should feel the pressure here, since it is the same step.

Example. Someone says the Doomsday argument is obviously wrong because the future is not determined by where you happen to be born. Is that the right diagnosis?

No, and it misunderstands the argument, which does not claim your birth position causes anything. It claims your birth position is evidence about the total, in the way that drawing ball number 7 from an urn is evidence that the urn is small rather than large, without your draw affecting the contents. That inference is perfectly sound for urns, and the argument's error, if there is one, is in whether you are relevantly like a ball drawn from an urn. Rejecting a correct probabilistic inference because it sounds like magical causation is a standard error, and it leaves the actual argument untouched. The real objections are the ones about the reference class.

Now you. How does the anthropic principle undercut the fine-tuning argument without undercutting the contingency argument?

This is the question in the course where the temptation to overclaim is strongest, in both directions. One camp treats the size of the universe as settling it: billions of galaxies, so of course there is life. The other treats the silence as settling it: nobody has called, so we are alone. Neither inference works, and the machinery of lessons five, six and thirteen is what shows why.

The Drake equation, honestly

Frank Drake wrote his equation in 1961 for the agenda of a small meeting at Green Bank. It expresses the number of communicating civilisations in the galaxy as a product of factors: the rate of star formation, the fraction with planets, the number of habitable planets per system, the fraction where life arises, the fraction where life becomes intelligent, the fraction that develop detectable communication, and the length of time they stay detectable.

Drake was explicit that it was not a calculation. It was a way of organising a discussion by naming the unknowns, so that a meeting of ten people could work through them in order.

That is exactly how it should be used, and almost never is. The first three factors are now measured reasonably well, and the news is good: planets are common, and estimates from the Kepler mission put roughly one in five Sun-like stars as hosting an Earth-sized planet in the habitable zone, though the figure depends heavily on how the zone is defined.

The last four are unknown. Not imprecisely known, unknown, in the sense that credible published estimates differ by ten or twenty orders of magnitude. When a product contains a factor uncertain by twenty orders of magnitude, the product is uncertain by twenty orders of magnitude, and reporting a single number from it is not a result.

Example. Someone says the universe contains 10^22 stars, so even if life is a one in a billion chance, there must be trillions of civilisations. What is wrong with the reasoning?

The "one in a billion" was invented. It sounds conservative, and conservatism is a rhetorical property rather than an epistemic one: nobody knows whether abiogenesis is a one in a billion event, a near certainty on any wet rock, or a one in ${10}^{40}$ fluke that happened once. Assuming a number in the range that makes the argument work is assuming the conclusion. Notice that the same trick runs in reverse, since a pessimist can pick a tiny probability and derive that we are alone with equal apparent rigour. The honest statement is that the number of stars is known and multiplies an unknown, and that a large known times an unknown is unknown.

Now you. We have one data point: life arose on Earth, apparently quite early in its history. Why is this weak evidence that abiogenesis is easy?

Fermi's question

The story is that Enrico Fermi, at Los Alamos in 1950 over lunch, listened to a conversation about flying saucers and interstellar travel and asked: where is everybody?

The question is sharper than the equation. Take the galaxy at roughly 100,000 light years across and 10 billion years old. A civilisation expanding at even one thousandth the speed of light, which requires no new physics, crosses it in 100 million years. That is one percent of the galaxy's age. So if technological civilisations arise with any regularity at all, the galaxy should have been settled many times over, and it visibly has not been.

The force of this is that it does not depend on radio. It is an argument from the absence of physical presence, over a timescale where the expansion would have been finished long before the Earth formed.

Example. Someone replies that advanced civilisations would have no interest in expanding, so Fermi's argument fails. Assess it.

The reply is legitimate and it has to be much stronger than it sounds to work. It is not enough that most civilisations lose interest in expansion, because the argument only needs one that does not, over ten billion years, and expansion is self-perpetuating once started. So the premise required is that essentially every civilisation, everywhere, permanently declines to expand or to send self-replicating probes, with no exceptions across the whole history of the galaxy. Universal claims about the motives of unknown beings are exactly the sort of thing lesson six warns about, since the reasoning is anthropocentric in both directions: projecting our expansionism onto them, and then projecting our imagined wisdom onto them. The reply survives as a possibility and cannot be leaned on as a solution.

Now you. Why is the Fermi question a better argument than the observation that SETI has found nothing?

The Great Filter

Robin Hanson's 1996 framing is the most useful way to hold the problem. Somewhere between dead matter and a galaxy-spanning civilisation there is at least one step that is extraordinarily improbable. The question is where.

If the filter is behind us, in abiogenesis, or in the transition to complex cells, or in the emergence of intelligence, then we have passed it and the future may be open. The single origin of eukaryotic cells, apparently from one endosymbiotic event that the evolution course describes, is a candidate: it happened once in four billion years, which is what a hard step looks like.

If the filter is ahead of us, then technological civilisations reliably destroy themselves or are destroyed, and we should expect to as well. This is why the Fermi question is not idle: it bears on how worried to be about our own prospects.

Nick Bostrom drew the uncomfortable corollary. Finding independent life on Mars would be bad news, since it would move probability away from abiogenesis being the hard step and toward the filter being somewhere later, possibly ahead. The more life we find, and the more easily it arises, the worse the news.

The rare Earth response, from Peter Ward and Donald Brownlee in 2000, argues the filter is behind us and is made of many small steps: a large moon stabilising the axial tilt, plate tectonics recycling carbon, a gas giant in the right orbit, a quiet stellar neighbourhood. Each is plausible, none is established, and the hypothesis has the shape lesson nine warned about, since it can absorb any new discovery by adding another requirement.

Example. A 2018 paper by Sandberg, Drexler and Ord argued that we should not be surprised by the silence. What did they do differently?

They propagated the uncertainty instead of multiplying point estimates. If you take the scientific uncertainty in each Drake factor seriously and represent it as a distribution, then multiply the distributions rather than best guesses, the result is not a number but a very wide spread, and a substantial portion of it lies below one civilisation per galaxy. So the appearance of a paradox came from the arithmetic: multiplying central estimates of quantities with enormous log-scale uncertainty produces a confident answer that the underlying uncertainty does not support. The result does not show we are alone, it shows that being alone was never surprising and the Fermi paradox may be an artefact of doing the sum badly.

Now you. Does the silence tell us anything at all?

That completes the three questions. What remains is to put the pieces together and hold a position, which is what the last lesson asks you to do.

The course has been a tour of arguments. This lesson asks you to stop touring and stand somewhere, which is a different skill and the one the whole thing was for.

Holding a position is not the same as being confident. It means four things: saying what you think, saying which premise of the best argument against you that you deny, saying what your own view costs, and naming what would change your mind. A view that cannot do the fourth is not a position, it is an attachment.

The three arguments, in one page each

Everything in the course reduces to three valid arguments. Each is sound or unsound, and each position available to you is a choice about which premise to give up.

The sceptical argument. You do not know you are not a brain in a vat. If you know you have hands, then, since having hands entails not being a vat brain, you know you are not one. So you do not know you have hands.

Deny the first premise and you are with Moore or with the abductive reply of lesson four, holding that the external world is far and away the best explanation of experience and that this is what knowing amounts to. Deny the second and you are with Nozick, rejecting closure and accepting the abominable conjunction. Accept both and you are a sceptic, which almost nobody is, or a contextualist, holding that the argument is sound in the seminar and irrelevant outside it.

The design argument. The constants of physics fall in a narrow life-permitting range. That is very unlikely without a designer and likely with one. So the constants are evidence for a designer.

Deny the first premise by disputing the range, which is a live question in physics. Deny the second in either of two places: the denominator, by arguing that anthropic selection in an ensemble makes a life-permitting observation certain for any observer, which is lesson thirteen; or the numerator, by arguing that nobody has specified what a designer makes probable, which is lesson nine's demand that a hypothesis forbid something. Accept both and you have an argument for a designer, thin but real, which still has the distance problem of lesson ten.

The evidential problem of evil. There is suffering that an omnipotent, omniscient being could have prevented without losing a greater good. A perfectly good being would prevent such suffering. So no such being exists.

Deny the first with sceptical theism, at the price lesson nine named and lesson eleven spelled out. Deny the second with a theodicy, which requires an account that covers animal suffering and natural disaster rather than only moral evil. Accept both and you have a strong argument against the God of theism which leaves the deistic first cause standing.

Example. A reader says: "I am a naturalist. I think the physical world is all there is, it was not designed, and there is no God." Which premises are they committed to denying?

At least three, and they should know which. On the sceptical argument they need a reply, most naturally the abductive one, since a naturalist who cannot say why the external world is the better explanation has helped themselves to the physical world they are claiming exhausts reality. On the design argument they must deny a premise, and the honest choice is the denominator via anthropic selection, which as lesson thirteen showed commits them to an ensemble with real variation, which is a substantive bet on unsettled physics. On the contingency argument of lesson ten, which is not on the list above because the naturalist usually forgets it, they must either say the universe exists necessarily or accept a brute fact. Naming all three is what turns a mood into a position, and notice that two of the three cost something.

Now you. Do the same for someone who says: "I believe in God, and I accept everything science says."

How to hold a view under uncertainty

Three habits, each of which is a lesson of this course compressed.

Keep credences rather than sides. You do not have to choose between certainty and paralysis. Lesson five's apparatus lets you say that the external world is overwhelmingly likely, that theism is somewhat unlikely, and that whether we are alone is close to unknown, and those three different attitudes are the correct response to three different evidential situations. Treating every question as though it demanded the same confidence is the error underneath most bad argument.

Apply your standards in both directions. This is the single most useful discipline the course offers and the rarest. If unfalsifiability is a defect when a theist appeals to inscrutable divine purposes, it is a defect when a physicalist explains away every apparent counterexample to physicalism. If a selection effect undercuts the fine-tuning argument, the same reasoning undercuts the optimistic reading of life arising early on Earth. Lesson six's point was not that your opponents are biased, it was that you are.

Distinguish what you believe from what you can show. Lesson twelve's agnostic atheist is the model: a low credence, held honestly, without the claim to have demonstrated anything. That combination is stable, defensible and much commoner among people who have thought hard than the public argument suggests.

Example. Two people agree on every argument in this course and end up with different views on theism. Is one of them making a mistake?

Not necessarily, and understanding why is the most grown-up thing in the lesson. Lesson five noted that Bayes tells you how to update and not where to begin. Two people who agree about the force of every argument can still differ in their priors, and priors are shaped by background commitments about what kinds of thing exist, which are themselves not settled by any of the arguments here. That is a real and respectable source of disagreement, and it is quite different from one party having missed a step. What it does not license is treating every disagreement as a difference in priors, which is a way of avoiding argument. The test is whether you can say what your prior is and why, and whether you would revise it under the conditions in the final section.

Now you. Someone says this means the whole subject is a matter of opinion. Why is that the wrong conclusion?

What would change your mind

Finish by writing the answer down, because it is the test of whether you have a position at all.

Some specimen answers, to show what a good one looks like. A physicalist should be moved by well-controlled evidence of mental causation without physical mechanism. An atheist should be moved by a successful theodicy covering natural evil, or by a demonstration that the space of possible physical constants is well defined and the life-permitting region is vanishingly small with no ensemble to draw from. A theist should be moved by a physical account of why the constants take the values they do, or by the multiverse becoming well confirmed for independent reasons. Someone confident we are alone should be moved by an independent origin of life on Mars or Europa, which as lesson fourteen noted would be bad news in another sense. Someone confident the universe is teeming should be moved by another fifty years of silence combined with better limits.

Notice what these have in common. Each is specific, each is at least conceivably obtainable, and none is "convincing evidence", which is not an answer but a refusal dressed as one.

If you cannot produce such a statement for your own view, that is worth knowing, and it does not mean the view is wrong. It means you hold it for reasons you have not articulated, which is the ordinary human condition and the thing fifteen lessons of this kind are meant to improve.

Example. Someone answers the question with: "I would change my mind about God if God appeared to me personally." Is that a good answer?

It is honest and nearly useless, for two reasons the course has covered. Lesson six explains why a private experience is weak evidence even to the person having it, since agency detection and motivated reasoning produce exactly such experiences whether or not anything is there, and the same person would presumably not accept someone else's private experience as evidence. And the answer sets a condition the answerer has no way to pursue, which makes it unfalsifiable in practice: nothing they could do would ever trigger it. A better answer names something public and at least approachable, such as a theodicy that handles animal suffering, or a specific result in cosmology. The test of a good answer is whether someone else could go and look.

Now you. What is the strongest objection to the position you now hold, and what is your answer to it?