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?
Answer
It counts for something and much less than it is usually made to carry. Theism does posit an additional kind of entity, and by the rule above that is a genuine cost that has to be paid for by explanatory work, which is exactly what the arguments of lesson ten attempt. The mistake is to treat parsimony as decisive on its own, because a theory that posits more can still win by explaining more: physics posits a great many entities nobody had imagined, and earns them. So the honest statement is that theism starts with a handicap and can overcome it by explaining things atheism cannot, and the dispute is about whether it does. Anyone who says the razor settles the matter has skipped the part where the explanatory ledger is totalled, which is a way of announcing a conclusion rather than reaching one.
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?
Answer
Reliable evidence of mental causation with no physical mechanism would do it: a thought that moved something without any energy transfer, or a mind operating with the brain destroyed, established under controlled conditions. That is a real answer, which means physicalism is not in the Last Thursday category: it forbids something, and it has survived the failure of a century of attempts to demonstrate exactly those things. The harder question is whether the reverse holds, and it mostly does not. Dualism as usually stated forbids very little, because the correlates are compatible with it, which is a weakness its defenders should own. Noticing that one side of a dispute is exposed to refutation and the other is not is a genuine asymmetry, and it is not the same as either side having been proved.
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?
Answer
No, and the distinction matters. A multiverse invoked solely to explain fine-tuning, with no independent motivation and no other consequences, would be an ad hoc rescue of exactly the Last Thursday kind. But the leading multiverse proposals are not like that: eternal inflation and the string landscape were developed to solve problems in cosmology and particle physics respectively, and they imply many universes as a consequence rather than being introduced to supply them. A hypothesis that was already on the table for other reasons, and then turns out to explain something else, is the opposite of ad hoc, and that pattern is one of the strongest signs a theory is getting something right. Whether those proposals are correct is an open question in physics; the point here is that the charge of unfalsifiability has to be argued case by case rather than asserted, and lesson thirteen does that.