1.1. Presenting the argument

Smith's endorses:

He says, ‘B provides a safe basis upon which to judge that P just in case, in all those possible worlds in which B is true and which are very similar to or closely resemble the actual world, P is true too’ (168, bold emphasis mine).Footnote ⁵ If P is based on a safe basis, then P is safe in the sense explained in the introduction. Yet not all safe bases are created equal, and Smith introduces a number of terms to keep track of when P is held on a good basis.

A safe basis B is a contributing safe basis for P just in case B contributes to the safety of P, or explains why P is safe. In other words, B is a contributing safe basis for P just in case P is safe ‘in virtue of the modal relationship between B and P. This is the case when B is the animals are black and white, striped and equine and P is the animals are zebras’ (170, emphasis original). It is clear that, in this case, B contributes to P's safety because B makes P safer than it is when it isn't based on anything. That is, worlds in which the animals are not zebras are closer to the actual world than the worlds in which the animals are black and white, striped, and equine and yet are still not zebras. This basis makes it harder for P to be false by making us go further away from the actual world to find a case in which P is false. A contributing safe basis is, in a sense, the good kind of safe basis.

A safe basis B is a non-contributing safe basis for P just in case B doesn't contribute to the safety of P, or doesn't explain why P is safe. In other words, B is a non-contributing safe basis for P just in case P is safe ‘purely in virtue of the modal profile of P. This is the case when B is the animals are black and white, striped and equine and P is the animals are not disguised mules’ (170, emphasis original).Footnote ⁶ According to Smith, B doesn't contribute to the safety of P in this case, because it doesn't make P safer than it is when it isn't based on anything. The worlds in which the animals are black and white, striped and equine and yet really are disguised mules are just the worlds in which the animals are disguised mules. A non-contributing safe basis is, in a sense, the bad kind of safe basis.

A proposition P is content-safe just in case it is safe in virtue of its content, which, for Smith, means that it has at least some degree of safety independently of its basis. As I shall stress in §2, if P is content-safe and is held on the basis of B, it does not follow that B is non-contributing. B might, for example, contribute to P's safety by making P safer than it was in virtue of its content. If P is content-safe and it isn't held on any contributing bases, P is purely content-safe.

Safety, according to Smith, is an explanatory condition on knowledge: ‘Suppose that one knows that Q. I take it that the safety of one's belief that Q is part of what explains its qualifying as knowledge’ (172). If S knows Q and Q's satisfying C is part of what explains why S knows Q, we can call C an explanatory condition (for S's knowledge that Q).Footnote ⁷ Q cannot qualify as knowledge unless 2 + 2 = 4, so this mathematical truth is a necessary condition on S's knowing that Q. Yet this mathematical condition is clearly not explanatory, i.e. its satisfaction is not part of what explains why S's belief that Q counts as knowledge (unless, for example, Q is itself the proposition that 2 + 2 = 4).

Smith uses Safety to defend his transmission principle:

In the example, the conclusion, Q, is purely content-safe, so P is a non-contributing safe-basis for Q. In other words, the inference from P does not contribute to the safety of Q. So far, so good. Yet, in this passage, Smith merely assumes that if an inference fails to make its conclusion safe, then it fails to transmit knowledge; however, this assumption is hardly obvious.

Smith concedes that even if the inference doesn't explain why Q is safe, ‘the inference from P may yet play some role in ensuring that further conditions for knowledge are satisfied’ (172). One might argue that even if the inference P therefore Q (or the Zebra Deduction!) fails to explain why its conclusion is safe, it transmits knowledge because it explains why some other explanatory condition on knowledge is satisfied.Footnote ⁸ Smith insists, however, that ‘even if the inference is playing some such role, it would be wrong to claim that one's belief that Q qualifies as knowledge in virtue of it’ (172). Why? He assumes that an inference transmits knowledge to its conclusion only if the conclusion's status as known is ‘explained exclusively in terms of the inference that one has drawn and the resultant basis of one's belief’ (172, emphasis original).

Smith's use of ‘exclusively’ is a bit unfortunate, because, as a referee pointed out, it suggests that a belief is known only if it is held on exactly one basis. Smith's use of the term does not have this undesirable result, however. In the sense at issue, an inference is the exclusive explanation of a conclusion's status as knowledge just in case the inference explains by itself why the conclusion satisfies all explanatory conditions. If I have multiple, independent arguments for P, each argument might explain by itself why the conclusion satisfies all explanatory conditions. Or, more carefully, if I infer P from the premises of each argument, each inference might by itself explain why the conclusion satisfies all explanatory conditions. In such a case, the conclusion's status as knowledge would be overdetermined, but this is presumably the right result when you make multiple inferences to P, each of which is sufficient to make P known. With this clarification of ‘exclusivity’ in mind, we can see that Smith is defending this requirement:

Recall that Smith endorses:

The conjunction of Exclusivity and Explanatory Safety entail:

1.2. Exclusivity leads to rampant transmission failure

Smith's argument for his transmission principle fails because one of its key premises, Exclusivity, is dubious at least in its current form. The problem is that, given just about any view of inferential knowledge, Exclusivity entails that virtually no inference transmits knowledge from the premise to the conclusion.

S makes an inference ‘B therefore P’ just in case S bases her belief in P on her belief in B. Given this definition, not every instance of basing a belief on something counts as an inference. If I were to base my belief in P on an experience, then I wouldn't be making an inference. An inference just is the act of basing one belief on another belief (or perhaps the content of another belief). Given this understanding of inference, Exclusivity is equivalent to:

This claim is merely a more transparent version of Exclusivity. Once clarified, though, Exclusivity is seen to be implausible.

Nearly every epistemologist will endorse some explanatory condition, such that an inference virtually never explains why that condition is satisfied. For example, most epistemologists would endorse some version of this explanatory condition on inferential knowledge: S knows that P on the basis of some belief B only if B is known or justified or true. If an inference from B makes P known, part of what explains why P is known is the fact that B is itself known, justified or true.Footnote ¹⁰ Yet it is virtually never the case that an inference B therefore P (i.e. S's basing her belief in P on her belief in B) explains why B is known, justified or true. Consequently, the inference from B is not the exclusive explanation for why S knows P. Exclusivity, therefore, has the unpalatable result that virtually no inference transmits knowledge.

Also consider (i) various no defeater conditions and (ii) the truth of the conclusion. If (i) and (ii) are intended as explanatory conditions on knowledge, then I could give a similar argument relying on these conditions. Regarding (i), one's making an inference generally does not explain why one doesn't have any relevant counterevidence or why there is no true proposition D, such that were one to have justification for D, then one wouldn't have justification for the conclusion. Regarding (ii), knowledge that P requires that P be true, but one's inferring P is generally irrelevant to why P is true. On the basis of some historical evidence, I might infer and thereby know that Napoleon was short, but my inference doesn't have anything to do with why Napoleon was short. Again, Exclusivity seems to have the undesirable result that virtually no inference transmits knowledge.

Smith has at least three options available to him. The first option has two components: (a) accept the conclusion that, strictly speaking, virtually no inference transmits knowledge to its conclusion but (b) refine Exclusivity so that it concerns when a certain kind of inference transmits knowledge. Call an inference from known premises a ‘knowledgeable inference’. An associate editor suggested that Smith could say that many knowledgeable inferences might provide the exclusive explanation for why their conclusions are known. If the suggestion is correct, then Smith might have a suitable replacement for Exclusivity ready to hand.

Recall that Exclusivity plays a very important role in Smith's argument. He needs Exclusivity to block the following way of defending the Zebra Deduction: even though the Zebra Deduction doesn't make its conclusion safer, it still transmits knowledge because it explains why the conclusion satisfies some other explanatory condition on knowledge. The key feature of Exclusivity is that it requires something to explain why the conclusion satisfies every explanatory condition on knowledge. But knowledgeable inferences seem even more poorly suited to explain why the conclusion satisfies every such condition than just plain ol’ inferences. Suppose that a conclusion is known only if the premise is known, and that this is an explanatory condition on knowledge. It is not even possible for a knowledgeable inference to explain why the premise is known. To say that some inference is knowledgeable is to say (I) it's an inference and (K) that the premise is known. While the conjunction of I and K entails that the premise is known, it can never explain why the premise is known. Furthermore, knowledgeable inferences fare no better than inferences at explaining why the conclusion is true – recall the Napoleon case, for instance – or why there are no defeaters for the conclusion. Smith, therefore, gains no help from the associate editor's suggestion.

I do think, however, that this option can make some progress when it comes to the requirement that the premise be prima facie justified, i.e. justified in the absence of defeaters. Let us say that an inference is well-grounded just in case all of its essential premises are themselves based on adequate grounds. Smith might propose Exclusivity*: a well-grounded inference transmits knowledge only if, for every explanatory condition C for S's knowledge that P, the well-grounded inference by itself explains why P satisfies C. Suppose it is an explanatory condition on inferential knowledge that the premise be prima facie justified. Since a premise's being based on adequate grounds does explain why it is prima facie justified (we can suppose), a well-grounded inference can explain why the premise is prima facie justified. So Exclusivity* is better than Exclusivity when it comes to the explanatory condition that one's premises be prima facie justified. Nonetheless, Exclusivity* doesn't fare any better when we consider the requirements that the premise and conclusion be true or that there be no defeaters. Nor does the broader strategy suggested by first option seem well suited to explain these other requirements either. Still, Exclusivity* counts as some progress.

The second option is to deny that one or more of the alleged explanatory conditions are in fact explanatory. Suppose that absences cannot explain anything. If so, then an absence of defeaters could not explain why P is known, and, consequently, the various no defeater conditions would not be explanatory conditions after all. Given a certain controversial view about explanation, the second option could make some progress. Yet based on correspondence, Smith is not inclined to take this option with respect to the requirement that the basis be true, because he thinks that that requirement is an explanatory condition on knowledge.

Each of the first two options has its advantages, and as it happens, I think the most promising option is the third: combine the first two options. The third option, more specifically, is to use the first option in response to some of the conditions whose satisfaction isn't generally explained by inferences (e.g. the condition that the essential premises be prima facie justified), and use the second option in response to the rest of the relevant conditions. I think it is at least somewhat plausible that this third option will result in a successful version of Exclusivity, and perhaps it is also plausible – though I am somewhat less optimistic here – that the successful version of Exclusivity will be suitable for Smith's purposes. In any event, Smith's current version of Exclusivity seems highly problematic, and he has some substantial theorising to do before he finds a plausible and suitable replacement for Exclusivity and, thereby, adequately supports his transmission principle.Footnote ¹¹

2.1. The application presented

When Smith applies his transmission principle to the Zebra Deduction, he assumes:

B makes P safer than it is in virtue of its content just in case B makes it harder for P to be false. More precisely, B makes P safer than it is in virtue of its content just in case the worlds in which B is true and P is false are less similar to the actual world than the most similar worlds in which P is false (173–4).

Necessity is the bridge between Smith's Transmission Principle and the natural idea. Smith's Transmission Principle says that an inference B therefore P transmits only if it explains by itself why P is safe. Necessity says that the inference explains by itself why P is safe only if it makes P safer than it already is in virtue of its content. The conjunction of these two claims entails:

Smith argues that the Zebra Deduction fails to satisfy the necessary condition laid down by the natural idea. In other words, he argues for:

The proposition (P1) the animals before me are not disguised mules is safe in virtue of its content. Smith explains: ‘the most similar worlds in which the animals are disguised mules – that is the most similar worlds in which [P1] is false – are too dissimilar to be taken into consideration for the purposes of safety’ (169). According to Smith, the basis in the Zebra Deduction is something like (B1) that the animals appear to be black and white, striped and equine.Footnote ¹³ Yet B1 does not make P1 any safer than it is in virtue of its content, because ‘the most similar worlds in which [B1] is true and [P1] is false are simply amongst the most similar worlds in which [P1] is false’ (173). Hence, No Safer is true.

So far in this section I have reconstructed Smith's reasoning as follows. Smith derives the natural idea from the conjunction of his Transmission Principle and Necessity. This idea holds that an inference transmits only if it makes its conclusion safer than it already is in virtue of its content. No Safer says that the Zebra Deduction fails to make its conclusion safer in the relevant way. Hence, the conjunction of the natural idea and No Safer entail:

Although the natural idea leads to the claim that the Zebra Deduction cannot transmit knowledge to the content-safe conclusion, P1, it does allow some inferences to transmit knowledge to this conclusion. Consider DNA Basis, the claim that a DNA test yielded the result that the animals are Zebras. DNA Basis does make P1 safer than it already is in virtue of its content.

Since DNA Basis makes P1 safer than it is in virtue of its content, the natural idea does not entail that the inference DNA Basis therefore P1 fails to transmit. This is a welcome result. DNA Basis therefore P1 seems capable of transmitting knowledge to its conclusion, so it is a problem for any view that says otherwise.

2.2. Exclusivity and overdetermination

In the previous sub-section, I agreed with Smith that DNA Basis (a DNA test says the animals are zebras) can transmit knowledge to P1 (the animals are not cleverly disguised mules), and it can do so even though P1 is content-safe. Yet the truth of Smith's Transmission Principle makes it difficult to explain how this is possible.Footnote ¹⁴ Smith's Transmission Principle holds that an inference B therefore P transmits knowledge to P only if it explains why P is safe. But then:

Smith might remind us that he explained how a basis B can make some P safer than it is in virtue of its content. He even provided an example: P1 is content-safe but DNA basis makes it even safer. Fair enough, but we still lack an answer to the Pressing Question. Smith does not explain how B can make P safe when P is already content-safe; rather, he explains how B can make P gratuitously safe when P is already content-safe.

Consider an analogy. Donny loves doughnuts, especially ones that are gratuitously frosted. Donny sneaks into the local Dunkin’ Donuts after hours and is amazed by the splendour set before him. Donny ignores the unfrosted donuts in favour of their frosted counterparts. Whenever he finds such a doughnut, he slathers it with additional frosting. In this case, Donny's activities do not explain why any doughnuts are frosted; some independent explanation, namely the activity of the bakers, is needed to explain that fact. Yet Donny's activities do explain why several donuts are gratuitously frosted. The moral is that one can explain why something is gratuitously F without explaining why that thing is F. Smith explains how it is possible for a basis to contribute to a conclusion's gratuitous safety when that conclusion is already content-safe. By itself, an explanation of a conclusion's gratuitous safety is not an answer to the Pressing Question.

Suppose that P is content-safe and that the inference B therefore P makes P gratuitously safe. We can assume that the inference explains why P is gratuitously safe. There are three options for explaining why P is safe. The first is:

This option makes B analogous to Donny. Donny doesn't explain why any doughnut is iced, but he does explain why some donuts are gratuitously iced. Likewise, when P is content-safe, B never explains why P is safe, but it does explain why P is gratuitously safe.

When combined with Smith's Transmission Principle, No Overdetermination entails that no inference can transmit knowledge to a content-safe conclusion. No Overdetermination holds that, in such cases, bases do not explain why conclusions satisfy Safety. Smith's Transmission Principle therefore prevents such inferences from transmitting knowledge to their conclusions. This result is undesirable since DNA Basis does seem to transmit knowledge to the content-safe conclusion that the animals are not cleverly disguised mules. Hence, Smith must choose one of the other two options.

The second option is:

Suppose two bricks strike a window at exactly the same time. Each brick is sufficient to break the window by itself, but what causes the window to break when both bricks hit the window at exactly the same time? The Composite Cause option is analogous to saying that neither brick breaks the window by itself, but the two bricks, taken together, are a composite cause of the window's breaking. This option denies that the inference, by itself, explains why P is safe. Per Smith's Transmission Principle, it follows that no inference transmits knowledge when its conclusion is content-safe.

Since both No Overdetermination and Common Cause prevent the DNA inference from transmitting knowledge to its conclusion, it seems that Smith must endorse the third option, namely:

Consider again the case where both bricks hit the window. The Individual Cause option is analogous to saying that each brick individually breaks the window. This option allows the modal relationship between B and P, by itself, to explain why P is safe, even though P is also safe in virtue of its content. Since the modal relationship between B and P makes P safe by itself, the inference B therefore P would satisfy the stringent standards of Smith's Transmission Principle.Footnote ¹⁵

Smith's Transmission Principle forces Smith to endorse Individual Cause, which allows inferences to overdetermine the safety of content-safe conclusions, at least when the inference also explains the gratuitous safety of P. Yet once we allow overdetermination in these cases, it is at least plausible that:

The Explanation Principle is a rejection of Necessity. Necessity holds that a deduction from prior knowledge that B explains why P is safe only if it improves P's safety. The Explanation Principle, on the other hand, holds that all such deductions explain why their conclusions are safe. Yet the principle does not entail that every competent deduction transmits knowledge. It might be that some such deduction fails to transmit knowledge, not because it fails to explain why its conclusion satisfies Safety, but because it fails to explain why P satisfies some other condition on knowledge. Since the natural idea was supposed to follow from the conjunction of Smith's Transmission Principle and Necessity, the Explanation Principle provides a way of accepting Smith's Transmission Principle (transmission requires the inference to explain why the conclusion is safe) while rejecting the natural idea (transmission requires the inference to improve the conclusion's safety).Footnote ¹⁶

The Explanation Principle also can be used to defend the Zebra Deduction. Provided that one knows the Zebra Premise, the principle entails that the Zebra Deduction explains the safety of its conclusion. Since the conclusion of this deduction is content-safe, the deduction would explain the safety of its conclusion by overdetermining its safety.

We should be clear about the dialectical situation. I am not attempting to argue that the Explanation Principle is true and that Necessity is false. For all I care, both principles are false, and Smith's Transmission Principle is just altogether wrong-headed.Footnote ¹⁷ To adequately defend the natural idea and the claim that the Zebra Deduction is an instance of transmission failure, Smith needs a good reason for preferring Necessity over the Explanation Principle. All I need to show is that Smith has no good reason for preferring the former over the latter, and to do that, I do not need to show that the Explanation Principle is true.

Smith cannot reject the Explanation Principle on the grounds that there is something problematic about overdetermination as such. Since he is committed to Individual Cause, he is committed to condoning overdetermination in some cases. Nor does the amount of overdetermination provide a promising way of defending Necessity. When combined with Individual Cause, Necessity restricts overdetermination only to cases in which B explains why P is gratuitously safe. The Explanation Principle is committed to overdetermination in other cases as well. So Necessity is committed to less overdetermination than the Explanation Principle is. Even supposing that it is an advantage to be committed to less overdetermination, it is not clear that this advantage was properly earned. To the extent that Necessity restricts overdetermination without some explanation of why this is a sensible way of restricting the overdetermination, Necessity seems ad hoc. In other words, Necessity's ad hoc restriction of overdetermination is a disadvantage, and this disadvantage neutralises any advantage there may be in being committed to less overdetermination.

Smith might say that we should prefer Necessity over the Explanation Principle, because only the former prevents the Zebra Deduction from transmitting knowledge to its conclusion. But not everyone holds that the Zebra Deduction is an instance of transmission failure.Footnote ¹⁸ And even if it were allowed that the Necessity would have some small advantage because it prevents the Zebra Deduction from transmitting, this advantage would be at least counterbalanced, if not outweighed, by the following liability.

Necessity forces Smith to restrict his transmission failure principle to inferences with contingent conclusions (175). Since necessary truths are maximally safe, no inference can make them any safer. Yet surely some such inferences transmit knowledge to their conclusions. If Smith endorsed the Explanation Principle, he would not need to restrict his account of transmission failure to inferences with contingent conclusions. Hence, the Explanation Principle enjoys one considerable advantage.

Given a popular conjunction, the restriction to contingent truths poses a further problem. This paper has been focused on:

Contrast the Zebra Deduction with:

Intuitively, a successful account of transmission failure needs to treat these two deductions in parallel fashion. If one fails to transmit knowledge, they both fail to transmit knowledge and do so for the same reason. Smith commits himself to a very particular explanation of how the first deduction fails to transmit; however, given a popular conjunction, he is forced to appeal to an entirely independent explanation of why the latter deduction fails to transmit. Borrowing from David Manley (Reference Manley2007: 420), ‘How can [Smith's account of transmission failure] be taken seriously if it does not also block the inference from ‘that animal is a zebra’ to ‘that animal is not a cleverly disguised mule’?’

Suppose there is a zebra in front of me. Contrast two different conclusions that I might draw: (i) the animal before me is not a cleverly disguised mule and (ii) that animal is not a cleverly disguised mule. (i) is contingently true because some other animal could have been standing before me, including a cleverly disguised mule; however, the conjunction of object dependence, species essentialism and the standard modal semantics entails that (ii) is necessarily true.

Object-dependence holds that the proposition expressed by ‘that animal is not a cleverly disguised mule’ exists in a world only if that animal, which we are supposing is a zebra, exists in that world.Footnote ¹⁹ Had a different animal been standing before me, I would have been thinking a different proposition. Species essentialism holds that an animal could not be a different species than it actually is and remain the same animal. Since that animal is a zebra, that animal is necessarily a zebra. The former thesis says that the proposition exists only if the zebra exists. The latter thesis holds that the zebra exists only if it is a zebra (and so not a mule, cleverly disguised or otherwise). Hence, the proposition expressed by ‘that animal is not a cleverly disguised mule’ is true at every world in which it exists, because at every world in which it exists the relevant animal is a zebra rather than a mule. The standard modal semantics holds that, if a proposition is true at every world in which it exists, then it is necessarily true. When you conjoin these three theses, it follows that ‘that animal is not a cleverly disguised mule’ expresses a necessary truth (when the animal before one is a zebra).

Smith's commitment to necessity forces him to restrict his account of transmission failure to inferences with contingent truths. But given the popular conjunction of object-dependence, species essentialism and the standard modal semantics, Zebra Deduction*'s conclusion is a necessary truth. Hence, Smith's commitment to necessity prevents his explanation from applying to Zebra Deduction*. This result violates the intuitive idea that Zebra Deduction and Zebra Deduction* should be treated in parallel fashion. Smith is forced to treat like cases differently.Footnote ²⁰

P1, that the animals are not cleverly disguised mules, is safe independently of its modal relationship to any basis. Nonetheless, a plausible transmission principle should allow DNA Basis to transmit knowledge to P1. Smith's Transmission Principle can do so only in conjunction with Individual Cause. Yet Individual Cause countenances a type of overdetermination that can be used not only to reject the natural idea, but also to defend the claim that the Zebra Deduction satisfies Smith's Transmission Principle. To block these manoeuvres, Smith needs a good reason to allow overdetermination only when an inference makes its conclusion gratuitously safe. No such reason seems forthcoming.