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2. First Reflections on the Problem of Easy Knowledge

© 2017 Mark McBride, CC BY 4.0 https://doi.org/10.11647/OBP.0104.04

Continuing with the pattern of objection to dogmatism, immediate justification, and basic knowledge, I examine, and ultimately reject, Zalabardo’s (2005) radical response to Cohen’s (2002, 2005) problem of easy knowledge. Along the way, I discuss warrant, inference, and transmission in some detail.

0.1 Stewart Cohen (2002, 2005) considers a case in which his son wants a red table for his room. Cohen and his son go to the furniture store. Cohen’s son is concerned that the table his father is considering purchasing, which appears red, may in fact be white with red lights shining on it. Cohen (2005: 418) responds with the following reasoning:

(WARRANT FOR 1) The table looks red.

(EK)

(1) The table is red.

(2) If the table is red, then it is not white with red lights shining on it.

(3) The table is not white with red lights shining on it.

(The (EK) argument is what was earlier — in the Introduction — called the (TABLE) argument.) If one reasons thus, say one’s engaged in (EK)-reasoning. Cohen finds such a response to his son’s concern unsatisfactory. Intuitively, believing (1) on the basis of the experience described in (WARRANT FOR 1), and then reasoning one’s way to (3), is not a way of coming to know — finding out, confirming — that (3) is true. It is too easy.

0.2 Structurally similar reasoning delivers (knowledge of)1 the falsity of sceptical hypotheses concerning the external world, testimony, other minds etc. Consider the testimony case:

(WARRANT FOR 1) Danny tells me he has a red table in his office.

(1) Danny has a red table in his office.

(2) If Danny has a red table in his office, then it is not the case that Danny has no red table but told me that he does have.

(3) It is not the case that Danny has no red table but told me that he does have.

Here, the intuition is that believing (1) on the basis of Danny’s testimony, and then reasoning one’s way to (3), is not a way of coming to know that (3) is true — it is not a way of confirming that Danny told the truth, and not a way of ruling out the possibility that he spoke falsely. It is too easy. The unsatisfactoriness, therefore, threatens to generalise.

0.3 (EK)-reasoning in outline: In each of our two examples (and in other examples with the same structure), the immediate transition from the experience or evidence described in (WARRANT FOR 1) to knowledge of (1) involves reliance on a potential source of knowledge — visual perception or being told by Danny. The transition would apparently be blocked by acceptance of:

KR A potential knowledge source K can yield knowledge for S, only if S knows K is reliable.2 (Cohen 2002: 309)

But rejection of KR is not, by itself, sufficient to underwrite the transition, because the mere possibility of cases in which some source delivers knowledge prior to my knowing that the source is reliable does not entail that the present case is one such. Moreover, rejection of KR leaves open that there are other necessary conditions on a knowledge source yielding knowledge — conditions which may not be met. Cohen (2002: 310) calls knowledge delivered “prior to one’s knowing that the source is reliable” basic knowledge. Many epistemologists — including Alston, Dretske, Ginet, Goldman, Klein, Nozick, Pollock, Pryor, and Sosa — reject KR, for various reasons, and with various qualifications. (For Cohen and KR, see n. 4.) Such epistemologists allow for the possibility of basic knowledge. The problem is that basic knowledge of (1) seems to lead to too-easy knowledge of (3). The conditional premise (2) is knowable a priori. If I know (1) and (2) then, given a plausible knowledge-closure principle,3I can seemingly come to know (3) by (EK)-reasoning. Thus (EK)-reasoning transforms basic knowledge of an everyday proposition about the colour of a table into easy knowledge of the falsity of a sceptical hypothesis. The generation of easy knowledge “suggests that we were wrong to think we had the basic knowledge in the first place” (Cohen 2002: 311). Thus the problem of easy knowledge.4

0.4 Cohen is convinced that (EK)-reasoning is an unsatisfactory response to his son:

[I]t seems very implausible to say I could in this way come to know that I’m not seeing a white table illuminated by red lights. Note that on this view, my inductive evidence against the possibility that there are red lights shining on the table turns out to be irrelevant to my knowing that the table is not white with red lights shining on it. This is surely a strange result. (Cohen 2002: 313)

We’ll follow Cohen by talking of the unsatisfactoriness of (EK)-reasoning, but such talk involves no suggestion that the reasoning is somehow invalid. Nor are we committed to denying many plausible knowledge-closure principles (cf. n. 3 supra). It is a further — so-called bootstrapping — question whether S is in a position to know, in some way, that K is reliable. Instead, all we mean is that a subject is epistemically criticisable in attempting to acquire knowledge of (3) — to find out or to confirm that (3) is true — by means of (EK)-reasoning.

1. Zalabardo’s Response

1.1 I want to sketch (one strand of)5 José Zalabardo’s (2005) original and heterodox response to the problem of easy knowledge. By consideration of Zalabardo’s response we can gain insight into the nature of warrant, inference, and transmission (of warrant).

1.2 Before reconstructing Zalabardo’s argument, let’s take note of two key principles (or: schemata) operative therein (where ‘S’ is a placeholder for a subject, and ‘p’ and ‘q’ for propositions):

Closure: If p has warrant for S,6 and S knows that p entails q, then q has warrant for S. (36)

Transmission: If p entails q and S knows that p,7 then inferring q from p8 would enable S to obtain warrant for q. (39)

When I talk generically I’ll use lower-case ‘closure’ and ‘transmission’. Closure and Transmission are valid schemata just in case — iff — they have no false instances; invalid otherwise.9 Thus we can talk of the truth or falsity of an instance of the schema Closure. The schema will be instantiated to a particular subject and a particular set of propositions. For brevity, and somewhat loosely, we can talk of an instance of Closure in an argument. And we can talk of the truth or falsity of an instance of Transmission in a particular piece of reasoning with an argument.10 Say there is Transmission (of warrant) — warrant Transmits — just in case, the instance of the schema Transmission, in a particular piece of reasoning, has a true antecedent and a true consequent. (So this is equivalent to an instance of Transmission’s non-vacuous truth.) And say there is not Transmission (of warrant) just in case, in a particular piece of reasoning, Transmission has either a false antecedent or a true antecedent and a false consequent. (So this is equivalent, respectively, to either an instance of Transmission’s vacuous truth or its falsity.) And say finally there is Transmission failure — or non-Transmission — just in case, in a particular piece of reasoning, Transmission has a true antecedent and a false consequent. (So this is equivalent to an instance of Transmission’s falsity.) So, that there is not Transmission does not entail Transmission failure; the converse entailment, however, holds.

1.3 We might reconstruct Zalabardo’s response to the problem of easy knowledge as follows:

(ZALABARDO)

(A) The problem of easy knowledge presupposes Transmission of warrant in (EK)-reasoning.

(B) Transmission of warrant in (EK)-reasoning presupposes the falsity of an instance of Closure in (EK).

(C) But Closure is valid, and thus has no false instances.

(D) So, from (B) and (C): There is no Transmission of warrant in (EK)-reasoning.

(E) So, from (A) and (D): There is no problem of easy knowledge.

The argument is clearly valid. If it is to be resisted, one or other of its premises must be shown to be false.

1.4 Argument (A)-(E) needs unpacking. We need to cash out Zalabardo’s closure and transmission principles. Zalabardo remarks (39):

[T]ransmission is different from, and independent of, Closure. Transmission postulates a sufficient condition for an inference to have the power to furnish the subject with warrant for its conclusion. Closure, by contrast, imposes a constraint on an admissible combination of warrant attributions to a subject: that for all propositions p, q and every subject S, if we ascribe to S knowledge that p entails q, we should not ascribe to her warrant for p without also ascribing to her warrant for q. (footnote omitted)

Note that Transmission is posed as a sufficient (and not necessary) condition. Thus it is left open that other transmission principles are operative.11 A result of this is that the fact that there is not Transmission in a piece of reasoning does not entail that that piece of reasoning does not transmit warrant. And nor does the fact that there is Transmission failure in reasoning entail that that reasoning suffers transmission failure.

1.5 For Zalabardo, “when p is true and S believes that p, S will know that p just in case p has warrant for S” (33). In other words, ‘warrant’ operates as a placeholder for whatever is required, in addition to a true belief, to constitute knowledge (see Plantinga 1993).12 Let’s locate this usage of ‘warrant’ with respect to two prominent types of warrant — propositional and doxastic. A subject, S, has propositional warrant for a proposition, p, iff it is epistemically appropriate for S to believe p (notwithstanding S may not in fact believe p) (see Goldman 1979). (I leave open whether a thinker could have propositional warrant to believe a proposition p even though the thinker had never even conceptualised the proposition, p.) And if this is the case, one can talk of S having warrant to believe p (or warrant for (believing) p).13 Meanwhile, S has doxastic warrant for p iff S has propositional warrant for p and S believes p on the basis of14 his propositional warrant for p. If this is the case, one can talk of S having a warranted belief in p.

How does Zalabardo’s (Plantingan) notion of warrant fit into this taxonomy? First, it’s not-merely-propositional, as there is nothing in the definition of propositional warrant which guarantees — as Zalabardo’s warrant does — that adding it to a true belief gets one knowledge. For one thing, one’s having propositional warrant leaves open that one’s true belief is not based on the propositional warrant: the mere availability of a warrant, even availability to the thinker in question, is not sufficient, when added to a true belief, for knowledge. Additionally, it’s not doxastic, as it’s left open that Zalabardo’s warrant is in place for a proposition absent that proposition being believed. So Zalabardo’s (Plantingan) warrant occupies a middle ground of being not-merely-propositional but not doxastic either.15

1.6 Insofar as Zalabardo’s notion of warrant is not the notion of warranted belief — doxastic warrant — consider Nicholas Silins’s (2005: 75–77) claim that debates over transmission of warrant oughtn’t to be conducted in terms of the notion of warrant to believe — propositional warrant (cf. also Tucker (2010)):

[I]t is too demanding to define transmission of warrant in terms of acquisition of [propositional] warrant […] To see this, note that many cases of transmission of [propositional] warrant […] would be automatic. For example, if you believe on the basis of some warrant that Moby Dick is a whale (and you know that all whales are mammals), then you have [propositional] warrant […] that Moby Dick is a mammal regardless of whether you have inferred the conclusion or not. Moreover, you cannot acquire [propositional] warrant […] that Moby Dick is a mammal by reasoning from the proposition that Moby Dick is a whale. Rather than provide you with new evidence to believe that Moby Dick is a mammal, the inference would instead allow you to base a belief on evidence you already had to believe the conclusion. The upshot is that, if we define transmission of warrant so as to require the acquisition of [propositional] warrant […], many legitimate pieces of reasoning will then suffer from failure of transmission of warrant. For example your inference that Moby Dick is a mammal from the proposition that Moby Dick is a whale will fail to transmit warrant. But such a verdict is far too harsh. After all, you can acquire [doxastic] warrant […] [for] the conclusion through the inference, that is, you can come to believe the conclusion on the basis of a warrant through the inference.

Closure of propositional warrant under known entailment (CPW) requires that, if a thinker has some warrant or other to believe p and knows that p entails q, then that thinker has some warrant or other to believe q. As a conceptual point, CPW does not impose any constraints on the nature of the warrant to believe q. It does not say, for example, that the warrant to believe q should be partly constituted out of the warrant to believe p. For example, suppose that (contrary to fact) it were a metaphysical necessity that, for each thinker x, if x is situated in such a way that a warrant to believe p (Moby Dick is a whale) becomes available to x and x knows that p entails q, then x is visited by the oracle and is told on the highest epistemic authority that q, thereby being provided with a warrant to believe q (Moby Dick is a mammal). That would be sufficient for the metaphysically necessary satisfaction of CPW in this case. But the foregoing is not what Silins describes as automatic transmission of propositional warrant. The warrant to believe q that Silins says one has automatically, if one has a warrant to believe p and knows that p entails q, has the following property: if a thinker were to base his belief on the propositional warrant that is automatically ‘transmitted’ then that thinker would be basing his belief q in part on the propositional warrant to believe p (and in part on the warrant to take the step of inference from p to q). In contrast, if the thinker in our strange story were to base his belief on the propositional warrant to believe q that makes CPW come out true (that is, were to base his belief on the word of the oracle),16 then that thinker would not be basing his belief q in part on the propositional warrant to believe p. In our strange story, a thinker who bases his belief that Moby Dick is a mammal on the word of the oracle is basing his belief on a warrant that is epistemically independent from, and not epistemically posterior to, the warrant to believe that Moby Dick is a whale. In contrast, the warrant to believe that Moby Dick is a mammal, which is (according to Silins) automatically available to a thinker who has a warrant to believe that Moby Dick is a whale and who knows that all whales are mammals, is epistemically dependent on, and epistemically posterior to, the warrant to believe that Moby Dick is a whale.

If Silins were right that having a warrant to believe p and knowing that p entails q (and being a competent thinker, perhaps) adds up to having a warrant to believe q,17 then this fact would guarantee CPW (for competent thinkers). But, conversely, CPW does not guarantee that Silins is right. Again, if Silins were right, he might call the principle that he would be right about: transmission of propositional warrant under known entailment (for competent thinkers) — TPW. TPW might even be exceptionless: that is, there might be no failures of TPW. If there were no failures of this kind of transmission of warrant, then we might infer that this kind of transmission of warrant was not exactly what was under discussion in debates over failures of warrant transmission.18

In sum, and returning to the excerpted passage, Silins imagines that friends of transmission failure might say that transmission of propositional warrant across known entailment (TPW) is too easy. It does not really require anything of the thinker (other than perhaps that the thinker should be competent). Silins then imagines that friends of transmission failure might try to make transmission more demanding on the thinker. Perhaps — new proposal — warrant transmission should be a matter of the thinker acquiring a new warrant (that is, a new propositional warrant) by carrying out a particular bit of reasoning. Silins’s point in response to this suggestion is that, if a warrant to believe q is automatically available to a thinker who has a warrant to believe p and knows that p entails q, then nothing that the thinker can do (whether carrying out some reasoning or anything else) can make that very same warrant to believe q newly available to the thinker. Before the thinker did anything, the warrant to believe q was already automatically available. So, following the new proposal, there would be too much transmission failure. Of course, the thinker could do something to make a different warrant to believe q newly available. The thinker could, for example, go and visit the oracle. But making a different warrant newly available — a warrant that is epistemically independent from the warrant to believe p — would not be warrant transmission. Overall, Silin’s point seems to be that, if warrant transmission is defined wholly in terms of propositional warrant — warrant to believe — then there will either be no transmission failure or else too much. I leave explicit discussion of Silins here, but the points raised will be relevant in what follows.

1.7 So, returning to (ZALABARDO) itself: whence premise (A)?

(A) The problem of easy knowledge presupposes Transmission of warrant in (EK)-reasoning.

The problem of easy knowledge is the problem of (EK)-reasoning providing knowledge that the table is not white with red lights shining on it. It’s not the problem of possessing knowledge that the table is not white with red lights shining on it. Most philosophers can agree that one could obtain and use inductive evidence against the possibility that there are red lights shining on the table to come to know this proposition. Indeed closer visual scrutiny of the table and its environs could rule out this local sceptical hypothesis. So, as only Transmission — and not, crucially, Closure — poses a requirement on how knowledge that the table is not white with red lights shining on it is acquired, it is the principle directly germane to the problem of easy knowledge.

Note premise (A) is not in conflict with the following remark from Cohen (2005: 418): “Since I know [(2)] a priori, then given [deductive closure], I can come to know [(3)], on the basis of [(1)] and [(2)].” Cohen here locates the problem of easy knowledge as a problem centred on closure, rather than transmission (cf. Klein 2004: 165). But this is an apparent — rather than a genuine — conflict with Zalabardo because Cohen operates with a closure principle that is distinct from Zalabardo’s. Cohen’s closure principle is “DC: If S knows P and S competently deduces Q from P, then S knows Q”19 — a principle, crucially, requiring an act of inference. Thus, the difference in location of the problem of easy knowledge does not reflect a deep disagreement between Zalabardo and Cohen.

1.8 Whence premise (B) (cf. (38–39)) — the main load-bearing component in Zalabardo’s argument?

(B) Transmission of warrant in (EK)-reasoning presupposes the falsity of an instance of Closure in (EK).

Closure, assuming I have warrant for (1) and know (2), mandates I have some warrant or other to believe (3)20 — the warrant to believe (3) might be epistemically antecedent to, epistemically posterior to (dependent on), or epistemically independent from the thinker’s warrant to believe (1). (More on this later.) Closure does not commit on the origins of that warrant. Suppose it is a warrant to believe (3) that does not depend on my actually carrying out the inference from (1) and (2) to (3). It might be a propositional warrant automatically transmitted from (1), warrant from the oracle, or an a priori default warrant. Now suppose I engage in (EK)-reasoning and perform an (EK)-inference. Zalabardo maintains (as would Silins) that, assuming Closure — which guarantees that I have warrant to believe (3) regardless of whether I engage in (EK)-reasoning — there’s no sense in which I can — as warrant Transmission requires — obtain warrant to believe (3) by engaging in (EK)-reasoning. I cannot newly enter the condition of having a warrant to believe (3) because, ex hypothesi, I am already in that condition; I already have such a propositional warrant.21

Premise (B) has, seemingly, been vindicated: Transmission of warrant in (EK)-reasoning presupposes the falsity of an instance of Closure in (EK).22 But, before proceeding further with (ZALABARDO), we must pause to reflect on precisely how Zalabardo vindicates premise (B) — in particular, drawing on our work in the Introduction, we must spell out the implicitly temporal nature of Zalabardo’s operative transmission principle.

1.9 It’s clear that ‘obtain’ is bearing great weight in Transmission, and thus in vindicating premise (B): to obtain warrant for (3) it’s necessary that one not already have warrant for (3). As a purely conceptual matter, this is questionable: consider cases in which S already has warrant for (3) but this is epistemically independent from S’s warrant for (1), say from an alternative knowledge source (cf. Silins 2005: 83–84). Why should that conceptually preclude S from obtaining additional warrant for (3)?

So, if we were being uncharitable to Zalabardo we might straightaway conclude that premise (B) is false. To avoid such uncharitability, it’s plain we need to draw out the implicitly temporal nature of Transmission. It must be taken to read instead: ‘obtain warrant for q for the first time’ or ‘for the first time, enter the state of having warrant for q’. (Hereinafter read this into Transmission.) We now straightforwardly have a vindication of premise (B): Closure would ensure that S would already have warrant to believe (3), even before engaging in the inference.

Now inferences take place in time. That much is clear. What’s less clear is how relevant temporal — as opposed to epistemic — antecedence is to any plausible transmission principle. I want to claim epistemic antecedence (and dependence) is the key to transmission questions. Here is my strategy: I want to draw out the different analysis of (EK) which arises when we switch from Zalabardo’s Transmission to a plausible transmission principle, framed instead in terms of epistemic dependence, which I’ll call Epistemic Transmission.23 Then in section 2 I’ll vindicate my preference for a focus on epistemic antecedence by demonstrating a principle to which Transmission, but not Epistemic Transmission, is committed.24 This principle is 2.4’s (~K-ENT). And I come to show that endorsement of (~K-ENT) is associated with serious costs.

Consider, then (modelled on Zalabardo’s Transmission):

Epistemic Transmission: if p entails q, S knows that p, S infers q from p, and S’s warrant for p isn’t epistemically dependent on S’s warrant for q, then S thereby obtains warrant for q.25

In Epistemic Transmission, there is warrant transmission — not epistemic circularity and not transmission failure — even if S has some warrant or other for q before inferring q from p. Epistemic Transmission mandates warrant transmission in (EK)-reasoning unless warrant for (1) epistemically depends on warrant for (3).26 And this is all just to say that Epistemic Transmission doesn’t endorse premise (B) (with Epistemic Transmission replacing Transmission therein).

1.10 Returning to (ZALABARDO) itself, (D) and (E) are straightforward deductive consequences of (B) and (C) ((C) is an unargued assumption which I grant for the purposes of the present discussion), and (A) and (D), respectively. Nevertheless, there is more to be said about premise (B).

2. Exploring Premise (B) Further: Upshots of Zalabardo’s Response

2.1 Recall premise (B):

(B) Transmission of warrant in (EK)-reasoning presupposes the falsity of an instance of Closure in (EK).

Why is Zalabardo committed to premise (B) rather than only to some weaker principle? Why, for example, does Transmission of warrant in (EK)-reasoning presuppose the falsity — and not just the false-false vacuous truth (i.e. false antecedent-false consequent) — of an instance of Closure in (EK)? Put differently: isn’t there Transmission of warrant in (EK)-reasoning when an instance of Closure is false-false vacuously true — and not false — in (EK)?

For the reader’s ease, let me, at this juncture, repeat Zalabardo’s operative principles:

Closure: If p has warrant for S, and S knows that p entails q, then q has warrant for S. (36)

Transmission: If p entails q and S knows that p, then inferring q from p would enable S to obtain warrant for q. (39)

If Closure’s antecedent is stipulated to be false then either (i) p fails to have warrant for S or (ii) S fails to know that p entails q (or both). If (i), then Transmission’s antecedent is, by stipulation, false (as if p fails to have warrant for S, it follows that S fails to know that p). We’ve thereby stipulated that there is not Transmission in (EK)-reasoning when an instance of Closure is false-false vacuously true in (EK). So option (i) gets us nowhere. What if — option (ii) — one doesn’t, prior to performing a competent inference, antecedently know the entailment which licenses that inference. We might, moreover, suppose that one can come to know that p entails q as a result of competent inference (more on this later). At base, however: suppose one’s antecedently failing to know that p entails q is no bar to competently inferring q from p. If this is so, then it’s not that Transmission in (EK)-reasoning presupposes the falsity of an instance of Closure in (EK); it just presupposes its falsity or false-false vacuous truth.

But it should be clear that this challenge to premise (B) — viz. pointing to the possibility of Closure being false-false vacuously true — simply isn’t open in dealing with the problem of easy knowledge. As the problem of easy knowledge is set up, one, by stipulation, knows the premises of (EK) — viz. (1), and (2) (the relevant entailment) — prior to an act of inference.27 When facing the problem of easy knowledge, the antecedent of Closure is true in (EK): Closure, in (EK), can’t be false-false vacuously true. So Zalabardo is indeed committed to premise (B) (and not to some weakened variant thereof).

2.2 We made Zalabardo’s argument as strong as possible by making premise (B) as weak as possible: it only makes claims about (EK), and reasoning therewith. But Closure and Transmission are general principles. Consider, then:

(GENERALISED B) Transmission of warrant presupposes the invalidity of Closure.

Glossing (GENERALISED B): in order for any competent inference to enable one to obtain warrant for the inferred proposition, Closure must have at least one false instance — in particular, it must have a false instance in the particular argument in which one is performing the inference. Is Zalabardo committed to (GENERALISED B)?

2.3 The answer is ‘no’. But seeing why he isn’t so committed leads us to a further principle to which Zalabardo is committed. Commitment to that further principle reveals some interesting upshots of his response. Let’s back up a little. Note that we can reformulate (EK) — indeed some, although not Cohen, have done so — thus:

(WARRANT FOR 1*)

The table looks red.

(EK*)

(1*) The table is red.

So:

(2*) The table is not white with red lights shining on it.

That is, we can suppress the conditional in (EK). (EK*)-reasoning is analogous to the commonly discussed a priori deduction of ‘Something is coloured’ from ‘Something is red’. And there are many more such deductions. Consider, then, the following two (single-inference) argument schemata (and assume p entails q):

(MP)

(1) p

(MP*)

(1*) p

(2) If p then q

So:

(3) So: q

(2*) q

We want to allow that competent (deductive) inferences need not consist of formally valid arguments: the a priori consequences of a claim can be drawn out without one’s reasoning being formally valid. And it would be mistaken to insist that ostensible (MP*)-reasoning is enthymematic.28 In sum, abstracting from the problem of easy knowledge, we want to allow for a subject competently inferring q from p while failing to know that p entails q.

Standardly, however, in order for a proposition to function as a premise for a subject, it must be warrantedly believed or known by that subject.29 Thus (MP) — but not (MP*) — has a requirement that a propounder of an instance of schema (MP) have, at least, a warranted belief in the relevant conditional and, ex hypothesi, the relevant entailment. It follows, modulo our assumptions concerning warrant (see 1.5 supra), and p entailing q, that (MP) — but not (MP*) — has a requirement that a propounder of an instance of schema (MP) know the relevant entailment (though (MP*) is, of course, compatible with such knowledge).30

2.4 So it turns out Zalabardo isn’t committed to (GENERALISED B):31 Transmission of warrant is compatible with the false-false vacuous truth of Closure just in case the relevant entailment is not known by the reasoner prior to an act of inference. In other words, Zalabardo’s Closure and Transmission principles — which interact in premise (B) — commit him to the following principle:

(~K-ENT) Warrant Transmits in reasoning, only if32 the reasoner does not know the relevant entailment proposition prior to an act of inference.

Why so? Because, according to Closure, it’s only if our propounder fails to know the relevant entailment prior to an act of inference that the propounder can fail to have warrant already for the argument’s conclusion.33 By contrast, Epistemic Transmission isn’t committed to (~K-ENT) (with Epistemically Transmits replacing Transmits therein): even if our propounder knows the entailment, and thus has a warrant for the conclusion prior to inference, warrant Epistemically Transmits provided warrant for the premise(s) does not epistemically depend on warrant for the conclusion.

Now let us note two interesting upshots of (~K-ENT) — upshots of ascending importance. First, consider a rough continuum within the set of single-inference arguments (our focus), ranging from simple to complex inferences: the more complex an inference, the more readily foreseeable it is that a subject may fail to know the relevant entailment prior to an act of inference. By (~K-ENT), the more complex the relevant entailment, the more likely it is that reasoning employing that entailment Transmits warrant for the propounder. For some, this would seem, if anything, to get things the wrong way round. For Zalabardo, however, this is perfectly intuitive: the more complex the entailment, the more likely it is that inferential reasoning will provide you with something you don’t already have.

Second, and more importantly, let us focus on some interesting specific cases of what (~K-ENT) permits by way of warrant Transmission. (~K-ENT) permits Transmission of warrant in reasoning with arguments — of the form either (MP)34 or (MP*) — in which one comes to know the relevant entailment in the act of35 competent inference. (~K-ENT) permits Transmission of warrant in reasoning with arguments of the form (MP*) — but not (MP) — in which one comes to know the relevant entailment as a result of competent inference.36 Why this difference between (MP)-reasoning and (MP*)-reasoning when one comes to know the relevant entailment as a result of competent inference? Because we are positing the performance of a competent inference prior to knowledge of the relevant entailment — a posit forbidden by constituting an argument in the form (MP).

Thus we can conclude that the only circumstances in which (MP)-reasoning Transmits warrant are those in which one comes to know the relevant entailment in the act of competent inference. For some, this would seem unduly restrictive. Be that as it may, given the fundamentality of (MP)-reasoning, and given the only circumstances in which it Transmits warrant are those in which the act of competent inference and the acquisition of knowledge of the relevant entailment are simultaneous, one would like to hear more about the nature of this form of inference. It is not merely — as with certain instances of (MP*)-reasoning — that one comes to know the relevant entailment as a result of competent inference: this is an interesting feature of certain inferences, but we have a rough idea of how such a performance — or series of performances — can (causally) lead to such knowledge. The process of drawing an inference — or series of such inferences — can make it appropriate, after completion of the process, to ascribe knowledge of the relevant entailment to the reasoner. By contrast, instances of (MP)-reasoning which Transmit warrant have a quite exceptional, and underexplored, feature: one comes to know the relevant entailment in the act of — simultaneously with — competent inference. Put differently: coming to know the relevant entailment is, in some sense, constitutive of this type of inference. This putative feature of certain inferences warrants further scrutiny.37 In sum, given (~K-ENT) is a presupposition of premise (B), should (~K-ENT) prove to be unsustainable, so too will be Zalabardo’s response to the problem of easy knowledge.

2.5 Is, then, (~K-ENT) unsustainable? I have no principled objection to the possibility of any of the foregoing types of inference permitted by (~K-ENT).38 Thus, I have no straightforward objection to (~K-ENT) to the effect that it permits inferences which ought not to be permitted. Let me, instead, gesture at a more cautious objection to (~K-ENT) to the effect that its defenders have an explanatory burden which they have yet to discharge. The explanatory burden arises given two assumptions. First, assume it is a desideratum on any theoretical account such as Zalabardo’s that it be able — given adequate information — to accurately classify or characterise the form of argument involved in as many successful inferences,39 of those to which it speaks, as possible — here, whether (MP) or (MP*). Second, assume that many successful inferences involve the form of argument (MP). I take each of these assumptions to be relatively uncontroversial.

Now, on the back of these assumptions, let us make two particular suppositions in advance of outlining the explanatory burden faced by a defender of (~K-ENT): first, suppose that a reasoner does not know the relevant entailment prior to an act of inference. Second, suppose that the inference in question is performed competently. Now, whether the form of argument involved in this inference is (MP) or (MP*) (in part) depends on whether our reasoner comes to know the relevant entailment in the act of — simultaneously with — competent inference. If he so comes to know, we have a candidate case of (MP)-reasoning (though also a candidate case of (MP*)-reasoning).40 And if he fails to so come to know, we have a case of (MP*)-reasoning (and not also a candidate case of (MP)-reasoning).41

Now, here is our explanatory challenge: defenders of (~K-ENT) must offer clear, prospective individuation conditions for the type of inference in which one comes to know the relevant entailment in the act of — simultaneously with — competent inference. We can call these knowledge-constitutive inferences. And we can call those inferences in which one comes to know the relevant entailment as a result of competent inference, knowledge-resulting inferences. In particular, then, such individuation conditions must enable us to distinguish between knowledge-constitutive and knowledge-resulting inferences.

We can dramatise the urgency of this challenge by contrasting two inferences — one knowledge-constitutive and one knowledge-resulting (yet suppose the two inferences are otherwise identical, in advance of determining the form of argument involved therein). We can stipulate that the knowledge-resulting inference is one in which, as a matter of fact, the reasoner acquires knowledge of the relevant entailment a millisecond (or less) after completing the inference (cf. n. 35 supra). The point is that in the absence of clear, prospective individuation conditions for knowledge-constitutive inferences it is unclear how — even given adequate information about how, independently of whether known, the relevant entailment features in the reasoner’s reasoning process etc. (cf. n. 40) — we can distinguish between these two inferences.42 Without such conditions we can, in this and like cases, have no idea whether the form of argument involved in the inferences in question is (MP) or (MP*). And it follows, given (~K-ENT), that we can have no idea when a successful piece of (MP)-reasoning has taken place.43

In sum, in advance of defenders of (~K-ENT), like Zalabardo, discharging this explanatory burden, we can enter a provisional verdict: (~K-ENT) is, without more, unsustainable, and so too, without more, is Zalabardo’s response to the problem of easy knowledge.


1 I use this parenthetical device again in Chapter Three: it signals that the key issue up for debate is whether such knowledge is indeed delivered.

2 Assume that the fact that a knowledge source is reliable does not guarantee that the knowledge source always delivers truths. So, to accept KR, know K is reliable, and then to engage in (EK)-reasoning is to learn something new, viz.: K is not misleading on this particular occasion. How counterintuitive this is (if at all), I leave to the reader. I also bracket problems concerning the individuation of knowledge sources. Finally, I read Cohen to take KR to make knowledge of the reliability of a source merely a corequisite, and not — more strongly — a prerequisite, for having knowledge by means of that source. For further exploration of this distinction, cf. Sosa (2009) and Van Cleve (2011).

3 Say: If S knows p and S knows p entails q, then S knows (or at least is in a position to know) q. Knowledge-closure principles have been denied by Dretske (1970, 1971, 2005) and Nozick (1981). This denial hasn’t proven popular, however (see Hawthorne 2005). (Knowledge-closure is discussed in detail in Chapters Six and Seven.)

4 Cohen’s response to the problem (2002, 2005) involves distinguishing between animal and reflective knowledge (cf. Sosa 2007, 2009). KR is rejected when considering animal knowledge, but so is deductive closure (cf. 1.7 infra). When considering reflective knowledge, meanwhile, KR is accepted. Either way: no problem of easy knowledge. Cohen (2002: sec. VI, 322), more positively, appeals to a holism on which “[g]radually, as we acquire more and more sensory evidence, thereby accumulating a relatively large and coherent set of beliefs, those beliefs, including the belief that our cognitive faculties (perception, memory, reasoning) are reliable become knowledge”.

5 Another strand — Zalabardo’s starting point — focuses on bootstrapping.

6 My note: ‘p has warrant for S’ is equivalent to ‘S has warrant for p’.

7 My note: (1) Could we, without loss, weaken the antecedent of Transmission by replacing ‘S knows that p’ with ‘p has warrant for S’? Or indeed, weaker still, saying nothing about S’s epistemic position vis-a-vis p? (Suppose S has no warrant for p, but has warrant for a proposition in the neighbourhood of p, p´. Could S infer q from p and thereby obtain p´-warrant for q?) Perhaps. I suspect Zalabardo wants to sidestep issues over inferring from unknown premises. (2) As hinted at already, Transmission is somewhat strange on account of the antecedent not explicitly mentioning warrant (yet that is what is supposed to be transmitted).

8 The inference of q from p must, I take it, be deductive — though the deduction need not consist of a formally valid argument — and performed competently (cf. Hawthorne 2004: 34–35).

9 Note that Zalabardo is not endorsing Transmission’s — cf. Closure’s — validity, given he allows for instances of transmission failure. Thus, to give a complete account of transmission, it would seem that Zalabardo must either reformulate Transmission to render it valid (e.g. for him, as we’ll see, making ‘S has no warrant for q prior to inference’ a condition of the antecedent), or supplement Transmission with a trouser-wearing, putatively valid (sufficient) condition for transmission failure.

10 Transmission is an indicative conditional whose consequent is a subjunctive conditional. In evaluating Transmission in a particular piece of reasoning with an argument we assume the truth of the antecedent of that subjunctive conditional — we assume, that is, the performance of an inference. In what follows we are investigating the (temporal) preconditions on inference.

11 Often, though, proponents of sufficient transmission conditions (tacitly) take them to be lone sufficient conditions.

12 So the possibility of Gettierisation is stipulated away. I don’t question Closure’s validity in this chapter, though it is psychologically questionable on account of this usage of ‘warrant’. Principles like Closure, operating with this Plantingan, Gettier-proof notion of warrant, have not received much scrutiny.

13 The propositional reading of the ‘warrant for believing’ locution is not, it seems, in line with Silins (2005: 74), but is in line with Pryor (2001: 104) and others.

14 The basing relation is left undeveloped here (see Korcz 2006).

15 The basing relation presents a bit of a problem for Zalabardo’s (Plantingan) approach. If true belief plus warrant equals knowledge, then warrant needs to include basing. But it is not easy to see how warrant that includes basing could be present in the absence of belief.

16 Perhaps it can be shown that an epistemically ideal thinker would never base his belief q on the warrant made available by the oracle; but neither Transmission nor Closure says anything about epistemically ideal thinkers.

17 Admittedly, Silins just talks of “many cases” of automatic transmission, but I take it that our stipulation here that our thinker knows that p entails q (and is competent, perhaps) is sufficient to commit Silins to this claim.

18 Suppose the exceptionless principle of transmission of propositional warrant does require that the thinker should actually take the step of inference (competently). We would still say that, in that case, this was not what people had in mind in discussion of transmission failure.

19 It is a good exercise to probe the difference between closure principles, such as Cohen’s, which require an act of inference, and transmission principles.

20 I here gloss Zalabardo’s warrant as ‘warrant to believe’ (though we’ve seen it has properties additional to those had by propositional warrant — see 1.5 supra).

21 There is one sense in which, for Zalabardo, you could obtain warrant to believe a proposition for which you already have warrant: when you come into a new relation to the proposition that would make you have warrant to believe the proposition if your original source of warrant wasn’t there. (EK)-reasoning (and like reasoning), though, doesn’t satisfy this condition, since, if the original source of warrant to believe (3) wasn’t there, by Closure you wouldn’t have warrant to believe (1).

22 Thus the unorthodoxy of Zalabardo’s response: the received wisdom seems to be that, put crudely, transmission entails closure but that closure does not entail transmission. Wright (1985, 1991, 2003, 2004), for example, always makes the point that transmission failure is consistent with closure. But, for Zalabardo, put crudely, Transmission entails Closure’s falsity in (EK)-reasoning (and so Closure entails Transmission’s falsity in (EK)-reasoning). More on this, and on Zalabardo on the relationship between Transmission and Closure in general, in section 2.

23 The points will generalise: from (EK) to other arguments, and from Epistemic Transmission to other plausible such transmission principles. Of course, Zalabardo’s Transmission is an epistemic principle — framed in terms of warrant and knowledge. So the contrast here is with Zalabardo’s focus on temporal antecedence.

24 This commitment arises on the assumption of Closure — an assumption Zalabardo, my interlocutor, makes.

25 I don’t suggest this is an optimal such principle; rather the aim — served by modelling it on Zalabardo’s principle — is merely for contrast.

26 Modulo the other conditions in its antecedent being met. Thus, unlike Zalabardo’s principle, this principle has a shot at being valid (cf. n. 9 supra).

27 Two related points. First, what do I mean by ‘knowing (or having warrant for) the relevant entailment’ — a locution which features prominently in the remainder of this chapter? (2) is a conditional expressing an entailment relation. Thus, to know (2) is to know the relevant entailment relation expressed by (2). And we can refer to the proposition expressed by (2) as the relevant entailment proposition. Importantly, such knowledge does not entail that one knows that: [(1) and (2)] entail (3) (and so on). Second, and relatedly, the set-up for (EK) does not, however, require that: one knows that premise (1) and premise (2) together entail conclusion (3). It follows from this (I leave the proof to the reader) that a revised premise (B), operating instead with the following plausible two-premise versions of Transmission and Closure, would, without more, be false:

Two-premise Transmission: If p1 and p2 together entail q, and if S knows that p1 and S knows that p2, then (competently) inferring q from p1 and p2 would enable S to obtain a warrant to believe q.

Two-premise Closure: If S has a warrant to believe p1, and S has a warrant to believe p2, and S knows that p1 and p2 together entail q, then S has a warrant to believe q.

The moral for Zalabardo is: don’t construct the argument with these two-premise principles.

28 Wright (2007: sections II and IV) presents a series of “justificational triads concluding with the falsity of sceptical hypotheses concerning the external world, testimony, other minds etc., which share (MP*)’s property of not being formally valid.

29 Hawthorne and Stanley (2008) argue a premise must be known by a subject engaging in practical reasoning, and note that such a requirement also seems plausible in the domain of theoretical reasoning. If Hawthorne and Stanley are right on this latter claim, my conclusion that a propounder of an instance of schema (MP) must know the relevant entailment can be reached directly.

30 Even in (MP) the three propositions — premises (1) and (2) and conclusion (3) — do not tell the whole story. There is also a rule of inference. In (MP*) there is also a rule of inference — not a logical rule of inference, but still a rule of (proper or non-logical) inference that is a priori valid. There is no evident requirement, however, that the thinker should have formulated as a proposition, and should have a warrant to believe, the relevant rule of inference (in the case of (MP), the rule modus ponens). All we assume is that the thinker in question is a competent reasoner.

31 This is a good thing. Given Zalabardo assumes the validity of Closure, if premise (B) were to have generalised in this way, Zalabardo would have been in the unenviable position of ruling out Transmission of warrant tout court.

32 Not ‘if’: there is not, for Zalabardo, Transmission in reasoning if the reasoner has an a priori default warrant for the conclusion (though any such cases are bracketed here).

33 And, of course, a propounder can fail to meet this necessary condition — can know the relevant entailment prior to an act of inference — whether the argument with which he reasons is constituted in the form (MP) or (MP*).

34 Thus, on this view, (EK)-reasoning as understood with respect to the problem of easy knowledge, in which one knows the relevant entailment prior to an act of inference, is but one form of (MP)-reasoning.

35 A key issue here, relevant to our simple/complex inference distinction, will be individuating acts of inference. When do they start? When do they end? When is warrant obtained? A defender of (~K-ENT) owes us an answer to these questions (cf. 2.5 infra).

36 (~K-ENT) permits warrant Transmission in reasoning with arguments of the form (MP*) — but not (MP) — in which one does not come to know the relevant entailment at all.

37 To switch emphasis: This putative feature of certain instances of coming to know an entailment warrants further scrutiny.

38 While, as far as I am aware, none of the foregoing types of inference permitted by (~K-ENT) has received detailed discussion in the literature, none is straightforwardly unintuitive. I do not attempt to go beyond the basic adumbration of the foregoing types of inference permitted by (~K-ENT) provided in 2.4 (an adumbration which, saliently, does not provide an account of what it is to know an entailment); indeed, given the shape of my coming objection to (~K-ENT) — which takes the form of an explanatory challenge for defenders of (~K-ENT) — it would be unwise of me to do so.

39 I will stipulate that a successful inference just is a competent inference plus whatever additional constraints, if any, are required in order for the inference in question to furnish the subject with warrant for that which is inferred. For Zalabardo, thus, (~K-ENT) would be such an additional constraint. Thus, what counts as a successful inference, in this sense, will vary depending on the theoretical account in question.

40 (MP*)-reasoning is, I take it, compatible with such knowledge. (At any rate, in advance of further information on the nature of such inferences we must assume this to be the case.) I take it that further information about how such knowledge features in the reasoner’s psychology — how, independently of whether known, the relevant entailment features in his reasoning process — will determine whether the argument involved in this inference is (MP) or (MP*). Note that such facts about a reasoner’s psychology alone cannot determine the form of argument involved; it is such facts in combination with whether, and when, the reasoner knows the relevant entailment.

41 To fail to make our supposition that the inference is performed competently, both the foregoing cases may be cases of non-successful — failed — reasoning (cf. n. 39 supra).

42 Why not, instead, begin at the other end with a search for clear, prospective individuation conditions for knowledge-resulting inferences? To my mind this would not be a fruitful way to proceed (though defenders of (~K-ENT) are free to adopt this strategy if they so wish). First, I take it that knowledge-resulting inferences are a motley group of inferences, with potentially little conceptually to unite any two such inferences. Second, and relatedly, I do not see how, even assuming some such set of individuation conditions could be reached, such conditions could help us distinguish between the two inferences in our dramatisation.

43 Doesn’t this explanatory challenge arise regardless of (~K-ENT)’s truth-value? Yes — but with less urgency if (~K-ENT) is false. The challenge is less urgent because if (and only if) (~K-ENT) is false, it’s no longer the case that the only circumstances in which (MP)-reasoning furnishes the subject with warrant for its conclusion are knowledge-constitutive inferences. That is, if (and only if) (~K-ENT) is false, cases in which the relevant entailment is known prior to an act of inference can serve as quotidian cases in which the inference in question is successful — furnishes the subject with warrant for that which is inferred (cf. n. 40 supra). Given adequate information, we can accurately classify or characterise the form of argument involved in such cases on a case by case basis (cf. n. 38 supra). Clearly, in such circumstances the need to provide clear, prospective individuation conditions for knowledge-constitutive inferences is less urgent (cf. our two assumptions made two paragraphs ago in the main text).