Abstract
The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the relation of evidential support is not closed under known entailment. Therefore the evidence-for relation is deductively open regardless of whether evidence is probabilistic or not. Given even a weak dependence of empirical knowledge on evidence, we argue that empirical knowledge is also open. On this basis, we also respond to the strongest argument in support of knowledge closure (Hawthorne 2004a). Finally, we present a number of significant benefits of our position, namely, offering a unified explanation for a range of epistemological puzzles.
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Notes
The term “open knowledge” was first coined (as far as we know) by Nozick (1981: 208) and refers to the view to which he had subscribed, namely, that knowledge is not closed under known entailment.
If you think the evidence in such cases is different, e.g. the evidence is not the appearance of the watch but that the time is three, simply adjust the example. As we show later, the argument relies on purely formal features of the relation between evidence and that which it supports. In fact, even if the evidence is that the time is three, since you acquire this evidence by looking at your watch it still seems odd that you could learn on the basis of such evidence that your watch hasn’t stopped a half hour ago.
Together with a priori propositions, we do treat necessary contingent propositions, e.g. “I exist” and, if Williamson is right, “there is at least one believer” (Williamson 1986) etc., as having probability 1. We also assume that evidence has a probability 1 and that some knowledge has less than probability 1, i.e. that some knowledge is not evidence. In particular, although in some cases it seems plausible to associate probability 1 to known propositions, we do not accept that this is the case across the board. Some of the arguments proposed below can be reformulated as a challenge to those who, following Williamson (2000: 184–237), view knowledge as always having probability 1. Besides our problems with regard to the way Williamson characterizes prior probabilities, there are also epistemological problems with this account (see footnote 50 below for some more details and our 2013).
Note that this criterion does not require raising of probabilities.
Some may be worried that not all evidence is propositional, that experiences, for instance, such as the experience of a blue patch in one’s visual field, may be evidence for one that there is something blue in the vicinity. If you have such worries, take as the relata figuring in EC (and the other evidence principles below) the proposition that S is experiencing a blue patch in his field of vision. We propose this measure only in order to sidestep this thorny issue.
“⇒” denotes strict implication (usually either logical implication or some other sort of a priori implication). Epistemologists tend to be quite relaxed in their usage of the terms “implies” and “entails,” usually not taking much care to distinguish strict implication, or entailment, from material implication. Following this usage, let us note however that all implications referred to in this article are necessary, or a priori knowable, strict implications. Similar remarks are in order with respect to equivalence by which we mean not logical equivalence, but conceptual, or a priori, equivalence, symbolized by “⇔”. We use “⊃” for material implication. Other symbols are standard unless explicitly defined.
Let us show that Pr(e ⊃ c|e) < Pr(e ⊃ c). First, Pr(~(e ⊃ c)|e) ≥ Pr(~(e ⊃ c)), since:
-
1.
Pr(~(e ⊃ c)|e) = Pr((e∧~c)∧e)/Pr(e) = Pr(e∧~c)/Pr(e)
-
2.
Pr(~(e ⊃ c)) = Pr(e∧~c)
Assuming that 0 < Pr(e) < 1, (Pr(e ∧ ~c)/Pr(e)) > Pr(e ∧ ~c), so Pr(e ⊃ c|e) ≤ Pr(e ⊃ c).
Second, assuming as we are throughout that the probability of e∧~c is not zero (i.e. that c is known fallibly and is not a necessary truth), the right side of the inequation is greater than the left. Thus: Pr(e ⊃ c|e) < Pr(e ⊃ c).
-
1.
The problem we discus here is similar to the problem discussed in Hawthorne (2004a: 73–78) and in Cohen (2005). As will become apparent, the core issue we believe relates to the failure of evidence closure and differs significantly with respect to the analysis and solution of these problems. We are, nevertheless, indebted to their groundbreaking work on these issues.
These are, respectively, versions of what has come to be known as the “easy knowledge” problem (Cohen 2002, 2005) and Kripke’s dogmatism puzzle (2011). The following sentence in the text presents an instance of the phenomenon of epistemic ascent. For a focused discussion of all three issues and the how they are related see our 2010 and MS. Notice that our formulation of the problem is general in that it does not rely on the intuition that knowledge is gained too easily (Cohen 2002, 2005) nor on the intuitive oddity of bootstrapping oneself into knowledge of the reliability of one’s sources (Vogel 2000, 2007). As will become evident in what follows we rely solely on structural features of evidence and the principles governing the relation of evidential support. Thus, contrary to what some have alleged, the denial of closure is motivated not merely by the desire to avoid Cartesian skepticism. Epistemic closure is implicated in many epistemic puzzles, including, in addition to those already mentioned, the lottery paradox (see Vogel 1990; Hawthorne 2004a), some of the semantic self-knowledge puzzles and probably some other problems that are less central in current writings. There is a further brief discussion of this issue below.
This is not to say that contextualism or subject sensitive invariantism entail closure of knowledge. Both are compatible with open-knowledge and can be employed to explain certain epistemic phenomena.
Further clauses can be added to these principles, see Hawthorne (2004a: 39), but for simplicity we omit them here. Nothing in our argument turns on this simplification.
Hawthorne (2004a: 41, note 99) notes that, strictly speaking, that a thing is a zebra does not logically imply that it is not a painted mule. Recent reports indicate that zebras may also be mules or at least horses. But let us not allow the facts ruin a good example.
Hawthorne (2004a: 112). Others have simply called the principle “intuitive closure” (Williamson 2000: 117), claimed that rejecting closure is “intuitively bizarre” (DeRose 1995: 201), or “one of the least plausible ideas to gain currency in epistemology in recent years” (Feldman 1995: 95), and that closure is “something like an axiom about knowledge” (Cohen 2005: 312).
There is no essential probabilistic point here. All that we are claiming is that some measure of support is given to DM by a visual observation of a zebra looking animal.
We will later discuss the relation between these principles and their epistemic analogues.
In terms of a coarse-grained possible world semantics, we might say that any evidence that the actual world is one of the h 1-worlds (the possible worlds in which h 1 is true) is also evidence that the actual world is an h 2-world, since in those terms the sentences express the same proposition. EEQ is justified by the claim that any evidence that the actual world is one of the h 1-worlds is also evidence that the world is an h 2-world if “h 1” and “h 2” are true in the same worlds.
For the argument below all that is needed is that there are some cases of (inductive) underdetermination.
In social sciences instances of such underdetermining evidence seem to be even more prevalent and easier to describe. Take, for example, the debate between the “directional” and the “proximity” models of special representation of voting preferences. In 1999 two scholars claimed that “the existing data contain insufficient information with which to distinguish the two theories.” (Lewis and King 1999). The claim was repeated in 2006 (by Van Houweling, Tomz and Sniderman (unpublished manuscript)). This conclusion may certainly be debated, but for the purposes of this argument the possibility of its truth suffices.
The proof is straightforward. First, from left to right: Given that T 1 ⇒ ~T 2 and assuming T 1 ∨ ~T 2, either T 1 is true, in which case so is ~T 2 (by the implication), or ~T 2 is true. So T 1 ∨ ~T 2 implies ~T 2. Now from right to left, ~T 2 clearly implies the disjunction T 1 ∨ ~T 2. Hence, T 1 ∨ ~T 2 ⇔ ~T 2.
The Nicod principle: “For any object a and any properties F and G, the proposition that a has both F and G confirms the proposition that every F is G” (Fitelson 2006: 95–96).
This is easy to demonstrate within a probabilistic framework for evidence. Given the assumption that evidence just is the raising of probabilities, both hypotheses’ probabilities are raised by a ∧ b (see proof of lemma in note 35 below). But if we have a long conjunction with only the difference of two propositions, it seems safe to say that even without appeal to probabilities the evidence supports two incompatible conjunctions.
The absurdity is even more pronounced given the following assumption that one who accept EAD would find hard to deny: if e is evidence for p-or-q, and e is not evidence for q, then e is evidence for p. Since a ∧ b is evidence neither for c, nor for ~c (as we have supposed), this would entail, absurdly, that a ∧ b is evidence for the falsity of atomic a or of atomic proposition b. Though at this stage the appeal to atomic propositions is not important. We would like to thank an anonymous referee for pointing this out.
This is not entirely precise. EEQ relates to a priori equivalence whereas the paradox of confirmation turns on logical equivalence. Thus, although they are very similar and seem to be motivated by the same considerations, one may want to retain the logical equivalence of evidence while rejecting EEQ.
Since the probability of T 2 was stipulated to be 0.2, the probability of ~T 2 is 0.8, and the probability of T 1 ∧ ~T 2 is just the probability of T 1.
This assumption is not to be confused with the stronger claim that evidence just is the increasing of probability. Here we are merely assuming that evidence cannot lower the probability that the proposition it supports is true (see EC above).
This is shown by a simple application of Bayes’ theorem.
Starting with a stronger assumption than the one we have been employing, i.e. that evidence is defined by the raising of probabilities, that denial of EEQ conflicts with the Kolmogorov (1956) axioms. Let us assume that p and q are equivalent. Since p entails q, the probability of p cannot be greater than q. Likewise, since q entails p, q’s probability cannot be greater than p. Hence, their probability before and after the evidence is taken in must be the same, hence, if e is evidence for p it is evidence for q.
Hempel (1965: 31–33) argues that if evidence is closed under strict implication, every proposition is evidence for any other. We present Carnap’s example since, as will become evident, it relates directly to the principles that we have been concerned with. Namely, EAD and EDIS. Hempel’s argument proceeds via what he labels the “converse consequence condition.” But here is another more general way to proceed: Assuming that a proposition e is evidence for a proposition h iff the probability of h given e is higher than the probability of h (E(e, h) = def Pr(h|e) > Pr(h)), let us first establish a lemma:
Lemma. For all empirical propositions p and q, if p entails q, then q is evidence for p.
Recall the definition of conditional probability: Pr(p|q) = Pr(p ∧ q)/Pr(q). Now let us assume (as is plausible if we are considering empirical matters) that 0 < Pr(q) < 1 and that p strictly implies q. It then follows that:
(1)
(p ⇒ q) ⇒ [Pr(p) = Pr(p∧q)]
[Since p and p ∧ q are equivalent, Kolmogorov axioms]
(2)
Pr(p ∧ q)/Pr(q) > Pr(p)
[1,since 0 < Pr(q) < 1 and Pr(p ∧ q) = Pr(p)]
(3)
Pr(p|q) > Pr(p)
[2,conditional probability]
(4)
E(q,p)
[3, Evidence def.]
Now, the lemma entails:
(5)
∀p∀qE(p, p ∧ q)
[Lemma]
Assuming for reductio that evidence is closed under (known) entailment we have:
(6)
∀p∀q∀r(E(p, q) ∧ (q ⇒ r)) ⇒ E(p,r ))
But then since q follows from p ∧ q, we have the triviality result:
(7)
∀p∀qE(p,q)
[5,6]
(7) is surely unacceptable, so one must either reject evidence closure or the proposed definition of evidence (or the Kolmogorov axioms). By relying on the weaker criterion EC rather than on the definition of evidence as the raising of probabilities, I avoid the rejection of the proposed definition of evidence as a reply to the argument against evidence closure. Another version of Hempel’s argument—similar to the one presented here—can be found in Kaplan (1996: 45–56).
Notice that this principle is stronger than the one our main argument utilizes, namely, EC. Giving up the probabilistic analysis of evidence expressed by ES, therefore, while useful against Carnap’s argument will not resolve non-probabilistic argument nor cases such as the watch case.
Note that Carnap’s example shows more than our argument requires, although by appeal to a stronger principle. It demonstrates that e can raise the probability of each of two propositions in isolation while lowering their disjunction. What we have relied on is merely that e can raise the probability of one of the disjuncts (p) while lowering probability the disjunction p ∨ q. Notice also how strange it is that one could have evidence for p and evidence for q, yet lack evidence for either p or q. Asserting as much in ordinary conversation would seem very strange. This connects directly with DeRose’s argument from abominable conjunctions to closed knowledge. See footnote 48 for further detail.
We are here strengthening the antecedent by adding conditions b and c not to beg any question against a would be proponent of evidential closure.
In the final analysis it seems that even CS is not essential to the argument for open evidence as shown by the argument above: (19)–(22).
The same explanation, in essence, can account for cases involving disjunction and conjunction. It cannot be used to explain cases involving equivalence, which is one reason to think we have taken the correct track here in response to the cases we have been considering.
The notion of counting against in ED can be interpreted probabilistically, or, in light of the forgoing discussion, non-probabilistically. The probabilistic reading of ED can be objectivist or subjectivist with respect to the likelihoods (the probability of the evidence given the hypothesis).
Note that we do not regard ED as a principle. Nevertheless, it becomes evident that this claims holds for many cases (or at least some) when the background assumptions are made explicit, such as: S has not corrected her reasoning, received the kind of evidence that inspires her to realize that she has made a mistake, or remember that she has evidence she completely forgot about, etc.
Proof Let us take as our q proposition the proposition ~(e ∧ ~p) entailed by p. While raising the probability of p, e lowers the probability of this proposition. On standard assumptions, since e does not entail p, the probability of e ∧ ~p is <1. By the definition of conditional probability:
(1)
Pr(e ∧ ~p|e) = Pr(e ∧ ~p∧e)/Pr(e) = Pr(e∧ ~p)/Pr(e)
Assuming that 0 < Pr(e) < 1 (as we must), we have:
(2)
Pr(e ∧ ~p|e) > Pr(e ∧ ~p)
Thus:
(3)
Pr(~(e ∧ ~p)|e) < Pr(~(e ∧ ~p))
By EC, e supports p, but not a proposition a priori known to be entailed by it.
Note that this is not peculiars to q propositions the negations of which entail the evidence. As long as the evidence is supported by the ~q, the probability of q will be lowered by the evidence. To see this we need only use Bayes’ theorem as follows:
(4)
Pr(p|e) = [Pr(e|p)/Pr(e)]Pr(p)
(5)
Pr(e|p)/Pr(e))Pr(p) > Pr(p) ⇔ (Pr(e|p)/Pr(e)) > 1
[4]
(6)
Pr(e|p)/Pr(e)) > 1 ⇔ Pr(e|p) > Pr(e)
[5]
(7)
Pr(e|p) > Pr(e) ⇒ Pr(p) < Pr(p|e)
[4, 5, 6]
The examples employed in the text, then (watch, zebra, car, etcetera), are but a small sample of a pervasive phenomenon.
Taking p itself as one’s new evidence will not essentially effect the argument. Standard conditionalization is unwarranted on p since its probability is <1 (doing so would allow unreasonable amplification of probabilities—just think of the special case of Pr(p|p) = 1), and using Jeffrey conditionalization will leave things as they stand.
Nozick’s and Dreske’s rejection of closure is a consequence of their theories of knowledge. In doing so they make inconsistent commitments. Nozick rejects DIS and accepts AD (1981: 236) and EQ (1981: 690 note 60). Thus he is vulnerable to Hawthorne’s first argument. Dretske on the other hand is vulnerable to Hawthorne’s second argument, since he endorses DIS (1970: 1009) and though he is less than explicit about it, implicitly accepts EQ, as he recognizes in (Dretske 2005a, b).
Perhaps the most influential argument against open knowledge is due to its entailing what DeRose (1995) called “abominable conjunctions” (conjunctions of the form “He knows this is a zebra, but does not know that it’s not a disguised mule”). Such assertions indeed sound odd, but we do not regard this as a reason to endorse closure for the following reasons. First, the oddity of such conjunctions meshes with an explanation of the force of closure-based skeptical arguments. There’s thus something to be said for simply accepting a measure of unintuitiveness involved in epistemic openness, particularly when it is explained in terms of the underlying evidential structure. Second, as we have shown abominable evidence construction are unavoidable (e.g. “Her evidence supports p and q, but does not support p nor does it support q”; “his evidence supports p and supports q, but does not support either p or q”). Such conjunctions are a problem for everyone and given the connection between knowledge and evidence it should come as no big surprise to find similar constructions with respect to knowledge.
We have in mind reasons related to preface paradox-type considerations and difficulties that arise from the requisite distinction between objective and epistemic probabilities of known propositions. See our (2013). There we elaborate on several other aspects of the conception of knowledge as having probability 1, and among other things, show that if justification depends on evidence, justification is not deductively closed.
The following proves that: For all empirical propositions p and q, if p entails q and can serve as evidence for it, then p is conclusive evidence for q.
(1)
(p ⇒ q) ⊃ Pr(p) = Pr(p ∧ q)
[EQ]
(2)
Pr(p ∧ q)/Pr(p) = 1
[1]
(3)
Pr(q|p) = 1
[2, conditional probability def.]
For an argument that these (Kripke style) dogmatic beliefs are not known, see our (2010).
If a known proposition can count as evidence for other beliefs Multi-Premise Closure is also valid. The main reasons for questioning Multi-Premise closure is that the risks of falsehood accumulate with each premise and can add up to risk that puts the credibility of one’s belief beneath the threshold necessary for knowledge (see Hawthorne 2004a: 46–48 and Stanley 2005: 18). But if the evidence is knowledge, then every known proposition is supported by itself so the risk is annulled. Hence, if knowledge is evidence, and one knows mundane empirical truths, Multi-Premise Closure based on such beliefs is as valid as Single-Premise Closure. But this would saddle us once again with the problems faced by infallibilism. See Hawthorne and Lasonen-Aarnio (2009) and our (2013).
This is made evident by the following observation. Suppose, given the rate of breakdowns of your watch, the fact that it shows “3:00” raises the probability that it is three o’clock to 0.9. Suppose further that this is enough to know that it is three o’clock and that this knowledge is now your evidence that your watch is accurate. Presumably, since this latter proposition is entailed by what you know, its probability is no less than 0.9. Now if you receive some weak evidence suggesting that the watch is malfunctioning, we do not say that since you have stronger evidence that the watch is accurate you know this. We do not weigh the new evidence against p. The belief that the watch is accurate, it seems, requires some independent support in order to count as knowledge. The support of p does not aid q if the latter is not itself supported by the evidence. But now if, as we have seen is possible, e provides no support for q (and assuming there’s no other source of evidence), how can the mere presence of p improve one’s evidential situation at this moment?
It is important to note that ED is not a threshold claim. It concerns the “direction” of support and not its magnitude. Stating the point with regard to the current example, if you do not know beforehand (say by looking at the car) that my car is not one of the cars stolen from a specific vicinity, knowing that I remember parking it there will not allow you to go from ignorance to knowledge that it has not been stolen from that vicinity.
One might claim that a priori knowledge of this type is not available for conditionalization, but this must be considered a desperate ad hoc measure. A priori knowledge, i.e. knowledge that does not require relevant evidence, is exactly the kind of knowledge that we can and should normally be warranted perhaps even required to conditionalize on.
We have shown (footnote 42) that for every proposition that is not based on conclusive evidence and is known, there are many propositions that follow from it that are not supported by the totality of one’s evidence. As long as the known proposition does not have probability 1, the same will hold when we add background a priori knowledge to the totality of a subject’s evidence. Stated differently, the argument is this. Since we can prove that for all p and all a priori knowledge (AK), if Pr(p|E ∧ AK) < 1 there is a proposition q that follows from p such that Pr(q|E ∧ AK) < Pr(q), it follows from the current proposal that q must be known without evidence and is not known a priori (if it is known a priori, it should be part of AK and hence the inequality is false rendering false the assumption that Pr(p|E ∧ AK) < 1). Hence it seems we are left with the following choices: Either q-type propositions are known a priori and knowledge is infallible (contrary to our assumption), or they are known a posteriori and ED is false. But disregarding ED while maintaining fallibilism is incoherent as well since, as we have seen probabilistically and non-probabilistically, every proposition supported by a total body of a subject’s evidence that does not entail that proposition has consequences that are not supported by the totality of one’s evidence. And so unless we want to distinguish knowledge not based on evidence of this kind from a priori knowledge, the only option we are left with is that knowledge is infallible and a priori knowledge is much more widespread than we may have imagined. In any event pending any new suggestion of how it may still cohere, the prospects of the suggestion that fallible knowledge can be combined with closure look dim.
Even if we assume that this defense of knowledge-closure can be made to work, it does not support the claim that knowledge can be extended by proper deductive inference, which is a major driving force of the closure intuition Williamson (2000: 117) (if the extension is known, it is known a priori so inference is superfluous).
This example can also be used to show that the order of receiving the evidence should not make an epistemic difference, unless, of course, it is claimed, implausibly, that only you know where your car is and I do not. Moreover, the thought that somehow the background knowledge can be in place since the evidence can first raise the probability of the conditional and then have it go down slightly without destroying one’s knowledge, will not work on this and many similar examples.
Notice that although there is a failure of warrant transmission in the cases we are inspecting (Wright 2000; Davies 2000), warrant transmission failure does not fill the evidential lacuna required for preservation of knowledge closure. In other words, transmission failure cannot answer the challenge posed here to epistemic closure unless it is accompanied by an explanation of how the requisite background knowledge is attained, an explanation, we argue, that is not possible given fallibilist assumptions. If fallibilism is not assumed, then there is no room for transmission failure. We would like to thank an anonymous referee for making us think harder about the relations between these two issues.
It might be thought that since the probability of q cannot be lower than that of p, if p is known q must be known, or at least knowable, as well. But as the case of lotteries shows high probability conditional on the total evidence does not guarantee knowledge. Our argument concerns what one has evidence for, i.e. relative to any state what does one have evidence for given all of one’s evidence, and not on the probability of propositions on one’s total evidence or the degree of rational credence (which is influenced by initial credence assignments). See Sect. 4.2.
For every body of evidence that does not entail the known proposition p, there will be some proposition q entailed by p but not supported by the evidence supporting p as can be proven by taking e* to be the total evidence and q to be ~(~p ∧ e*). See footnote 42.
Some might be tempted to offer a contextualist (or subject sensitive invariantists) reply to the above argument. The basic idea is that inferring from a known proposition sometimes changes standards for knowledge ascriptions resulting in loss of prior knowledge rather than gaining knowledge of what is inferred. Knowledge, then, remains deductively closed. We do not deny that the plausibility of such cases, but they do not seem to cover all instances of apparent closure failure. To properly respond to the argument from Evidence Dependence standard-shifts must be shown to occur with systematic congruence with evidential support relations. The features commonly associated with shifting standards—practical environments, salience, etc.—do not characterize many of the problematic cases we have been looking at. Realizing this, leading proponents of contextualism and subject sensitive invariantism, e.g. Cohen (2002, 2005), have not relied on standard-shifting to handle some of the cases that fall under the ED claim. See Hawthorne (2004) for similar remarks regarding Cohen’s easy knowledge problem.
High probability conditional on one’s total evidence, is influenced decisively by subjective prior probabilities and therefore should not be confused with having evidence in favor of a proposition. Gettier examples, lotteries and skeptical hypotheses demonstrate that high subjective probability is insufficient (on its own) for knowledge. To go from ignorance to knowledge one needs to gain evidence supporting the proposition, regardless of its credence or probability.
Klein (2004). While we find Klein’s arguments problematic, we cannot address them here.
A mundane skeptic is one that does not target entire realms of knowledge in one fell swoop (“there’s no knowledge of the external world”), but rather works piecemeal (“how do you know it’s a zebra if you don’t know it’s not a disguised mule?”). She utilizes the gap of fallibility between knowledge and evidence and points out the implications of the proposed knowledge for which one lacks evidence (the gap guarantees that there are such possibilities). Since her opponent has no evidence for such propositions, he is expected to take back his original knowledge claim. By demonstrating that this maneuver can be used for all fallible knowledge, the mundane skeptic gains the upper hand. Her appeal is to a method rather than a hypothesis (as is common with e.g. the skeptical argument from illusion). See Vogel (1990) for an argument of this type.
It also avoids the Gettier style problems we raise in our (2010) and one of the problems for compatibilism of semantic externalism with first-person access (see Brown 2004: 239–242) and can explain failures of warrant transmission. This is perhaps the place to note that the watch example represents a type of case not covered by the standard account of transmission failure (even those who think warrant for believing an animal is not a disguised mule is a necessary precondition for knowing that it is a zebra, will, we presume, agree that to know that it’s three o’clock one does not need to be already warranted in believing that even if the watch is broken it is showing the right time now). See Wright (2000) and Davies (2000).
For a similar distinction see Engel (1992).
The distinction does not relate to the degree of justification. Few of our beliefs are as justified, probabilistically speaking, as our beliefs in lottery propositions.
This is shown by the following consideration. Suppose S has justification for p. Forming the justified belief that p, S then infers from it that p is true. Surely her inferred belief does not enjoy a greater degree of justification than her original belief. Inference does not itself provide justification; rather it is supposed to be a mechanism of transmitting justification from premises to conclusion. If p implies q, the truth of p guarantees the truth of q, and therefore, presumably, whatever justifies the belief in p is also reason for believing that q is true.
There are various ways of measuring this dimension.
This example is inspired by Kaplan (1996: 45).
There can be contexts in which one emphasizes “why do you know that p?” in which this sentence makes sense, perhaps because p was not supposed to be public information.
Our use of this notion is akin to Parfit’s, despite the obvious difference in context. As Parfit says, agent-relative reasons “are reasons only for the agent…When I call some reason agent-relative, I am not claiming that this reason cannot be a reason for other agents. All that I am claiming is that it may not be” Parfit (1986: 143). The fact that p coheres with my beliefs may be a reason for me to believe it, but might not be a reason for you if your doxastic repertoire is different from mine. It is interesting to note that in the cases we have been discussing whether one’s evidence supports p, and thus provides reason for believing q, depends on one’s belief states. Since the evidence in each case supports both p and not-q (e.g. that I have a hand or that I’m experiencing vat hands), whether it counts as a reason for believing q or not depends on whether one believes that p is true. In general epistemologists neglect the fact that there are those who hold such things as true. Gnostics, for instance, believed that our world is governed by an evil deity while the benevolent God is in exile. Berkeley believed that there are no external material objects. Taking these and other positions more seriously would perhaps facilitate greater appreciation of the kind of justification we are trying to demarcate. While you might be justified in believing that there are material external objects, Berkeley might not have been. But this does not mean you have better evidence then he did.
The same thought, we take it, is behind reliabilism and sensitivity theories of knowledge—it is not enough that one has reason to believe something is true, or that the belief is in itself justified (perhaps it is not even necessary), one must stand in a certain epistemic relation to it.
Notice that Gettier employs closure of justification, not of knowledge. “[F]or any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.” (Gettier 1963).
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Acknowledgments
Versions of this paper were presented at the 2007–2008 NYU/Columbia Graduate Student Philosophy Conference, The 12th Conference of the New Israeli Philosophical Association at the Open University of Israel, and The Istanbul Bogazici University “Knowledge, Evidence and Probability” Conference; at the Philosophy Departments’ colloquia of Bar-Ilan University, The Hebrew University, Ben Gurion University, and The Central European University; and at Stockholm University’s “Logic and Language”, Stanford’s 2008 advanced modal logic “Logic and Rational Agency”, and The University of Arizona’s philosophy seminars. We wish to thank the participants in those forums for very helpful comments, in particular: Per Martin-Löf, Dag Prawitz, Johan Van Benthem and Timothy Williamson. For many discussions, comments, and suggestions, thanks to: Hagit Benbaji, David Enoch, Dan Halliday, Mattias Högsröm, Mikael Janvid, Maria Lasonen-Aarnio, Krista Lawlor, Gilad Liberman, Ofra Magidor, Itamar Pitowsky, Ruth Weintraub, Åsa Wikforss, and Jonathan Yaari. Special thanks to Stewart Cohen, John Hawthorne, Karl Karlander, Avishai Margalit, Jim Pryor, and Peter Pagin for many engaging conversations that significantly influenced our thinking about the issues of this paper.
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Sharon, A., Spectre, L. Evidence and the openness of knowledge. Philos Stud 174, 1001–1037 (2017). https://doi.org/10.1007/s11098-016-0723-2
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DOI: https://doi.org/10.1007/s11098-016-0723-2