Closure and Factivity Benjamin Sparkes December 18, 2016 he paper is comprised of two sections: In section I, I argue that the problem of scepticism can arise independently form the closure of knowledge under known entailment. he section begins with a non-standard approach to deriving a sceptical paradox, via the factivity of knowledge, and builds a case for the problem of scepticism arising from closure before arguing against the general permissibility of this reasoning. In short, I propose the factual claim that I am not a brain-in-a-vat is as problematic as the epistemic claim that I know I am not a brain-ina-vat. his paper does not give a response to sceptical challenges. Indeed, I feel the intuitive pull against both the factual and epistemic claims, though it is not clear that everyone does, and attempt to bolster these intuitions with additional argumentation. However, I assume that one does, at least, feel the pull of the latter intuition. My goal is to highlight the assumptions about knowledge that the sceptic can draw upon to raise sceptical doubts, and observe certain consequences of these assumptions. I conclude this section by showing scepticism in the context of factivity is stronger than scepticism in the context of closure, in the sense that the latter follows from the former, and explore the relationship between factivity and closure. In section II, I argue that the observations developed in section I lead to issues with relevant alternative analyses of knowledge. I begin by developing these in the context of Schafer contrastive analysis of knowledge, before extending the line of argument to relative alternative analyses in general. I conclude this section and the paper by showing how Wright analysis of warrant transmission may be used to identify the issues in sceptical paradoxes as arising from the factivity of knowledge, thereby giving a framework to analyse the issues raised in section I. his paper, therefore, does not seek to give a response to issues raised by scepticism. Our goal, rather, is to show that these issues can be raised independently from the closure of knowledge under known entailment, and further, from what is typically taken to be a fundamental conceptual truth about knowledge—i.e. that it is a factive mental state—an explore certain consequences of this observation. 1 I 1. You can’t teach an old dog new tricks, as the saying goes, and scepticism with regards to knowledge is a very old dog indeed. However, it is important to distinguish the dog from their tricks. he dog here, the sceptic, is a simple question: is that really the case? Where ‘that’ features as an indexical for a prior claim made. he trick is causing one to doubt knowledge they take themselves to have.1 2. Let h be any proposition about the external world you have knowledge of, for example that you have hands. And, let b be any proposition whose negation you know to be inconsistent with h, for example that you are a handless brain-in-a-vat. We will use these stock examples through the paper, though the arguments made can be formulated with any h; b pairing. Now, as h and b are inconsistent it must be the case that :.h ^ b/, and so by classical reasoning2 we have h ! :b, where the conditional ‘!’ captures preservation of truth. Further, we assumed you knew :.h ^ b/, and as we simply reformulated this, it seems you know h ! :b. To this we add that knowledge is factive, and as such K' ! ' for any proposition '. Now, we have two premisses: a) Kh, and b) K.h ! :b/ and the schema of factivity: K' ! '. hese allow us to perform the following derivation, read from top to bottom. Kh Kh ! h K.h ! :b/ K.h ! :b/ ! .h ! :b/ h h ! :b :b Figure 1: .Kh ^ K.h ! :b// ! :b Each line represents an inference from the propositions expressed above the line, to the proposition expressed below. If a proposition follows from an empty line this expresses that the proposition is true simpliciter. hus, we take instances of the factivity schema to be true, independently of any other proposition(s).3 If a proposition occurs without a corresponding inference then this proposition is assumed to be true. We do not intend to give a precise interpretation of this notion of an assumption, above the possibility that the proposition is not true. For example, while I take it to be the case that I know I hands, this may as a matter of fact be false, and thus we treat is as an assumption.4 And, the inferences which do not instantiate the factivity of knowledge 1 he ‘tick’ locution used may suggest that we view scepticism as something of a ruse. his is not the case, and we shall remain neutral on the status of scepticism. One may, if they prefer, read ‘stratagem’ for ‘trick’, or any other term that coveys that scepticism raises issues for one’s everyday reasoning. 2 hat is, :.h ^ b/  .:h _ :b/  .h ! :b/, but there are numerous other ways to derive this. 3 One may argue this follows from factivity being constitutive of the concept of knowledge, however for the purposes of this paper we will simply assume this position. 4 If one does not think it possible that such knowledge could be false, then many of the examples used in this paper will be unconvincing. However, one can surely ind a corresponding empirical proposition that one can conjure corresponding doubt to. For example, one typically holds themselves to know where they parked their bicycle, yet one is oten mistaken in this self-attribution of knowledge. 2 are each applications of modus ponens to the conditional ‘!’. At this point the old dog, the sceptic, may be thought ready to perform his trick, that is, some may balk at the fact we have inferred from a), b), factivity and modus ponens that one is not a brain-in-a-vat. Given that we do not seem in a position to assert that this proposition is true, one of the above or our reasoning must be at fault. However, standard presentations of the sceptics’ trick add a further inference, shown in igure 2. :: : :b K:b Figure 2: .Kh ^ K.h ! :b// ! K:b hat from the above reasoning in igure 1 one knows that they are not a brain-in-a-vat.5 3. Whether there is a signiicant diference between concluding one’s deduction at :b, or continuing to K:b is not clear to me, and I shall argue below that reasoning to the truth of :b is suiciently problematic. Yet, the above additional inference to K:b sides with more standard presentations of the problem of scepticism. For example, Hawke (2016) following Nozick (1981), gives the schema c) .K' ^ K.' ! // ! K , which we term ‘unrestricted closure’.6 his schema, for sure, instantiated with h for ' and :b for would licence the above inference to K:b, given the assumptions made, and independently of factivity. Figure 3 shows how this may be done with the rule of conjunction introduction. Kh K.h ! :b/ Kh ^ K.h ! :b/ .Kh ^ K.h ! :b// ! K:b K:b Figure 3: .Kh ^ K.h ! :b// ! K:b If one inds the inference to :b suiciently problematic, then either a), b), factivity, or modus ponens must be rejected. However, if one balks at the conclusion of K:b but not at that of :b, then one may add c) to the list of steps, one of which must be rejected. Further, if only K:b is held problematic then one is in a position to focus on c), for it is only by applying this that the conclusion is obtained. 5 As Hawke (2016) observes, the correct interpretation of closure may not make reference to the propositional attitude of knowledge, but a weaker notion of ‘knowabilty’—that one has sufficient informational resources to know the proposition under the scope of K in the consequent of the instantiation of the closure schema (2016, 2763). We will continue to speak of knowledge, as this complication would not impact the greater part of our reasoning, and no arguments essentially rely on this reading of closure. 6 Our presentation of the schema difers from Hawke’s, who captures closure by the schema .K'^.' ) // ! K , where ' ) is read as ' (deductively) entails , which is treated as equivalent to the necessity of ' ! . If one prefers this interpretation, nothing in the paper hangs on taking K.' ! / over ' ) , and indeed the reasoning above is consistent with this interpretation. 3 his highlights the importance of distinguishing the sceptic from their trick. For, given the diferent requirements made in the reasoning of igures 1 and 3, it is arguable the case that two diferent tricks are being performed. Yet, the question that leads to the performance of these tricks is the same in both cases. 4. It seems to me that if igure 3 is taken to capture the problematic reasoning then one is in a good position to either reject or restrict the unrestricted closure schema, as modus ponens and conjunction introduction play only a cursory role in this derivation. However, it is important to note that c) can be understood as codifying the above steps and adding that these are suicient for knowledge. hat is, c) simply states that the assumptions and inferences made in igure 1 are suicient for knowledge, as captured by the inference in igure 2. For sure, it allows one to avoid applications of factivity when inferring K:b, and therefore sidesteps the issue of ‘raising’ :b to the status of something known once it has been derived in the above manner. 5. Yet, it is unclear to me that c) must be read as stating only that knowledge is preserved when reasoning with factivity and modus ponens. One may argue that we have antecedent conviction in some kind of closure condition for knowledge under known entailment, and the reasoning in igure a) is an instance of the permissibility of this more general schema. his point is perhaps best illustrated by adding to the assumptions of a) and b) the additional assumption that one does not know :b.7 Modifying igure 2 to accommodate this assumption and the conclusion of (d) :b ^ :K:b can be drawn, with conjunction introduction. Figure 1 .. .. :b :K:b :b ^ :K:b Figure 4: .Kh ^ K.h ! :b/ ^ :K:b/ ! .:b ^ :K:b/ he conclusion draw in igure 4 seems to me highly suspect given the reasoning it draws on. No doubt in schematic form there are many true instances of ' ^ :K:'. However, in our case one has deductively inferred ' from what one knows, and therefore intuitively one knows '. If this is correct, then a close connexion between problems arising from unrestricted closure and from the factivity of knowledge. From the perspective of factivity we see where the desire for a closure condition naturally arises. hat is, in the case of igure 1, the salient problem may be the inability for one, in certain cases, to raise what we know must be the case to the status of knowledge. 6. Given knowledge of a entailment ' ! , DeRose (1995) labels conjunctions of the form K' ^ :K ‘abominable’, and given factivity ' ^ :K clearly follows 7 We treat this as an independent assumption, though it seems to me that factivity may play a signiicant role in supporting this. For, 4 from the given abominable conjunction which may explain one’s intuitive response to certain instances. However, ' ^ :K seems to me abominable. hough, not necessarily independently of its relation to the relevant abominable conjunction, following the reasoning above. he intuition may be phrased in terms of the previous paragraph, that one should raise what must be the case to the status of knowledge. Still, any analysis of knowledge which retains a), b), factivity, and c) will be saddled with abominable conjunctions of the form ' ^:K , and if the only explanation of why these are abominable is the intuitive desire for a closure condition then once the impermissibility of closure is stated the conjunction should be permissible. I think this is a plausible analysis of the unintuitiveness of ' ^ :K . Still, I do not think this is the only analysis of the impermissibility of ' ^ :K . Ater introducing the reasoning shown in igure 1 we immediately moved to satisfy the idea that for the sceptic to perform their trick we need to show the conclusion derived, :b, was incompatible with the intuitive claim that one does not know that :b. his moved us into the territory of closure, and the position we are in now. 7. As remarked, it is not clear to me that there is a signiicant diference between concluding one’s derivation at :b or concluding with K:b. hat is, one may feel that the argument to :b is suicient in and of itself to warrant scepticism—that one can reason from the fact that they know they have hands, to the truth of the negation of any claim incompatible with that fact. And, if this is the case, arguable the abominableness of conjunctions such as ' ^ :K does not derive solely from the conjoining of two claims, but from the former conjunct. If you share this intuition, then all the better for it. I do not need to convince you that closure is required for the sceptic to perform their trick, and we can proceed to investigate the status of our shared intuition, and how it fares with respect to the assumptions and principles used to generate it. If you do not share this intuition then I doubt abstract argumentation can help. Instead, let us consider some concrete cases, as shown in igure 5. I. I know I have a hand II. I have a hand III. I am not a handless brain-in-a-vat I. Perceptual experience of a hand II. here is a hand III. here is an external world (a) Knowledge (b) Perception I. Sue realised the wall was red II. he wall Sue saw was red III. he wall Sue saw wasn’t white lit red I. Sensation of water being cold II. he water is cold III. One is not the victim of priming (c) Realisation (d) Sensation Figure 5: I-II-III Type Arguments he arguments in igure 5 follow Wright (2004) schematic formulation of sceptical arguments (cf. 2004, 9). We will return to Wright’s analyses of these arguments below. 5 For now, I take it these a paradigmatic instances of the sceptic performing their trick. What I wish to highlight at present is that only type-I propositions make explicit reference to one’s epistemic state, whether this be in the form of knowledge, perception, realisation, and so on.8 Prima facie, then, it seems that the move from type-I propositions to type-II propositions in 5a–5d can be read as an application of factivity. One knows, perceives, realises, … a proposition, and therefore infers the truth of that proposition, and proceeds in their reasoning from there. 8. One may object at this point by arguing that factivity is not leading one from a certain attitude to the truth of the proposition within the scope of that attitude, but moving to some other epistemic relation in the type-II and type-III proposition, for example Wright’s notion of warrant. Factivity, then, does not properly enter the picture, and so the problematic conjunction is not explained via the desire for closure, but from the fact that we’ve been implicitly relativising our factual claims to some other epistemic notion. his is kind of an error theory about factive inferences, and to some extent it must be correct. We never do escape our cognition, so to speak. here is no clear sense by which I can separate the claims I make from my own cognition, and therefore even if knowledge is factive it is impossible to verify that I know any given proposition that is independent of my cognition, for it is impossible to ensure by independent means that the given proposition is true. Given this, the prima facie applications of factivity in moving from type-I propositions to type-II propositions in 5a–5d, above, is merely a irst impression. On further inspection we do not move to truths about the external world, for an implicit epistemic operator must be involved. Further, this line of reasoning suggests that our development of scepticism in the context of factivity was mistaken. It is illegitimate to infer from the the knowledge that I have hands, to the truth of my having hands, for in making the latter claim I have not escaped my own cognition. his may be seen to reinforce the appeal to closure, for one does not move to factual claims, but merely suppresses these in further reasoning—there is no strict sense in which I move from claims about my epistemic state to claims about the world. 9. While the above line of thought has not been clearly developed, e.g. I have said nothing about what the implicit epistemic operator is, I have no doubt that the inescapability of our own cognition is correct. Still, the extent to which this undermines applications of factivity is suspect. For, note that in developing the reasoning of igure 1 we did not conclude that :b was true, but only that :b was true given our assumptions of Kh and K.h ! :b/.9 he above line of objection to the role of factivity confuses the inference to the truth of :b with the truth of :b, independent of any assumptions. To draw an analogy con8 Strictly speaking, type-I proposition may not be propositions, but a ‘species of epistemic warrant’ (cf. Wright 2012, 472). Still, as they may also have a propositional representation in our reasoning, we treat them propositionally. 9 Note we assumed each instance of the schema K !  is true, and true independently of our own reasoning, but nothing rests on this assumption. For, questioning this only leads to questioning the factivity of knowledge, which may be done, though we take it as irm datum in this paper. 6 sider proving that 2C2 D 4 from the Peano Axioms. his is a tedious afair but demonstrably can be done. However, in doing so this does not establish that 2 C 2 D 4, unless the Peano Axioms are true, thus this claim is implicitly relativised to the Peano Axioms, but would be true simpliciter, if the Peano Axioms were also true simpliciter. his undercuts the idea that an implicit epistemic operator occurs in type-II and type-III propositions of any robust importance, for the relevance of one’s epistemic state is guaranteed by the premisses one is reasoning from. We do not deny that one’s epistemic state is crucial to inferring :b. Yet, even if one introduced an operator to make this explicit it is unclear that this operator would be equivalent to that of knowledge. For, all this would show is the dependence of one’s reasoning on one actually being in the factive state they take themselves to be in.10 10. It seems to me the above arguments should be suicient to dispel worries about factivity being the key inference applied in igures 5a–5a—the prima facie appeal to factivity can be maintained so long as one keeps in mind that the reasoning involved rests on the status of type-I propositions being true. he sceptic can perform a trick by directly questioning the truth of type-I propositions, and thus we may question our reasoning in such cases as sound, but as it appears to me the prima facie interpretation of igures 5a—5d as involving factivity gives rise to valid arguments. So, given that we took igures 5a—5d to be paradigmatic of the sceptic performing their trick, we seem in a good position to identify the force of the sceptics’ trick as arising from the inference to a factual reading of type-III propositions. 11. Furthermore, a factive analysis of igures 5a—5d afords a uniied approach to identifying what is problematic in the arguments. For note that one who wishes to analyse the arguments in terms of closure must, in addition to explaining why applications of factivity are illegitimate, either (a) propose independent closure conditions for each relevant verb in type-I propositions, or (b) argue that closure only applies to knowledge claims, and postulate that each of the relevant verbs is properly understood as stating a claim about the agent’s knowledge. Option (a) has apparent problems. It is hard to see how closure conditions are to be formulated for each relevant verb, and why these closure conditions should be distinct. For example, it is hard to see how a closure condition for perception is to be properly understood. his may be taken as support for the position in the context of worries about scepticism, but it seems perception is closed in less extravagant cases. For example, if one perceives a well lit room, one also perceive that there must be a source of light for that room, but how does this difer from realising the same thing? Option (b) sufers no such defects, such faces a problem in that what seems to unify these verbs is that they are factive. Indeed, I suggest that the problematic aspect of igures 5a—5d arises for any factive verb. One may argue that every instance of a factive verb can be analysed in terms of knowledge. he principle that for any factive verb V , S V 0 s that  10 A further advantage of this perspective is that factivity seems to play a key role in the exchange of information. For example, if tell who lives next to a sign which reads “TRESPASSERS W”, and you trust my testimony, then this information gained does not need to be relativised by you to my epistemic state—it can straightforwardly enrich your reasoning about the world. hat is, you do not only know that I know where Piglet lives, you also simply know where Piglet lives. 7 only if S knows that  is intuitively plausible, and that this extends to factive attitudes also. However, for cases of admissible closure where the factive verb is present in both the premisses and conclusion, the defender of option (b) must then explain why from the fact that one knows that  on the basis of the fact that they V that , and therefore in conjunction with their knowledge that  entails , is able to claim that they V that . Following the previous example, if one perceives a well lit room the defender will have no problem in asserting that one knows there must be a source of light, yet why this is also perceived is unclear. 12. he issues that arise for options (a) and (b) are not decisive. Still, they incur certain burdens that a reading of igures 5a—5d which identiies the move form type-I to type-II propositions as an application of factivity avoids. For, if the issue is identiied with an application of factivity then any analysis made on this ground will apply to all factive verbs, with the issue in reasoning to type-III propositions arising from the permissibility of one’s reasoning about matters of fact given a factive attitude toward a certain proposition. 13. here remains a certain sense in which closure persists as an issue if the analysis I have been suggesting is adopted, for in reasoning to a type-III proposition one is still ‘closing’ factive attitudes under entailment. his sense of closure is akin to the kind of closure operators found in formal logic. For, given certain rules that allow one to derive conclusions from premisses, e.g. modus ponens, one can close a given set of formulas under applications of these rules. Indeed, this is part of the reasoning in igure 1, where we ‘closed’ the premisses of h and h ! :b via modus ponens to obtain :b. Further, in the case of the problematic inferences such a closure relation is epistemically constrained, for it requires the elements of the premise set to be known. hat is, we derived both h and h ! :b from Kh and K.h ! ˇ/, by applying modus pones and instances of the factivity schema—if, for example, it is also true but not known that h !  for some proposition , then  would not be included in these applications of ‘closure’. However, while functionally this application of closure in on par with the kind of closure detailed above, and it too is epistemically constrained, this closure relation is clearly weaker, for it is not the closure of knowledge, but of factual matters given a proposition one has a factive attitude toward. So, given the functional equivalence one may argue that closure remains the key to the sceptic performing their trick, and what distinguishes the two cases is that in deriving K:b one is applying the principle of .K ^ K. ! // ! K. his is certainly plausible, and I am inclined to agree. Yet this weakens closure beyond reasonable doubt, as closure now amounts to the drawing of conclusions by deductive inference. his observation, then, does little to support the analysis of igures 5a—5d as involving the closure of knowledge. 14. In the previous paragraphs we presented paradigmatic instances of the sceptic performing their trick in type-I-II-III arguments, and argued that the prima facie read8 ing of these arguments as involving applications to the factivity of knowledge should be understood as correct, and provided additional lines of argumentation to support this reading. On the basis of this, then, for the sceptic to perform their trick one does not need to assume that knowledge is closed under known entailment, but relies only on the principle of factivity and one’s deductive reasoning. his ofers considerable support for our earlier claim that an inference to :b on the basis of Kh ^ K.h ! :b/ is itself problematic, and the intuitive pull against conjunctions such as :b ^ :K:b should not be analysed in terms of the failure of deriving :b to amount to knowledge of :b, but in terms of the conjunct :b itself. Further, if it is problematic to infer :b then closure under known entailment must be restricted, given the factivity of knowledge, for it it is permissible for one to infer K:b, then by factivity :b follows. his is demonstrated in igure 6b. Kh blank Kh ! h K.h ! :b/ K.h ! :b/ ! .h ! :b/ h h ! :b :b (a) :b via factivity Kh K.h ! :b/ Kh ^ K.h ! :b/ .Kh ^ K.h ! :b// ! K:b K:b :b K:b ! :b (b) :b via closure and factivity Figure 6: Inferring :b In this sense, rejection of the reasoning in igures 5a—5d entails the impermissibility of unrestricted closure under known entailment. Still, a diferent perspective is ofered on the failure of unrestricted closure. For, if sceptics’ trick depends on impermissible reasoning via factivity and reasoning with factual information (as opposed to information under the scope of an epistemic operator), then it seems natural to postulate that knowledge is closed under permissible applications of such reasoning. his reinforces our understanding of the intuition noted above that the reasoning exhibited in igure 1 is suicient for knowledge, and therefore that conjunction such as :b ^ :K:b are problematic for the former conjunct should have the status of knowledge given the permissibility of the process by which it was inferred. What difers here is the way in which this intuition kicks in. For, in the context of closure we require the independent assumption that :K:b in order for the conjunction of :b ^ :K:b to be problematic once :b is established. However, in the context of factivity, independent conviction of :K:b is not required, for K:b should intuitively follow from the permissibility of establishing :b, and therefore observing :b ^ :K:b only highlights that something in one’s factual reasoning was impermissible, for it failed to extend ones knowledge. 9 15. his is a signiicant upshot of identifying the force of the sceptics’ trick as arising from a combination of factivity and factual reasoning, as it allows one to preserve the idea that knowledge extends under entailment, so long as the factual counterpart to this entailment holds. To illustrate, consider Descartes demonstration that he exists. I. I realise I am thinking II. I am thinking III. I exist Given that the premise of this argument is unavoidable true, it seems one is in a position to infer the conclusion that they exist, and moreover that they know that they exist. Note, however, that this does not secure the permissibility of the closure of knowledge under known entailment, as further argumentation may show issues with closure that arise independently of one’s factual reasoning. Yet in absence of such issues being present, the above line of argument suggests that the intuition which motivate a natural form of closure under known entailment can be held, by showing that this intuition is a consequence of what is established via permissible instances of factual reasoning from known premises—one does not need appeal to the permissibility of certain instances of the closure schema, and then factivity to be sure that one, as a matter of fact, exists. II 16. We have argued for three key claims. First, that the sceptics can—and should in certain cases—be understood as relying on a fault in our factual reasoning from premises we take ourselves to know. Second, that this analysis is distinct from analyses which understand scepticism as relying on the closure of knowledge under known entailment. And, third, that understanding the scepticism as relying on a fault in our factual reasoning from premises we take ourselves to know may allow for one to preserve certain intuitions behind the closure of knowledge under known entailment. We have not argued for an analysis of the problematic aspects of our factual reasoning from known premises, nor have we shown how this perspective relates to extant analyses of the sceptics’ trick. In this section we highlight how this perspective on the sceptics’ trick causes issues for certain analyses of it. We begin by focusing of Schafer’s contrastive analysis of knowledge, before generalising the issues raised to relevant alternative analyses of knowledge in general. We then apply the framework Wright uses to analyse warrant transmission to highlights the problematic aspects of factual reasoning from premises taken to be known. 17. Before continuing let us crystallise the issue the above claims lead to. In certain cases one is impermissible for one to infer from a known proposition  and a known entailment  ! , that is the case, and as a consequence of this one does not know that is the case. For example, I know I have hands, and I know that having hands entails that I am not a handless brain-in-a-vat, yet it is impermissible for me to reason from these two 10 premisses that I am not a handless brain-in-a-vat. And, as a consequence of this I do not know that I am not a handless brain-in-a-vat. Further, one only needs to appeal to the factivity of knowledge and modus ponens to derive from K and K. ! / to the conclusion that , and not the closure of knowledge under known entailment—.K ^ K. ! // ! K . 18. his issue leads to clear problems for certain analyses of knowledge which deny closure but retain factivity and modus pones. Consider the contrastive analysis of knowledge as proposed by Schafer. Roughly put, knowledge is analysed a ternary relation between a subject, and known proposition, and a contrast proposition. For example, one may know that one has hands rather than stumps, but one may not know that one has hands rather than than the stimulated appearance of hands while being a handless brain-in-a-vat Schafer (cf. 2004, 80). Schafer holds that the contrast proposition is given by standard mechanism for saturating argument places, which may include the ‘the alternatives under inquiry’ or be ‘pragmatically constructed’ (2004, 80). he speciics of saturation need not concern us. For ease of illustrate let us assume that one knows that if they have hands then they are not a brain-in-a-vat rather than any other proposition, given that the failure of the entailment is a contradiction, and that one does not know that they are not a handless brain-in-a-vat rather than that they have stumps. Unrestricted closure under known entailment fails on such a contrastive account, for when closing one’s knowledge under the known entailment is not preserved under contrastive statements. hus, one knows they have hands in contrast to having stumps, and knows that if they have hands then they are not a brain-in-a-vat, in contrast to having stumps. But it does not follow that one knows that they are not a brain-in-a-vat in contrast to having stumps.11 hus, the contrastivist is able to explain why one is able to know that they have hands, but fail to know that they are not a handless brain-in-a-vat.Yet, if one also holds that contrastive knowledge is factive—Schafer explicitly endorses the factivity of knowledge such that the factual instance of the known proposition does not require contrast (cf. 2007, 224)—the contrastivist is unable to explain the impermissibility of the reasoning expressed in igure 1. Hence it seems the contrastivist, without further argumentation, is committed to the conjunction of statements of the form ‘I am not a brain-in-a-vat but I do not know that I am not a brain-in-a-vat rather than a brain-in-a-vat.’ Schematically :b ^ :K:bjs, where ‘j’ expresses contrast, as s is the proposition that the agent has stumps. Indeed, Schafer (2007) highlights that contrastivism avoid abominable conjunctions of the form Kh ^ :K:b, for ‘there is no single value of q that can vindicate: “s does not know that she is not a brain-in-a-vat [rather than q], but s does not that she has hands [rather than q]”’ (2007, 246–247). But given that this relies on the contrastive nature of knowledge, the reasoning does not extend to a factual instance of the former conjunct. hus, even if constrastivism is correct, and gives a reasonable response to the 11 One may also argue that the proposition that one is not a brain-in-a-vat causes a contrastive shit, for example such that the saturated contrast is that they are a handless brain-in-a-vat, or that they are sufering massive sensory deception (cf. Hawke 2016, 2768). 11 sceptics’ trick in the context of closure, this strategy does not extend to the sceptics’ trick in the context of factivity. herefore, it seems a contrastive account of knowledge can at best be seen as a partial account of the problematic reasoning the sceptics’ trick highlights. 19. While the above took contrastivism as its focus, I see no reason to think that analogous reasoning given a relevant alternative semantics for knowledge. Roughly put, such an analysis holds an agent knows a proposition by virtue of ruling out certain alternatives, and holds that in many cases an agent is not required to rule out propositions such as :b. his voids the general validity closure of knowledge under known entailment, for the proposition that occurs in the consequent of a closure schema may introduce relevant alternatives that would undermine one’s knowledge of propositions in the antecedent of the schema.12 Still, given the factivity of knowledge, it is unclear to what extent a defender of this approach can resist the reasoning exhibited in igure 1, and block reasoning to :b, which we have argued to be suicient for the sceptic to perform their trick, given a situation in which the relevant alternatives allow one knowledge of h and of .h ! :b/. 20. However, the defender of a relevant alternatives analysis of knowledge has a potential response. For, we observed in paragraph 9. that the factivity of knowledge does not guarantee that one knows a proposition that they take themselves to know. It states only that if one does in fact know a proposition then that proposition is true. herefore, the defender of a relevant alternatives analysis of knowledge may argue that the derivation of :b causes a shit in the alternatives the agent is required to rule out to know h and .h ! :b/. In this sense the the conclusion of the reasoning in igure 1 undermines the truth of the premisses, which in turn invalidates the support the one has for :b.13 his strategy rejects unrestricted closure, but only indirectly, for it is the inference to a factual proposition that causes a shit in the alternative that one’s prior knowledge claim are required to rule out—the problem in one’s reasoning is retaining knowledge established by ruling out certain alternatives when further alternatives are introduced. Yet it seems to me that while this position is coherent, it is inherently unstable. For, given that the entailment of .h ! :b/ is guaranteed by logical impossibility of .h ^ b/, this is available to an agent with respect to any class of alternatives. herefore, if an agent takes themselves to know h, then by the factivity of knowledge they will necessarily be in a position to derive :b, thereby inducing a shit in the alternatives ruled out in establishing that they know h, which will undermine their knowledge of h, by factual reasoning. And, if a shit in alternatives is not induced, the agent will be in a position to establish :b regardless of whether they know it, which we have argued to be a problematic consequence in and of itself.14 12 See Hawke (2016, §3) for a detailed overview of relevant alternative analyses. he brief sketch given above omits many details which are not pertinent to the given argument. 13 he dynamics of information change in the above reasoning are complex, for example, assertions of ' and you don’t know that ' are puzzling, but can be analysed in a coherent way. For example, via dynamic epistemic logic with public announcements. See Pacuit (2013, 818–819) for an illustration. 14 An alternative option is to revise our understanding of factivity, or our factual reasoning. 12 21. From the above, it seems that for a defender of a relevant alternative analysis of knowledge one either has a sureire way to undermine any factual proposition they take themselves to know by applying the factivity of knowledge to derive a factual proposition that induces a shit in the alternatives ruled out to establish the knowledge they took themselves to have, or are committed to the permissibility of reasoning to intuitively problematic conclusions.15 hese observations are obscured by focus on closure and the intuition that one does not know propositions such as :b—the factivity of knowledge and factual reasoning are suicient for problematic aspects of our reasoning to arise form knowledge of propositions such as h. Still, this is not a mark against relevant alternative analyses of knowledge per se, as these may be supported by argumentation independent from the problems of scepticism. What we have shown is that these analyses face sceptical issues, even if they show how instances of Kh ^ :K:b are permissible. his concludes our argument for why the perspective on the sceptics’ trick that takes factivity and factual reasoning as prime causes issues for certain analyses of knowledge. We now turn to illustrating how an alternative analysis of knowledge can illustrate why the reasoning shown in igure 1 is problematic. 22. Wright (2004, 2007, 2012, 2013) analyses the problematic reasoning exhibited in the I-II-III type arguments of igure 5 as a failure of warrant transmission. Generally speaking, type-I propositions provide epistemic warrant for type-II propositions, one’s knowledge, perception, sensation, and so on, of the content of a particular proposition, such as that one has hands, a wall is red, or that the water is cold. his notion of warrant may be considered theoretic parlance, as Wright (2004) puts it, the general issue is ‘under what circumstances a valid argument is indeed at the service of proof—i.e. the generation of a rational conviction of—or the rational overcoming of For example, Yablo (2015) analyses knowledge in terms of subject matter, and holds ‘I know that p if (1) p is how matters stand be wrt (contextually indicated subject matter) m (2) p is how I think matters stand wrt m (3) I would have noticed had things been diferent wrt m (4) some sort of positive ground for my belief that p.’ (2015, 11–12). Condition (2) of Yablo’s analysis is an analogue of factivity, and therefore knowing p does not entail that p is true simpliciter on Yablo’s analysis. his difers from our understanding of factivity, and may be considered a rejection of it. However, for Yablo subject matter is ‘contextually variable to the extent that our sense of the factors controlling p’s truth–value is inluenced by how we conceptualize p’ (2015, 15). hus, if to conceptualise p an antecedent subject matter is required, Yablo’s formulation of factivity is arguably not distinct from the one given in the body of this paper, but merely highlights the role of an antecedent subject matter one is committed to in reasoning about factual matters. herefore, Yablo may argue that to derive :b from Kh and K.h ! :b/ one may reject the subject matter implicit in this derivation, and consequently one’s conceptualisation of h or :b. A full discussion of this analysis is beyond the scope of this paper, though it seems quite unintuitive to think that my conceptualisation of h changes to allow the derivation of :b in certain cases and not others, as .h ! :b/ was derived by taking an arbitrary proposition b inconsistent with h. Note Yablo does not give a response to how this analysis resolves sceptical problems, and is concerned with the closure of knowledge under known entailment (cf. 2015, 15). 15 One may further argue that if the latter option is taken, then given that one has establish a proposition such as :b is true, then this allows one to ‘bootstrap’ the truth of this proposition to knowledge, for any alternative incompatible with :b must be false. However, it is not clear to me that this argument will hold for all implementations, and so given the above cursory sketch of relevant alternative analysis we shall not push this line of argumentation. 13 doubt about—the truth of its conclusion’ (2004, 229). What is at issue is the failure for the relevant warrant for type-II proposition to transmit to type-III propositions. Wright’s analysis is that ‘a particular warrant for its premises transmits across an entailment only when one’s path to that warrant does not require picking up knowledge of the conclusion en route’ (2004, 229).16 his analysis is expanded in Wright (2012) with the notion of a cognitive project. his is a pair h; i, where  is a question and  is a procedure one might use in order to resolve . And deines an authenticity condition relative to a project as; ‘any condition doubt about which would rationally require doubt about the eicacy of the proposed method of executing the project, or about the signiicance of its result, irrespective of what that result might be’ (2012, 466—467).17 Authenticity conditions can typically be taken for granted in the execution of a cognitive project. However, at the core of Wright’s analysis is that ‘you cannot rationally transmit a claim to warrant for certain premises across an entailment to anything that is an authenticity-condition for (any among) the very cognitive project(s) which purportedly generate(s) that claim to warrant’ (emphasis Wright’s, 2012, 467–468). Plausibly, then, in the I-II-III type arguments of igure 5 each type III proposition is a required authenticity condition for establishing the relevant type II proposition on the basis of the type I propositions. For example, in argument 5d, if it were the case that one had been primed to feel lukewarm water as cold, one would not be in a position to infer that the water is cold from one’s sensation that the water is cold. herefore, that one has not been primed is an authenticity-condition for establishing that the water is cold on the basis of one’s sensations. As such, the warrant claimed by this experience for the type-II proposition does not transfer to the type-III proposition. Wright argues for a conservative approach to authenticity conditions, requiring that one must have warrant that authenticity conditions obtain. So, as each of the arguments in igure 5 appear to be in the service of transferring the warrant obtained for the typeII proposition by the type-I proposition to the type-III proposition, these arguments exhibit problematic reasoning, for warrant cannot be transmitted in this manner. In contrast, a liberal approach to authenticity (for example Pryor (2004, 2012)) conditions does not require one to have warrant for certain authenticity conditions—it is suicient that one has no reason to doubt it obtains (cf. Wright 2012, 472). I lag the opposing positions to highlight that the analysis of type I-II-III arguments in terms of warrant transmission does not commit one to a decisive reading of the arguments. hat is, one is not, on this analysis committed to analysing any instance of these arguments as problematic. See, for examples, Pryor’s defence of liberalism (2004; 2012). Our interest is only in Wright’s analysis of these arguments as relying on authenticity conditions. 16 Consider, for example, Descartes’ argument as presented in paragraph 15. 17 Examples of authenticity conditions are ‘normal and proper functioning of relevant cognitive faculties, the reliability of instruments utilized, the amenability of the circumstances to the proposed method of investigation, the correctness of relevant theory, the soundness of relevant principles of inference utilized in developing and collating one’s results, the good standing of relevant concepts used in any aspect of the enquiry, and so on’ (2012, 467) 14 23. For, the notion of an authenticity condition may be understand as highlighting the factivity of the relevant state in type-I propositions. Indeed, if, as we argued above, moving from type-I propositions to type-II propositions is merely an application of factivity, then it follows from this observation taken together with Wright’s analysis that a relevant authenticity condition must be met in order to appeal to the factivity of the relevant state in the type-I proposition. herefore, as each type-III proposition would void the factivity of the relevant state used to infer the truth of the type-II proposition, the authenticity condition for the warrant one has for the type-II proposition entails the truth of the type-III proposition. his reasoning is reminiscent of that found in paragraph 20. where we noted that one only reasons to :b by taking oneself to know h and .h ! :b/. However, it adds to this that :b independently follows from one’s taking themselves to know h. In this sense :b is not establish on the basis of one’s knowledge that h (and (h ! :b)), but establishes the basis for one’s knowledge that h, though it may not do so in such transparent terms. hat is, Wright analysis of warrant transmission allows us to identify the issues that arise from I-II-III type arguments as arising from the factivity of knowledge, perception, sensation, and so on. 24. Wright does not address how warrant transmission relates to the factivity of knowledge.18 herefore, the above is an application of Wright’s framework, and not an explanation of Wright view. Still, it seems to me a natural application, and one that is implicit in much of Wright’s work on the topic. Further, one inds no fault in one’s factual reasoning, such as that exhibited in igure 1, and the move from type-II to type-III propositions, for the issue is conined to the assumptions made in order to perform the reasoning. And, the factivity of knowledge and the relevant states in type-I propositions may be taken to explain why analogous issues do not arise for non-factive states, such as belief, and seeming. 25. his does not speak to an account of the sceptics’ ticks—the above only highlights the role of factivity. Nor does it speak to the dispute between Wright and Pryor over whether one should be a conservative or a liberal with respect to certain authenticity conditions. If one takes a conservative approach to authenticity conditions, then the reasoning exhibited in the arguments of igure 5 are problematic, for the warrant given to the typeII proposition by the factivity of the attitude in type-I propositions does not transmit to type-III propositions, and thus explain why the reasoning exhibited in igure 1 and igure 5 is problematic. While, if a liberal approach to authenticity conditions is taken, one is in a clear position to argue, by the factivity of the relevant states, that one achieves certain warrant for the type-III propositions. he approach taken need not be uniform across all factive attitudes, as point Wright highlights with respect to authenticity conditions in general (cf. 2012, 473). he conclusion I wish to draw from Wright analysis is that the framework of warrant transmission 18 hough he does distance warrant transmission from the closure of knowledge under known entailment (cf. Wright 2012, 451,455) 15 ofers useful way to isolate the issue of factivity in the role of reasoning, and in light of the sceptic. And, further, that by identifying factivity as a core component of certain issues that arise in cases of warrant transmission that additional light may be shed on the status of certain authenticity conditions. For example, let us suppose the two of us are at a party, and you have a glass of water, with your arms crossed, the glass partly concealed by your hand, resting on your opposing upper arm. I, somewhat tipsy, assume you’ve moved onto the hard stuf, and have poured yourself a glass of gin. ‘Ah! Pour me a glass of the good stuf ’, I remark. You, taking advantage of my slightly inebriated state and decide to tease me a little. Yet, there is a clear diference between you asking ‘are you sure it’s not water?’ and ‘are you sure you’re not drunk?’ he former question raises doubts about what I perceive, but not that my perception is factive, ater all, a glass of water and a glass of gin look the same. he latter question, by contrast, seems to imply that I am suiciently inebriated such that I should not be sure you are in fact drinking anything at all, ater all, you may only have your arms crossed. Being only somewhat tipsy the latter interrogative would not doubt fall lat, but no doubt if I were intoxicated you could cause consternation about how much I’ve had to drink, and whether I can continue to be warranted in what I take myself to see. Outside of sceptical concerns the factive status of certain attitudes seems diicult to shake one’s conidence in. To conclude, I have argued that sceptical issues arise independently from the closure of knowledge under known entailment, and can be obtained solely form the factivity of knowledge, in conjunction with factual reasoning—reasoning that does not occur inside the scope of an epistemic operator. I then argued that this raised issues for analyses of knowledge via the ruling out of relevant alternatives which held to the factivity of knowledge. Finally, I argued that Wright’s framework of account of authenticity conditions allows one a clear perspective of the problems that may arise when reasoning from the factivity of knowledge, and thus a theoretical position from which these issues can be investigated. 16 References DeRose, Keith (1995). “Solving the Skeptical Problem”. In: Philosophical Review 104.1, pp. 1–52. Hawke, Peter (2016). “Questions, Topics and Restricted Closure”. In: Philosophical Studies 173.10, pp. 2759–2784. Nozick, Robert (1981). Philosophical Explanations. Harvard University Press. Pacuit, Eric (2013). “Dynamic Epistemic Logic II: Logics of Information Change”. In: Philosophy Compass 8.9, pp. 815–833. Pryor, James (2004). “What’s Wrong with Moore’s Argument?” In: Philosophical Issues 14.1, pp. 349–378. — (2012). “When Warrant Transmits”. In: Mind, Meaning, and Knowledge: hemes From the Philosophy of Crispin Wright. Ed. by Annalisa Coliva. Oxford University Press. 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