So far it seems none of the anti-sceptical arguments we have sketched have been able to answer the sceptic properly. We are left with an intuitive problem that casts doubt on all of our knowledge at once. We have seen arguments, such as Moore's and Austin's, which seem to provide us with other intuitive possibilities, but sceptical arguments remain. Rather than try to provide alternatives to sceptical positions, or try to show the sceptic to be wrong by coming up with a definitive refutation, it would seem wise to examine the intuitive nature of the sceptical argument, and see if we can find some leeway there.


As we have seen, Quine, Nozick, Dretske, Austin and Moore have failed to answer the sceptic. Scepticism remains as a powerful argument against the possibility of knowledge and is difficult, if not impossible, to approach due to its simple, intuitive form; anti-sceptical responses seem artificial, pretentious and difficult to come to terms with compared to scepticism's elegance. In this way, scepticism's lack of theoretical presupposition gives it resilience to criticism. It arises from everyday notions of knowledge; our options in responding to it then are to either deny principles of knowledge that we all find perfectly reasonable, or to put forward contentious theoretical ideas that fail to convince. We cannot contradict the sceptic, because in doing so we are contradicting our own intuitions. Nozick and Dretske seem to do just this; by denying closure they hope to do away with scepticism, but in doing so they would also do away with a principle of knowledge that seems perfectly reasonable. By attacking scepticism, Nozick and Dretske inadvertently attack our intuitions about knowledge. We also cannot respond to the sceptic with novel theories of knowledge, because in order to avoid scepticism novel theories must avoid the intuitive ideas of knowledge that scepticism makes use of, giving them unintuitive consequences. Quine seems to do just this; his naturalized epistemology is a radical shift from what our normal ideas of knowledge are, and as such it misses the epistemological point altogether. In an attempt to avoid scepticism it diverges so radically from our intuitive ideas of knowledge that it ceases to be relevant. Next to the intuitive considerations that lead to scepticism, Quine's naturalized epistemology is a very hard sell.

We seem to be in a dilemma; any response we give to scepticism, in an attempt to rid ourselves of the paradox of our concepts of knowledge robbing us of knowledge, seems to result in its own paradox. We are left with criticisms of scepticism that dispose of intuitive principles of knowledge, such as that of closure, or theories that are unpalatable next to scepticism, such as naturalized epistemology. In short, it seems every response to scepticism hits us just as hard as scepticism; in responding to the sceptic we must make concessions to her that are unpalatable. If scepticism is based on everyday ideas of knowledge that run deep in our intuitions, then in criticizing scepticism we are arguing with ourselves, so to speak. If scepticism is based on ordinary ways of thinking, and anti-sceptical arguments must criticize ordinary ways of thinking or propose theories that diverge from intuitive ways of thinking, then it seems that criticizing scepticism is ultimately just another way of agreeing with the sceptic (Williams, Unnatural Doubts 19). In making epistemological theories to replace scepticism, or in denying the intuitive principles used by scepticism, we deny that our own ideas of knowledge are legitimate.

Williams calls this the epistemologist's dilemma. The intuitive nature of scepticism means that responding to the sceptic damages our knowledge in some way, and amounts to no more than a concession to the sceptic. As Williams puts it:

... we can either accept scepticism, or make changes to our pre-theoretical thinking about knowledge that shrink the domain, or alter the status, of what we previously thought of as knowledge of objective fact. In making such changes, however, we inevitably appear to be making very large concessions to the sceptic. (Williams, Unnatural Doubts 22)

The intuitive basis of scepticism leaves us with few options.

The only anti-sceptical option that remains is to try to show the sceptic's position to be incoherent. Williams calls this approach definitive refutation (Williams, Unnatural Doubts 32). But as we have seen, definitive refutations are difficult to accept; if the sceptic is incoherent, then it is difficult to explain how we can make sense of him so easily. This is especially so if we take the sceptic's position to be intuitive; how are we to make sense of an argument that is meant to show that an intuitive argument is nonsense? To do so it seems we would have to show our own intuitions to be incoherent; scepticism merely takes ideas and principles that we make use of everyday when making knowledge claims, and from those principles it determines that we have no knowledge. We cannot deflate the sceptic's position, because in doing so we must presumably deflate the very everyday knowledge we wish to uphold.

Further, this assumes we can even deploy such arguments. It is difficult to see how we are to show that an intuitive argument is incoherent. Are we to use intuitive ideas to show that the intuitive sceptical argument is incoherent, or some other theoretical ideas? Using our intuitions to perform a reductio ad absurdum on themselves in order to show that scepticism is incoherent seems like simply another form of scepticism. And it is hard to say how a theory could show our intuitions to be incoherent; the theory, which defies our intuitions, would seem like nonsense if it clashed with intuitions. In short, we cannot seem to make sense of an argument that would show scepticism, which is intuitive, to be incoherent; we do understand the sceptic just fine. As such, most definitive refutations must end up doing something other than show the sceptic to be incoherent, and the only possibility seems to lead to an epistemologist's dilemma.

Austin's anti-sceptical arguments seem to fall into this trouble. He intends to show that the sceptic cannot mean what he says he means, by showing the way our normal language is really used. But, given the intuitive nature of scepticism, it is seemingly impossible to understand how such a thing is possible. As such, Austin's attempt to show the sceptic to be incoherent turns into a sort of tacit agreement with the sceptic; the sceptic ends up meeting the two principles that Austin puts forward, meaning the sceptic's argument is coherent and effective. Austin cannot make the argument he wishes to make, and as a result ends up falling into one of the two possibilities mentioned earlier that make up the epistemologist's dilemma.

The only anti-sceptical argument that does not seem to fall into the epistemologist's dilemma or attempt a definitive refutation is Moore's. Moore seems to simply butt heads with the sceptic by employing other intuitive arguments and facts, with the sceptic ultimately winning. But why does the sceptic win? Moore straightforwardly answers the sceptic's conclusions with his own intuitive conclusions, but fails. Why does the argument work in the sceptic's direction, from intuitive ideas to lack of knowledge, but not in Moore's direction, from intuitive pieces of knowledge to the disproof of scepticism? It seems we must investigate the intuitive nature of scepticism if we are to get any answers.


Williams' answer to scepticism is different from the strategies we surveyed in the last chapter. He sees a general inability to succeed in every response to scepticism. This is because in responding to the sceptic, anti-sceptics fall into the epistemologist's dilemma. As such, Williams does not want to try to stubbornly answer the sceptic directly as Moore does, or try to show that the sceptic is unable to mean what he says as Austin does, or attempt a radical transformation of our epistemological practices as Quine, Nozick and Dretske do. Instead he wants to turn away from answering the sceptic and try to show the sceptic's arguments to be theoretically contentious; he wants to attack the sceptic's seemingly strongest asset, rather than answer scepticism on the sceptic's terms.

As we have seen, the strength of the sceptic's position is that her arguments are taken to be intuitive; that is, they supposedly follow from concepts of knowledge that we all find plausible. Any theoretical response to scepticism, such as Quine's, Nozick's or Dretske's, will seem unpalatable compared to the intuitive arguments of the sceptic; the sceptic will win on intuitive plausibility, no matter how well thought out the anti-sceptic's response is. Further, deflationist views, such as those similar to Austin's anti-scepticism, will be difficult to accept given scepticism's intuitive nature; it is not easy to see how the sceptic can fail to mean anything when we so intuitively understand her arguments. The sceptic's seemingly intuitive arguments afford considerable strength and resilience to the sceptical position, making it look intractable.

This is where Williams wants to dig in: by questioning the intuitive nature of the sceptical argument that puts scepticism beyond the reach of almost all criticism. As he puts it, he wants to shift the burden of theory onto the sceptic (Williams, Unnatural Doubts 31). Rather than try to respond to the sceptic on her own grounds, Williams wants to question the sceptic's grounds and show them to be theoretically loaded, as opposed to intuitively motivated; if we can show scepticism to be just as theoretically committed as many other epistemological positions, we take away a great deal of its strength, and bring it down to the same level as many other epistemological positions. If we can show that sceptical doubts are not as natural as they seem, then we can show that scepticism is not forced on us by everyday ways of thinking about knowledge, and that some anti-sceptical responses are not implausible simply due to their less intuitive nature; some plausible, anti-sceptical epistemological positions will be at worst equally theoretically loaded as scepticism.

Williams dubs this particular approach to anti-scepticism theoretical diagnosis; the purpose of theoretical diagnosis is to show that scepticism does have theoretical commitments (Williams, Unnatural Doubts 32). This is contrasted with what Williams calls therapeutic diagnosis; therapeutic diagnosis takes for granted, whether knowingly or not, that sceptical arguments are intuitive, and then attempts a theoretical response. According to proponents of a therapeutic approach, the intuitive nature of scepticism means we have only a few options: remain pessimistic about the inevitability of scepticism, attempt a radical conceptual shift in our epistemic standards, or show the sceptic to be unable to mean anything through definitive refutation. Pessimism is obviously unpalatable for many, and radical conceptual change leads to a tacit concession to the sceptic, so a therapeutic approach is most promising given scepticism's intuitiveness. Accordingly, the best approach is to try to dissolve scepticism by showing it to be incoherent. But as we have seen this is a difficult, if not impossible, task, given that the proponent of a therapeutic diagnosis has accepted that scepticism is intuitive; any attempt at showing scepticism to be incoherent seems doomed to failure, because if scepticism is intuitive, then we do seem to understand it in some way or another.

Therapeutic responses fail, according to Williams, when they take for granted the intuitive nature of scepticism, making the sceptical position seemingly unapproachable. But it is at least possible that we can take a step further back in the sceptic's argument and question the very intuitive nature that presents us with problems (Williams, Unnatural Doubts 35). For example, it may be the case that the sceptic gets our everyday ideas of knowledge wrong. We have everyday, intuitive ideas of what constitutes knowledge, but they are not always obvious; any attempt to spell out our everyday ideas of knowledge can be contested, in an Agrippan manner. If someone says, "The everyday, intuitive notion of knowledge is X," we may ask, "How do you know that? Are you assuming it, or is your support for it novel evidence or circular presuppositions?" If the sceptic must have a contentious theory of what our everyday ideas are, then the sceptical position will be shown to have theoretical commitments, and we may contest those commitments with other, equally plausible, but anti-sceptical, theories.

Further, sceptical conclusions, as we have seen in Moore's arguments, seem absurd; no reasonable person believes that we do not know where we are or if we are human or brains in vats, and so on. In everyday circumstances we take it as obvious that we know we are humans, and that we are on the planet Earth, and so on. Yet the conclusions of sceptical arguments contradict these obvious knowledge claims; scepticism's intuitive arguments lead to deeply unintuitive conclusions. So, if sceptical arguments are in fact intuitive, it seems the sceptic may need a theory to explain why intuitive arguments lead to these unintuitive conclusions. Further, the unintuitive nature of the sceptic's conclusions seems not to spill over into everyday life, where we do not ever take them to be as serious as their intuitive arguments imply we ought to; scepticism is supposedly derived from everyday concepts of knowledge, yet they do not affect our everyday knowledge claims. The sceptic may need a theoretical explanation of why common attributions of knowledge, such as those Moore presented, seem immune to sceptical doubts in everyday situations; as Williams says, the sceptic must have a theory to show why scepticism is only persuasive in detached, objective, philosophical contexts, and not everyday contexts (Williams, Unnatural Doubts 35). In short, the sceptic must explain the context-sensitivity of his arguments.

The sceptic's position seems unstable in everyday contexts; we take Moorean propositions to be perfectly reasonable, and almost ridiculous in their obviousness. Of course we know that we are on the planet Earth right now; it is so obvious that stating it seems out of place. Yet the sceptic must hold that his discovery that we have no knowledge affects all our knowledge in general. This is another way in which the sceptic may hold theoretical commitments: if the sceptic must have a theory about how scepticism can affect our knowledge in everyday contexts, then our everyday knowledge is insulated from the intuitive nature of scepticism. As Williams explains:

Although we cannot simply assert the commonsense outlook against the results of philosophical reflection, the fact that our ordinary epistemic attitudes are at variance with the sceptic's conclusions is prima facie evidence that the sceptic's principles do not reflect our ordinary way of thinking about knowledge. (Williams, Unnatural Doubts 82)

Scepticism may be an intuitive argument, but only in philosophical contexts; if the sceptic is to show that everyday knowledge is affected by scepticism, she must take on theoretical commitments, in which case scepticism is as vulnerable as any epistemological theory to criticism, and other epistemological theories may be just as plausible in comparison.

So, it is not implausible to think that the sceptic does have some sort of theoretical commitments, and that the sceptical position is not as invulnerable to criticism as it seems. It is possible that the sceptic has an implicit theory of the way in which philosophical reflection and everyday knowledge are related, so that all knowledge can be cast into doubt by scepticism. If this is the case, then the sceptic has a difficult task ahead of himself: he must acknowledge the contextual sensitivity of sceptical doubts, while still being able to show that scepticism is generally threatening and genuinely conflicted with Moorean propositions. This will be a task that will most likely take some theoretical work, but it will also take some work to show that the sceptic is in fact in this position of theoretical commitment.

In this way, Williams takes theoretical diagnosis to be incompatible with any therapeutic diagnosis. In order to show that the sceptic has tacit theoretical commitments, we must make full sense of the sceptical position, excluding any possibility of showing the sceptic to be incoherent. We must understand what the sceptic means to begin a theoretical diagnosis.

Williams takes the theoretical diagnosis approach to be most promising (Williams, Unnatural Doubts 35). We must put scepticism into a theoretical context, in the ways mentioned above, by showing that it is committed to a connection with some sort of theoretical epistemological project, and not just supported by intuitive notions of knowledge that we all take to be obvious. This epistemological project must have certain concepts of knowledge that make scepticism seem plausible, convincing and inevitable. But once we show that these epistemological concepts are part of the theoretical commitments of a specific epistemological project, and not of intuitive ideas we all hold about knowledge, we can begin to show ways in which those theoretical commitments are not compelling; we may respond with our own theories and not have to worry about scepticism winning by intuitive default. The theoretical diagnosis approach is to show that scepticism is a genuine problem that we can understand, but only given certain theories about knowledge; that is, only given certain contexts of epistemological enquiry.


Williams sees a common root in sceptical problems that he calls epistemological realism. This is a theoretical doctrine that some epistemologies, sometimes unknowingly, use as the framework to support their position. It shapes the character of epistemological positions, such as foundationalism and coherentism, with certain principles that make the path to scepticism almost inevitable.

Epistemological realism is the position that certain propositions are better suited for justification because of intrinsic properties they possess. Further, propositions are better suited for justification on account of their content; that is, the intrinsic property of a proposition that makes it justificatory is its content.

In this way, epistemological realism holds that beliefs and propositions are divided up into certain kinds, and that these kinds are either basic and justificatory, or demanding of justification, and that they are divided into these kinds only by their content, and by not other considerations. A proposition's status as justificatory is determined only by its content, and by no other considerations.


By exposing the theoretical commitments of scepticism, Williams plans to show its arguments not to be intuitive. These theoretical commitments will have to be part of some sort of contentious epistemological project. We have seen that epistemological realism has been identified as a root of sceptical problems. But epistemological realism is a broad commitment, and a particular epistemological project must be identified to show how scepticism is born.

Williams identifies foundationalism as the implicit theoretical project giving scepticism the principles necessary to make it seem unavoidable and insurmountable. The standard view of foundationalism is that there are foundational propositions that do not require further justification; they are meant to be the end of justification, so to speak. It is the theory that there are points of knowledge from which the rest of our knowledge is produced. But this is not the part of foundationalism that Williams is worried about. He is concerned with the specific types of propositions that are taken to be foundational, and with the way foundationalism divides our beliefs up into justificatory and non-justificatory propositions or beliefs.

The important part of foundationalism, says Williams, is that there are certain types of beliefs or propositions that act as the fixed points of justification in our knowledge. Foundationalism is a form of epistemological realism, in that it holds that certain propositions are epistemologically prior to others; that is, certain types of propositions are better suited to play the role of justification for all other propositions, due to their intrinsically justificatory properties. Foundational propositions are justificatory due to their content alone; a foundational proposition is epistemologically prior to other propositions permanently, due only to its own content. These propositions form the foundation of justification for all of our knowledge about the world; without these foundational propositions none of our propositions can be justified, because they are the only justification we have, and they are the only type of proposition that can play the role of justification.

In this way, Williams identifies two aspects of foundationalism; foundationalism holds that justification starts from certain points of knowledge, and that those points are fixed as certain types of propositions with inherent justificatory properties due to their content. Williams calls this particular form of foundationalism substantive foundationalism, although it will be referred to simply as foundationalism throughout this essay. As Williams explains:

Thus for the (substantive) foundationalist beliefs have an intrinsic epistemological status that accounts for their ability to play one or other of the formal roles the theory allows. Beliefs of one kind can be treated as epistemologically prior to beliefs of some other kind because they are epistemologically prior; some beliefs play the role of basic beliefs because they are basic; others receive inferential justification because they require it; and all because of the kinds of beliefs they are. (Williams, Unnatural Doubts 115)

This is contrasted with formal foundationalism, which only holds that justification begins at certain points, and not that those points are fixed permanently by any particular properties of propositions. Formal foundationalism does not on the face of it have the sceptical qualities of substantive foundationalism, because it does not presuppose epistemological realism. Without an account of what types of propositions are intrinsically justificatory, formal foundationalism avoids scepticism (Williams, Unnatural Doubts 115).

The particular type of proposition that plays the justificatory role, according to foundationalism, is experiential statements; that is, statements about what we see, hear, feel, and so on. The statement, "I see the image of an apple in front of me," serves as justification for the statement, "There is an actual apple in front of me," and it is the only type of statement that can be used to justify belief in external apples. All of our statements about the world are ultimately supported by such experiential statements, because of their special status as justificatory statements; if we lose them, we lose all of our knowledge about the world. Experiential statements take priority over all other statements in providing justification, so if they can all be doubted, we are left with no justification at all.

Here we can see the beginnings of how scepticism might emerge from specific theoretical commitments, particularly foundationalism; and if we can show that radical scepticism requires epistemological foundationalism to reach its negative conclusion about all of our knowledge of the world, we can show that scepticism is avoidable, and that it can be contested by other theories.

But merely pointing out that scepticism may hold such tacit foundational commitments is not enough. Defenders of scepticism who take scepticism to be intuitive in nature will argue that, contrary to requiring foundational presuppositions, scepticism actually generates foundationalism; foundationalism falls out of scepticism once we realize that all of our knowledge is called into question by doubting that we can know the existence of external objects by inference from sense experience. We make the discovery of foundationalism when scepticism shows us the importance of experiential statements. Sceptical arguments present a challenge to our knowledge and foundationalism answers that challenge by giving experiential beliefs priority: the problem of scepticism is that we are not justified in holding any beliefs about the external world true, and in response foundationalism presents us with the idea that experiential beliefs are intrinsically justificatory, so that we are justified in holding beliefs about external objects true so long as those beliefs are based on experience. The next step is for the sceptic to show that even by foundationalist lights we are not justified in holding beliefs about the external world, so that we once again have no knowledge of the external world.

The challenge now for Williams' anti-scepticism is to show that foundationalism is required for scepticism, and not the other way around; we must show that sceptical arguments have the strength they do only because of foundational epistemology, and not that foundationalism exists only because of sceptical considerations. If we can accomplish this, then we can show that, only given foundationalism and sceptical arguments do we have no knowledge; and we may then proceed to reject foundationalism. We may argue that scepticism is only possible in the context of epistemological foundationalism, and we may put forward contexts of our own, contexts in which scepticism is not an issue. If it can be shown that there are implicit foundationalist presuppositions in scepticism, because scepticism requires foundationalist principles in order to be convincing, then we will have shown that scepticism is just as theoretically contentious as any other epistemological theory. We will no longer be stuck in the position of being forced to accept the epistemological paradox of our everyday concepts of knowledge intuitively leading to the denial of all of our everyday assertions of knowledge, because the so-called intuitive premises will be shown to be the theoretically contentious principles of foundationalism. We may begin the work of showing scepticism to be an unpalatable consequence of the particular theoretical, epistemological project of foundationalism. This will make scepticism begin to look less appealing, and more like the beginnings of a reductio ad absurdum of foundationalism. But first, we must show that scepticism does in fact require foundationalism.


The task for the anti-sceptic is now to show that foundationalism must be a precondition for scepticism. The sceptic, then, must be able to show that foundationalism is instead a by-product of scepticism. In order to do this the sceptic will first have to give the most intuitive argument available, which forces us to ground knowledge of the world on sense experiences. Once this is accomplished the second task for the sceptic is to show that grounding knowledge of the world in sense experience results in knowledge being unobtainable. This can be done by, for example, noting that we can never know whether we are dreaming through sense experience alone, and if we are dreaming we do not know anything about the external world from our sense experiences. If sceptical arguments do in fact play out in this way, with foundationalism being produced by scepticism and then being proven ineffective at giving us knowledge, then the anti-sceptic may be accused of only focussing on the second stage of the argument; the anti-sceptic only responds to the attack on foundational knowledge, and not on the intuitive arguments that set up scepticism in the first place (Williams, Unnatural Doubts 59). The anti-sceptic will have mistaken the presuppositions of the foundationalism that is forced on him with the presuppositions of all of scepticism. If this is so, scepticism cannot be avoided, and we are forced to accept the priority of experience put forth by foundationalism, and all its shortcomings.

The most intuitive, simple and straightforward form of scepticism seems to be Agrippa's Trilemma. Take a simple argument for the existence of external objects, similar to Moore's: 1) I am having an experience of a chipmunk; 2) There is a chipmunk here; 3) There is an external object here. The difficulty is that the first premise only supports the second premise if the third is true. Someone may simply ask, in an Agrippan manner, "How do you know that seeing a chipmunk means that a chipmunk exists?" If we respond by explaining that we know so because of the fact that there is a chipmunk here, then we are arguing circularly; we know there is a chipmunk here because we see there is a chipmunk, and if we see there is a chipmunk then we know there is a chipmunk here. The response then, is to propose foundationalism; our argument seems to support the idea that sense experience is prior to other knowledge, because we intuitively understand it this way. It seems intuitive to all of us that seeing a chipmunk means a chipmunk being there. But without foundationalism the Moorean argument fails under Agrippan considerations. So, we propose foundationalism out of the Agrippan sceptical argument: sense experience claims are prior to knowledge claims, so that our claim that seeing a chipmunk means knowing a chipmunk is there is justified. This seems to be a fair, reasonable and intuitive move. But at this point the sceptic proceeds in a familiar manner by pointing out that we cannot know by experience whether we are dreaming or are brains in vats and so on, and if we are dreaming or are brains in vats, then we cannot know by sense experience about the external world. This is the sceptic's best bet for showing that foundationalism comes out of sceptical considerations, and that foundationalism is then shown to be inadequate by familiar sceptical reasoning, which the anti-sceptic responds to.

The difficulty with this approach to scepticism is that Agrippa's Trilemma is a very broad strategy that can be applied to any argument or premise. The sceptic may ask, in an Agrippan manner, how we know that seeing a chipmunk means that a chipmunk is here, but we may also ask, "How do you know that you are experiencing the image of a chipmunk?" If the answer is that it is known that a chipmunk experience is being had because that is what is being experienced, then the argument is circular. The other possibilities are assumption and regress.

So, the Trilemma can be shown to call into question the very experience used as the first premise, just as much as it can call into question the move from the first premise to the second. If this is the case, then foundationalism does not get off the ground; sense experience is not prior to other knowledge, because we can question the reliability of experience in an Agrippan manner. If this is so, then the intuitive sceptical strategy that the sceptic would use to show that foundationalism supposedly falls out of sceptical considerations can also be used to show that foundationalism does not fall out of such strategies: the Trilemma shows that sense experience does not support external knowledge of objects, which would lead us to propose foundationalism; but it also shows that sense experiences are just as dubitable as knowledge of objects, which would mean we could not propose the priority of experience that is foundationalism.

Agrippa's Trilemma does not give us reason to propose foundationalism any more than it does to oppose foundationalism; the most intuitive sceptical argument available to the sceptic is neutral in regards to the adoption of foundationalism. The Trilemma is such a broad strategy that it can be used against the sceptic as easily as the sceptic can use it. As such, the sceptic has not proven that foundationalism falls out of sceptical considerations. Rather, the Trilemma seems to show that the sceptic must adopt foundationalism as a contentious theoretical doctrine in order to support Humean and Cartesian scepticism that makes use of dream-arguments; the most intuitive of sceptical arguments does not support scepticism, so unless we can come up with other intuitive sceptical arguments, it seems radical scepticism does not have as its roots intuitive arguments, or at least not the Trilemma. Without an intuitive argument to ground foundationalism in the sceptic is left with only the second stage of the argument: a Moorean argument for knowledge of the world is put forward, and the sceptic makes the dream or brain in a vat argument, which only works if foundationalism is presupposed.

These considerations are supported by comments made by Wittgenstein, as Williams explains (Williams, Unnatural Doubts 70). Wittgenstein notes that, "My having two hands is, in normal circumstances, as certain as anything I could produce in evidence for it" (Wittgenstein 250). In other words, proposing that knowledge of the external world requires sense experience as evidence is just as plausible as proposing that knowledge of sense experience requires the external world as evidence. The process of justification can work either way, because, as the Trilemma has shown, we are at best equally certain or uncertain about external objects as we are about our sense experiences. The only way that sense experience becomes more certain than propositions or beliefs about external objects is if we adopt a foundationalist epistemology.

This bears on another potential argument that the sceptic might use to support the case that foundationalism is produced from intuitive scepticism. All that is required, the sceptic argues, is that the logical gap between experience and knowledge of the external world be recognized; all our experiences are compatible with the external world existing as we see it or not existing at all, or being completely different from what we experience. There is no logical connection between our experiences and the way the external world actually is.

But, as Williams explains, a simple logical point such as this does not make an epistemological point about the priority of experience over knowledge of the external world. The logical point is just that there is a gap between experience and the way the external world is, and it does not insist on or even recognize a direction in which that gap is most deficient. We cannot infer from a logical gap between experience and the world that experience takes priority over knowledge of the world any more than we can infer that knowledge of the world takes priority over experience. If, as Wittgenstein noted, having two hands is as certain as anything that can be produced in evidence for it, then it is just as reasonable (or unreasonable) to produce sense experience as evidence for our having two hands as it is to produce our having two hands as evidence for our experience. If anything, the logical gap between experience and knowledge of the world shows that experience and knowledge of the world are just equal in status; it shows that we ought not to draw any conclusions at all about epistemological priority. If the two are equal, then this is not the intuitive argument that the sceptic hopes will show that foundationalism falls out of scepticism; it shows nothing of the sort, and instead shows that the opposite thesis, that knowledge of the world takes priority over experience, is equally plausible.

In order to get the epistemological conclusion that the sceptic wishes to get out of the logical point about the gap between sense and experience, we see that the sceptic needs to presuppose foundationalism; the logical gap between experience and knowledge of the world is unbiased in its direction, and so does not support foundationalism any more than the opposing thesis of priority of knowledge of the world over experience. Williams refers to this as the neutrality of experience: (Williams, Unnatural Doubts 73-79) a statement about the world can go beyond our experiences just as much as a statement about experience can go beyond the world.

It seems that scepticism requires some sort of epistemological priority, specifically foundationalism; but due to the neutrality of experience pointed out by Williams and supported by Wittgenstein and Agrippa's Trilemma, the logical gap that the sceptic presents as an intuitive argument for foundationalism could just as easily work against the sceptic. Statements about experience and statements about the world are epistemologically on par before we introduce any epistemological theories that involve priority. To expand on our earlier quote, Wittgenstein says:

My having two hands is, in normal circumstances, as certain as anything I could produce in evidence for it. That is why I am not in a position to take the sight of my hand as evidence for it. (Wittgenstein 250)

But further:

... a proposition saying that here is a physical object may have the same logical status as one saying here is a red patch. (Wittgenstein 53)

The priority of experience over knowledge of the world requires that knowledge of the world be more dubitable than our experiences, but the neutrality of experience shows this not to be the case, unless we make epistemological, theoretical presuppositions. To put the argument into a form that might be more familiar, the neutrality of experience supports the argument that we cannot know about the world if we are dreaming just as much as it supports the argument that we are not dreaming because we know things about the world. This is reminiscent of Moore, who argued that because he knows many obvious things, scepticism must be incorrect. This is the opposite of the sceptic's argument that because we do not know if we are dreaming, Moore's propositions must be incorrect. But we also see how Moore went wrong: he was right to point out that the sceptic's conclusions about knowledge were not necessarily better than his, but he attacked the sceptic head on and failed to question the sceptic's presuppositions; and with foundational presuppositions thus intact, the sceptical conclusion maintained its resilience to Moore's knowledge statements.

Here too we may be reminded of the principle of logical presupposition that Nozick and Dretske mistook for the principle of epistemic closure. The principle of epistemic presupposition requires that we must first know that we are not dreaming before we can know anything about the world. But, as we have seen, the neutrality of experience shows that it is reasonable to argue that we know that we are not dreaming because we know things about the world. And if we know that we are not dreaming, then we have met the principle of epistemic presupposition's requirements, just in a roundabout way: we want knowledge of the world, but the principle of presupposition says we must know we are not dreaming first, so we show that we know we are not dreaming by showing how much knowledge of the world we have. The neutrality of experience supports this possibility as much as it supports the sceptical one. But this seems strange, because it is a circular argument, but not viciously so. We have knowledge of the world already, so why use it to show that we are not dreaming in order to show that we have knowledge of the world? In other words, why propose the principle of epistemic presupposition at all? Why suppose that we must first know that we are not dreaming before we know anything else, when the neutrality of experience supports adopting this principle as much as it supports it being useless?

The only reason for adopting it as a reasonable principle is if we first adopt the priority of experience over knowledge of the world. The principle of epistemic presupposition seems to be reasonable if we prioritize the sense experience side of the logical gap, but pointless if we prioritize the knowledge of the world side. But if we presuppose foundationalism it suddenly becomes much more forceful: we may no longer make the move from having knowledge of the world to knowledge of not dreaming, because in order to have knowledge of the world, according to foundationalism, we must proceed from our experiences, and our experiences cannot tell us whether or not we are dreaming. If experiences cannot tell us whether or not we are dreaming, and experience is all we have, then the requirement that we must know if we are dreaming to know anything about the world becomes incredibly epistemologically restrictive: we cannot know we are dreaming, under foundationalism, so we cannot know anything about the world under the principle of epistemic closure. Without foundationalism the principle of epistemic presupposition is unnecessary and strange, but with foundationalism it is powerful. So why adopt the principle at all? The upshot is that there is no reason, as far as we have seen, unless we have presupposed foundationalism and wish to get scepticism.

The next obvious question is, why suppose foundationalism at all? It seems there is no reason. From the sceptic's most intuitive arguments we do not get foundationalism, but rather the neutrality of experience, which gives us no reason to adopt anything like the principle of epistemic presupposition or foundationalism. Contrary to forcing us to adopt foundationalism and all its epistemological flaws, the intuitive arguments proposed by the sceptic require foundationalism to have any radically sceptical edge. Adopting such principles and theories simply seems to impose theoretical restrictions on our knowledge that are not supported by any intuitive argument.

As such, to get scepticism about the external world the sceptic needs to conjoin Agrippa's Trilemma or the logical gap between experience and knowledge of the world with a foundationalist conception of knowledge, giving them an epistemological bite, and forcing the gap between experience and knowledge of the world to work only in one direction. But we do not have any compelling reason to do this unless one wants to be a foundationalist; we have been given no good reason for supposing that foundationalism is forced on us; so adoption of it seems to be choice of theory, and choice of contentious theory at that. The sceptic's attempts to show that intuitive sceptical arguments lead to foundationalism have failed so far, and instead we have support for the idea that foundationalism must be presupposed by scepticism. Unless the sceptic has another intuitive argument that leads to foundationalism, it seems she must be using a contentious theory like foundationalism to get to scepticism. But if this is the case, then the sceptic cannot use scepticism to produce foundationalism; this would be obviously circular.

In light of this, foundationalism begins to look more like an optional, contentious theory that is necessary for scepticism, as we hoped to show; if foundationalism is not forced on us by scepticism, and must instead be presupposed by scepticism in order for scepticism to succeed, we have a case for denying foundationalism in favour of other theories, without having to worry about damaging our intuitive principles of knowledge.


So far we have made a case against scepticism being an intuitive argument, and for it presupposing a foundational epistemology. If the foundational commitments of scepticism have been revealed, then the door is open to proposing anti-sceptical epistemologies to replace foundationalism.

Coherence theorists hold such a position; they present a theory that is anti-foundational and anti-sceptical. Coherence theories are many and varied 1, so I will focus on one particular formulation of it that I take to be a strong representative, presented by Williams, who has drawn a great deal from Bonjour (Williams, Problems of Knowledge 117). Proponents of coherence theories hold that foundationalism's commitment to linear inference poses sceptical difficulties. Linear inference requires that justification come out of arguments from premises to conclusions according to certain rules of inference. Coherence theorists reject this conception of inference in favour of a non-linear form of justification; beliefs are connected in a variety of logical ways, but this does not make justification. Justification is instead a property of entire systems of belief; individual beliefs are justified not by being supported by other particular beliefs, but by being part of a coherent total world-view of beliefs (Williams, Problems of Knowledge 117).

So coherence theorists hold that a belief cannot be justified on its own, as in foundationalism; no belief is epistemologically prior to any other, and a belief cannot be justified simply by being the conclusion in a linear inferential argument with justified beliefs as premises. Rather, beliefs are justified when they fit into a justified system of beliefs, where a system of beliefs is more or less justified depending on how well the beliefs hang together as a whole. The important point is that the entire set of beliefs is taken as the unit that is justified; justification of individual beliefs depends on the coherent properties of total belief systems or world-views. This focus on total systems of beliefs as justificatory is radical holism. So coherence is a theory of justification distinguished from foundationalism negatively, by rejection of the idea of intrinsically credible basic beliefs that function as the beginnings of linear justification, and positively by the adoption of radical holism (Williams, Problems of Knowledge 117-118).

It is worth distinguishing two characterizations of coherence. Relational coherence holds simply that a belief is justified if it fits into a set of other beliefs; the properties of the belief in question are what matters. In this way, foundationalism may be considered a coherence epistemology: a belief is justified if it coheres with other beliefs that are epistemologically prior, through a linear inferential argument (Williams, Problems of Knowledge 117). This is not the brand of coherence that will be focused on; coherence is meant to be anti-sceptical by its rejection of foundational principles of justification, so a coherence theory that is inclusive of foundationalism obviously won't do. As such, we will focus on systematic coherence. This is the type of coherence we have just surveyed, in which the epistemological status of a belief depends on the way that the entire belief system surrounding that belief fits together. Systematic coherence is radically holistic. Radical holism rejects all of foundationalism's standards of justification.

A response to coherence seems evident: normally we do not do anything like what the coherence theorist suggests when we justify a belief. Normally we use particular pieces of evidence to support particular beliefs, making no reference to anything like a total view of the world that would act to justify. This is referred to as local justification. In order for the coherence theory's radical holism to remain relevant, then, our coherence theorist must hold that if local justification is found to be credible, it must be because the system of background beliefs being used in local justification must be maximally coherent. This is global justification. We may take for granted that global considerations are what ultimately justify and assume that our background system of beliefs is coherent, but all local justification depends on global justification nonetheless; global justification is necessary for local justification at all (Williams, Problems of Knowledge 118).

A few facets of coherence are necessary to make it robust. The first is to draw focus not just on the lack of conflict between beliefs when determining the coherence of a system, but on positive connections between beliefs. These might be considered explanatory relations. The requirement for positive explanatory relations means that our beliefs must not only be compatible, that is not conflict with one another, but should also hang together theoretically; coherence is not just made or broken by logical connections, but also by epistemological connections. These explanatory connections between beliefs are what we make use of in linear justification, but are also important holistically, in that a robust series of individual belief-to-belief relations make a more genuine system than any arbitrary collection of beliefs; the more dense a set of belief-to-belief explanatory relations are, the better chance they have of being a genuine system, rather than a collection of unrelated beliefs. With more solid internal logical, explanatory and epistemological connections between particular beliefs comes more relevance between those beliefs, and thus better global justification; a set of beliefs related by explanatory connections is more globally justificatory than a set of beliefs made up of less explanatory connections. Thus, a coherent system with solid explanatory belief-connections is more desirable than one with fewer or more dubitable explanatory connections (Williams, Problems of Knowledge 119-120).

Two additional facets of coherentism needed to make coherentism more robust are the related concepts of comprehensiveness and conservatism. Comprehensiveness states that a system is more coherent the more beliefs it takes in, explains and anticipates. This is meant to stave off the objection that it may be more coherent to keep a small, exclusive set of beliefs that conveniently ignores facts contradictory to it. Comprehensiveness ensures that we make our total view more coherent by making it more, not less, complete (Harman 159). This relates to the conservatism requirement, which states that when we are faced with a problem in our system of beliefs, we should make changes that result in the least damage possible to our total view. This is best understood as a requirement coming out of comprehensiveness: in order to keep our system of beliefs comprehensive, we avoid taking on beliefs that would require us to dispose of large parts of an otherwise plausible system, so we keep our system as expansive as possible. This does not forbid the adoption of beliefs that force the disposal of other beliefs in our system, because we can accept a loss in comprehensiveness if a sizeable gain in integration of beliefs follows. For example, beliefs we gain through experience may reasonably be added to our overall system even if they damage some aspects of it; it would be unreasonable to ignore them. Experiential beliefs are sometimes referred to as "cognitiviely spontaneous beliefs." Coherence only requires conservatism in that comprehensiveness holds a certain priority over integration so that we may have a useful system. As long as the system remains useful, and does not become a system of arbitrary beliefs or fairy tales, we may jettison some beliefs in favour of others that increase coherence. But if a belief would damage our system of beliefs drastically, then we ought not to adopt it (Williams, Problems of Knowledge 120).

Finally, a full account of coherence requires that cognitively spontaneous beliefs are included in the beliefs that make up the total view that we are to justify by making maximally coherent; beliefs about the world and beliefs about experience are both included in the same system. This allows external input into our system of beliefs, so that it is not simply a set of belief-to-belief relations cut off from the world, so to speak; cognitively spontaneous beliefs, that is experiential beliefs, ensure that our system of beliefs have something to do with the world by allowing the external world to influence our system of beliefs. But these cognitively spontaneous beliefs are also subject to assessment according to a selection of beliefs about our abilities as perceptual observers; in other words, our total belief system must also include epistemic, or reliability, beliefs. For example, we have beliefs about how reliable we are in certain circumstances; for example, we believe that in low light our perceptual beliefs are less reliable, or that someone who has had a few drinks is less reliable than someone who is sober. So, spontaneous beliefs are regulated by epistemic beliefs, both of which are included in the total set of beliefs. This allows for the input of observational beliefs, so that a system of beliefs cannot remain rationally insulated from experiences by simply ignoring problematic observations in favour of keeping the system coherent, while allowing for mistaken observations, so that not just any observation can lay waste to the system of beliefs. For example, an experiment with results that do not cohere with certain parts of our belief system may be reasonably ignored if it resists replication; in this case, an epistemic belief that holds that observations must be repeatable allows for the possibility of error in an observation. This set of considerations is referred to by Williams as the rationalized input requirement (Williams, Problems of Knowledge 122), who draws from BonJour (BonJour Ch. 6).

These considerations, which we shall call the criteria of coherence, make the coherence theory more robust. The requirement for explanatory relations, comprehensiveness and conservatism blocks arguments like the "many systems objection," which states that an infinite selection of beliefs could be considered coherent, even fairy tales, making our selection of coherent belief-system arbitrary (Williams, Problems of Knowledge 119); and the rationalized input requirement blocks the "isolation objection," which states that a system of beliefs about other beliefs will be cut off from the world, so to speak, so that it may have no relevance at all to the way the world is, and so be irrelevant. (Williams, Problems of Knowledge 119) The result is an anti-sceptical epistemology; sceptical beliefs are not incorporated into our total view because they would force us to discard an innumerable number of beliefs, limiting the comprehensiveness of the system and violating the conservatism requirement, while presumably offering no gain in integrity or coherence.

So far coherence sounds like an attractive alternative to foundationalism. But it is worth examining coherentism's anti-foundational tenets, in order to see if it is in fact as decisive a rejection of foundationalism, and thus scepticism, as it seems.

As we have seen, coherence theory holds, contrary to foundationalism, that there are no privileged beliefs and no fixed points of knowledge from which linear justification may proceed; in theory any belief whatsoever may be discarded if it is deemed problematic. In coherence theory the rules of logic, math, and deduction all lose their a priori status, and so are potentially revisable given the right circumstances. This goes so far as to include the criteria that guide us in determining when a system of beliefs is in fact maximally coherent; the requirements of comprehensiveness, conservatism, rationalized input, even the basic ideas that there are no privileged beliefs and that a system is justified when its beliefs are coherent, may be discarded if they become problematic for the justification of our system of beliefs.

So why suppose we must make inferences from one system of belief to another when looking to justify our beliefs at all? There may not be any reason to. If we wish to hold on to our beliefs in light of problematic evidence we may question the criteria of coherence just as well as we may question any beliefs or epistemic principles or theories; everything is potentially up for grabs in coherence theory, including the criteria of coherence (Williams, Problems of Knowledge 134-135). In principle, coherence theory could come to be regulated by foundationalist principles. This possibility is dangerous for coherence theory; if coherence theory does break down into foundationalism, then it loses its claim to being an anti-foundationalist, holistic theory of justification, and no longer holds any anti-sceptical weight. The coherence theorist must have some explanation for why this cannot happen, or risk breaking down into foundationalism.

The reason coherentism does not break down into another epistemologicaly, such as foundationalism, is that coherence theory seems to implicitly give the criteria of coherence a privileged epistemic status (Williams, Problems of Knowledge 135). Unfortunately for coherence theory, this amounts to a concession to foundationalism anyway; for the only way coherence theory can avoid the possibility of the rejection of coherentist principles by coherentist standards, leaving it open to foundationalist revisions, is to give the criteria of coherence foundational status so that they cannot be revised. The coherence theorist wishes to deny that any beliefs or rules of inference or logic that connect those beliefs are privileged, but then goes on to privilege beliefs about the criteria of coherence; the criteria of coherence are fixed points from which acceptance of beliefs is regulated. In other words, the criteria of coherence are foundational beliefs; they act as the beginning point from which linear justification must be performed. Just as a foundational belief about the world is justified by an epistemologically prior experiential belief earlier in a linear chain of justification, so too is a belief about the world justified by the criteria of coherence earlier in a linear chain of justification. Individual beliefs may be justified by any number of systems of belief without any special epistemological status, but those systems of belief may only be recognized as justificatory by the criteria of coherence, which must take priority or risk becoming irrelevant to justification by their own lights (Williams, Problems of Knowledge 135).

The coherence theory may be forced to collapse into foundationalism in another way as well. Bonjour presents the Doxastic Presumption as a way of strengthening the coherence theory (BonJour 81-82). According to the Doxastic Presumption, the coherence theory must presuppose two things: that each individual has a primitive sense of what her beliefs are, and that we are entitled to presume that this primitive sense of our beliefs is more or less accurate. The difficulty with this is that there are simple, familiar ways that we know what we believe; if someone were to ask us our belief about a subject, we would have no serious difficulty giving one, so long as we did in fact have one. But this does not resemble the way in which we must know what we believe according to coherence; this simple conception of beliefs is not how coherence theory demands our knowledge of beliefs behave. Instead, coherence theory asks of us that we know the scope, structure and accuracy of our total belief system as a whole. This is an incredibly complex piece of knowledge, and it seems that we have no such sense of our total system of beliefs. How would we even go about thinking about or explaining what our total belief system is? It is hard to say that we could give an account of what our total belief system is; even if it were in principle possible to do so, we do not seem to have the capacity to assess all of our beliefs at once as an entire unit of justification.

As Williams explains, (Williams, Problems of Knowledge 136-137) the Doxastic Presumption seems to be a doxastic assumption; we have no reason to think that presuming that we have a primitive sense of the structure of our belief system is warranted, so it seems to be a brute assumption. The presumption seems to exist only to prevent a regress in our justification. If our knowledge of our system of beliefs can be questioned, then it has to be supported by some sort of justifying inference. Otherwise we do not know when our system of beliefs is a justified one, and so cannot begin to pick a most coherent set of beliefs; we must justify our choice of justified system of beliefs. But this meta-justification must then be included in our system of beliefs: coherence theory is radically holistic, and so all of our beliefs must be included in our total view, including meta-justificatory beliefs about the system. Of course, this meta-justification must then itself be justified, and so a meta-meta-justification must be given, which then also must be integrated into our total view, and so on; an infinite regress of justification ensues. The only way to halt this regress is to introduce a presumption that the chain must stop at some point. This stopping point of course takes on foundational status: justification proceeds linearly from the doxastic presumption, which has epistemological priority over other forms of justificatory beliefs, given that the rest of justification is unwarranted without it. Coherence theory is in fact foundational, even if at a global level.

Coherence theory, despite its anti-foundational agenda, seems to actually be foundationalism in disguise (Williams, Problems of Knowledge 134-135). If this is the case, as it seems to be, and coherence theory holds foundational views, why not then just allow privileged beliefs and linear inference among all our beliefs, and not just at the meta-level where we have beliefs about what beliefs are justified? It seems there is no reason not to, especially considering that linear inference seems to resemble our simple, everyday epistemic practices better than coherence theory. And of course, as we have seen, if we allow foundational aspects to be presupposed by an epistemology, then there is a strong case for thinking that we are on our way to scepticism. Coherence fails to be radically holistic, allowing in privileged beliefs and linear justification, and more importantly for our purposes, most likely fails to be anti-sceptical. All the sceptic has to do, once we have shown that all knowledge depends on foundational beliefs such as the criteria of coherence or the doxastic presumption, is show that the foundational beliefs in question fail to give us knowledge. Familiar arguments about brains in vats or dreams will most likely do the job: if the criteria of coherence are epistemologically prior to all forms of justification, then the sceptic contends that we may be dreaming, and thus that we do not even know the criteria of coherence, and that we do not know anything that follows. In order to know that we are dreaming, we need the criteria of coherence, but to know the criteria of coherence to justify our belief system, we must first know we are not dreaming. Though they may take on different appearances to account for the meta-level of some of coherence theory's implicit foundational commitments, sceptical arguments apply so long as foundational commitments are present.


We have seen that coherence theory fails as a response to foundationalism; it holds tacit foundational principles of its own, and likely leads to sceptical worries because of them. If we cannot find an epistemology that avoids foundational principles, then we are stuck with foundationalism and the scepticism that follows. Either that or we reject foundationalism and are left floating free epistemologically, with no account of how we know anything. This would seem to be a sort of scepticism by default. For if there is no possible account of knowledge once foundationalism is rejected, why suppose there is any knowledge at all? We must then propose an epistemological account that avoids foundationalism better than coherence theory, an account that must not give priority to any kind of belief.

Contextualism may accomplish this. There is a variety of theories that don the name of contextualism, but they do not necessarily share epistemological affinities.2 For this reason we will focus just on Williams' account, which is presented in tandem with his anti-sceptical arguments. According to contextualism, and contrary to foundationalism, the standards for attributing knowledge are not fixed, but vary with the circumstances of enquiry, or the context. There are five contextual constraints that guide knowledge attributions: intelligibility, methodological, dialectical, economic and situational constraints (Williams, Problems of Knowledge 159-162).

Intelligibility or semantic constraints come out of a remark by Wittgenstein that, "A doubt that doubted everything would not be a doubt" (Wittgenstein 457). In other words, it is necessary that some things be not doubted for intelligible inquiry to even begin. We have entitled presuppositions that make the acts of questioning and inquiring possible, because holding some beliefs true and not subjecting them to attributions of error is a condition of being intelligible at all when questioning; not doubting certain propositions, which are presupposed in a particular context, is required to ask questions at all (Williams, Problems of Knowledge 159-160). As Wittgenstein says, "It may be for example that all enquiry on our part is set so as to exempt certain propositions from doubt, if they are ever formulated. They lie apart from the route travelled by enquiry" (Wittgenstein 90). Without holding some things as right, it is not clear what we are talking about, if anything. If we were to discuss with someone the mechanics of pool balls on a table, but at every turn she said she was in doubt of the existence of pool balls and cues and tables and you and me, we would not be able to discuss anything with her. We cannot remain doubtful of everything at once if we are to be understood as saying anything; for if we can doubt everything, we have no reason not to doubt that we can even understand the words we are saying when we doubt, so that we cannot make sense of anything. Eventually the process of doubting shifts from acknowledging the possibility of mistake until it makes us unable to perform any knowledge related tasks, including the task of reasonable doubting (Wittgenstein 35).

If for example someone doubted that he knew what the number four was, or that he knew how to perform any mathematical operation, he could not get from 4 and 3 to 4+3=7; when we asked him what 4+3 was, he might say, "I'm not sure; what is a'4'?" If we told him that it was one less than 5 and one more than 3, he might ask, "What is a '5'?" He would not just be making mistakes by not knowing the answer. When we make a mistake we can always go about correcting it; we know algebra, but sometimes we have a lapse of concentration or a moment of bad reasoning and so on. However, the man who doubts all of math, so that he has to ask what the fact of the matter is about every number and operation, could not be said to have any idea of what math was in the first place; he would have no grasp at all of the concepts, and so his questions would be unintelligible. We could not understand what he was asking, because it would have nothing to do with what we do when we do math -- questioning what every number is just is not a possible way of doing math. The math-doubter would not understand arithmetic or numbers, because by questioning everything about math he would have no place to begin when trying to understand. When we do math we take for granted what each number is and what each operation means and so on; so to do math, some beliefs must be exempt from doubt. Thus certain questions are exempt from doubt in math, so that math may proceed at all. Doubting what a number is does not enlighten us to new ways of understanding math; rather, it exempts math from being done at all.

But there is not an instant switch from doubting to unintelligibility. Rather, it is a fuzzy distinction between mistake and incomprehension. Perhaps someone could be mistaken about how long-division works, and so would fail consistently at doing certain types of math; and we might then say that he does not understand math, in some way. But we could presumably correct him, so that he performed properly, so long as he understood the rest of math properly or at least some significant part of it. If he did not have any idea what anything in math was, we would have to begin from the start, and maybe we could teach him from the beginning. Presumably he could gain comprehension at some point. But where he went from not understanding math to understanding would not be determinate. Nonetheless, if everything is doubted, then nothing can be known; if the math-doubter did not accept any part of what we taught him about math as true, he could never be taken to comprehend math.

For this reason the contextualist must be careful in acknowledging that any belief may be up for grabs, so to speak. If no beliefs have any special status over any others, then we may be able to question them all, and so a contextualist epistemology would lead to unintelligibility of all beliefs, if the sceptic chose to argue in such a way.

This is where the contextualist stresses the importance of context to knowledge, justified belief, and inquiry: it is not true that just anything can be called into question in any situation. To ask a question requires setting an epistemic stage, so that some things cannot be questioned in that context, in order for inquiry to be intelligible. This is true of all forms of questioning, inquiry and doubting, including sceptical forms. So the intelligibility constraint of contextualism has to do with being able to ask meaningful questions at all, which necessarily involves leaving some things out of doubt, depending on the context of inquiry.

Methodological constraints are another way in which some doubts are excluded in particular contexts; methodological constraints exclude some doubts not just so that we can make sense of inquiry at all, but so that questions of a specific kind can be raised within a broad field of inquiry (Williams, Problems of Knowledge 160); for example, so that questions aboutbraham Lincoln can be asked in history. Methodological constraints exempt propositions that are necessary for specific questioning to take place; and these exempted propositions or beliefs are called methodologically necessary by Williams. It is worth noting that there does not have to be a sharp distinction between beliefs that are methodologically necessary and beliefs that are necessary for intelligibility; depending on the way inquiry goes and the context, the same proposition may not be methodologically necessary or necessary for the preservation of intelligibility (Williams, Problems of Knowledge 160). To do history we have to presume the existence of people. We would be unable to follow the line of questioning about European history, for example, if we kept asking whether people existed when trying to find out particular facts about Europeans. This might be considered a methodological necessity for European history in this situation, or even necessary for intelligibility; for how could we doubt the existence of people, when we are people? To do geography we do not necessarily need the same presupposition, but we would have to presume the existence of the Earth to remain intelligible, or that specific parts of the Earth were inhabited at certain periods of time to ask specific kinds of questions. The point is that propositions are not methodologically necessary on their own; they require a context of inquiry to be considered presuppositions, and in different contexts different beliefs will be methodologically necessary or necessary for intelligibility.

Methodological constraints also give direction to inquiry (Williams, Problems of Knowledge 160-161). Intelligibility constraints often exempt doubts about objects existing or about our having existed a few moments ago, and so allow us to ask questions at all. Doubting propositions that are necessary for intelligibility does not increase the rigour of, say, historical investigations; it would just stop investigation altogether. Methodological constraints on doubt, on the other hand, are associated with the logic of particular inquiry; methodological constraints do not make a sceptical point about our practical limitations when asking questions, but make a point about putting some questions aside so that our historical inquiry may take a certain direction. We may ask a historical question about whether Brutus existed, but the methodological constraints in this situation will give our inquiry another direction than if we were asking about what Brutus did in his life. Asking whether Brutus existed is not a stricter way of doing history; it is just a different way of doing history, which takes a different direction. We may lower or raise our standards when asking questions, but some questions must be set aside to do history in a certain way. To doubt that all records ever written are reliable would stop us from doing history at all; to ask whether a particular record is forged is to give historical study a certain direction, which is a methodological constraint. So what we are studying depends on what we leave out (Wittgenstein 341-343). If we were to question everything in a field of study we would have no direction at all when inquiring; methodological constraints make focussed questioning possible.

Given a certain direction of inquiry, dialectical constraints, the third kind of contextual constraint, require that certain objections to a line of inquiry may or may not be legitimately brought up: some objections are available given the methodological and intelligibility constraints in play, and some are not (Williams, Problems of Knowledge 161). If a claim does face a persistent, legitimate objection in a context of inquiry, then it will not play the role of a presupposition in that context.3 Likewise, a proposition or belief that does act as a presupposition may cease to act as such when new problems, objections or questions are brought into play. Thus the status of a claim, belief or proposition changes with the dialectical landscape.

The fourth variety of contextual constraint is the economic constraint, which stresses that objections to a claim in a particular context do not gain relevance simply by being mentioned; there needs to be a reason to think the objection holds (Williams, Problems of Knowledge 161). Our level of strictness or scrutiny during an inquiry is fixed by the sort of objections that hold. This is where varying standards of strictness come into play when doing, for example, history.

We impose high standards of justification in a context if we rule out even remote possibilities of error in order to avoid objections, and we impose lower standards if we let certain error-possibilities slide. But we do not simply set high or low standards for no reason. Instead, economic factors play an important role in deciding when it is reasonable to be loose about not considering certain objections or strict in fielding many objections.4 If reaching a decision is a priority, and error would not bring great costs, or being correct would be very beneficial, it may be reasonable to relax our standards in accepting or considering objections to a claim. On the other hand, if the cost of error is severe, then it may be reasonable to enforce higher standards. Balancing the issues of cost, benefit, and decision-making priority will determine the strictness of justification in our inquiry, and how we balance them depends on the situation.

For example, if we must test a newly synthesized chemical to determine what properties it has, we may only do three out of four possible tests; perhaps the first three tests make the possibility of the chemical having the property identified by the fourth test remote. If there are time constraints on when the chemical's properties must be identified, perhaps if someone's health depends on the chemical having the properties identified by the tests, then we have further reason to avoid doing the final test. It is not epistemically irresponsible or inadequate to forego the final test, because the situation calls for certain economic restraints on inquiry and objections, even though doing the final test would presumably increase our knowledge by letting us know that the chemical definitely does or does not have a certain property. If on the other hand, the final test would reveal to us whether the chemical has a property that is harmful to the patient, it would seem reasonable to adopt higher standards; the costs of error are high, so our standards ought to be more stringent.

The last constraint is the situational constraint (Williams, Problems of Knowledge 162). Methodological and dialectic considerations do not exhaust the possibilities for justification or error of epistemic contexts; facts about the situation in which inquiry is done matter too. In other words, objective matters are important to inquiry, because when we hold a belief we commit ourselves to its being objectively well-grounded. As such, we must always be open to the possibility of self-correction, since there may always be ways that we could go wrong that we have overlooked. This does not mean that we must always field objections and counter-arguments, but that we must be open to the possibility that, in the future, matters may surface that alter the outcome of our inquiry, even if we performed an epistemically reasonable and responsible line of inquiry. The purpose of asking questions is to better understand the world, so it goes without saying that we may have to ask questions about how we have gone about what we thought was justified if we are to make progress.

The methodological, dialectical and economic constraints are examples of constraints that determine when our claims are epistemically responsible or justified; they describe when it is acceptable, reasonable and appropriate to doubt, question, accept or ask questions of knowledge claims in a particular context (Williams, Problems of Knowledge 161). The situational constraint is not about the appropriateness of inquiry, but about the objective grounding of our claims, so that our claims are not insulated from the way the world is (Williams, Problems of Knowledge 162). Of importance is the fact that this constraint displays the externalist nature of contextualism. We need not always be aware of our grounds for belief to be epistemically responsible; we do not need to know that we know. Nonetheless, what real-world possibilities our grounds must exclude is determined by our interests, so that even the objective adequacy of our claims is not free from considerations about epistemic responsibility.

These considerations illustrate an epistemology that is anti-foundational: justification does not depend on any particular kind of belief at all. For example, beliefs of a perceptual kind do not hold priority over any other beliefs simply due to their being perceptual. In fact, there is no need to postulate any kinds of beliefs at all. This does not mean that we are prohibited from interpreting beliefs in such a way that they are divided into various kinds, so that some beliefs are called "perceptual," others "logical," and so on, but it does mean that beliefs do not have any special properties, justificatory or otherwise, due to their kind. Whether a belief plays a justificatory role depends on a number of contextually variable factors. Thus the same belief can slip from being justificatory in one context to non-justificatory in another, depending on how inquiry proceeds. As such there is no need for epistemically different beliefs in the first place, not to mention that the idea of beliefs being divided into epistemological kinds runs counter to the intentions of contextualism.

So contextualism is opposed to foundationalism's account of beliefs, in which intrinsic credibility makes individual, basic beliefs justified on their own because of their content, regardless of other beliefs, or of the context or situation in which they are brought up. Contextualism is also opposed to foundationalism's justification process, in which non-basic beliefs are justified only by epistemologically basic beliefs. Contextualism proposes that in any context of justification there may always be a large number of beliefs or commitments importantly involved, not just non-basic and epistemologically-prior basic beliefs.

With these considerations in mind, it is worth noting that contextualism may still be formally foundational (Williams, Problems of Knowledge 164-165). Certain beliefs act as the foundation for other beliefs in a given context, depending on what issue is in question. Foundationalism of this formal variety, as we noted earlier, does not bring along any sceptical baggage, because it does not involve beliefs that have special epistemological status that confers priority upon them in all situations; instead a belief can be formally foundational in one direction of inquiry and not in another. It might even be the case that some beliefs tend to act as formal foundations in a range of contexts, but they need not be foundational in the traditional, and scepticism-prone, way. Instead of having intrinsic content, these contextual, formally foundational beliefs get their content from the practices of inquiry and justification that they are part of in a given context (Williams, Problems of Knowledge 165). For example, when doing history about Abraham Lincoln, we take for granted that he existed; for if we did not presuppose the existence of him, then we would not be able to ask questions about him at all. We could of course question the existence of Lincoln, but we would be embarking on a new line of inquiry, and so different considerations would come into effect, and different beliefs would become important; the subject would be changed. If we felt so inclined, we could question the existence of physical objects generally, but we would definitely not be doing history any more. If we found that we had no reason to believe objects exist, then presumably we would have reason to think that Abraham Lincoln also did not exist; but this particular context of inquiry and its presuppositions do not have any priority over the rest of our beliefs or contexts of inquiry. Questioning the existence of external objects is not out of the question, but it is a particular form of inquiry and cannot be done at just any time without changing the study of history about Lincoln, for example, into epistemological scepticism. To believe in the existence of Lincoln is just to recognize certain possibilities of error and not others, so that inquiry may proceed by asking for particular evidence. If we did not carry out inquiry in this way -- by presupposing the truth of some beliefs given the context -- inquiry would be unintelligible.

It is worth noting that it is very unlikely that the constraints and presuppositions of context could be codified into any particular set of rules, so that we could say, "These are the rules of context that must be followed to ensure justification." We can follow the direction of inquiry in a particular context, but the constraints and presuppositions of all possible contexts are so varied and heterogeneous that we may not be able to explicitly state what the exact constraints or presuppositions are. There is no simple set of exhaustive rules that would point us towards the correct presuppositions. Even if we could explicitly state rules that identified what presuppositions to hold, it is doubtful that they would be of any use in inquiry, because learning to follow a line of inquiry is a process of learning how to recognize contextually relevant evidence, objections and replies. Rules about such things would not illuminate the process of inquiry any more than rules about playing guitar would make someone a good guitar player; both require practice. We must master the practical forms of discourse and inquiry, so that knowing that essentially involves knowing how.

To sum up, for contextualism all questions of justification arise against and depend for their intelligibility on presuppositions that are reasonably not in question. Some presuppositions will tend to be held in place across many investigative contexts; some will only be relevant to the matter at hand. But no belief takes priority over any other. Questioning one presupposition just shifts the focus of inquiry so that other beliefs naturally become presuppositions. If we exempt some propositions from doubt, so that the direction of inquiry is fixed in a particular context, it is because presupposed beliefs play a normative role.

So the anti-sceptical case has been made: scepticism seemed to be an intractable problem because of its intuitive arguments. So the supposedly intuitive nature of scepticism was examined, and what seemed to be intuitive was in fact shown to require foundational presuppositions, with foundationalism being a contentious epistemological theory. Once it was shown that foundationalism was required for scepticism, and that foundationalism was not forced on us in any way, the case had been made for discarding foundationalism in favour of another, non-sceptical epistemology. But coherentism does not fit this bill, because it has tacit foundational commitments itself, and so contextualism was presented as a non-realist, formally foundational, anti-sceptical conception of the way knowledge behaves.