Moore’s Proof, Theory-Ladenness of Perception, and Many Proofs

1. Introductory Much recent writing on Moore’s proof schematizes it along these lines:

Moore’s Proof of an External Material World M1: Here is a hand. M2: If there is a hand, then there is an external material world. MC: There is an external material world.1

Most grant Moore that the premises of his proof (hereafter ‘Moore’s Proof’) are known. This coupled

with the fact that the argument is in valid form suggests a powerful case against the skeptic. After all, if it is true

that the premises are true and the argument valid, then necessary and sufficient conditions are met for a sound

argument.2 Yet most commentators think that the argument has little force against the determined skeptic.3

Much intellectual effort has been devoted to trying to pinpoint exactly where the (apparently) sound argument

misfires against the skeptic.

I suspect that what makes Moore’s Proof so intriguing for many of us is what I shall refer to as ‘Moore’s

Method’, which works as follows: it is epistemically permissible to take an everyday knowledge claim like M1

to derive a substantive metaphysical conclusion like MC with anti-skeptical consequences. In particular, the

most intriguing aspect of Moore’s Method is that the transition from the everyday knowledge claim to the

substantive metaphysical conclusion is not mediated by extensive philosophical theorizing. As Crispin Wright

and others point out, Moore’s justification for M1 is perceptually based, while the justification for M2 is based

on the meaning of the word ‘hand’.4 Thus, Moore’s Method does not require the heavy philosophical machinery

as so many other well-known responses to skepticism do, e.g., Descartes’ proof of God as an epistemic

guarantor, Locke’s appeal to inference to the best explanation, a transcendental deduction of the sort Kant

1 Annalisa Coliva, “The Paradox of Moore’s Proof of an External World,” The Philosophical Quarterly 58, no. 231 (2007): 234–243. I have added ‘material’ here to clarify a contrast which will later become important. It is clear that Moore takes hands to be examples of “material” or “physical objects”. Indeed, Crispin Wright suggests that the proof depends on the “conceptual necessity that any hand is a material object existing in space.” (Crispin Wright, “The Perils of Dogmatism,” Themes from GE Moore: New Essays in Epistemol-ogy and Ethics, 2007, 25–48. At 26.) Moore, as I understand him, takes it that there can be external objects that are not physical or material objects. Moore appeals to shadows as an example of objects which are not material or physical, but can be met in space. 2 Anonymous, “Validity and Soundness,” International Encyclopedia of Philosophy, n.d., https://www.iep.utm.edu/val-snd/.3 Even those sympathetic to Moore’s Proof, e.g., James Pryor, believe that it is not successful against the determined skeptic. Pryor, however, says the fault lies with the skeptic not with the proof. James Pryor, “What’s Wrong with Moore’s Argument?,” Philosophical Issues 14, no. 1 (2004): 349–378.4 Wright, “The Perils of Dogmatism.”

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proposes, Wittgenstein’s hinge propositions, etc. A homely analogy: The promise of Moore’s Method is similar

to that of someone telling you that your daily, frustrating, 55-minute commute to work can be shortened to a

mere ten minutes by taking a little-known back route. It is easy to imagine being intrigued by the claim, even if

one is very doubtful.

To explain the strategy of this paper it will be necessary to make a preliminary contrast between

dogmatism and skepticism (the contrast will be discussed further in section 8). Following the Ancients, we will

understand ‘dogmatism’ as the view that one has justified belief about some philosophical position P.5 Moore,

then, is a dogmatist in this sense, since he believes that he has justified belief about MC. We will understand

‘skepticism’, as Sextus Empiricus suggests, as a view involving (at least) the suspension of belief about

substantive philosophical conclusions.6 So, for example, the skeptic who suggests that Descartes’ evil demon

could be tricking us into believing we have hands is not a dogmatist about the evil demon hypothesis. Rather,

the idea behind this form of underdetermination skepticism is that MC has no more going for it, evidentially

speaking, than the evil demon hypothesis, so one ought to suspend judgment about which view is true.7

Rather than taking the customary route, which involves considering directly whether Moore’s Proof is

successful against the skeptic, I shall take an indirect approach. The basic point I shall try to develop is that if

we allow that Moore’s Method can be used to support Moore’s Proof, then we should accept that Moore’s

Method can be used to support a variety of incompatible forms of dogmatism. I shall refer to this as “the

problem of many proofs”. The problem of many proofs, I claim, stems from the theory-ladenness of perception.

I shall argue further that this plethora of dogmatic proofs for incompatible positions leads to a darker form of

skepticism, one which maintains that each of the dogmatic views is probably false. We will conclude by

considering various ways a Moorean might respond to these difficulties.

2. Moore’s Standards for Proof Moore maintains there are three necessary conditions for a successful proof:

Of course, it would not have been a proof unless three conditions were satisfied; namely (1) unless the premiss which I adduced as proof of the conclusion was different from the

5 Sextus Empiricus, Outlines of Scepticism (Cambridge: Cambridge University Press, 1994). This use of ‘dogmatist’ is substantially different from other uses of the term, see for example: Chris Tucker, Seemings and Justification: New Essays on Dogmatism and Phenomenal Conservatism (Oxford University Press, 2013).6 I say “at least” since, as we shall see below, there is a “darker” form of skepticism that recommends a stronger reaction to the claims of dogmatists, namely: the dogmatists’ views are wrong, or probably wrong. 7 For more on underdetermination skepticism see Duncan Pritchard, Epistemic Angst: Radical Skepticism and the Groundlessness of Our Believing (Princeton University Press, 2015).

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conclusion I adduced it to prove; (2) unless the premiss which adduced was something which I knew to be the case, and not merely something which I believed but which was by no means certain, or something which, though in fact true, I did not know to be so; and (3) unless the conclusion did really follow from the premiss.8

It is clear that Moore’s Proof meets conditions 1 and 3. As Moore notes in his discussion of his proof, the fact

that M1 is different from MC follows from the fact that MC could be true, while M1 is false. And condition 3 is

clearly met, for if we assume there is no equivocation in the argument, then the conclusion clearly follows as an

instance of modus ponens.

For those who take skepticism about the external material world seriously, condition 2 appears to be the

most contentious of Moore’s claims for his proof. In defense of 2, Moore suggests:

(2) I certainly did at the moment know that which I expressed by the combination of certain gestures with saying the words 'Here is one hand and here is another'. I knew that there was one hand in the place indicated by combining a certain gesture with my first utterance of 'here' and that there was another in the different place indicated by combining a certain gesture with my second utterance of 'here'. How absurd it would be to suggest that I did not know it, but only believed it, and that perhaps it was not the case! You might as well suggest that I do not know that I am now standing up and talking - that perhaps after all I'm not, and that it's not quite certain that I am!9

Moore’s defense here is mostly rhetorical bluster rather than an argumentative defense of 2.10 After all, if the

skeptic is right, then it is not absurd to suggest that Moore does not know that he has hands.11

In any event, a little later in the essay Moore makes a crucial move to bolster his case. He considers the

objection that 2 is not met because he has not proved the premises of his argument. Moore’s retort here is that “I

can know things, which I cannot prove…”12 So, Moore’s position is that proof is not necessary for knowledge.

In other words, the following conditional is false: if S knows that P, then S can prove that P.

A sympathetic reading suggests the following assessment of the dialectic, at least as Moore sees it. The

skeptic demands a proof of the premises as a condition of knowing the premises, but this assumes that proof is

8 George Edward Moore, “Proof of an External World,” in Philosophical Papers (Routledge, 1993), 147–70. 1669 Moore. 166-7.10 Some commentators try to bolster Moore’s argument here by referring to other anti-skeptical work by Moore. In particular, Moore at various stages of his career asserted that the skeptic’s position depends on assumptions that are less certain than his appeal to everyday claims like “Here is a hand”. I do not address this point directly in the paper. See, for example, James Owen Weatherall, “On GE Moore’s ‘Proof of an External World,’” Pacific Philosophical Quarterly 98, no. 2 (2017): 219–250.11 Below, we will consider this passage further in terms of a potential ambiguity. 12 Moore, “Proof of an External World.” 170.

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necessary for knowledge. Since, according to Moore, proof is not necessary for knowledge, the skeptic’s case

against Moore’s knowledge claim fails.13

3. Two More Proofs In this section, we will examine two additional proofs for different metaphysical conclusions using

Moore’s Method. Like Moore, the proponents of these views are dogmatists: they believe that they have

justified belief about their philosophical views.

Imagine a possible world where Berkeley’s metaphysical view had achieved a certain cultural

hegemony. At least part of our thought experiment can be grounded in actual historical events. In 1725 Bishop

Berkeley initiated a project to found a college in Bermuda for the training of missionaries in the new world.

Bermuda was selected in part for its isolation, which would make the education of its students easier (since it

would be harder for them to run away):

To what hath been said, it may not be improper to add, that young Americans, educated in an island at some distance from their own country, will more easily be kept under discipline till they have attained a compleat education, than on the continent; where they might find opportunities of running away to their countrymen, and returning to their brutal customs, before they were thoroughly imbued with good principles and habits.14

Berkeley failed to raise sufficient funds for his project, but imagine Berkeley succeeded in founding a college.

The university, of course, taught Berkeley’s immaterialism. Suppose a plague developed several decades later,

wiping out most of the human population. Bermuda was spared during the initial onslaught because of its

relative isolation. By the time the virus reached Bermuda it had lost most of its virulence: only 5% of the

Bermuda population succumbed to the virus, as opposed to 99.8% in most parts of the world. The people of

Bermuda believed they were spared because of their belief in the true teachings of Berkeley. Belief in a material

world came to be identified with the beliefs of those who suffered from the plague and were damned by God.

Suppose after a few hundred years, a few rogue philosophers raise skeptical doubts about immaterialism.

They wonder how one might prove common sense (i.e. immaterialism) against skeptical worries that perhaps

we should suspend belief about immaterialism, since it seems possible that what everyone sees is a material

world. These rogue philosophers are not dogmatic about materialism: they simply ask what reason there is to

13 Annalisa Coliva, “Moore and Mooreanism,” Skepticism: From Antiquity to the Present, 2018, 467.14 George Berkeley, A Proposal for the Better Supplying of Churches in Our Foreign Plantations and for Converting the Savage Americans to Christianity. By George Berkeley (H. Woodfall, 1725). 6

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favor the immaterial world hypothesis over the material world hypothesis. A philosopher named G. E. Less, a

devout follower of Berkeley, offers the following response in his “Proof of an Immaterial World”:

Less’ Proof of an Immaterial World L1: Here is a hand.L2: If there is a hand, then there is an immaterial world. LC: There is an immaterial world

We can imagine that Less defends his proof in much the same way as Moore: Less notes that condition 1 is met,

since the conclusion could be true, while L1 is false. And condition 3 is met if we assume the argument does not

contain an equivocation, for then it is valid by modus ponens. And finally, in defense of condition 2, Less

claims to know the premises even though he cannot prove them.15,16

For the third proof, suppose that a group of physicists become convinced that our reality is some virtual

reality created by some more technologically advanced person or persons. They reason from results in physics

that indicate our reality is a projection from a deeper reality, and they also believe that the virtual reality

hypothesis is the only plausible explanation for the Fermi paradox.17 This is the foundation of their metaphysical

view: virtualism. They isolate themselves on some remote island in the south Pacific and all inhabitants sing,

with sincerity in their hearts, in praise of the technologically advance race, in the hopes that this will encourage

the system operators to continue our virtual reality. Several generations later a few rogue philosophers in their

community raise skeptical doubts about virtualism. They wonder how one might prove common sense (i.e.

virtualism) against skeptical worries that what we see is a material world. These rogue philosophers are not

dogmatic about materialism: they simply ask what reason there is to favor the virtual world hypothesis over the

material world hypothesis. The most philosophical amongst the community, Neo (named after the protagonist in

15 Below, we will consider the point that it is not sufficient to be in a position to claim knowledge, one must actually know the premises. 16 Before one gets too excited about the prospect of dismissing this as a mere thought experiment, recall that even the most cursory review of the history of human thought reveals that there is a plethora of views about the ultimate nature of reality. There is a long tradition of idealism in Hindu and Buddhist thinking (Poolla Tirupati Raju, Idealistic Thought of India, vol. 14 (Routledge, 2013).) Animism, the idea that reality is infused with spirits rather than dead matter, is also a common metaphysics (N. Bird-David, “Animism Revisited: Personhood, Environment, and Relational Epistemology,” Current Anthropology 40 (1991): 67–91. Some Australian Aboriginals believe that rocks listen (Elizabeth A. Povinelli, “Do Rocks Listen? The Cultural Politics of Apprehending Australian Aboriginal Labor,” American Anthropologist 97, no. 3 (1995): 505–518.) My point here is simply that it is wrong to suppose that a material metaphysics is somehow the default metaphysical view of reality. I am not making the claim that each of these views is true, or epistemically on par with a material metaphysics. 17 See [Author Reference].

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the Matrix movie series), is tasked with responding to such skeptical worries before the rest of the community is

infected with heresies. Neo offers the following response in his “Proof of a Virtual World”

Neo’s Proof of Virtual World N1: Here is a hand. N2: If there is a hand, then there is a virtual world. NC: There is a virtual world.

Neo defends his proof in much the same way as Moore and Less: Neo notes that condition 1 is met,

since the conclusion could be true, while N1 is false. And condition 3 is met if we assume the argument does

not contain an equivocation, as it is then valid by modus ponens. And finally, in defense of 2, Neo claims to

know the premises even though he cannot prove them.

Word eventually gets out that there are three conflicting proofs about the world. The Dogmatist

International Conference is convened in an attempt to settle the matter. As you can imagine, Moore, Less, and

Neo are the keynote speakers. Hands fly everywhere in support of grand metaphysical consequences. But, alas,

nothing is settled. Moore is no more convinced of idealism by Less’ demonstration than Less is convinced by

Moore’s demonstration. All parties accuse the other disputants of mere hand waving, rather than properly

engaging in the dialectic.

4. The Conditional Premises Our three dogmatists each appeal to Moore’s Method, but at most only one can know his preferred

metaphysical view. After all, assuming with Moore that knowing P entails that P is true, it follows that at least

two (putative) knowledge claims are false. In other words, MC, LC, and NC are contraries, so at most one is

true. Since the arguments are in valid form, it follows that at least one premise from at least two of the three

proofs must be false. So it follows that at least two of our heroes falsely claim to know at least one premise

each. Our question then, is whether we can find fault with at least two of the proofs within the framework

Moore has set out, that is, within Moore’s Method. Since all three proofs appear to agree on the first premise,

the obvious place to investigate this issue is with the conditional premise of each. To this task we now turn.

Let’s start by reviewing Moore’s reasoning for M2. It is sometimes suggested that its truth is a

conceptual necessity or a linguistic truth. Thus, Wright argues that its truth is founded on “the conceptual

necessity that any hand is a material object existing in space.”18 Moore appeals to (putative) linguistic facts to

18 Wright, “The Perils of Dogmatism.” At 26.6

establish M2. As I understand him, what Moore writes in the following passage about soap-bubbles, which

immediately precedes the proof itself, also applies to the term ‘hand’:

If I say of anything which I am perceiving, 'That is a soap-bubble', I am, it seems to me, certainly implying that there would be no contradiction in asserting that it existed before I perceived it and that it will continue to exist, even if I cease to perceive it. This seems to me to be part of what is meant by saying that it is a real soap-bubble, as distinguished, for instance, from an hallucination of a soap-bubble….That is to say, from the proposition with regard to anything which I am perceiving that it is a soap-bubble, there follows the proposition that it is external to my mind. But if, when I say that anything which I perceive is a soap-bubble, I am implying that it is external to my mind, I am, I think, certainly also implying that it is also external to all other minds: I am implying that it is not a thing of a sort such that things of that sort can only exist at a time when somebody is having an experience. I think, therefore, that from any proposition of the form 'There's a soap-bubble!' there does really follow the proposition 'There's an external object!' 'There's an object external to all our minds!'19

As noted, Moore thinks the same reasoning applies to the use of the word ‘hand’. That is, Moore’s position is

that just as part of what we mean by ‘soap-bubble’ is that it is a material thing that may exist independently of

being perceived, so too does ‘hand’ have as part of its meaning the idea of a material thing that may exist

independently of being perceived by anyone. The trouble is that it appears to be appropriate to use ‘hand’ in

reference to immaterial things. Consider in Dickens’ A Christmas Carol, Scrooge asks: “"I am in the presence

of the Ghost of Christmas Yet To Come?" The Spirit answered not, but pointed onward with its hand.”20 It

would seem that in writing this passage, Dickens is very confused about the nature of hands if Moore is correct,

since hands are material objects. After all, ghosts are not material, but immaterial beings. Similar things might

be said of virtual reality: the writers of the movie The Matrix have little compunction about referring to the

things at the end of the virtual arms as ‘hands’. Perhaps it will be remarked on Moore’s behalf that these are

non-standard—possibly metaphorical—uses of the word ‘hand’. Fortunately, as we shall see, we need not

decide the controversy about the meaning of the word ‘hand’.

To clarify further what is at issue, some stipulative definitions will help. Let us define an ‘mhand’ as the

sort of thing that looks like what Moore is waving when promulgating M1, and is constituted by material stuff.

An ‘ihand’ we will define as the sort of thing that looks like what Less is waving when promulgating L1 and is

constituted by immaterial stuff. A ‘vhand’ we will define as the sort of thing that looks like what Neo is waving 19 Moore, “Proof of an External World.” 164.20 Charles Dickens, Christmas Carol (Alma Books, 2018). P. 64. Dickens appears to leave open the possibility that the ghosts are merely dreamt, which would satisfy the idea that they exist only so long as they are perceived.

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when promulgating N1 and is a virtually generated by a computer. Finally, a ‘dhand’ refers to the disjunction of

mhand, ihand, and vhand. Thus, the following conditionals are true: If X is a dhand, then X is either an mhand,

ihand, or vhand; if X is an mhand, then X is a dhand; if X is an ihand, then X is a dhand, and if X is a vhand,

then X is a dhand. The converse of the last three conditionals are false.

Suppose the word ‘hand’ in English means something like ‘dhand’. In which case we have a tidy

explanation how it is that Dickens and the writers of The Matrix are not confused about the meaning of the term

‘hand’. But also, if ‘hand’ means ‘dhand’, then clearly M2 is false. After all, instances where there are ihands or

vhands only are instances where the antecedent is true and the consequent false.

Let us grant that Moore is correct that in his dialect of English, ‘hand’ is a synonym for ‘mhand’.

Admittedly, this does not amount to much of a concession, for even if Moore is wrong about this, he could

simply stipulate that he means ‘mhand’ by ‘hand’.

When we turn to Less’ and Neo’s conditional premises, the pressure to think there may be different

meanings for the word ‘hand’ only increases, for if ‘hand’ means ‘mhand’ in their dialects, then both Less and

Neo have greatly misunderstood the extension of the term. And if ‘hand’ means something like ‘dhand’ in their

dialects, then their second premise is false, just as M2 is false under this condition. Extending the same charity

to Less and Neo, let us grant that in Less’ dialectic, ‘hand’ means ‘ihand, and in Neo’s dialectic, ‘hand’ means

‘vhand’.

5. The non-Conditional Premise The upshot of the previous section is that if we are to avoid any misunderstanding about what the word

‘hand’ might mean, then we should restate, using stipulative definitions, the conditional premise of three proofs.

Just to be clear: there is no pretense here that these reformulations do anything towards the task of clarifying

what ‘hand’ means in ordinary English. Rather, the problem is simply bypassed. Obviously, this means that the

non-conditional premise must also be reformulated to preserve cogency. The proofs, then, can be rewritten as:

Moore Less Neo

M1*: Here is an mhand. M2*: If there is an mhand, then there is an external material world. MC: There is an external material world.

L1*: Here is an ihand.L2*: If there is an ihand, then there is an immaterial world. LC: There is an immaterial world

N1*: Here is a vhand. N2*: If there is a vhand, then there is a virtual world. NC: There is a virtual world.

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Since the definitions are stipulative, there is no reason to suppose that Moore, Less, or Neo have any

reason to deny the second premise of any of the redux proofs, since the conditionals are now analytically true in

virtue of the stipulative definitions.

The residual disagreement is about the non-conditional premise. As we noted above, the first premise is

asserted based on perceptual justification. Applying this insight to the reformulated argument, we should

understand Moore as claiming that his knowledge of M1* is based on the fact that it perceptually appears to him

that he has an mhand. Similarly, it appears to Less that he has an ihand, and to Neo that he has a vhand.

As noted above, my contention is that the dispute about the first premise of each proof is best explained

in terms of the doctrine of theory-ladenness of observation. To this doctrine we now turn.

6. Theory-Ladenness of Observation and the Bracketing Method In his seminal discussion of the theory-ladenness of observation, N. R. Hanson concludes:

There is a sense, then, in which seeing is a ‘theory-laden’ undertaking. Observation of x is shaped by prior knowledge of x. Another influence on observation rests in language or notation used to express what we know, and without which there would be little we could recognize as knowledge.21

As Hanson indicates, both knowledge and language might influence what we observe. The former we

will refer to as ‘doxastic loading’ and the latter as ‘semantic loading’. According to proponents of the theory-

ladenness of observation, if perceptual reports are doxastically loaded or semantically loaded, then we have

reason to believe that observation is not appropriately neutral when it comes to theory adjudication.

To illustrate the ideas of doxastic and semantic loading in a non-scientific context, consider the

following example. Four friends are at a coffee shop when one asks, “Don’t you people know the person across

the street?” In unison, the other three make contrary assertions: “Yes, there’s Bill”, “Yes, there’s Dill”, and

“Yes, there’s Phil”. The explanation for the disagreement is that the three friends did not know that Bill, Dill,

and Phil are identical triplets.

We may think of this example as competing theories—the Bill, Dill, and Phil hypotheses—about the

identity of the person across the street. Let us assume that from that distance, Bill, Dill, and Phil are

perceptually indistinguishable: to the unaided human eye there are no visual features that can be detected which

distinguish Bill, Dill, and Phil. Given this proviso, it is clear that the contrary assertions of the three friends are

21 Norwood Russell Hanson, Patterns of Discovery: An Inquiry into the Conceptual Foundations of Science (Cambridge University Press, 1965).

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not to be explained solely in terms of what they perceive, and that there are no additional considerations that

might favor thinking it is one triplet in particular, for example, knowing that two of the three left for Antarctica

a couple of days ago. Rather, the difference should be explained in terms of doxastic loading: the three friends

were introduced to a different triplet and they had no idea that the person they previously had been introduced

to (either Bill, Dill, or Phil) was an identical triplet. The relative rarity of identical triplets in part explains their

confidence that the person they report seeing is the one person they were previously introduced to. This doxastic

loading goes together with semantic loading: the observational reports— “Yes, there’s Bill”, “Yes, there’s Dill”,

and “Yes, there’s Phil” —are not neutral amongst the three theories about the identity of the person across the

street.

The doxastic and semantic loading of the three friends can straightforwardly be neutralized. We might

imagine they revise their observation reports once they find out that the person they known is an identical

triplet. They might “disjunctively bracket” their revised version of what they see as follows, “Yes, the person

across the street is either Bill, Dill, or Phil”. Similarly, if the three friends believe the disjunctive bracket rather

than their original observation reports, this would remove the previous doxastic loading in favoring one of the

three triplets.

There are at least two senses in which observational reports might be neutral. The more ambitious form,

absolute neutrality, aims for observational reports that make no theoretical commitments. It may well be that

this standard cannot be met. Dispute neutrality is the less ambitious standard: it seeks to neutralize the doxastic

and semantic loading when it comes to a particular dispute. To describe the person across the street as either

Bill, Dill, or Phil is not dispute neutral, since such a description is not neutral in the dispute between the three

friends. Describing what they see as “a person” is dispute neutral, since all three agree that they see a human

across the street. But describing what they see as a human is not absolutely neutral as such a description is

loaded against the possibility that what they see is not a human, e.g., an alien made to look like a human, a

shared hallucination, a shared illusion, etc. Our concern here is with dispute neutrality, so we need not weigh in

on the possibility of absolute neutrality of observational reports.

The fact that observation does not confirm which of the three triplets is across the street does not mean

that further observations cannot adjudicate the debate, e.g., perhaps on closer inspection Bill, Dill, and Phil can

be identified by their tattoos, or by simply asking the person across the street his name.

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Given the stipulations of the example, it would be epistemically irrational for the friends to continue to

believe that their original belief was correct. The stipulations, again, are that perceptual evidence does not favor

one hypothesis about what they see over the other two, that there is no additional evidence (e.g., that two of the

three left the country two days ago for Antarctica) that favors a verdict about one triplet over the other two, and

that at most one of the three friends can be correct. Under these conditions, the rational thing to believe is that

the person they see is probably not Bill, Dill, or Phil even if it is very highly probable that it is one of the three

triplets.22 So, given these stipulations, each friend should think that she was probably wrong in her initial

judgement of who she saw.

7. The Three Proofs and the Bracketing Method The metaphysical analogue of disjunctive bracketing in the Bill, Dill, or Phil example is as follows:

Dispute Neutral Proof (DNP)

TN1: Here is a dhand (that is, an mhand, or an ihand, or a vhand). TN2: If there is a dhand, then there is an external material world, an immaterial world, or a virtual world. TNC: There is an external material world, an immaterial world, or a virtual world.

Whether further observations might adjudicate the dispute is a more contentious question. Movies like

The Matrix, The Thirteenth Floor, etc., suggest that it is possible to obtain observational evidence that strongly

supports the idea one is, or was, in a virtual simulation. With the help of God, one might put Berkeley’s

hypothesis to the test, e.g., imagine asking God not to see a ring locked in a box. The thought behind this test is

that if esse est percipi, then the ring ought to be absent when the box is reopened. Another possibility is to

upgrade our epistemic capacities: Kant considers the possibility that God and the angels have better epistemic

capacities in the form of an intellectual intuition that would allow them to know things in themselves.23

Presumably this sort of upgrade would allow us to adjudicate in favor of one particular disjunct in DNP.

Whether there are possible observations that confirm or refute the metaphysical hypotheses is of little

consequence for the argument. Even if we can’t in principle determine which theory is true, it is still the case

that the three hypotheses are contraries. Similarly, it is the case that the person across the street is either Bill,

Dill, or Phil, even if it turns out to be impossible to verify or falsify who it is. (Imagine a meteorite wipes out

22 I take it that this is the sort of belief we might have about the epistemic possibility of a set of lottery tickets: each is probably not the winner even if we belief that the winner is amongst the set of lottery tickets. 23 See [author reference].

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the person across the street and his two brothers waiting in a nearby car. With all physical evidence destroyed, it

would remain forever a mystery which of the three triplets was standing across the street.)

Suppose Moore, Less, and Neo grant the following claims: (i) perception is the sole source of

justification for the non-conditional premise of each argument, (ii) their initial proofs are dispute theory-

ladened, and (iii) that there can be at most one successful proof. Under these conditions our heroes should

accept they should renounce their original views and accept DNP. That is, they should accept that each

metaphysical hypothesis is probably false, since it has less going for it, evidentially speaking, than the

combined epistemic probability that one of the other two hypotheses is true.24 In other words, it would be

epistemically irrational to grant these assumptions and continue to believe that their preferred view is justified.

Moore, Less, and Neo should each think that each of the hypotheses is probably false.

8. Skepticism, Dogmatism, and Skeptical-Dogmatism In this section, I hope to situate the dialectic thus far in terms of skepticism, dogmatism, and a third

position we have yet to consider: skeptical dogmatism.

Starting with skepticism, we should distinguish it in terms of both scope and strength. In terms of scope,

the most general form of skepticism, “global skepticism about perception”, questions the competency of

perception to deliver justification for any of our perceptually based beliefs. This seems to be the sort of

skepticism that many commentators on Moore have in mind.25 A more limited form of skepticism, metaphysical

skepticism, limits skepticism to the claim that perception alone is not sufficient to adjudicate between

competing metaphysical explanations as to the ultimate metaphysical cause of our perception. By ‘metaphysical

explanations,’ I mean the sorts of different explanations that Moore, Less, and Neo offer in terms of the causes

of our experience.

For present purposes, there are two relevant “strengths of skepticism”. The first is the idea of suspending

judgement about whether P is true, or not-P is true. This is the sense, noted above, endorsed by the ancient

24 Note that this is weaker than the Laplacian assumption that all three are equiprobable. The principle here says simply that no one possibility is more likely than the combined probability of the other two possibilities. 25 This point will be explored below.

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skeptics like Sextus Empiricus.26 Let us refer to this as ‘agnostic skepticism’.27 The second is the idea that one is

a skeptic about P if one holds that one is justified in believing that P is false or probably false. Let us refer to

this as ‘error skepticism’. Both forms of skepticism suggest doubt about some dogmatic claim P. In the case of

agnostic skepticism, one doubts P because one finds no reason to think that P is true or more likely true than

not. In the case of error skepticism, the idea is that there is reason to think that P is false, or probably false.

Let’s think of error skepticism about each of three or more contrary positions to a particular question as

‘skeptical dogmatism’. The most straightforward version of skeptical dogmatism is one where each disputed

position is equally probable. Think again about the case of Bill, Dill, and Phil. Assuming they are the only three

candidates, then in credence talk, this would amount to a credence of 0.33 that the three friends are looking at

Bill, 0.33 credence that they are looking at Dill, and 0.33 credence that they are looking at Phil.28 Skeptical

dogmatism is consistent with unequal probabilities of each of the contraries, so long as no one hypothesis is

equal or more probable than the combined probability of the other two. So, skeptical dogmatism is consistent

with a much higher credence in the Bill hypothesis as compared individually with the other two, e.g., a credence

of 0.48 in the Bill hypothesis, with only a 0.26 credence in the Dill hypothesis, and a 0.26 credence in the Phil

hypothesis. Even with the much higher credence in the Bill hypothesis, it is still the case that it is true that each

hypothesis is probably false, hence, this qualifies as skeptical dogmatism.

Applying this to the dialectic, our three heroes started out as dogmatists about their preferred

metaphysical positions and thus as so committed to the rejection of global and metaphysical skepticism about

perception. As noted above, Wright (among others) emphasizes it is the thought that it perceptually appears to

Moore that he has hands that underwrites M1.29 This shows that global perceptual skepticism is off the table for

Moore, as he thinks that perception provides justification for M1. And indeed, metaphysical perceptual

skepticism is off the table as well, since Moore believes perception justifies his belief that M1 is true over

competing metaphysical explanations. Similar points apply to the thinking of Less and Neo. That is, Less does

26 Sextus says, “The Skeptic Way is a disposition to oppose phenomena and noumena to one another in any way whatever, with the result that, owing to the equipollence among the things and statements thus opposed, we are brought first to epoché and then to ataraxia…..By "equipollence" we mean equality as regards credibility and the lack of it, that is, that no one of the inconsistent statements takes precedence over any other as being more credible.” Benson Mates, The Skeptic Way (New York: Oxford University Press, 1996).27 Empiricus, Outlines of Scepticism. Some writers insist that this is the only sort of skepticism that properly deserves the name, e.g., Annalisa Coliva, Moore and Wittgenstein: Scepticism, Certainty, and Common Sense (Palgrave MacMillan, 2010).28 To translate this to belief talk, the idea would be to believe “there is an epistemic probability of 0.33 for each hypothesis”. 29 Wright, “The Perils of Dogmatism.” P. 6.

13

not doubt that perception is competent to deliver knowledge of LC, and Neo does not doubt that perception is

competent to deliver knowledge that NC is true.

Although dogmatists about their preferred positions, Moore, Less, and Neo are error skeptics about the

positions of their colleagues. Moore, for example, is a dogmatist about MC and an error skeptic about LC and

NC. As noted, this is just the trivial point that if one is a dogmatist about one’s position, one is rationally

committed to doubting logically contrary positions.

We noted above that where Moore, Less, and Neo accept (i), (ii), and (iii) they should accept that each

metaphysical hypothesis (MC, LC, and VC) is probably false, since it has less going for it evidentially speaking

than the combined epistemic probability that one of the other two hypotheses is true. This amounts to the claim

that under these circumstances they should be skeptical dogmatists about the three metaphysical positions.

Taking the most straightforward version of skeptical dogmatism, this amounts to a credence of 0.33 that MC is

true, a 0.33 credence that LC is true, and a 0.33 credence that NC is true.30

A couple of consequences should be noted. First, it has been suggested by some that the alternative to

dogmatism about MC is global skepticism.31 Our discussion shows this is a false dilemma. One can consistently

reject global skepticism about perception while endorsing metaphysical skepticism. That is, although as

skeptical dogmatists they agree that their current stock of perceptual evidence is not sufficient to rule in favor of

one metaphysical hypothesis to the exclusion of others, they need not, and let us suppose do not, doubt the

competency of perception to provide any information about the environment. Imagine, for example, the three

walking down the street deep in discussion about these issues. There is no inconsistency if the three thank you

for the warning that they should look where they are going because they are about to walk into either a material

mailbox, an immaterial mailbox, or a virtual mailbox. The point of course is that it doesn’t matter for such

practical purposes which of the hypotheses is true: it will hurt to walk into it no matter which metaphysical

hypothesis of the three disputed metaphysical hypotheses is true. Perception is not so unreliable that it cannot

alert us to the fact that there is either a material, immaterial, or virtual mailbox to be avoided.

30 To translate this to belief talk, the idea would be to believe “there is an epistemic probability of 0.33 for each hypothesis”. 31 Pryor writes, “We’ve focused on the skeptic who doubts whether our perceptual experiences give us any justification at all for our perceptual beliefs. (Pryor, “What’s Wrong with Moore’s Argument?”). Crispin Wright writes, “It is of paramount importance to us to find our way around the world, make use of its resources, avoid danger, and so on. If we are to do these things, we need to be able to form reliable beliefs about the locations and dispositions of material objects. Crispin Wright, “Warrant for Nothing (and Foundations for Free)?,” in Aristotelian Society Supplementary Volume, vol. 78, 2004, 167–212. At 186.

14

Consider the distinction between global and metaphysical skepticism in connection with this passage

from Moore (quoted above):

How absurd it would be to suggest that I did not know it [here is one hand, and here is another], but only believed it, and that perhaps it was not the case! You might as well suggest that I do not know that I am now standing up and talking - that perhaps after all I'm not, and that it's not quite certain that I am!32

The rhetorical force of this quote seems stronger against global perceptual skepticism: on this reading, Moore

should be understood as saying that it would be absurd to doubt that perception can deliver knowledge that there

even is a dhand or that, using the same disjunction bracketing strategy, that Moore is dstanding or dtalking. Yet

a commitment to metaphysical skepticism does not commit one to deny that Moore knows that there is a dhand,

or that he is dstanding or dtalking. Moore has done little to show why we should think it is absurd to deny “here

is an mhand” when we allow that “here is a dhand”, that is, to show why metaphysical skepticism is absurd

when we admit that global skepticism about perception is absurd.

Second, agnostic skepticism is not at issue at any point in the dialectic. As noted, in the original version

of the dispute, our three heroes are dogmatists. When using the disjunctive bracketing strategy, agnostic

skepticism is also not at issue. Recall that agnostic skepticism says that we should suspend judgment in cases

where P and not-P are equally probable. Yet, when the three use the disjunctive bracketing strategy, P and not-P

are not equally probable. If, for example, we let P = LC, then P and not-P are not equally probable. The reason

is that the probability of not-P is the probability of (MC or NC), which, by supposition is greater than the

probability of LC. So, agnostic skepticism is not at issue; rather, skeptical dogmatism is called for.

We might describe the form of skepticism we are left with as ‘metaphysical skeptical dogmatism about

perception’. It is ‘metaphysical’ rather than ‘global’ because we have not challenged the competency of

perception in general. It is skeptical dogmatism, rather than the more familiar agnostic skepticism, because the

verdict is not to suspend judgment about each of the metaphysical views but to take the dogmatic and skeptical

attitude that each is probably false.

32 Moore, “Proof of an External World.” 166-7.15

9. Too Many Proofs Philosophy is, or often seems to be, the art of the least bad choice. If this is the case, then even if one

finds metaphysical skeptical dogmatism an unappealing result, this need not be a decisive point against it, since

to be the best choice, metaphysical skeptical dogmatism need only be the least bad choice.

The dialectic thus far indicates that the question of whether we should adopt the disjunctive bracketing

strategy, and so accept metaphysical skeptical dogmatism, resolves to the question of whether there is a more

favorable response to the problem of many proofs. To this end we will examine rejecting (iii) in this section,

and in the following section, consider the plausibility of rejecting (i) or (ii).

Rejecting (iii)—the idea that there can be at most one successful proof—immediately relieves the

dialectical pressure that leads to skeptical dogmatism. Here we might imagine that Moore says that he has a

perfectly good proof for MC, but this does not impugn Less’ claim to have a perfectly good proof for LC, and

Neo’s claim for a perfectly good proof for NC.

One consequence of rejecting (iii) is that paradox seems to follow. On the one hand, if Moore’s Method

works, then there is a perfectly good proof that LC is true. For example, we noticed that Less is entitled to take

an ordinary claim, like “Here is an ihand”, and derive a substantive metaphysical conclusion: LC is true. But if

LC is true, then Moore’s Method provides a proof that MC and NC are false, since MC and NC are contraries of

LC. On the other hand, Moore’s Method provides perfectly good proofs that MC and NC are true. If LC and NC

are true, then Moore’s Method proves that LC is false. So, Moore’s Method maybe be used to prove that LC is

both true and false.33

Even putting the very serious problem of paradox aside, a second consequence seems to be that Moore’s

Method does not offer a non-arbitrary answer to which metaphysical hypothesis to endorse. Imagine Danielle

has grown up in disjunction land. Denizens of disjunction land do not favor any of the three particular

metaphysical views: they are metaphysical skeptical dogmatists about perception. When they say ‘hand’ they

mean ‘dhand’. Danielle rejects her heritage as too skeptical. She feels a metaphysical yearning to commit to a

particular metaphysical hypothesis. It seems that Moore’s Method offers little guidance here. As we have seen,

Moore, Less, and Neo follow the same methodology to different conclusions. For Danielle, with her heart set on

33 I won’t consider here the possibility of relativizing truth or proof to a “framework”, a “form of life”, etc. to relieve the paradox. 16

endorsing a particular metaphysical hypothesis, there are too many proofs. It seems entirely arbitrary, from an

epistemic perspective, for Danielle to endorse LC, MC, or NC over the other two.

10. Unique Proof More plausibly, let us imagine that proponents of Moore’s Method agree that if Moore’s Method is

viable, then it must provide a unique proof. One line of thought in support is that Moore’s Method, as described

above, does not actually capture what is essential to Moore’ Proof. Moore’s Method, according to this line of

objection, assumes that confidentially claiming knowledge about some everyday proposition is sufficient for

proof. But the fact that Less, Neo, and Moore all confidently claim knowledge that L1*, N1*, or M1* is true,

does not suffice for knowledge. Indeed, since we know that L1*, N1*, or M1* are contraries, it follows that at

most one of the three claims is true. So at most only one of Less, Neo, or Moore has knowledge of the first

proposition of his proof.

The idea, then, is that we should understand Moore as advocating “Moore’s Alethic Methodology”,

which works as follows: anti-skepticism can be supported by invoking knowledge (rather than merely

confidently claiming knowledge) about an everyday proposition and deriving a substantive metaphysical

conclusion. This immediately relieves the paradox discussed in the previous section. For example, suppose Less

is correct that he knows that he has ihands. It follows that his proof is perfectly consistent with Moore’s Alethic

Methodology. So, the fact that Less knows LC and he knows that LC implies the falsity of MC and NC means

that Less is in a position to know that MC and NC are false. Furthermore, he is in a position to know that Moore

and Neo do not have a proof that meets the standards of “Moore’s Alethic Methodology”. Although it may

appear to Moore and Neo that they have perfectly symmetrical proofs, they do not, because their putative

proofs involve falsehoods. They merely claim to know, but they do not know. Hence, if Less has a proof, then

Moore and Neo do not have proofs—they merely think they do.

Moore’s Alethic Methodology may solve the problems associated with many proofs, but, as already

intimated, in itself it does not show that Moore’s Proof is in fact a proof. Rather, what Moore’s Alethic

Methodology shows is that at most one of the three previous putative proofs is a proof. Moore’s Alethic

Methodology does not tell us which, if any, is the proof. Consider what advice Moore’s Alethic Methodology

might provide to Danielle if she were to make enquires at the Dogmatist International Conference. Naturally,

we would not be surprised if Moore, Less, and Neo all answer in favor of their views in response to her

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enquiries. But, as we have noted, at least two of these answers must be wrong using Moore’s Alethic

Methodology—at least two are not proofs at all. The correct but unhelpful answer is that Danielle should

endorse the view that is true. But this does not tell us which the true view is. This is as helpful as the teacher’s

advice about how to do well on the final exam: “Don’t make any mistakes”. Invoking a strong link between

truth and proof will make whichever is the proof unique, but not necessarily Moore’s version of the proof.

To press the point, consider these three conditionals:

A1: If there is a proof for MC, then Moore knows M1*. A2: If there is a proof for LC, then Less knows that L1*.A3: If there is a proof for NC, then Neo knows N1*.

Let us suppose further that Danielle is aware that at most one of the three metaphysicians is correct. It follows

that Danielle is in a position to know that at most one of the three antecedents is true. But without further

evidence that favors one antecedent over the combined probability of the other two, Danielle is in a position to

justifiably believe that each antecedent is probably false, since each consequent is probably false. So simply

adding a truth requirement to Moore’s Method may solve the problem of too many proofs, but a consequence is

that it only reinforces the argument for skeptical dogmatism.

The lesson then is that what is required is both a reason to think a particular proof is unique, and that

there is reason to favor one metaphysical view over the others. One way to do this would be to deny (i), that is,

the claim that perception is the sole source of justification for the non-conditional premise of each argument. As

noted above, Descartes invoked God to support his version of dogmatism. Some hold that MC is justified in

terms of super-empirical virtues like simplicity.34 Others have thought we have some non-evidential but

epistemic reasons for adopting a particular metaphysical hypothesis.35 But if such considerations are invoked,

then Moore’s Proof changes substantially.

To illustrate, consider the appeal to super-empirical virtues like simplicity. The modified version of

Moore’s proof now claims that M1* is the simplest hypothesis, and the simplest hypothesis is likely true, so it is

likely true that “There is an mhand.” It is arguable to what extent (if any) Moore was attracted by the inference

to the best explanation strategy.36 But suppose for the moment this is something that tempts Moore and 34 Jonathan Vogel, “Cartesian Skepticism and Inference to the Best Explanation,” Journal of Philosophy 87, no. 11 (1990): 658–66.35 Wright, “Warrant for Nothing (and Foundations for Free)?”36 Coliva, “Moore and Mooreanism.” N Lemos, “Moore and Skepticism,” in The Oxford Handbook of Skepticism (Oxford University Press, 2008).

18

Mooreans. Moore’s Supplementary Method, as we might term it, then goes something like this: an ordinary

knowledge claim is conjoined with a philosophical argument, e.g., inference to the best explanation, to a

substantive anti-skeptical conclusion. This would be a disappointing result—to say the least. After all, in effect,

the modified proof in Moore’s mouth becomes: “Here is a hand. And in my other hand is an argument

concerning inference to the best explanation, which shows that the material world hypothesis is the simplest and

so most likely explanation. Therefore, there is a material external world.”

This is (obviously) not the place to adjudicate among all the possible variants of Moore’s Supplementary

Method but the upshot should be clear: if Moore’s Proof relies on one or more of these traditional responses to

skepticism, then much of what is intriguing about Moore’s Proof is thereby vanquished. As we noted above,

Moore’s Proof promises to refute skepticism without the “heavy philosophical machinery” of more traditional

responses to skepticism. But Moore’s Supplementary Method invites the heavy philosophical machinery in

through the backdoor.

The last possible response on behalf of Moore that we should consider is to question (ii) above, namely,

the idea that all three proofs are theory-ladened. The proposal is that there is one non-theory-ladened way to

understand perception advocated by either Moore, Less, or Neo, while the other two bring in extraneous

metaphysical theorizing.

But even granting, for the sake of the argument, that one of the three perceptual reports, M1*, L1*, or

N1* is “pure”, that is, is not metaphysically theory-ladened, still the question remains which one deserves the

crown of the pure observation report. Consider that Berkeley argued strenuously that his view accorded well

with the “rest of mankind”, it is only atheists and philosophers who might find otherwise:

I don’t argue against the existence of any one thing that we can take in, either by sense or reflection. I don’t in the least question that the things I see with my eyes and touch with my hands do exist, really exist. The only thing whose existence I deny is what philosophers call ‘matter’ or ‘corporeal substance’. And in denying this I do no harm to the rest of mankind—·that is, to people other than philosophers·— because they will never miss it. The atheist indeed will lose the rhetorical help he gets from an empty name, ‘matter’, which he uses to support his impiety; and the philosophers may find that they have lost a great opportunity for word spinning and disputation.37

I’m not suggesting that Berkeley is correct here, only that it is far from obvious that we should accept that there

is such a pure observational report, and even if there is such purity to be had, which of the three views deserves 37 George Berkeley, A Treatise Concerning the Principles of Human Knowledge (Hackett Publishing, 1982). Section 35.

19

the crown of the pure observational report. In any event, Moore and the Mooreans have fallen short on two

accounts: (a) they have provided no reason to suppose that there is one such pure observational report, and (b)

that if (a), then M1* deserves the crown of the pure observational report.

Contra the Mooreans, I have suggested above that it is plausible to assume that all three views are

theory-ladened. To put it bluntly, it is not because we see better, or that our perception is purer that explains

why we favor observational reports that favor materialism. Our cultural and linguistic heritage better explains

why we might describe something as an mhand, rather than thinking that there is some metaphysically pure way

of describing what we see. Again, it does not follow that each view is equally good. What follows is that if there

is one preferred theory-ladened view that is more probable than the combined probability of the other two, then

there are non-perceptually based reasons for this. For example, nothing argued here is inconsistent with the

claim that inference to the best explanation shows why a materialist language is more likely to provide a true

description of the world than an idealistic or virtual language.

11. Denouement I have argued that the theory-ladenness of perception leads to a problem for Moore’s Method, namely, it

permits numerous contrary proofs. I’ll conclude with a couple of general points.

First, I’m no historian, and this is not the place in any event for an historical enquiry in any event, but

we can learn something from thinking about Moore’s reaction to the problem of theory-ladenness of

observation. As noted above, the conditional premise in the standard version of Moore’s Proof is rarely

examined, and even less frequently criticized. Suppose, however, that the discussion in the Proof of an External

World was motivated at least in part by Moore’s awareness of how his idealist foes might react to the argument.

This seems a plausible assumption given Moore’s long interaction with idealists in both the empiricist tradition

(Berkeley and some phenomenalists) and in the German tradition (whose influence Moore felt directly with his

connection with Bradley, a British Hegelian). At least some idealists in both traditions thought that their views

were perfectly consistent with common sense. Moore’s effort to claim that there is an analytic connection

between our everyday vocabulary like ‘hand’ and a non-idealist metaphysics can be understood as at least an

indirect criticism of this view. As noted, it is this connection that helps Moore bridge the (seeming at least) gap

between an everyday claim like ‘here is a hand’, to the conclusion that there is a material external world. It

seems that Moore was quite happy to insist that our ordinary language is theory-ladened in this way, since it is

20

the bridge that seems necessary for his argument. The extended discussion of soap bubbles, discussed above,

makes it clear that Moore realized that this was an essential element of his proof.

But even supposing our everyday language is theory-ladened in the way that Moore claims—and I am

far from convinced that it is—it is clear that, like the proverbial bubble in the carpet, this only pushes the

problem somewhere else. The problem then is that it seems we should ask whether the metaphysics of

“common sense” and our everyday language is indeed the correct metaphysics. After all, as we have seen, it is

at odds with other possible languages with different metaphysical assumptions. Recall that we imagined that

Less may insist that ‘hand’ means ‘ihand’, and Neo may insist that ‘hand’ means ‘vhand’. At least in Proof of

the External World, Moore seems completely oblivious to the need to say why his way of describing what he

sees when—to put it neutrally—he holds up a dhand, namely, that he sees an mhand, is the right way to

describe what he has seen. Merely pointing out that common sense language presupposes a materialist

metaphysics works only in conjunction with the thought that common sense is true indicative. But Moore has

given us no reason to think that common sense is truth indicative. In any event, for defenders of Moore, this is a

problem that should be put front and center.

Second, the dialectic we have examined is relevant to the oft-made claim that skepticism raises the

standards for justification or knowledge. By this I mean the familiar criticism that skepticism requires a higher

standard than everyday standards for justification. And while we have found that Moore’s Method seems to

invite a form of skepticism, the “darker” skeptical dogmatism—it is crucial to see that this is a product of a

prior dispute between dogmatists. The relevance here is that dogmatists have a vested interest in not inflating

the standards for justification or knowledge too high, otherwise this seems to load the dialectic in favor of some

form of skepticism. But as we have seen, the perils of lowering the standards is that it may license too many

incompatible forms of dogmatism: a variety of forms of dogmatism might appeal to Moore’s Method. The

means to avoid the problem of many proofs is to raise the standards for justification or knowledge. Yet the

stretch of the dialectic we have examined suggests that adding additional requirements to Moore’s Method

encourages either some form of skepticism or invoking elaborate philosophical machinery to respond to

skepticism. But again, the important upshot here is that this raising of the standards is a result of dogmatists

responding to the challenge of their fellow dogmatists: skepticism is the effect, not the cause. Going forward,

the moral for dogmatists is to aim for a sweet spot—assuming there is one—where the standards for

21

justification or knowledge are not so low as to allow too many proofs, while not being too high to make the

standards impossible to meet. As argued here, the prospects for a particularly Moorean answer to finding the

sweet spot do not look particularly good.

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