The Bishop’s Church: Berkeley’s Master Argument and the Paradox of Knowability

Abstract

We can find in the passages that set out the Master Argument a precursor to the paradox of knowability. That paradox shows that if all truths are knowable, all truths are known. Similarly, Berkeley might be read as proposing that if all sensible objects are (distinctly) conceivable, then all sensible objects are conceived.

1. Introduction

This is Berkeley’s Master Argument as formulated in the Dialogues:

Philonous: … I am content to put the whole upon this issue. If you can conceive it possible for any mixture or combination of qualities, or any sensible object whatever, to exist without the mind, then I will grant it actually to be so.

Hylas: If it comes to that, the point will soon be decided. What more easy than to conceive a tree or house existing by itself, independent of, and unperceived by any mind whatsoever? I do at this present time conceive them existing after that manner.

Philonous: How say you, Hylas, can you see a thing which is at the same time unseen?

Hylas: No, that were a contradiction.

Philonous: Is it not as great a contradiction to talk of conceiving a thing which is unconceived?

Hylas: It is.

Philonous: The tree or house therefore which you think of, is conceived by you.

Hylas: How should it be otherwise?

Philonous: And what is conceived, is surely in the mind.

Hylas: Without question, that which is conceived is in the mind.

Philonous: How then came you to say, you conceived a house or tree existing independent and out of all minds, whatsoever?

Hylas: That was I own an oversight […] I may indeed conceive in my own thoughts the idea of a tree, or a house, or a mountain, but this is all. And this is far from proving, that I can conceive them existing out of the minds of all spirits. (Berkeley 1999, 139–40)

Some (e.g., Prior 1955, Gallois 1974) read the above passage (and the related one in the Principles (Berkeley 1999, 33–34) as, roughly, an attempt to show that all sensible things are conceived, and thus within the mind. Others (e.g., Stoneham 2002, Holden 2019) see Berkeley as merely attempting to rebut a materialist objection to his idealism—that mind-independent matter is surely conceivable and thus possible. Whichever of these tacks we take, it is unclear exactly what Berkeley’s argument is.

On some readings of key claims in the Master Argument, Berkeley makes relatively obvious reasoning errors. Thus, we might complain (with Prior 1955) that Berkeley fallaciously conflates the claim that one conceives that there is something unconceived with the claim that there is something that one conceives which is unconceived. Or we might think that Berkeley confuses the claim that it cannot both be that we conceive of a particular thing and that this thing is unconceived, which is true, with the claim that we cannot conceive of a thing as unconceived, which is false: I can conceive of the laptop on which I am writing this paper as existing unconceived, even though, in so doing, I conceive of the laptop (see e.g., Pitcher 1977, 113–15). More charitable readings of the argument see Berkeley as making the point that, roughly, we cannot represent something as being unconceived because we cannot experience the property of being unconceived (Gallois 1974, Campbell 2002). Other readings, such as that of Samuel Rickless (2013), rest upon the claims that, for Berkeley, only ideas are conceived (“If X conceives T, then T is an idea.” [135]), and it is impossible for ideas to exist unconceived (“If T is an idea, then it is impossible that T exists unconceived” [136]). These readings of Berkeley are free of (obvious) reasoning errors, but lack the idea that Berkeley is making a point about the logic of conceivability and render somewhat mysterious Berkeley’s willingness to “put the whole on this issue,” especially since these readings assume much of Berkeley’s metaphysics of ideas. ¹

I suggest we can find in these passages a precursor to the paradox of knowability. ² That paradox shows that if all truths are knowable, all truths are known. Similarly, Berkeley can fruitfully be read as proposing that if all sensible objects are (distinctly) conceivable, then all sensible objects are conceived. My aim is to offer a reconstruction of Berkeley’s Master Argument that (a) does significant justice to his willingness to put the whole on this issue, (b) cleaves close to Berkeley’s aims and words, and (c) brings out the similarities in Berkeley’s argument to the paradox presented by Church and Fitch.

2. Philonous’s promise

Let us begin with the crucial initial promise by Philonous:

PP: If you can conceive it possible for any mixture or combination of qualities, or any sensible object whatever, to exist without the mind, then I will grant it actually to be so.

This sentence raises multiple interpretive issues. I shall list them and state (while supplying some justification for) how I think they should be resolved.

A. Philonous states his promise in terms of conceiving a sensible object’s existing without the mind. Most commentators have proposed that Berkeley’s main argument more directly concerns conceiving of a sensible object as unconceived. This is, after all, what generates the apparent contradiction (“Is it not as great a contradiction to talk of conceiving a thing which is unconceived?”). Our reformulation of Philonous’s promise, then, will concern the possibility of conceiving of something unconceived.

B. Zoltán Gendler Szabó (2005) points out that one (modal) element of Philonous’s promise (that we are asked to conceive it possible for some sensible thing to exist without the mind) is dropped as the passage develops—Philonous and Hylas immediately start discussing whether one can conceive of some sensible thing existing unconceived, rather than whether one can conceive it possible for something to exist unconceived. I shall follow their (i.e., Berkeley’s) lead in this and remove this modal element in my reformulation of Philonous’s promise.

C. Another interpretative issue concerns the scope of the quantification over sensible objects—is it within or without the “conceives” operator? Here are two possibilities (where the content of the conception is specified by the italicized phrase):

(Narrow) We can/cannot conceive: a sensible thing existing unconceived.

(Wide) There is some sensible object, s, such that we can/cannot conceive: s existing unconceived.

I shall read Berkeley in the latter way. One consideration in favor of this reading is that it makes sense of Philonous’s remark that “The tree or house therefore which you think of, is conceived by you.” If we read this sentence as entailing (or presupposing) that there is a tree (or house) of which Hylas conceives, then Philonous’s felicitously inferring it from Hylas’s claim to have conceived a tree unconceived supposes a wide-scope reading of this latter claim. This is because the inference from the narrow-scoped “I conceive an unconceived tree” to “There is a tree of which I conceive” is invalid, but the inference from the wide-scoped “There is a tree which I conceive to be unconceived” to “There is a tree of which I conceive” is valid.

Such a reason to prefer the wide-scope reading is inconclusive. The narrow-scope reading can be squared with Philonous’s inference if we read the definite description in “The tree or house therefore which you think of, is conceived by you” as lacking existential import. If you conceive of a ferocious dragon (understanding this as a narrow-scope claim), it seems legitimate to infer from this the claim (suitably understood) that the dragon you conceive is ferocious, despite there being no dragons. The sentence “the dragon you conceive is ferocious,” then, need not entail or presuppose that there exists something picked out by the definite description “the dragon you conceive.” One might argue that given this inference is legitimate so too is Philonous’s, even on a narrow-scope reading of Hylas’s claim. ³

This issue, then, revolves around whether or not we take the sentence “The tree or house therefore which you think of, is conceived by you” to entail or presuppose that there is a tree (or house) conceived by Hylas. Both readings (existential and nonexistential) are available. One difference between this sentence and “the dragon you conceive is ferocious” is the following. Most naturally understood, the latter sentence attributes ferocity to the imagined dragon only under an implicit “according your conception” operator—we are saying that you conceive the dragon to be ferocious, not that it really is. This reading is natural partly because it is compatible with the fact that there are no dragons. The most natural reading of Philonous’s sentence, however, is not that the tree (or house) is conceived by Hylas according to Hylas’s conception, but simply that it is conceived by Hylas. It is less clear that such a claim is compatible with there being no tree (or house) of which Hylas conceives.

A wide-scope interpretation of Hylas’s claim also fits well with Philonous’s thesis that “what is conceived, is surely in the mind.” Most straightforwardly understood, this tells us that, for all x, if x is conceived, x is in the mind. Combined with the claim that there is a tree conceived by Hylas, we may infer that there is a tree in the mind (and it is surely Berkeley’s intention that we make some such inference). On a narrow-scope reading of Hylas’s claim, however, there need be no such tree and thus it is no longer obvious how we might infer that there is a tree in the mind.

This said, in my view, both wide-scope and narrow-scope readings are compatible with the text. Each is worth exploring. In this paper, I wish to show that the wide-scope reading not only stays close to Berkeley’s text, but also figures in an argument that is logically rigorous, independently interesting, and is in considerable harmony with Berkeley’s aims. ⁴

A final note on the wide-scope reading: I shall understand conceiving of a particular sensible thing existing unconceived to amount to conceiving that it is unconceived. We may thus distinguish the propositional attitude of conceiving that something is the case (which corresponds with the sentential operator “conceives that”) and the attribute of being conceived which applies to objects (and corresponds with the predicate “is conceived”). We shall explore the relationship between these notions further in sections 3 and 4.

D. Philonous’s promise is directly addressed to Hylas (and Berkeley’s to his audience): “If you can conceive… .” It is clear, however, that Berkeley takes the point to be entirely general—his argument is not based on our limitations as conceivers, but on the limits of conceivability. We can thus read “if you can conceive” as “if it is conceivable (by any possible mind) that.”

Putting all this together, we have the following reformulation of Philonous’s promise:

If there is some sensible object, s, such that it is conceivable that s is unconceived, then (I am willing to grant that) s is unconceived.

I wish to make one final amendment to the above formulation. After Hylas attempts to meet the challenge by conceiving of a sensible thing existing unconceived, Philonous points out that the sensible thing Hylas conceives as existing unconceived is conceived by Hylas. They both seem to take this to show that Hylas has failed to conceive of some sensible thing as existing unconceived. But if this is what they are doing, it seems they are mistaken. The tree that Hylas conceives of as existing unconceived is indeed conceived by Hylas, but it remains perfectly true that Hylas conceives of it as existing unconceived. The worry that Berkeley has made a logical blunder raises its head once again. As I say above, we might think that Berkeley confuses the claim that it cannot both be that we conceive of a particular thing and that this thing is unconceived, which is true but trivial, with the claim that we cannot conceive of a thing as unconceived, which is simply false.

We can resolve this worry, however, if we understand Philonous as challenging not the mere conceivability of some sensible thing existing unconceived, but the distinct conceivability of some sensible thing existing unconceived. In the light of Philonous’s promise, both he and Hylas are working on the assumption that if Hylas manages to pull off the task of conceiving of some sensible thing as existing unconceived, then that thing is unconceived. Hylas’s task, as he and Philonous think of it, is to distinctly conceive of some particular sensible object as existing unconceived, where this amounts to conceiving of this sensible thing as existing unconceived and its really being unconceived. It is this which Philonous is claiming to be impossible.

This interpretation of the passage both makes sense of Philonous’s promise and frees Berkeley from the reasoning error above. This way of construing Berkeley (as talking of distinct conception) is also not without precedent. For example, Prior (1955) and Mackie (1964) interpret Berkeley in much the same way. ⁵ Note also that we naturally interpret other arguments in a similar way. Consider Descartes’s claim that one cannot doubt that one exists, for one must exist to doubt it (see, e.g., The Second Meditation, Descartes 1993). This argument would be a nonstarter unless we read “cannot doubt” as something like “cannot truthfully doubt.” Descartes’s worry (at least on a reasonable understanding) is that doubting one’s own existence is self-refuting, not that it is literally impossible. ⁶

One might have the following worry about reading Berkeley as talking about distinct conception. ⁷ It is unclear that Berkeley’s philosophy allows for such a notion, because it suggests that what we conceive represents (truly or falsely) some distinct reality. This in turn suggests an indirect theory of perception according to which our ideas represent an external reality. Berkeley, of course, rejects such theories (indeed, much of his Principles and Dialogues is concerned with such a rejection). How, then, are we to square distinct conception with Berkeley’s wider philosophy?

In response to this worry, consider again how Philonous puts his promise: “If you can conceive it possible for any mixture or combination of qualities, or any sensible object whatever, to exist without the mind, then I will grant it actually to be so.” Regardless of what tacks we take concerning interpretive issues A–D, Philonous explicitly talks of something’s being conceived (or conceived possible) and this thing’s being actually so. While he does this in the course of arguing that the thing in question is not possible to conceive (or, as I say, distinctly conceive), Philonous’s promise strongly suggests that he (and thus Berkeley) thinks it is possible in principle to meet this kind of challenge (that is, it is possible both for something to be so and for someone to conceive it is so). This is just as well for Berkeley because of course such a thing is possible. It is possible, for instance, that grass is green and that someone conceives that grass is green. On my understanding, this is all it takes for it to be distinctly conceivable that grass is green. Thus, whether Berkeley is invoking distinct conceivability in propounding the Master Argument, it is an unproblematic notion the coherence of which is presupposed in Berkeley’s exposition of the argument. ⁸

Interpreting Berkeley as meaning distinct conception, then, is charitable (it allows us to attribute an interesting and logically rigorous argument to Berkeley), illuminating (it makes sense of the exchange between Philonous and Hylas), precedented (see the references to Prior and Mackie above), and in harmony with interpretations of other arguments (such as Descartes’s cogito).

I thus suggest the following formulation of Philonous’s promise:

PP: If there is some sensible object, s, such that it is distinctly conceivable that s is unconceived, then (I am willing to grant that) s is unconceived.

Thus understood, Philonous is saying that for some sensible thing, if it is even possible for there to be a distinct conception of this sensible thing as existing unconceived, then he is willing to grant that this sensible thing is unconceived. ⁹

3. The impossibility of distinctly conceiving of unconceived sensible things

The antecedent of Philonous’s promise, let’s call it Philonous’s target (PT), is this:

PT: There is some sensible object, s, such that it is distinctly conceivable that s is unconceived.

In other words, there is some sensible thing, s, such that it is possible to distinctly conceive that s is unconceived. Seeing as Philonous rejects the claim that there is an unconceived sensible thing, but accepts (or is at least willing to grant) that if PT obtains there is an unconceived sensible thing, then Philonous must reject PT. It is this rejection that takes up much of the succeeding passage. ¹⁰

After Philonous’s promise, Hylas says this:

What more easy than to conceive a tree or house existing by itself, independent of, and unperceived by any mind whatsoever? I do at this present time conceive them existing after that manner.

We may see Hylas as doing two important things here. First, he invokes a particular instance of PT. Call the tree Hylas conceives of as existing unconceived “Tree.” Hylas proceeds to assume, for the purposes of existential elimination:

H1: It is possible to distinctly conceive that Tree is unconceived.

Second, Hylas doesn’t just suggest that it is possible to distinctly conceive that Tree is unconceived, but that Tree is distinctly conceived (by him) to be unconceived. Thus, Hylas claims:

H2: It is distinctly conceived that Tree is unconceived.

It is this claim that Philonous then argues leads to a contradiction:

Philonous: How say you, Hylas, can you see a thing which is at the same time unseen?

Hylas: No, that were a contradiction.

Philonous: Is it not as great a contradiction to talk of conceiving a thing which is unconceived?

Hylas: It is.

Philonous: The tree or house therefore which you think of, is conceived by you.

It is not fully explicit in Berkeley’s writing what licenses him to suggest that Philonous has caught Hylas in a contradiction. I suggest that Berkeley is relying on two inferences that were seen by him to be obvious. It is obviously necessary, given how we are understanding distinct conception, that if it is distinctly conceived that Tree is unconceived, then Tree is unconceived. Thus, H2 entails:

H3. Tree is unconceived.

It is also necessary that if Hylas (or anyone) conceives (distinctly or otherwise) that Tree exists unconceived, then Tree is conceived: “The tree or house therefore which you think of, is conceived by you.” This claim is perhaps less obviously true than the first. Indeed, similar claims concerning other attitudes are straightforwardly false. As an anonymous referee puts it:

I can know that Jack brought me a gift but not know Jack, I can see that my pen is missing from its case and not see my pen, and I can hate that Jill did not call me without hating Jill.

Why, given this, should we accept that Hylas’s conceiving that Tree is unconceived entails that Tree is conceived? One immediate answer is simply that such an inference is far more plausible than those others mentioned above; just as we are skilled enough at telling these are bad inferences, we can tell our proposed inference is a good one. ¹¹

We needn’t rest content with a mere appeal to plausibility, however. To see this, suppose that there is a sense in which one may conceive of some particular thing that is a certain way without conceiving of this thing. On this supposition, it is perfectly possible for Hylas to (distinctly) conceive that Tree is unconceived and many people conceive that Tree is a certain way. Even if it is possible for Hylas to do this, however, Hylas does not thereby meet Philonous’s challenge. Hylas is supposed to conceive that no one even conceives that Tree is some way or other. For Berkeley, and for Philonous, what is important is whether sensible things can fail to figure in any mind’s conception of things (it is a meek materialist indeed who insists that there are sensible things which are unconceived, but concedes that, for each sensible thing, it is explicitly conceived by some mind or other that this sensible thing is a certain way). Given this, the claim that Tree is unconceived should be understood to encompass the claim that no one conceives that Tree is some way or other. And if this is right, the fact that Hylas conceives that Tree is unconceived does indeed entail that Tree is conceived (because it entails that someone conceives that Tree is some way or other). In essence, all we need to reach an interesting idealistic conclusion is a sense of “conceive” according to which explicitly figuring in the content of some conception suffices for being conceived. It is this sense which we shall assume going forward and which validates the inference from H2 to:

H4. Tree is conceived.

The conjunction of H3 and H4 is, as Philonous points out, a contradiction. Seeing as H2 entails a contradiction, H2 is false. Not only this. From the fact that H2 entails a contradiction, we may infer that H2 isn’t even possibly true. This type of inference would certainly be embraced by Berkeley. Consider, for instance, the following later exchange in the Dialogues:

Philonous: When is a thing shewn to be impossible?

Hylas: When a repugnancy is demonstrated between the ideas comprehended in its definition. (1999, 167)

For Berkeley, anything which gives rise to a contradiction (or, as he sometimes terms it, a repugnancy) is impossible (see Holden 2019). I suggest Berkeley is making such an inference in the Master Argument. From H2 we can demonstrate a contradiction, from which we may infer that H2 is impossible. Seeing as H1 simply states H2’s possibility, Berkeley has shown H1 (and thus PT) to be false.

4. Why disprove Philonous’s target?

Is this the extent of Berkeley’s argument? If it is, one might wonder why he rests such a great deal of importance on the Master Argument, or what might motivate him to argue for the falsehood of PT. There surely is something more afoot. Prior (1955) surmises (when couched in my terminology) that Berkeley confuses PT (i.e., the claim that there is some sensible object, s, such that it is distinctly conceivable that s is unconceived) with the claim that it is distinctly conceivable that there is some unconceived sensible object, and thus erroneously takes himself to have shown that it is not possible to distinctly conceive that there are unconceived sensible objects. In Prior’s view, if Berkeley had shown this latter claim to be true it would have supported his immaterialism, but he has done no such thing (though see McGlynn [2019] for an interesting intuitionist reply to this worry).

In my view, Prior has overlooked another way we might use the negation of PT in an argument with a distinctively Berkelian conclusion that does not rest on a logical confusion. One natural reason Berkeley might want to argue that PT is false is that he sees it as something which a materialist (understood here as someone who believes that there exist sensible things without the mind and thus unconceived) might accept. But why might a materialist accept PT? Perhaps because she accepts this natural argument for PT:

Distinct Conceivability Principle (DCP): For any sensible thing, s, and any thinkable quality, q, if s has q (or lacks q), it is possible to distinctly conceive that s has q (or lacks q).

Materialist Thesis (MT): Some sensible things have the thinkable quality of being unconceived (or, if you prefer, some sensible things lack the thinkable quality of being conceived).

PT: (Therefore) there is some sensible thing, s, such that it is distinctly conceivable that s is unconceived.

A thinkable quality, as I shall understand it, is one that can be conceived to belong to some object or other—a quality that some mind can grasp as being had by something.

One may worry that being conceived, or being unconceived, are not thinkable qualities, or, indeed, qualities at all (at least for early modern philosophers like Berkeley). ¹² For one thing, one might think that the qualities presented to us in conception are intrinsic properties of sensible things, rather than their relational properties (such as being conceived). For another, if being conceived is a quality, it is unclear how being conceived is related to the attitude of conceiving that something is the case (which is associated with the sentential operator “it is conceived that”).

I do not mean to rest anything of importance on the term “quality.” I use it merely to pick out anything that can be predicated of something. The property of being conceived is a quality in this sense simply because things can be conceived. It is a thinkable quality simply because it can be thought that something is conceived (or not conceived). It is only in this thin sense do I use the term “thinkable quality.”

These points understood, it seems clear that something may be conceived to have a relational property (like being conceived or being unconceived), and that Berkeley would concur. In general, conception does not limit itself to intrinsic qualities—I may conceive, for example, that Tree is next to a dog, or, to use an example from the Principles, “I can imagine … the upper parts of a man joined to the body of a horse” (1999, 11). Indeed, Berkeley explicitly allows that we conceive not only ideas but spirits, and how spirits and ideas relate. Thus, to take but one example, Philonous says “it is very conceivable that [ideas] should exist in, and be produced by, a spirit; since this is no more than I daily experience in myself” (155). ¹³ Note also that this constitutes an example of distinct conception (as I use the term); Philonous conceives something is so, and (indeed, because) it is so.

The relationship between the quality of being conceived and the attitude of conceiving that such-and-such is simple to specify. As I understand it, conceiving that Tree is green (or next to a dog, etc.) suffices for Tree’s being conceived, because what is meant by “Tree is conceived” encompasses “It is conceived that Tree is some way.” That is, that Tree is conceived either amounts to the claim that someone conceives that Tree is some way or amounts to a disjunction, one of the disjuncts of which is that someone conceives that Tree is some way (another disjunct perhaps being the claim that Tree is conceived in a purely objectual way—it is before the mind without being thought of as being some way). As I argue in section 3, such an understanding of being conceived still serves Berkeley’s idealistic aims; his argument runs counter to the materialist who countenances the existence of sensible things that do not figure in our conceptions in either such way.

In essence, then, a materialist might accept PT because she believes that there are indeed unconceived sensible things, and that, if a sensible thing has/lacks a (thinkable) property, it is possible for there to be somebody who distinctly conceives that this sensible thing has/lacks this property. We may see, then, PT as an instance of the more general DCP, on the materialist assumption that there are indeed unconceived sensible things.

Something like this argument must underlie Berkeley’s thinking (on the assumption that my reading of Philonous’s promise is substantially correct and Berkeley is not guilty of the confusion Prior attributes to him). A materialist who maintains PT subsumes it under a more general principle concerning what can be distinctly conceived (it is not as if such a materialist thinks that it is possible to distinctly conceive only that certain sensible things are unconceived). To be sure, there are other relatively natural principles of which PT might be an instance. Consider the following principles (their differences from DCP are in italics):

For any sensible thing, s, and any thinkable quality, q, if it is possible that s has q (or lacks q), then it distinctly conceivable that s has q (or lacks q).

For anything, x, and any quality, q, if x has q (or lacks q), then it is distinctly conceivable that x has q (or lacks q).

Necessarily, for any sensible thing, s, and any thinkable quality, q, if s has q (or lacks q), then it is distinctly conceivable that s has q (or lacks q).

It is difficult to say exactly what general principle Berkeley might be invoking when attributing PT to certain type of materialist, but I shall assume it is DCP for the following reasons. First, it is the weakest of the above principles; it is entailed by the others but does not entail any of them. Second, it is not artificially weak; DCP is a simple, rather elegant, and even plausible principle absent any murkily motivated modifications. Third, as we shall see, despite its relative weakness, DCP can play a crucial role in Berkeley’s support of idealism.

Aside from DCP’s initial plausibility, is there any reason why one might accept it? The main reason is that it may be seen as spelling out, in part, what it takes for a sensible thing to have a thinkable quality. All sensible things are things that can be grasped by the mind (or, at least, some mind). This is not yet to accept the idealist claim that all sensible things are grasped by some mind, but merely that it is possible for them to be. Recall that a thinkable quality is one that can be conceived to belong to some object or other—a quality that some mind can grasp as being had by something. If a sensible thing, then, has (or lacks) some thinkable quality, some mind can conceive that it has (or lacks) such a quality. Should a sensible thing have a thinkable quality, its having this quality is a state of affairs that can itself be grasped. We may call a truth of the form s has [or lacks] q (where “s” denotes a sensible thing and “q” a thinkable quality) a thinkable truth. Thinkable truths are, very plausibly, open to the mind—facts which some mind can grasp (i.e., distinctly conceive).

Given this rough case for DCP, we now have the outline of an argument for idealism (or at least the idealist thesis that all sensible things are in the mind): DCP and MT together entail PT; PT is false (see section 3 above); thus either DCP is false or MT is false; DCP is not false; therefore, MT is false. And if MT is false, then all sensible things are conceived (and thus in the mind).

There is little explicit textual evidence that Berkeley himself accepted something like DCP—the best evidence that he did is that DCP renders his notorious Master Argument logically rigorous and largely independent of any idiosyncratic element of Berkeley’s metaphysics (and thus something upon which Berkeley might rest the whole issue). But note also that DCP is certainly within the spirit of Berkeley’s worldview—for Berkeley the esse of sensible things is percipi. DCP is a rather cautious relative of this claim that might be readily accepted by nonidealists—sensible things are open to being distinctly captured by some (perhaps merely) possible mind.

DCP is also, as far as I can tell, perfectly consistent with Berkeley’s explicit views. To be sure, there are times when Berkeley seems to draw attention to the limits of human conception. For example, later in the dialogues, Philonous says this of the stars:

How vivid and radiant is the lustre of the fixed stars! … The feeble narrow sense cannot descry innumerable worlds revolving round the central fires; and in those worlds the energy of an all-perfect mind displayed in endless forms. But neither sense nor imagination are big enough to comprehend the boundless extent with all its glittering furniture. Though the labouring mind exert and strain each power to its utmost reach, there still stands out ungrasped a surplusage immeasurable. (Berkeley 1999, 151)

Thomas Holden (2019) argues that these and related passages are strong evidence against the claim that Berkeley believed that inconceivability entails impossibility. One might also suggest they tell against Berkeley’s adherence to a (much weaker) principle like DCP. Such a conclusion would be hasty, however. The target of Holden’s criticism is the view that Berkeley deemed inconceivability by us (i.e., humans) sufficient for impossibility. DCP concerns (distinct) conceivability by some possible mind (including God’s). Not only is Berkeley above discussing the limits of our conceivability, he does so by way of contrast to that of an “all-perfect mind.”

Perhaps this is too quick. As an anonymous referee points out, the above passage is naturally read as referring to the all-perfect mind’s causal powers, rather than its powers of (distinct) conception. However, Berkeley takes God’s power to produce such ideas to show that God understands these ideas. Thus, Philonous says all of the following, “sensible things do really exist: and if they really exist, they are necessarily perceived by an infinite mind: therefore there is an infinite mind, or God” (1999, 153); “the things by me perceived are known by the understanding, and produced by the will, of an infinite spirit” (156); “to a Christian it cannot surely be shocking to say, the real tree existing without his mind is truly known and comprehended by (that is, exists in) the infinite mind of God” (177). Each of these strongly suggest that Berkeley would advocate something like DCP, as least as it pertains to God. ¹⁴

What’s more, I argue below (in section 8) that there is a reading of Berkeley on which he need not accept DCP. Rather, on this reading, Berkeley is simply disproving a certain kind of materialist thesis that maintains both DCP and MT. Such a thesis Berkeley can reduce to absurdity without invoking the truth of DCP.

5. Church and Fitch’s paradox of knowability

On my understanding of Berkeley’s Master Argument, Berkeley shows that distinct conceivability is subject to a certain modal collapse. If all sensible objects can be distinctly conceived, then all sensible objects are conceived. This collapse is strongly reminiscent of Alonzo Church’s and Frederic Fitch’s paradox of knowability (Church 2009, Fitch 1963), which proves (at least to most people’s satisfaction) that if all truths are knowable, then all truths are known. The rough idea is this: if all truths are knowable and yet not all truths are known, then some p is both true and unknown. This conjunction is itself knowable: it is knowable that p is true and unknown. Assume someone knows it. This person will know both conjuncts—he will know p and he will know that p is unknown. Seeing as knowledge is factive, p is indeed unknown. But it is also known. So, p is both known and unknown. Reductio!

It is worth setting out a standard formalization of the paradox of knowability (the following formalization is taken from Brogaard and Salnero [2013], accompanied by my comments and a slight change in what variable letters are used). The paradox sets out to prove the inconsistency of two theses, the Knowability Principle and Non-omniscience (where “q” is a sentential variable, and “K” means “it is known that”):

(KP) ∀q(q → ◊Kq)

(NonO) ∃q(q ∧ ¬Kq)

The argument proceeds by assuming both theses and deriving a contradiction. The first part of the argument runs as follows:

We can then prove (3) false as follows. First, we appeal to four highly plausible principles (knowledge of a conjunction entails knowledge of its conjuncts, knowledge entails truth, all theorems are necessary, and the necessity of a claim’s negation entails the impossibility of the claim):

(A) K(q ∧ r) ⊢ Kq ∧ Kr

(B) Kq ⊢ q

(C) If ⊢ q, then ⊢□q

(D) □¬q ⊢ ¬◊q

The argument continues as follows:

(9) is the negation of (3). KP and NonO together lead to a contradiction. Assuming we accept KP, then, we must also accept the negation of NonO:

(10) ¬∃q(q ∧ ¬Kq)

Which entails, albeit strictly classically, that all truths are known:

(11) ∀q(q → Kq)

In essence, then, the paradox of knowability provides a surprising proof that if all truths are knowable then all truths are known. Might we formalize Berkeley’s Master Argument in a similar way?

6. Berkeley’s Master Argument

We might, and the similarities are striking. The Master Argument (or, as we might call my reading of it, the paradox of distinct conceivability) sets out to prove the inconsistency of two theses: the Distinct Conceivability Principle and the Materialist Thesis. Let “s” range over sensible objects and “F” over thinkable qualities (and their absences); let “D” be a sentential operator meaning “It is distinctly conceived that” and “C” a predicate meaning “is conceived.” We may thus formalize DCP and MT so:

(DCP) ∀s∀F(Fs→ ◊D(Fs))

(MT) ∃s(¬Cs)

DCP and MT are strong analogues of KP and NonO respectively. Both DCP and KP tell us that all truths (or all truths of a certain kind) can figure in the content of certain mental states (distinct conception and knowledge respectively). MT and NonO tell us that there are certain things that are not in fact conceived/known.

The argument proceeds, just as in the previous argument, by assuming both theses and deriving a contradiction. The first part of the argument runs as follows, and in much the same way as the argument above:

We can then prove (3’) false as follows. First, we appeal to four highly plausible principles (that s is distinctly conceived to be F entails that s is conceived, that it is distinctly conceived q entails that q, all theorems are necessary, and the necessity of a claim’s negation entails the impossibility of the claim:

(A’) D(Fs) ⊢ Cs

(B’) Dq ⊢ q

(C’) If ⊢ q, then ⊢□q

(D’) □¬q ⊢ ¬◊q

Note that these latter two principles, (C’) and (D’), are identical to (C) and (D) of the previous argument. (B’) expresses the factivity of distinct conception just as (B) above expresses the factivity of knowledge. Even (A’) and (A), despite their obvious differences, share a striking similarity. (A) tells us that knowledge of a conjunction entails knowledge of each conjunct, while (A’) tells us that (distinctly) conceiving a claim about a certain sensible thing entails that this sensible thing is conceived (which, given our above understanding of being conceived, is valid). In both cases, having a certain mental attitude (knowledge or conception) towards a certain type of proposition (a conjunction, or a claim about a sensible thing) entails having this attitude towards some element of the proposition (a conjunct of the conjunction, or the sensible thing that the proposition concerns).

The argument continues in similar (though not identical) fashion to the previous argument. We start by assuming Hylas’s claim that there is a particular sensible object which he distinctly conceives to be unconceived. Following Philonous, we then show that this assumption leads to a contradiction and is thus necessarily false (and so not possibly true):

(10’) is the negation of (3’). DCP and MT together lead to a contradiction. Assuming we accept DCP, then, we must also accept the negation of MT:

(11’) ¬∃s(¬Cs)

Which entails that all sensible things are conceived:

(12’) ∀s(Cs)

Philonous triumphs.

7. Fortunes and choices

Berkeley’s Master Argument and the paradox of knowability have enjoyed rather different fortunes. While some have found philosophical worth in Berkeley’s argument, others find it ill-equipped to support any interesting conclusion (Stove [1995] considers it to be an example of the “worst argument in the world”). Church and Fitch’s paradox and variations on it, on the other hand, have been effectively wielded against versions of verificationism and antirealism according to which all truths are verifiable (see, e.g., Hart [1979], who deems the paradox an “unjustly neglected logical gem”, Mackie [1980]). In light of this, the paradox has forced those sympathetic with such views either to find subtle logical problems with it (Edgington 1985) or to attempt to produce versions of antirealism that are immune to it (Dummett 2001, Tennant 2002). If I am right, this disparity in how the two arguments are received is unjustified—the Master Argument is in fact a variation of the paradox of knowability. ¹⁵

The explanation for such a disparity is relatively obvious. Fitch and Church present the paradox of knowability formally, explicitly, and comprehensively. Berkeley’s Master Argument leaves premises, lemmas, and even his conclusion either unstated, stated ambiguously, or missing vital information. It is no small wonder, then, that Berkeley’s argument has given rise to multiple (and often unflattering) interpretations.

On my reading, the Master Argument is much stronger than it is often taken to be—it is valid, its main premise (DCP) is rather plausible, its conclusion is far from trivial, it casts its net wide (i.e., it does not rely on some idiosyncratic element of Berkeley’s metaphysics), it does not entail solipsism, it is not confused or equivocal. It is the type of argument, dare I say, upon which one might rest the whole issue.

I take the most interesting result of (my reading of) the Master Argument is that the distinct conceivability of sensible things entails the actual conception of sensible things. While Philonous might embrace the former and infer the latter, we are free to reject the latter and thus also reject the former. The important point is that the argument forces just this choice upon us.

This choice, of course, mirrors the decision we are presented with in the light of the knowability paradox. While some may accept KP and come to accept that all truths are known, we are more likely to reject KP. Indeed, that KP collapses possible knowledge into actual knowledge is precisely what leads antirealists to reformulate their views. Antirealists have little wish to claim that all is known, but simply that all is in reach of the mind. The paradox of knowability raises the question of whether antirealists can truly make this distinction. The Master Argument does much the same thing. We might have held out hope that sensible things are mind-independent entities which can be fully open to the mind. Berkeley’s argument casts doubt on this kind of position.

8. The whole upon this issue

Casting such doubt is a far cry from showing that sensible things are within the mind, however. Should we conclude, then, that the Master Argument, though it shows us a certain interesting modal collapse, is ultimately a failure because its main principle (DCP) should be rejected, rather than its conclusion (that all sensible things are conceived) accepted? Not necessarily, and for two reasons.

The first reason is, in short, that DCP is more plausible than KP and thus might be more readily accepted. Unlike KP, which concerns all truths, DCP restricts its domain to thinkable truths about sensible objects. While the materialist might claim that certain things are beyond our ken—exotic microscopic physical particles, bizarre quantum properties we cannot begin to imagine, etc.—even he will find attractive the idea that at least sensible things are open to the mind. Indeed, we might reasonably claim that this is simply part of what it is for them to be sensible things. Furthermore, DCP does not tell us that thinkable truths about sensible objects are knowable, only that they are distinctly conceivable. While distinct conceivability has some constraints (consistency, coherence, etc.), these constraints are shared by knowledge, while knowledge brings with it further constraints (justification, belief, nonaccidentality) that are harder to meet.

Of course, once we reason through the Master Argument, we see that DCP is not entirely modest. The fact that it entails that all sensible things are conceived is on its own enough for us to bring the principle into question. What’s more, the way DCP entails that all sensible things are conceived seems like a logical trick—whatever we turn our minds to is perforce something we are thinking about, and thus obviously we cannot distinctly think of something unthought.

Still, dismissing DCP on this kind of basis (that it has unwelcome entailments that result from a logical trick) is dialectically suspect. A proponent of my version of Berkeley’s Master Argument might complain that it is question-begging to reject DCP on the basis that it entails the negation of MT, and that the supposed “logical trick” is just a clever yet valid application of the principle. We might reply that he is in no better position than us; he cannot simply insist that we embrace DCP and thus reject MT. The considerations in favor of DCP that I mention above—that sensible things are, by their nature, transparent to our conception—are suggestive, but too controversial to lend DCP substantial support.

Berkeley has not shown us, then, that we must conclude that all sensible things are conceived, and to this extent, the Master Argument is not a total success. However, there is another reason why we should not deem Berkeley’s argument a failure given his purposes. As I mentioned in the introduction to this paper, we may interpret Berkeley’s aim in a stronger or a weaker fashion. The strong interpretation has it that Berkeley asserts DCP and concludes that all sensible things are in the mind. On this interpretation, one may indeed respond to Berkeley by rejecting DCP. On the weaker interpretation, however, Berkeley’s aim is merely to rebut a certain materialist view. Given my interpretation of the Master Argument, Berkeley’s aim (on its weaker reading) is to force materialists to choose between two unpalatable options: the idealist claim that all sensible things are in the mind or the claim that certain thinkable truths about sensible objects simply cannot be grasped distinctly by the mind. On this reading of Berkeley’s purpose, he is attempting to show that materialists cannot have their cake and eat it by embracing a position according to which sensible things can be grasped fully by the mind but are nevertheless not always within it.

Just before the Master Argument is brought up in the Dialogues, Philonous is complaining about a position that Hylas proposes that matter is a substratum that supports sensible attributes but is not itself open to the senses (or even conception). Philonous sums up his complaint as follows:

Philonous: It seems then you have no idea at all, neither relative nor positive of matter; you know neither what it is in itself, nor what relation it bears to accidents.

Hylas: I acknowledge it.

Philonous: And yet you asserted, that you could not conceive how qualities or accidents should really exist, without conceiving at the same time a material support of them.

Hylas: I did.

Philonous: That is to say, when you conceive the real existence of qualities, you do withal conceive something which you cannot conceive. (Berkeley 1999, 138)

Hylas does not resist Philonous’s charge, nor try to show that such a position is acceptable. Instead, he admits he was wrong and then changes tack:

Now, I grant that each quality cannot singly subsist without the mind. Colour cannot without extension, neither can figure without some other sensible quality. But as the several qualities united or blended together form entire sensible things, nothing hinders why such things may not be supposed to exist without the mind. (138–39)

Hylas gives up the idea of a material substratum inaccessible to the mind and suggests instead that sensible things can exist independently of the mind. In other words, Hylas can be seen as trying to embrace the have-your-cake-and-eat-it materialism mentioned above—sensible objects can and often do exist without the mind, but can, nevertheless, be fully grasped by it. In reply, Philonous first points out that the arguments he has thus far presented show not that sensible qualities can’t exist alone without the mind but that they cannot exist at all without the mind. He then goes on to present the Master Argument, which (as I have it) shows that the domain of distinctly conceivable sensible things must be conceived and thus within the mind.

We may suggest, then, that the Master Argument is aimed at the view that Hylas is espousing just before the Master Argument is presented by Philonous. Philonous shows that Hylas cannot maintain that objects can be without the mind and still be fully and distinctly conceivable to us. Philonous is willing to “put the whole on this issue,” on this interpretation, because Philonous has already shown that a materialist position that makes out mind-independent objects to be inconceivable is absurd (“That is to say, when you conceive the real existence of qualities, you do withal conceive something which you cannot conceive.”), and thus, now that Philonous has shown that a materialist position that makes out mind-independent objects to be conceivable is also absurd, Philonous has put all materialist views to rest. ¹⁶

9. Conclusion

Far from being an embarrassing blunder, Berkeley’s Master Argument can be read as a subtle and ingenious piece of reasoning. Like Church and Fitch’s paradox of knowability, it shows us that if the world (or some aspect of it, such as the domain of sensible things) is suitably open to our minds, it is in our minds. Either the sensible lies within us or some of its truths must forever remain hidden from us.