No one objects to admitting regions of, e.g., Fiction and Imagination—why not then, also, allow this Region of Supposition—a region to the full as indispensable and still more populous, though, in part, even more removed from the solid ground of Fact? (Jones 1893a)

1 Introduction

One of the first women to study philosophy at the University of Cambridge, E. E. Constance Jones (1848–1922) developed a novel version of ontological pluralism—roughly, the view that there are different kinds of existence or being—over the course of her career.¹ On her view, there are many kinds of existence, including “physical existence” (which is had by King’s College Chapel, Cambridge but not fairies) and “existence in imagination” (which is had by fairies but perhaps not King’s College Chapel) (Jones 1890, 89, 90).² In addition, everything has “existence itself” (Jones 1890, 88, 90).

In this paper, I focus on a largely undiscussed aspect of Jones’s views about existence: namely, her claim that the round-square exists in what she calls “a Region of Supposition” (Jones 1893a, 455).³ We can attribute a consistent and well-worked-out view to her. On this view, ‘The round-square’ in

1. The round-square is impossible.

and

2. The round-square is non-existent.

applies to a thing, the round-square, which has a kind of existence; otherwise (1) and (2) wouldn’t be meaningful. (1) and (2) are true, because ‘impossible’ and ‘non-existent’ are read as ‘impossible in space’ and ‘non-existent in space’; and the round-square is impossible in, and doesn’t exist in, space.⁴ The reason it doesn’t exist in space is that it’s both round and square, and nothing in space is both. Instead of existing in space, it exists in a region of supposition, where existence in a region of supposition is a specific kind of existence distinct from physical existence, existence in imagination, and existence itself. What distinguishes things that have existence in this region is that they play a role in reasoning. The round-square plays a role in reasoning, including the reasoning that leads to the conclusion that it doesn’t exist in space. And, even though the round-square is both round and square, the Law of Contradiction needn’t be violated. For there are two forms of negation, and what follows from ‘The round-square is square’ is ‘The round-square is not-round’ (with negation in the predicate ‘not-round’) rather than ‘The round-square is-not round’ (with negation in the copula ‘is-not’).

The plan for the paper is as follows. I begin in Section 2 by situating Jones’s view within a family of views—held by some of her better-known male contemporaries, including William James (1842–1910), Alexius Meinong (1853–1920), G. F. Stout (1860–1944), Kazimierz Twardowski (1866–1938), and Bertrand Russell (1872–1970)—that, broadly speaking, attribute a positive status to things that we can think or talk about. In Section 3, I discuss “On the Nature of Logical Judgment” (published 1893), where she first says that round-squares exist in a region of supposition. In Section 4, I discuss A New Law of Thought and Its Logical Bearings (published 1911), where she argues that the round-square is both round and square and says that it plays a role in reasoning. Finally, in Section 5, I discuss how to reconcile her views about the round-square with her commitment to the Law of Contradiction.

2 Existence and Things

2.1 Existence

Some of Jones’s contemporaries held views that attribute a positive status to things on the basis of our ability to think or talk about them.⁵ Views in this family disagree about what that positive status is.

On Meinong’s (1899, 1904) view, the positive status is being an object. For example, we can think about the golden mountain and the round-square, so they’re objects, even if they don’t exist or have being.⁶ This view was also held by Twardowski (1894, 19, 21–22) and Stout (1896, 45).⁷

By contrast, on Russell’s (1898, 1903) view, the positive status is being. For example, we can think about “the Homeric gods” and “chimeras” (monsters combining parts of different animals), so they have being, even if they don’t exist (Russell 1903, 449).⁸

And, on James’s (1889) view, the positive status has to do with existence. For example, we can think about “mythical” objects, so they exist “in the strict and ultimate sense of the word” (James 1889, 331). Existence in this sense is what Jones (1890, 88 n. 2) calls existence itself. On James’s (1889, 328–29) view, there are also different “sub-universes,” “each with its own special and separate style of existence.” These sub-universes range from the “world of sense,” to “the world of the Iliad,” to “worlds of sheer madness” (James 1889, 328–29). So, in addition to having existence itself, Achilles and other things in the sub-universe of the Iliad have a “special” kind of existence that buildings and other physical things in the sub-universe of sense lack.

Jones’s view belongs in this family. On her view, the positive status has to do with existence. In the case of the round-square, that status includes both existence in a region of supposition and existence itself (since everything has existence itself).

In this respect, Jones’s view is closest to James’s. They agree that the things we can think or talk about have existence itself. On her view, some of these things also have existence in a region of supposition. On his view, some of these things also have specific kinds of existence corresponding to various sub-universes. But he doesn’t mention a sub-universe or region of supposition.

It’s tricky to say whether Jones agrees with Twardowski, Stout, Meinong, and Russell on questions of existence. They would say that they don’t agree with her. But she might say that they do.⁹ For example, Russell would say that he accepts, and Jones rejects,

3. Some object of thought has being, but it doesn’t exist.

But Jones (1910, 380 n. 1, 381 n. 2) identifies being and existence. So, when Russell says “Some object of thought has being,” she would regard him as agreeing with her that the object in question exists. Similarly, Twardowski, Stout, and Meinong would say that they accept, and Jones rejects,

4. The round-square is an object, but it doesn’t exist.

But Jones (1890, 87) attributes existence to every object. So, when they say “The round-square is an object,” she might regard them as agreeing with her that it exists.

2.2 Things

Views that attribute a positive status to things that we can think or talk about also disagree about which things those are.

Meinong’s (1899, 142; 1904, 83) view includes the claim that we can think, not only about possible things like the golden mountain, but also about impossible things like the round-square. This claim is sometimes described as the “novel part” or “the really revolutionary part” of his view (Simons 2012, 246). The claim is also part of Twardowski’s (1894) and Stout’s (1894, 1896) views.¹⁰

By contrast, James (1889) mentions only possible things.¹¹ Russell’s (1903) view is somewhat less clear, but in earlier work he restricts his view to an object or idea “which does not involve a contradiction.”¹²

On Jones’s view, we can think and talk about impossible things like the round-square.¹³ In this respect, her view is like Twardowski’s, Stout’s, and Meinong’s; and it’s unlike James’s view and, at least at one time, Russell’s. If the “novel” and “really revolutionary” part of Twardowski’s, Stout’s, and Meinong’s views is the claim that we can think and talk about the round-square, then Jones’s view is, it seems, no less novel and revolutionary.

2.3 Influence

Jones was familiar with James’s work, which she quotes in Elements of Logic as a Science of Propositions (see Jones 1890, 6 n. 1, 88 n. 2). She was undoubtedly influenced by his view that possible things we can think about have both existence itself and “special and separate” kinds of existence depending on which “sub-universes” they exist in. But James doesn’t mention existence in a region of supposition, nor does he extend his view to impossible things like the round-square.

Jones was familiar with Stout’s and Russell’s views, which she discusses starting in 1905 (Jones 1905, 81, 88 n. 1, 123–24; 1906–1907, 82–83). Jones, Stout, and Russell were all students of the psychologist James Ward. (See Jones 1922, 53–54; Russell 1967, 91, 115; Schaar 2013, 4). Jones (1922, 72) described Stout as having “approved and befriended” her project. He wrote the preface to A New Law and, later, her obituary. (See Stout 1911, 1922). They were her juniors at Cambridge.¹⁴ Jones knew of Meinong’s views from Russell’s (1905) “On Denoting” (see Jones 1910, 381). She might have met Meinong in Bologna in 1911 at the Fourth International Congress of Philosophy, which they both attended (see Jones 1911c; 1922, 86; Meinong 1911). She might have known of Twardowski’s views from Stout (1894). And, through the work of Franz Hillebrand (1891), she was familiar with the Brentanian background of Twardowski’s work.¹⁵ But I don’t know of any evidence that she was directly familiar with Meinong’s and Twardowski’s views. And her view that the round-square exists in a region of supposition was probably not directly influenced by Twardowski’s, Stout’s, Meinong’s, and Russell’s views described above, since she had come to her view by 1893, before she could have come across those views in print.

2.4 Kinds of existence

It can be tricky to explain one’s distinctions to those who don’t already accept them. For example, James doesn’t say what distinguishes the “special and separate” kind of existence that buildings have from the equally “special and separate” kind of existence that Achilles has. Similarly, in distinguishing being and existence, Russell (1898, 170) takes existence to be “unanalyzable.”

In much the same way, Jones doesn’t say what distinguishes existence in a region of supposition from other kinds of existence. But, on her view, distinctions between different kinds of existence aren’t distinctions without a difference, since what kind of existence something has is reflected in what attributes it has. She says, “The kind of existence anything has is shown by the predicates we can give it” (Jones 1911b, 63).¹⁶ She doesn’t say what attributes distinguish things that exist in a region of supposition, but her view in 1911 might be that what distinguishes them is that they play a role in reasoning. (See Section 4.4.) The round-square, Jones (1910, 178) says, can be “in some sense supposed.” (But it can’t be imagined, at least not by “any sane and trained mind” (Jones 1910, 178).)¹⁷

As I’m understanding it, existence in a region of supposition is a specific kind of existence, distinct from existence itself. Something has existence in a region of supposition when it plays an appropriate role in reasoning, but things that aren’t being reasoned about don’t have that kind of existence, even if they have existence itself.

Ontological pluralists face a common predicament. On the one hand, if they say too little about the distinctions that they make, they face the charge of obscurity or incoherence. But, on the other hand, if they say too much, they face the charge of being ontological monists in disguise. For example, Russell (1898, 170) says that things that exist are located in spacetime.¹⁸ Foes of ontological pluralism could say that he isn’t an ontological pluralist who distinguishes being and existence; rather, he’s an ontological monist who believes that everything exists, and in addition some (but not all) things are located in spacetime.¹⁹ Similarly, if Jones says that things that exist in a region of supposition play a role in reasoning, foes of ontological pluralism could say that she’s an ontological monist who believes that everything exists, and in addition some (but not all) things play a role in reasoning.

This is a general worry for ontological pluralists, one that isn’t peculiar to Jones. (It applies just as much to James, Russell, and Meinong.) I won’t defend the general intelligibility of ontological pluralism here.²⁰ But the worry is to some extent anachronistic. Talk of different kinds (or modes, or styles) of existence would have been familiar to Jones and her readers.²¹ So she might not have felt the need to explain her talk of kinds of existence or to fend off ontologically monistic re-interpretations of her view. In the rest of this paper, I follow her in assuming that talk of kinds of existence, including existence in a region of supposition, is intelligible.

3 “Logical Judgment” (and Before)

3.1 Jones’s 1893 view

In “Logical Judgment,” Jones’s view is that

5. Dragons are non-existent.

and

6. Round-squares are impossible.

are meaningful, because ‘Dragons’ and ‘Round-squares’ apply to things—namely, dragons and round-squares—that exist in a region of supposition. And the sentences are true, because ‘non-existent’ is read as ‘non-existent in nature’, and ‘impossible’ is read as ‘impossible in space’; and dragons don’t exist in nature, and round-squares are impossible in space.

3.2 Round-squares exist in a region of supposition

Dragons and round-squares exist in a region of supposition. Jones (1893a, 454–55) says,

surely the region of the Subjects of (5) and (6) is a region (exclusive of Nature, and actual or imagined space) in which Dragons and Round-squares respectively do exist for me at the time when I am talking of them—namely, a Region of Supposition.

‘Subject’ is ambiguous for Jones between ‘subject-name’ (which she distinguishes from ‘predicate’) and ‘subject of attributes’ (which she distinguishes from ‘attribute’). (See Jones 1890, 12, 96; 1893b, 221.) ‘Dragons’ and ‘Round-squares’ are the subject-names in (5) and (6); they apply to dragons and round-squares, which are subjects of attributes. I take it that “the Subjects of (5) and (6)” are the subjects of attributes—namely, dragons and round-squares—that the subject-names in (5) and (6)—namely, ‘Dragons’ and ‘Round-squares’—apply to. It’s these dragons and round-squares that are said to exist in a region of supposition, which Jones (1893a, 455) describes as “even more removed from the solid ground of Fact” and “still more populous” than regions of fiction and imagination but nonetheless “to the full as indispensable.”

Jones doesn’t say why she thinks that a region of supposition would be “more populous” than regions of fiction and imagination.²² If everything that we can suppose or talk about is something that we can tell a story about, and vice versa, then regions of fiction and supposition might be equally populous. But perhaps her view is that, although we can suppose or talk about everything imaginable, there are some things that we can suppose or talk about but can’t imagine, perhaps because we can’t form mental images of them or because we can only imagine things as being located in space. We might be able to suppose or talk about round-squares; but, she says, they’re excluded from “imagined space.”

“Logical Judgment,” which appeared in October 1893, is the first place where Jones explicitly asserts that round-squares have some kind of existence, and it’s the first place where she says that the kind of existence in question is existence in a region of supposition.²³ But, six months earlier, she published a reply to the first part of W. E. Johnson’s (1892) “Logical Calculus,” arguing against his claim that there can be “predication which is not predicated and cannot be predicated, of anything” Jones (1893b, 220 n. 3).²⁴ In her reply, she suggests that “a combination of properties X and Y,” such as being round and being square, “in a subject of which both are attributes,” such as a round-square, “must ‘exist’, somehow, in idea, in my mind” (Jones 1893b, 220–21 n. 3).²⁵

Things that exist in a region of supposition might lie in wait for us, existing independently of our activities. But, in “Logical Judgment,” Jones suggests that such things exist because we’re talking about them. Dragons and round-squares, she says above, “do exist for me at the time when I am talking of them.”²⁶ In the reply to Johnson, she suggests that round-squares exist before we talk about them, but only because we need to postulate them before we can talk about them. “Even if the speaker’s object is merely to deny the occurrence” of things that combine attributes such as being round and being square, she says, “this can only be done by first postulating such things” (Jones 1893b, 220 n. 3).

3.3 Round-squares are impossible in space

Although they exist in a region of supposition, dragons don’t exist in nature, and round-squares are impossible in space. (5) doesn’t say that dragons don’t exist anywhere, and (6) doesn’t say that round-squares are impossible everywhere; rather, (5) says that dragons don’t exist in some region, and (6) says that round-squares are impossible in some (other) region. Speaking of (5) and (6), Jones (1893a, 454) says,

I do of course mean to imply the non-existence and impossibility of Dragons and Round-squares respectively—but it is non-existence and impossibility in a certain region that is neither all-embracing nor even that to which I primarily refer.

The region that (5) says that dragons don’t exist in is nature, and the region that (6) says that round-squares are impossible in is space. Jones (1893a, 454) says, “The Predicate of (5) (‘non-existent [in Nature]’) refers to the region of physical Nature; of (6) (‘impossible [in space]’) to the region of Space (or Space-imagination).”²⁷

On a straightforward view, something is impossible if and only if it couldn’t possibly exist or have being. Twardowski, Stout, and Meinong can all say that round-squares are impossible in this sense. Indeed, Stout (1896, 45) says that a round-square has an “internal absurdity which excludes existence.” (See also Stout 1894, 275.) And Meinong (1904, 82–83) mentions a round-square as an object whose non-being “is necessary.” But Jones can’t say that, since on her view round-squares exist: they have both a specific kind of existence (namely, existence in a region of supposition) and existence itself. Instead, her view might be that round-squares are impossible in the sense that they couldn’t exist in space, since she reads ‘impossible’ in (6) as ‘impossible in space’. She later distinguishes “two regions or orders of possibility or existence which do not coincide” and says that a round-square “has not the more specific possibility of being actualised in space which we are accustomed to assign to geometrical figures.”²⁸

3.4 The existential theory of judgment

Sentences (5) and (6) are meaningful, because ‘Dragons’ and ‘Round-squares’ apply to things that exist in some region. Jones (1893a, 454–55) says,

Unless I refer to something, existent somehow, in some region, what is it of which I predicate non-existence or impossibility (within a given region), what is it which I exclude from those regions to which ‘non-existent’ and ‘impossible’ refer? If a thing is non-existent everywhere, what does the exclusion of it from a given region mean? …

… Unless ‘existence’ in some region is postulated, I am wholly unable to understand how any meaning can be given to a so-called ‘Proposition’. (Jones 1913, 527–28) ²⁹

Similarly, in the reply to Johnson she says that a sentence that affirms or denies some things that combine attributes such as being round and being square would be “unmeaning” unless those things “‘exist’, somehow” (Jones 1893b, 221 n. 3).

Jones’s remarks here reflect her commitment to what Russell (1903, 449–50) describes as “the existential theory of judgment—the theory, that is, that every proposition is concerned with something that exists.”³⁰ In a review of a book by Hillebrand (1891), one of Franz Brentano’s students, Jones attributes the existential theory to Brentano.³¹ She says, “In Brentano’s view, then, the mind in every judgment accepts some object as existent, and regards the proposition expressing the judgment as true” (Jones 1892b, 277). Jones accepts the existential theory. Speaking of the theory, she says, “If this might be understood to mean that every proposition ‘by its very nature lays claim to truth’, and that every proposition implies the acceptance (as existent) of the matter referred to, the doctrine seems to me indisputable” (Jones 1892b, 277).

3.5 Two regions

Twardowski, Stout, and Meinong would deny that dragons and round-squares exist or have being. So they can all say that (5) and (6) are true because dragons and round-squares, which don’t exist anywhere, are non-existent and impossible, respectively. But Jones can’t say that, because she rejects things that don’t exist anywhere or don’t have any kind of existence.

Instead, Jones says that two different regions are at issue in each of (5) and (6). For the sentences to be meaningful, ‘Dragons’ and ‘Round-squares’ must apply to things that exist in some region. But, for the sentences to be true, ‘non-existent’ and ‘impossible’ must exclude those things from other regions. She says,

With regard to the Propositions (5) and (6) above, I should be inclined to say that each has a certain reference to two regions—the force of the Propositions being to affirm the (5) non-existence and (6) impossibility in a region referred to by the Predicate of the Subjects in (5) and (6) respectively. (Jones 1893a, 455)

That is, (5) is true, because dragons, which exist in one region (namely, a region of supposition), don’t exist in a second region (namely, nature); and (6) is true, because round-squares, which exist in the first region (namely, a region of supposition), are impossible in a third region (namely, space). Or, as Jones (1893a, 454) puts it, “in order to predicate non-existence in one sphere it is necessary to postulate existence in another.”³²

In the reply to Johnson, Jones makes the parallel point that two kinds of existence must be at issue in sentences like

7. Round-squares exist.

and

8. Round-squares do not exist.

There must be one kind of existence that round-squares have if we can talk about them in (7) and (8); and there must be another kind of existence that (7) says that round-squares have and that (8) says that they lack. Speaking of the things that the subject-names in such sentences apply to, she says, “And since they must thus indisputably in any case ‘exist’ in idea, it must be some other ‘existence’ which is postulated, whether for affirmation or denial” (Jones 1893b, 221 n. 3).³³

4 A New Law (and After)

4.1 Jones’s 1911 view

In A New Law, Jones says that ‘The round-square’ in

9. The round-square is non-existent.

applies to the round-square, which exists in a region of supposition. And (9) is true, because ‘non-existent’ is read as ‘non-existent in space’, and the round-square doesn’t exist in space. So far this is all in keeping with her earlier view. But in A New Law she goes further, giving arguments for the claim that the round-square doesn’t exist in space (it’s both round and square, and nothing in space is both) and the claim that the round-square is both round and square (if it weren’t, it wouldn’t be self-contradictory). One feature of her new view is that the round-square plays a role in reasoning, including the reasoning that leads to the conclusion that it doesn’t exist in space.

4.2 The round-square is both round and square

In the reply to Johnson, Jones (1893b, 220 n. 3) suggests that the round-square isn’t both round and square, since being round and being square are “attributes which should be divided among two” things. But, in A New Law, she argues that the round-square is both round and square.³⁴ She considers (9) and argues as follows: we have reason to assert (9), and the round-square is problematic; but we wouldn’t have reason to assert (9), and the round-square wouldn’t be problematic, if it weren’t both round and square; so it must be both round and square. She says,

In such propositions as: ‘The round-square is non‑existent’, we cannot dispense with a one-ness of denotation (extension) in the subject[-name], because, without this, [the names] round and square would have simply their intensional diversity—there would be no even hypothetical joining together of [the attributes] round and square, no problem, no difficulty, no reason to assert “non-existence,” to raise any question. (Jones 1911b, 60)

Here, the denotation of ‘The round-square’ is what it applies to—namely, the round-square—and the intensions of ‘round’ and ‘square’ are the attributes being round and being square, respectively.³⁵ The denotation, the round-square, is problematic precisely because it joins together the intensions, being round and being square.

Jones offers a similar argument in a paper given to the Aristotelian Society shortly after the publication of A New Law.³⁶ She considers

10. The round-square is self-contradictory.

and argues as follows: we are justified in saying (10); but we wouldn’t be if the round-square weren’t both round and square; so it must be both. She says that we “quite justifiably” describe the round-square as “self-contradictory,” and “it is only the supposition of roundness and squareness … as co-existent attributes of an object which is both square and round, that is self-contradictory and gives rise to difficulty” (Jones 1910–1911, 178).³⁷

Meinong can say that the round-square is self-contradictory in the sense that it violates the Law of Contradiction.³⁸ But Jones can’t say that, since she accepts the Law of Contradiction. (See Section 5.) Her view might instead be that the round-square is self-contradictory in the sense that predicates like ‘round’ and ‘not-round’—which she describes as “contradictory predicates”—both apply to it (Jones 1910–1911, 179). But then she shouldn’t say that ‘round’ and ‘not-round’ are contradictory in the sense that they can’t apply to the same thing.³⁹ For, on her view, they both apply to the round-square. Instead, she can say that ‘round’ and ‘not-round’ are contradictory in the sense that they can’t apply to the same thing if it exists in space.

4.3 The round-square exists in a region of supposition, not in space

The round-square can’t exist in space, but it exists in a region of supposition. Jones endorses something like the following argument.

Speaking of the “qualifications” or attributes being round and being square, Jones (1911b, 60–61) says,

Since in space, as known to us, roundness cannot be square, and squareness cannot be round, the denotation to which the two qualifications are assigned can “exist” only in the universe (or region) of hypothesis or supposition. This hypothetical combination is denied a place in the “universe” of actual space.

Here, “the denotation to which the two qualifications are assigned” is the thing that ‘the round-square’ applies to: namely, the round-square. Since it combines being round and being square, it can’t exist “in the ‘universe’ of actual space”; instead, it exists “in the universe (or region) of hypothesis or supposition.”

Admittedly, the mere fact that the round-square doesn’t exist in space isn’t enough to guarantee that it exists in a region of supposition instead. On Jones’s view, all kinds of things exist in all kinds of regions. In a paper that appeared in Mind in January 1911, shortly before the publication of A New Law, she says that the things that a name applies to “may be material or immaterial; they may have a fixed and definite position in space and time, or be, on the other hand, ideal, imaginary, or merely suppositional” (Jones 1911a, 41 n. 1). Perhaps some ideal or imaginary things don’t exist either in space or in a region of supposition. Still, there might be specific reasons for thinking that the round-square is “merely suppositional” rather than ideal or imaginary. For example, Jones (1910–1911, 178) says that the round-square can’t be imagined (at least not by “any sane and trained mind”) but can be supposed.⁴⁰

As mentioned in Section 3.5, Twardowski, Stout, and Meinong can say that

is true because ‘Round-squares’ applies to round-squares, which don’t have any kind of existence. But Jones can’t say that. Instead, she uses the distinction between existence in space and existence in a region of supposition. On her view, when we say that round-squares “do not exist” what we really mean is that they don’t exist in space. After speaking of “the region or universe of space as known to us,” she says,

when we say Round-squares do not exist we assign only our Predicate to that same extended universe, and the Subject [of attributes] which is round and square belongs to a region of the merest, and we may even say wildest, hypothesis—a region entirely separate from the region in which squares that are merely square, and rounds that are simply round, have their “existence.” The round-squares are declared to be non-existent …

But that non-existence does not signify complete and unmitigated non-existence, but only the absence of spatial existence. (Jones 1911b, 62)

Because we can talk about them, round-squares have one kind of existence (namely, existence in a region of supposition); but it’s because they lack another kind of existence (namely, spatial existence) that we can truly say that they “do not exist.”⁴¹ Jones’s account of negative existentials here is an implementation of her suggestion in the reply to Johnson that, in addition to the kind of existence had by the things that we’re talking about, there must “some other ‘existence’ which is postulated.”

In the 1911 Aristotelian Society paper, Jones uses a distinction between two kinds of existence to account for

11. The existent-round-square is not existent.

She says that, if (11) is true, then the first ‘existent’ means “existent in a region of supposition,” and the second ‘existent’ means “existent in physical space” (Jones 1910–1911, 179).⁴² The round-square that exists in a region of supposition doesn’t exist in physical space.

4.4 The round-square plays a role in reasoning

We have reason to say that the round-square can’t exist in space. This reason comes from the argument discussed at the beginning of the previous subsection. And that argument begins with a premise about the round-square: namely, that it’s both round and square. The round-square thus plays a role in reasoning and, indeed, in the very reasoning that leads to the conclusion that it can’t exist in space.

We can suppose that the round-square is both round and square and draw conclusions from that supposition. Speaking of conjoining the attributes being round and being square in the round-square, Jones (1911b, 61) says, “We may ‘suppose’ the conjunction…, we can assert it, and trace its consequences, but that is all,—as I might suppose that I could fly like an eagle, swim like a fish, and be stronger than an elephant, and deduce various things that I could do on these suppositions.” One of the consequences that we can trace from our supposition about the round-square is that it can’t exist in space.

Jones makes a similar point in a paper prepared for a joint session of the Aristotelian Society, the British Psychological Society, and the Mind Association in 1915.⁴³ Speaking of supposing that the round-square is both round and square, she says, “And we have to suppose this, after some fashion, in order even to recognise its self-contradictoriness, and to reject it” (Jones 1914–1915, 361). The self-contradictoriness being recognized here is the self-contradictoriness of the round-square, and what’s being rejected is its existence in space.

Jones doesn’t say how a region of supposition is related to other regions, including a region of imagination. If what distinguishes things that exist in a region of supposition is that they play a role in reasoning, then what happens when we reason about whether dragons, for example, exist in a region of imagination?⁴⁴ Jones allows things to have more than one kind of existence. (For example, the round-square has both existence in a region of supposition and existence itself.) It might be that, when we reason about dragons and conclude that they don’t exist in space but do exist in a region of imagination, they exist both in a region of supposition and—assuming our conclusion is correct—a region of imagination. Similarly, when we reason about King’s College Chapel, it would exist both in a region of supposition and in space.

5 Avoiding Contradiction

5.1 One problem and three responses

Any view that posits a round-square runs the risk of contradiction. If the round-square is both round and square, and everything square isn’t round, then the round-square both is, and isn’t, round. This is as much a risk for Jones’s view as it is for Twardowski’s, Stout’s, and Meinong’s. Indeed, Russell (1905, 483) takes it to be the “chief objection” to Meinong’s view. But there are responses.

First, an easy response is to deny that the round-square is both round and square. More recently, Tim Crane (2013, 23, 27, 58–59) might favor this response. But it isn’t available to Jones in 1911, since on her view the round-square is both round and square. This response isn’t available to Meinong or Twardowski either.

Second, a hard response is to accept that some contradictions are true: the round-square is round, and it isn’t. More recently, Richard Sylvan (1980, 497–99, 503–6) might favor this response. And Meinong (1907, 14–20) might be sympathetic to it. But it isn’t available to Jones, since she accepts the Law of Contradiction (see below).

Third, a moderate response is to say that, although the round-square is both round and square, it doesn’t follow that it isn’t round, because it’s not the case that everything square isn’t round. More recently, Terence Parsons (1980, 38–42) has defended this response. This response is available to Jones. She might grant that everything square isn’t round if it exists in space but say that something square might be round if it doesn’t exist in space. On this view, the round-square is round, and it’s square; but, because it doesn’t exist in space, there’s no incompatibility between its being round and its being square.

5.2 Two kinds of negation

Jones distinguishes two kinds of negation. For example, she distinguishes sentences of the form A is-not A, where the negation is in the copula ‘is-not’, from sentences of the form A is not-A, where the negation is in the predicate ‘not-A’.⁴⁵ (She even discusses sentences of the form A is-not not-A, which contain both kinds of negation. See Jones (1890, 48, 51–52; 1911a, 42.) So she would distinguish two kinds of negation of

12. The round-square is round.

On the one hand, there’s

which contains copula-negation; and, on the other hand, there’s

which contains predicate-negation. And she can distinguish two formulations of the Law of Contradiction.

(LC) implies that (12) and (~12) can’t both be true, since they’re of the form S is P and S is‑not P; whereas (LC-pred) implies that (12) and (~12­‑­pred) can’t both be true, since they’re of the form S is P and S is not-P. I take (LC) to be Jones’s official formulation of the Law of Contradiction (see Jones 1910–1911, 169; 1911b, 2, 16). She sometimes suggests that (LC) and (LC-pred) are equivalent (Jones 1910–1911, 169; 1911b, 17–18). But I think the case of the round-square reveals that they’re not and that she shouldn’t accept (LC-pred).

Jones accepts both (12) and

13. The round-square is square.

And she takes (12) to imply (~12-pred). (12) and (~12-pred) violate (LC-pred) but not (LC). In the 1911 Aristotelian Society paper, she says,

If we have admitted a Term containing self-contradictory elements, there is no further difficulty in asserting of it contradictory predicates. A round-square is round, and it is also square, i.e., not-round. The predicates are contradictory certainly, but they follow from the Subject[-name]; the contradictory statements are analytic. (Jones 1910–1911, 179)

Here, the term “containing self-contradictory elements” is ‘the round-square’, and the “contradictory predicates” are ‘round’ and ‘not-round’.⁴⁶ The predicates ‘round’ and ‘not-round’ “follow from” the subject-name ‘the round-square’ in the sense that (12) and (13) are analytic, and (13) analytically implies (~12-pred). It might seem that “the contradictory statements” that Jones is saying are analytic are (12) and (~12), which would violate (LC). But, in light of her distinction between two kinds of negation (and her focus on contradictory subject-names and predicates in the passage quoted above), I think she should be read instead as saying that it’s (12) and (~12-pred) that are analytic. And (12) and (~12-pred) are consistent with (LC).

There’s a well-known argument against impossible worlds due to David Lewis. He says,

suppose travellers told of a place in this world—a marvellous mountain, far away in the bush—where contradictions are true. Allegedly we have truths of the form ‘On the mountain both P and not P’. But … the alleged truth ‘On the mountain both P and not P’ is equivalent to the overt contradiction ‘On the mountain P, and not: on the mountain P’ … So to tell the alleged truth about the marvellously contradictory things that happen on the mountain is no different from contradicting yourself. But there is no subject matter, however marvellous, about which you can tell the truth by contradicting yourself … An impossible world where contradictions are true would be no better. (Lewis 1986, 7 n. 3)

As William Lycan (1994, 40) points out, one way to block Lewis’s argument is to deny the inference from

14. On the mountain, the round-square is-not round.

(which contains negation inside the scope of “On the mountain”) to

15. It is-not the case that, on the mountain, the round-square is round.

(which contains negation outside the scope of “On the mountain”).⁴⁷ But Jones can offer a different reply. She can say that (14), which contains copula-negation, is false and that what’s true instead is

16. On the mountain, the round-square is not-round.

which contains predicate-negation. On her view, there’s a place where there’s a round-square, which is round and square (and also not-round and not-square). But this marvellous place is, if not the actual world, then at least a region of supposition; and it’s not a place where contradictions are true.⁴⁸

Acknowledgements

For comments and discussion, thanks to Einar Duenger Bøhn, Brad Cokelet, Dale Dorsey, Ben Eggleston, Zach Elmer, Damian Fisher, Clint Hurshman, Scott Jenkins, Marcy Lascano, Eileen Nutting, Alex Radulescu, Jason Raibley, Tom Tuozzo, other colleagues and students at the University of Kansas, and several anonymous referees.