Friday, September 3, 2021

The Bakhtin Circle

 The Bakhtin Circle was a 20th century school of Russian thought which centered on the work of Mikhail Mikhailovich Bakhtin (1895-1975). The circle addressed philosophically the social and cultural issues posed by the Russian Revolution and its degeneration into the Stalin dictatorship. Their work focused on the centrality of questions of significance in social life in general and artistic creation in particular, examining the way in which language registered the conflicts between social groups. The key views of the circle are that linguistic production is essentially dialogic, formed in the process of social interaction, and that this leads to the interaction of different social values being registered in terms of reaccentuation of the speech of others. While the ruling stratum tries to posit a single discourse as exemplary, the subordinate classes are inclined to subvert this monologic closure. In the sphere of literature, poetry and epics represent the centripetal forces within the cultural arena whereas the novel is the structurally elaborated expression of popular ideologiekritik, the radical criticism of society. Members of the circle included Matvei Isaevich Kagan (1889-1937); Pavel Nikolaevich Medvedev (1891-1938); Lev Vasilievich Pumpianskii (1891-1940); Ivan Ivanovich Sollertinskii (1902-1944); Valentin Nikolaevich Voloshinov (1895-1936); and others.

M.M. Bakhtin and his circle began meeting in the Belorussian towns of Nevel and Vitebsk in 1918 before moving to Leningrad in 1924. Their group meetings were terminated due to the arrest of many of the group in 1929. From this time until his death in 1975, Bakhtin continued to work on the topics which had occupied his group, living in internal exile first in Kustanai (Kazakhstan, 1930-36), Savelovo (about 100 km from Moscow, 1937-45), Saransk (Mordovia, 1936-7, 1945-69) and finally moving in 1969 to Moscow, where he died at the age of eighty. In Saransk Bakhtin worked at the Mordov Pedagogical Institute (now University) until retirement in 1961.

 

The Bakhtin circle is reputed to have been initiated by Kagan on his return from Germany, where he had studied philosophy in Leipzig, Berlin and Marburg. He had been a pupil of the founder of Marburg Neo-Kantianism Herman Cohen and had attended lectures by Ernst Cassirer. Kagan established a “Kantian Seminar” at which various philosophical, religious and cultural issues were discussed. Kagan was a Jewish intellectual who had been a member of the Social Democratic Party (the precursor of the Bolsheviks and Mensheviks) and he may have been attracted to Cohen’s philosophy for its supposed affinity with Marxism (Cohen regarded his ethical philosophy as completely compatible with that of Marx), while rejecting the atheism of Russian Communism. Whatever the truth of the matter, the members of the circle did not restrict themselves to academic philosophy but became closely involved in the radical cultural activities of the time, activities which became more intense with the movement of the group to Vitebsk, where many important avant-garde artists such as Malevich and Chagall had settled to avoid the privations of the Civil War. One of the group, Pavel Medvedev, a graduate in law from Petrograd University, became rector of the Vitebsk Proletarian University, editing the town’s cultural journalIskusstvo (Art) to which he and Voloshinov contributed articles, while Bakhtin and Pumpianskii both gave public lectures on a variety of philosophical and cultural topics, as seen in recently published student notes. Pumpianskii, it is known, never finished his studies at Petrograd university, while it is doubtful whether Bakhtin had any formal higher education at all despite his claims, now disproven, to have graduated from the same University in 1918. It seems that Bakhtin attempted to gain acceptance in academic circles by adopting aspects of his older brother’s biography. Nikolai Bakhtin had a solid classical education from his German governess and graduated from Petrograd University, where he had been a pupil of the renowned classicist F.F. Zelinskii. Bakhtin had therefore been exposed to philosophical ideas since his youth. After Nikolai’s departure for the Crimea, and Mikhail’s move to Nevel, it seems that Kagan took the place of his brother as unofficial mentor, having an important influence on Bakhtin’s philosophy in a new and exciting cultural environment, although the two friends went their separate ways in 1921, the year Bakhtin married.

 

Kagan, however, moved to take up a teaching position at the newly established provincial university in Orel in 1921. While there he published the only sustained piece of philosophy to be published by a member of the group before the late 1920s entitled “Kak vozmozhna istoria” (How Is History Possible) in 1922. The same year he produced an obituary of Hermann Cohen in which he stressed the historical and sociological aspects of Cohen’s philosophy and wrote other unpublished works. 1922 also saw the publication of Pumpianskii’s paper “Dostoevskii i antichnost´” (Dostoyevsky and Antiquity), a theme that was to recur in Bakhtin’s work for many years. While Bakhtin himself did not publish any substantial work until 1929, he was clearly working on matters related to Neo-Kantian philosophy and the problem of authorship at this time. Bakhtin’s earliest published work is the two page “Iskusstvo i otvetstvennost´” (Art and Answerability) from 1919 and fragments of a larger project on moral philosophy written between 1920 and 1924, now usually referred to as K filosofii postupka (Towards a Philosophy of the Act).

 

Most of the group’s significant work was produced after their move to Leningrad in 1924. It seems that there the group became acutely aware of the challenge posed by Saussurean linguistics and its development in the work of the Formalists. Thus there emerges a new awareness of the importance of the philosophy of language in philosophy and poetics. The most significant work on the philosophy of language was published in the period 1926-1930 by Voloshinov: a series of articles and a book entitledMarksizm i filosofia iazyka (Marxism and the Philosophy of Language) (1929). Medvedev, who had been put in charge of the archive of the symbolist poet Aleksandr Blok, participated in the vigorous discussions between Marxist and formalist literary theorists with a series of articles and a book, Formal´lnyi metod v literaturovedenii (The Formal Method in Literary Scholarship) (1928) and the first book-length study of Blok’s work. Voloshinov also published an article and a book (1925, 1926) on the debate which raged around Freudianism at the time. In 1929 Bakhtin produced the first edition of his famous monograph Problemy tvorchestva Dostoevskogo (Problems of Dostoyevsky’s Work), but many other works dating from 1924-9 remained unpublished and usually unfinished. Among these was a critical essay on formalism called “Problema soderzheniia i formy v slovesnom khudozhestvennom tvorchestve” (The Problem of Content, Material and Form in Verbal Artistic Creation) (1924) and a book length study called “Avtor i geroi v esteticheskoi deiatel´nosti” (Author and Hero in Aesthetic Activity) (1924-7).

 

Since the 1970s the works published under the names of Voloshinov and Medvedev have often been ascribed to Bakhtin, who neither consented nor objected. A voluminous, ideologically motivated, often bad-tempered and largely futile body of literature has grown up to contest the issue one way or another, but since there is no concrete evidence to suggest that the published authors were not responsible for the texts which bear their names, there seems no real case to answer. It seems much more likely that the materials were written as a result of lively group discussions around these issues, which group members wrote up according to their own perspectives afterwards. There are clearly many philosophical, ideological and stylistic discrepancies which, despite the presence of certain parallels and points of agreement, suggest these very different works were largely the work of different authors. In accordance with Bakhtin’s own philosophy, it seems logical to treat them as rejoinders in ongoing dialogues between group members on the one hand and between the group and other contemporary thinkers on the other.

 

The sharp deterioration in the situation of unorthodox intellectuals in the Soviet Union at the end of 1928 effectively broke the Bakhtin circle up. Bakhtin, whose health had already begun to deteriorate, was arrested, presumably because of his connection with the St. Petersburg Religious-Philosophical society, and was sentenced to ten years on the Solovetskii Islands. After vigorous intercession by Bakhtin’s friends, a favourable review of his Dostoyevsky book by Commissar of Enlightenment Lunacharskii and a personal appeal by Maksim Gor´kii, this was commuted to six years exile in Kazakhstan. With the tightening of censorship at the time, very little was published by Voloshinov, while Medvedev published a book on theories of authorship V laboratorii pisatelia (In the Laboratory of the Writer) in 1933 and a new version of the Formalism study, revised to fit in more closely with the ideological requirements of the time, in 1934. Medvedev was appointed full professor at the Leningrad Historico-Philological Institute but was arrested and disappeared during the terror of 1938. Voloshinov worked at the Herzen Pedagogical Institute in Leningrad until 1934 when he contracted tuberculosis. He died in a sanitorium two year later leaving unfinished a translation of the first volume of Ernst Cassirer’s The Philosophy of Symbolic Forms, a book which is of considerable importance in the work of the circle. Kagan died of angina in 1937 after working as editor of an encyclopedic atlas of energy resources in the Soviet Union for many years. Pumpianskii pursued a successful career as Professor of Literature at Leningrad University, but published only short articles and introductions to works of Russian authors, most notably Turgenev. Sollertinskii joined the Leningrad Philharmonic in 1927 as a lecturer, but soon established himself as one of the leading Soviet musicologists, producing over two hundred articles, books and reviews. He died of a heart attack, probably resulting from the privations of the Leningrad blockade, in 1944.

 

While in Kazakhstan Bakhtin began work on his now famous theory of the novel which resulted in the now famous articles Slovo v romane (Discourse in the Novel) (1934-5), Iz predystorii romannogo slovo (From the Prehistory of Novelistic Discourse) (1940), Epos i roman (Epic and Novel) (1941),Formy vremeni i khronotopa v romane (Forms of Time and Chronotope in the Novel) (1937-8). Between 1936 and 1938 he completed a book on the Bildungsroman and its significance in the history of realism which was lost when the publishing house at which the manuscript was lying awaiting publication was destroyed in the early days of the German invasion of the Soviet Union in 1941. Voluminous, most still unpublished, preparatory material still exists, although part is lost, allegedly because Bakhtin used it for cigarette papers during the wartime paper shortage. Bakhtin’s exceptional productiveness at this time is further accentuated when one considers that one of his legs was amputated in February 1938. He had suffered from inflammation of the bone marrow, osteomyelitis, for many years, which gave him a lot of pain, high temperatures, and often confined him to bed for weeks on end. This had been a factor in the appeals of his friends and acquaintances for clemency when he was internally exiled, a factor that may well have saved his life. This did not, however, prevent him from presenting a now famous doctoral thesis on Rabelais to the Gor´kii Institute of World Literature in 1940. The work proved extremely controversial in the hostile ideological climate of the time and it was not until 1951 that Bakhtin was eventually granted the qualification of kandidat. It was not published in book form until 1965.

 

The period between the completion of the Rabelais study and the second edition of the Dostoyevsky study in 1963 is perhaps the least well known of Bakhtin’s life in terms of work produced. This has been recently (1996) rectified with the publication of archival materials from this period, when Bakhtin was working as a lecturer at the Mordov Pedagogical Institute. The most substantial work dating from this period is Problema rechevykh zhanrov (The Problem of Speech Genres) which was most likely produced in response to the reorganisation of Soviet linguistics in the wake of Stalin’s article Marksizm i voprosy iazykoznaniia (Marxism and Questions of Linguistics) of 1953. Many other fragments exist from this time, including notes for a planned article about Maiakovskii and more methodological comments on the study of the novel.

 

In the more liberal atmosphere of the so-called “thaw” following Khruschev’s accession, Bakhtin’s work on Dostoyevsky came to the attention of a group of younger scholars led by Vadim Kozhinov who, upon finding out that he was still alive, contacted Bakhtin and tried to convince him to republish the 1929 Dostoyevsky book. After some initial hesitation, Bakhtin responded by significantly expanding and fundamentally altering the overall project. It was accepted for publication in September 1963 and received a generally favourable reception. Publication of the Rabelais study, newly edited for purposes of acceptability (mainly the toning down of scatology and an analysis of a speech by Lenin) followed soon after. As Bakhtin’s health continued to decline, he was taken to hospital in Moscow in 1969 and in May 1970 he and his wife, who died a year later, were moved into a retirement home just outside Moscow. Bakhtin continued to work until just before his death in 1975, producing work of a mainly methodological character.

 

Since Bakhtin’s death, several collections of his work have appeared in Russian and many translations have followed. English language translations have been appearing since 1968, although the quality of translation and systematicity of publication has been uneven. Up to ten different translators have published work by a writer whose terminology is very specific, often rendering key concepts in a variety of different ways. This has exacerbated problems of interpretation and questions of theoretical heritage, especially since there is a quite sharp distinction between works written before and after the 1929 Dostoyevsky study. Another problem has been the questions of authorship of the Bakhtin circle and the extent to which a Marxist vocabulary in the works of Voloshinov and Medvedev should be taken at face value. Those, for example, who argue Bakhtin was the author of these works also tend to argue that the vocabulary is mere “window dressing” to facilitate publication, while those who support the authenticity of the original publications also tend to take the Marxist arguments seriously. As a result writers about Bakhtin have tended to choose one period of Bakhtin’s career and treat it as definitive, a practice which has produced a variety of divergent versions of “Bakhtinian” thought. The recent appearance of the first volume of a collected works in Russian might help to overcome the problems which have dogged Bakhtin studies.

Thursday, July 29, 2021

The Analytic/Synthetic Distinction

 An “analytic” sentence, such as “Ophthalmologists are doctors,” has historically been characterized as one whose truth depends upon the meanings of its constituent terms (and how they’re combined) alone, as opposed to a more usual “synthetic” sentence, such as “Ophthalmologists are rich,” whose truth depends also upon the facts about the world that the sentence represents, e.g., that ophthalmologists are rich. This is sometimes called the “metaphysical” characterization of the distinction, concerned with the source of the truth of the sentences. A more cautious, epistemological characterization is that analytic sentences are those whose truth can be known merely by knowing the meanings of the constituent terms, as opposed to having also to know something about the represented world. Beginning with Frege, many philosophers hoped to show that the truths of logic and mathematics and other apparently a priori domains, such as much of philosophy and the foundations of science, could be shown to be at least epistemically analytic by careful “conceptual analysis.” This project encountered a number of problems that have seemed so intractable as to lead some philosophers, particularly Quine, to doubt the reality of the distinction. Surprisingly, this led him and others to doubt the reality and determinacy of psychological states. There have been a number of interesting reactions to this scepticism, both in philosophy and in linguistics, but, while the reality of psychological states might be saved, it has yet to be shown that appeals to the analytic will ever be able to ground the a priori in the way that philosophers had hoped

Saturday, July 10, 2021

Implicit Bias

 Research on “implicit bias” suggests that people can act on the basis of prejudice and stereotypes without intending to do so. While psychologists in the field of “implicit social cognition” study consumer products, self-esteem, food, alcohol, political values, and more, the most striking and well-known research has focused on implicit biases toward members of socially stigmatized groups, such as African-Americans, women, and the LGBTQ community. For example, imagine Frank, who explicitly believes that women and men are equally suited for careers outside the home. Despite his explicitly egalitarian belief, Frank might nevertheless behave in any number of biased ways, from distrusting feedback from female co-workers to hiring equally qualified men over women. Part of the reason for Frank’s discriminatory behavior might be an implicit gender bias. Psychological research on implicit bias has grown steadily , raising metaphysical , epistemological , and ethical questions

 

While Allport’s (1954) The Nature of Prejudice remains a touchstone for psychological research on prejudice, the study of implicit social cognition has two distinct and more recent sets of roots. The first stems from the distinction between “controlled” and “automatic” information processing made by cognitive psychologists in the 1970s (e.g., Shiffrin & Schneider 1977). While controlled processing was thought to be voluntary, attention-demanding, and of limited capacity, automatic processing was thought to unfold without attention, to have nearly unlimited capacity, and to be hard to suppress voluntarily (Payne & Gawronski 2010; see also Bargh 1994). In important early work on implicit cognition, Fazio and colleagues showed that attitudes can be understood as activated by either controlled or automatic processes. In Fazio’s (1995) “sequential priming” task, for example, following exposure to social group labels (e.g., “black”, “women”, etc.), subjects’ reaction times (or “response latencies”) to stereotypic words (e.g., “lazy” or “nurturing”) are measured. People respond more quickly to concepts closely linked together in memory, and most subjects in the sequential priming task are quicker to respond to words like “lazy” following exposure to “black” than “white”. Researchers standardly take this pattern to indicate a prejudiced automatic association between semantic concepts. The broader notion embedded in this research was that subjects’ automatic responses were thought to be “uncontaminated” by controlled or strategic responses (Amodio & Devine 2009).

 

While this first stream of research focused on automaticity, a second stream focused on (un)consciousness. Many studies demonstrated that awareness of stereotypes can affect social judgment and behavior in relative independence from subjects’ reported attitudes (Devine 1989; Devine & Monteith 1999; Dovidio & Gaertner 2004; Greenwald & Banaji 1995; Banaji et al. 1993). These studies were influenced by theories of implicit memory (e.g., Jacoby & Dallas 1981; Schacter 1987), leading to Greenwald & Banaji’s original definition of “implicit attitudes” as

 

·         introspectively unidentified (or inaccurately identified) traces of past experience that mediate favorable or unfavorable feeling, thought, or action toward social objects. (1995: 8)

 

·         The guiding idea here, as Dovidio and Gaertner (1986) put it, is that in the modern world prejudice has been “driven underground,” that is, out of conscious awareness. This idea has led to the common view that what makes a bias implicit is that a person is unwilling or unable to report it. Recent findings have challenged this view, however .

 

Implicit Measures

What a person says is not necessarily a good representation of the whole of what she feels and thinks, nor of how she will behave. Arguably, the central advance of research on implicit social cognition is the ability to assess people’s thoughts, feelings, and behavior without having to ask them directly, “what do you think/feel about X?” or “what would you do in X situation?”

 

Implicit measures, then, might be thought of as instruments that assess people’s thoughts, feelings, and behavior indirectly, that is, without relying on “self-report.” This is too quick, however. For example, a survey that asks “what do you think of black people” is explicit and direct, in the sense that the subject’s judgment is both explicitly reported and the subject is being directly asked about the topic of interest to the researchers. However, a survey that asks “what do you think about Darnell” (i.e., a person with a stereotypically black name) is explicit and indirect, because the subject’s judgment is explicitly reported but the content of what is being judged (i.e., the subject’s attitudes toward race) is inferred by the researcher. The distinction between direct and indirect measures is also relative rather than absolute. Even in some direct measures, such as personality inventories, subjects may not be completely aware of what is being studied.

 

In the literature, “implicit” is used to refer to at least four distinct things (Gawronski & Brannon 2017): (1) a distinctive psychological construct, such as an “implicit attitude,” which is assessed by a variety of instruments; (2) a family of instruments, called “implicit measures,” that assess people’s thoughts and feelings in a specific way (e.g., in a way that minimizes subjects’ reliance on introspection and their ability to respond strategically); (3) a set of cognitive and affective processes—“implicit processes”—that affect responses on a variety of measures; and (4) a kind of evaluative behavior—e.g., a categorization judgment—elicited by specific circumstances, such as cognitive load.

 

Monday, July 5, 2021

Abstract Objects

  It is widely supposed that every entity falls into one of two categories: Some are concrete; the rest abstract. The distinction is supposed to be of fundamental significance for metaphysics and epistemology.

 

 The abstract/concrete distinction has a curious status in contemporary philosophy. It is widely agreed that the distinction is of fundamental importance. And yet there is no standard account of how it should be drawn. There is a great deal of agreement about how to classify certain paradigm cases. Thus it is universally acknowledged that numbers and the other objects of pure mathematics are abstract (if they exist), whereas rocks and trees and human beings are concrete. Some clear cases of abstracta are classes, propositions, concepts, the letter ‘A’, and Dante’s Inferno. Some clear cases of concreta are stars, protons, electromagnetic fields, the chalk tokens of the letter ‘A’ written on a certain blackboard, and James Joyce’s copy of Dante’s Inferno.

 

The challenge is to say what underlies this dichotomy, either by defining the terms explicitly, or by embedding them in a theory that makes their connections to other important categories more explicit. In the absence of such an account, the philosophical significance of the contrast remains uncertain. We may know how to classify things as abstract or concrete by appeal to intuition. But in the absence of theoretical articulation, it will be hard to know what (if anything) hangs on the classification.

 

It should be stressed that there need not be one single “correct” way of explaining the abstract/concrete distinction. Any plausible account will classify the paradigm cases in the standard way, and any interesting account will draw a clear and philosophically significant line in the domain of objects. Yet there may be many equally interesting ways of accomplishing these two goals, and if we find ourselves with two or more accounts that do the job rather well, there will be no point in asking which corresponds to the real abstract/concrete distinction. This illustrates a general point: when technical terminology is introduced in philosophy by means of examples but without explicit definition or theoretical elaboration, the resulting vocabulary is often vague or indeterminate in reference. In such cases, it is normally pointless to seek a single correct account. A philosopher may find himself asking questions like, ‘What is idealism?’ or ‘What is a substance?’ and treating these questions as difficult questions about the underlying nature of a certain determinate philosophical category. A better approach is to recognize that in many cases of this sort, we simply have not made up our minds about how the term is to be understood, and that what we seek is not a precise account of what this term already means, but rather a proposal for how it might fruitfully be used in the future. Anyone who believes that something in the vicinity of the abstract/concrete distinction matters for philosophy would be well advised to approach the project of explaining the distinction with this in mind.

 

2. Historical Remarks

The contemporary distinction between abstract and concrete is not an ancient one. Indeed, there is a strong case for the view that despite occasional anticipations, it played no significant role in philosophy before the 20th century. The modern distinction bears some resemblance to Plato’s distinction between Forms and Sensibles. But Plato’s Forms were supposed to be causes par excellence, whereas abstract objects are generally supposed to be causally inert in every sense. The original ‘abstract’/‘concrete’ distinction was a distinction among words or terms. Traditional grammar distinguishes the abstract noun ‘whiteness’ from the concrete noun ‘white’ without implying that this linguistic contrast corresponds to a metaphysical distinction in what these words stand for. In the 17th century this grammatical distinction was transposed to the domain of ideas. Locke speaks of the general idea of a triangle which is “neither Oblique nor Rectangle, neither Equilateral, Equicrural nor Scalenon [Scalene]; but all and none of these at once,” remarking that even this idea is not among the most “abstract, comprehensive and difficult” (Essay IV.vii.9). Locke’s conception of an abstract idea as one that is formed from concrete ideas by the omission of distinguishing detail was immediately rejected by Berkeley and then by Hume. But even for Locke there was no suggestion that the distinction between abstract ideas and concrete or particular ideas corresponds to a distinction among objects. “It is plain, …” Locke writes, “that General and Universal, belong not to the real existence of things; but are Inventions and Creatures of the Understanding, made by it for its own use, and concern only signs, whether Words or Ideas”

 

The abstract/concrete distinction in its modern form is meant to mark a line in the domain of objects or entities. So conceived, the distinction becomes a central focus for philosophical discussion only in the 20th century. The origins of this development are obscure, but one crucial factor appears to have been the breakdown of the allegedly exhaustive distinction between the mental and the material that had formed the main division for ontologically minded philosophers since Descartes. One signal event in this development is Frege’s insistence that the objectivity and aprioricity of the truths of mathematics entail that numbers are neither material beings nor ideas in the mind. If numbers were material things (or properties of material things), the laws of arithmetic would have the status of empirical generalizations. If numbers were ideas in the mind, then the same difficulty would arise, as would countless others. (Whose mind contains the number 17? Is there one 17 in your mind and another in mine? In that case, the appearance of a common mathematical subject matter is an illusion.) In The Foundations of Arithmetic (1884), Frege concludes that numbers are neither external ‘concrete’ things nor mental entities of any sort. Later, in his essay “The Thought” (Frege 1918), he claims the same status for the items he calls thoughts—the senses of declarative sentences—and also, by implication, for their constituents, the senses of subsentential expressions. Frege does not say that senses are ‘abstract’. He says that they belong to a ‘third realm’ distinct both from the sensible external world and from the internal world of consciousness. Similar claims had been made by Bolzano (1837), and later by Brentano (1874) and his pupils, including Meinong and Husserl. The common theme in these developments is the felt need in semantics and psychology as well as in mathematics for a class of objective (i.e., non-mental) supersensible entities. As this new ‘realism’ was absorbed into English speaking philosophy, the traditional term ‘abstract’ was enlisted to apply to the denizens of this ‘third realm’.

 

Philosophers who affirm the existence of abstract objects are sometimes called platonists; those who deny their existence are sometimes called nominalists. This terminology is lamentable, since these words have established senses in the history of philosophy, where they denote positions that have little to do with the modern notion of an abstract object. However, the contemporary senses of these terms are now established, and so the reader should be aware of them. (In Anglophone philosophy, the most important source for this terminological innovation is Quine. See especially Goodman and Quine 1947.) In this connection, it is essential to bear in mind that modern platonists (with a small ‘p’) need not accept any of the distinctive metaphysical and epistemological doctrines of Plato, just as modern nominalists need not accept the distinctive doctrines of the medieval nominalists. Insofar as these terms are useful in a contemporary setting, they stand for thin doctrines: platonism is the thesis that there is at least one abstract object; nominalism is the thesis that the number of abstract objects is exactly zero (Field 1980). The details of this dispute are discussed in the article on nominalism in metaphysics. (See also the entry on platonism in metaphysics.) The aim of the present article is not to describe the case for or against the existence of abstract objects, but rather to say what an abstract object would be if such things existed.