Dale Jacquette's research while affiliated with Universität Bern and other places
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Publications (138)
A conceptual analysis of the problem of induction suggests that the difficulty of justifying probabilistic reasoning depends on a mistaken comparison between deductive and inductive inference.
Inductive reasoning is accordingly thought to stand in need of special justification because it does not measure up to the standard of conditional absolute c...
Cambridge Core - English Language and Linguistics: General Interest - Frege - by Dale Jacquette
A non-Fregean solution is offered to the problem of understanding the meaning of quotation statements. Quotations are analyzed by Frege in terms of a distinction that is judged unnecessary and counterintuitive, between customary and quoted indirect reference interpreted as customary sense. There are intuitive objections to Frege’s maneuver that are...
The object of inquiry in these pages is to arrive at a better understanding of a frequently used but seldom explained terminology in the history of modern philosophy. The distinction is that ostensibly between seventeenth-century Rationalism and eighteenth-century Empiricism. The division is of immediate relevance in historically situating the phil...
Wittgenstein is simultaneously famous and notorious for his tantalizing illustration-free remarks about ‘simple objects’ (einfache Gegenstände) in TractatusLogico-Philosophicus (TLP). What does Wittgenstein, among great theorists of objects in the history of philosophy, mean by an ‘object’, and in what sense are TLP objects ‘simple’? I consider an...
Wittgenstein's thought was profoundly shaped in both Tractatus and post-Tractatus periods by Schopenhauer's transcendental idealism. In the later Philosophical Investigations, posthumously published in 1953, Wittgenstein identifies rules of philosophical grammar for language-games in relation to their pragmatic point and purpose, practically ground...
An unconventional formalization of the canonical (Aristotelian-Boethian) square of opposition in the notation of classical symbolic logic secures all but one of the canonical square’s grid of logical interrelations between four A-E-I-O categorical sentence types. The canonical square is first formalized in the functional calculus in Frege’s Begriff...
The questions at issue in this discussion of Hilary Putnam’s Twin Earth thought experiment include the scope and limits of narrow versus wide meaning, the role of attempting to successfully refer as opposed to successfully referring in determining where meaning resides and how thought functions in relation to the meanings of words and sentences. Tw...
This essay takes a critical look at Jonathan Berg’s theory of direct belief. Berg’s analysis of the concept of direct belief is considered insightful, but doubts are raised concerning his generalization of the purely extensional truth conditional semantics of direct belief ascription sentences to the truth conditional semantics of all belief ascrip...
Category systems are explained and defined. Historical examples are discussed in relation to the concept of a taxonomy in which one category subsumes another subcategory. The task of category selection and arrangement is characterized as the work of conceptual analysis of the same body of facts or relations. Category system building is further desc...
In his essay, ‘Truth in Fiction’, David Lewis raises four objections to a Meinongian semantics of fiction. Meinongian semantic domains admit existent and nonexistent objects, including objects ostensibly referred to in fiction, and permit reference and true predication of constitutive properties to existent and nonexistent objects alike. Lewis prop...
This essay considers Meinong’s object theory in light of criticisms originating in Russell’s 1905 essay ‘On Denoting’. A general defense of object theory exposes misinterpretations of Meinong’s writings on Russell’s part, and explains some of the main strengths and advantages of Meinong’s logic and semantic theory overriding Russell’s objections. T...
Meinong’s mature doctrine of the Außersein of the pure object implies that any intended object can be considered independently of its ontic status, literally outside of being and non-being (jenseits von Sein und Nichtsein). The doctrine is crucial to Meinong’s inclusion in the object theory domain of every intended object without consideration for...
Meinong introduces the concept of implexive being and non-being to explain the metaphysics of universals, and as a contribution to the theory of reference and perception. Meinong accounts for Aristotle’s doctrine of the inherence of secondary substances in primary substances in object theory terms as the implection of incomplete universals in compl...
Biography of Meinong, emphasizing his studies with Brentano and the role of intentionality theory in Meinong’s thought as an offshoot of the Brentano school. The facts of Meinong’s life and education, academic advancement and scientific and philosophical contributions, are presented as background to the main principles of his philosophy. Meinong at...
The possibilities are explored of considering nothing as the intended object of thoughts that are literally about the concept of nothing(ness) first, and thereby of nothing(ness). Nothing(ness), on the proposed analysis, turns out to be nothing other than the property of being an intendable object. There are propositions that look to be both true a...
Meinong’s fundamental distinction between constitutive (nuclear) and extraconstitutive (extranuclear) properties is discussed and defended against an alternative suggestion based on Meinong’s student Mally’s distinction between two modes of predication for properties that are themselves undistinguished as to assumability or unassumability. Constitu...
The origins of object theory in the philosophical psychology and semantic theory of Meinong and the Graz school he fledged can be traced both to the insight and failure of Brentano’s immanent objectivity or intentional in-existence thesis. The immanence thesis is documented, together with its critical reception in Höfler’s Logik, Twardowski’s Zur L...
Tarski’s model set theoretical analysis of logical truth presupposes a reduction principle, according to which, if a universally quantified sentence is true, then all of its instances are logically true. Etchemendy, in a recent critique, rejects the reduction principle on the basis of what he finds to be intuitive counterexamples. He proposes a phi...
A Meinongian metaphysics makes aesthetic value a matter of subjective feeling rather than an objective property of an aesthetically appreciated object. An intended object is intentionally related to the aesthetically appreciated object. The advantages of a Meinongian subjectivistic aesthetic value theory are explained and defended on multiple groun...
This book explores the thought of Alexius Meinong, a philosopher known for his unconventional theory of reference and predication. The chapters cover a natural progression of topics, beginning with the origins of Gegenstandstheorie, Meinong’s theory of objects, and his discovery of assumptions as a fourth category of mental states to supplement his...
Meinong’s object theory has been the subject of neglect and ridicule ever since Russell, Ryle and others criticized the logic and predicational semantics of existent and nonexistent objects as internally inconsistent. The fact that these objections were misinformed and fully answerable does not imply that the perpetrators did not accomplish lots of...
Meinong’s object theory suggests the possibility of making progress in a third alternative with respect to the long-standing apparently intractable collision in the metaphysics of Platonic realism versus nominalism. Meinong’s own views on the existence of such abstract mathematical entities as numbers and geometrical figures are considered, and the...
Critical exposition is offered of Kripke’s actualist interpretation of the meaning of fiction, against the background of his actualist modal metaphysics. Kripke is committed to the proposition that Sherlock Holmes not only does not happen to exist in the actual world, but for that reason cannot possibly exist in any nonactual merely possible world....
The heart of Meinongian object theory is its intensional identity conditions for existent and nonexistent objects alike. An object, conceived independently of its ontic status, is supposed to be identified by its constitutive properties, and possesses those properties, consequently, independently of its ontic status. Since not all properties are co...
The interpretation of quantum indeterminacy is relevant to Meinongian object theory because it suggests that with no ability simultaenously to determine a microparticle’s position and momentum there is something metaphysically incomplete about all of physical reality. We do not want to say that the Taj Mahal is an incomplete nonexistent Meinongian...
It is a momentous and as yet unsolved, perhaps unsolvable, question in the philosophy of logic, as to whether there is a single universal logic. The alternative is to maintain that there are only fundamentally distinct logics, some similar to others in some but not other ways, and each reflecting another logical dimension of what for convenience ca...
R. G. Collingwood’s philosophical analysis of religious atonement as a dialectical process of mortal repentance and divine forgiveness is explained and criticized. Collingwood’s Christian concept of atonement, in which Christ \(=\) the Atonement (and also \(=\) the Incarnation), is subject in turn to another kind of dialectic, in which some of Coll...
A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary...
In several of his writings, Isaac Newton proposed that physical space is God's "emanative effect" or "sensorium," revealing something interesting about the metaphysics underlying his mathematical physics. Newton's conjectures depart from Plato and Aristotle's metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophi...
The ideological and methodological oppositions that divide philosophy generally into realisms and idealisms, objectivisms and subjectivisms, also pervade aesthetic theory. The question arises whether there was beauty in the world prior to the emergence of intelligent perceivers like
ourselves, or whether beauty itself comes into existence only thro...
The concept of a dialogue is considered in general terms from the standpoint of its referential presuppositions. The semantics of dialogue implies that dialogue participants must generally have a collective intentionality of agreed-upon references that is minimally sufficient for them to be able to disagree about other things, and ideally for outst...
The object of this essay is to discuss Ludwig Wittgenstein's remarks in Philosophical Investigations and elsewhere in the posthumously published writings concerning the role of therapy in relation to philosophy. Wittgenstein's reflections seem to suggest that there is a kind of philosophy or mode of investigation targeting the philosophical grammar...
This essay asks whether there is a relation between action-serving and meaning-serving intentions. The idea that the intentions involved in meaning and action are nominally designated alike as intentionalities does not guarantee any special logical or conceptual connections between the intentionality of referential thoughts and thought-expressive s...
In Plato’s dialogues, the Phaedo, Laches, and Republic, Socrates warns his interlocutors about the dangers of misology. Misology is explained by analogy with misanthropy, not as the hatred of other human beings, but as the hatred of the logos or reasonable discourse. According to Socrates, misology arises when a person alternates between believing...
The thesis that entities exist in, at, or in relation to logically possible worlds is criticized. The suggestion that actually nonexistent fictional characters might nevertheless exist in nonactual merely logically possible worlds runs afoul of the most general transworld identity requirements. An influential philosophical argument for the concept...
This essay considers arguments for and against syntactical constraints on the proper formalization of definitions, originally owing to Alfred Tarski. It discusses and refutes an application of the constraints generalized to include a prohibition against not only object‐place but also predicate‐place variables in higher‐order logic in a criticism of...
Propositional belief state intensity is equivalently spoken of colloquially but no less phenomenologically as the strength of a believer’s belief. Belief state intensity is experienced first-hand when we know ourselves to accept a proposition’s truth with greater or lesser sense of importance or urgency and priority or precedence than in the case o...
The interconnectedness of all events in the causal matrix suggests that the so-called informal fallacy of post hoc, ergo propter hoc reasoning is not deductively invalid. It may be preferable then to consider post hoc, propter hoc as violating a pragmatic concept of causal relevance. A leading pragmatic account of relevance defines it as the caused...
A complete philosophy of mathematics must address Paul Benacerraf’s dilemma. The requirements of a general semantics for the truth of mathematical theorems that coheres also with the meaning and truth conditions for non-mathematical sentences, according to Benacerraf, should ideally be coupled with an adequate epistemology for the discovery of math...
The graphic meaning and formal implications of the canonical Aristotelian square of opposition are favorably compared with alternative ways of representing subsyllogistic logical relations among the four categorical AEIO propositions of syllogistic logic. The canonical arrangement of AEIO propositions in the square is justified by an exhaustive sur...
This essay examines an argument of perennial importance against naive Leibnizian absolute identity theory, originating with Ruth Barcan in 1947 (Barcan, R. 1947. ‘The identity of individuals in a strict functional 3 calculus of second order’, Journal of Symbolic Logic, 12, 12–15), and developed by Arthur Prior in 1962 (Prior, A.N. 1962. Formal Logi...
The question whether qualities are metaphysically more fundamental than or mere limiting cases of relations can be addressed
in an applied symbolic logic. There exists a logical equivalence between qualitative and relational predications, in which
qualities are represented as one-argument-place property predicates, and relations as more-than-one-ar...
This essay offers a detailed philosophical criticism of Frege’s popular thesis that identity is a relation of names. I consider
Frege’s position as articulated both in ‘On Sense and Reference’, and in the Grundgesetze, where he appears to take an objectual view of identity, arguing that in both cases Frege is clearly committed to the proposition
th...
Marx and Engels argue that capitalism must ultimately destroy itself because it contains an internal contradiction: Capitalism requires wage laborers at first to be in competitive isolation from one another, lest their common interests become transparent and they unite collectively to improve their employment conditions. At a certain later stage of...
If conceptual analysis is possible for finite thinkers, then there must ultimately be a distinction between complex and primitive
or irreducible and unanalyzable concepts, by which complex concepts are analyzed as relations among primitive concepts. This
investigation considers the advantages of categorizing intentionality as a primitiverather than...
An elementary exercise in symbolizing an existential to universal relation reveals expressive limitations in standard first-order predicate-quantificational logic. Alternative translations of a sample some-every sentence are considered and rejected after criticism, leaving as the best choice a particular structure that demonstrably does not serve f...
Philosophical semantics requires an ontology that includes negative as well as positive states of affairs as truth-makers
and truth-breakers. Theories that try to do without negative states of affairs while interpreting propositional truth as positive
correspondence with existent states of affairs are inherently inadequate and incomplete. A semanti...
Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication
to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata
stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or...
In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symboli...
John Barker, in two recent essays, raises a variety of intriguing criticisms to challenge my interpretation of the liar paradox and the type of solution I propose in 'Denying the Liar' and 'Denying the Liar Reaffirmed.' Barker continues to believe that I have misunderstood the logical structure of the liar sentence and its expression, and that as a...
In his early (1860–1891) pre-Monist writings, Peirce regards logic as involving only ‘general terms’ for universal concepts, thereby excluding proper names as terms of singular reference. Against a background of historical commentary on Peirce’s scattered remarks on the semiotic of denotation, this essay systematically develops a neo-Peirce...
This chapter presents the principles of Boole's algebraic logic that have unlimitedly many uses. Boole in his philosophical moments seems to have thought that the extension of his logic to probability theory and its use in what he refers to as the use of logic in the further investigation of the mind are its most important applications. The judgmen...
The uses and interpretation of reductio ad absurdum argument-ation in mathematical proof and dis-covery are examined, illustrated with elementary and progressively sophisti-cated examples, and explained. Against Arthur Schopenhauer's ob-jections, reductio reasoning is defen-ded as a method of uncovering new mathematical truths, and not merely of co...
The preface paradox is the apparent pragmatic inconsistency that occurs when the author of a book declares in its preface that despite believing that it is highly probable that everything the book maintains is true it is also highly probable that the book contains at least some errors. The preface paradox has often been presented as an example of a...
Presented here are translations of two essays of the Austrian logician, philosopher and experimental psychologist Ernst Mally, originally delivered at the Third International Congress of Philosophy in Heidelberg, Germany. Both essays conclude with discussion between Mally and Kurt Grelling. Mally was a student of Alexius Meinong and a contributor t...
Resenha do livro "Shakespeare’s Philosophy: Discovering the meaning Behind the Plays [A filosofia de Shakespeare: descobrindo o significado atrás das peças], de McGinn, Coli. New York: Harper, 2008. 230 páginas
Seneca in his Moral Epistles to Lucilium ridicules Protagoras’ claim that both sides of any position can be equally well argued. Cicero, on the contrary, in the surviving
fragments of his dialogue, the Republic, maintains in the person of Laelius that the thorough exploration of the strengths and weaknesses of any position pro and
con is the best a...
Mind‐body identity theories are standardly supposed to be logically contingent. Kripke defends a quasi‐Cartesian property dualism by observing that bodies and minds or mental and neurophysiological events or event‐types can always be assigned distinct rigid designators. The concept of rigid designation implies that possibly nonidentical rigidly des...
This essay proposes and defends a general thesis concerning the nature of fallacies of reasoning. These in distinctive ways
are all said to be deductively invalid. More importantly, the most accurate, complete and charitable reconstructions of these
species and specimens of the informal fallacies are instructive with respect to the individual chara...
The traditional conception of knowledge as justified true belief is refuted in two famous counterexamples by Edmund L. Gettier. Roderick M. Chisholm has attempted to rescue a version of the traditional conception by distinguishing between defective and nondefective kinds of justification, and redefining knowledge more specifically as nondefectively...
Psychologism is a philosophical ideology that seeks to explain the principles of logic, metaphysics, and epistemology as psychological phenomena. Psychologism has been the storm center of concerted criticisms since the nineteenth century, and is thought by many to have been refuted once and for all by Kant, Frege, Husserl, and others. The project o...
If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist
mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics
of modal logic, the ontology of logically possible worlds, and the controversy over modal realism...
An argument against multiply instantiable universals is considered in neglected essays by Stanislaw Lesniewski and I.M. Bochenski.
Bochenski further applies Lesniewski’s refutation of universals by maintaining that identity principles for individuals must
be different than property identity principles. Lesniewski’s argument is formalized for purpos...
Trying to make sense of abstract painting has resulted in interesting but often inexact and inadequately motivated efforts
to characterize what is distinctive about modern art. The present account begins with Gertrude Stein's description of the
fascination she experiences in viewing painted surfaces and proceeds through a number of efforts to justi...
In his philosophy of culture, Joseph Margolis maintains that, although human beings and human societies have a history, there is no human nature in the sense of a fixed essence. I consider objections to Margolis's thesis, beginning with the possibility that nonhuman intelligent species might be in a position to study human behavior from its origins...
The heterological paradox of Kurt Grelling is often mentioned but seldom critically examined in the history of symbolic logic. The paradox is that heterologicality, the property of not being truly predicated of itself, is itself heterological if and only if it is not heterological. The paradox is sometimes thought to make a compelling argument for...
Bernard Williams's essay ‘Wittgenstein and Idealism’ argues that that the conventionality of language entails the dependence of the truth of sentences and ultimately of corresponding states of affairs as truth-makers on the existence of thinking subjects. Peter Winch and Colin Lyas try to avoid William's paradox by distinguishing between the existe...
Franz Brentano (1838-1917) led an intellectual revolution that sought to revitalize German-language philosophy and to reverse its post-Kantian direction. This volume brings together newly commissioned chapters on his important work in theory of judgement, reform of syllogistic logic, theory of intentionality, empirical descriptive psychology and ph...
Meinong explains assumptions (Annahmen) as a fourth class of psychical phenomena, belonging to an intermediate class supplementing Brentano’s division between presentations (Vorstellungen), judgments (Urteile), and emotions (Gefühle). If thought is free to assume anything, even nonactual and metaphysically predicationally impossible intended object...
In La Téntation de Saint Antoine Gustave Flaubert dramatizes a philosophical exchange about the nature of divine providence and the efficacy of petitionary prayer. The Devil and Antony consider the question of whether God can be called upon for relief from suffering. The Saint assumes as popular religion teaches that it is possible to ask for God's...
Philosophy as LogicLogic and Philosophy of LanguageModes and Methods of Philosophical LogicLogic as Philosophy in Philosophical LogicOn Philosophical Presuppositions and Copia of Logical Systems
The family of diagonalization techniques in logic and mathematics supports important mathematical theorems and rigorously demonstrates philosophically interesting formal and metatheoretical results. Diagonalization methods underwrite Cantor’s proof of transfinite mathematics, the generalizability of the power set theorem to the infinite and transfi...
I consider three conditions to explain the emergence of scientific philosophy in Austrian thought at the turn of the century, concentrating on Vienna and Graz as distinct centers of philosophical development: (1) An outlook that seeks philosophical truth in sound reasoning, combined with a commitment to developing and practicing a methodology that...
In Moral Literacy, or How to Do the Right Thing, Colin McGinn proposes a consequentialist solution to the abortion dilemma. McGinn interprets moral rights and moral interests as attributable only to actually sentient beings by virtue of their ability to experience pleasure or pain. McGinn argues against the moral rights of potentially conscious hum...
L'A. souleve les difficultes que pose la formulation naive de la loi des indiscernables chez Leibniz au regard des inferences de l'identite et de la non-identite. Examinant le cas de l'erreur intentionnelle et soulignant la limitation de la loi de Leibniz aux proprietes intentionnelles non-reciproques, l'A. propose une revision du principe d'identi...
Indulging in intellectual autobiography, I sketch the reasons and ways I became a practicing Meinongian logician. The path involves a chain of transgressions, especially of extensionalist presuppositions, and a struggle against widespread misinterpretations of Meinong’s object theory. Although the opposition toward Meinong’s theory of object persis...
Citations
... Meinog clarified that an object can 'subsist' before and regardless its existence, inasmuch as the existence is a contingent quality that denotes the material and temporal being of an object (Meinong 1960;cf. also Albertazzi et al. 2001;Valsiner 2014). ...
... Hrsgs.]' I discuss Frege's Begriffsschrift square in further detail in Jacquette[7]. ...
... In general, the trustor beliefs are not black and white, in the sense that a trustor needs to believe that a trustee either has a certain Disposition (or Intention) or not. In fact, they have an intrinsic quality that corresponds to the strength of a trustor belief (Jacquette, 2013). For instance, it may be the case that "Alice believes more strongly that Burger King is capable of making a good hamburger than it is capable of delivering orders on time". ...
... Leibniz is considered in many ways as the precursor of modern logic. How to interpret the square of opposition from the point of view of modern logic-in particular first-order logic-is not necessarily straightforward, Dale Jacquette in his paper "Subalternation and existence presuppositions in an unconventionally formalized canonical square of opposition" [25] makes a comparative study of two formalizations. ...
Reference: The Vatican Square
... 6 It has been observed that some contemporary forms of Meinongianism are significantly similar to realist views about abstract objects (Linsky & Zalta, 1995). 7 See Jacquette (1989Jacquette ( , 1996Jacquette ( , 2001, Parsons (1978Parsons ( , 1979Parsons ( , 1980Parsons ( , 1982, Routley (1966Routley ( , 1980Routley ( , 1982Routley ( , 2003 and Sendlak (2013) 8 See Bueno and Zalta (2017), Castañeda (1972Castañeda ( , 1975, Linsky & Zalta (2006), Rapaport (1978), and Zalta (1983Zalta ( , 1988Zalta ( , 2000. 9 See Berto (2008Berto ( , 2011Berto ( , 2013, Berto & Priest (2014), and Priest (2003Priest ( , 2005. 10 To be sure, if there is a true sentence such that the referent of does not exist, then in general, ⊨ ∃ is not formally valid because it is logically possible for the extension of to exceed the range of ∃. ...
Reference: Fictionalism and Meinongianism
... Husserl remarked in i929 that Brentanf's discovery of intentionality "never led to seeing in it a complex of performances, wHich are included as sedimented history in the currently constituted intentional unity and ~ks current manners of givenness-a history that one can always uncover following a stricf methoif' (Husserl 1969:245). I Already in early essays, e.g., his 1894 review of Twardowski;f On the Concept and Object of Presentations (Husserl 1994: 388-95) and his unfin~shed 1894-8 essay "Intentional Objects" (Husserl 1994: 345-87), Husserl offered a morf complex account of the "being of the intentional object;' specifically addressing the problem of so-called objectless presentations, i.e., presentations to which no existing qbject corresponds, e.g., "centaur," "round square;' "the present King of France;' orig~nally discussed by Bolzano in his Wissenschaftslehre [Theory of Science], and subsequently taken up by I Twardowski, Meinong, Russell, among others (Jacquette 2015). In 1~94, the mathematician Gottlob Frege reviewed Husserl's Philosophy of Arithmetic an1 accused him, perhaps unfairly, of psychologism (Mohanty 1982). ...
... The move to a paraconsistent logic would be under the assumption that there is good revelationary evidence that supports it. Resorting to a paraconsistent logic should not be a default move when faced with an apparent contradiction (for how paraconsistent logic cannot be considered a universal remedy to all of our problems see Jacquette [49]. There ought to be substantial evidence in which the contradictory theologian can fall back on. ...
... The passage from the possibility to the necessity is not warranted by the agent, rather by the nature of characters, and, more generally, of abstract objects. Incidentally, this argument could be used to reply to Jacquette (2015) in which the author argues that the objects in OT must be mind-independent. ...
... On the approach discussed here, seeLinsky and Zalta (1994). For other options seeGarson (1984). ...
Reference: Logic without metaphysics
... Arts theories and arts research frequently consider a piece of art to become meaningful only through spectators' involvement, encountering, and interpretation (Carrier, 1986;Jacquette, 2014), which resonates with the concept of beholder's share discussed above. For example, curator Achim Borchardt-Hume, describing Mark Rothko's work, contemplates that the paintings are incomplete if one of the three is missing: the painter, the painting as an object, or the viewer, who was always in Rothko's mind when he was painting (Tate Modern, 2019). ...