The Influence of Wittgenstein’s ‘Middle-Period’ Philosophy of Mathematics on his Later Account of Possibility.

Michael Nielson

Ludwig Wittgenstein held various beliefs through the publication of the Tractatus Logico-Philosophicus that he would later come to repudiate in the Philosophical Investigations.  One of these was the atomistic notion that sentences which could be understood could also be analyzed into elementary propositions, termed by Diane Gottlieb in “The Tractatus View of Rules” as ‘the truth-functional thesis’.  One of the primary reasons for this rejection of the truth-functional thesis in the Tractatus Logico-Philosophicus is its conception of rules being motivated by an idealized picture of language’s use.    In the next phase of his career, he would become preoccupied with the philosophy of mathematics and forge an attack on the idea of infinite mathematical sets as anything more than possibilities due to their reliance on finite mathematical calculi.  While in the TLP rules were given a much more strict application and “alone determined meaning”, in the PI meaning and truth could only “be accounted for only in the context of practice”[1]. During this later period, he would return his focus to language, and though it would deviate from the middle period, his discoveries about the nature of mathematics would come to transform many of Wittgenstein’s ideas through the development of language-games, allowing him to account for the variation and possibility in our languages. 

            In order to illustrate the effect his philosophy of mathematics had on the evolution of his conception of rules, I will first outline the view of rules in Wittgenstein’s Tractatus, and examine both syntactical and translation rules.  Next I will detail how his preoccupation with mathematics led him to classify various mathematical propositions, such as set theory and infinite numbers, not as mathematical calculi in and of themselves, but instead as a mere infinite possibilities.  Finally, I will explain how, despite the differences between the two, this questioning of mathematical propositions would play a factor in the Philosophical Investigations repudiation of the truth-functional thesis within logical atomism, as well as the rejection of a rule functioning inside any sort of mental mechanism.

The Early Wittgenstein  

In the only work published during his lifetime, the Tractatus Logico –Philosophicus(TLP), Ludwig Wittgenstein expounded a picture-theory of meaning.  At the foundation of this picture-theory was logical atomism.  According to this doctrine, both meaning and language were examined “in terms of logical form and definiteness of sense”[2].   This theory held the essential metaphysical form of the world and the logical form of language were isomorphic with one another due to their similar structure[3].   Consequently, the objects that the names stood for had to be indestructible,[4] and therefore definite.

Central to Wittgenstein’s atomism was ‘the truth-functional thesis’, which “held that on any occasion when a sentence of ordinary language was meant and understood, the sentence was analyzable into elementary propositions of which it was a logical product”[5].  Implicit within the truth-functional thesis, according to Diane Gottlieb, are rules[6].  These rules are defined in two distinct ways within the TLP, as rules of translation and rules of syntax.

3.334 – The rules of logical syntax must go without saying, once we know how each individual sign signifies

3.343 – Definitions are rules for translating from one language into another.  Any correct sign-language must be translatable into any other in accordance with such rules: it is this that they all have in common.[7]

The rules of definition “play a role in the processes of meaning and understanding”[8].  The rules of logical syntax on the other hand were much more definite, and though it is unclear how Wittgenstein saw them, Hans-Johann Glock theorizes he felt that they mirrored “the essence of reality”[9].  A single logical syntax was “the logico-metaphysical structure which all meaningful languages…must have in common”[10].  However, during his post-TLP sabbatical from philosophy, the Vienna Circle would develop their own unique interpretation of the rules of syntax as “arbitrary conventions governing the use of signs”[11].  Despite these differences both interpretations share the commonality that the only contexts they were able to be discussed was with regard to their use.

            As opposed to these implicit rules, it was explicit within the truth-functional thesis that “all sentences with sense…are in perfect logical order” and possess “a determinate or definite sense” with little account taken for possibility[12].  It was in reference to this that the rules of the TLP lacked any sense of possibility.  This is one of the multiple reasons I theorize why Wittgenstein would came to question the TLP and view logical atomism as dogmatic in character[13].  These factors caused him to see at the root of logical atomism was “a false and idealized picture of the use of language” that would cause him to first leave philosophy entirely before ultimately reassessing his philosophical system upon his return[14].

The Middle Wittgenstein & The Philosophy of Mathematics

Though his philosophical system would progress and evolve after the completion of the TLP, a formalistic conception of mathematics was always foundational to his system[15].  Formalism in mathematics is identified as “the philosophical theory that formal (logical or mathematical) statements have no meaning but that its symbols (regarded as physical entities) exhibit a form that has useful applications”[16].  These mathematical views would take center stage in the middle period of his career after Wittgenstein attended Vienna lecture entitled ‘Science, Mathematics and Language’ by L.E.J Brouwer on March 10, 1928 and became more aware of the interpretations of the TLP[17].  This period is often seen as a black hole in Wittgenstein’s philosophy and is termed by Steve Gerrard in “Wittgenstein’s Philosophies of Mathematics” as ‘the calculus conception of mathematics’.

During this period Wittgenstein would carry from the TLP “his strong brand of formalism, according to which…we invent mathematics, bit-by-little-bit”[18].  Due to being our own creation mathematical propositions only have “intra-systemic meaning, which is wholly determined by its syntactical relations to other propositions of the calculus”[19].  Mathematics was “a closed, self-contained system” where rules were given a much larger role and “alone determined meaning, and thus became the final and only court of appeal”[20].  This reformulation of mathematical rules was only the first of the changes that will be discussed as ultimately crossing over into his later periods philosophy of language and his conception of rules.

Despite these loyalties to a formalistic idea of mathematics, in this period much of his focus would shift to rejecting “quantification over an infinite mathematical domain”[21].  The idea of an infinite class does not have the same syntax as a finite class, because “an infinite mathematical extension is a contradiction in terms”[22].  To further illuminate this, Wittgenstein is quoted in the Philosophical Grammer(PG) as saying “the infinite is understood rightly when it is understood, not as a quantity, but as an ‘infinite possibility’”[23].  We are only able to know it as a possibility through acquaintance with the “criteria for the truth of similar propositions”[24].  In other words, infinite mathematical sets can only be understood in reference to finite propositions because “there are no criteria for mathematical correctness outside the rules of individual calculi”[25].  We are unequipped to even consider grasping anything more than this mere possibility.

Regardless of this rejection of infinite number sets, Wittgenstein did not completely object to the idea of an underlying mathematical reality[26].  What he rejected was “a conception of mathematical reality that is independent of our practice and language” and “is capable of overruling how we actually do mathematics”[27].  This ‘faulty conception of mathematical reality’ can be seen as leading him to critique various mathematical theories surrounding the concept of an infinite set.  Two examples of these theories examined by Victor Rodych in the Stanford Encyclopedia of Philosophy include ‘Fetmat’s Last Theorem’ and ‘Goldbach’s Conjecture’.  The formal statements for both appear as follows:

                            -----------------------------------------------------------------

[28]

----------------------------------------------------------------

[29]

-----------------------------------------------------------------

            Goldbach’s conjecture, which to this day has yet to be proven, was first discovered in 1742 in a letter written to Euler by Goldbach, in which he states “at least it seems that every number that is greater than 2 is the sum of three primes”[30].  The other example, Fermat’s last theorem, was first discovered posthumously in the margin of his copy of Arithmetica by Diophantus, appeared as follows:

"It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain”[31].

What both of these theories had in common is that the use of the variable ‘n’ designates the n^th number, and leads to a set of ‘any number’ or ‘every number’ that is greater than ‘x’.  Because these theories are based around this conception of a set including any or every number greater than ‘x’, “contrary to our proof it could be false that there is not a largest number”[32].  We can never fully prove these equations because when we examine an infinite set, it “resides only in recursive rules”.  Further exploration into Wittgenstein’s reasoning behind rejecting anything more than this possibility when dealing with infinite number sets will further illuminate the evolution of the concept of rules and why at the base of this was a “faulty conception…of a mathematical reality that is capable of overruling how we actually do mathematics”[33]. 

The Later Wittgenstein and his Return to Language

Around 1944 this faulty conception of mathematics would cause Wittgenstein to once again return his focus to language, in a period viewed by Gerrard as ‘the language-game conception of mathematics’[34].  This both deviates from and carries over many of the concepts within the calculus conception[35].  Although he continues his “formalistic conception of mathematical propositions and terms” he would reject the calculus conception based on mistakes that “come from reaching too far and from unnecessarily restricting the scope of language”[36].  These mistakes involving the restricted scope of language run parallel to many of the same errors that were fundamental to the critique of the truth-functional thesis and rules of syntax, in that both failed to take full account for possibility.

This new conception of both language and mathematics would strip itself of his previous mistakes regarding definiteness by taking “account for the change and growth of mathematics”[37] and both meaning and truth were “accounted for only in the context of a practice”[38].  This would move the idea of a criterion for mathematical correctness from the rules of the calculi to the mathematical practice itself[39].  The reasoning behind this shift from the calculus conception can be seen in its inability to account for change, growth and possibility in mathematics and language[40].  This section of the paper will introduce just a few aspects of the PI and detail how they both deviated from and built upon his earlier career, leading him to take account for this possibility in language by viewing it within “the context of a practice”[41].

One of these aspects was another dualism within Wittgenstein’s philosophy identified by Gottlieb, only this time instead of identification with rules, it concerned connections.  The first of these connections are set up by a calculus, here the result “is not dependent upon, nor vulnerable to, the accidents of fortune”[42].  The other is set up in a mechanism where “the effect can unexpectedly be determined by some unforeseen occurrence such as the malfunctioning of the mechanism for various reasons”[43].  Through the acknowledgement of this mechanistic aspect of connections two key notions in the PI are addressed.  The first is that the “rules of language ought not be presumed to have strict application” and the second is the logical inconsistency in thinking of a rule of language “as something functioning in a mental medium”[44].

Sections 193 and 194 of the PI concern themselves with this distinction between both types of connections by using an example of machines to both expound his new view and further the critique of syntactical and translational rules[45].  The distinction he has made between the ideal machine, or machine-as-symbol, and the actual machine builds upon the notion of the rules themselves functioning outside of the mental mechanism.  The ideal machine can be seen as merely a blueprint or design of the machine, it does not account for any sort of possibility that may occur and acts “as if the parts of the machine ‘could do no other’”[46].  This classification of an ideal machine can be seen as acknowledging many of the same problems he had found within the conception of anything more than a possibility of an infinite set. 

In PI 193 Wittgenstein draws a parallel between the assumption that someone “will derive the movement of the parts from” this ideal machine and telling someone “it is the twenty-fifth number in the series 1, 4, 9, 16, …”[47].  This comparison serves as an example that similar to middle period’s criticisms of Goldbach’s Conjecture and Fermat’s Last Theorem, merely telling someone the twenty-fifth number in a sequence is unable to prove anything more than a possibility.  The most we can comprehend is a possibility, “the movement of the machine-as-symbol is predetermined in a different sense from that in which the movement of any given, actual machine is predetermined”[48].

On the other hand, the actual machine does take account for actual movements, and the possibility of the machine bending, breaking or evolving[49], placing him at odds with the view presented in the TLP[50].  These possibilities of movement are identified by Wittgenstein through a vague example as “the shadow of the movement”[51]  However, Wittgenstein takes this notion of possibility to be much more foundational, and critiquing the picture theory, he states that a possibility of movement “stands in a unique relation to the movement; closer than that of a picture to its subject”[52].  Because of this possibility “we are at liberty to construct novel calculi, constrained only by the demand for consistence and considerations like ease of explanation and avoidance of puzzlement”[53].  This possibility within language depicted by the machine analogy can be seen as building upon many notions of his philosophy of mathematics.  The analogy serves as an example of the influence Wittgenstein’s belief that we were only able know an infinite set as a possibility, as opposed to being the genuine result of a mathematical calculi, had on both his philosophy of language during the final stages of his career and criticisms of both his conception of rules and the truth-functional thesis within the TLP.

Conclusion

            Wittgenstein was able to take account for the possibility within both language and mathematics through the more fluid and constructivist approach developed in the PI.  This stands in a sharp contrast to the more definite view found in the TLP.  Many of these contrasts between the early and late system were greatly influenced by the function rules were given to perform.  Wittgenstein’s mathematical formalism and criticisms of theories regarding infinite sets shed light motives behind this shift in thought, of which the most notable consequences were the more fluid account of language.

Notes

---

[1] Gerrard, Steve. “Wittgenstein’s Philosophies of Mathematics.” Synthese 87.1 (1991): 126

[2] Gerrard, 131

[3] Glock, Hans-Johann. “The Development of Wittgenstein’s Philosophy.” Wittgenstein: A Critical Reader. Ed. Hans-Johann Glock. Massachusetts and Oxford: Blackwell Publishing, 2001:7.

[4] Glock. “The Development of Wittgenstein”, 8.

[5] Gottlieb, Diane F. “Wittgenstein’s Critique of the ‘Tractatus’ View of Rules.” Synthese 56.2 (1983):  239.

[6] Gottlieb, 241.

[7] Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Trans. D.F. Pears and B.F. McGuinness. London and New York: Routledge Classics, 2008: 20-21.

[8] Gottlieb, 241.

[9] Glock. “The Development of Wittgenstein”, 11.

[10]Glock, Hans-Johann. “The Development of Analytic Philosophy: Wittgenstein and After.”  The Routledge Companion to Twentieth Century Philosophy. Ed. Dermot Moran. London and New York: Routledge, 2008: 82.

[11] Glock. “The Development of Wittgenstein”, 11.

[12] Gottlieb, 240-241.

[13]Biletzki, Anat. “Ludwig Wittgenstein.” Stanford Encyclopedia of Philosophy. 23 Feb. 2007. http://plato.stanford.edu/entries/wittgenstein, 29 Nov. 2009. 3.1.

[14] Gottlieb, 242.

[15] Rodych, Victor. “Wittgenstein’s Philosophy of Mathematics.” Stanford Encyclopedia of Philosophy. 23 Feb. 2007. http://plato.stanford.edu/entries/wittgenstein-mathematics, 16 Dec. 2009. 1.0.

[16] “Formalism.” Princeton WordNet. Princeton University, http://wordnetweb.princeton.edu/perl/webwn?s=formalism. 8 May. 2010.

[17] Rodych, 2.0.

[18] Rodych, 2.1.

[19] Rodych, 2.1.

[20] Gerrard, 126.

[21] Rodych, 2.2.

[22] Rodych, 2.2.

[23] Rodych, 2.2.

[24] Rodych, 2.4.

[25] Gerrard, 131.

[26] Gerrard, 128.

[27] Gerrard, 128.

[28] “Fermat’s Last Theorem.” Wolfram Alpha. http://www.wolframalpha.com/input/?i=fermat%27s+last+theorum. 8 May 2010.

[29] “Goldbach Conjecture.” Wolfram Alpha. http://www.wolframalpha.com/input/?i=goldbach+conjecture. 8 May 2010.

[30] Weisstein, Eric W. "Goldbach Conjecture." Wolfram MathWorld. http://mathworld.wolfram.com/GoldbachConjecture.html. 8 May 2010.

[31] Weisstein, Eric W. "Fermat's Last Theorem." Wolfram MathWorld. http://mathworld.wolfram.com/FermatsLastTheorem.html. 8 May 2010.

[32] Gerrard, 130.

[33] Gerrard, 128.

[34] Gerrard, 126.

[35] Gerrard, 126.

[36] Gerrard, 132.

[37] Gerrard, 132.

[38] Gerrard, 126.

[39] Gerrard, 131.

[40] Gerrard, 132.

[41] Gerrard, 126.

[42] Gottlieb, 243.

[43] Gottlieb, 243.

[44] Gottlieb, 243.

[45]Wittgenstein, Ludwig. Philosophical Investigations. Trans. G.E.M. Anscombe. Massachusetts and Oxford: Blackwell Publishing, 1999. 77-79.

[46] Gottlieb, 247.

[47] Wittgenstein. Philosophical Investigations, 79.

[48] Wittgenstein. Philosophical Investigations, 77-78.

[49] Wittgenstein. Philosophical Investigations, 79

[50] Glock. “The Development of Analytic”, 82.

[51] Wittgenstein. Philosophical Investigations, 79.

[52] Wittgenstein. Philosophical Investigations, 79.

[53] Glock. “The Development of Analytic”, 82.

It's Been A Pleasure

Short film I did for a cinema class, focused on producing and directing.  Thanks to everyone who helped  by donating their time, skills and/or art to this project.  It would have never gotten completed without all your help, THANK YOU!

The Treatment of Beauty & Sublimity in Arthur Danto’s The Abuse of Beauty

I want to eventually have this be the first chapter in my expository book on the sublime, feedback welcomed:

The Treatment of Beauty & Sublimity in Arthur Danto’s The Abuse of Beauty

By Michael Nielson

            After a focus on the more art-centric “philosophy of art” for most of his career, over the course of the last decade Arthur Danto changed his focus toward the field of aesthetic sensations.  As of now, the exemplary source on this recent trend in Danto is The Abuse of Beauty: Aesthetics and the Concept of Art, a book which reexamines the place these sensations hold in the art-world.  Clearly influenced by G.W.F. Hegel, he ends the book by championing beauty as the sole aesthetic quality that transcends art and aesthetics to hold a place of value in any life a human being would want to lead.  However, upon further examination, there are numerous difficulties that begin to emerge in the book.

These difficulties first became apparent to me due to the vagueness in both his conclusion and the examples he used from both philosophy and art to support this conclusion.  Within a large number of these examples there is a longstanding Hegelian misconception manifesting itself in one of two ways: (1) an over-emphasization of beauty in his examples, namely creating a distinction between meaning-driven “internal beauty” and content-driven “external beauty”, resulting in his misconstrued interpretation of Robert Motherwell’s Elegy to the Spanish Republic No. 172 (with blood), a painting Danto presents as simply beautiful despite Motherwell’s insistence on the sublimity inherent within his paintings; (2) a deemphasizing of sublimity in his examples by disregarding what Kant distinguished as the dynamical kind of sublimity, instead presenting sublimity as one-dimensional and almost always related to what Kant distinguished as the mathematical sublime. 

Danto’s tendency to over-inflate the dimensionality of beauty while deflating that of sublimity I feel has a common root in his preference for Hegel over all other foundational aesthetic thinkers.  The central purpose of my paper is not to argue against Danto’s interpretation of beauty, because like him, I believe that this aesthetic quality plays a unique and powerful role in the complete human life.  What I intend to argue, however, is that the sublime holds a comparable role, in that no human life would be complete without it.  In reaching this conclusion, I focus on two key aspects of the sublime: (1) the sublime is exclusively associated with a feeling Motherwell identified as ‘the despair of the aesthetic,’ which occurs when the artist makes an choice in spite of the seemingly infinite possibilities they could have make; (2) Kant closely aligns the dynamical sublime with our reason, and this connection not only helps to unify his philosophical system as a whole, but more importantly, unlike mathematical sublimity, when this aesthetic quality provokes a feeling of grief, it and only it allows us to move past a tragedy and rediscover not just the beauty Danto was so fascinated with, but also a sense of normalcy within our lives.  Based on these unique functions of the sublime which allow us to move past both the despair and tragedy every human being experiences in one form or another during the course of their life, I argue that the sublime also holds a place of value in any life worth living.

            My examination into the sublime’s importance in our lives is divided into five concise sections.   I begin by examining the distinction Danto draws between internal and external beauty, ultimately illustrating that while this distinction is not entirely off-base, he over-emphasizes the dimensionality of beauty.  Secondly, I briefly discuss Kant’s conception of the sublime, detailing his distinction between the dynamical and mathematical kinds.  I believe this distinction shows that Danto brushes aside the dynamical sublime for reasons I believe are tied with deemphasizing the sublime’s importance in our lives.  Thirdly, I examine the roots of Danto’s deemphasization of the sublime, tracing them to the treatment of the sublime within Hegel’s system.  Fourthly, I return the discussion toward sublimity, presenting Motherwell’s views on the role of the feeling in his paintings, ultimately illustrating that Danto disregards this important aspect of the Elegies series in his interpretation.  Finally, I return to Kant in order to identify a crucial and unique role he saw sublimity having in our lives, a role that I believe elevates sublimity to the level of value Danto regards beauty.

1. Internal and External Beauty

Arthur Danto became intrigued by the idea of aesthetic beauty when in 1993 he heard David Hickey’s prediction that beauty “would be the defining problem of the decade”.[1]  This initially resulted in his observation that beauty had been missing from the philosophical definitions of art presented since the 1960s.[2]  Danto feels this absence was a response to an overly idealistic view of beauty that once dominated the field of aesthetics (Danto 2002, 39).  In his view, for beauty’s role in art to be fully understood we must free ourselves from both the axioms which state “all good art is categorically beautiful” as well as the responses which completely ignored it (Danto, 2002, 42).  His examination began in his 2002 article “The Abuse of Beauty,” in which he concluded that only after we had freed ourselves from these axioms can we begin to rediscover beauty as “one mode among many through which thoughts are presented in art to human sensibility −−− disgust, horror, sublimity, and sexuality are still others.  These modes explain the relevance of art to human existence, and room for them all must be found in an adequate definition of art” (Danto 2002, 56).

In order to support this important place he saw aesthetic qualities holding in art, Danto draws a distinction between internal beauty and external beauty.  ”External beauty” he defines as “external to the thought” and often connected with a more formal beauty (Danto 2002, 55).  Exemplary of this was Andy Warhol’s Brillo Boxes, one in a series of pop culture replications which stood out from all the others to Danto because of the beauty inherent in artist James Harvey’s original design (Danto 2003, 5).  “Internal beauty” is juxtaposed against this and crucial to Danto’s overall schema because it allowed him to redefine beauty as internally related to the meaning of a particular work.  A painting Danto saw as exemplary of this kind of beauty was No. 172 because he considers its beauty as connected with its meaning as an elegy[3] (Danto 2002, 110-111).   Like Danto, I feel that beauty can be deeply connected with the meaning of a work, as he observes it is within the Vietnam War Memorial.  In the case of the Elegies, however, I feel the paintings are misrepresented when classified as beautiful, and this classification I feel occurs in order to support his largely Hegelian schema.

This misclassification of The Elegies becomes more evident as Danto develops his thesis in the subsequent book of the same title.  Here this misconception directly leads to an over-inflation of the importance of beauty by concluding that alone among all the aesthetic qualities initially considered, only beauty holds a place of value in life as we would want to lead it.  (Danto 2003, 160).  While I will not argue against Danto’s assertion that beauty holds a place of value in a life, I will argue against beauty alone holding a place of value in our lives.  I will progress toward this conclusion in the following section when I introduce the aesthetic quality known as sublimity and its presentation in Kant’s third critique as well as Danto’s Abuse of Beauty.

2. Mathematical and Dynamical Sublimity

            Of all the foundational aesthetic thinkers, one of the most referenced and argued over is Immanuel Kant, and Danto’s own writing is no exception to this.  Of the contrasts Kant makes between the beautiful and the sublime, one of the most striking is that unlike beauty, which can be found in an object, sublimity “must always have reference to our way of thinking.” [4]  He identifies the feeling associated with the sublime as a mental agitation.  Through this agitation the imagination dualistically refers “either to the cognitive power or to the power of desire, but in both cases the purposiveness of the given presentation is judged only with regard to these powers (without any purpose or interest).  The first kind of agitation is a mathematical, the second a dynamical, attunement of the mind.  And so we attribute both these kinds of agitation to the object, and hence present the object as sublime in these two ways” (Kant 1987, 101).  The mathematical sublime is connected with our cognition as presented in the Critique on Pure Reason, and thus serves our understanding.  In contrast, the dynamical sublime is connected with our desire and serves our reason as presented in the Critique on Practical Reason, and its importance begins to emerge through its “foundation in human nature: in something that, along with common sense, we may require and demand of everyone” (Kant 1987, 125).  Like beauty, Kant felt sublimity aided in coherently unifying his entire philosophy, and thus an account for each kind is crucial to his philosophical system as a whole (Kant 1987, 17).   However, as opposed to the mathematical sublime, which despite its close connection with our understanding Kant rarely lifts out of the realm of aesthetics, the dynamical sublime has a unique function which transcends aesthetics due to its close connection with our powers of desire and reason This transcendence allows us to “consider nature as a might that has no dominance over us” and arouses fear within us (Kant 1987, 119).

            Before reaching his conclusion in The Abuse of Beauty, Danto uses much of the concluding chapter to discredit the sublime; however, he almost entirely disregards dynamical sublimity in his investigation.  This is best reflected in his direct reference to Kant’s definition for mathematical sublimity when defining sublimity in general, stating that in the sublime feeling “the mind has a power surpassing any standard of sense” (Danto 2003, 147; Kant 1987, 106).  While Danto does recognize the sublime as entailing “something more than great size” and would introduce both terror and wonder to the concept, his examples of the sublime’s place in art still centers on its being “internally related to size, indeed to vastness” as opposed to its dynamical power (Danto 2003, 154-155).  This exclusive focus on the mathematical sublime I believe led Danto to consider aspects of the Elegies series as internally beautiful, when in fact these aspects are closely aligned with dynamical sublimity.  However, it is first necessary to further examine how Danto’s own preference for Hegel had caused him to deemphasize the sublime before these sublime aspects of the Elegies can be better illuminated

3. Hegel and the Sublime

The conflict on how to treat aesthetic qualities dates back to ancient philosophy, but it was not until the emergence of Kant and Hegel that many of these differences became concrete.  The most striking of these differences are rooted in Hegel’s reaction to Kant’s cognitive approach, and are best represented in his account of the historical progression of art through three stages of history.[5]  The first stage is symbolic.  This stage is exemplified in architecture and the conflict the viewer feels “between content and form” (Knox 1958, 85; 88).  Hegel saw the symbolic as the means through which we experienced the sublime, though much like Kant, it is never fully rendered in the object itself and the feeling exists only within us subjectively (Knox 1958, 85; 182).  After the symbolic stage, art progresses onto the classical stage, exemplified by Greek sculpture.  Viewing these artworks allows us to appreciate beauty in the human form as “ideally depicted, as a representation of the universal human mind, as the visible vesture of mind, as individually and concretely determinate spirituality” (Knox 1958, 87).  The concluding stage is the romantic, through which classically beauty progresses and the conflict of symbolic art between the content and form returns, “but on a spiritually higher level” connected with our reason (Knox 1958, 88-89). 

After the resolution of this conflict is the death of art, an idea that had a profound effect on not just Danto’s thesis in “The End of Art,” but is also foundational to his system (Danto 1986).  This death or end is a point at which “the [aesthetic] activity. . .became a mode of apprehending the Absolute, of solving the great philosophical problem” (Knox 1958, 93).  However, when considering the place of reason in the realization of this end, a far-reaching failure to acknowledge a connection with sublimity is found.  Reason’s place in connection with the feeling of sublimity first came to me reading Iris Murdoch’s observation that for both Hegel and Kant, reason “is the faculty which seeks systematic wholeness and abhors incompleteness and juxtaposition.”[6]  Despite these similarities, there are also striking differences in how each philosopher dealt with the role of the sublime.  While Hegel relegated it exclusively to the early stages of artistic development, leading him to a deeper appreciation of beauty, in Kant’s more cognitive approach, the sublime is tied closely together with our reason, and because of this, just as crucial as beauty in the context of the three critiques as a whole.  The following section will examine Robert Motherwell’s views of sublimity, views that stands more closely aligned with Kant’s than Danto’s.  Examining Motherwell’s view will illustrate not just the misconceptions in Danto’s interpretation of No 172, but also a connection between the sublime and our reason that results in a unique healing power crucial to a functioning human life.

4. Motherwell and the Sublime

Despite Motherwell taking graduate level courses in philosophy at prestigious schools, Danto viewed him as having “no sense of…ever having a philosophical background or any great interest in the subject” (Danto 2002, 13).  However, in reading Motherwell’s writing, one quickly finds he did have a philosophical background, but his interests were in the same vein as those who Danto brings to task for an abuse of beauty.  Based on this, it is not surprising that in spite of their friendship, their interpretations of the Elegies conflicted.  I believe Motherwell intended the paintings to be sublime metaphors, while Danto had classified these sublime aspects as internally beautiful.  Before examining why Motherwell intended these paintings to be sublime, I first direct my examination toward his views on both the school of painting he was a part of, Abstract Expressionism, as well as aspects of his own artistic process.

            Despite being the youngest of the group, Motherwell’s writings are one of the definitive primary sources on Abstract Expressionism because his education allowed him to articulate many commonalities among the group.  To him, here was a style of art that attempts to project the experiences of the artist through a process of emphasis termed as abstraction.[7]  Unlike the name suggests, however, abstract is not meant to be an adjective describing a painting, but instead, an action verb describing a process[8] (Motherwell 2007, 270).  Motherwell viewed his own art as deeply rooted in any aesthetic decisions he made regarding selections of form and color “on the basis of the most concrete personal feeling” (Motherwell 2007, 196).  These aesthetic decisions are closely linked with ethics, as he considered painting to be “a series of moral decisions about the aesthetic” (Motherwell 2007, 196; 206).  These decisions are akin to an idea he first discovered within Søren Kierkegaard identified as ‘the despair of the aesthetic’ (Motherwell 2007, 172).  This despair occurs when one is allowed to use any color, any shape, any series of relations, to the point that the possibilities are so innumerable and “the ultimate decision so arbitrary and tedious, that a kind of anguish overcomes you that, say, the medieval painter, who had to paint the Virgin’s mantle blue, did not dream of” (Motherwell 2007, 172).  These ethical decisions by the painter are “the absolute, and in all eternity the highest value,” because without them “a painter is only a decorator” and his audience relegated to, as his contemporary Barrnett Newman suggested in the film Painters Painting: The New York Art Scene 1940-1970, “mere aesthetes” (Motherwell 2007, 178).[9]

Based on the close connection Kant had drawn between sublimity and reason, it is not surprising that for Motherwell himself these ethical choices involved in his painting are also connected with the feeling of sublimity (Motherwell 2007, 178).  As Dore Ashton observes in “Robert Motherwell: The Painter and His Poets,” Motherwell viewed his paintings as “oblique metaphors, [that] hold fast to the Mallarméan rule that things must be suggested or evoked, and not described”.[10]  Aston observed these subtle sublime themes are often placed in juxtaposition with themes Motherwell considered to be tragic (Ashton 1983, 9), and in the case of the Elegies in particular, these sublime themes are connected with the despair he felt while painting. 

Based on this, it is not at all surprising that for Motherwell the sublime was not a concrete, static thing, but instead, a possibility of an aesthetic experience (Motherwell 2007, 63).  Sublimity, in his view, occurs when “the artist transcends his personal anguish” by ultimately making an aesthetic choice despite the seemingly infinite number of other aesthetic possibilities (Motherwell 2007, 63).  The sublimity in this vast number of possibilities is at least part of what I feel he was attempting to express in both the Elegies and Open series, because the original form abstracted from in each series, other than slight variations, was essentially the same throughout, however, no two were ever identical either.  This function the sublime has in our lives becomes amplified when considering a healing power connected with grief that Kant identified solely with the dynamical sublime.

5. The Healing Sublime

This idea of a healing grief connected with sublimity is something Kant only identifies in the later sections of the Analytic of the Sublime.  “This comment is intended only as a reminder that even grief (but not a dejected kind of sadness) may be included among the vigorous affects, if it has the basis in moral ideas.  If, on the other hand, it is based on sympathy, then it may indeed be lovable, but belongs merely to the languid affects.  My point is to draw attention to the fact that only in the first case is the mental attunement sublime” (Kant 1987, 137).  The connection Kant saw between the sublime and moral ideas only manifests itself in this particular kind of healing grief, a grief exclusively connected with dynamical sublimity.  Thus it is in this kind of sublimity that we can recognize the very important value the sublime has in regards to our lives. 

I believe this dynamically sublime grief Kant identified is akin the despair Motherwell transcended in the repetitious series like the Elegies and Open.  Danto’s Hegelian tendencies in his project to defend beauty cause him to shut himself off from not just these aspects, but also the importance of the sublime in a functioning life.  I believe this dynamically sublime grief allows us not only to come to terms with events outside our understanding, which for Motherwell was the infinitely possible number of choices we could make, or for another could be an event like death that escapes our understanding, but ultimately to move past them and not just find beauty in art and the world around us once again, but to continue on living our lives.  Because of this unique, yet essential, function of the sublime, I feel that alongside beauty and numerous other aesthetic qualities, it holds a place of value in a life as we would want to live it.

6. Conclusion

In The Abuse of Beauty Arthur Danto had viewed beauty as the sole aesthetic quality crucial to a desirable life; however, I believe that sublimity serves an equally unique and important role as that of beauty.  This role can be seen in connection with a healing key aspect of the sublime I have identified in the preceding paper, namely a healing quality identified by both the aesthetician Kant and the artist Motherwell.  This failure to account for sublimities role in the full human life I believe led Danto to not just misclassify paintings like the Elegies, and the cause for it can be seen in an implicit preference for the philosophy of Hegel throughout his career.

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NOTES

[1] Arthur Danto, The Abuse of Beauty (Chicago: Open Court, 2003): 103.

[2] Arthur Danto, “The Abuse of Beauty,” American Academy of Arts & Sciences 131.4 (2002): 37.

[3] An elegy is an art-form which he defined as possessing a beauty that “works as a catalyst,

transforming raw grief into a tranquil sadness, helping the tears to flow and, at the same time,

one might say, putting the loss into a certain philosophical perspective” (Danto 2002, 110-111).

[4] Immanuel Kant, Critique of Judgment, trans: Pluhar. (Indianapolis: Hackett, 1987): 137.

[5] Josef Chytry. The Aesthetic State. (Los Angeles: University of California Press, 1989).

  Kai Hammermeister. The German Aesthetic Tradition. (Cambridge: University Press, 2002).

  Israel Knox. The Aesthetic Theories of Kant, Hegel, and Schopenhauer. (New York: Humanities Press, 1958).

[6] Murdoch, Iris. “The Sublime and the Good,” Chicago Review. 13.3 (1959): 45

[7] Motherwell, Robert. The Writings of Robert Motherwell. Ed: Dore Ashton. (Los Angeles: University of California Press, 200/7): 159.

[8] Motherwell even went as far as classifying it as a form of mysticism.  Much like mysticism, a

process found in all cultures that views its processes both “as part of a larger undertaking aimed

at human transformation” (Gellman 2010), Motherwell viewed abstraction as making a parallel

effort “to close the void that modern men feel” (Motherwell 2007, 159)

[9] Painters Painting: The New York Art Scene 1940-1970. Dir: Emile de Antonio. Perf: Wiliam de Kooning, Andy Warhol, Robert Motherwell, Barnett Newman. (Mystic Fire Video, 1973), 116 min. VHS.

[10] Ashton, Dore. Introduction. Robert Motherwell. By H.H. Amason. (New York: Harry N. Abrahms, Inc, 1983), 8.

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Works Cited

Amason, H. Harvard. Robert Motherwell. (New York: Harry N.Abrahms, Inc, 1983).

Ashton, Dore. Introduction. Robert Motherwell. By H.H. Amason. (New York: Harry N. Abrahms, Inc, 1983): 8-16.

Chytry, Josef. The Aesthetic State. (Los Angeles: University of California Press, 1989).

Danto, Arthur. “The Abuse of Beauty,” American Academy of Arts & Sciences. 131.4 (2002).

−−−. The Abuse of Beauty. (Chicago: Open Court, 2003).

−−−. Beyond the Brillo Box. (Las Angeles: University of California Press, 1992).

−−−. The Madonna of the Future. (Los Angeles: University of California Press, 2000).

−−−. “The End of Art,” The Philosophical Disenfranchisement of Art. (New York: Columbia University Press, 1986): 81-115.

−−−. “The Art-World,”

−−−. “The ‘Original Creative Principle’: Motherwell and Psychic Autmatism,” Philosophizing Art: Selected Essays. (Los Angeles: University of California Press, 1999).

Fenves, Peter. “Taking Stock of the Kantian Sublime,” Eighteenth-Century Studies. 28.1 (1994): 65-82.

Gellman, Jerom­e. "Mysticism," The Stanford Encyclopedia of Philosophy, Ed: Edward N. Zalta, Febuary 9, 2010, http://plato.stanford.edu/archives/sum2011/entries/mysticism.

Hammermeister, Kai. The German Aesthetic Tradition. (Cambridge: University Press, 2002).

Hobbes, Robert C. “Robert Motherwell’s Elegies to the Spanish Republic,” Reading Abstract Expressionism Ed. Ellen G. Landau. (Yale University Press, 2005).

Kant, Immanuel. The Critique of Judgment, Trans: Werner Pluhar. (Indianapolis: Hackett, 1987).

Knox, Israel. The Aesthetic Theories of Kant, Hegel, and Schopenhauer. (New York: Humanities Press, 1958).

Motherwell, Robert. The Writings of Robert Motherwell. Ed: Dore Ashton. (Los Angeles: University of California Press, 200/7).

Murdoch, Iris. “The Sublime and the Good,” Chicago Review. 13.3 (1959).

Painters Painting: The New York Art Scene 1940-1970. Dir: Emile de Antonio. Perf: Wiliam de Kooning, Andy Warhol, Robert Motherwell, Barnett Newman. (Mystic Fire Video, 1973), 116 min. VHS.

Works Referenced

Alberro, Alexander. “Beauty Knows No Pain,” Art Journal. 63.2 (2004): 36-43.

Budd, Macolm. “The Sublime in Nature,” Kant’s Critique of the Power of Judgment: Critical Essays. Ed: Paul Guyer. (New York: Rowman & Littlefield Publishers, Inc, 2003).

Burnham, Douglas. An Introduction to Kant’s Critique of Judgment. (Edinburgh University Press, 2000).

Crowther, Paul. “Barnett Newman and the Sublime,” Oxford Art Journal. 7.2 (1984): 52-59.

Engström, Timothy H. “The Postmodern Sublime?: Philosophical Rehabilitations and Pragmatic Evasions,” Boundary. 20.2 (1993): 190-204.

Gasché, Rodolphe. “The Sublime, Ontologically Speaking,” Yale French Studies. 99 (2001): 117-128.

Harries, Karsten. “Hegel on the Future of Art,” The Review of Metaphysics. 27.4 (1974): 677-696.

Lacoue-Labarthe, Phillip and David Kuchta. “Sublime Truth (Part 1),” Cultural Critique. 18 (1991): 5-31.

−−−. “Sublime Truth (Part 2),” Cultural Critique. 20 (1991-1992): 207-229.

Loesberg, Jonathan. “Dickensian Deformed Children and the Hegelian Sublime,” Victorian Studies. 40.4 (1997): 625-654.

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McCloskey, Mary A. Kant’s Aesthetics. (New York: State University of New York Press), 1987.

Robert Motherwell and the New York School: Storming the Citidal. Dir: Catherine Tatge. Perf: Robert Motherwell, Kenneth Cavander. (Phaidon Press, 1990), 55 min. VHS.

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Shapiro, Gary. “From the Sublime to the Political: Some Historical Notes,” New Literary History. 16.2 (1985): 213-235.

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Wicks, Robert. “Reviving the Remains of Hege’s Aesthetics,” Journal of Aesthetic Education. 36.1 (2002): 100-110.

New video of sorts, of course, of course.

Part music video, part compilation, here is something I edited together on a sleepless night before an early flight.  All the footage was collected from Surka's youtube and the music is from the band she works with, Dumptruck Butterlips.  Expect lots more stuff with these guys soon, hopefully a music video, but at least a long reel of short promo spots and some live performances.