Susan Howe, the “Pierce-Arrow,” and Occam’s Razor

Susan Howe’s Pierce-Arrow collects manuscript materials from Charles Sanders Peirce’s private papers, Charles Swinburne’s and George Meredith’s papers, quotations from Pope’s translation of Homer’s Iliad, and alludes to the Tristan and Iseult narrative.  The combination of sources allows the reader to make diverse associations, and Howe’s poetic is less traditionally lyrical than philosophical, not only in handling “existential” themes of loss and trauma, but in its emphasis on logic and language.  In this way, Howe could very well be the most “logic friendly” poet in America today.  This is not to say that her language is mathematical or scientific, rather her unique lyricism is associative in that it is visually inferential: each word, phrase, sentence, and image, even sections in the book, are tied together into intricate, often paradoxical, logical patterns.  One segment follows from or leads to another and the end wraps up the beginning, QED.

Howe quotes Peirce’s review of the English philosopher Victoria Lady Welby, “But we fear that she [Welby] does not realize how deep the knife would have to go into the body of speech to make it really scientific.  We should have to use words like those the chemists use—if they can be called words.”  Then Howe comments, “Perhaps the Word, giving rise to all pictures and graphs, is at the center of Peirce’s philosophy.  There always was and always will be a secret affinity between symbolic logic and poetry.” Howe is a lyricist because, like Yeats, she would assert that “Words alone are certain good.”  Her work is uniquely philosophical because she is much influenced by Peirce’s logical system, which pervaded every aspect of his thought.  In addition, she consistently concentrates on the connection between words and things, and thoughts and words.  These philosophical issues–the “secret affinity between symbolic logic and poetry–profoundly contribute to  Howe’s poetic.

As stated, Howe’s concerns are more oriented to problems in logic and language, and meaning and reference, rather than with the traditional lyric.  In this way, her work has more in common with Ludwig Wittgenstein’s Tractatus and the Blue and Brown Books.  Although the Tractatus asserts aphoristic theses, both texts demonstrate thought processes in associative, nearly stream-of-consciousness ways.  David Antin believes that the numbering system in the Tractatus is disorderly and its images are organized “poetically” rather than logically.  For him, Wittgenstein’s early treatise can be treated as literature.  Both texts contain logical symbols, illustrations, graphs, and truth tables.

Howe’s discursive tableaux resemble a logician’s deductive formulae and are inferential pathways that reveal hidden associations, dialogic allusions, and overtones of our linguistic practices.  But why would a poet be concerned with philosophy and logic?  Because Howe’s poetic entry presumes a logic of tense and temporal modalities.  Peirce’s innovative contributions in logic lends itself to Howe’s concerns because he provided criteria and logical notation for formally representing relations between things and history.  Also, Peirce’s “pragmatist” views are relevant to Howe because, like her, he was absorbed with the ‘ethics of belief’—the logical permissibility of rational decision-making and actions—not ‘how’ or ‘why’ we believe in P, but ‘when.’

In this way, Howe puzzles over the ways we form beliefs, asking readers to consider some of the following questions: Is it irrational or wrong to hold a belief on insufficient evidence? Is it rational or right to believe on the basis of sufficient evidence or to withhold belief in the absence of it? To what extent are we obligated to find all the evidence for a belief?

Howe is not a skeptic, and neither was Peirce, as were some latter-day pragmatists, such as W.V.O Quine.   As Peirce was, Howe is interested in the logic of belief; her poetic skates the margins of history, biography, memoir, and temporal non-existence, employing the law of non-contradiction in advancing numerous correspondences.  The motivation of recognizing correspondences, and forming attendant beliefs, is “inductive” in Peirce’s sense; thus, Howe’s poetic proceeds by way of the scientific method with data, evidence, and testimony playing central roles.

I wish I had the space here (and I will elsewhere) to show the connections between Howe’s poetic and Peirce’s pragmatism.  The latter is as unconventionally ‘pragmatic’ as Howe’s poetic is untraditionally lyrical.  These connections are crucial in understanding Howe’s integration of historical and biographical sources.

Certainly, there is a subtle connection between “Pierce Arrow” in the title and the philosopher Charles Sanders Peirce.  The juxtaposition of “Pierce / Peirce” would be otherwise inexplicable.  As antique automobile dealers likely know, a pierce arrow was a popular car at the turn of the twentieth-century.  The Pierce Arrow factory, since turned into a museum, is located in Howe’s Buffalo, NY.

Howe’s pierce arrow refers to a car and its innovative mechanics, but it also tacitly refers to Peirce’s logic-based scientific ideas.  “The arrow” is a symbol (not unlike Zeno’s arrow) which signifies Peirce’s very complicated synthesis of logic and evolutionary theory (the progress of time).  Also, Peirce’s arrow could very well refer to his innovations in logical notation—the symbol for material (not causal) implication: “If P, then Q.”  Rather than write out all the words, a logician simply abbreviates the logical function with an arrow: P→Q.  In the context of “Pierce Arrow,” wherein Howe cites lines from Pope’s translation of Homer’s Iliad, Peirce’s arrow, signifying logic as a tool or weapon, takes its place alongside references to the shields and spears of warrior heroes.  As Howe notes, Peirce had an unsuccessful academic career, his reputation faltered, and he struggled with private demons made public.

Moreover, Peirce’s arrow could refer to the logical maneuver involved in the philosopher’s ambition to slice everyday speech into more formal language (scientific and logical).  Peirce suggests this point in his statement to Lady Welby, which I cited earlier, that Howe quotes. In this way, Peirce’s arrow is analogous to the symbolism of Ockham’s razor.

Ockham’s razor is a principle of economy and simplicity.  Ockham, the medieval logician, wanted to eliminate metaphysical relations in preference to the thing itself; in terms of causality, he preceded Hume in thinking that causation is nearly coincidental by association or succession.  In modern scientific terms, we think the razor limits a hypothesis to the fewest assumptions necessary for the simplest explanation of the empirical data.

Ockham’s razor meets Wittgenstein in the Tractatus:  “If a sign is not necessary then it is meaningless. That is the meaning of Occam’s razor” (3.328); “In the proposition there must be exactly as many things distinguishable as there are in the state of affairs which it represents. They must both possess the same logical (mathematical) multiplicity (cf. Hertz’s Mechanics, on Dynamic Models)”; “Occam’s razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that unnecessary elements in a symbolism mean nothing.  Signs which serve one purpose are logically equivalent; signs which serve no purpose are logically meaningless” (5.47).

Ockham’s razor meets Peirce’s arrow.  Peirce’s main contribution in logic was his invention of logical syntax notation, which is similar to Russell’s later developments in syntax.  He developed graphs for a two-dimensional syntax (often represented in a three-dimensional graphic plane).  He called the first an “entitative graph,” which described disjunction and negation.   He called the second system “existential graphs,” which described conjunction and negation.  Peirce’s illustrations are pictorial “tunnel-bridges” (or fornices) that elaborate a logical syntax for propositional logic, quantificational logic, and meta- and modal logic.

In “Description of a Notation for the Logic of Relatives” (1870) Peirce introduces a logical syntax for the logic of relations.  He provides means for negating and combining relations, and for quantifying existentially and universally.  Around 1883 or so, Peirce introduced the material implication (hypothetical or conditional function) symbol into logic, that is, what I have been calling the Peirce arrow: →.

The application of the Peirce arrow culminated in what has been called “the Principle of Reduction”: all relations can be constituted from triadic relations (challenged by W.V.O Quine but later proven within the last two decades).  Briefly, Peirce was right: the issue turns on the simplicity or economy (hence the arrow’s similarity to a razor) of constructive resources that are used in forming relations.  Peirce’s thesis was shown to be correct only in the case that constructive resources include negation.

Howe provides several graphs, or logic notes, which show Peirce working out the details of relations.  These would eventually develop into his famous syllogism of ‘transposed quantity,’ which runs as follows: a binary relation B is defined by a set S, such that two premises are true of the following relation– for all x there is a y such that Bxy; for all x, y, z, Bxz and Byz implies that x = y; thus, for all x there exists a y such that Byx.  Peirce gives an example (as grim as it is): Everyone kills someone; no one is killed by more than someone; thus, everyone is killed by someone.   Of course, this is a valid argument (provided that the set of ‘everyone’ is finite, not infinite).

The other way that the Pierce / Peirce arrows are connected has to do with manuscripts or official documents.  The Pierce Arrow Society website says the following:

“The Pierce-Arrow Corporation (successor to the Pierce-Arrow Motor Car Company) went out of business in 1938. The assets of the company were liquidated and the proceeds were distributed to the creditors. A Pierce-Arrow stock certificate has no value as a security. Original certificates, however, have value as a collector’s item.

Unfortunately, most of the Pierce-Arrow stock certificates in circulation are reproductions that have only a nominal value as a novelty. Over the last 50 years, there have been several recreations of Pierce-Arrow stock certificates. Most of these fakes use standard stock certificate forms with the Pierce-Arrow name printed on them. A “corporate seal” is usually applied and some have rubber-stamped or hand-written dates and signatures. Watch out for certificates that request a Social Security number. Since the Social Security Act was not passed until 1936, any certificate requesting a Social Security number, but dated before 1936, is a fake.”  The main concern here is about reproductions and fakes.

There are similar manuscript issues concerning Peirce’s papers.  As Howe indicates, his publications are scattered and have been difficult to collect. Following Peirce’s death, his widow Juliette sold his unpublished manuscripts to the Department of Philosophy at Harvard University.  The papers were improperly stored and many of them were misplaced or lost. A trunk of Peirce’s manuscripts was discovered in the 1950s, but it remained hidden for decades in a dank basement in Harvard’s Widener Library.

In the 1930’s, some of Peirce’s papers were published.  But the papers were tampered with and editors reproduced them with terrible mistakes.  Many of the papers contained entries that were not written by Peirce, but were stitched together by editors.  A single entry often consisted of snatches of writing from different periods of Peirce’s life, and the entries frequently contradicted or opposed each other.  Poor Peirce came across as way more obscure and difficult than he really was.  The initial publication of Peirce’s papers gave readers a false picture of the man as a thinker.  In other words, many of his posthumous published papers were fake reproductions.

Howe insists that Peirce’s graphs are reprinted from original manuscripts that were located at the Houghton Library—“they are not shot from microfilm copies or photocopies”—hence they preserve the “aura,” as Walter Benjamin would say, of the original inscription, the esoteric moment of creative vision.  Moreover, Howe says, “Some are from notebooks containing existential graphs.”  Not graphs per se, but logical tableaux.  Indeed, the manuscript illustrations are Peirce’s logic notes, which appear like “astonishing visual texts,” as Marjorie Perloff says.

Howe comments:

“It is strange how the dead appear in dreams where another space provides our living space as well.  Another language another way of speaking so quietly always there in the shape of memories, thoughts, feelings, which are extra-marginal outside of primary consciousness, yet must be classed as some sort of unawakened finite infinite articulation.  Documents resemble people talking in sleep.  To exist is one thing, to be perceived another.  I can spread historical information, words and words we can never touch hovering around subconscious life where enunciation is born, in distinction from what it enunciates when nothing rests in air when what is knowledge?”

When are we perceived?  When is knowledge?  In a strain that sounds like Wittgenstein on the nature of facts in the Tractatus:

“A person throws a stone

As fact through air not

fact but appearance of

fact floating on vacuua

Blind existential being

may possibly not occur

at all we know nothing

with absolute certainty

of existent things not even

the single “word” the

With her reference to “finite infinite” Howe seems to refer to Peirce’s notion of infinite sets (by the syllogism of transposed quantity a finite set can be transposed in relation to an infinite set, such that an infinite set can have a one-to-one correspondence with a subset of itself).  The mental contents that comprise the set of “primary consciousness” can be reduced to the subset, the “extra-marginal outside” of “subconscious life where enunciation is born.”

Also, the passage above seems to refer to Peirce’s unique theory of signs, which accounts for a triadic representing relation.  An object is represented by a subject that is represented to a third subject.  In actuality, there is an infinite series of subjects or “representamens” whenever a subject perceives an object, since a subject becomes an object that another subject observes.  The sign relation is a condition of the representing relation that occurs when the first subject (all members of the infinite series of subjects) has a mental cognition.  In the sign relation an object is signified by a sign to a mind.  The reason a thrown stone is not a fact but an “appearance of fact” is because belief and the acquisition of knowledge—what we might know with “absolute certainty”—can only occur within the scope of a triadic relation: “to be perceived.”  Thereby, our words could very well exist in a vacuum unless they are heard as signs by another person.

Again, as Howe says, “Time (take Zeno’s flying arrow) sets out in a past we place ourselves in.  If the present is connected to the past by a series of infinitesimal steps (The Law of Mind) a past cannot be wholly past.”  Here, Howe refers to Peirce’s notion of “synechism”—the idea that space, time, feeling, ideas, and perception form a continuum.  This is both a logical and scientific idea stipulating that nature exists in a continuum.  Peirce discovered this by studying Georg Cantor’s logic (via Aristotle and Kant), and by trying to solve Cantor’s paradox, thereby defining a continuum as an ordered infinite set S, such that for two different members of S there is a third member of S that separates them.  Each infinite subset of S is higher bound by density and is lower bound by “closedness.”  For further information on Peirce’s continuum, see the following: Peirce’s Continuum PDF.

As we know, Peirce is often labeled the father of American pragmatism, but he wanted his version to be distinguished from those of weaker proponents so he called his views “practism.” In one lyric, Howe seems to summarize Peirce’s “practism” in the philosopher’s own voice:

“I might have called

it ‘practism’ but

my dear Lady Welby

perfect accuracy of

thought is suspect

I doubt I shall ever

cross the water again

We say ‘type-written’

here something about

printer’s copy modern telepathy

What I want to write blurred in utmost

haste I call logic

to rhyme with metric

or optic very very

experimental ground

Always suspect a triad.”

Howe makes logic rhyme with reason, and Peirce’s arrow flies truly into the heart of poetry.  She shows us tenets of a philosophy that may never have been revealed to the world: the depths of a deeply mystical logic.  In Peircean terms, she allows us access to an ethics of belief, the evolution of love, and signs of self-sacrifice….


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