Detached Ideas

Photograph by Steven Pinker

Recently, I enjoyed reading Rebecca Goldstein’s  36 Argu­ments for the Existence of God: A Work of Fiction. It is a novel of ideas which explores the intersec­tion of intel­lec­tual life and spiritual life. The protagonist, Cass Seltzer, is an academic, a psychologist of religion whose sur­prise best-seller, Varieties of Religious Illusion, has led to his acclaim as “America’s favorite atheist.” More­over, Cass has just been offered a job by Harvard — the epitome of academic success. But in juxtaposition to this professional career, Cass reveals an inner life that is preoccu­pied with issues of meaning and trans­cen­dence. We observe those “obstinate question­ings of sense and out­ward things” that are characteristic of the religious percipient. So if this is atheism, we wonder, how is atheism essentially dif­fer­ent from theism?

Goldstein describes her point of departure for the novel as follows:

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In April of 2005, shortly after Larry Summers’ public comments which resulted in his resignation as president of Harvard, there was a debate between Steven Pinker and Elizabeth Spelke, both from the Harvard psychology department, on “The Science of Gender and Science.” Streaming video, a transcript, and slides from this debate are available on Edge – here. There are also comments on the debate by Nora Newcomb, David Haig, Alison Gopnik and Diane Halpern, with a response by Pinker —  here.

The question under debate was whether innate differences between the sexes might help account for the dearth of women tenure track faculty in the physical sciences, mathematics, and engineering at elite universities. At the beginning of his remarks, Steven Pinker made what seems to me to be a vital distinction:

[I]t is crucial to distinguish the moral proposition that people should not be discriminated against on account of their sex — which I take to be the core of feminism — and the empirical claim that males and females are biologically indistinguishable. They are not the same thing. Indeed, distinguishing them is essential to protecting the core of feminism. Anyone who takes an honest interest in science has to be prepared for the facts on a given issue to come out either way. And that makes it essential that we not hold the ideals of feminism hostage to the latest findings from the lab or field. . . . The truth can­not be sexist.

The debate proceeded mainly on empirical grounds, although there were also a few philo­so­phical moments. Elizabeth Spelke is the 2009 winner of the Jean Nicod Prize. Steven Pinker is author of The Blank Slate, among many other books, and is married to Rebecca Goldstein.

–Paul

It is a recurrent trope in writing about Thucydides to place him in opposition to Plato. I would like to consider some of the ramifications that this opposition may have for our understanding of Thucydides, and to evaluate its limitations. But first we must try to disentangle the various guises that it assumes.

At the most specific level, the contrast between Plato and Thucydides may be broken down into various small polarities, in each of which the two thinkers do indeed seem to hold irreconcilable views. Thus the Socratic maxim that no one does evil knowingly seems to directly contradict Thucydides’ tragic vision of human nature, as the Platonic search for universals stands in opposition to the Thucydidean concern with the con­crete particular. None of the individual contrasts between Plato and Thucydides, how­ever, adequately capture the opposition that historians and philosophers have argued exists between them. This opposition is taken, rather, to arise from a funda­mental difference in one’s way of seeing, which subsumes all of these smaller dis­tinctions, and which leads the two thinkers to systemically different conclusions.

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The name “positivism” comes from the writing of Auguste Comte, the 19th century philosopher of science and founder of sociology.  In his Course of Positive Philosophy, published from 1830 through 1842, Comte described human history as progressing through three distinct stages, which he called the theological, metaphysical, and positive – the final stage corresponding to the ordering of society by modern science. Comte’s positive philosophy was quite influential in the nineteenth century. According to Michel Bourdeau:

It is difficult today to appreciate the interest Comte’s thought enjoyed a century ago, for it has received almost no notice during the last five decades. Before the First World War, Comte’s movement was active nearly everywhere in the world. The best known case is that of Latin America: Brazil, which owes the motto on its flag ‘Ordem e Progresso’ (Order and Progress) to Comte and Mexico are two prominent examples. The positivists, i.e., the followers of Comte, were equally active in England, the United States and India. And in the case of Turkey, its modern secular character can be traced to Comte’s influence on the Young Turks.[1]

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1. Michel Bourdeau, “Auguste Comte”, Stanford Encyclopedia of Philosophy (2010). [↩]

Benjamin Peirce, the father of Charles Sanders Peirce, taught mathematics and astronomy at Harvard from 1831 until his death in 1880. and was probably the leading American mathe­matician of his time. He is best known, in the history of mathematics, for his Linear Asso­ci­ative Algebra of 1870, and for his proof, as a young man, that there is no odd perfect number with fewer than four distinct prime factors.[1] Benjamin also published over a dozen other mathema­tical texts and treatises, including his well known A System of Analytical Mechanics in 1855. He helped to create a modern science curriculum at Harvard, and was an importent force in the professionalization of mathematics and science education across America. [2]

Benjamin’s personality left a powerful impression on those who encountered him. Lawrence Lowell, president of Harvard from 1909 to 1933, described him as follows:

Looking back over the space of fifty years since I entered Harvard College, Benjamin Peirce still impresses me as having the most massive intellect with which I have ever come into close contact, and as being the most profoundly inspiring teacher that I ever had. His personal appearance, his powerful frame, and his majestic head seemed in harmony with his brain. [3]

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Stephen Toulmin died last month. He studied with Wittgenstein and was a reader, with Kolakowski, of Phil’s dissertation. Toulmin was probably best known for his 1958 book, The Uses of Argument, and for his seminal work on the philosophy of science. In a long and distinguished career, he taught at Oxford, Melbourne, Leeds, Brandeis, Columbia, Michigan State, Chicago, Northwestern, and USC. Here is the NYT obituary.

All three of us have been greatly influenced by a book that Toulmin wrote with Allan Janik in 1973 called Wittgenstein’s Vienna. A fasci­nating account of Viennese culture at the turn of the century, it is an indispensable book that everyone should read.

In 1997 Toulmin was honored by the NEH with the Jefferson Lecture.

Last week an unknown hacker — or inside whistleblower — distributed on the internet emails and documents apparently taken from the computers of the Climatic Research Unit at the University of East Anglia in England. The CRU and its director, Phil Jones, were central players in establishing the theory of anthropocentric global warming that is endorsed by the IPCC. In conjunction with the Hadley Centre of the UK Met Office, they maintain HadCRUTv3, one of the principal datasets of global temperature.

By now the purloined files have been disseminated throughout the internet, and have created quite a stir. The original zip file (62 MB) is here; when unzipped it contains about 160 MB of information, with over 1000 emails and 2000 other documents. The blogosphere has primarily focused on the emails, which include exchanges between Phil Jones and many leading climate scientists. There is now a searchable database of the emails and Bishop Hill provides a synopsis of some of the more interesting cases. The other documents — with data, code, and financial records — will probably have a greater impact over the long run. There are questions, for instance, about coding practice — see here. Evidence so far seems to indicate that all of this material is genuine; many recipients have confirmed the accuracy of emails, and as yet nothing has been disputed.

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Ludwig Wittgenstein once asked rhetorically, Do we bring up our children because we have found it pays? [1] This sounds absurd, yet in many ways our expressed thinking about children is utilitarian and fails to take them seriously as ends in themselves. Perhaps we are no longer driven to produce family heirs, but when we want to draw attention to the importance of educating children we still speak of them as “the leaders of tomorrow.” If we argue that the importance of children derives from the fact that they are future adults, we neglect to recognize any inherent value to child­hood itself. We look back with horror at Puritans who expected children to behave like little adults and viewed play as sin, but many developmental theories are still prone to analyze childhood as a series of stages leading to adulthood. In this case the mature adult remains the measure and the end of analysis, and childhood is just a means. Play is acceptable in children because we have recognized that through play various capacities are developed that we value in the mature adult. Does such thinking respect childhood, or have we raised the reductionism of our Puritan fore­bears to a new level of sophistication and subtlety? This is not to suggest that developmental models are not important and illuminating, but only that taken alone such models are inherently reductive and that perhaps we have not yet earned the right to look down on Puritans.

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We learn history not in order to know how to behave or how to succeed, but to know who we are.  –Leszek Kolakowski, from “The Idolatry of Politics”, 1986

We were saddened to learn this summer of the death of Leszek Kolakowski, the bril­liant Polish philosopher and historian of ideas. As a professor at Warsaw University, Kolakowski’s courageous criticism of Marxism in the 50’s and 60’s resulted in his books being banned and the loss of his job — and led to his emigration to the West in 1968. Kolakowski taught briefly at McGill University and at Berkeley before settling at All Souls College, Oxford. He also taught on the Committee for Social Thought, at Chicago, and was a reader for Phil’s disserta­tion. Here is the NYT obit­uary.

In 1978, Kolakowski published his monumental Main Currents of Marxism, an ex­haus­tive analysis (beginning with Plotinus) of such notions as the labor theory of value, dialectical materialism, and the concept of class struggle. He claimed that Stalinism was not an aberration, but a natural consequence of Marxist utopian­ism. He was an eclectic scholar whose interests were not confined to political philo­sophy; his books included: Positivist Philosophy (1971), The Presence of Myth (1972), Husserl and the Search for Certitude (1975), Bergson (1985), God Owes Us Nothing: A Brief Remark on Pascal’s Religion and on the Spirit of Jansenism (1995), and The Two Eyes of Spinoza (2004). Nathan’s and my initial exposure to Kolakowski was through Tales from the Kingdom of Lailonia, satirical fairy-tales written while he was still in Poland. Phil recommends Metaphysical Horror (1978), a collec­tion of essays on the history of philo­sophy, and Nathan recommends Religion: If There is no God… (2001).

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God created the integers; the rest is the work of man.

– Leopold Kronecker

I.

What are we saying when we talk about music?

This question captures the paradox that lies at the heart of musical theory. Put in its most basic form, the problem that has dogged musical theory since Boethius has to do with the relationship between reason and the esthetic sense. The earliest theories show that the coexistence between the two was never an entirely easy one:

In the final analysis, it was to this that the Pythagoreans’ harmonic analysis of the universe led: the discovery of incommensurables. And no matter how they might juxtapose the numbers, no matter to what lengths they might extend their mathematical circumlocutions, one fact remained, a fact that has ever since proved resistant to mathematical rationalization: there is no fraction m/n that will divide the whole-tone into two equal parts.[1]

The Pythagorean construction of music was an attempt at reconciling the rational and the beautiful — at showing that they are, indeed, one and the same. In this sense it was a corollary to the impulse behind the Parthenon: the Athenians believed that the golden ratio, applied to every dimension of a structure, would create something that was beautiful precisely because of its mathematical perfection.

In music, as mentioned in the previous quote, this dream was quickly shown to be illusory. While the Parthenon was constructed ex nihilo, and could perfectly mirror the rational dreams of its designers, the Pythagorean theorists of music were con­fronted from the beginning with a stubborn fact: there were pre-existing and deeply engrained notions of what constituted the proper and beautiful in music — the whole tone, the semi-tone, the modes, the tuning of the lyre — and, although they hovered tantalizingly close to the realm of reason, they ultimately eluded its grasp.

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Over the past decade the identity of Spengler, the pseudonymous Asian Times colum­nist, has been the subject of considerable speculation. Last week, Spengler finally revealed himself to be David P. Goldman — classical musician, philo­sopher, conser­va­tive economist, and senior financial officer for Bear Stearns, Credit Suisse, and Bank of America.

Spengler’s columns are dense, oracular, and provocative — it is prudent to ingest them in small quantities. They are remarkably erudite, and show an impressive command of cultural and religious history. Although I might take issue with particular conclusions, the scope and intensity of his thought is invariably bracing.  By his own esti­mate, the Asian Times columns reached a million readers, and the high level of pub­lic interest is evidenced by the 5000 or so registered participants in the Spengler Forum.

Some interesting Spengler essays to try are:

Overcoming ethnicity
Socrates the destroyer
Tolkien’s Ring: When immortality is not enough
Benedict XVI is magnificently right
This almost-chosen, almost-pregnant land

The most recent Spengler column is about the Susan Boyle phe­nomenon.  He says:

Meanwhile, in China, 60 million children are learning Western classi­cal music under the gimlet gaze of strict teachers. East Asian singers, parti­cularly Koreans, are working their way up the ranks of provincial opera companies, and every one of them sings better than Boyle. Who do you think is going to run the world 20 years from now? As the Italians say, we’re bolliti, “boiled”.  Now we can spell it with a “y”.  I hate to always be the one to say this, but the hope is fatuous. No, you can’t.

These talent spectacles, Spengler observes, betray an undercurrent of self-worship; we choose to pay homage to what is like us rather than what is above us.

David Goldman has a new home as associate editor at First Things.

–Paul

I have long been an admirer of Charles Murray, a good man whose extra­ordinary political courage captures what is best in the Quaker tradi­tion. His recent essay, The Europe Syndrome and the Challenge to American Exceptionalism, makes a case for American excep­tion­alism that is based upon the idea that the purpose of government is to facilitate the pursuit of happiness — as understood in an Aristotelian sense:

My argument is drawn from Federalist Paper No. 62, probably written by James Madison: “A good government implies two things: first, fidelity to the object of government, which is the happiness of the people; secondly, a knowledge of the means by which that object can be best attained.” Note the word: happiness. Not prosperity. Not security. Not equality. Happiness, which the Founders used in its Aristotelian sense of lasting and justified satisfaction with life as a whole.

Murray claims that there are only four “institutions” in society within which human beings can attain this kind of deep satisfaction: family, community, vocation, and faith.

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Peter Smith, of Logic Matters, has noticed a new Stanford Encyclopedia of Philosophy entry, Set Theory: Constructive and Intuitionistic ZF.  Constructive and intuitionistic set theories result from the rejection of the law of excluded middle, and effectively restrict set theoretical ontology to poten­tially infinite sets:

The shift from classical to intuitionistic logic, as well as the requirement of predicativity, reflects a conflict between the classical and the constructive view of the universe of sets. This also relates to the time-honoured distinction between actual and potential infinity. According to one view often associated to classical set theory, our mathematical activity can be seen as a gradual disclosure of properties of the universe of sets, whose existence is independent of us. This tenet is bound up with the assumed validity of classical logic on that universe. Brouwer abandoned classical logic and embarked on an ambitious programme to renovate the whole mathematical landscape. He denounced that classical logic had wrongly been extrapolated from the mathematics of finite sets, had been made independent from mathematics, and illicitly applied to infinite totalities.

In a constructive context, where the rejection of classical logic meets the requirement of predicativity, the universe is an open concept, a universe “in fieri”. This coheres with the constructive rejection of actual infinity (Dummett 2000, Fletcher 2007). Intuitionism stressed the dependency of mathematical objects on the thinking subject. Following this line of thought, predicativity appears as a natural and fundamental component of the constructive view. If we construct mathematical objects, then resorting to impredicative definitions would produce an undesirable form of circularity. We can thus view the universe of constructive sets as built up in stages by our own mathematical activity and thus open-ended. [SEP]

This article might interest our BA Seminar students, as well as students in Programming Languages who have recently encountered Curry-Howard Isomorphism — the correspondence between intuitionistic logic and CL_K.

–Paul

Alasdair MacIntyre’s recent book, Dependent Rational Animals, offers us a picture of the human situation as fundamentally dependent and derives from this a corresponding picture of the relationship between rationality and various virtues.   In the last chapter he concludes that “we are able to become and to continue as practical reasoners only in and through our relationships to others,” and hence that, “rational enquiry is essentially social.”   It is “not something that I undertake by attempting to separate myself from the whole set of my beliefs, relationships, and commitments and to view them from some external standpoint.  It is something that we undertake from within our shared mode of practice” (MacIntyre 1999 156-157).  While I ultimately share these conclusions, it is valuable to consider how some of MacIntyre’s specific arguments and discussions undermine this general insight.  At various points he himself falls prey to what he calls “illusions of self-sufficiency” by supposing that critique requires transcendence, that accountable practical reasoners must be independent practical reasoners, and that speaking with “my own voice” must replace “my originally infantile desire to please others.” I will suggest that these assumptions are residues of a Kantian picture of reason and morality which are inappropriate to the essentially social nature of being dependent rational animals.

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Socrates wrote nothing.  Plato more than com­pensated for this deficit; for nearly fifty years he fashioned brilliant dialogs in which Socrates was the central figure. His early dialogs were written shortly after the events they depicted — maybe around 395 BC — and were intended for a critical audience who would have remem­bered Socrates. They show Socrates conversing with the citizens of Athens, and describe the events surround­ing his trial and death. These dialogs typically end with­out concep­tual reso­lu­tion, without answers to the questions they pose. In this sense, the philo­sophical impact of Socrates is mainly destructive; he stings like a torpedo fish and his opponents slink away. On the other hand, the early dialogs provide fascinating glimpses into the char­acter of Socrates — a character so compelling that we begin to understand why Plato could not bring himself to move on, why he built such a remark­able monu­ment to this man.

In Plato’s Symposium, Alcibiades crashes the party — drunk — and proposes a eulogy of Socrates.  He first compares him to the sileni to be found in the statuaries stalls, which when opened reveal figures of the gods inside.  He then describes the effect that Socrates, “with nothing but a few simple words”,  had upon his listeners:

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We have had some rather vigorous discussions on platonism in our BA Seminar. Recently the discussion centered on the existence of “natural kinds” — the question, for instance, of whether biological species are arbitrary distinctions or grounded in reality. In a famous passage from the Phaedrus, Plato talks about dividing things into forms “following the objective articulation; we are not to attempt to hack off parts like a clumsy butcher. . .” (265e)  Most of our students, it seems, tend to be nominalists rather than realists [which is not meant to imply that they are clumsy butchers]. Thinking about platonism reminded me of the following cartoon — linked in a comment to our GRE post. It is from a nice site, xkcd: A Webcomic of Romance, Sarcasm, Math and Language.

–Paul

On September 12, 2006, Pope Benedict XVI gave an address to the Faculty of Science at the University of Regensburg entitled Faith, Reason and the University: Memories and Reflections. This address was widely reported by the press, especially the Pope’s remarks about Islam in which he cited the Byzantine emperor Manuel II Paleologus’ contention that violence is incompatible with the nature of God.  In the aftermath there were riots and demonstrations, diplomatic protests were lodged throughout the world, and a nun was killed in Mogadishu. Here is the Wikipedia description of the con­tro­versy.

More interesting to me, and not reported by the press much at all, is the rest of what Benedict had to say at Regensburg.  At risk of simplifying, I will pick out three major points:

1) Benedict claimed that Christianity must be viewed within the broader context of Greek philosophy. “This inner rapprochement between Biblical faith and Greek philosophical inquiry was an event of decisive importance not only from the standpoint of the history of religions, but also from that of world history — it is an event which concerns us even today.”  (This is in response to what the Pope referred to as the “call for the dehellenization of Christianity”.)

2) He positioned the Church explicitly on the side of modern science. ”The scien­tific ethos, moreover, is. . .the will to be obedient to the truth, and, as such, it embodies an attitude which belongs to the essential decisions of the Christian spirit.”

3) He called into question logical positivism — citing the unity of human reason and the “intrin­sically Platonic element” in science.

Spengler remarks somewhere that the Catholic Church is one of the few modern institutions that finishes its conversations. This should be reason enough, I think, to attend to the remainder of Benedict’s address. In my opinion, there is considerable philosophical sophistication in the Pope’s comments.  Even for those of us who are not Catholic, the Regensburg address provides a refreshing counterpoint to the flat land­scape of postmodernism.  I recommend that you read it.

–Paul

I.

To analyze Josquin is to confront, head on, the incommensur­ability between analytical systems and true artistic greatness.  There is a sense in which approaching him with modern tools of dissection is catching sand in a sieve; no tool of deeper analysis — of the sort favored by composers and theoreticians from the common practice period to the present — will ever yield an entirely satisfactory understanding of his music.  The analysis may indeed provide insight into the less fundamental levels of a works’ structure: motivic parsing may yield a facile understanding of the linear building blocks of a work, and the study of fugal techniques might explain, simply enough, the manner of their deployment. But all of this is on the surface. At the basic, “skeletal” level, an ordinary structural analysis turns up strangely blank. When we ask the most important question—the question of what gives the work meaning, direction, unity—the answer proves opaque.  The explanation why follows an obscure path outward, through questions that are technical, linguistic, and finally philosophical.

There are probably three fundamental paradigms through which the deeper structure of music can be approached.  These I will term, for the sake of this argument, the Schenkerian, the Schoenbergian, and the architectonic.  Each must be carefully turned over, its relevance to the music of the early Renaissance deciphered, and the rest, for the moment, thrown out.  From the remnants, and from a largely unguided study of the score of Josquin’s Missa L’Homme Armé Super Voces Musicales, I will attempt to construct a method which is technically and philosophically coherent with Josquin’s music.  This, hopefully, will itself provide further insight into the score.

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Robert L. Horn was a philosopher, scholar, teacher and mentor to several gene­rations of students and young philo­sophers. He grew up near Richmond, Indiana, earned his B.A. from Earlham College, his Th.D. from Union Theological Semi­nary, taught at Haver­ford Col­lege (1958-1961), Union Theological Seminary (1960-1966), and was a visiting professor at the University of Chicago Divinity School. In 1966 he was lured back to Earlham, where he taught for roughly thirty years. His area of specialization was in Kant, Hegel, and the Danish Hegelians who com­prised the context for Søren Kierkegaard. He also had a deep interest in Plato, especially in the illumi­na­tion of the dialogues by historical and archaeolo­gical research. as well as in Native American culture and astronomy.

It was with great pleasure that I learned, last year, of the publication of Robert Leslie Horn, Positivity and Dialectic: A Study of the Theological Method of Hans Lassen Mar­ten­sen, Søren Kierkegaard Research Centre and C. A. Rietzel, Copenhagen, 2007.  I think Bob might have been pleased that it was published by Kierkegaard’s publisher, Rietzel. Here are some snippets from the editor’s introduction:

The present work was originally a dissertation for the degree of Th.D. at the Union Theological Semi­nary in New York City in 1969.  For years now, it has been known as a kind of insider’s tip among the small circle of Anglophone scholars interested in Danish Golden Age theology. Unfortunately, the work was never published, and its reception has until now been limited to those who personally knew the author or had access to it via the university microfilm dissertation service. . .

Although it was written more than twenty-five years ago, this text still today must be regarded as one of the leading works on Danish Golden Age philosophy and theology in the English language. . . .the present work can be said to anticipate a number of historically oriented studies of Søren Kierkegaard’s works that have been published over the last decade or so by leading scholars. . . .In this respect it is to be praised as an outstanding pioneering effort in the field.  However, unlike many other pioneering works, its scholarly standard is extremely high. . .

There can be no doubt that when this work comes to be more generally known by students and scholars alike, it will contribute immensely to our appreciation of the work of Hans Lassen Martensen. Moreover, it will help to put the philosophy and theology of Søren Kierkegaard in a new perspective. . .

There is so much more that could be said about Bob Horn. It was an extraordinary privilege to study with him. I thought of Bob when I read Nathan’s post mentioning Schoenberg’s comment to Karl Kraus: “I have per­haps learned more from you than one is permitted to learn if one wishes to remain independent.”

–Paul

In the literature on Schoenberg, there is surprisingly little material that deals comprehensively with his relation to the broader intel­lectual trends of fin-de-siècle Vienna.  We are provided with snap­shots, from this angle or that; the full picture remains elusive.

The contemporary interpretations we have of Schoenberg’s relation to his Viennese milieu fall, broadly speaking, into two categories.  These categories reflect two competing interpretations of his broader musical significance, which themselves correspond to two distinct and occasionally contradictory sides of Schoenberg’s nature.  These interpretations we may call the rational-technical, and the ethical-religious.  There are also, notably, a small number of works that attempt to synthesize these two approaches, but as of yet none do full justice to their subject. It is in this field—the consideration of Schoenberg in his sometimes paradoxical totality—that the richest work remains to be done.

———

The first school of interpretation, and that which was predominant for much of the mid-twentieth century, is the rational-technical.  This itself is intimately related to the school of technical analysis which tends to address itself exclusively to the linguistic and formal elements of Schoenberg’s musical language.

The rational-technical interpretation of Schoenberg might also be called the positivist interpretation.  Those who endorse this view of Schoenberg tend to see him, where they relate him to contemporary intellectual phenomena, predominantly in the light of the logical positivism of the Wiener Kreis, or Vienna Circle, a discussion group that grew up around the philosopher Moritz Schlick.  They also, concordantly, place considerable emphasis on Schoenberg’s relation to Ludwig Wittgenstein’s Tractatus Logico-Philosophicus, the most important philosophical document of the period, and one by which the logical positivists set considerable store.

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I am not much interested in the hidden intentions Shakespeare had in writing Macbeth, whether he was striving to portray the immortal torment of the human soul or merely to flatter the self-importance of an English King. I’ll leave that to the scholars and hecklers of the human spirit who can find nothing better to do than to dig around in the dust-bins of history. I am interested in the play as it stands. In particular, I am interested in the “weird sisters.” I think we should take the damn witches seriously.

Readers have scoffed for centuries at the three witches in Macbeth. But nowadays we are not satisfied with scoffing at witches, and we seek to go further. Nowadays our literary critics herald “the death of the author” as Nietzsche once spoke of “the death of God.” There is only the text, they say, and the doer behind the deed is a metaphysical fiction. But if skepticism is our value we should also show skepticism about our skepticism. We should be suspicious of the grandiose claims of Nietzsche and our contemporary literary critics and suspect, in the spirit of Mark Twain, that reports of the death of God and of authorship are greatly exaggerated. Authors and gods are tough things to kill. As Shakespeare wove the witches into Macbeth in diverse and subtle ways, gods and authors weave themselves into the fabric of our world. Perhaps in time we could “kill them,” but should we? Would life be better, more worth living, in a disenchanted world?

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Logical positivism was a philosophical movement that flourished in Vienna during the years following the First World War. It grew out of a discussion group, the so-called “Vienna Circle”, that included such figures as Moritz Schlick, Otto Neurath, Friedrich Waismann, Gustav Bergmann, Hans Hahn, Herbert Feigl, Edgar Zilsel, Victor Kraft, Karl Menger and Rudolf Carnap. Although they differed in regard to many of the details, the common program of this group was to provide an analysis of modern science that clearly distinguished it from metaphysics, theology and ethics. Only science and mathematics, the positivists thought, can produce genuine knowledge.

Logical positivists emphasized the unity of the sciences, and as a consequence tended to be reductionists. They used the increasingly sophisticated logical and linguistic tools of the time to help clarify both the connections between the individual sciences and the relationship between theory and obser­vation. Positivists were also empir­icists. They eventually adopted the name “logical empiricism”, and they had ante­cedents in an empirical tradition that extended back through Ernst Mach and Bertrand Russell to David Hume. Many positivists subscribed to some form of phenomenalism. Rudolf Carnap, for instance, in The Logical Structure of the World, described the con­struction of the world out of what he called “elemen­tary exper­iences”. [1]

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Philosophers have never felt comfortable speaking about silence. Why should they? At best such efforts are ironic; undertaking them literally is generally thought to involve performative contradictions, since the content of what we are trying to say contradicts the fact that we are saying it. When mystics claim to have an ineffable, or inexpressible, knowledge of ultimate realities, philosophers are naturally curious to hear more about it, but of course anything intelligible the mystics may say, including the very idea of the ineffable, is by definition not ineffable but expressed, and hence self-refuting. It seems that the best solution is for mystics to maintain total silence. But even then Hegel does not leave the mystics alone. He dismisses their silent knowledge as “the night in which all cows are black” – in other words, as a presumptuous and ultimately empty achievement.

Trying to speak about silence is akin to the ontological task of trying to get something from nothing. Maybe God can create ex nihilo, but the rest of us find this hard to understand, and doing it is totally beyond us. Most philosophers cannot even bake a cake. Even ordinary people find it hard to argue with the principle ex nihilo, nihil fit (from nothing, nothing comes) — and when philo­sophers are asked to make something of nothing, they seem compelled to employ humor to effect their escape. For example, in the Encyclopedia of Philosophy P. L. Heath writes:

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Raymond Smullyan is 89 years old, and lives across the Hudson in the Catskill mountains. A distinguished mathematician, logician, and philosopher, he has written over 20 books, which have been translated into more than 17 languages. Smullyan is the Oscar Ewing Professor Emeritus of Philosophy at Indiana University and played a prominent role in the history of modern logic. In 1957, he wrote an influential paper for the Journal of Symbolic Logic, called “Languages in Which Self-Reference is Possible,” showing that Gödel incompleteness holds for many formal systems more elementary than those considered by Gödel. Georg Kreisel described Smullyan’s Theory of Formal Systems as “the most elegant exposition of the theory of recursively enumerable (r.e.) sets in existence.” Smullyan is probably best-known, though, for his popular collections of logic puzzles. When my children were growing up, they spent many hours with The Lady or the Tiger. My own favorite is To Mock a Mockingbird, which is about combinatory logic and the lambda calculus, one of the foundations of computer science.

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There is a story behind the title of this blog.  In 1897, Charles Peirce was invited by his friend William James to give a series of philosophy lectures in Cambridge, MA. Peirce prepared a daunting set of lectures on formal logic and, in December of 1897, sent an outline of these lectures to James. But James, sensing a mis­match between Peirce’s outline and the prospective audience, wrote back to Peirce begging him to reconsider the topic. “There are only three men,” James wrote, “who could possibly follow your graphs and relatives.” James implored Peirce to “be a good boy” and to think out a more popular plan; and James went on to make the rather unfortunate suggestion that “separate topics of a vitally important character would do perfectly well.”

Peirce was annoyed by this response (although it would have taken more than this to diminish his affection for James). He imme­diately set about revising his lectures, bestowing upon them the new title “Detached Ideas On Topics of Vital Importance.” There was considerable irony to this title, since Peirce thought there was little to be gained from either “detached ideas” or reasoning about “topics of vital impor­tance”. The latter was held up to particular ridicule in the draft of a new opening lecture that Peirce called “On Detached Ideas in General and on Vitally Important Topics” [1.649-677]. This draft is not available electron­ically, as far as I know, but it has influenced twentieth century Peirce scholarship through its inclusion in The Collected Papers of Charles Sanders Peirce. [Hartshorne and Weiss, 1931] What follows is my own gloss on this text — with extended quotations to help convey the flavor of Peirce’s writing.

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