## Sunday, May 27, 2018

Is nature continuous or discrete? How the atomist error was born

[[A little difficult, but an excellent example of how deep msitakes can go, and how subtle our world is - or I should say "looks" under this latest comment.]]

is associate professor of philosophy at the University of Denver. His latest book is Lucretius I: An Ontology of Motion (2018).
The modern idea that nature is discrete originated in Ancient Greek atomism. Leucippus, Democritus and Epicurus all argued that nature was composed of what they called τομος (átomos) or ‘indivisible individuals’. Nature was, for them, the totality of discrete atoms in motion. There was no creator god, no immortality of the soul, and nothing static (except for the immutable internal nature of the atoms themselves). Nature was atomic matter in motion and complex composition – no more, no less.
Despite its historical influence, however, atomism was eventually all but wiped out by Platonism, Aristotelianism and the Christian tradition that followed throughout the Middle Ages. Plato told his followers to destroy Democritus’ books whenever they found them, and later the Christian tradition made good on this demand. Today, nothing but a few short letters from Epicurus remain.
Atomism was not finished, however. It reemerged in 1417, when an Italian book-hunter named Poggio Bracciolini discovered a copy of an ancient poem in a remote monastery: De Rerum Natura (On the Nature of Things), written by Lucretius (c99-55 BCE), a Roman poet heavily influenced by Epicurus. This book-length philosophical poem in epic verse puts forward the most detailed and systematic account of ancient materialism that we’ve been fortunate enough to inherit. In it, Lucretius advances a breathtakingly bold theory on foundational issues in everything from physics to ethics, aesthetics, history, meteorology and religion. Against the wishes and best efforts of the Christian church, Bracciolini managed to get it into print, and it soon circulated across Europe.
This book was one of the most important sources of inspiration for the scientific revolution of the 16th and 17th centuries. Nearly every Renaissance and Enlightenment intellectual read it and became an atomist to some degree (they often made allowances for God and the soul). Indeed, this is the reason why, to make a long and important story very short, science and philosophy even today still tend to look for and assume a fundamental discreteness in nature. Thanks in no small part to Lucretius’ influence, the search for discreteness became part of our historical DNA. The interpretive method and orientation of modern science in the West literally owe their philosophical foundations to ancient atomism via Lucretius’ little book on nature. Lucretius, as Stephen Greenblatt says in his book The Swerve (2011), is ‘how the world became modern’.
There is a problem, however. If this story is true, then modern Western thought is based on a complete misreading of Lucretius’ poem. It was not a wilful misreading, of course, but one in which readers committed the simple error of projecting what little they knew second-hand about Greek atomism (mostly from the testimonia of its enemies) onto Lucretius’ text. They assumed a closer relationship between Lucretius’ work and that of his predecessors than actually exists. Crucially, they inserted the words ‘atom’ and ‘particle’ into the translated text, even though Lucretius never used them. Not even once! A rather odd omission for a so-called ‘atomist’ to make, no? Lucretius could easily have used the Latin words atomus (smallest particle) or particula (particle), but he went out of his way not to. Despite his best efforts, however, the two very different Latin terms he did use, corpora(matters) and rerum (things), were routinely translated and interpreted as synonymous with discrete ‘atoms’.
Further, the moderns either translated out or ignored altogether the nearly ubiquitous language of continuum and folding used throughout his book, in phrases such as ‘solida primordia simplicitate’ (simplex continuum). As a rare breed of scholar interested in both classical texts and quantum physics, the existence of this material continuum in the original Latin struck me quite profoundly. I have tried to show all of this in my recent translation and commentary, Lucretius I: An Ontology of Motion (2018), but here is the punchline: this simple but systematic and ubiquitous interpretive error constitutes what might well be the single biggest mistake in the history of modern science and philosophy.
This mistake sent modern science and philosophy on a 500-year quest for what Sean Carroll in his 2012 book called the ‘particle at the end of the universe’. It gave birth to the laudable virtues of various naturalisms and materialisms, but also to less praiseworthy mechanistic reductionisms, patriarchal rationalisms, and the overt domination of nature by humans, none of which can be found in Lucretius’ original Latin writings. What’s more, even when confronted with apparently continuous phenomena such as gravity, electric and magnetic fields, and eventually space-time, Isaac Newton, James Maxwell and even Albert Einstein fell back on the idea of an atomistic ‘aether’ to explain them. All the way back to the ancients, aether was thought to be a subtle fluid-like substance composed of insensibly tiny particles. Today, we no longer believe in the aether or read Lucretius as an authoritative scientific text. Yet in our own way, we still confront the same problem of continuity vs discreteness originally bequeathed to us by the moderns: in quantum physics.
Bottom of Form
Theoretical physics today is at a critical turning point. General relativity and quantum field theory are the two biggest parts of what physicists now call ‘the standard model’, which has enjoyed incredible predictive success. The problem, however, is that they have not yet been unified as two aspects of one overarching theory. Most physicists think that such unification is only a matter of time, even though the current theoretical frontrunners (string theory and loop quantum gravity) have yet to produce experimental confirmations.
Quantum gravity is of enormous importance. According to its proponents, it stands poised to show the world that the ultimate fabric of nature (space-time) is not continuous at all, but granular, and fundamentally discrete. The atomist legacy might finally be secured, despite its origins in an interpretive error.
There is just one nagging problem: quantum field theory claims that all discrete quanta of energy (particles) are merely the excitations or fluctuations in completely continuous quantum fields. Fields are notfundamentally granular. For quantum field theory, everything might be made of granules, but all granules are made of folded-up continuous fields that we simply measure as granular. This is what physicists call ‘perturbation theory’: the discrete measure of that which is infinitely continuous and so ‘perturbs one’s complete discrete measurement’, as Frank Close puts it in The Infinity Puzzle (2011). Physicists also have a name for the sub-granular movement of this continuous field: ‘vacuum fluctuations’. Quantum fields are nothing but matter in constant motion (energy and momentum). They are therefore never ‘nothing’, but more like a completely positive void (the flux of the vacuum itself) or an undulating ocean (appropriately called ‘the Dirac sea’) in which all discrete things are its folded-up bubbles washed ashore, as Carlo Rovelli puts it in Reality Is Not What it Seems (2016). Discrete particles, in other words, are folds in continuous fields.
The answer to the central question at the heart of modern science, ‘Is nature continuous or discrete?’ is as radical as it is simple. Space-time is not continuous because it is made of quantum granules, but quantum granules are not discrete because they are folds of infinitely continuous vibrating fields. Nature is thus not simply continuous, but an enfolded continuum.
This brings us right back to Lucretius and our original error. Working at once within and against the atomist tradition, Lucretius put forward the first materialist philosophy of an infinitely continuous nature in constant flux and motion. Things, for Lucretius, are nothing but folds (duplex), pleats (plex), bubbles or pores (foramina) in a single continuous fabric (textum) woven by its own undulations. Nature is infinitely turbulent or perturbing, but it also washes ashore, like the birth of Venus, in meta-stable forms – as Lucretius writes in the opening lines of De Rerum Natura: ‘Without you [Venus] nothing emerges into the sunlit shores of light.’ It has taken 2,000 years, but perhaps Lucretius has finally become our contemporary.

Two recent critical views of Biblical Criticism

Recent Trends in Biblical Source Criticism: A Draft
by David Stern

[[Many thanks to David Greenberg for sending me this. It more than verifies my piecemeal critiques of Biblical Criticism over the years. I had no idea that the people in the field finally woke up to the reality that there was no substance to their ideas. Has Richard Elliot Friedman given up?]]

http://www.lookstein.org/articles/Biblical_Criticism.htm
all hypotheses are working proposals until confirmed in detail, and many must be discarded while others will require drastic overhauling in the face of new evidence. There is a grave temptation to hold on to a hypothesis that has served well in the past, and the more serious temptation to bend data to fit, or to dismiss what cannot be accommodated into the system. The commitment must always be to observable or discoverable data, and not to a hypothesis, which is always expendable. 1
The mid-eighties and the early nineties witnessed a resurgence of biblical scholars challenging, revising, and even rejecting the documentary hypothesis.2 First and foremost, scholars relinquished claims to a scientific methodology. In Empirical Models for Biblical Criticism, Jeffery Tigay insists that "The degree of subjectivity which such hypothetical [source critical] procedures permit is notorious."3 In fact, Tigay characterizes these procedures as "reading between the lines."4 Moreover, Edward Greenstein maintains that source critical analysis is analogous to the blind men and the elephant: "each of five blind men approaches a different part of an elephant's anatomy. Perceiving only part of the elephant, each man draws a different conclusion as to the identity of what he encounters."5 According to the preceding remarks, not only are source critical methods subjective, they also account for only a fraction of the total evidence. Especially when analyzing a literary corpus "as bulky and complex as an elephant,"6 a system which fails to consider all the evidence and wherein "scholars shape the data into the configurations of their own imagination"7 hardly warrants the label scientific.
While surveying many conflicting proposals for the nature of the hypothetical sources, Gerhard Larsson gives a more specific account of the methodological shortcomings. He says that "there is no sound objective method for recognizing the different sources, there is also no real consensus about the character and extant of sources like J and E, [and] no unity concerning limits between original sources and the insertions made by redactors."8 Rather as Greenstein says: "each scholar defines and adapts the evidence according to his own point of view."9 Such an approach not only yields results which are, as Tigay highlights, "hypothetical (witness the term 'documentary hypothesis'),"10 but, as David Noel Freedman declares, allows and encourages, "the pages of our literature [to be] filled with endless arguments between scholars who simply reiterate their prejudices."11
The lack of a sound and rigorous methodology leads scholars to produce varying and even contradictory theories, which ultimately undermine the enterprise as a whole. In addition to Wellhausen's four sources J, E, P, and D, some scholars speculate about sources labeled Lay (L), Nomadic (N), Kenite (K), Southern or Seir (S) and the "foundational source" Grundlage (G). Not only do scholars "multiply" the number of sources, some, applying the same methodology, "fragment" J, E, P, and D into further subdivisions, and view these documents as products of "schools" which "shaped and reshaped these documents by further additions."12 After summarizing the different opinions,13 Pauline Viviano says, "The more 'sources' one finds, the more tenuous the evidence for the existence of continuous documents becomes, and the less likely that four unified documents ever existed. Even for those able to avoid skepticism and confusion in the face of the ever increasing number of sources, the only logical conclusion seems to be to move away from [Wellhausen's] Documentary Hypothesis toward a position closer to the Fragmentary Hypothesis."14
In addition to being a victim of its own ambition, the documentary hypothesis suffered many challenges from the time of its inception through contemporary scholarship. Scholars have contested and even refuted the arguments from Divine names, doublets, contradictions, late words, late morphology, aramaisms, and every other aspect of the documentary hypothesis.15As a result, some scholars denounce source criticism en toto,16 while others posit alternate hypotheses. However, one wonders if these hypotheses will not share the same fate as the ones they just disproved.
These problems have brought source criticism to a sad state. In Greenstein's words, "Many contemporary Biblicists are experiencing a crisis in faith. The objective truths of the past we increasingly understand as the creations of our own vision."17 He continues, "all scholarship relies on theories and methods that come and go, and modern critical approaches are no more or less than our own midrash."18 This "crisis," or "breakdown" to use Jon Levenson's characterization,19 has encouraged droves of scholars to study the Bible synchronically,20 a method which effectively renders source criticism irrelevant.21
Among other advantages, the synchronic method of Biblical study encourages scholars to detect textual phenomena which, upon reflection, seem obvious, but have not been recognized until recently. Levenson explains these recent detections as follows: "Many scholars whose deans think they are studying the Hebrew Bible are, instead, concentrating on Syrio-Palestinian archeology, the historical grammar of Biblical Hebrew, Northwest Semitic epigraphy, or the like-all of which are essential, but no combination of which produces a Biblical scholar. The context often supplants the text and, far worse, blinds the interpreters to features of the text that their method has not predisposed them to see."22 This statement could not be truer when referring to source criticism, and to this end Larsson says, albeit in a harsher tone: "Source criticism obscures the analysis. Only when the text is considered as a whole do the special features and structures of the final version emerge."23
The rediscovery of the Bible's special features and structures has proven to be extremely rewarding in its own right, and, in addition, it has recurrently forced scholars to revise and even reject source critical theories. Larrson states this latter statement quite clearly: "many scholars have found that when the different [patriarchal] cycles are studied in depth it is no longer possible to support the traditional documentary hypothesis."24 Even the flood narrative, traditionally lauded as two independent strands (J and P) woven together, has been unified by scholars who perceive a chiastic structure integrating the various sections of the story.25 In fact, a statistical analysis of linguistic features in Genesis lead by Yehuda Radday and Haim Shore demonstrates that "with all due respect to the illustrious documentarians past and present, there is massive evidence that the pre-biblical triplicity of Genesis, which their line of thought postulates to have been worked over by a late and gifted editor into a trinity, is actually a unity."26

1Freedman, David Noel. "On Method in Biblical Studies: The Old Testament." Divine Commitment and Human Obligation: Selected Writings of David Noel Freedman. Volume 1. Ed. by John R. Huddlestun. Grand Rapids, Michigan: Eerdmans, 1997a. 160
3Tigay 1985:2. He says this despite the fact that his book attempts to demonstrate that other features of source criticism are methodologically sound.
4Ibid what page ????
5Greenstein 1990a:164.
6Ibid.
7Greenstein 1990b:30.
8Larsson, Gerhard. "Documentary Hypothesis and Chronological Structure of the Old Testament" ZAW 97 (1985) 319.
9Greenstein 1990b:31
10Tigay 1985:2.
11Freedman 1997a:153.
12Viviano 1993: 43.
13Ibid. 43-44.
14Ibid 44.
15See Viviano 1993 especially note 29, Walker 1986, WhyBray 1987 and many others.
16 See for example Brichto, Herbert Chanan. The Names of God: Poetic Readings in Biblical Beginnings. New York: Oxford University Press, 1998. ix.
17Greenstein 1990b: 36.
18Ibid 37.
19Levenson 1990:47.
20"Plainly things have changed. The study of narrative in the Hebrew Bible has altered dramatically in the past ten years, at least as far as professional biblical studies is concerned. That is now a truism." >From Gunn, David N. "New Directions in the Study of Biblical Hebrew Narrative." Beyond Form Criticism: Essays in Old Testament Literary Criticism. 1987. Ed. House, Paul R. Sources for Biblical and Theological Study volume 2. general ed. David W. Baker. Winnona Lake, Indiana: Eisenbrauns. 1992. 412-423.See Alter, Robert and Frank Kermode eds. The Literary Guide to the Bible. Cambridge, Massachusetts: Harvard University Press, 1987. 4, and see 6 "Literary criticism, long thought to be peripheral or even irrelevant to biblical studies, has emerged since the mid-1970's as a new major focus of academic biblical scholarship." For a more detailed discussion see House, Paul R. "The Rise and Current Status of Literary Criticism of the Old Testament." Beyond Form Criticism: Essays in Old Testament Literary Criticism. Ed. House, Paul R. Sources for Biblical and Theological Study volume 2. general ed. David W. Baker. Winnona Lake, Indiana: Eisenbrauns. 1992. 3-22. See also Berlin, Adele A Search for a New Biblical Hermeneutics." The Study of the Ancient Near East in the 21st Century.Eds. Cooper, Jerrold S. and Glenn M. Schwartz Eisenbrauns, 1996. 195-208.
21See Friedman, Richard Elliot. "The Recession of Biblical Source Criticism." The Future of Biblical Studies:THe Hebrew Scriptures. Eds. Friedman, Richard Elliot and H. G. M. Willaimson. Atlanta, Georgia: Scholars Press, 1987. 81., who bemoans the fact that "Most biblical scholars of our own generation have studied, but do not practice, source-critical analysis. And the current literary study of the Bible usually ignores it."
22Levenson 1990:51.
23Larrson 1985:322.
24Ibid.
25Wenham 1991, and see Emerton, J.A. "An Examination of Some Attempts to Defend the Unity of the Flood Narrative in Genesis." Vetus Testamentus 38 (1988) 1-21.

Excerpts from the introduction and conclusion of Inconsistency in the Torah : ancient literary convention and the limits of source criticism by Joshua A. Berman. Emphasis is mine throughout.

Introduction

On a Sunday morning in May 2013, nearly one hundred scholars from around the world awaited the beginning of the proceedings of a conference titled, “Convergence and Divergence in Pentateuchal Theory: Bridging the Academic Cultures of Israel, North America, and Europe”
The conference opened with a report of the group’s accomplishments over that time. Speaking on behalf of the conveners, Bernard M. Levinson explained that the discipline is in a state of fragmentary discourse, where scholars talk past  each other, and mean different things even when they use the same terms. As he put it, “scholars tend to operate from such different premises, employing such divergent methods, and reaching such inconsistent results, that meaningful progress has become impossible. The models continue to proliferate, but the communication seems only to diminish.”1

The root of the problem heretofore, according to this movement, is that scholars have rooted their compositional theories for the growth of the biblical text entirely in their own intuition of what constitutes literary unity. For those of us working in this new movement, the time has come to root compositional theory in the so-called empirical findings of the writings of the ancient Near East. We must canvas and analyze documented examples of compositional growth and editing across a wide field of ancient Near Eastern texts, both within ancient Israel and outside it.4 How did these scribes go about editing and revising revered texts? What editorial trends do we see when we compare earlier versions of a text to later ones? For these scholars it is an axiom that the Hebrew Bible, and with it the Torah, is a product of an ancient Near Eastern milieu, which deeply influences not only its content, but also its poetics and process of composition. The turn by these scholars toward empirical models for compositional theory has met with resistance in some quarters, because essentially, these scholars claim that the only way to right the ship is by jettisoning many sacred cows of compositional theory, and effectively throwing them overboard. Whereas other scholars have examined the editorial practices of ancient scribes, I seek here to question our own notions of consistency and unity in a text, in light of what we discover from the writings of the ancient Near East. Scholars have long known that this corpus can surprise us with the seeming “inconsistencies” that it yields.

A foundational staple of early Penateuchal criticism maintained that the disparity of divine names found in the Torah was itself proof positive of composite authorship, and a key to determining and delimiting its sources.5 This axiom had to be walked back, however, in light of evidence that the ancients were quite comfortable referring to the same deity by multiple names, even within a single passage. Witness what we find in Tablet IV of the Ugaritic Ba’al Cycle: “Baʽlu’s enemies grasp hold of (the trees of ) the forest, Haddu’s adversaries (grasp hold of ) the flanks of the mountain(s). Mighty Baʽlu speaks up:  Enemies of Haddu, why do you shake with fear?” (4, vi.36–vii.38). In like fashion, the alternation in address between singular and plural pronouns, sometimes referred to as Numeruswechsel, was thought to designate various sources or strata in the Hebrew Bible. However, the phenomenon is also found in the Sefire treaty, that is, in a literary setting where we cannot propose diachronic composition. In Stele III, the suzerain commands the vassal to hand over fugitives, warning him that if he fails to do so, “You (pl.) shall have been unfaithful to all the gods of the treaty” (III:4; cf. similarly, ll. 16 and 23). However, further on, the suzerain demands freedom of passage in the vassal’s territory, and warns him that if he fails to do so, “you (s.) shall be unfaithful to this treaty” (cf. similarly ll. 14, 20, and 27).

These examples serve as a warning flag for scholars looking to parse the text on the basis of their own notions of literary unity. The ancient text is a minefield of literary phenomena that are culturally dependent. The diachronic scholar who treads there based solely on his own modern notions of literary unity risks serious interpretive missteps. Passages such as that from the Baal cycle above, or from the Sefire treaty can be safely assumed to have been written by a single hand. The rhetoric we find in these comparative materials can offer a control. Of course, the presence of these phenomena elsewhere does not prove that the Torah must be read this way as well. Even if we assume that the passage from the Baal Cyle cited above was composed by one hand, this does not mandate that the presence of two (or even three) divine names in Genesis must all stem from the same authorial hand—but it should, at the very least, place a check on the confidence that a modern exegete can have when approaching the biblical text and encountering literary phenomena that seem inconsistent. Perhaps the most prudent lesson from such examples is that we must attain competency as readers before we engage the text—and this we can do only by canvassing the available cognate materials.
………………..

I seek to address these issues in chapter 11, “A Critical Intellectual History of the Historical-Critical Paradigm in Biblical Studies.” My goal is to understand the origins of the intellectual commitments that shape the discipline today, and its reluctant disposition toward empirical models of textual growth. I examine how theorists over three centuries have entertained the most fundamental questions: what is the goal of the historical-critical study of the Hebrew Bible? What is the probative value of evidence internal within the text itself, relative to evidence from external sources? What is the role of intuition in the scholar’s work? What is the role of methodological control? The axioms that governed nineteenth-century German scholarship were at a great remove from those that governed earlier historical-critical scholarship, in the thought of critics such as Spinoza. These axioms were based in intellectual currents that were particular to the nineteenth century, and especially so in Germany. From there, I  offer a brief summary of the claims of contemporary scholars who are looking toward empirical models to reconstruct the textual development of Hebrew scriptures. I conclude by demonstrating how this vein of scholarship undermines an array of nineteenth-century intellectual assumptions, but would have been quite at home in the earlier periods of the discipline’s history, and call for a return to Spinozan hermeneutics.

I continue my critique of current historical-critical method in chapter  12, “The Abuses of Negation, Bisection, and Suppression in the Dating of Biblical Texts: The Rescue of Moses (Exodus 2:1–10).” Here I maintain that the scholarly aim to clearly delineate and definitively date layers in a text unwittingly leads to three malpractices of historical-critical method. Handling complex evidence in a reductive fashion, scholars routinely engage in what I call, respectively, the undue negation of evidence, the suppression of evidence, and the forced bisection of a text. Scholarship on the account of the rescue of Moses serves as an illustration. The division of the Genesis flood account is one of the most celebrated achievements of modern biblical criticism. In chapter  13, “Source Criticism and Its Biases: The Flood Narrative of Genesis 6–9,” I take a critical look at the source-critical paradigm and examine its hermeneutics. Here, too, we will see that historical-critical scholarship applies a series of double standards that all work in concert to support the source-critical aims and results. Moreover, it consistently suppresses evidence adduced from cognate materials (particularly from the Mesopotamian version of the flood story contained in Tablet XI of the Giglamesh Epic) that threatens its validity by simply ignoring it, or otherwise negating the validity of that evidence through unwarranted means. In the Conclusion, I offer a new path forward for historical-critical study of the Hebrew Bible, calling for three imperatives. First, I suggest an epistemological shift that soberly acknowledges the limits of what we may determine, both in terms of the dates of the texts we study, and of the prehistory of those texts.

Conclusion:
A New Path Forward The methodological impasse gripping the field, its extreme fragmentation and seemingly unbridgeable diversity, should give us pause and encourage us to explore some of the fundamental assumptions that have girded diachronic study for two centuries. To renew the field of pentateuchal criticism—and indeed, the historical-critical paradigm in biblical studies more broadly—I believe that historical-critical scholars will need to adopt three new priorities in their work. The first is an epistemological shift toward modesty in our goals and toward accepting contingency in our results. ……..As I demonstrated in chapter 11, historical criticism is caught in a vicious loop. The holy grail of historical criticism of the Hebrew Bible is the attainment of answers to four fundamental questions: who wrote this text? When was it written? What are the historical circumstances that occasioned its composition? What were the stages of the text’s development? Because these questions are fundamental to the discipline’s self-identity, scholars take it as axiomatic that they possess the capacity to provide reliable answers to these questions. The possibility that we may not have this capacity is not widely entertained, for if that really were the case, the very enterprise of understanding the biblical texts in historical context is threatened. This in turn leads to scholarship biased toward producing results that answer these questions. In chapter 12, I showed how scholarship on the question of the dating of the account of the rescue of Moses in Exodus 2:1–10 handles complex evidence in a reductive fashion so that the passage may be firmly dated. And in chapter 13 I highlighted the many ways in which source-critical scholars display a proclivity and predisposition to parse evidence in an unfounded way, but one that serves the goal of discovering within the Genesis flood narrative two original sources.

We are committed to two methodological callings. As biblicists, we are called to examine the texts we work with in their historical and social settings. But no less, as scientific investigators, we are called to put forth arguments only to the degree that they are supported by the evidence. It must be starkly admitted that these two callings stand in fundamental tension, especially when we are dealing with the texts of the Pentateuch, where the events recorded have scant attestation outside of the Hebrew Bible. Out of a healthy commitment to examining texts within a specific historical setting we too often compromise on the second calling: to offer a specific historical setting for a text only when the evidence for it is strong and unambiguous. Responsible scholarship mandates a proper ordering of first questions. The classical questions that address historical context are vital ones. But the sine qua non of any critical quest must begin with the frank and sober question: what are the limits of what we may know? What will be the controls in place that check our conclusions? The warning of the eminent historian Arnaldo Momigliano is in order: “The most dangerous type of researcher in any historical field is the man who, because he is intelligent enough to ask a good question, believes that he is good enough to give a satisfactory answer.”

This will require biblicists to think differently about their work. To animate just how difficult—and yet necessary—this is, I draw attention to a similar change of mindset now underway in a distant branch of the academy. No field of academic study today is in as much turmoil as the field of economics. The financial collapse of 2008 was predicted by only a handful of doomsday prophets, who were largely ignored. The Nobel laureate in economics, Paul Krugman, asks how it is that the entire guild of economists—himself included—got it so wrong.2 Krugman concludes: “As I see it the economics profession went astray because economists, as a group, mistook beauty, for truth. The central cause of the profession’s failure,” he goes on, “was the desire for an all-encompassing, intellectually elegant approach that also gave economists a chance to show off their mathematical prowess.” Krugman details how the neoclassical belief in markets had an allure because it allowed scholars to do macroeconomics with clarity, completeness, and beauty. The approach seemed to explain so many things. Krugman’s analysis of what happened to an entire guild of economists should give us pause for reflection as biblicists. Could it be that we, too, fall victim to the allure of mistaking beauty for truth? By positing the date of a text and the stages of its composition, we create an elegant narrative of the text’s history and of the evolution of religious ideas in ancient Israel. But could we, too, be mistaking beauty for truth—the truth that dating biblical texts and recovering their stages of growth is harder than we would like to admit? Or the truth that we actually have limited access to the minds and hearts of the scribes of ancient Israel, and cannot know the full range of motivations that drove them to compose the texts they did? Krugman writes, “if the economics profession is to redeem itself, it will have to reconcile itself to a less alluring vision,” and that, “what’s almost certain is that economists will have to learn to live with messiness.” That constituted an incredibly bitter pill for economists to swallow. Possessed with elegant models that claimed to predict economic performance in the future, economists became indispensible figures, necessary to the financial prosperity of those who would hire their services. To admit that the economic world is “messy” is, essentially, to concede defeat. If, at best, economists can describe only the past, then the field of economics loses its lofty status, and is reduced to merely a subsection of the history department.

Perhaps we, too, “will have to learn to live with messiness” and avoid the pitfall of mistaking beauty for truth. Perhaps we, too, may have to settle for the realization that we cannot work back from a received text and reconstruct its compositional history with clarity. Finally, this epistemological shift will need to necessitate a rethinking of the habits of biblicists with regard to the relationship between the processes of dating a text and uncovering its meaning. There exists a pervasive but mistaken assumption that if an idea is particularly relevant to one historical era, it must have originated in that era. The covenant curses of Leviticus 26 and Deuteronomy 28 warn of exile; but this does not ensure that these texts were composed following the exile.
After all, the Bible claims that Israel’s origins are outside the land of Canaan, and that the land is a divine gift, denied to the Amorites because of their wickedness (Gen 15:16; Deut 9:5). Genesis tells us that Adam himself had been exiled from the Garden of Eden (Gen 3:23–24). The notion of exile is integral to the warp and woof of many Pentateuchal texts. Another example: the boundaries of the promised land in Gen 15:18–21 correspond to those of the empire of David and Solomon, as portrayed in 1 Kgs 4:21. For some, this suggests that the border list of Gen 15:18–21 originates from this period.11 But, in theory, writers from either earlier or later periods could also have yearned for stronger borders and greater hegemony than was available in their own day. Moreover, the impulse to date a text based on an idea it presents overlooks the fact that these texts were copied and handed down across many generations and many historical circumstances. These texts endured precisely because they were seen as transcending the original setting of their composition and offering insights into the human condition and the condition of the people Israel. The inheritors of these texts deemed them relevant long after the original historical and social conditions of their composition were forgotten. Phenomenologists of religion such as Moshe Idel and Mircea Eliade have taught us that we need to be open to the possibility that the intuitions of a religious text can be understood as timeless.

# Self-verifying theories

[[So all the philosophical baloney about the impossibility of knowing that you are consistent etc. is non-sense.....]]

Self-verifying theories are consistent first-order systems of arithmetic much weaker than Peano arithmetic that are capable of proving their own consistencyDan Willard was the first to investigate their properties, and he has described a family of such systems. According to Gödel's incompleteness theorem, these systems cannot contain the theory of Peano arithmetic, and in fact, not even its weak fragment Robinson arithmetic; nonetheless, they can contain strong theorems.
In outline, the key to Willard's construction of his system is to formalise enough of the Gödel machinery to talk about provability internally without being able to formalise diagonalisation. Diagonalisation depends upon being able to prove that multiplication is a total function (and in the earlier versions of the result, addition also). Addition and multiplication are not function symbols of Willard's language; instead, subtraction and division are, with the addition and multiplication predicates being defined in terms of these. Here, one cannot prove the ${\displaystyle \Pi _{2}^{0}}$ sentence expressing totality of multiplication:
${\displaystyle (\forall x,y)\ (\exists z)\ {\rm {multiply}}(x,y,z).}$
where ${\displaystyle {\rm {multiply}}}$ is the three-place predicate which stands for ${\displaystyle z/y=x}$. When the operations are expressed in this way, provability of a given sentence can be encoded as an arithmetic sentence describing termination of an analytic tableau. Provability of consistency can then simply be added as an axiom. The resulting system can be proven consistent by means of a relative consistency argument with respect to ordinary arithmetic.
We can add any true ${\displaystyle \Pi _{1}^{0}}$ sentence of arithmetic to the theory and still remain consistent.