CYBER-HISTORY: Applied Heuretics; Section 2, Part 1: Setting the stage for the Neo-Scholastics: the Summulae Logicales of Petrus Hispanus and Meno's Paradox

In the seventeenth century, the theologian Richard Burthogge wrote, Ratiocination Speculative, is either Euretick or Hermeneutick, Inventive or Interpretive…’ (Burthogge [1678], 48, quoted in Ulmer 2004, 33). It is only since the mid-16th century that invention and method began to be excised from rhetoric. The method of invention was, in classical rhetoric, seen analogically as a visit to the places or topoi of the topics to look for a statement (Ong 2004). Scholastic reforms in the 16th century linked method with doctrina/teaching and theory within a structure of logic that was formal and spatial. The space of this logic was highly abstract: it was conceived as being analogous to the space of geometry, creating the possibility for topics to become arguments transformed into scientific instruments. This discursive space is the abstract space of the diagram: it is visual and comfortingly quantifiable. Inventio and dispositio/arrangement, displaced from rhetoric to a logic that is profoundly visual, became conceived by analogy with visually perceived spatial patterns and diagrammatic spatial arrangements (Ong 2004). The neat placement of discursive content in a geometrically stable space, a diagramable space, makes discursive movement a matter of hermeneutics, the logic of interpretation. Consistent with the removal of invention from the systems of logical discourse, the study of discourse interpretation (especially that of written discourse) has gathered a great deal of study under the heading hermeneutics, with sources and examples spanning from antiquity to the present, while its contrapuntal neologism, ‘euretics’, the logic of invention, has been forgotten and has yet to generate a field of its own to guide speculation.

‘Euretics’ takes its name from the Greek word ‘eureka’, meaning ‘I’ve found it!’ This exclamation was made famous through its being shouted by Archimedes during his naked run through the streets of Syracuse after having discovered the means to calculate density using volume while sitting in his bath. Today, euretics is being explored by Greg Ulmer to develop a rhetoric for digital media. Digital media that includes the capability for working with text, image, sound, and movement simultaneously and rapidly through a common base of binary code, makes for a fecund invention apparatus. Just as the technology of writing enhanced humanity’s memory, granting freedom to develop increasingly abstract systems of reason, digital media is a powerful prosthesis of human intellection. But unlike the written word, little has yet been done to establish a system of rules tuned to the rigors necessitated by new media. Ulmer’s heuretics is meant to be the speculative production of such rules: a digital rhetoric. To better understand the specific context that heuretics is intended to augment, we should examine the historical development of the relationship between rhetoric, invention, and logic.

In medieval Europe, the curriculum that would lead students from the start of their studies as children, through early university arts courses and perhaps on to professional education in law or medicine, established grammar and rhetoric of Latin and Greek as elementary subjects. This grammar instruction was followed by the study of logic by students who were still barely teenagers. The culmination of study with a terminal Master of Arts or Doctor of Philosophy degree was attained by young men aged eighteen to twenty, who would then be considered ready to teach students seeking those same degrees (ibid, 62). There was little room for subtlety or ambiguity in this fast-paced curriculum; what instructors needed were manuals that rendered the complexities of logic and rhetoric as concisely as possible, clear and ready for reception in the minds of young children (ibid). One such manual was Peter of Spain’s highly influential Summulae Logicales of the thirteenth century.

Peter’s Summulae Logicales attempted to present straightforward treatments of works on method, logic, and rhetoric that formed the foundation of rigorous study in discourse and thought, namely the works of Aristotle and his subsequent translators and commentators. The first simplification effected by the Summulae Logicales is the equation of method and logic found in its famous opening definition of dialectic: ‘Dialectic is the art of arts and the science of sciences, possessing the way to the principles of all curriculum subjects’ (ibid, 56). Dialectic, or the dialectical method, is a way of working through uncertainties and disagreements between parties with dialogue and argument. Peter’s text does not define logic separately from dialectic, and the Summulae Logicales was presented by instructors in the arts curriculum as the ‘door to all logic’ (ibid, 56-7). The Summulae blurs the traditional distinction between conceptual tools that were developed for treating situations where scientific certainty is the goal (logic), and the tools of dialectic, which were developed by Aristotle for situations that would remain mired in uncertainty and probability, where the ultimate goal was persuasion (ibid, 60-1). So, the notion that reasoned argument would proceed by logic to use discursive tools toward the ultimate attainment of any certain truth is a conflation of two distinct fields of reasoning to attain some degree of didactic clarity in a manual written for teenagers, with the result that ‘logic’ would increasingly dominate general discussions of thought, communication, and creative activity in the fifteenth and sixteenth centuries.

The simplifications of Peter’s Summulae and other contemporary teaching manuals on logic came after a series of upheavals and transformations in how the liberal arts were conceived and taught in Medieval Europe. Medieval scholar Richard McKeon summed up the slow obfuscation in the Middle Ages of Aristotle’s distinction between logic, dialectic, poetic, sophistic, and rhetoric by identifying changes in predominant texts, grouped into four general periods. First, until the tenth century, elements of logic were learned from the logical treatises of pseudo-Augustine, whose Categoriae Decem was a Latin summary of Aristotle’s Categories, and sections on dialectic in handbooks by Martianus Capella, Cassiodorus, and Isidore of Seville. Rhetoric was concerned with moral and political questions of civil philosophy, and was learned from texts by Cicero, Hermagoras of Temnos, Sulpitius Victor, and other authors of works on oration (McKeon 1942, 7-8, 13-14). A second major period in the conception of logic and rhetoric is identifiable after the influential late tenth century curriculum written by Gerbert d’Aurillac, Pope Sylvester II, when he was teaching in Reims and Paris. Gerbert’s curriculum presents Dialectic through those sections of Aristotle’s Organon that had been translated into Latin at that time by Boethius: Categories and On Interpretation, an introduction to Categories by Porphyry, and several original works by Boethius (ibid, 8; 15-16). Boethius considered dialectic and rhetoric to be parts of logic, and thus it was in Gerbert’s curriculum. In this period from the tenth to the twelfth century, rhetoric saw several of its components as developed by Aristotle—commonplaces, definition, and proof—moved to the purview of dialectic, and its traditional civil subject matter largely shifted to the realm of theology (ibid, 14). This slow stripping of rhetoric’s proper material and uses and their assignment to other areas of intellection would continue in the following centuries until, by the time of the Renaissance, only some vague and superficial notion of style would remain in rhetoric’s domain.

In the twelfth century, study of rhetoric, dialectic, and logic was enriched by the translation of the remaining four books of Aristotle’s Organon into Latin. These texts, Prior Analytics, Posterior Analytics, Topics, and Sophistical Refutations, would become known as the ‘New Logic’ in McKeon’s third period, and those parts of the arts curriculum popular before this twelfth century influx, Categories, On Interpretation, Porphyry’s Isagoge, Boethius, and Cicero, were now called the ‘Old Logic’ (ibid, 16; Paetow 1927, 20). The increase in the influence of the New Logic led to a distinction between scientific demonstrative proof and probable proof dealing with uncertainties, with rhetoric and dialectic were placed within the latter. The dissemination of the full Organon, with its subtle and complex differentiations, would lead to manualists’ attempts to simplify this material for use in the arts curriculum, with the most prominent examples being Lambert of Auxerre’s Logica, William of Sherwood’s Introductiones in Logicam and Syncategoremata, and the most popular of all, the Summulae of Petrus Hispanus (McKeon 1942, 8).

The Summulae Logicales, with its reduction of all discursive methods to a conflation of logic and dialectic, left the Medieval arts student with a limited set of conceptual tools with which to treat the entirety of discourse. This situation made the student into a bricoleur, intuitively using a set stock of materials and manners of relation for purposes other than those for which they were created. Each application of the tools is improvised, and while the products may adequately fit the circumstances at hand, the techniques will always lack precision. In sketching a simplified intellectual system, the Summulae removed obscurity from the teaching material, placing it instead in the mind of the student left to cobble methods together from heterogeneous impulses and materials in an attempt to construct meaning. This is student as tribesman, constructing a cosmogony, a map of the vast unknown time and space of the universe using bits and pieces of the world as personally known to the individual, simple things that are familiar and thus always at hand. The student as bricoleur:

The ‘bricoleur is adept at performing a large number of diverse tasks; but unlike the engineer, he does not subordinate each of them to the availability of raw materials and tools conceived and procured for the purpose of the project. His universe of instruments is closed and the rules of his game are always to make do with ‘whatever is at hand,’ that is to say with a set of tools and materials which is always finite and is also heterogeneous because what it contains bears no relation to the current project, or indeed to any particular project, but is the contingent result of all the occasions there have been to renew or enrich the stock or to maintain it with the remains of previous constructions or destructions. (Lévi-Strauss 1966, 17)

This quote from Lévi-Strauss’s The Savage Mind contrasts the bricoleur with the engineer, but earlier in the same text, this handyman-of-sorts is also contrasted with the craftsman and the work of bricolage is imbued with a dubious character. Bricolage is derived by Lévi-Strauss from the French verb bricoleur, used in ball games like billiards or in hunting to describe a rebounding, or straying movement. ‘And in our own time the “bricoleur” is still someone who works with his hands and uses devious means compared to those of a craftsman’ (ibid, 16).

The Organon was compiled by Aristotle’s commentators to gather and organize his works on logic and thus provide a full catalogue of logical methods and techniques for treating any material, a kind of map for the intellectual technician. This document can be seen as the earliest attempt in Western culture to avoid intellectual bricolage. Its components are On Interpretation, which handles the combination of subjects and predicates to form propositions, and the Categories, which deals with the terms individually (Grote 1883, 57). These two works deal with declared truth. Next come works that present Aristotle’s theory of the syllogism: the Prior Analytics, and the Posterior Analytics, which treat demonstration and demonstrative science; the Topics on the art of Dialectic, covering debate and argument of probabilities outside the purview of absolute truth, and Sophistical Refutations on fallacies (ibid, 141-2). Aristotle’s Rhetoric, a treatise on the art of persuasion in three books, stands separate from the Organon, his works on logic, wherein we find discussion of dialectic. Also separate from the Organon is Aristotle’s Poetics on drama and poetry.

Poetry, persuasion, argument, and science each had a specific logic governing their appropriate, or proper, construction in the Corpus Aristotelicum. The multivalent drift of generations of scholars that took inventive liberties with this corpus, making changes and charting their own courses through the field of staggering variety that is human thought, has had the effect of clumping materials and actions of the mind under the heading of logic at the expense of other forms of reason that we use everyday, like rhetoric. Starting with a dazzling if flawed array of mental work codified by Aristotle, we have ended up with an overextension of logic through the allure of absolute truth at the expense of the relative but concrete indications constantly provided by our feelings. The sections of the Corpus Aristotelicum that treat logic have been made to eclipse their context of relativity and affective persuasion through accretive historical synecdoche; what was once a constitutive piece now stands for the whole.

History provides us with a convenient filter to sort the various tendencies of authors treating logic in the Middle Ages through the popularity of a single manual on logic; Peter of Spain’s Summulae Logicales was so popular by the early fourteenth century that his particular treatment of logic had become synonymous with the tradition of logic in its entirety, and first year students studying logic in bachelor of arts programs were called ‘Summulistae’ (Ong 2004, 58). While it was written as an introductory textbook on notions associated with Aristotle’s logic, some of the most influential material in Peter’s manual was decidedly new, including a section featuring the first definitive formulation of supposition theory, a branch of logic that would dominate its field until the Renaissance (ibid, 57). The Summulae covers the basic content of Porphyry’s Isagoge, Aristotle’s Organon, and related works and commentaries like Boethius’ De topicis differentiis. Peter then added treatises on medieval logic that together would be called the Little Logicals (Parva logicalia) (ibid, 56-7). This non-Aristotelian, medieval content of the Summulae was its most popular component in the universities of the fourteenth century (ibid, 58). Thus, Peter’s logic, considered the ‘door to all logic’ by Arts faculties, was very much a medieval system, wherein ‘dialectic’ is indiscernible from ‘logic’, and the key to the popular Parva logicalia is its section on supposition, the cornerstone of a logical system that would later cover material similar to that of quantification in modern mathematical logic (ibid, 57), all under the aegis of introducing the important, necessary principles of Aristotle’s Organon.

Another important difference between Peter’s Summulae and the Aristotelian tradition cited as its source is the amount of attention given to the notion of topics while neglecting discussion of demonstration, placing the work in closer relation to the probable logics, like rhetoric, than to science and the logics of certainty (ibid, 60). Aristotle’s treatment of dialectic is covered in the Topics, a work that explores the rules and goals for argument with information culled from popularly accepted opinions. Topics are also treated in Aristotle’s Posterior Analytics: topics as they pertain not to probabilities, but to scientific certainty. Peter’s manual was in part an attempt to simplify this complex use of topics for both scientific demonstration and dialectic in Aristotle’s theory of the syllogism as found in the New Logic (Prior Analytics, Posterior Analytics, Topics, and Sophistical Refutations).

Aristotle’s development of the syllogism was a key moment in the intellectual history of the Western world. The theory of the syllogism is clearly recorded in the Prior Analytics: ‘A deduction [syllogismos] is discourse in which certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that it follows because of them, and by this, that no further term is required from without in order to make the consequence necessary’ (Aristotle 1984, Prior Analytics I, 24b19-24b 22 [In-text citations to this source refer to Bekker Numbers listed in the source, rather than page numbers.]). Aristotle’s exploration of deductive reasoning was an attempt to improve on the cognitive theories of his immediate predecessors, Socrates and Plato. In the Meno, Plato gives account of Socrates’ ‘theory of recollection’, whereby man’s soul has accrued knowledge of everything there is to know over the course of its previous lives. Thus, man cannot learn, he only comes to recollect material that his soul knows but in his present life he has forgotten (Plato 1985, 63-81). This recollection is the purpose of Socratic dialogue: through inquiry, the student will remember the forgotten knowledge he is seeking, or will realize his ignorance by recognizing the lack of certainty in what is knowable about the given material.

To explain learning and creativity, Aristotle chose to elaborate the syllogism as a practical theory of inference, applicable to all forms of cognition and intellection. The painstaking catalogue of logical permutations that the Organon documents would continue to be a touchstone for intellectual rigor until the modern era, even as the field of logic would follow various tacks that had little relation to Aristotle’s theories. Furthermore, although ancient Greece had many rhetoricians skilled in the use of language, there was hardly any systematic study of language as such before Aristotle’s Organon and the theory of the syllogism (Grote 1883, 153).

Syllogism is deductive reasoning, or deductive inference, and Aristotle explains its components and the conditions in which it is valid in the Prior Analytics. A valid syllogism contains three terms: two premises and a conclusion; the minor premise shares a term with the subject of the conclusion, the major premise shares a term with the predicate of the conclusion. The basic components are: propositions [protasis], statements affirming or denying something of something; while a term is ‘that into which the proposition is resolved, i.e. both the predicate and that of which it is predicated, ‘is’ or ‘is not’ being added’ (Aristotle 1984, Prior Analytics I, 24a10- 24b18). Syllogism can be used for two distinct purposes: demonstration or scientific teaching (outlined in the Posterior Analytics), and dialectic or argumentative debate (outlined in the Topics) (Grote 1883, 265).

Dialectical syllogism and demonstrative syllogism share formal conditions and the axioms of deductive reasoning but differ in their subject matter. Demonstrative syllogism only applies to a small number of sciences wherein primary, undemonstrable but certain truths provide the basis for all subsequent deductive inferences; dialectical syllogism applies to all matters, its premises need not be certain and are borrowed from any authoritative source (ibid, 265-6). This distinction between the demonstration of science with its purpose of teaching or learning, and dialectic with the purpose of persuasion, represents another step beyond the dialogic methods of Plato and Socrates, where persuasion and instruction were conflated (ibid, 266), and marks the point where medieval treatments of logic and dialectic would take a step backward.

Aristotle distinguishes dialectic and demonstration through the establishment of certainty. The sciences proceed through demonstration of certain propositions to certain conclusions. This certainty is ultimately based in principia, primary, undemonstrable truths that every demonstration presupposes (ibid, 265). These principia are obtained by inductive inference, inference from particulars to a general condition. There is an ultimate adjacency of uncertainties (argument or debate) and absolute truth in the theory of the syllogism: dialectic is used as a test to scrutinize possible principia to see if objections can be met with sufficient reply (ibid, 273). Compared to the ideal immutability Plato’s universals—known by the mind from pre-existence and recalled through dialectic—Aristotle’s collectively constructed and tested principia resemble Kuhnian paradigms (Kuhn 1962), those aspects of a science that are not currently debated, the contents of which must be taken as essential and true as a precondition for any valid demonstration. Opinion, argument, and persuasion are ultimately intertwined with truth through their role in the formation of principia (Aristotle 1984, Posterior Analytics I, 77-8).

When Peter of Spain attempted to simplify Aristotle’s theory of syllogism, he confused the necessary coexistence of opinion and certainty. In the Corpus Aristotelicum, demonstrative sciences based on certainties are carved out of the vast common land of dialectic, and between these forms of intellection lays the intermediate area occupied by subjects that each have their own proper level of exactitude (Aristotle 1984, Metaphysics, 995a15; Nicomachean Ethics I, 1094b12-25). Peter’s Summulae logicales inverts this intellectual landscape, where debate and persuasion are exercises or excursions that take place within a larger context of truth. Not only did Peter’s supreme dialectic support the slow decay of argument and rhetoric into unnecessary flourishes of style or outright dissimulation in medieval Arts courses, it also led to problems explaining how learning and invention can take place at all, precisely the problem that Aristotle sought to solve with the syllogism.

Meno’s Paradox, the syllogism, and the problem of discovery

Aristotle’s theory of the syllogism offers an improvement over Plato’s theory of recollection in its attempts to explain how discovery or invention of new material takes place. In the Meno, Socrates seems to use the theory of recollection to deny the possibility of discovery as invention during discussion of Meno’s paradox. While engaged in discussion of virtue and how to properly proceed via inquiry to better understand it, Meno puts the challenge thusly: ‘how will you inquire, Socrates, into something when you don’t know at all what it is? . . . Or even if you really stumble upon it, how will you know that this is the thing you didn’t know before?’ (Scott 2006, 76; quoting Meno, 80d5-8) This challenge implies that inquiry into what you do not already know is impossible. Socrates responds by restating the challenge in more general terms, his series of propositions and conclusion can be represented as: 1 - If you know the object already, you cannot genuinely inquire into it; 2 - If you do not know the object you cannot inquire into it because you do not know into what you will inquire; 3 - (implicit) Either you know something completely or you do not know it at all; 4 - Therefore, you cannot inquire into any object (Scott 2006, 78; from Meno, 80e1-5). This version of the dilemma challenges the possibility of all inquiry, and the theory of recollection is proposed as the solution, offering the possibility that a person be apparently ignorant of something that their immortal soul already knows. Both versions of the dilemma can be disarmed by allowing for partial knowledge of the object of inquiry (Scott 2006, 79-80).

Careful analysis reveals that Plato might not have proposed the theory of recollection in the Meno out of concern for the possibility of inquiry, but rather as a component in a larger discussion centered on the problem of discovery and how to properly guide inquiry. This reading of Meno’s paradox places importance on the facts that the theory of recollection is insufficient to resolve the dilemma and Socrates and Meno’s earlier discussion of the distinction between knowledge, requiring that one has reasoned through the explanation, and true opinion/belief presents material that adequately solves the problem (ibid, 19, 82). Socrates and Meno are attempting to attain knowledge of the true nature of virtue, and their beliefs offer a starting point for discussion, without the necessity of complete knowledge of the object being discussed. They may have true beliefs about virtue from the beginning, and through discussion they might gather other true beliefs, and they do offer multiple definitions of virtue as the dialogue progresses. But, if this is the nature of their inquiry, ‘they will always be trapped within a circle of belief’, and complete knowledge will lie outside their grasp (ibid, 84). In the Meno, both the theory of recollection and the path of dialogue offer an incomplete rendering of successful inquiry.

Aristotle’s theory of the syllogism places inquiry’s ‘circle of belief’ in a context including varying degrees of certainty, kinds of reasoning, and the uses of persuasion to resolve the problem of discovery. In Aristotle’s works we find a distinction between two kinds of cognition: absolute knowledge, and partial, incomplete or qualified knowledge (Grote 1883, 212). Only the latter can be learned, and this is done through the formal inferences of the syllogism. However, hiding deep in Aristotle’s theory of cognition, the problem of discovery survives. The earliest evidence of its existence is in the first Western philosophical text, the poetic fragments of Parmenides, where it is claimed that what-is cannot be derived from what-is-not, and the only guide for method is toward what-is, establishing a static immutability to all being. The problem appears again in the form of the Platonic absolute, addressed by the theory of recollection in the Meno, and Aristotle begins his Posterior Analytics with the claim that, ‘[a]ll teaching and all intellectual learning come about from already existing knowledge’ (Aristotle 1984, 71a1).

In the nineteenth century, John Stuart Mill identified the part of Aristotle’s syllogism that perpetuates the problem of discovery: in every syllogism, there is a petitio principii (Grote 1883, 213; Mill 1865, v.1, 205). Mill uses two examples, first: All men are mortal; Socrates is a man; therefore, Socrates is mortal (ibid). He stresses that the proposition, Socrates is mortal, is presupposed in the assumption that all men are mortal, ‘we cannot be assured of the mortality of all men, unless we are already certain of the mortality of every individual man’ (ibid). He adds to this syllogism the example of belief in the mortality of a contemporary, living man; he believed the Duke of Wellington to be mortal, but did not know this from direct observation (ibid, 206-7). Mill tweaks Aristotle’s theory by focusing not on the syllogism, but rather on varieties of inference: ‘the proposition that the Duke of Wellington is mortal, is evidently an inference; it is got as a conclusion from something else’ (ibid, 207-8). The general truth of the mortality of all men is an aggregate of particular truths, some observed directly, some noted; and indeed the inference of a general condition is effected by a gathering of notes (ibid, 208-10). To arrive at the application of this general truth, we proceed downhill again by deciphering our notes. What we end up with in Mill’s system of inference is not a vicious circle of belief so much as a folded landscape of inferences, up from particulars to generalities, down again, from generalities to particulars, from particulars to other particulars, and so on. Mill presents a beautiful example that dovetails with our larger inquiry into tactical discourse, an example we can call ‘the general’:

An old warrior, on a rapid glance at the outlines of the ground, is able at once to give the necessary orders for a skillful arrangement of his troops; though if he has received little theoretical instruction, and has seldom been called upon to answer to other people for his conduct, he may never have had in his mind a single general theorem respecting the relation between ground and array. But his experience of encampments, in circumstances more or less similar, has left a number of vivid, unexpressed, ungeneralized analogies in his mind, the most appropriate of which, instantly suggesting itself, determines him to a judicious arrangement. (ibid, 211)

Mill’s general allows us to link the history of dialectic to the movements of Xenophon, as we search for historical inquiry that adequately models the condition of discovery as the navigation of an inferential landscape.

< Section 1

History as Anabasis

Section 2, Part 2 >

Barthes’ Seven Days of Rhetoric


Ramus and the conflation of dialectic,

method, and reason


  • Aristotle. 1984. The Complete Works of Aristotle: the Revised Oxford Translation. J. Barnes ed. Princeton University Press: Princeton, NJ.

  • Burthogge, R. [1678] 1921. ‘Organum Vetus et Novum, or a Discourse of Reason and Truth.’ In M. Landes, ed. The Philosophical Writings of Richard Burthogge. The Open Court Publishing Company: Chicago.

  • Grote, G. 1883. Aristotle. Murray: London.

  • Kuhn, T. 1962. The Structure of Scientific Revolution. University of Chicago Press: Chicago.

  • Lévi-Strauss, C. 1966. The Savage Mind. University of Chicago Press: Chicago.

  • McKeon, R. 1942. ‘Rhetoric in the Middle Ages.’ Speculum, Vol. 18, no. 1 (January).

  • Mill, J. S. 1865. A System of Logic, Ratiocinative and Inductive: being a connected view of the principles of evidence and the methods of scientific investigation. Longmans, Green, and co.: London.

  • Ong, W. 2004. Ramus: Method and the Decay of Dialogue: From the Art of Discourse to the Art of Reason. University of Chicago Press: Chicago.

  • Paetow, L. J. 1927. Two Medieval Satires of the University of Paris: La battail des VII ars of Henri d’Andeli, and the Morale Scolarium of John of Garland. University of California Press: Berkeley.

  • Plato 1985. Meno. R. W. Sharples trans. Bolchazy-Carducci Publishers: Chicago.

  • Scott, D. 2006. Plato’s Meno. Cambridge University Press: New York.

  • Ulmer, G. 2004. Teletheory. Atropos Press: New York.

#ulmer #heuretics #dialectic #syllogism #meno

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