Science by Conceptual Analysis: The Genius of the Late Scholastics

The late scholastics— from the fourteenth to the seventeenth centuries—have suffered from a severe reputational problem. Attacked by every major thinker from Descartes to the Encyclopedists, they were a favourite target of abuse for Enlightenment rewritings of intellectual history, representing the darkness from which the Enlightened offered to rescue humanity. When scholasticism did revive in the late nineteenth century, it was largely Thomist, and twentieth- century neo-Thomism was fond of blaming the “decadent scholastics” and their “Suarezian errors” for the decline of Catholic philosophy. Their works are still mostly untranslated, so with the loss of Latin as a widely-read language, their thought has become increasingly inaccessible.1 That failure of understanding applies not only to the late scholastics’ strictly philosophical views, but to the contributions they made to wider spheres of thought by the deployment of their skills of conceptual analysis to topics other than philosophy. Their contributions are in many cases “known” to experts in the history of particular fields, but somehow not generally understood outside each field, and hence invisible “in the mass”. The purpose of this article is to give a short overview of some of their main achievements that have proved to be lasting contributions to intellectual history. The article aims at breadth rather than depth but provides substantial references for further study.

Section 1: The natural and mathematical sciences

The scholastics adopted the Aristotelian ideal of the intellectual enterprise, as described in Aristotle’s Posterior Analytics and implemented in Euclid’s Elements: that certain knowledge could be gained by the intellect’s reflection on experience, and organised as a deductive structure following from simple axioms known with certainty.2 They added to that ideal a training in argument designed to reveal the true axioms and to refute errors, and an embodiment of the result in a textual tradition and an institution designed to carry the tradition forward from generation to generation, the university. Not all branches of knowledge are well adapted to that mode of discovery and transmission. What is remarkable, as the late scholastics showed, is how many are. 

1.1 Mathematics: The analysis of continuous change 

The work of the fourteenth-century “Merton School” and its French collabo- rators Jean Buridan (c. 1300 – c. 1359) and Nicole Oresme (c. 1322 – 1382) has been well-known since Duhem and has been intensively studied by Maier, Sylla and others and well displayed in many selections in Grant’s Source Book in Medieval Science.3 It has been highlighted again in Hannam’s recent book on the medieval roots of modern science, God’s Philosophers.4 However it has usually been thought of as part of physics, and the scholastics have been regarded as “forerunners of Galileo” (in the title of Maier’s book5). That is true as far as it goes, but it dis- tracts attention from their achievements in the pure analysis of continuity and change. Their discoveries are better explained in Boyer’s History of Calculus, where they are recognised as an essential part of the process of the analysis of rates and change that was completed by the calculus of Newton and Leibniz.6

Mathematics is usually thought to be a model of absolute clarity of thought, achieved with the use of symbols, and hence no place for scholastics to be delving in. But a pre-requisite of most mathematics is analysis of concepts confusedly present in experience, and in this the scholastics were masters. Ancient math- ematics, mainly mathematical astronomy, had some understanding of large-scale uniform motions and their combinations, but there was no understanding of small-scale motions. For example, there is no unit of speed (such as “miles per hour”) in ancient languages, no doubt largely due to the impossibility of measur- ing small units of time. The first thing needed to begin the study of motion (or any other rate of change) is to distinguish between uniform and non-uniform speeds — in mathematical terms, between a first and a second derivative. That distinction is a matter of pure conceptual analysis. The fourteenth century cal- culators not only did that, but distinguished further between uniform and non- uniform accelerations. Then they showed a deep understanding of uniform acceleration by proving the “Merton mean speed theorem”: that a uniformly accelerated body travels the same distance as a body of uniform speed whose speed equals half the final speed of the accelerated body.7 In the later language of calculus, that is to show that the integral of a constant function is a linear function. It is true that the scholastics did not establish the main application of their analysis in physics, the fact that heavy bodies dropped near the earth’s surface are uniformly accelerated. That is a difficult fact to discover, because the fall of such bodies is too fast to measure easily (without modern technology such as time-lapse photography). It was established with considerable experimental ingenuity by Galileo. Nevertheless the suggestion that falling bodies might be uniformly accelerated was made by a scholastic whose work was known to Galileo, Domingo de Soto (1494–1560), in his Questions on the Eight Books of Aristotle’s Physics (1551).8 Indeed, as Wallace’s careful studies showed, the early Galileo was a late scholastic himself.9 For example, his graphical proof of the mean speed theorem is very close to Oresme’s.10

Oresme also invented the concept of graphs, one of the few mathematical discoveries since ancient times that are familiar to every reader of newspapers, and one of the crucial tools for thinking about functions. A page of graphs from a manuscript of Oresme’s Tractatus de latitudinibus formarum (1486) (MPIWG Library, Berlin) Analysis of infinities and the continuum is also suited to the conceptual methods of the scholastics;11 Albert of Saxony (c. 1320–1390) pairs off infinite sets “in the imagination” in the same style as Cantor.12

1.2 Mathematical physics 

The situation is partly but not wholly different for physics. The thesis of Duhem, that much of early modern physics was anticipated by the Merton School and associated scholastics in the fourteenth century, is well known and has been the object of much discussion. Despite some qualifications, it has largely stood the test of time.13 But physics is not the subject in which the scholastics show to best advantage. While the medieval aversion to observation and experi- ence in general is much exaggerated, and while the idea of mathematised science was understood, it is undeniable that controlled experiment and accurate measure- ment were largely absent from medieval science.14 The medievals supported their physical theories with “experience”, but they usually meant common experience, “what everyone knows”. Without careful measurement and experiment, the conceptual analysis that is the strong point of the scholastic method could make only limited progress in physics, and it is Galileo’s addition of those ingredients to the recipe of science that make his reputation for originality entirely deserved. Still, purely conceptual work, combined with everyday experience, can result in some good physics as well as good social science or law— statics, the subject of Duhem’s original work,15 can progress a good way purely on symmetry con- siderations, while the distinction between velocity and acceleration, necessary for any serious work on motion, is as we saw purely a matter of mathematical concepts. It is certainly possible to criticize the late scholastics for doing physics without proper experimentation and measurement. However, it is not customary to criticize Einstein for his lack of experiment. Analysis and theory are crucial to physics (and even more so to mathematics). For the same reason but more so, the more down-to-earth empirical sciences were inappropriate for the scholastic method. Chemistry, pharmacology and metallurgy are examples: knowledge about the effects of chemicals and drugs and the strength of materials is so heavily empirical that looking into oneself and analysing concepts will not make much progress, however good a memory one has. It is not an accident that these disciplines were undeveloped before very modern times. What knowledge there was in them was more a mass of engineering expertise than a scientifically grounded body of facts. In particular, they lacked a methodology for improving themselves. 

1.3 Probability and risk 

Probability, on the other hand, is perfect for conceptual analysis. Indeed, the continuing controversies in the philosophy of probability show how difficult the analysis is. Probability is essentially of two kinds, at least on the surface. On the one hand, there is logical probability, dealing with the relation of evidence to conclu- sion in such areas as legal “proof beyond reasonable doubt” and the evidence for scientific theories. On the other, there is factual or stochastic probability, dealing with the long-run frequencies in the patternless outcomes of chance phenomena like the throwing of dice and coins.16 Both kinds of probability became well understood, in a qualitative and conceptual way, in the late scholastic period prior to the foundation of the mathematical theory of probability by Pascal and Fermat’s correspondence of 1654. The central story of the developing understanding of logical probability lies in the law of evidence. Based on scattered remarks of ancient Roman law, the legal scholarship of the Glossators and Post-Glossators (12th–14th centuries) developed an elaborate grading of proofs— from suspicions and “indications” through half- proofs to “evident and manifest” proofs and “violent presumptions”, up to the “proofs clearer than light” required for conviction in a criminal case.17 The full theory was laid out with many distinctions in the commentaries of Baldus de Ubaldis (1327–1400). He writes, for example, Note that two imperfect kinds of proof, and two presumptions of different sorts, and one witness to truth, and two to reputation do not make full proof in a criminal case; for there is only the single witness to truth [not the two required by the Biblical two-witness rule].18

That theory was familiar in legal circles in the 16th and 17th centuries, being elaborated in huge treatises on proofs and presumptions such as those of Jacobus Menochius (1532–1607) and Josephus Mascardus († 1588). These works are re- ferred to by Leibniz and by 19th century English and American writers on the law of evidence, indicating the extraordinary power of legal tradition to preserve and propagate ideas.19 The ideas percolated into society more generally via canon law and the theory of casuistry (moral analysis of particular cases), developed because the confes- sional was thought of as a miniature court of canon law. It was this context that produced the 16th century scholastics’ moral doctrine of probabilism, the theory that in case of doubt as to the morality of an action, one might follow a sufficiently probable course, even if the opposite opinion was more probable. “Probable” here refers to the balance of reasons and authorities in favour of an opinion. The possible consequences of this doctrine for laxity in morals became a matter of intense public debate through the celebrated attack on Jesuit proba- bilism in Pascal’s Provincial Letters of 1656.20 Discussion of factual probability was found mostly in legal and moral works on “aleatory contracts”— contracts whose outcome depends on some matter of chance, such as insurance, life annuities, options contracts, speculative invest- ments and gambling. It was understood that in such contracts a payment was made for a “hope”, “peril” or “risk”, that is, for a probability based on how oen some outcome tended to occur, and that this distinguished such contracts from usury, the lending of money at interest.21 Thus Domingo de Soto, answering the objection that insurance appears to involve a payment for nothing, compares it to a game of chance: For anything that can be estimated at a price, one can receive a fee: to render a thing safe [insure it], which is exposed to peril, can be estimated at a price … we say of a fair game: whether it will rain tomorrow or not, etc; so in the same way it is permitted to expose a thousand ducats, say, to peril with the hope of making fi or sixty. There are some who regard it as stupid to allow the peril of someone’s ship worth perhaps twenty or thirty thousand, in the hope of making a hundred or a thousand. To this we reply that it is not for us to dispute about prices: these can be just or unjust, but it is for the contracting parties to decide them. But there is no stupidity or folly in accepting this kind of peril at the going price; in fact nothing is more obvi- ous than that insurances can expect to gain. They may lose sometimes, but at other times they accumulate gain.22Gambling, lotteries and other bets was one of the topics discussed under aleatory contracts. Antonio Escobar y Mendoza (1589–1669), the casuist most vigorously attacked in Pascal’s Provincial Letters, argued that for games to be per- mitted, equality of the stakes was normally required but that a player might licitly stake less money if his potential winnings were greater.23 These questions are close to the case of conscience which led Pascal and Fermat to their mathematical calculations, the just division of the stake in an interrupted game of chance.24

Section 2: The social sciences and psychology

It is a commonplace that the contemporary social sciences are riven by dis- putes about theory in a way that the natural sciences are not. Economics, an- thropology, and legal and political theory are still full of vigorous debates about what concepts should be used to organise and ask questions about the empirical data— even debates about whether there are any empirical data free of theoretical perspectives. That is an indication that those fields are prime candidates for the conceptual analysis that was the strong suit of the late scholastics. 

2.1 Legal theory

The law of evidence is only one example of the deep influence of late scho- lasticism on later legal theory. Modern law — especially Anglo-American law, which does not depend directly on the Roman texts — shows many evidences of its centuries of development under the scholastic intellectual oikumene. In intel- lectual style, the law is still very close to the scholastic method, with its respect for old authorities and its endlessly elaborating commentary and formal dispute on conceptual points and fine distinctions, comparison of texts, and logical ar- gument for and against propositions25 (and in many countries still, in its style of dress). Western law has also inherited from the scholastics and canon lawyers a special concern for the relation between ethical principles and the law as it stands, with principles of justice, fairness and equity being regarded as essential values that positive law cannot transgress.26 The process by which this came about has been closely studied for the law of contract, in Gordley’s Philosophical Origins of Modern Contract Doctrine. The largely unexplained rules of ancient Roman law were given explanations in terms of Aristotelian concepts of the nature of contract, and the Spanish scholastics of the sixteenth century were responsible for a synthesis, Aristotelian in concep- tion and Roman in detail, involving a casuistry of will, consent, fraud, mistake, duress and so on. Later legal theorists up to the present retained the scholastic language and distinctions, though ignoring as far as possible the underlying Aristotelian philosophy.27 A similar story is told in Brian Tierney’s work on the origin of natural rights theories, the conception of pre-legal human rights that has had such success since the 1948 Universal Declaration of Human Rights. Scholastic debate on the conflicting jurisdictions of the middle ages, church and civil, led William of Ockham and later scholastic writers to a theory of individual rights existing prior to any human laws, and constituting a moral foundation that human laws were bound (morally) not to transgress. It was transmitted to later centuries by sev- enteenth-century writers such as Grotius.28 Related conceptions dealing with the ethical protection of individuals became even more deeply embedded in Western law, notably the principle of equality before the law29 and the presumption of innocence for the defendant in criminal cases. The formulation “everyone is presumed innocent, unless proved guilty” is found in the canon lawyer Johannes Monachus about 1300.30 For both of these principles there are brief Roman law origins, but the development of them as moral concepts fundamental to the law is a scholastic achievement.

The Spanish scholastics of the sixteenth century were the most influential thinkers on law, ethics and the intersection of the two. Especially prominent were their contributions to international law, which, not being under the con- trol of any king, legislature or court, has a character more suited to the abstract discussion of the scholastics than the law of individual states. It was studied in the fourteenth century when it was recognised that Italian city states were de facto independent, whatever the pretensions of the Empire. The history of international law has had many decades to absorb the inclusion of the works of Francisco de Vitoria (c. 1492–1546) and Francisco Suárez (1548–1617), in English, in Scott’s Classics of International Law, but credit for those scholastics’ ideas is still oen given to later thinkers like Grotius and Pufendorf.31 A characteristic problem in the area, considered by Suarez and others, is the right and duty of humanitarian intervention on behalf of peoples oppressed by a tyrant; the issue remains as relevant as ever.32 Law is particularly important for the early modern development of ideas because of the large place it held in public life and intellectual training. Of the founders of modern thought, Copernicus, Bacon, Fermat, Huygens and Leibniz were professional lawyers, Montaigne a judge, Machiavelli, Pascal and Arnauld the sons of lawyers, and Petrarch, Rabelais, Luther, Calvin, Donne and Descartes former law students.33 

2.2 Political theory 

Political theory was conceived in legal and moral terms and the concepts of those disciplines formed the language in which political debates took place. Notions of constitutional government, the restraints of custom and tradition, and the subtle relations between legitimacy of government and popular consent, are medieval achievements in both theory and practice.34 The reasonableness of scholastic discussions of those matters is in some ways only now being attained again, aer many unhappy detours through extremist theories of absolute mon- archy, the divine right of kings, utopianism, theocracy, revolution and class war. The one-sidedness of such theories accounts for their memorability, and hence the corresponding difficulty of remembering more nuanced theories. It accounts also for their disastrous consequences in practice. Simplified counterfactual situations are a staple of scholastic analysis in all fields. In political theory, they include the long-running scenario of a “state of nature” in which all are “born free and equal”, which was considered by Suarez in his considerations on the native Americans.35 

2.3 Economics 

In economic history, the idea that the serious development of theory began with the seventeenth-century Mercantilists (perhaps with Aristotle deserving some passing mention) was exploded by Schumpeter and others, with their examination of the scholastics of, especially, the sixteenth century,36 but it can hardly be said to be common property even now. Concepts like demand, capital, labour, utility, scarcity and the cost of lost opportunity were developed at length by the scholastics, based on Aristotle’s brief remarks. It is difficult to evaluate the contribution of the business community itself to these notions, for lack of evidence, but at present it seems that the explicit names and distinctions were due more to the scholastics’ need for precision in ethical and legal discussions than to any strictly business requirements. In any case, the distinction between ethics and business was once not so rigidly drawn. Oresme’s monetary theory is only one of the connections between the scholastics and more applied and mathematical investigations into business.37 

2.4 Psychology 

Psychology, especially of the introspective kind, was also well-adapted to the scholastic method, although in this case the main developments came earlier. The general medieval concentration on the inner life encouraged by Augustine, the self-examination of enforced confession and Aristotle’s De anima is reflected in the extensive attention given to the mind and soul in scholastic works from the time of Albert the Great and Aquinas, and the large number of texts on psychological subjects in the sixteenth and seventeenth centuries.38 One of the longest-running themes in the history of psychology is “faculty psychology”, as advanced by Avicenna and his Western scholastic followers from Aquinas on. Faculty psychology holds that human cognition is decomposable into largely distinct tasks like sensation, comparison of different sensory modali- ties, memory and so on, which are undertaken by different “faculties” located in different regions of the brain. It was the natural way of organising psychological data for many centuries,39 and its (Latin) language is the way we still express our “folk” psychological explanations of behaviour in terms of aspirations, sensations, imagination, actions, motives, emotions and so on.40 As with the language of science, it is no accident that these words are Latin and the senses in which we use them are medieval more than classical. As a typical example, the OED traces the etymology of “imagination” thus: in classical Latin, it means the action of forming mental images, but in medieval Latin and European vernaculars, it is in the first instance the faculty in which mental images are formed: in Old French c. 1174, Catalan and Italian late 13th century, Spanish and Portuguese 14th century, English c. 1340.41While the approach was disparaged in the 1950s heyday of behaviourism, the revival of faculty psychology under various names has been one vigorous strand in more recent cognitive psychology.42 

2.5 Linguistics 

Grammar was a foundation stone of medieval education, and the inherited texts were from the 12th century subjected to the same process as legal texts, of glossing and commentary in search of the philosophical principles underlying them. Many of the concerns of modern semiotics on the different ways in which words can have meaning are visible in medieval debates about signs. For example, Augustine’s conception of a sign as something that is perceived and suggests something else to some mind raises questions about signs of the non-existent, signs not interpreted by any mind, and about the sameness of the “mental words” in the minds of speakers of different languages.43

Vocabulary is one of great hidden successes of scholasticism. The present-day international language, in which this article is written, is a blend of Old English, Norman French and scholastic Latin; and it is the vast inheritance of scholastic vocabulary, mostly still carrying its medieval meaning, that bears the weight of academic discussion on all subjects.44 Consider the current section in general, or the present sentence in particular, or examine adjacent portions of the text, for a variety of natural and artificial examples of scholastic abstract vocabulary. 

2.6 Philosophy 

While this article is focussed on the scholastics’ contribution in areas other than their philosophical doctrines, the story would be incomplete without men- tioning that they had a largely hidden influence on the conceptual apparatus of modern philosophy, just as they had in mathematics, law and the social sciences. Since Gilson’s studies a hundred years ago of Descartes’ scholastic vocabulary, there has been much work on the dependence of the founders of modern philoso- phy on the conceptual apparatus of scholasticism.45 The scholastics controlled the well-funded university posts, the academic presses and the curricula; their logic and philosophy were a central part of what every educated person had to learn.46 The rationalists and empiricists who attacked the scholastics so force- fully provide perfect examples of the old topos of students and their teachers disagreeing heatedly on answers, but exhibiting a unity of questions, unspoken assumptions and concepts. The fiercest opponents at, so to speak, the species level are found to be united at the genus level. Descartes and Locke underwent particularly heavy exposure to scholasticism in their formative years, and the questions they ask, and the vocabulary of their answers, stray remarkably little from their teachers’ practice. Gassendi very pointedly asks why the Cartesian ego, having doubted everything and put aside all prejudice and tradition, is still spouting scholastic terminology.47

Conclusion

There is less than meets the eye to the explosion of knowledge of which contemporary intellectual life boasts. Vast quantities of new empirical facts have indeed been observed and theories verified, but the conceptual superstructure into which they have been integrated is an old one. It is the one bequeathed to modern times by the later scholastics.