Prelude
Searching for a metaphysica paupera between the Middle Ages and the Renaissance means paying attention to at least two points. On the one hand, it means taking into account small, poor, and everyday objects, or minor values, which are included in attempts to explain the meaning of the world coherently from first principles. On the other hand, it refers not only to objects, but also to the kind of metaphysical view that has poor features, such as an awareness of the limited possibility of finding a definitive and certain foundation for the principles of the world, or the fact that it pays attention to things not for their substantive aspects, but for their relations, in order to show the interconnectedness of the cosmos. In this perspective, we can consider critical and sceptical attitudes, that propose principles which are not properly grounded theoretically, but principally serve ethical and political purposes. Or we can consider other attitudes that, at their core, are based on inferior senses such as sensation.
In this article, the question of metaphysica paupera will not be addressed in the sense in which it would be if one were to study the critical thought of Nicholas of Autrécourt (see, for example, Salvestrini Reference Salvestrini, Brinzei, Caiazzo, Grellard and Robert2024b), where constant doubt and a foundationalist perspective allow him to propose an epistemology and a metaphysics based on the probable and open, also in a rhetorical way, to the constitution of social life.
Here, the idea of metaphysica paupera will rather be explored in relation to an intellectual figure such as Friar Luca Pacioli who, in certain respects, can be considered a strong thinker because of his commitment to a mathematical foundation of the cosmos and human knowledge, derived from both a Neo-Platonic and Euclidean perspective.
In order to understand the poor aspects of Pacioli’s metaphysics, we will focus on three issues: 1) the constitution of a relational principle of things that has at its core the idea of a proportional and harmonious beauty; 2) the inclusion of vulgar, poor, and minor arts in his metaphysical vision; and 3) the Franciscan theological and philosophical framework, which reinterpreted certain aspects of the spiritual teaching of Francis of Assisi on a speculative level and seems to offer a condition of possibility for the amplification of those aspects of Pacioli’s thought that go towards a metaphysics of poverty.
The argument is divided into two sections. The first section outlines the genesis of the proportional and relational idea of beauty within the Franciscan tradition, first in the earliest sources and later in Bonaventure’s thought. The second section highlights the poor aspects of the Franciscan metaphysical framework, by focusing firstly on Pacioli’s idea of divina proportione, and then on his commitment to dignifying the vulgar arts starting from the mathematical foundation of theoretical and practical knowledge.
Franciscan ‘minor’ beauty
As I have argued in a previous work (Salvestrini Reference Salvestrini2023b), there are reasons to believe that some aspects of the constitution of the proportional and harmonious idea of beauty in Franciscan texts derive not only from the intersection of traditions such as the Neo-Platonic and the Augustinian in the philosophical field, or the rhetorical-musical one, but also from specific inspiration provided from the teachings of Francis of Assisi. The outcome of this interweaving of meanings is certainly diachronic, but it defines a particular idea of beauty, which we could call a ‘poor’ or ‘minor beauty,’ because it concerns, on the one hand, the attribution of dignity to minor values, such as poverty, simplicity, and humility, or to the humblest things in the scale of society and of being, such as illness, animals, or even every small creature of God (Sorrell Reference Sorrell1988; Merlo Reference Merlo2003). On the other hand, it concerns the possibility of the metaphysical concept of beauty being linked to the lowest things of the world, of lowering its ontological status, and of being a relational rather than a substantive principle.
For the purposes of our discussion of metaphysica paupera, it is interesting to underline the correlation between the semantic field of beauty and poverty. The question is a broad one in the Franciscan sources of the 13th century and falls beyond the scope of this paper. It could also be addressed by referring to other connections of the concept of beauty, for example, with humility, creatures, and stigmata, which highlight minor things or values, or even with the lowering of the God to the human level. The passage from Franciscan sources such as the texts by Francis of Assisi, Clare of Assisi, and the Life by Thomas of Celano, to Bonaventure’s Life reflects a kind of transposition into a speculative and often metaphysical sphere, of values and features initially approached from a narrative or spiritual perspective.
In sources such as the Forma vitae ordinis sororum pauperum by Clare of Assisi and the Vita beati Francisci by Thomas of Celano, the ideal poor life, altissima paupertas, is associated with the semantic field of beauty, through a lexicon that underlines interesting variations and nuances of meaning, including those of proportion, splendour, and elevation. In the Forma vitae the correlation between the poor life and moral sublimity is highlighted:
This is that summit of the highest poverty which has established you, my dearest sister, heiresses and queens of the Kingdom of Heaven; it has made you poor in things but exalted your virtueFootnote 1. (Clare of Assisi Reference Armstrong2006: 119-120)
The semantic variant of beauty of interest for our purposes is the ‘sublime,’ which has both a rhetorical and a theological use. In this period, it often signifies a moral quality, underlining a kind of disproportion between the human and the divine spheres. But it also means the elevation of the subject to the non-human and divine realms for a moral commitment. The ‘sublime’ also emphasizes an aesthetic quality derived from the moral one (see Deproost Reference Deproost2019; Jaeger Reference Jaeger2010, Reference Jaeger2022 and Reference Jaeger2024), and in this case it is noteworthy that living a poor life, with poor things, leads to moral elevation.
In the Vita prima sancti Francisci, Thomas of Celano repeatedly presents the personification of Paupertas as a beautiful woman and bride, highlighting once again a transvaluation of traditional values in the correlation between the poor life and the semantic field of beauty. In the passage I would like to recall, Thomas uses two words from this semantic field, pulchrum and forma:
People thought he wanted to get married, and they would ask him: ‘Do you want to get married, Francis?’ He replied: ‘I will take a bride more noble and more beautiful than you have ever seen, and she will surpass the rest in beauty and Excel all Others in wisdom’Footnote 2. (Thomas of Celano 1999: 188)
In this dialogue, Francis underlines some significant features of Paupertas, turning it from a condition of social marginalization to an elevated quality to which one can aspire: Paupertas is noble and beautiful, that is, she is of a high rank, good-looking, and a source of wisdom – qualities that are contrary to those commonly assigned to her.
A thinker like Bonaventure transposes Franciscan values such as humility, simplicity, and poverty into a more precise metaphysical framework. Once again, the idea of beauty is representative of these semantic shifts. In some Franciscan texts such as in the Legenda maior and De perfectione evangelica, the semantic field of beauty is found in relation to the moral value of a way of life ordered in conformity with the life of Christ, according to an imitatio Christi exemplified by Francis.
In the Legenda maior, Bonaventure recalls the episode in which, during a journey to Siena, Francis was greeted by three poor women, an episode interpreted as a sign that Francis had the perfectio evangelica. The evangelical perfection in Francis is a particular state of grace that is also visible outwardly because Bonaventure emphasizes the kind of beauty emanating from him:
Clearly, it would seem that through those three poor women so alike in appearance, offering such an unusual greeting, and disappearing so quickly, the beauty of Gospel perfection, consisting in poverty, chastity, and obedience was fittingly revealed to be shining perfectly in the man of God in an equal way. Nonetheless, he had chosen to glory above all in the privilege of poverty which he was accustomed to call his mother, his bride, and his ladyFootnote 3. (Bonaventure Reference Armstrong, Hellmann and Short2000: 581)
The appearance of the three ladies shows in an appropriate way (conveniens) the beauty (formositas) of the evangelical perfection in the man of God. Here Bonaventure not only applies a rhetorical term to beauty (conveniens) that indicates the appropriate way in which the three virtues of evangelical perfection appear in the guise of the three women, but also uses the word formositas, which has an interesting history in Christian spirituality, if we think, for example, of the Song of Songs, where the bride is described as beautiful in the sense of Formosa. The evangelical virtues, namely chastity, obedience, and poverty, belong to Francis, but he chooses to privilege poverty, and here, in Bonaventure’s text, the allusion to the formositas of the Song of Songs acquires its full meaning because he underlines that the friar usually calls Paupertas not only mother and lady but also his bride.
Therefore, the way of imitatio Christi leads to a particular kind of moral and aesthetic beauty, which presupposes the annihilation or debasement of the self in order to overcome pride, as we can read in the Quaestiones disputatae de perfectione evangelica. The first question is devoted to the virtue of humility. Bonaventure argues that humility involves the act of debasing oneself. It is also in this context that one can observe another use of the lexicon of beauty to characterize the moral and aesthetic path of the imitatio Christi. In the arguments in favor of the humility-debasement nexus, Bonaventure writes:
Again, in Philippians 2: Let your attitude be identical to that of Christ Jesus, though he was in the form of God, etc.; but to empty oneself is nothing else than to debase oneself. Therefore, if we are to imitate Christ in this, self-emptying and debasement are part of evangelical perfectionFootnote 4. (Bonaventure Reference a S. Bonaventura1891a: 117, my translation)
The path to the imitation of Christ passes through the emptying and debasement of the self, which are convenientes, i.e., suitably adapted, in the sense of the suitably beautiful, for the achievement of evangelical perfection.
If the moral commitment to evangelical perfection in the imitation of Christ also leads to a kind of moral and aesthetic beauty – which can perhaps be called a ‘poor’ or ‘minor beauty’ – what is the metaphysical foundation of this kind of beauty? To understand this conceptual passage, we can read the splendid pages of the Itinerarium mentis in Deum, where Bonaventure grounds the origin of all beauty, in a relational sense, in the Son as summa aequalitas Footnote 5.
In the second chapter, describing the beauty (proportio) of the creatures observed by the beholder, who experiences pleasure when the object is perceived in an appropriate, harmonious way by the senses – for example, by the eyes (that implies pulchrum) or the ears (that implies suavitas) –, Bonaventure underlines the reason for the pleasure that results from harmonious proportionsFootnote 6. The reason lies in a peculiar relationship, also known as numerus or proportio, which Augustine had already identified in De musica Footnote 7. Retracing Augustine’s path from the sensible to the intelligible, Bonaventure arrives at the numbers of judgement, which are immutable epistemological and aesthetic criteria, inner images of eternal reasons:
Perception and pleasure are followed by judgment. And through this judgment one judges not only whether a thing is white or black (for this pertains to a particular sense), and not only whether it is healthful or harmful (for this pertains to the interior sense)—but one also judges and receives an explanation as to why the senses derive pleasure from the sense object. This happens when one looks for the reason why an object is called beautiful, sweet, or wholesome, and finds out that this reason lies in the proportion of equalityFootnote 8. (Bonaventure Reference a S. Bonaventura1891b: II, 6)
The proportio aequalitatis is the trace in sensible things of the intelligible criteria underlying the world, of the images that represent metaphysical principles. This metaphysical foundation, according to Bonaventure, is the first ratio of aequalitas, i.e., that between the Father and the Son in the intra-Trinitarian relationships:
For all these things are vestiges, in which we can see our God … Therefore, if all knowable things have the ability to generate their own shape, they openly proclaim that the eternal generation of the Word, the Image, and the Son eternally proceeding from God the Father can be observed in them as in mirrors. Now sensual shape, which gives delight in this way, i.e., as beautiful, sweet, and wholesome, suggests that in that original shape or form, there is that original beauty, sweetness, and wholesomeness, in which is found the highest proportionality and equality in relation to the one who generates itFootnote 9. (Bonaventure Reference a S. Bonaventura1891b: II, 7-8)
The summa aequalitas is, therefore, the origin and the model of all relationships and individual forms of beauty, because it is the first relation of equality, i.e., that between the Father and the Son. In the ars aeterna, in the eternal Word of the Son, all things are generated. The origin of the multiplicity of things, then, is in this summa aequalitas but, even if the Trinity at the basis of the cosmos and its beauty refers to the unitary principle of God, it is important to emphasize that the intra-Trinitarian relationships describe the relational metaphysical foundation at the basis of a relational cosmos.
At this point, it is important to emphasize two fundamental aspects for the development of our argument in the next section. Firstly, in the Franciscan texts, one can observe a particular characterization of the beauty implied by the Franciscan forma vitae or perfectio evangelica, which is shown by the semantic field that includes words such as sublimis, pulchrum, conveniens, formositas, etc. The particular kind of beauty associated with poverty and humility can define the limits of what we have called ‘poor’ or ‘minor beauty.’ Secondly, this kind of beauty has a metaphysical foundation, which Bonaventure describes in various texts, such as in the Itinerarium, where he defines the origin of all beauty in the summa proportion and equality. On the one hand, a metaphysical foundation can be called ‘poor’ or ‘minor’ because it highlights a relational principle that is reflected in beings that are captured not in their substantial being, but in their mutual relations. On the other hand, the very principle of all beauty is the Son, who accepted to lower his divine nature, emptying, annihilating, and debasing himself, according to the same virtue of humility that Franciscans pursue to reach evangelical perfection in the imitatio Christi.
Friar Luca Pacioli and the ‘divina proportione’
The case of the Franciscan friar Luca Pacioli of Sansepolcro is very interesting for the purposes of our inquiry. In the framework of the mathematization of knowledge, Pacioli, on the one hand, establishes the principle of divine proportion (divina proportione) in a relational sense and, on the other, outlines a particular kind of system of human knowledge, which, according to his metaphysics, can also include minores and viles arts – or even, in Poliziano’s words, sordidae … ac sellulariae (Angelini Reference Angelini, Blanchard and Severi2018).
The treatise De divina proportione concerns a particular kind of proportion, the golden ratio, or the ‘proportion that has a mean and two extremes.’ According to the divine proportion, the ratio of the whole segment to the largest segment is like that of the largest segment to the smallest (Ciocci Reference Ciocci2003). In order to understand the sense in which Pacioli’s metaphysics is a metaphysica paupera, it is important to bear in mind the philosophical presuppositions of his divine proportion.
In Chapter 5 of De divina proportione, Luca Pacioli underlines the reasons why the subject is suitable (conveniens) both for the title of the treatise and for God. After noting that the divine proportion is one, just as God is one, he illustrates the second convenientia, which is particularly interesting for our discussion and concerns the Trinity:
The second convenientia relates to the Holy Trinity as, just as in God there is one substance for the three persons Father, Son, and Holy Spirit, similarly a selfsame proportion is to be found for three terms. And it can be found in neither more nor less terms, as it will be explainedFootnote 10. (Pacioli Reference Pacioli1956: 21, my translation)
The divine proportion is appropriate to God because, just as the Trinity in its unity concerns the relationship between three terms, namely the Father, the Son, and the Holy Spirit, so the divine proportion is always a relationship between three terms.
Bonaventure’s text on summa proportionalitas et aequalitas gives us the proper metaphysical meaning of this conceptual passage, which we will discuss in more detail shortly, but which is important to recall here. According to Bonaventure, the relationship between the Father and the Son is a relationship of equality, the first relationship that underlies all relationships in the world. The suitable or harmonious ratios, or proportiones, in things reveal a relational beauty of which that of the Son is the metaphysical model. In the above-quoted passage, Luca Pacioli links the idea of proportion to the Trinitarian relationship, as two relational principles at the basis of the world that mirror each other.
In order to better understand Pacioli’s idea of the metaphysical foundation of divine proportion, we can examine the metaphysical sense of proportional beauty associated with the Trinity in the reflections of a thinker whom Pacioli quotes in the previous pages, namely Augustine. We will thus see how the metaphysical reflection of the friar of Sansepolcro uses conceptual tools from the Platonic-Augustinian (and Franciscan) tradition to justify his project of mathematizing knowledge.
Luca Pacioli quotes Augustine of Hippo on the creation of the world according to measure, number, and weight, a statement that comes from the Book of Wisdom:
As we said, the sciences and the mathematical disciplines belong to the first degree of certainty; they are followed by all the natural disciplines, and without their knowledge it is impossible to understand the others. In the Book of Wisdom, it is written: ‘That all things consist in number, weight, and measure’, viz. everything that unfolds in the lower and higher universe is necessarily subject to number, weight, and measure. And Aurelius Augustine, in De Civitate Dei, says that the Supreme Maker is to be highly praised for putting in these three things ‘things that were not’Footnote 11. (Pacioli Reference Pacioli1956: 9, my translation)
Pacioli is probably quoting Augustine by heart in this passage. One of the passages in De Civitate Dei that comes closest to what the Friar of Sansepolcro means is a point in Book XI, where Augustine considers the significance of the symbolism of numbers in the Scripture. At the end of an analysis of the perfection of the number six, Augustine states:
And, therefore, we must not despise the science of numbers, which, in many passages of holy Scripture, is found to be of eminent service to the careful interpreter. Neither has it been without reason numbered among God’s praises, ‘Thou hast ordered all things in number, and measure, and weight’ [Wisdom 11.20]Footnote 12. (Augustine Reference Schaff1886: XI, 30)
But what does Augustine mean by quoting this passage from Wisdom? And why is it important to establish the mathematical foundation of things?
In the Augustinian view, creation by measure, number, and weight gives the world a relational structure that reproduces the Trinitarian articulation (Father-being, Son-knowing, and Spirit-willing). Number establishes unity, measure concerns the relationship between different things, while weight concerns the tendency of one thing to another, specifically to its place or position in the world (Parodi Reference Parodi and Badaloni1984; Bettetini Reference Bettetini1994). Therefore, the criteria with which the Opifex Summus has created the world are mathematical and relational, because they are capable of establishing iterative unities and their mutual relationships. So, they are the expression of the Trinitarian articulation of the principle of all things and the basis of a cosmos whose elements are considered precisely in their relations.
In De Trinitate Augustine specifies the idea of relation as the basis of the trinitarian articulation of God. He observes that in God nothing can be predicated in an accidental sense, so that relation, which according to Aristotelian logic is an accidental predication, is only predicated in an essential sense in the case of GodFootnote 13. As some scholars have pointed out, in this way Augustine deified the category of relationship, a metaphysical principle, and a cosmos structure that describes not an ontology but a relational metaphysics, i.e., a prostilogia (Parodi Reference Parodi2006: 117–118). The Trinitarian articulation, therefore, expresses an essential relationship: there are not three terms, but there is the relationship between the Father and the Son, while the Holy Spirit is nothing but their relationship, just as – Augustine says in the following pages where he proposes a path through the sensible trinities best known to us to arrive at the divine one – love between lover and beloved is not a third term but the relationship itself; or again just as the inclination towards something, the intentionality of the subject towards the object is not a third term but again the relationship itself. Among the auctoritates cited by Luca Pacioli, Augustine therefore plays a pivotal role in arguing for the relational and mathematical foundation of all things.
The Augustinian framework of the metaphysical foundation of the divine proportion receives a Franciscan twist, especially in Christocentrism. Pacioli in his Summa (Reference Pacioli1494: 16 r) underlines that just as Christ is incarnate, becoming man while retaining his divine nature, so the divine proportion is like other proportions of its kind while retaining unique properties that make it divine (Ciocci Reference Ciocci2003). In addition to the analogical nature of reasoning, which is also proportional, this aspect recalls the metaphysical function of Christ, especially in his emptying, annihilation, or debasement while retaining his divine nature. The divine proportion in this sense circumscribes a metaphysics of poverty since it is the principle and origin of all things. In a sense, it is capable of ‘emptying’ itself by also constituting the structure, always relational, of lower things.
We have seen the idea of divine proportion as a relational metaphysical principle. We can now see how this principle became the basis for the genesis and the creation of things. Luca Pacioli takes this step by relying on Plato’s Timaeus, known from medieval sources (Calcidius), and Campano’s commentary on Euclid’s Elements (Ciocci Reference Ciocci2003, Reference Ciocci, Hernández-Esteve and Martelli2018). According to Pacioli, proportion gives the numerical and relational structure to the regular polyhedra that form the basis of the four elements. In particular, the divine proportion constitutes the duodecedron, the polyhedron that forms the fifth element (Virtù Celeste) at the basis of all the other elements:
The fifth convenientia can rightfully be added to the previous ones: as, just as God gives being to the Heavenly Virtue, also called the Fifth Essence, and through it to the other four simple bodies, viz. the four elements Earth, Water, Air, and Fire, and through these to every other thing in nature; then, according to time-honored Plato’s Timaeus, this holy proportion of ours gives formal being to heaven by yielding it the shape of the body called dodecahedron, or body composed of 12 pentagons, which, as it will be shown later, could not be formed without our proportion. Similarly, it assigns their own shapes to each other element, which in no way coincide with one another: to the fire it assigns the shape of the pyramid, called the tetrahedron, to the earth the cubic shape or hexahedron, to the air the octahedron, and to the water the icosahedronFootnote 14. (Pacioli Reference Pacioli1956: 21-22, my translation)
The formation of the four elements at the basis of the cosmos thus entails God’s bestowal of being on the fifth element, ether, also known as the Virtù Celeste or Quinta Essentia, constructed by the duodecedron. Following the Timaeus, Pacioli compares the other elements to the conformation of the other regular polyhedra: fire corresponds to the pyramid (tetracedron), earth to the cube (exacedron), air to the octocedron made up of eight triangular faces, and water to the icocedron made up of 20 triangular faces. The shape of each of these solids is the most suited to the nature of the corresponding element, e.g., the triangle that makes up fire increases its mobility, while the cube that structures the earth increases its stability. Furthermore, the proportions of the different solids in relation to the diameter of the sphere that circumscribes them are regular in all cases except for the icocedron and the duodocedron, which have an irrational ratio based on the golden section.
The cosmos outlined by Pacioli is thus governed by proportions, that is, by relations between different elements, among which the divine proportion has primacy. In order to confirm the peculiar relational nature of Pacioli’s metaphysics, I believe it is useful to observe the kind of argumentation found in his pages, namely analogy. This is an argumentative form that has at its core preciely the structure of proportionality (or proportionalitas, to use the medieval technical term), namely a similarity of relations such as a:b = b:c (Perelman & Olbrechts-Tyteca Reference Perelman and Olbrechts-Tyteca1971; Parodi Reference Parodi2006), but which, far from having demonstrative force, is one of the most interesting rhetorical forms of argumentation, widely used not only in the Timaeus but also in the Augustinian tradition.
Proportion as the principle and structure of the cosmos also governs human activities. It is this last aspect of Pacioli’s metaphysics, and its implications for the human world, that I would like to recall here since it is thanks to mathematical structuring that those arts traditionally considered minores or viles acquire full dignity in the reflection of the friar from Sansepolcro.
We can distinguish two areas of Pacioli’s operation of dignifying the arts: the drawing arts, and the viles or mechanical arts. As regards the first area, Pacioli’s operation is close to other operations of his time, such as those of Leon Battista Alberti and Leonardo da Vinci, in that it aims to raise the arti del disegno (drawing arts), namely painting, architecture, and sculpture, to the same dignity as the liberal artsFootnote 15. In this context, it is very interesting to recall the dispute evoked at the beginning of De divina proportione (Pacioli Reference Pacioli1956: 15 ff)Footnote 16 in which both Pacioli and Leonardo pointed out that painting (prospective, in this context) must attain the dignity of the liberal arts because of its mathematical foundation, otherwise, music should not be included among the liberal arts either, since it is based on the same harmonic relationships that lead to pleasure in the observer or listenerFootnote 17. A similar argument, with a slightly different purpose, can be found in Alberti’s De re aedificatoria for architecture, which is based on the same relational proportions as music (Alberti Reference Alberti and Rykwert1988; Di Stefano Reference Di Stefano2000), and in Leonardo’s Trattato sulla pittura, which proclaims the superiority of paintings for reasons similar to Pacioli’s text, namely its mathematical foundation and the primacy of the sense of sight (Leonardo da Vinci Reference da Vinci and Pedretti1964 [First Part]; Ciocci Reference Ciocci and Martelli2014; Winternitz Reference Winternitz and Natanson1970).
On the other hand, in accordance with his metaphysical perspective and perhaps with his Franciscan inspiration, Luca Pacioli includes in the mathematical dignity all the human activities, all the arts, not only those of the trivium and quadrivium but also those traditionally considered as minores and viles, namely tailoring, carpentry, shipbuilding, ironworking, commerce, military strategy, etc. (Pacioli Reference Pacioli1494: 45ff, 56 ff; Ciocci Reference Ciocci2003). As we can see both in the Epistola to Guidobaldo da Montefeltro and in d. 6, tr. 1, a 2 of his Summa de arithmetica, geometria, proportioni et proportionalitas, mathematics and proportions are central to all human knowledge: all the sciences and arts are governed by proportions, from astrology to painting, architecture, and the mechanical arts. For example, in the art of commerce, the elimination of number and calculation would eliminate all its operations; in the arte militare, the construction of all artillery and defensive devices (such as bastions, bombards, fortresses, and towers) involves the use of proportions (Pacioli Reference Pacioli1494: 2 v). Similarly, a woodworker could not do without the knowledge of proportions, just as a shipbuilder would need it to build boats, sails, and oars (Pacioli Reference Pacioli1494: 69 r). Pacioli continues and concludes his discourse on the mechanical arts by returning once again to the metaphysical foundation:
Weavers, wool-makers, and ultimately all other craftsmen always work with due proportion in order to do their work well … It follows that in all questions, reasons, and cases of the world, due proportion is sought in number, weight, and measure’Footnote 18. (Pacioli Reference Pacioli1494: 69r, my translation)
Proportion as a principle, and the golden ratio in particular, is thus the metaphysical foundation of a cosmos, whose primary forms, the regular solids, structure the five elements from which all things derive. Human activities, both the sciences and the arts, whether arts of design or mechanical arts, are fully embedded in this relational metaphysical framework. Pacioli thus outlines a metaphysica paupera based on a minor proportional beauty, we might say, since it is capable of encompassing within itself, and, like Christ, of ‘lowering,’ even the humblest of human activities.
Concluding remarks
In our discussion, we have considered the constitution of the metaphysics of poverty through the theme of beauty in three fundamental stages. First, in early Franciscanism and in the early biographers of Francis of Assisi, we have seen how poverty, especially when it is personified, but also when it is a dimension of the form of life, is often related to beauty.
Second, the theme of minor and poor beauty in Bonaventure appears on various levels, but in these pages, we have seen how its concrete dimension, linked to the form of life aimed at achieving evangelical perfection, receives a metaphysical foundation in the idea of proportio, which unites in a harmonious way everything that touches the senses and arouses pleasure, and in the fundamental idea of the summa proportio et aequalitas of the Son in the intra-Trinitarian relationship. In this way, a metaphysica paupera is defined both by its relational character and by the connection between beauty, poverty, and humility.
Finally, Luca Pacioli highlighted the central role of the divina proportio both as a metaphysical principle of things – relational in that it is closely linked to the Trinitarian articulation – and as the foundation of the creation of the world. The regular solids that structure the five elements are governed by proportions among which the golden ratio is predominant, so much so that it gives form to the fifth element, the condition of all the others. The same relational metaphysical framework provides the conditions of possibility for a mathematization of knowledge that includes the liberal arts, the arts of design, but also the mechanical arts, which at this point rise to full dignity among the others. To the metaphysica paupera derived from Augustin and found in Bonaventure, Pacioli adds the humanist intention of overcoming the traditional division of knowledge, even going beyond, in a different way, the similar proposals by Alberti and Leonardo.
Some concluding remarks can thus be made on the passage from the Middle Ages to the Renaissance in a Franciscan context. On the one hand, it is possible to highlight the persistence of a model of beauty as proportion and of a relational metaphysics based on a Trinitarian articulation derived from Augustinian thought; on the other hand, a meaningful variation of the idea of beauty as proportion, capable of encompassing all spheres of being and knowledge, even the lesser, poorer, and humbler ones, can be ascertained. Therefore, in a humanist context, we can see how, thanks to Pacioli, the idea of a minor beauty that extends to human activities is constituted, a minor beauty that is also capable of giving a new meaning to a metaphysica paupera.
Funding
This research was supported by Fondazione Cariplo – Grant n. 2023-1129 (Project HarmoPicta: Harmonia et Affectus. Franciscan Aesthetics, Giottesque Painting, and Humanists). Thanks to Professor Fosca Mariani Zini for encouraging my research on the Renaissance, at least since the Conference on Metaphysica paupera in June 2022 at the Université de Tours.
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