Periodic Reporting for period 2 - CALCULATORES (Imaginable Impossibilities and Thought Experiments. The Tradition of the Oxford Calculators and its Influence on Early-Modern Logic and Natural Philosophy)
Periodo di rendicontazione: 2021-09-01 al 2022-08-31
The project was aimed at investigating the tradition of the Oxford Calculators with a special focus on their theories of modalities and modal logic. Particular attention was paid to the use, in the Calculators’ tradition, of the concepts of impossibility and imaginability, and the application of these concepts in logic and in scientific thought experiments. The Oxford Calculators were a group of scholars active at Oxford between 1325 and 1350. An element of novelty in the sophismata of the Calculators is that purely logical techniques were applied to the discussion of mathematical and physical issues Moreover, their sophismata often involved the use of thought experiments, in which many sorts of intricate non-naturalistic cases and impossible scenarios were posited as conceivable or imaginable, and some theoretical inferences were drawn from them. For a long time, however, it has been unclear whether and to what extent these imaginative scenarios were aimed at challenging and revising parts of the Aristotelian physics. Another element that had not been addressed in detail by previous research is whether these authors were referring to a consistent and systematic theory of modalities, and which connections there were between their use of modal terms and the theories and logics of modalities available in the previous centuries. Our project allowed us to address these issues in detail. Besides its historical interest, the project is related to many philosophical issues that are significant in the contemporary debate, such as the ones concerning the nature and varieties of modalities, or the role that thought experiments play in philosophical and scientific methodology.
The project was conceived around 4 main areas of research:
1: Medieval theories of modalities up to the early 14th century
The starting point of the research has been collecting textual evidence and analyzing the medieval theories of modalities advanced in the 12th, 13th and 14th century, especially in the Parisian and Oxonian contexts. This was necessary to see the Calculators' modal theories in a wider historical context. This research led to the publication of 5 scientific publications and the participation to 6 international conferences. Moreover, the research on medieval theories of modalities led to the organization of the international conference on “Late Medieval Logic and Modalities”, held in Parma in October 2022.
2: Medieval ways of reasoning with the impossible
One important line of research concerned the logic and metaphysics of impossibility in 13th- and 14th-century logical texts. The main authors examined have been the first and second generation of the Oxford Calculators and their 13th-14th century background. Historical theories of impossibilities have been seen in connection to contemporary views on the logic and epistemology of the impossible, especially with respect to the issues of counterpossible conditionals and the relation between imaginability/conceivability of the impossible. On the topic of the logic of impossibility, several scientific events were organized, among which (1) the seminar series “It’s Impossible! Historical and Philosophical Perspectives on the Logic and Epistemology of Modalities”, and (2) the international workshop “Beyond Impossible. Logical and Philosophical Perspectives”, co-organized in collaboration with M. Carrara and B. Jespersen (Padova, October 2021).
Another important result connected to this area of research has been the organization of a joint-course co-taught in collaboration with Peter King (Toronto), devoted to medieval theories of impossibility.
3: The Oxford Calculators and modal theories
During the 3 years of project, the researcher undertook the study of some of the main logical texts of the Oxford Calculators, connecting the theories advanced in them with the logical developments and modal developments of the previous centuries. This research resulted in 2 scientific publications: the journal article: "Medieval theories on the conceivability of the impossible: A survey of impossible positio in ars obligatioria during the 13th–14th centuries” (Noctua, 2022) and the special issue "Logic and Modalities in the Late Middle Ages. The Tradition of the Calculators” (Noctua, 2022). Another result was the organization of an online seminar course on the topic of the Calculators and their philosophical tradition. This seminar series, organized in collaboration with Dr S. Roudaut (Stockholm), included 6 meetings dedicated to different aspects of the Calculators’ work (their logic, natural philosophy, ethics, theology, their predecessors and successors).
4: Imagination and Thought Experiments
A fourth line of research focused on theories and uses of thought experiments in Late Medieval and Early Modern philosophy. In particular, the role of thought experiments in Galileo Galilei’s works and his relation with Late Medieval example of secundum imaginationem reasoning have been studied. This topic has been seen in connection to contemporary debates on thought experiments and imagination.
With some colleagues of the University of Parma, we established the research group “Prisma” (“Parma research group on imagination in sciences, mind and the arts”) now officially recognized by the Department. The group organized many scientific and outreach activities, among which the international conference “Imagination and its constraints” and an outreach presentation for the European Night of Research 2021. Together with W. Huemer and D. Molinari, the researcher has also completed 2 outreach publications on the project’s topics and one scientific publication, currently under review.
1: Medieval theories of modalities up to the early 14th century
The starting point of the research has been collecting textual evidence and analyzing the medieval theories of modalities advanced in the 12th, 13th and 14th century, especially in the Parisian and Oxonian contexts. This was necessary to see the Calculators' modal theories in a wider historical context. This research led to the publication of 5 scientific publications and the participation to 6 international conferences. Moreover, the research on medieval theories of modalities led to the organization of the international conference on “Late Medieval Logic and Modalities”, held in Parma in October 2022.
2: Medieval ways of reasoning with the impossible
One important line of research concerned the logic and metaphysics of impossibility in 13th- and 14th-century logical texts. The main authors examined have been the first and second generation of the Oxford Calculators and their 13th-14th century background. Historical theories of impossibilities have been seen in connection to contemporary views on the logic and epistemology of the impossible, especially with respect to the issues of counterpossible conditionals and the relation between imaginability/conceivability of the impossible. On the topic of the logic of impossibility, several scientific events were organized, among which (1) the seminar series “It’s Impossible! Historical and Philosophical Perspectives on the Logic and Epistemology of Modalities”, and (2) the international workshop “Beyond Impossible. Logical and Philosophical Perspectives”, co-organized in collaboration with M. Carrara and B. Jespersen (Padova, October 2021).
Another important result connected to this area of research has been the organization of a joint-course co-taught in collaboration with Peter King (Toronto), devoted to medieval theories of impossibility.
3: The Oxford Calculators and modal theories
During the 3 years of project, the researcher undertook the study of some of the main logical texts of the Oxford Calculators, connecting the theories advanced in them with the logical developments and modal developments of the previous centuries. This research resulted in 2 scientific publications: the journal article: "Medieval theories on the conceivability of the impossible: A survey of impossible positio in ars obligatioria during the 13th–14th centuries” (Noctua, 2022) and the special issue "Logic and Modalities in the Late Middle Ages. The Tradition of the Calculators” (Noctua, 2022). Another result was the organization of an online seminar course on the topic of the Calculators and their philosophical tradition. This seminar series, organized in collaboration with Dr S. Roudaut (Stockholm), included 6 meetings dedicated to different aspects of the Calculators’ work (their logic, natural philosophy, ethics, theology, their predecessors and successors).
4: Imagination and Thought Experiments
A fourth line of research focused on theories and uses of thought experiments in Late Medieval and Early Modern philosophy. In particular, the role of thought experiments in Galileo Galilei’s works and his relation with Late Medieval example of secundum imaginationem reasoning have been studied. This topic has been seen in connection to contemporary debates on thought experiments and imagination.
With some colleagues of the University of Parma, we established the research group “Prisma” (“Parma research group on imagination in sciences, mind and the arts”) now officially recognized by the Department. The group organized many scientific and outreach activities, among which the international conference “Imagination and its constraints” and an outreach presentation for the European Night of Research 2021. Together with W. Huemer and D. Molinari, the researcher has also completed 2 outreach publications on the project’s topics and one scientific publication, currently under review.
With respect to the state of art, one important contribution of the project has been to present new evidence on the philosophical and logical background of the Calculators, and in particular their relation with the 13th century tradition of obligations, which importantly shaped the views on modalities later adopted in the 14th century. Publications of the project show that during the 13th century a profound interest on the notion of impossibility began, especially in the Oxonian context. This new interest resulted in the first taxonomy of impossibility, which distinguished different kinds of impossible propositions or impossible scenarios, and established a relation between the modal notion of impossibility and our epistemic capacities to conceive or imagine the impossible. This relation between impossibility and conceivability/imaginability was pivotal to ground the Calculators' views on the admissibility of impossible scenarios and the reliability of reasoning "secundum imaginationem".
Another contribution of the project was to emphasize the way in which the "domain of imaginability" - i.e. the boundaries of what is considered imaginable or conceivable despite being naturally impossible - significantly changes between the late medieval period and early modernity. More specifically, many natural philosophers between the 15th and early 17th centuries, while still making use of many impossible cases and thought experiments involving impossible scenarios which were already used by their medieval predecessors, refused to consider as "imaginable" or "conceivable" certain kinds of impossibility, and consequently denied that these impossibilities could be used in scientific contexts to draw relevant conclusions on the way things are.
Another contribution of the project was to emphasize the way in which the "domain of imaginability" - i.e. the boundaries of what is considered imaginable or conceivable despite being naturally impossible - significantly changes between the late medieval period and early modernity. More specifically, many natural philosophers between the 15th and early 17th centuries, while still making use of many impossible cases and thought experiments involving impossible scenarios which were already used by their medieval predecessors, refused to consider as "imaginable" or "conceivable" certain kinds of impossibility, and consequently denied that these impossibilities could be used in scientific contexts to draw relevant conclusions on the way things are.