Free will in antiquity is a concept that varied significantly across different cultures, philosophical schools, and religious traditions. Here are some key perspectives from various ancient civilizations: ### Ancient Greece 1. **Philosophical Views**: - **Socrates**: Suggested that virtue is tied to knowledge. If people knew what was right, they would choose it. This implies a form of free will since knowing the good would lead to good actions.

In Mormonism, or The Church of Jesus Christ of Latter-day Saints (LDS Church), "agency" refers to the God-given ability and right of individuals to make choices and act for themselves. This concept is central to LDS theology and is tied to the belief that human beings are created with the capacity to choose between good and evil, which is essential for moral accountability and spiritual growth.

Arbitrariness generally refers to a lack of a clear or inherent connection between two things. In different fields, it can take on specific meanings: 1. **Linguistics**: In the study of language, arbitrariness refers to the relationship between a word and its meaning. For example, the word “dog” does not have an inherent connection to the animal it represents; it is a social convention agreed upon by speakers of English.

Higher-order volition refers to the complex process of reflecting on and evaluating one’s desires, intentions, and motivations at a level beyond mere immediate impulses or basic desires. In this context, higher-order volition involves not just experiencing a desire but also having the capacity to endorse or reject that desire based on deeper values, principles, or long-term goals.

Logical determinism is a philosophical concept that posits that every proposition, whether it is true or false, has a determined truth value regardless of the context or the state of the world. In simpler terms, it suggests that if a statement about the future is true, then it must be true in a way that is independent of anyone's knowledge or beliefs about it. The notion is closely related to discussions in metaphysics, particularly in the context of free will and moral responsibility.

Lorenzo Valla's "Dialogue on Free Will" (often referred to as "De Voluntate") is a significant philosophical work where Valla engages with the concept of free will, a crucial topic in both philosophy and theology during the Renaissance. The dialogue is structured as a conversation among several characters who explore the nature of free will, its implications for moral responsibility, and its relationship to divine foreknowledge.

The Rubicon Model is a psychological framework developed by German psychologist Heinz Heckhausen and his collaborators. It focuses on the processes involved in decision-making and goal achievement, particularly the transition from motivation to action. The model distinguishes between different phases in this process, highlighting how individuals move from the stage of consideration to the execution of their goals.

Jean Gaston Darboux was a prominent French mathematician known for his contributions in various areas of mathematics, particularly in geometry and calculus. He was born on August 14, 1842, and passed away on February 23, 1917. Darboux is particularly noted for his work in differential geometry and the theory of functions.

Michel Chasles (1793–1880) was a French mathematician known for his contributions to geometry and projective geometry, as well as to the study of conics and other areas of mathematical analysis. He is best known for Chasles' theorem, which pertains to the relationship between geometrical figures and their transforms, particularly in projective geometry. Chasles was also involved in the study of the historical development of mathematics and contributed to various forms of mathematical communication.

Émile Lemoine is a name associated with various individuals and roles, but one notable figure is Émile Lemoine (1816-1883), who was a French mathematician known for his work in the fields of geometry and algebra. In a broader context, Lemoine might refer to various subjects in academia, literature, or other fields, depending on the context.

Antoine André Louis Reynaud is a French figure known primarily for his contributions to the field of mathematics, specifically in the area of research and analysis. However, there may be several individuals with similar names or varying significance.

Here's an overview of notable French mathematicians categorized by century: ### 17th Century - **René Descartes (1596–1650)**: Known for Cartesian geometry and the Cartesian coordinate system. - **Blaise Pascal (1623–1662)**: Contributed to probability theory and projective geometry.

Medieval French mathematicians played a significant role in the development of mathematics during the Middle Ages, particularly from the 12th to the 15th centuries. This period was characterized by the transmission of knowledge from the Islamic world and ancient Greek sources, along with original contributions by European scholars. Some key aspects of medieval French mathematics include: 1. **Transmission of Knowledge:** French mathematicians were instrumental in the translation and dissemination of mathematical texts from Arabic to Latin.

Hélène Frankowska is a notable figure in the field of philosophy, particularly known for her work in the philosophy of language, the philosophy of mind, and epistemology. She has contributed to discussions on issues such as reference, truth, and the nature of belief. Additionally, Frankowska is recognized for her work on topics related to social and feminist philosophy.

Bernadette Perrin-Riou is a prominent French mathematician known for her contributions to the field of mathematics, particularly in the areas of number theory and algebraic geometry. She has made significant advancements in the theory of L-functions, modular forms, and p-adic analysis. Her work often involves deep connections between various mathematical concepts and has garnered international recognition.

Claude Sabbah is a French mathematician known for his contributions to several areas of mathematics, including algebraic geometry, complex analysis, and the theory of D-modules. He is particularly recognized for his work on the theory of perverse sheaves and their applications in various mathematical contexts. Sabbah has made significant contributions to the understanding of singularities and the behavior of differential equations in complex geometry. His research has influenced both theoretical and applied aspects of mathematics.

Monique Jeanblanc is a prominent French statistician known for her contributions to the fields of statistics and biostatistics. She has worked on various topics, including survival analysis, clinical trials, and statistical methods in epidemiology. Jeanblanc is noted for her academic work and publications that have impacted research in these areas.

Henri Dulac is often recognized as a French artist or may refer to various figures associated with that name, but the specific context is unclear without more information.

Jean-Marie Souriau (1910-1997) was a French philosopher best known for his contributions to the philosophy of science and metaphysics. He is recognized for his work on the relationship between time, space, and existence, as well as his philosophical reflections on the nature of reality and human experience. One of his notable contributions is the exploration of the concept of "event" and how it relates to the experience of time and space.

Jean François Niceron (1613–c. 1635) was a French mathematician and an important figure in the field of optics and geometry, particularly known for his work on perspective and the theory of lenses. He is best remembered for his book, "La perspective" (published in 1638), which elaborated on the principles of perspective in art and visual representation.