The definition "Mathematics is a way to settle in the mode, a habit of reasoning" is given by :

Question

Accepted Answer

The statement "Mathematics is a way to settle in the mode, a habit of reasoning" is attributed to John Locke, making Option 1 the correct answer. Here's a detailed explanation supporting this choice:

1. **Justification for Option 1 (Locke):**
   - John Locke was a prominent philosopher known for his work in empiricism and the theory of knowledge. His philosophical approach emphasized the importance of reasoning and the development of habits of thought. Locke believed that education should cultivate the ability to think critically and reason logically, which aligns with the idea of mathematics as a habit of reasoning. His emphasis on rational thought and the development of intellectual habits supports the attribution of this definition to him.

2. **Explanation for why other options are incorrect:**

- **Option 2 (Galileo):**
     - Galileo Galilei was a renowned scientist and mathematician, known for his contributions to physics and astronomy. While he valued mathematics as a tool for scientific inquiry, his focus was more on empirical observation and experimentation rather than defining mathematics as a habit of reasoning in the philosophical sense attributed to Locke.

- **Option 3 (Bruner):**
     - Jerome Bruner was a psychologist known for his work in cognitive psychology and education. Although he emphasized the importance of understanding and reasoning in learning, his contributions were more related to educational psychology and cognitive development rather than providing a philosophical definition of mathematics as a habit of reasoning.

- **Option 4 (Napoleon):**
     - Napoleon Bonaparte, while known for his military and political leadership, did not contribute to the philosophical or educational discourse on mathematics. His interest in mathematics was more practical, related to its applications in military strategy and engineering, rather than defining it as a habit of reasoning.

In conclusion, the attribution of the definition "Mathematics is a way to settle in the mode, a habit of reasoning" to John Locke is consistent with his philosophical emphasis on reasoning and intellectual development, making Option 1 the correct choice.