The difference between realism and rationalism, according to the provided reference, lies in their focus: realism concerns the nature of the objects being studied, while rationalism concerns the method of acquiring knowledge about them.
In the specific context provided, particularly concerning mathematics and other formal sciences, the terms realism and rationalism address distinct aspects of knowledge and existence.
Here's a breakdown based on the reference:
Realism Explained
- According to the reference, realism here means that the objects of study in mathematics and other formal sciences are abstract.
- This perspective holds that mathematical entities (like numbers, sets, functions) and concepts in formal logic exist independently of human thought, though they do not exist in the physical world. They have a reality of their own in an abstract realm.
- Think of it as asserting the existence and nature of the things being studied in these fields.
Rationalism Explained
- The reference states that rationalism means that our knowledge of them [the abstract objects] is not empirical.
- This position argues that our understanding and knowledge of these abstract objects and the truths within formal sciences are not derived from sensory experience or observation (which would be empirical).
- Instead, knowledge is obtained through reason, intuition, or logical deduction.
- This focuses on the method by which we come to know these abstract realities.
Comparing Realism and Rationalism (Based on Reference)
Based on the definitions provided in the reference, we can highlight the difference:
| Feature | Realism (in this context) | Rationalism (in this context) |
|---|---|---|
| Focus | The nature and existence of study objects | The method of acquiring knowledge about study objects |
| Core Idea | Objects (in formal sciences) are abstract | Knowledge (of these objects) is not empirical |
| What it addresses | What is the object like? (Its nature) | How do we know about the object? (Method of knowledge) |
The reference notes that Katz uses this combined position (realism about abstract objects + rationalism about non-empirical knowledge) to address challenges to realism. This suggests that believing abstract objects exist independently (realism) might necessitate a non-empirical way of knowing about them (rationalism), as they aren't accessible through the senses.
