Final answer:
An example of something that requires equal or greater formal reality to have objective reality is mathematical truths. These truths hold despite individual thought and are examples of objective realities underpinned by an abstract formal existence.
Step-by-step explanation:
The concept of formal reality versus objective reality can be difficult to comprehend, but it essentially deals with the nature of existence. In the framework of Cartesian philosophy, formal reality pertains to the actual existence of something, whereas objective reality refers to the existence of something as an idea or within the mind. The question of whether there must be equal or greater formal reality to have objective reality can be illustrated by considering the example of a painting. A painting that exists both in the mind of an artist and as a physical artwork has a greater formal reality than a painting that exists only as an idea in the artist's mind.
When addressing the provided options — dreams, mathematical truths, personal opinions, and illusions — mathematical truths are the best example of something that requires equal or greater formal reality to have objective reality. Mathematical truths are abstract concepts that exist as formal realities regardless of whether any individual has thought of them. They are objective in the sense that they hold true irrespective of human opinion or knowledge. Therefore, the formal reality of the abstract concepts that underpin mathematical truths ensures their objective reality.