Final answer:
Glaucon's perspective on geometry, as reflected in Plato's 'The Republic,' aligns with the view that geometry should be used for developing abstract reasoning and understanding the Forms, rather than for practical or artistic purposes.
Step-by-step explanation:
In what ways does Glaucon think geometry should be used? Glaucon, as described in Plato's 'The Republic,' indirectly supports the idea that geometry should be used not as a practical tool for everyday activities, but rather for the development of abstract reasoning and the study of forms, which closely resembles option B: For the development of abstract reasoning and the study of forms. While 'The Republic' primarily discusses philosophical ideas and the concept of the Forms, and does not explicitly cover Glaucon's views on the use of geometry, it is heavily implied through the dialogue regarding the philosophical teachings of Socrates and Plato's own beliefs about the role of the philosopher. These teachings support the use of geometry as a tool to understand the unchangeable truths about the world, expressed through the concept of Forms, and not merely for practical or artistic purposes.
Plato, through his dialogues, makes it clear that he believes the senses are unreliable and that only through the intellect can one apprehend the true Forms of things. To Plato, abstract concepts such as mathematics play a crucial role in this discovery process. Therefore, the study of geometry, by extension, serves as a means to comprehend the immaterial realm of forms, which in Plato's viewpoint, holds the ultimate truth.
Glaucon's agreement with the idea that people can be misled by their senses, as in the allegory of the cave, aligns with the belief that knowledge should be sought beyond sensory experiences, and in the case of geometry, beyond simple visual and tactile interaction with shapes and objects.