Final answer:
The question appears to be asking for the four degrees of a specific philosopher's brotherhood, but the provided information does not conclusively point to a known brotherhood with four degrees. References are made to both Plato's and Mencius's philosophical ideas and to a historical monastic vow, but they do not clarify the four degrees in question.
Step-by-step explanation:
The question appears to revolve around a historical or philosophical context, and it may refer to degrees of a philosophical brotherhood or society which is not explicitly named in the provided text. The reference to Plato and Socrates within the context of 'The Republic' suggests a philosophical framework, while the mention of the 'order of swordbearers' relates to a historical monk's vow. However, without specific context, it is challenging to name the four degrees of this philosopher's brotherhood with confidence as the provided information does not conclusively tie to a single well-known brotherhood with four distinct degrees. Instead, we see references to three tiers of society in Plato's notion, as well as the three-fold monk's vow noted in the historical context of swordbearers.In the philosophical context, Plato describes three parts of the soul and a three-tiered class structure in society within 'The Republic.' Similarly, the historical 'order of swordbearers' took a three-fold vow. We also have a connection to the five relationships mentioned by Mencius, and while this relates to classical Chinese philosophy, it does not align with the concept of a brotherhood's degrees.If the student is referring to a specific historical or philosophical brotherhood with four degrees, further information or clarification from the student would be needed to provide a factually accurate response.