Analysis and Philosophical Methods

Analysis can be characterized as a thought process in which something is broken down into its parts, traced back to its fundamental principles, transformed or interpreted in terms of logic or some other language or framework, and perhaps more.
Philosophical methods are methods used in philosophical thinking and work.
What methods for philosophical thinking are effective and why? How do you approach a philosophical problem and why?
In this meetup we'll discuss the possible merits and shortcomings of different ways of approaching philosophy. I will also bring with me a short list of philosophical questions so that people can have a tangible problem to refer to or use as an example for different kinds of philosophical thinking.
I may add more information here over the coming days.

The attendee limit might be relaxed. I want everyone to come, but I also want to lower the probability of having difficulty finding seating. Let me know if you have any questions or requests.