Project by: Joshua Sapira (11th Grade)
Project Advisor: Sergei Mikhelson
Student(s)’s Advisor(s): Jess Prohias Gardiner

Description of the Project: While this project initially started with the intentions of learning proofs, it has developed more into a project on logic. In this project, I have learned and will continue to learn the basics of the study of logic, and how they relate to proofs.

Final Product (e.g., documents, images, video, audio, poster, display, etc.):

Final Reflection on Learning:

Update on Progress from Weeks 1-3 (include any photos or video if relevant): In these past few weeks, Sergei and I have met twice to discuss. In the first meeting, we went over our goals for the project: what I wanted to achieve and how I wanted to achieve it. We decided to it would be best to start our study of proofs by looking into logics, and the way we went about this was by reading Lewis Carrol’s “The Game of Logic”. I have begun reading it, and while it goes over concepts that are difficult to wrap your mind around, I feel like I’m on my way to getting the hang of it. In our second meeting, we went over the content of the first chapter of “The Game of Logic”. This included the correct use of “some”, “none”, and “all”, as well as syllogisms and fallacies. It has been very interesting so far and I am looking forward to continuing with my project!

Update on Progress from Weeks 4-6 (include any photos or video if relevant): This project has shifted from learning proofs to more of a project about learning logic, which is a fundamental piece of the foundation of proofs. On top of continuing to read Lewis Carrol’s “The Game of Logic”, we have began studying the square of opposition and looking into the logic hexagon. We have also gone more into depth on categorical syllogisms; we have looked at what shapes they take, how to visually represent one, and how they may lead to logical fallacies (another topic we have begun looking at).

Update on Progress from Weeks 7-9 (include any photos or video if relevant): Having met with Sergei for the last time this trimester today, I am very proud of the progress I have made throughout this project. What started as a small interest originating from a book I was reading grew into a genuine interest in logic and its application in mathematics. I have learned to solve problems using matrices and truth tables and have tested my abilities through GRE questions. While this honors project is over, it is definitely not the end of my learning logic and proofs. Sergei and I discussed how we would continue our work in other honors projects next year, and I am very much looking forward to doing so.