Are contradictions meaningful?

Introduction

In this essay I answer the question in the title with a very confident “Yes”, I give multiple arguments for this answer. For the purposes of this essay a pluralistic proposition theory of truth carriers with sentences as secondary truth carriers is assumed. The background and the reason for writing this essay is that many people deny that they understand sentences that are contradictory. They deny to understand sentences such as: “Emil is sitting in his favorite char and Emil is not sitting in his favorite chair.” Or the contracted version: “Emil both is and is not sitting in his favorite chair.” They claim that:

P1. For any sentence, if that sentence is contradictory, then it is meaningless.

But still the very same people believe that such sentences are false. This is inconsistent. My claim is that P1 is false and that P2 and P3 are true:

P2. For any sentence, if that sentence is contradictory, then it is meaningful.

P3. There is a sentence such that it is contradictory and meaningful.

For each argument used, there is a proof of that argument's validity in the appendix. Are contradictions meaningful