At Intercom, product principles are centered around starting with the problem to achieve better solutions. This principle is crucial as it ensures that companies focus on real customer problems and avoid building solutions without a clear understanding of the issue. The company values principles over process, prioritizing problem definition and understanding over immediate progress or glamor. They recognize that people are wired to think in solutions, but emphasize the importance of taking time to break down and analyze customer problems. Intercom's engineering team uses a system view to understand how their product works or doesn't work together, and involves multiple stakeholders in researching and solving problems. By starting with the problem, the company aims to create more thoughtful and suitable solutions that meet customer needs.