Building and expanding on principles of statistics, machine learning, and the sciences, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework is comprised of both a workflow and documentation and aims to provide responsible, reliable, reproducible, and transparent results across the entire data science life cycle. The PCS workflow uses predictability as a reality check and considers the importance of computation in data collection/storage and algorithm design. It augments predictability and computability with an overarching stability principle for the data science life cycle. Stability expands on statistical uncertainty considerations to assess how human judgment calls impact data results through data and model/algorithm perturbations. We develop inference procedures that build on PCS, namely PCS perturbation intervals and PCS hypothesis testing, to investigate the stability of data results relative to problem formulation, data cleaning, modeling decisions, and interpretations. Moreover, we propose PCS documentation based on R Markdown or Jupyter Notebook, with publicly available, reproducible codes and narratives to back up human choices made throughout an analysis. The PCS framework will be illustrated through examples in social science and a case study from neuroscience for movie reconstruction using brain signals.