This paper examines the Platonic view based on the Platonic Representation Hypothesis (PRH), which holds that as the design space of self-supervised learning (SSL) expands, all representations converge to the same ideal representation, despite different methods and approaches. This paper synthesizes evidence from Identifiability Theory (IT) to show that PRH can emerge in SSL, but currently IT cannot explain the empirical success of SSL. To bridge this gap between theory and practice, this paper proposes extending IT to a broader theoretical framework, Singular Identifiability Theory (SITh), that encompasses the entire SSL pipeline. SITh can provide deeper insights into the implicit data assumptions of SSL and advance the field toward learning more interpretable and generalizable representations. We present three important directions for future research: 1. the training dynamics and convergence properties of SSL; 2. the impact of finite samples, batch sizes, and data diversity; and 3. the role of inductive bias in architectures, augmentations, initialization schemes, and optimizers.