This thesis explores the challenges of algorithmic fairness and proposes a novel framework for developing fair algorithmic systems based on philosophical theories of justice. A historical view of the problem is presented, considering the foundation of fairness research in computer systems, related problems in psychometrics, and an elaborated view of the current issues in algorithmic fairness. The research establishes algorithmic fairness as a wicked problem due to the lack of a widely accepted definition, resulting in conflicting mathematical fairness metrics. To address this, the study reframes the discussion around algorithmic justice, which expands the scope of analysis beyond specific decision points and considers the voices of the ones impacted by algorithmic systems. Moreover, the Substantive algorithmic fairness framework is introduced as a means to promote justice in practice and address social hierarchies in algorithmic decision-making. Building upon this framework, the thesis presents a novel analytical approach that connects relational and structural considerations with representational and allocative harms. By using theories of justice, potential reforms can be identified to create fair algorithmic systems. Through experiments and qualitative analysis, the proposed approach is applied to transformer models, revealing biases related to multiple categories and inconsistencies in the model outputs. The study concludes that integrating philosophical theories of justice can lead to fair algorithmic systems that align with societal principles and benefit humanity as a whole, offering new avenues for addressing the wickedness of algorithmic fairness.