The philosophical approach to the study of political theory is one of the oldest and most traditional methods, deeply rooted in the works of ancient Greek thinkers like Plato and Aristotle. This approach is primarily normative and prescriptive, focusing on what ought to be rather than merely what is. It seeks to understand the fundamental nature of political life, the ideal state, justice, liberty, equality, and the moral foundations of political authority.

Key characteristics of the philosophical approach include:

1. Normative and Ethical Focus: It is concerned with values, ideals, and moral principles. Political philosophers ask questions about the good life, the just society, and the ethical responsibilities of rulers and citizens. They aim to establish standards for evaluating political systems and actions.
2. Speculative and Deductive: This approach often involves abstract reasoning and speculation. It starts with fundamental assumptions about human nature, society, and morality, and then deduces conclusions about the best forms of government or political arrangements. It relies heavily on logical argumentation and conceptual analysis.
3. Search for the Ideal: A central goal is to construct models of ideal political systems or principles that can guide political practice. Plato's 'Republic' is a classic example, outlining an ideal state governed by philosopher-kings based on justice.
4. Historical Context: While normative, philosophical inquiry is often deeply embedded in its historical context, responding to the political and social challenges of its time. However, its insights often transcend specific historical moments, offering universal principles.
5. Emphasis on Concepts: It involves rigorous analysis of core political concepts such as power, authority, legitimacy, rights, and obligations, seeking to clarify their meaning and interrelationships.

Methodology: The philosophical approach employs methods such as:

• Conceptual Analysis: Deconstructing and clarifying political concepts.
• Logical Argumentation: Building coherent arguments based on premises and deductions.
• Ethical Reasoning: Applying moral principles to political problems.
• Historical Interpretation: Engaging with the ideas of past thinkers to understand their relevance.

Relevance and Criticisms: Its relevance lies in its ability to provide a moral compass for political action, inspire critical thinking about existing systems, and explore the ultimate goals of political life. It reminds us that politics is not just about power, but also about purpose and values.

However, it has been criticized for being:

• Utopian and Unrealistic: Its focus on ideals can sometimes lead to proposals that are impractical or unattainable in the real world.
• Subjective: Its reliance on values can make it seem less objective or scientific compared to empirical approaches.
• Lack of Empirical Verification: Its conclusions are not typically testable through observation or experimentation.

Despite these criticisms, the philosophical approach remains indispensable for understanding the enduring questions of political life and for providing a normative framework within which political action can be evaluated and guided.