In mathematics, a formal system is loosely the concept of having a relatively small set of underlying assumptions - or axioms - from which one deduces a large body of theorems that follow logically from the assumptions. For example, in Einsteins special relativity, that the speed of light is constant is one of his axioms from which many testable conclusions are drawn.

Thinking in terms of a formal system where one carefully delineates axioms and deductions is an excellent heuristic because it allows us to be clear about the assumptions in underlying statements that are possibly quite far away from the initial axioms. The interrelationship of statements is often lost outside of the context of a formal system. Not all statements have equal weight (a prediction about the orbit of mercury derived from general relativity is far less profound than the accepted axioms of general relativity), and delineating them in this way allows us to see the larger structure and important truths.

Given the mathematical motivation, let us apply this idea to politics. This can actually be applied in innumerable places, but perhaps one of the most interesting ones is by equating political values with the axioms of a formal system. So one could put "liberty" or "equality" as a fundamental value, or axiom, in a political system. Extending the analogy, policies that one advocates for can be deduced as following from the specific set of axiomatic values one has.

Too often in politics, we are presented with a wide range of specific policies that at first glance may seem disjoint and disparate. Upon closer inspection, there is often considerable interconnectedness of ideas where many policies stem from a small set of values. For instance, the highly partisan disbelief in global warming may be partially deduced from a more sweeping axiom about anti-governmental sentiment in the right given how currently proposed solutions to global warming are largely governmental in nature.

Democratic processes are particularly apt at determining the aggregate values of a society. What is the correct balance between freedom and equality (in as far as these are contradictory values)? This is a question we must answer democratically as a society. Democratic processes are less apt at determining the policies to optimize the value mix. Indeed, I think that the public is often very poor at analyzing optimal policies which may require specific and detailed economic, scientific or other knowledge. It is easy to agree on the value of preserving our planet for our children, it is quite a bit harder to analyze the data to determine the optimal course of action to achieve this.

For anyone interested in analyzing and advocating for policies, this is where we can come in. We can accept the axioms of the formal system - the democratically determined values of society - and attempt to deduce as objectively and logically as possible appropriate policies.

This formal system analogy can be considered both descriptively and normatively. Descriptively, it is a useful tool for analyzing political claims and their interdependencies and roots as I have mentioned. I am much more wary with the normative sense, however, since I tend to shy away from ideological standpoints (such as the one axiom ideology of libertarianism which accepts that freedom is the ultimate value). Too often the complexity of politics invalidates the creation of a simple axiom list of values instead necessitating a more pragmatic and relativist approach. At best we can use this idea in the normative sense to create a general operating framework of democratically determined values. Nonetheless, the ability to describe politics in this sense remains an excellent heuristic.

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