First principles Did You Mean First?

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First Principles is also the title of a work by Herbert Spencer.

In a formal logical system, that is, a set of propositions that are consistent with one another, it is probable that some of the statements can be deduced from one another. For example, in the syllogism, "All men are mortal; Socrates is a man; Socrates is mortal" the last claim can be deduced from the former two.

A first principle is one that cannot be deduced from any other. The classic example is that of Euclid's geometry; its hundreds of propositions can be deduced from a set of definitions, postulates, and common notions: all three of which constitute "First Principles".

Aristotle, author of the earliest surviving text on logic, formulated a principle that later achieved the historical distinction of being called the first principle as a proper name. It occurs in those of his writings that have come to be called the Metaphysics. The principle in Greek transliteration is (Meta ta physica, 1005b):

"to gar hama hyparchein te kai me hyparchein adynaton to auto kai kata to auto."

and in English translation:

"For the same (characteristic) simultaneously to belong and not belong to the same (object) in the same (way) is impossible."

This principle is the first expression of consistency in western thought. Any defining and reasoning in any language on any topic assumes it a priori. It cannot be doubted, as all doubting is based on inconsistency, which assumes consistency a priori.

There have been many attempts in the history of Western metaphysics to elaborate a single set of first principles. If a thinking person wants to make his or her knowledge internally consistent and make as much sense as possible, a set of first principles is necessary.

Some thinkers, especially in the 20th century, have savaged the notion that true first principles are available. In his Principia Mathematica, Bertrand Russell attempted to subsume all mathematical truths under the first principles of formal logic; however, Kurt Godel launched a savage attack not only on Russell's system but on the very possibility of such a system, contending that any logical system that was consistent could not be complete, and any system that was complete could not be entirely self-consistent.

Likewise, Heidegger attacked something perhaps underlying the notion of first principle, that is, the need to represent the world, and the dualism that that task, in his view, entails.

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Euclid's Elements

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