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, in hundreds of propositions can be deduced from a set of definitions, postulates, and common notions: all three of which constitute "First Principles".

Aristotle attempts to elucidate some of these principles describing the world itself, rather than mathematics, in those of his writings that have come to be called the Metaphysics.

There have been many attempts in the history of Western metaphysics to elaborate a single set of first principles. Seeing that a thinking person wants to make his or her knowledge hang together and make as much sense as possible, a well-known 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 mathemetical 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.

See also

• Ab initio
• Metaphysics

External links

• Euclid's Elements