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. In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). ...

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". Euclid of Alexandria (Greek: ) (circa 365–275 BC) was a Greek mathematician, now known as the father of geometry. He was probably alive during the reign of Ptolemy I, (306-233 B.C.E). ...

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. Aristotle (sculpture) Aristotle (Greek: Αριστοτέλης Aristotelēs) (384 BC – March 7, 322 BC) was an ancient Greek philosopher. ... Metaphysics (Greek words meta = after/beyond and physics = nature) is a branch of philosophy concerned with the study of first principles and being (ontology). ...

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. Metaphysics (Greek words meta = after/beyond and physics = nature) is a branch of philosophy concerned with the study of first principles and being (ontology). ...

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. For Isaac Newtons 1687 book containing basic laws of physics, see Philosophiae Naturalis Principia Mathematica The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Bertrand Russell and Alfred North Whitehead and published in 1910-1913. ... Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell (May 18, 1872–February 2, 1970) was an influential mathematician, philosopher, and logician of the modern age, working mostly in the 20th century. ... Logic (from ancient Greek λόγος (logos), meaning reason) is the study of arguments. ... Kurt Gödel Kurt Gödel [ kurt gøːdl ], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics, whose biography lists quite a few nations, although he is usually associated with Austria. ...

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. Martin Heidegger Martin Heidegger (September 26, 1889 – May 26, 1976) was a German philosopher. ... The term dualism is the state of being dual, or having a twofold division. ...

See also

• Ab initio
• Metaphysics

The Latin term ab initio means from the beginning and is used in several contexts: when describing literature: told from the beginning as opposed to in medias res (meaning starting in the middle of the story). ... Metaphysics (Greek words meta = after/beyond and physics = nature) is a branch of philosophy concerned with the study of first principles and being (ontology). ...

External links

• Euclid's Elements (http://aleph0.clarku.edu/~djoyce/java/elements/elements.html)