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EspañolFIRST PRINCIPLES
:'''First Principles' is also the title of a work by Herbert Spencer.''
In philosophy, 'first principles' are a set of basic, foundational propositions or assumptions that cannot be deduced from any other proposition or assumption. In mathematics, the equivalent concept is called axioms or postulates.
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 (see Euclid's Elements) 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, and its transliteration, is (''Meta ta physica'', 1005b):
:"τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό"
:"to gar auto 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.
In physics, a calculation is said to be ''from first principles'', or ab initio, if it starts directly at the level of established laws of physics and does not make assumptions such as model and fitting parameters.
For example, calculation or simulation of stereoelectronics using Schrödinger's equation directly is an ''ab initio'' approach, since the equation is just a definition of energy on the quantum level.
★ Axiom
★ Ab initio
★ Metaphysics
★ Euclid's Elements
In philosophy, 'first principles' are a set of basic, foundational propositions or assumptions that cannot be deduced from any other proposition or assumption. In mathematics, the equivalent concept is called axioms or postulates.
| Contents |
| First principles in formal logic |
| Aristotle's contribution |
| In physics |
| See also |
| External links |
First principles in formal logic
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 (see Euclid's Elements) 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's contribution
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, and its transliteration, is (''Meta ta physica'', 1005b):
:"τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό"
:"to gar auto 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.
In physics
In physics, a calculation is said to be ''from first principles'', or ab initio, if it starts directly at the level of established laws of physics and does not make assumptions such as model and fitting parameters.
For example, calculation or simulation of stereoelectronics using Schrödinger's equation directly is an ''ab initio'' approach, since the equation is just a definition of energy on the quantum level.
See also
★ Axiom
★ Ab initio
★ Metaphysics
External links
★ Euclid's Elements
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