In philosophy and science, a first principle is a basic proposition or axiom that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause[Vernon Bourke, Ethics, (New York: The Macmillan Co., 1966), 14.]
In mathematics and formal logic, first principles are referred to as or postulates. In physics and other sciences, theoretical work is said to be from first principles, or ab initio, if it starts directly at the level of established science and does not make assumptions such as empirical model and parameter fitting. "First principles thinking" consists of decomposing things down to the fundamental in the given arena, before reasoning up by asking which ones are relevant to the question at hand, then cross referencing conclusions based on chosen axioms and making sure conclusions do not violate any fundamental laws. include counterintuitive concepts with iteration.
In formal logic
In a formal
logical system—that is, a set of
that are consistent with one another—it is possible that some of the statements can be deduced from other statements. For example, in the
syllogism,
"All men are mortal; Socrates is a man; Socrates is mortal" the last claim can be deduced from the first two.
A first principle is an axiom that cannot be deduced from any other within that system. The classic example is that of Euclid's Elements; its hundreds of geometric propositions can be deduced from a set of definitions, postulates, and : all three types constitute first principles.
Philosophy
In philosophy, "first principles" are from
first cause[ attitudes commonly referred to as a priori terms and arguments, which are contrasted to a posteriori terms, reasoning, or arguments, in that the former are simply assumed and exist prior to the reasoning process, and the latter are deduced or inferred after the initial reasoning process. First principles are generally treated in the realm of philosophy known as epistemology but are an important factor in any Metaphysics speculation.
]
In philosophy, "first principles" are often somewhat synonymous with a priori, datum, and axiomatic reasoning.
Ancient Greek philosophy
In ancient Greek philosophy, a first principle from which other principles are derived is called an arche[ἐξ ἀρχῆς λόγος:] and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", or "authorities".[in plural: ἀρχαί] The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophy and Plato before being formalized as a part of metaphysics by Aristotle. Arche,[ἐξ ἀρχῆς] from the beginning, οr the original argument, "command".[ ἀρχή, A Greek-English Lexicon] The first principle or element corresponds to the "ultimate underlying substance" and "ultimate indemonstrable principle".[Peters Lexicon:1967:23]
Mythical cosmogonies
The heritage of Greek mythology already embodied the desire to articulate reality as a whole and this universalizing impulse was fundamental for the first projects of speculative theorizing. It appears that the order of "being" was first imaginatively visualized before it was abstractly thought.[ p.28,42]
In the mythological cosmogonies of the Near East, the universe is formless and empty and the only existing thing prior to creation was the water abyss. In the creation story, Enuma Elish, the primordial world is described as a "watery chaos" from which everything else appeared.
This watery chaos has similarities in the cosmogony of the Greek mythographer Pherecydes of Syros.
In the mythical
Greece cosmogony of
Hesiod (8th to 7th century BC), the origin of the world is Chaos, considered as a divine primordial condition, from which everything else appeared. In the creation "chaos" is a gaping-void, but later the word is used to describe the space between the Earth and the sky, after their separation. "Chaos" may mean infinite space, or a formless matter which can be differentiated.
[This is described as a large windy-gap, almost unlimited (abyss) where are the roots and the ends of the Earth, sky, sea and Tartarus: online The Theogony of Hesiod. Translation H.G.Evelyn White (1914): 116, 736-744] The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality.
[ p 83] The conception of the "divine" as an origin influenced the first Greek philosophers.
[The phrase: "Divine is that which had no beginning, neither end" is attributed to Thales] In the
Orphic cosmogony, the unaging
Chronos produced Aether and Chaos and made in divine Aether a silvery egg, from which everything else appeared.
[ p.24]
Ionian school
The earliest Pre-Socratic philosophers, the Ionian material monists, sought to explain all of nature (
physis) in terms of one unifying
arche. Among the material monists were the three Milesian philosophers:
Thales, who believed that everything was composed of water;
Anaximander, who believed it was
apeiron; and Anaximenes, who believed it was air. This is considered as a permanent substance or either one or more which is conserved in the generation of rest of it. From this all things first come to be and into this they are resolved in a final state. This source of entity is always preserved.
[Aristotle, Metaphysics A, 983, b6ff).] Although their theories were primitive, these philosophers were the first to give an explanation of the physical world without referencing the supernatural; this opened the way for much of modern
science (and philosophy), which has the same goal of explaining the world without dependence on the supernatural.
[Lindberg, David C., The Beginnings of Western Science (University of Chicago Press, 2010), pp. 28–9.]
Thales of Miletus (7th to 6th century BC), known as "the father of philosophy",[DK] and considered it as a substance that contains in it motion and change. His theory was supported by the observation of moisture throughout the world and coincided with his theory that the Earth floated on water. His ideas were influenced by the Near-Eastern mythological cosmogony and probably by the Homeric statement that the surrounding Oceanus (ocean) is the source of all springs and rivers.
p 89, 93, 94
Anaximander argued that water could not be the arche, because it could not give rise to its opposite, fire. Anaximander claimed that none of the elements (earth, fire, air, water) could be arche for the same reason. Instead, he proposed the existence of the apeiron, an indefinite substance from which all things are born and to which all things will return.[Simplicius, Comments on Aristotle's Physics (24, 13).DK][Curd, Patricia, A Presocratics Reader: Selected Fragments and Testimonia (Hackett Publishing, 1996), pp. 9, 11 & 14.] Apeiron (endless or boundless) is something completely indefinite; and Anaximander was probably influenced by the original chaos of Hesiod (yawning abyss).
Anaximander was the first philosopher to use arche for that which writers from Aristotle onwards called "the substratum" (Simplicius Phys. 150, 22).
p 55, 77 He probably intended it to mean primarily "indefinite in kind" but assumed it also to be "of unlimited extent and duration".
[ p 110] The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality and Anaximander's description was in terms appropriate to this conception. This
arche is called "eternal and ageless". (Hippolitus I,6, I;DK B2)
[ p 83]
Anaximenes, Anaximander's pupil, advanced yet another theory. He returns to the elemental theory, but this time posits air, rather than water, as the arche and ascribes to it divine attributes. He was the first recorded philosopher who provided a theory of change and supported it with observation. Using two contrary processes of rarefaction and condensation (thinning or thickening), he explains how air is part of a series of changes. Rarefied air becomes fire, condensed it becomes first wind, then cloud, water, earth, and stone in order.[Daniel W. Graham, The Internet Encyclopedia of Philosophy. Anaximenes.]
p 144 The
arche is technically what underlies all of reality/appearances.
Aristotle
Terence Irwin writes:
Modern philosophy
Descartes
Profoundly influenced by
Euclid,
Descartes was a
rationalist who invented the
foundationalist system of philosophy. He used the
method of doubt, now called
Cartesian doubt, to systematically doubt everything he could possibly doubt until he was left with what he saw as purely indubitable truths. Using these self-evident propositions as his axioms, or foundations, he went on to deduce his entire body of knowledge from them. The foundations are also called
a priori truths. His most famous proposition is "Je pense, donc je suis" (
I think, therefore I am, or
Cogito ergo sum), which he indicated in his Discourse on the Method was "the first principle of the philosophy of which I was in search."
Descartes describes the concept of a first principle in the following excerpt from the preface to the Principles of Philosophy (1644):
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 empirical
Physical model and
Curve fitting parameters.
For example, calculation of electronic structure using the Schrödinger equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.
See also
Notes
Further reading
