# First principles

In mathematics, first principles are referred to as axioms or postulates.

In philosophy, a first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption.

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 fitting parameters.

## 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 first 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 types constitute first principles.

## Aristotle's contribution

Terence Irwin writes:

When Aristotle explains in general terms what he tries to do in his philosophical works, he says he is looking for "first principles" (or "origins"; archai):
In every systematic inquiry (methodos) where there are first principles, or causes, or elements, knowledge and science result from acquiring knowledge of these; for we think we know something just in case we acquire knowledge of the primary causes, the primary first principles, all the way to the elements. It is clear, then, that in the science of nature as elsewhere, we should try first to determine questions about the first principles. The naturally proper direction of our road is from things better known and clearer to us, to things that are clearer and better known by nature; for the things known to us are not the same as the things known unconditionally (haplôs). Hence it is necessary for us to progress, following this procedure, from the things that are less clear by nature, but clearer to us, towards things that are clearer and better known by nature. (Phys. 184a10–21)

The connection between knowledge and first principles is not axiomatic as expressed in Aristotle's account of a first principle (in one sense) as "the first basis from which a thing is known" (Met. 1013a14–15). The search for first principles is not peculiar to philosophy; philosophy shares this aim with biological, meteorological, and historical inquiries, among others. But Aristotle's references to first principles in this opening passage of the Physics and at the start of other philosophical inquiries imply that it is a primary task of philosophy.[1]

## 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 I think, therefore I am, or Cogito ergo sum.

Descartes describes the concept of a first principle in the follow excerpt from the preface to the Principles of Philosophy (1644):

I should have desired, in the first place, to explain in it what philosophy is, by commencing with the most common matters, as, for example, that the word philosophy signifies the study of wisdom, and that by wisdom is to be understood not merely prudence in the management of affairs, but a perfect knowledge of all that man can know, as well for the conduct of his life as for the preservation of his health and the discovery of all the arts, and that knowledge to subserve these ends must necessarily be deduced from first causes; so that in order to study the acquisition of it (which is properly called [284] philosophizing), we must commence with the investigation of those first causes which are called Principles. Now these principles must possess two conditions: in the first place, they must be so clear and evident that the human mind, when it attentively considers them, cannot doubt of their truth; in the second place, the knowledge of other things must be so dependent on them as that though the principles themselves may indeed be known apart from what depends on them, the latter cannot nevertheless be known apart from the former. It will accordingly be necessary thereafter to endeavor so to deduce from those principles the knowledge of the things that depend on them, as that there may be nothing in the whole series of deductions which is not perfectly manifest.[2]

## 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 model and fitting parameters.

For example, calculation of electronic structure using Schrödinger's equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.

## Notes

1. ^ Irwin, Terence. Aristotle's First Principles. Oxford: Oxford University Press. ISBN 0-19-824290-5 [Amazon-US | Amazon-UK].
2. ^ VOL I, Principles, Preface to the French edition. Author’s letter to the translator of the book which may here serve as a preface, p. 181