First principles thinking, which is sometimes called reasoning from first principles, is one of the most effective strategies you can employ for breaking down complicated problems and generating original solutions. It also might be the single best approach to learn how to think for yourself.

The first principles approach has been used by many great thinkers .. especially:

 ELON MUSK

and also including inventor Johannes Gutenberg, military strategist John Boyd, and the ancient philosopher Aristotle, but no one embodies the philosophy of first principles thinking more effectively than entrepreneur Elon Musk.

In 2002, Musk began his quest to send the first rocket to Mars—an idea that would eventually become the aerospace company SpaceX.

He ran into a major challenge right off the bat. After visiting a number of aerospace manufacturers around the world, Musk discovered the cost of purchasing a rocket was astronomical—up to $65 million. Given the high price, he began to rethink the problem.

“I tend to approach things from a physics framework,” Musk said in an interview. “Physics teaches you to reason from first principles rather than by analogy. So I said, okay, let’s look at the first principles. What is a rocket made of? Aerospace-grade aluminum alloys, plus some titanium, copper, and carbon fiber. Then I asked, what is the value of those materials on the commodity market? It turned out that the materials cost of a rocket was around two percent of the typical price.”

Instead of buying a finished rocket for tens of millions, Musk decided to create his own company, purchase the raw materials for cheap, and build the rockets himself. SpaceX was born.

Within a few years, SpaceX had cut the price of launching a rocket by nearly 10x while still making a profit. Musk used first principles thinking to break the situation down to the fundamentals, bypass the high prices of the aerospace industry, and create a more effective solution.

First principles thinking is the act of boiling a process down to the fundamental parts that you know are true and building up from there. Let’s discuss how you can utilize first principles thinking in your life and work.

Defining First Principles Thinking

A first principle is a basic assumption that cannot be deduced any further. Over two thousand years ago, Aristotle defined a first principle as “the first basis from which a thing is known.”

First principles thinking is a fancy way of saying “think like a scientist.” Scientists don’t assume anything. They start with questions like, What are we absolutely sure is true? What has been proven?

In theory, first principles thinking requires you to dig deeper and deeper until you are left with only the foundational truths of a situation. Rene Descartes, the French philosopher and scientist, embraced this approach with a method now called Cartesian Doubt in which he would “systematically doubt everything he could possibly doubt until he was left with what he saw as purely indubitable truths.”

In practice, you don’t have to simplify every problem down to the atomic level to get the benefits of first principles thinking. You just need to go one or two levels deeper than most people. Different solutions present themselves at different layers of abstraction. John Boyd, the famous fighter pilot and military strategist, created the following thought experiment which showcases how to use first principles thinking in a practical way.

Imagine you have three things:

• A motorboat with a skier behind it
• A military tank
• A bicycle

Now, let’s break these items down into their constituent parts:

• Motorboat: motor, the hull of a boat, and a pair of skis.
• Tank: metal treads, steel armor plates, and a gun.
• Bicycle: handlebars, wheels, gears, and a seat.

What can you create from these individual parts? One option is to make a snowmobile by combining the handlebars and seat from the bike, the metal treads from the tank, and the motor and skis from the boat.

This is the process of first principles thinking in a nutshell. It is a cycle of breaking a situation down into the core pieces and then putting them all back together in a more effective way. Deconstruct then reconstruct.

How First Principles Drive Innovation

The snowmobile example also highlights another hallmark of first principles thinking, which is the combination of ideas from seemingly unrelated fields. A tank and a bicycle appear to have nothing in common, but pieces of a tank and a bicycle can be combined to develop innovations like a snowmobile.

Many of the most groundbreaking ideas in history have been a result of boiling things down to the first principles and then substituting a more effective solution for one of the key parts.

For instance, Johannes Gutenberg combined the technology of a screw press—a device used for making wine—with movable type, paper, and ink to create the printing press. Movable type had been used for centuries, but Gutenberg was the first person to consider the constituent parts of the process and adapt technology from an entirely different field to make printing far more efficient. The result was a world-changing innovation and the widespread distribution of information for the first time in history.

The best solution is not where everyone is already looking.

First principles thinking helps you to cobble together information from different disciplines to create new ideas and innovations. You start by getting to the facts. Once you have a foundation of facts, you can make a plan to improve each little piece. This process naturally leads to exploring widely for better substitutes.

The Challenge of Reasoning From First Principles

First principles thinking can be easy to describe, but quite difficult to practice. One of the primary obstacles to first principles thinking is our tendency to optimize form rather than function. The story of the suitcase provides a perfect example.

In ancient Rome, soldiers used leather messenger bags and satchels to carry food while riding across the countryside. At the same time, the Romans had many vehicles with wheels like chariots, carriages, and wagons. And yet, for thousands of years, nobody thought to combine the bag and the wheel. The first rolling suitcase wasn’t invented until 1970 when Bernard Sadow was hauling his luggage through an airport and saw a worker rolling a heavy machine on a wheeled skid.

Throughout the 1800s and 1900s, leather bags were specialized for particular uses—backpacks for school, rucksacks for hiking, suitcases for travel. Zippers were added to bags in 1938. Nylon backpacks were first sold in 1967. Despite these improvements, the form of the bag remained largely the same. Innovators spent all of their time making slight iterations on the same theme.

What looks like innovation is often an iteration of previous forms rather than an improvement of the core function. While everyone else was focused on how to build a better bag (form), Sadow considered how to store and move things more efficiently (function).

How to Think for Yourself

The human tendency for imitation is a common roadblock to first principles thinking. When most people envision the future, they project the current form forward rather than projecting the function forward and abandoning the form.

For instance, when criticizing technological progress some people ask, “Where are the flying cars?”

Here’s the thing: We have flying cars. They’re called airplanes. People who ask this question are so focused on form (a flying object that looks like a car) that they overlook the function (transportation by flight). This is what Elon Musk is referring to when he says that people often “live life by analogy.”

Be wary of the ideas you inherit. Old conventions and previous forms are often accepted without question and, once accepted, they set a boundary around creativity.

This difference is one of the key distinctions between continuous improvement and first principles thinking. Continuous improvement tends to occur within the boundary set by the original vision. By comparison, first principles thinking requires you to abandon your allegiance to previous forms and put the function front and center. What are you trying to accomplish? What is the functional outcome you are looking to achieve?

Optimize the function. Ignore the form. This is how you learn to think for yourself.

The Power of First Principles

Ironically, perhaps the best way to develop cutting-edge ideas is to start by breaking things down to the fundamentals. Even if you aren’t trying to develop innovative ideas, understanding the first principles of your field is a smart use of your time. Without a firm grasp of the basics, there is little chance of mastering the details that make the difference at elite levels of competition.

Every innovation, including the most groundbreaking ones, requires a long period of iteration and improvement. The company at the beginning of this article, SpaceX, ran many simulations, made thousands of adjustments, and required multiple trials before they figured out how to build an affordable and reusable rocket.

First principles thinking does not remove the need for continuous improvement, but it does alter the direction of improvement. Without reasoning by first principles, you spend your time making small improvements to a bicycle rather than a snowmobile. First principles thinking sets you on a different trajectory.

If you want to enhance an existing process or belief, continuous improvement is a great option. If you want to learn how to think for yourself, reasoning from first principles is one of the best ways to do it.

In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause^[1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.^[2]

In mathematics and formal logic, first principles are referred to as axioms 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 axioms 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. Physicistsinclude counterintuitive concepts with reiteration.

In a formal logical system, that is, a set of propositions 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 primitive notions: all three types constitute first principles.

In philosophy, "first principles" are from first cause^[1] 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 metaphysical speculation.

In philosophy, "first principles" are often somewhat synonymous with a priori, datum, and axiomatic reasoning.

In Ancient Greek philosophy, a first principle from which other principles are derived is called an arche^{[note 1]} and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", "authorities"^{[note 2]} The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophyand Plato before being formalized as a part of metaphysics by Aristotle. Arche^{[note 3]} sometimes also transcribed as arkhé) is an Ancient Greek word with primary senses "beginning", "origin" or "source of action":^{[note 4]} from the beginning, οr the original argument, "command".^[3] The first principle or element corresponds to the "ultimate underlying substance" and "ultimate indemonstrable principle".^[4]

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.^[5]

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 Babylonian creation story, Enuma Elish, the primordial world is described as a "watery chaos" from which everything else appeared.^[6] This watery chaos has similarities in the cosmogony of the Greek mythographer Pherecydes of Syros.^[7]In the mythical Greek 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.^[8] The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality.^[9] The conception of the "divine" as an origin influenced the first Greek philosophers.^[10] In the Orphic cosmogony, the unaging Chronos produced Aether and Chaos and made in divine Aether a silvery egg, from which everything else appeared.^[11]

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.^[12] 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.^[13]

Thales of Miletus (7th to 6th century BC), known as "the father of philosophy",^[14] claimed that the first principle of all things is water,^[15] 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.^[16]

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.^[17][18] 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 that used arche for that which writers from Aristotle onwards called "the substratum" (Simplicius Phys. 150, 22).^[19] He probably intended it to mean primarily "indefinite in kind" but assumed it also to be "of unlimited extent and duration".^[20] 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)^[21]

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.^[22][23] The arche is technically what underlies all of reality/appearances.

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 that are 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). For Aristotle, the arche is the condition necessary for the existence of something, the basis for what he calls "first philosophy" or metaphysics.^[24] 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.^[25]

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):

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 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.^[26]

This section needs expansion. You can help by adding to it.  (July 2023)

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 the Schrödinger equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.

In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause^[1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.^[2]

In mathematics and formal logic, first principles are referred to as axioms 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 axioms 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. Physicistsinclude counterintuitive concepts with reiteration.

In a formal logical system, that is, a set of propositions 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 primitive notions: all three types constitute first principles.

In philosophy, "first principles" are from first cause^[1] 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 metaphysical speculation.

In philosophy, "first principles" are often somewhat synonymous with a priori, datum, and axiomatic reasoning.

In Ancient Greek philosophy, a first principle from which other principles are derived is called an arche^{[note 1]} and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", "authorities"^{[note 2]} The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophyand Plato before being formalized as a part of metaphysics by Aristotle. Arche^{[note 3]} sometimes also transcribed as arkhé) is an Ancient Greek word with primary senses "beginning", "origin" or "source of action":^{[note 4]} from the beginning, οr the original argument, "command".^[3] The first principle or element corresponds to the "ultimate underlying substance" and "ultimate indemonstrable principle".^[4]

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.^[5]

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 Babylonian creation story, Enuma Elish, the primordial world is described as a "watery chaos" from which everything else appeared.^[6] This watery chaos has similarities in the cosmogony of the Greek mythographer Pherecydes of Syros.^[7]In the mythical Greek 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.^[8] The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality.^[9] The conception of the "divine" as an origin influenced the first Greek philosophers.^[10] In the Orphic cosmogony, the unaging Chronos produced Aether and Chaos and made in divine Aether a silvery egg, from which everything else appeared.^[11]

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.^[12] 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.^[13]

Thales of Miletus (7th to 6th century BC), known as "the father of philosophy",^[14] claimed that the first principle of all things is water,^[15] 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.^[16]

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.^[17][18] 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 that used arche for that which writers from Aristotle onwards called "the substratum" (Simplicius Phys. 150, 22).^[19] He probably intended it to mean primarily "indefinite in kind" but assumed it also to be "of unlimited extent and duration".^[20] 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)^[21]

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.^[22][23] The arche is technically what underlies all of reality/appearances.

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 that are 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). For Aristotle, the arche is the condition necessary for the existence of something, the basis for what he calls "first philosophy" or metaphysics.^[24] 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.^[25]

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):

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 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.^[26]

This section needs expansion. You can help by adding to it.  (July 2023)

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 the Schrödinger equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach. philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause^[1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.^[2]

In mathematics and formal logic, first principles are referred to as axioms 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 axioms 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. Physicistsinclude counterintuitive concepts with reiteration.

In a formal logical system, that is, a set of propositions 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 primitive notions: all three types constitute first principles.

In philosophy, "first principles" are from first cause^[1] 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 metaphysical speculation.

In philosophy, "first principles" are often somewhat synonymous with a priori, datum, and axiomatic reasoning.

In Ancient Greek philosophy, a first principle from which other principles are derived is called an arche^{[note 1]} and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", "authorities"^{[note 2]} The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophyand Plato before being formalized as a part of metaphysics by Aristotle. Arche^{[note 3]} sometimes also transcribed as arkhé) is an Ancient Greek word with primary senses "beginning", "origin" or "source of action":^{[note 4]} from the beginning, οr the original argument, "command".^[3] The first principle or element corresponds to the "ultimate underlying substance" and "ultimate indemonstrable principle".^[4]

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.^[5]

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 Babylonian creation story, Enuma Elish, the primordial world is described as a "watery chaos" from which everything else appeared.^[6] This watery chaos has similarities in the cosmogony of the Greek mythographer Pherecydes of Syros.^[7]In the mythical Greek 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.^[8] The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality.^[9] The conception of the "divine" as an origin influenced the first Greek philosophers.^[10] In the Orphic cosmogony, the unaging Chronos produced Aether and Chaos and made in divine Aether a silvery egg, from which everything else appeared.^[11]

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.^[12] 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.^[13]

Thales of Miletus (7th to 6th century BC), known as "the father of philosophy",^[14] claimed that the first principle of all things is water,^[15] 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.^[16]

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.^[17][18] 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 that used arche for that which writers from Aristotle onwards called "the substratum" (Simplicius Phys. 150, 22).^[19] He probably intended it to mean primarily "indefinite in kind" but assumed it also to be "of unlimited extent and duration".^[20] 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)^[21]

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.^[22][23] The arche is technically what underlies all of reality/appearances.

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 that are 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). For Aristotle, the arche is the condition necessary for the existence of something, the basis for what he calls "first philosophy" or metaphysics.^[24] 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.^[25]

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):

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 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.^[26]

This section needs expansion. You can help by adding to it.  (July 2023)

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 the Schrödinger equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause^[1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.^[2]

In mathematics and formal logic, first principles are referred to as axioms 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 axioms 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. Physicistsinclude counterintuitive concepts with reiteration.

In a formal logical system, that is, a set of propositions 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 primitive notions: all three types constitute first principles.

In philosophy, "first principles" are from first cause^[1] 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 metaphysical speculation.

In philosophy, "first principles" are often somewhat synonymous with a priori, datum, and axiomatic reasoning.

In Ancient Greek philosophy, a first principle from which other principles are derived is called an arche^{[note 1]} and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", "authorities"^{[note 2]} The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophyand Plato before being formalized as a part of metaphysics by Aristotle. Arche^{[note 3]} sometimes also transcribed as arkhé) is an Ancient Greek word with primary senses "beginning", "origin" or "source of action":^{[note 4]} from the beginning, οr the original argument, "command".^[3] The first principle or element corresponds to the "ultimate underlying substance" and "ultimate indemonstrable principle".^[4]

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.^[5]

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 Babylonian creation story, Enuma Elish, the primordial world is described as a "watery chaos" from which everything else appeared.^[6] This watery chaos has similarities in the cosmogony of the Greek mythographer Pherecydes of Syros.^[7]In the mythical Greek 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.^[8] The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality.^[9] The conception of the "divine" as an origin influenced the first Greek philosophers.^[10] In the Orphic cosmogony, the unaging Chronos produced Aether and Chaos and made in divine Aether a silvery egg, from which everything else appeared.^[11]

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.^[12] 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.^[13]

Thales of Miletus (7th to 6th century BC), known as "the father of philosophy",^[14] claimed that the first principle of all things is water,^[15] 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.^[16]

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.^[17][18] 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 that used arche for that which writers from Aristotle onwards called "the substratum" (Simplicius Phys. 150, 22).^[19] He probably intended it to mean primarily "indefinite in kind" but assumed it also to be "of unlimited extent and duration".^[20] 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)^[21]

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.^[22][23] The arche is technically what underlies all of reality/appearances.

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 that are 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). For Aristotle, the arche is the condition necessary for the existence of something, the basis for what he calls "first philosophy" or metaphysics.^[24] 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.^[25]

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):

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 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.^[26]

This section needs expansion. You can help by adding to it.  (July 2023)

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 the Schrödinger equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.