For many centuries, Aristotle’s *Physics* was the essential starting point for anyone who wished to study the natural sciences. Aristotle (384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece. Along with Plato, he is considered the “Father of Western Philosophy”. Aristotle provided a complex and harmonious synthesis of the various existing philosophies prior to him, including those of Socrates and Plato, and it was above all from his teachings that the West inherited its fundamental intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be central to the contemporary philosophical discussion.

Francis Bacon, (1561 – 1626) was an English philosopher and statesman, who served as Attorney General, and as Lord Chancellor of England. His works are credited with developing the scientific method and remained influential through the scientific revolution.

*Essays: Religious Meditations* (1597) was the first published book by the philosopher, statesman and jurist Francis Bacon. The *Essays* are written in a wide range of styles, from the plain and unadorned to the epigrammatic. They cover topics drawn from both public and private life, and in each case the essays cover their topics systematically from a number of different angles, weighing one argument against another.

The New Organon by Francis Bacon

*The Novum Organum*, fully *Novum Organum Scientiarum* (‘new instrument of science’), is a philosophical work by Francis Bacon, written in Latin and published in 1620. The title is a reference to Aristotle’s work *Organon*, which was his treatise on logic and syllogism. In *Novum Organum*, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known as the Baconian method.

For Bacon, finding the essence of a thing was a simple process of reduction, and the use of inductive reasoning. In finding the cause of a ‘phenomenal nature’ such as heat, one must list all of the situations where heat is found. Then another list should be drawn up, listing situations that are similar to those of the first list except for the lack of heat. A third table lists situations where heat can vary. The ‘form nature’, or cause, of heat must be that which is common to all instances in the first table, is lacking from all instances of the second table and varies by degree in instances of the third table.

The Grounds for and Excellence of the Corpuscular or Mechanical Philosophy by Robert Boyle

Robert Boyle (1627 – 1691) was an Anglo-Irish natural philosopher, chemist, physicist, and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern chemistry, and one of the pioneers of the modern experimental scientific method. He is best known for Boyle’s law, which describes the inversely proportional relationship between the absolute pressure and volume of a gas if the temperature is kept constant within a closed system. Among his works, *The Sceptical Chymist* is seen as a cornerstone book in the field of chemistry. He was a devout and pious Anglican and is noted for his writings in theology.

Contributions to the Founding of the Theory of Transfinite Numbers by Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (1845 – 1918) was a German mathematician. He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor’s method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor’s work is of great philosophical interest, a fact he was well aware of.

Cantor’s theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Cantor, a devout Lutheran Christian, believed the theory had been communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor’s work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected.

The objections to Cantor’s work were occasionally fierce: Leopold Kronecker’s public opposition and personal attacks included describing Cantor as a “scientific charlatan”, a “renegade” and a “corrupter of youth”. Kronecker objected to Cantor’s proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics curriculum. Writing decades after Cantor’s death, Wittgenstein lamented that mathematics is “ridden through and through with the pernicious idioms of set theory”, which he dismissed as “utter nonsense” that is “laughable” and “wrong”.

The harsh criticism has been matched by later accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics. David Hilbert defended it from its critics by declaring, “No one shall expel us from the paradise that Cantor has created.”

On the Revolutions of the Heavenly Spheres (Dedication) by Nicolaus Copernicus

*On the Revolutions of the Heavenly Spheres* is the seminal work on the heliocentric theory of the astronomer Nicolaus Copernicus (1473–1543) of Polish Reneissance. The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy’s geocentric system, which had been widely accepted since ancient times.

On the Origin of Species by Means of Natural Selection by Charles Darwin

*On the Origin of Species* (or more completely, *On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life*), published on 24 November 1859, is a work of scientific literature by Charles Darwin which is considered to be the foundation of evolutionary biology. Darwin’s book introduced the scientific theory that populations evolve over the course of generations through a process of natural selection. It presented a body of evidence that the diversity of life arose by common descent through a branching pattern of evolution. Darwin included evidence that he had gathered on the Beagle expedition in the 1830s and his subsequent findings from research, correspondence, and experimentation.

Essays on the Theory of Numbers by Richard Dedekind

Julius Wilhelm Richard Dedekind (1831 – 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of *Dedekind cut*. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as *Logicism*.

The Principles of Quantum Mechanics by Paul Dirac

*The Principles of Quantum Mechanics* is an influential monograph on quantum mechanics written by Paul Dirac and first published by Oxford University Press in 1930. Dirac gives an account of quantum mechanics by “demonstrating how to construct a completely new theoretical framework from scratch”; “problems were tackled top-down, by working on the great principles, with the details left to look after themselves”. It leaves classical physics behind after the first chapter, presenting the subject with a logical structure. Its 82 sections contain 785 equations with no diagrams.

Relativity: The Special and General Theory by Albert Einstein

*Relativity: The Special and the General Theory* began as a short paper and was eventually published as a book written by Albert Einstein with the aim of giving “…an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.”

It was first published in German in 1916 and later translated into English in 1920. It is divided into three parts, the first dealing with special relativity, the second dealing with general relativity and the third dealing with considerations on the universe as a whole. There have been many versions published since the original in 1916, the latest in December 2011. The work has been labeled unique in that it gives readers an insight into the thought processes of one of the greatest minds of the 20th century.

The Feynman Lectures on Physics

*The Feynman Lectures on Physics* is a physics textbook based on some lectures by Richard P. Feynman, a Nobel laureate who has sometimes been called “The Great Explainer”. The lectures were presented before undergraduate students at the California Institute of Technology (Caltech), during 1961–1963. The book’s co-authors are Feynman, Robert B. Leighton, and Matthew Sands.

*The Feynman Lectures on Physics* is perhaps the most popular physics book ever written. More than 1.5 million English-language copies have been sold; probably even more copies have been sold in a dozen foreign-language editions. A 2013 review in *Nature* described the book as having “simplicity, beauty, unity … presented with enthusiasm and insight”.

The Meaning of It All by Richard P. Feynman

*The Meaning of It All: Thoughts of a Citizen Scientist* is a non-fiction book by the Nobel Prize-winning physicist Richard Feynman. It is a collection of three previously unpublished public lectures given by Feynman in 1963. *The Meaning of It All* is a non-technical book in which Feynman investigates the relationship between science and society.

The Foundation of Arithmetic by Gottlob Frege

*The Foundations of Arithmetic* is a book by Gottlob Frege, published in 1884, which investigates the philosophical foundations of arithmetic. Frege refutes other theories of number and develops his own theory of numbers. *The Foundations* also helped to motivate Frege’s later works in logicism. The book was not well received and was not read widely when it was published. It did, however, draw the attention of Bertrand Russell and Ludwig Wittgenstein, who were both heavily influenced by Frege’s philosophy.

The Assayer by Galileo Galilei

*The Assayer* was a book published in Rome by Galileo Galilei in October 1623 and is generally considered to be one of the pioneering works of the scientific method, first broaching the idea that the book of nature is to be read with mathematical tools rather than those of scholastic philosophy, as generally held at the time.

Dialogue Concerning the Two Chief World Systems by Galileo Galilei

*The Dialogue Concerning the Two Chief World Systems* is a 1632 Italian-language book by Galileo Galilei comparing the Copernican system with the traditional Ptolemaic system. It was translated into Latin as *Systema cosmicum* (English: Cosmic System) in 1635 by Matthias Bernegger. The book was dedicated to Galileo’s patron, Ferdinando II de’ Medici, Grand Duke of Tuscany, who received the first printed copy on February 22, 1632.

In the Copernican system, the Earth and other planets orbit the Sun, while in the Ptolemaic system, everything in the Universe circles around the Earth. *The Dialogue* was published in Florence under a formal license from the Inquisition. In 1633, Galileo was found to be “vehemently suspect of heresy” based on the book, which was then placed on the Index of Forbidden Books, from which it was not removed until 1835 (after the theories it discussed had been permitted in print in 1822). In an action that was not announced at the time, the publication of anything else he had written or ever might write was also banned in Catholic countries.

Kurt Gödel: Collected Works – Volume I

Kurt Gödel: Collected Works – Volume II

Kurt Gödel: Collected Works – Volume III

Kurt Gödel: Collected Works – Volume IV

Kurt Gödel: Collected Works – Volume V

Kurt Friedrich Gödel (1906 – 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege.

Gödel published his first incompleteness theorem in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any ω-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the natural numbers that can be neither proved nor disproved from the axioms. To prove this, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers. The second incompleteness theorem, which follows from the first, states that the system cannot prove its own consistency.

Gödel also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted Zermelo–Fraenkel set theory, assuming that its axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

A Brief History of Time by Stephen Hawking

*A Brief History of Time: From the Big Bang to Black Holes* is a popular-science book on cosmology (the study of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for nonspecialist readers with no prior knowledge of scientific theories.

In *A Brief History of Time*, Hawking writes in non-technical terms about the structure, origin, development and eventual fate of the universe, which is the object of study of astronomy and modern physics. He talks about basic concepts like space and time, basic building blocks that make up the universe (such as quarks) and the fundamental forces that govern it (such as gravity). He writes about cosmological phenomena such as the Big Bang and black holes. He discusses two major theories, general relativity and quantum mechanics, that modern scientists use to describe the universe. Finally, he talks about the search for a unifying theory that describes everything in the universe in a coherent manner.

Physics and Philosophy: The Revolution in Modern Science by Werner Heisenberg

Nobel Prize winner Werner Heisenberg’s classic account explains the central ideas of the quantum revolution and his celebrated Uncertainty Principle. The theme of Heisenberg’s exposition is that words and concepts familiar in daily life can lose their meaning in the world of relativity and quantum physics. This, in turn, has profound philosophical implications for the nature of reality and for our total world view.

Treatise on Light by Christiaan Huygens

*Treatise on Light* is a 1690 book written by the Dutch polymath Christiaan Huygens on his wave theory of light. Huygens’ starting point was Descartes’ theory, as presented in the *Dioptrique*, which Huygens aimed to supplant. Huygens’ theory is also seen as the historical rival of Newton’s theory, which was presented in the *Opticks*.

The Structure of Scientific Revolutions by Thomas Kuhn

*The Structure of Scientific Revolutions* (1962) is a book about the history of science by the philosopher Thomas S. Kuhn. Its publication was a landmark event in the history, philosophy, and sociology of scientific knowledge. Kuhn challenged the then prevailing view of progress in “normal science”. Normal scientific progress was viewed as “development-by-accumulation” of accepted facts and theories. Kuhn argued for an episodic model in which periods of such conceptual continuity in normal science were interrupted by periods of revolutionary science. The discovery of “anomalies” during revolutions in science leads to new paradigms. New paradigms then ask new questions of old data, move beyond the mere “puzzle-solving” of the previous paradigm, change the rules of the game and the “map” directing new research.

The Copernican Revolution by Thomas Kuhn

*The Copernican Revolution* is a 1957 book by the philosopher Thomas Kuhn, in which the author provides an analysis of the Copernican Revolution, documenting the pre-Ptolemaic understanding through the Ptolemaic system and its variants until the eventual acceptance of the Keplerian system.

Kuhn argues that the Ptolemaic system provided broader appeal than a simple astronomical system but also became intertwined in broader philosophical and theological beliefs. Kuhn argues that this broader appeal made it more difficult for other systems to be proposed.

The Mathematical Principles of Natural Philosophy by Sir Isaac Newton

*Philosophiæ Naturalis Principia Mathematica* (Latin for *Mathematical Principles of Natural Philosophy*), often referred to as simply the *Principia*, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions, in 1713 and 1726. The *Principia* states Newton’s laws of motion, forming the foundation of classical mechanics; Newton’s law of universal gravitation; and a derivation of Kepler’s laws of planetary motion (which Kepler first obtained empirically). The *Principia* is considered one of the most important works in the history of science.

*Timaeus* is one of Plato’s dialogues, mostly in the form of a long monologue given by the title character Timaeus of Locri, written c. 360 BC. The work puts forward speculation on the nature of the physical world and human beings and is followed by the dialogue *Critias*.

Participants in the dialogue include Socrates, Timaeus, Hermocrates, and Critias. Some scholars believe that it is not the Critias of the Thirty Tyrants who is appearing in this dialogue, but his grandfather, who is also named Critias. It has been suggested that Timaeus was influenced by a book about Pythagoras, written by Philolaus.

Science and Hypothesis by Henri Poincaré

*Science and Hypothesis* is a book by French mathematician Henri Poincaré, first published in 1902. Aimed at a non-specialist readership, it deals with mathematics, space, physics and nature. It puts forward the theses that absolute truth in science is unattainable, and that many commonly held beliefs of scientists are held as convenient conventions rather than because they are more valid than the alternatives.

In this book, Poincaré describes open scientific questions regarding the photo-electric effect, Brownian motion, and the relativity of physical laws in space. Reading this book inspired Albert Einstein’s subsequent *Annus Mirabilis* papers published in 1905.

Conjectures & Refutations by Karl Popper

Sir Karl Raimund Popper (1902 – 1994) was an Austrian-British philosopher and professor. Generally regarded as one of the 20th century’s greatest philosophers of science, Popper is known for his rejection of the classical inductivist views on the scientific method in favour of empirical falsification. A theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can and should be scrutinised by decisive experiments. Popper is also known for his opposition to the classical justificationist account of knowledge, which he replaced with critical rationalism, namely “the first non-justificational philosophy of criticism in the history of philosophy”.

In political discourse, he is known for his vigorous defence of liberal democracy and the principles of social criticism that he came to believe made a flourishing open society possible. His political philosophy embraces ideas from all major democratic political ideologies and attempts to reconcile them, namely socialism/social democracy, libertarianism/classical liberalism and conservatism.

The Logic of Scientific Discovery by Karl Popper

*The Logic of Scientific Discovery* is a 1959 book about the philosophy of science by Karl Popper. Popper argues that science should adopt a methodology based on falsifiability because no number of experiments can ever prove a theory, but a reproducible experiment or observation can refute one. According to Popper: “non-reproducible single occurrences are of no significance to science. Thus a few stray basic statements contradicting a theory will hardly induce us to reject it as falsified. We shall take it as falsified only if we discover a reproducible effect which refutes the theory”. Popper argues that science should adopt a methodology based on “an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements”.

Principles of Mathematics by Bertrand Russell

*Principles of Mathematics* is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. The book presents a view of the foundations of mathematics and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others. *Principles of Mathematics* consists of 59 chapters divided into seven parts: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion.

What is Life? by Erwin Schrödinger

Mind and Matter by Erwin Schrödinger

*What Is Life? The Physical Aspect of the Living Cell* is a 1944 science book written for the lay reader by physicist Erwin Schrödinger. The book was based on a course of public lectures delivered by Schrödinger in February 1943, under the auspices of the Dublin Institute for Advanced Studies at Trinity College, Dublin. The lectures attracted an audience of about 400, who were warned “that the subject-matter was a difficult one and that the lectures could not be termed popular, even though the physicist’s most dreaded weapon, mathematical deduction, would hardly be utilized.” Schrödinger’s lecture focused on one important question: “how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?”

In 1911, Schrödinger became an assistant to Exner. At an early age, Schrödinger was strongly influenced by Arthur Schopenhauer. As a result of his extensive reading of Schopenhauer’s works, he became deeply interested throughout his life in colour theory and philosophy. In his lecture *Mind and Matter*, he said that “The world extended in space and time is but our representation.” This is a repetition of the first words of Schopenhauer’s main work.

The Mathematical Theory of Communication by C.E. Shannon and Warren Weaver

*“*A Mathematical Theory of Communication*“* is an article by mathematician Claude E. Shannon published in *Bell System Technical Journal* in 1948. It was renamed *The Mathematical Theory of Communication* in the book of the same name, a small but significant title change after realizing the generality of this work. The article was the founding work of the field of information theory. The book contains an additional article by Warren Weaver, providing an overview of the theory for a more general audience.

The Physics of *The Healing* by Ibn Sīnā (Avicenna)

Avicenna’s *Physics *(c. 1027) is the very first volume that he wrote when he began his monumental encyclopedia of science and philosophy, *The Healing*. Avicenna’s reasons for beginning with *Physics* are numerous: it offers up the principles needed to understand such special natural sciences as psychology; it sets up many of the problems that take center stage in his *Metaphysics*; and it provides concrete examples of many of the abstract analytical tools that he would develop later in *Logic*.

While Avicenna’s *Physics* roughly follows the thought of Aristotle’s *Physics*, with its emphasis on natural causes, the nature of motion, and the conditions necessary for motion, the work is hardly derivative. It represents arguably the most brilliant mind of late antiquity grappling with and rethinking the entire tradition of natural philosophy inherited from the Greeks as well as the physical thought of Muslim speculative theologians. As such, *Physics* is essential reading for anyone interested in understanding Avicenna’s complete philosophical system, the history of science, or the history of ideas.

Principia Mathematica: Volume I by Alfred North Whitehead & Bertrand Russell

Principia Mathematica: Volume II by Alfred North Whitehead & Bertrand Russell

Principia Mathematica: Volume III by Alfred North Whitehead & Bertrand Russell

*The Principia Mathematica* (often abbreviated *PM*) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. *PM* was an attempt to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven. As such, this ambitious project is of great importance in the history of mathematics and philosophy, being one of the foremost products of the belief that such an undertaking may be achievable. However, in 1931, Gödel’s incompleteness theorem proved definitively that *PM*, and in fact any other attempt, could never achieve this lofty goal; that is, for any set of axioms and inference rules proposed to encapsulate mathematics, either the system must be inconsistent, or there must, in fact, be some truths of mathematics which could not be deduced from them.

One of the main inspirations and motivations for *PM* was the earlier work of Gottlob Frege on logic, which Russell discovered allowed for the construction of paradoxical sets. *PM* sought to avoid this problem by ruling out the unrestricted creation of arbitrary sets. This was achieved by replacing the notion of a general set with the notion of a hierarchy of sets of different ‘types’, a set of a certain type only allowed to contain sets of strictly lower types. Contemporary mathematics, however, avoids paradoxes such as Russell’s in less unwieldy ways, such as the system of Zermelo–Fraenkel set theory.

*PM* is not to be confused with Russell’s 1903 *The Principles of Mathematics*. *PM* has long been known for its typographical complexity. Famously, several hundred pages of *PM* precede the proof of the validity of the proposition 1+1=2. *The Modern Library* placed it 23rd in a list of the top 100 English-language nonfiction books of the twentieth century.

*Note: You can find free e-books and free online courses at Open Culture. Project Gutenberg and Internet Archive both host vast libraries of e-books for free to the public.*