An Account of Sir Isaac Newton's Philosophical Discoveries (1748), by Colin Maclaurin, who taught mathematics at the University of Edinburgh; you might begin with page 7 of Book I, Chapter I; find a discussion of Descartes in Book I, Chapter IV -- online book, pdf
An Enquiry Concerning Human Understanding (1748), by David Hume, a Scottish philosopher; note Hume's reference to Newton and his physics in a Section VII footnote -- online book (footnote : search for E 7.n16.1, SBN 73)
Elements (c. 300 BC), by Euclid, a Greek mathematician (translated into English from Ancient Greek, notes on the translation) -- online text
The Evolution of Physics (1938), by Albert Einstein, who needs no description, and Leopold Infeld, a Polish physicist; an introduction to vectors (by Einstein!) -- online book (begins on p.12, but you should start at the beginning)
Sir Francis Bacon
"Whereas a method rightly ordered leads by an unbroken route through the woods of experience to the open ground of axioms." (Novum Organum, Book I, Aphorism LXXXII)
"The formation of ideas and axioms by true induction is no doubt the proper remedy to be applied for the keeping off and clearing away of idols." (Ibid., Book I, Aphorism XL)
Novum Organum (1620), by Sir Francis Bacon, an English philosopher and politician, often called the father of empiricism and the scientific method; translated (info) into English from Latin -- online text
"Human knowledge and human power meet in one..." (Ibid.)
Bacon intends the axioms of science (the "laws of nature") to be established by induction based upon observation of Nature.
Take note of Bacon's criticism of Aristotle in Book I, Aphorisms LIV and LXIII, of his Novum Organum, (in English: New Organon). The name of this book, by the way, is a reference to Aristotle's Organon. (Organon is the Ancient Greek word for a tool, although the word is now taken to mean an instrument of thought.)
"Aristotelian philosophy had been based on the idea that one ought to be able to deduce sciences from generally accepted first principles, so that all science would be comparable to geometry." (The Invention of Science, by David Wootton, 2015, p. 83)
PlatO (l), Aristotle (R)
Fresco by Raphael, 1509
On the Nature of Things (c. 50 BC), by Lucretius, a Roman poet and philosopher; Lucretius sought to explain Epicurean philosophy to a Roman audience; Epicurus was a Greek philosopher (more specifically an atomic materialist) from around 300 BC; translated in English from Latin -- online text
This poem (or essay) is astonishing in its modernity. Epicurus (341-270 BC), following in the steps of Democritus, who died around 30 years prior to his birth, proposes the existence of atoms, the existence of a void (empty space), which was strongly denied by Aristotle, and the belief that gods are uninterested in human affairs and do not interfere in the world.
The poem, famous in antiquity, was largely lost to the world, then rediscovered in 1417.
Mathematical Principles of Natural Philosophy (1687), by Isaac Newton, of England; translated into English from Latin by Andrew Motte (1729) -- online book
The Harry Ransom Center at UT Austin has a rare first edition (1687) copy of Newton's famous Mathematical Principles..., often just called the Principia. They also possess a first English edition (1729). Both are available for viewing by the public. A few photos of these books are attached here.
The Republic (c. 380 BC), by Plato, a Greek philosopher; translated into English from Ancient Greek -- online text (find thoughts on knowledge at the end of Book VI ... search "province of geometry"; the famous Allegory of the Cave is in Book VII)
It's ... natural to suppose we "know only what we see," even though we may actually be "seeing what we know."
Theories are not simply fabricated explanations for what we observe -- they're tools by which our perception of the world is constructed !
- John Granville, channeling Thomas Kuhn
I like your design of adding something more particularly concerning the manner of philosophizing made use of in the Principia and wherein it differs from the method of others, viz. by deducing things mathematically from principles derived from phenomena by induction. These principles are the three laws of motion. And these laws in being deduced from phenomena by induction and backed with reason and the three general rules of philosophizing are distinguished from hypotheses and considered as axioms. Upon these are founded all the propositions in the first and second book. And these propositions are in the third book applied to the motions of the heavenly bodies. -- Newton, in an unsent letter to Roger Cotes, in 1713
quoted from an article by philosopher Stathis Psillos
Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences (1637), by René Descartes, a French philosopher, mathematician and scientist; translated into English from French -- online text, (online book in French)
Positive Feedbacks in Climate Change (2017), by Bruce Parker, visiting professor at the Center for Maritime Systems at the Stevens Institute of Technology -- online article
The Assayer (1623), by Galileo Galilei, an Italian mathematician and scientist; translated into English from Italian -- partial online text
The Dialogue Concerning the Two Chief World Systems (1632), by Galileo; translated into English from Italian; in which Galileo argues for the Copernican heliocentric model of the solar system -- online book
Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), by Galileo Galilei; translated in English from Italian -- online book
click to view photos from a rare first edition copy of Galileo's Dialogue..., published in Italian in 1632; photos taken at the Harry Ransom Center at UT Austin
This is but one video series in a larger collection, broadcast as a television program called Closer to Truth, which generally covers fundamental questions concerning physical reality and metaphysics. Videos are of interviews with leading experts in the various fields.
String Theory and Post-Empiricism (2014), an interview of Richard Dawid by Richard Marshall; this interview presents challenging and controversial ideas concerning the assessment of the validity of scientific theories in the lack of empirical evidence -- online magazine article
"God is always doing geometry."
-attributed to Plato
Induction and Deduction in Physics (1919), by Albert Einstein; originally published in a German-language newspaper in Berlin; translated into English from German -- online text
Geometry and Experience (1921), by Albert Einstein; from a lecture before the Prussian Academy of Sciences; translated into English from German -- online text
"What do artistic and scientific experience have in common? Where the world ceases to be the scene of personal hopes, wishes, wants, where we face it as free creatures, admiring, questioning, beholding, there we enter the realm of art and science. We do science when we reconstruct in the language of logic what we have seen and experienced; but when we communicate through forms whose connections are not accessible to the conscious mind, yet we intuitively recognize them as something meaningful —then we are doing art. Common to both is the loving devotion, the being above the personal, removed from our will." - Einstein
Resistance by Scientists to Scientific Discovery (1961), by Bernard Barber; Science 01 Sep 1961: Vol. 134, Issue 3479, pp. 596-602 -- online pdf of article
How Your Brain Tricks You Into Believing Fake News, by Katy Steinmetz, Time Magazine, August 20, 2018 -- pdf of article
Is Truth an Outdated Concept?, by Michael Shermer, Scientific American, March 1, 2018 -- pdf of article
"Individuals tend not to question the credibility of information unless it violates their preconceptions or they are incentivized to do so." (source)
(written c. 350 BC, translated from ancient Greek)
Karl Popper (1902-1994)
Science: Conjectures and Refutations, (from a lecture given at Peterhouse, Cambridge, Summer 1953) published in Conjectures and Refutations: The Growth of Scientific Knowledge (1963), by Karl Popper -- online text
The Paradox of Karl Popper (Aug 22, 2018), an entry in the blog Cross-Check, by John Horgan -- blog entry