Hallo, this is Dr. Bin Song in the course of “History of Modern Philosophy” at Washington College.

After reading Rene Descartes’s Meditations, we will learn another very different philosopher, who is representative for the so-called school of British empiricism, in order that you can get a more holistic picture of the development of modern philosophy. This philosopher is David Hume, and the “temperament” of his thought is modest, amicable, and always remains skeptical towards the over-speculation of philosophy in case that the philosophical speculation may fly too far away in one’s solitary thought from the everyday reality and the common sense of human fellows. For students who have learned western Ancient philosophy, you will find the difference between David Hume and Rene Descartes is similar to the one between Aristotle and Plato. Aristotle’s philosophy is quite empirically oriented. He thought human knowledge derives from observation and experience, and to live a good human life, humans need to follow the good customs of society and cultivate good habits so as to become virtuous. All these themes would be repeated by Hume’s empiricist philosophy to a certain extent. Whereas, Plato’s mind was always preoccupied with the world of the so-called “ideas” or “ideals,” just like Rene Descartes, whose Meditations intends to build the entire system of human knowledge from the most basic, allegedly innate ideas within human mind, such as soul, body and God.

In more concrete terms, the difference between Hume and Descartes can be envisioned in the following aspects:

Firstly, rather than treating “metaphysics” as lying in the root of the tree of philosophy and thus ascribing a fundamental role to it, Hume indicates in his writing a great suspicion towards the discipline of “metaphysics” in general. He thinks scholars’ discussions on metaphysical issues (such as the existence of God, the ultimate power and secret of nature, the essential and immortal nature of soul, the interaction between a thinking mind and an extended body, and other extravagantly abstract topics prevalent in modern philosophy) barely produced any certain result, and the debate on these issues seemed to be endless, if not desperately fruitless. In comparison with the very solid development of natural science in the era of Isaac Newton, who was both a compatriot and a slightly elder contemporary of Hume, Hume thinks that the discipline of metaphysics, as indicated by its poor performance in the early modern era, is deeply flawed. In order to rectify these flaws, Hume thinks that the primary task for philosophers is to imitate what Newton has achieved in natural science, and hence, to investigate the more fundamental topic of “human nature,” particularly the operations of human mind, before diverting our energy into those endless metaphysical debates. Hume’s suggestion is that through investigating the operations of human mind, we will get to know how human ideas are formed from their empirical origins, and how human mind associates these ideas so as to produce knowledge on different subjects. If we can pin down the origins of all the extravagantly abstract ideas in metaphysics, then, the language we use to discuss metaphysics will be more clear and we will therefore be able to grasp the limit of human knowledge lest our metaphysical thinking would have become a sheer speculation doomed into on-going, yet fruitless controversies and debates. (About Hume’s view on metaphysics, please refer to the assigned reading “Inquiry Concerning Human Understanding,” Section 1).

Secondly, a pattern of western philosophy is that idealistic thinkers normally quite cherish the distinctive value of mathematics. For them, such as Plato and Descartes, the empirical world cannot be where mathematical ideas derive, since all empirical knowledge lacks the universality and certainty of what mathematical reasoning can live up to. However, humans cannot arbitrarily manipulate mathematical ideas either, since mathematical objects have their stable traits and inviolate laws which human mind must obey. For Descartes, the two aforementioned reasons, viz., the non-empirical and the objective natures of mathematical knowledge, lead to his conclusion that fundamental mathematical ideas, such as size, magnitude, number, and in one word, “extension” of body, are innate. They are the blueprint of divine creation, which God imprints into human mind so as to inform humans of the essence of bodies which are also created by the same almighty God.

However, for Hume, just like for Aristotle, mathematical ideas do not occupy such a distinctive position in the world of ideas of human mind. Hume distinguishes all human perceptions into two groups according to their degrees of vivacity and strength: impressions and ideas. “Impressions” are those raw, vivid perceptions of the world which humans acquire from outer sense (such as vision, hearing, smell, etc.) and inner sense (such as our feeling of hunger, thirsty, pleasure, pain, etc.). However, when these raw impressions are stored into memory, revived in imagination or abstracted in intelligence, they will lose certain degrees of vivacity and turn into “ideas.” For Hume, all ideas, including mathematical ideas, derive from impressions, and thus, have an empirical origin. It seems that human mind can work on mathematical ideas alone in separation from the empirical world; however, according to Hume, this is because once abstracted from their empirical origins, the connection of mathematical ideas can be investigated according to the logical law of non-contradiction. Even if it seems we can acquire much knowledge of mathematical objects in reliance upon the work of human mind alone, the knowledge is just about the relation of “ideas,” and whether the knowledge can be applied to the everyday empirical world would still depend upon experience and observations. In other words, for Hume, the ideas of math derive from empirically given impressions, their relationship can be investigated by human mind alone, but whether mathematical ideas can be applied in the empirical world would still depend empirically. In a nutshell, there is no innate idea in the Cartesian sense, and all human knowledge derive ultimately from observation and experience, which is definitely a very different stance from Rene Descartes.

Thirdly, and most importantly, since experience and observation, rather than reason, plays the ultimately prominent role in the development of human knowledge, compared with Descartes, Hume also furnishes a much higher evaluation of the role of “customs and habits” in epistemology. As indicated by last unit’s reading, the hyperbolic method of doubt which Descartes uses in his Meditation I targeted customs and habits of human cognition that he inherited from his medieval scholastic background. For Descartes, nothing is more urgent to overthrow all those old ideas and beliefs in order to obtain an entirely new, and absolutely secured foundation of human knowledge. However, with a purpose of highlighting the irreplaceable roles of custom and habit in human knowledge, Hume asked an extremely consequential question for the further development of modern philosophy and for our general understanding of scientific knowledge. And the question is: on what basis shall we infer that an effect will be produced from a cause given our past observation of the constant conjunction of the two events identified respectively as a cause and an effect? For instance, we observed constantly in the past the rising of the sun can lead to the rising temperature of a stone; however, if we conclude “the rising of the sun causes the rising temperature of a stone” as a piece of knowledge, it will imply that in the future, the rising of the sun would always cause the rising temperature of the stone. But Hume’s question is that: how can we infer a future state of the worldly phenomenon based upon our past perception?

Hume does not think “reason,” in the form of demonstration which deduces one consequence from its premise according to the logical law of non-contradiction, can play any role in the aforementioned inference. This is because if the rising sun does not cause the rising temperature of the same stone in any future event, this does not bring any self-contradiction to our ideas. In other words, a different effect from a given cause is entirely possible, and thus, it is not self-contradictory to connect “a rising sun” to “the non-rising temperature of the stone.” In other words, the so-called causal reasoning is actually about matters of fact, which is different from the one about the relationship of ideas, and hence, it must be operated upon a completely different mechanism from the latter.

After surveying all possible answers to the above question, Hume concludes that it is nothing other than “custom and habit” that incline us to infer a stable repetition of future events from our past observation of the same events so as to develop our knowledge of causality and matters of fact. In Hume’s words, “After the constant conjunction of two objects – heat and flame, for instance, or weight and solidity – sheer habit makes us expect the one when we experience the other.” (pp.20, Inquiry Concerning Human Understanding.)

So, according to Hume, there is no secrete power or ultimate cause of nature which guarantees that nature will always proceed according to a fixed, unchangeable set of laws. Instead, Human knowledge of nature, viz., matters of fact in Hume’s words, solely and entirely derives from our observation and experience of the natural world, and thus, it is customs and habits, rather than any pre-established metaphysical reasoning, that help humans to know and adapt themselves to the constantly changing world with its discoverable, falsifiable and perfectible laws of causality. In other words, Hume’s “skepticism” employs customs and habits to remain suspicious towards metaphysical reasoning, while Descartes employs metaphysical reasoning to remain suspicious towards customs and habits. Shall we find a difference between Hume and Descartes more striking than this? I bet it would be very hard.

Nevertheless, despite that Hume’s philosophy can be read in a contrasting manner from Descartes in the above multiple aspects, Hume is surely still a “modern” thinker. His admiration towards Isaac Newton speaks to a common commitment among modern philosophers to the utilization of scientific method, the one of reducing complex issues into simple ones similar to what Descartes has articulated in the Discourse of Method, in the investigation of human mind. Also, Hume’s extraordinary work upon the study of the operations of mind represents another distinctive trait of modern philosophy which we analyzed before: its unusually intensive focus upon the subjective world of human mind. In fact, Hume is thought of as a pioneer of the modern discipline of psychology, and his study on the law of the association of ideas and the related moral philosophy which focuses upon sympathy continually generates great impact upon the study of psychology and the practice of psychotherapy even today.

Based upon the illustrated differences and similarity between Hume and Descartes, I would like to characterize Hume as a rebellious sibling of Descartes in the same family of modern thinkers.

Hallo, this is Dr. Bin Song at Washington College!

Let’s continue to talk of Descartes’s Meditations.

I described in last unit that Descartes’s philosophical Meditations share a similar structure to religious meditation which comprises a two-way practice of descending and re-ascending, or reduction and reunion. Therefore, after making sure the Archimedean point of human knowledge “I think therefore I am” in Meditation II and the Archimedean lever “God exists and He is not a deceiver” in Meditation III, Descartes starts to regain the validity of human knowledge that has been put into radical doubt in Meditation I. The overall thinking process of Meditation IV to VI can be summarized as follows: in Meditation IV, Descartes presents his theory of making good judgment: whenever we correctly use our freewill to judge vividly and clearly perceived ideas, we human beings would not make mistakes. Then, in Meditation V, using this theory, Descartes proves that mathematical knowledge is certain, and in Meditation VI, still using the same theory, Descartes proves the existence of body and the value of sensory perceptions of it. During the process, fundamental issues such as the existence of God and the distinction between mind and body are frequently revisited, and eventually, what Descartes contributed in his six Meditations counts nothing less than a prototype of modern philosophy: he demolishes all previous beliefs inherited from the scholastic past, and constructs something new that seems to provide solid knowledge on three most basic substances of the world: soul, body and God.

Although whether Descartes succeeds to argue in the most rigorous and impeccable way all the claims he intends to make in Meditations is up to debate, his thought on several major themes of Meditation IV-VI is of immense value for us to comprehend the nature of modern philosophy as a whole.

Firstly, Descartes resorts to old scholastic strategies to explain why God, as an omnibenevolent supreme being, allows the human creatures to be able to make mistakes in our cognitive activities of pursuing knowledge. Descartes says that as a creature, humans inherit “non-being” or “nothingness” in their nature, and thus, cannot avoid imperfections; moreover, imperfections of human beings serve the overall perfection of all creations by God. Therefore, there is really no reason for humans to blame God for human imperfections. However, since the overall creation can explain away human imperfections, Descartes asks a further question in Meditation IV that since this is the case, what is the overall purpose of God to put human beings in such a humble position among all his creations? At this juncture, Descartes indicates again the nature of his modern thought, that is, he would utilize pre-modern terms of theological thinking to argue for his modern cases. In other words, Descartes thinks that since God is infinite and humans are finite, there is no way for humans to understand the overall purpose of divine creation. Because of this, the just asked question has no way to get an answer from human intelligence, and as a consequence, there is no basis either to use “teleological” explanation in natural sciences.

We once read Aristotle’s Physics and On the Heavens where Aristotle characterizes “nature” in four connotations: a nature of an object can mean its material, form, efficient cause and purpose. For Aristotle, the cause of “purpose” is the most important since it indicates the overall order of worldly phenomena. However, for Descartes, since the purpose of God’s creation is unfathomable for human beings, nature just means “a fixed order in the sequence of cause and effect which operates upon things in the world.” In other words, Descartes’s understanding of “nature” becomes purely mechanical; the natural world is therefore thoroughly “disenchanted,” and this disenchanted worldview paves the way for the flourishing of modern natural science which is premised upon mechanistic explanation and mathematical reasoning. In this sense, the metaphysics of Descartes really serves as a “root” for his “physics” and other applied sciences, just as they are described in the “tree of philosophy.”

Secondly, although “I think therefore I am” speaks to the essence of “thought” or “thinking” for the substance of “soul” or “mind” in Descartes’s metaphysics, if we read carefully Meditation II and Meditation IV together, we would find such an essence would boil down to an acknowledge of “free will” as the genuine distinction of human beings from other beings. In Descartes’s theory of judgment, he instructs two forms of human freedom. One form is negative, which implies human will can suspend its approval or disapproval to ideas presented by human intelligence, and thus remain “indifferent” to the truth of those presented ideas. One best example of this negative freedom is when humans would simply doubt any piece of human knowledge, and thus, refuse to make any choice among presented ideas. Another form of freedom is a positive one, which implies the will of human beings approves or disapproves strongly the ideas that have been vividly and clearly perceived by human intelligence, and thus, is able to make swift decision regarding a variety issues of human life. For Descartes, the more knowledge humans have, the freer humans can be positively. However, the negative freedom is also fundamental, since it speaks to the fact that humans are not programmed machines, and can hence withhold judgments whenever our will would like to do so. Isn’t the “hyperbolic doubt” used by Descartes’s Mediation I such an example of the application of the negative form of human will? Yes, it is, since “doubting” is the activity of human will when ideas perceived by human intelligence are judged as not vivid or clear. In this sense “I think therefore I am” is actually “I doubt therefore I am,” which is furthermore equal to “I am free therefore I am.” In other words, the Archimedean point upon which all Descartes’s philosophical meditations are based upon is actually the self-affirmation of the freedom of human will, definitely a very strong indicator of the modern nature of Descartes’s thought.

Thirdly, one most interesting idea that Descartes contributes to his metaphysics is actually the one he mentions in the last Meditation, and he also didn’t address quite well. While asking himself what is the value of sensory perceptions such as the feelings of pain and pleasure caused by outside objects if most of these perceptions are so confusing and unclear that do not tell the truth of these outside objects, Descartes concludes that these perceptions mainly tell whether these objects are beneficial or harmful to humans, and therefore, speak to the close “union” of mind and body. Otherwise, Descartes continues to muse that, if mind and body are not closely united, then, if something hurts our body, we can just intellectually and abstractly perceive the body is undergoing certain damage without actually feeling the pains. Since we are indeed feeling the pains, this means the relationship between body and mind is different from the one where body is like a machine and mind is like an operator sitting in an air-conditioned control room to monitor the process of body movement. No, since we feel the pains on top of our intellectual perception of the damage of body, Descartes concludes that the real nature of human existence is actually neither body nor mind, but a close union between the two. However, if mind and body have been argued by Descartes in previous Meditations as two completely different substances, each of which has its distinctive nature called “extension” or “thought,” how can they be closely “united” and interact with each other? If we take the aforementioned concept of “free will” into consideration, then the asked question will indicate a further dimension: how can an utterly free human being live a life that is fully embedded in the world of machine-like “bodies” which, as Descartes argues in his concept of “nature,” follow exact mechanical and deterministic laws of causality? Furthermore, if “feelings,” “emotions,” and sensory perceptions are so important for the good human life , doesn’t it do a disservice to ourselves to mention this unique kind of worldly phenomena in the last place of the Meditations, and hence, get a somewhat perfunctory treatment in Descartes’s metaphysics in general?

I hope these last few questions can help to generate reflective thoughts on the nature of Descartes’s thought in particular, and of modern philosophy in general, so that perhaps, whenever you feel somewhat dissatisfied by the way of living of a modern human, you can find some clues or even make some breakthroughs through reading Descartes’s foundational modern thought.

Hallo, this is Dr. Bin Song at Washington College.

As explained in the previous unit of Modern Philosophy, underlying the enterprise of modern philosophy termed by Descartes as the “Tree of Philosophy” is the root of “metaphysics” which addresses the most generic traits of basic substances of the world, viz., soul, body and God. Therefore, to appreciate the title of Rene Descartes as “Father of Modern Philosophy,” we will spend the following two weeks to read the entirety of Descartes’s “Meditations on First Philosophy,” and I hope you can get as much insight as you can from this incredibly rich, and quintessentially “modern” text of philosophy.

Being among the enshrined modern philosophical classics, none of a single word in these Meditations can be overlooked by contemporary readers. However, these Meditations were after all written almost 400 years ago, which would naturally indicate some unfamiliar nature to readers today. One of the difficult reasons to read Descartes’s Meditations is to grasp how Descartes used old, scholastic terms and jargons to express his modern thought. If we gradually peel away these pre-modern layers from the kernel of his thought, we will find the distinctively modern traits of Descartes’s thought in the kernel, and thus, feel immediately connected to it. In the following, I will provide a brief and preliminary explanation of prominent themes of Meditation I-III, and I hope it can facilitate your actual reading of the book.

Firstly, the title of the book “Meditations” is fairly interesting. Starting from Aristotle’s “contemplative life,” running through Marcus Aurelius’s “Meditations” and Augustine’s “Confessions,” the philosophical tradition of the West evolved into Descartes’s “Meditations” to have indicated a rich “meditative” lineage where “meditation” is understood as a systematic reflection upon philosophical problems, and the reflection is aided by a certain kind of focused mental discipline. This richly meditative tradition of the West tends to be overlooked by contemporary readers since the current use of the term “meditation” is easier to be connected to Hindu, Buddhist or other non-Western practices of meditation. However, if we read the entirety of Descartes’s Meditations, we can still find some similarity between this meditation of a philosopher’s with other more religiously oriented ones. To put it briefly, this philosophical meditation also needs a two-way system of descending and ascending, or one of reduction and recovery. In Buddhist Chan meditation, for instance, you need to focus upon your breathing so as to reduce your consciousness to a peaceful and all-encompassing base, and then, employ that purified consciousness to re-contemplate worldly phenomena so as to live a mindful life here and now. Similarly, Descartes uses the method of “doubt” to challenge the validity of every piece of knowledge he acquired before; once he got to the bottom of his doubt, he found one piece of knowledge that he cannot doubt, viz., the existence of the thinking “I”; and then, he would do further contemplation upon all ideas that exist within this thinking “I” so as to check whether any of these ideas can provide certain knowledge of the outside world. I believe every reader, as long as they closely followed each word of Descartes’ Meditations, would also experience such an intense process of purification and reunification of human mind, which makes Descartes’ thought process deeply “practical” and “performative” in the regular sense of doing “meditation.”

Secondly, the method of “doubt” used by Descartes to get to the all-encompassing base consciousness of “I think,” is not a normal one. It is termed as the “hyperbolic doubt” which would consider any piece of human knowledge as completely false as long as it indicates a scintilla of uncertainty and dubitability. Using this hyperbolic doubt in Meditation I, Descartes threw away all pieces of knowledge, which he acquired through sense, imagination, memory and even pure intellect, with only the sheer activity of “I think” remaining as the rock bottom of human consciousness that cannot be thrown away any more. Here, the radical departure of Descartes’s philosophy from the pre-Modern Aristotelian one cannot be more visible: as we explained before, Aristotle’s natural philosophy is based upon the common-sensical observations of worldly phenomena. However, here, Descartes says that humans’ “common-sense” does not make any sense until every piece of it gets radically doubted and thoroughly scrutinized. Since doubting and scrutinizing require the ability of independent and free human thinking more than anything else, we can surely discern a distinctively “modern” sign of Descartes’s philosophy, just as we once characterized Copernicus’s heliocentric astronomy as indicating the same strength of human thinking and thus, as the starting point of modern scientific revolution.

Thirdly, since Descartes does not take “common-sensical” observation as the starting point of the pursuit of human knowledge, the more authentic approach to obtain human knowledge for Descartes is termed as “idealism,” which is distinguished from another very important, later lineage of modern thought, viz., “empiricism.” Descartes’s idealism suggests that in order to obtain human knowledge about anything in the world, we cannot start from a naïve perception of the world which takes the existence of things in it as granted, since the very existence of things in the world has been put into radical doubt in Meditation I. Rather, because the inner world of human subjectivity, which is termed by Descartes as “I think” or pure thinking, is more certain than anything else, we need to search for “ideas” that exist in our mind first, and then, infer whether these “ideas” correspond to realities outside the human mind; in other words, we need to examine whether these “ideas” can inform us of any knowledge about the outside world. Through this idealistic approach of epistemology, Descartes categorizes the origin of human ideas into three groups: ideas can be innate, invented, or affected from outside. Descartes also scrutinizes these ideas one after another regarding their validity of informing knowledge of objects outside human mind. In other words, rather than taking “realities” to be the prior origin of “ideas,” Descartes pays his primary attention to “ideas” in human mind, and then ask whether “ideas” inform humans of “realities.” Since “ideas” are more primary than “realities,” the role of autonomy and human free thinking gets prioritized and glorified during the process, which is surely a re-affirmation of the “modernity” of Descartes’s thought.

Finally, another significant aspect of Descartes’s Meditations is his theology, viz., his reflection on the existence of God and the role of the idea of God in regaining the validity of human knowledge that he has radically doubted prior to the conclusion of “I think; therefore I am.” For Descartes, it is a crucial step for the aforementioned epistemological approach of idealism to know that God is the creator of “I,” and more importantly, God is so good that He would not make “I” commit mistakes even on ideas which “I” can perceive vividly and clearly. Only after making sure the ultimate kindness of God, viz., “God is not a deceiver” in Descartes’s own words, Descartes thinks that we can believe our “natural tendency” to think of certain ideas in our mind, such as those mathematical ideas and sensory perceptions, as corresponding to realities outside of human mind. Be this as it may, our wondering is that: is God really an absolutely necessary idea to Descartes’s system? Or as some scholars intend to argue, is Descartes’s meandering thinking on God just a sign of Descartes’s “political shrewdness” since he did not want his writings and his person to undergo the same destiny of Galileo Galilei under the censorship of the Church? I would be very interested in hearing your thought on these questions.

In a word, in Meditation I-III, Descartes finds the undoubtable foundation of human knowledge, “I think therefore I am,” via a radical method of hyperbolic doubt, and then, after proving the existence of a kind God, he intends to re-ascend from the all-encompassing base consciousness of “I think,” and regain human knowledge via the approach of idealism. Please do read the Meditations word-by-word, and my summary here by no means captures the full glory of this quintessentially modern writing at the dawn of modern philosophy.

Hallo, This is Dr. Bin Song at Washington College.    

In 1644, Descartes published his Principles of Philosophy, and intended to promote it as a textbook of philosophy to be adopted by universities of Europe at that time. Descartes knew that this was deliberately to challenge the dominant role of Aristotelianism in the European academia. After all, the replacing of one textbook with another means a great deal. Although whether Descartes succeeded to promote his textbook in the institutional level is another story, he is indeed universally acclaimed by later historians as the father of modern philosophy.

Before Descartes, we discussed Aristotle, Copernicus, and Galileo in this second section of “modern scientific revolution” at the course of “Modern Philosophy.” We find that although Copernicus and Galileo laid out a very robust refutation against key points of Aristotle’s natural philosophy, none of these scientists’ thought is comprehensive enough to address the established Aristotelianism as a whole. As we have discussed, the philosophical system of Aristotle was so comprehensive as to be able to include everything that humans could know in his time. Therefore, to challenge the official status of Aristotelianism, Descartes’s philosophy must also be no less comprehensive. Descartes likened his comprehensive version of philosophy to a tree:

“Thus the whole of philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences, which may be reduced to three principal ones, namely medicine, mechanics and morals. By ‘morals’ I understand the highest and most perfect moral system, which presupposes a complete knowledge of the other sciences and is the ultimate level of wisdom.” (Principles, 9B:14)

Put in the background of the entire corpus of Descartes’s works, why Descartes thinks of philosophy as such would be more comprehensible. Metaphysics studies the most generic traits of things in the universe which exist under three major categories: soul, body and God. Physics studies the “body” part of the universe, and furnishes the laws of nature which explain the movement of varying bodies in the world. Medicine and Mechanics are two branches of applied physics, which are about how to cure human diseases and how to design technologies to alleviate human labor, two crucial areas pertaining to the convenience and sustainability of mundane human life. The “morals,” or the ethics is about what humans should do in varying situations, and according to Descartes, this is the highest branch of human knowledge since it needs all sorts of other knowledge in order to deliver the right ethical decisions.

Among all these parts of philosophy, we’ll focus upon “metaphysics” in the following weeks, where we’ll scrutinize Descartes’s famous argument for “I think therefore I am” and how he built his metaphysical system addressing the substances of soul, God and body. However, when Descartes presented his tree of philosophy in an intended textbook, his thought was in a relatively mature stage. The tree didn’t include much information about how he got to the root of his philosophy, viz., that dualistic metaphysics of soul and body, in the first hand. In order to understand how he got there and prepare our study of his metaphysics, we therefore need to trace his philosophical career back to a much earlier stage.

Before Descartes turned into his metaphysical thought in 1628, he was a very successful mathematician and physicist. Seen from the perspective of the on-going scientific revolution, the greatest contribution Descartes made as a scientist is surely his invention of analytic geometry, which unifies algebra and geometry, and hence, paves the way for the birth of calculus in Newton’s and Leibniz’s thought.

There are two major points we need to grasp in the ground-breaking work of the Geometry of Descartes.

Firstly, the unification of algebra and geometry leads to the full digitization of the objective natural world, which is unimaginable before Descartes. The crucial step for Descartes to achieve this is to illustrate that all major algebraic operations in Descartes’s time, including addition, subtraction, multiplication, division, and the square root, can correspond to a certain segment of a line, and hence, there is no reason to limit human imagination of a magnitude within three dimensions. Instead, a simple line segment can express a magnitude of any dimension, and once discovering the way how to express geometrical figures using algebraic means, the capacity of measuring and calculating natural movement in reality will be exponentially increased. If any one wonders where the idea of the digitization of the entire world in the movie of “Matrix” originally comes from, let’s ask Descartes.

Secondly, to resolve complex geometrical problems in his time, Descartes indicates an unusually high awareness towards the underlying “method” for the desired solutions. For instance, to resolve a geometrical problem, Descartes would firstly assign a letter to each of the known and unknown magnitudes. Then, he would write down as many equations as he can find to express the varying relationships between these unknown and known magnitudes. In the following, he would try to reduce the complex level of these equations so as to find a way to express the unknown from the known. Finally, once he found the answer of the unknown, Descartes would furthermore deduce complex relationships among magnitudes from the newly discovered simple ones. In the work of the Geometry, we can find many concrete examples about how Descartes described and applied this “method.” And the application of this method is so successful that Descartes furthermore thought he should use it to resolve all questions humans can ask, including those most abstruse and abstract ones in metaphysics.

Therefore, in 1637, Descartes published his “Discourse on the Method,” and generalized his “method” in four points:

“The first was never to accept anything as true if I didn’t have evident knowledge of its truth: that is, carefully to avoid jumping to conclusions and preserving old opinions, and to include in my judgements only what presented itself to my mind so vividly and so clearly that I had no basis of calling it in question. The second was to divide each of the difficulties I examine into as many parts as possible and as might be required in order to resolve them better. The third was to direct my thoughts in an orderly manner, by starting with the simplest and most easily known objects in order to move up gradually to the knowledge of the most complex, and by stipulating some order even among objects that have no natural order of precedence. The last was to make all my enumerations so complete, and my reviews so comprehensive, that I could be sure that I hadn’t overlooked anything.” (pp. 9, Discourse on the Method, trans. Jonathan Bennett 2017.)

The four rules are quite self-explanatory, and they can all be understood against the practice Descartes conducted in his analytical geometry. In other words, in any pursuit of human knowledge, Descartes believes we should aim for evident knowledge, which should be as vivid and clear as the one of math. Then, we would find all available chunks of information relevant to the solution of puzzles, put them into order, and then, reduce the complex ones to the simple ones, and address the simples ones first with a final synthesis to move from the simple to the complex. Since the aforementioned tree of philosophy is just a result of Descartes’s application of his method which ultimately derives from math, we can safely conclude that although metaphysics is seen as a root of the tree, the real soil to grow the entire tree of philosophy of Descartes is actually his mathematics. So, whoever said that nobody unfamiliar with math cannot learn philosophy? I hope you find some historical predecessor to Descartes’s thought here.

So, how would Descartes employ this “method” so as to create the dualistic metaphysics of “mind” vs “body” as the foundation of modern thought? That will be the question we will tackle for our following learning of modern philosophy. In general, Descartes’s thought is rigorous, methodic, systematic and creative, indeed a rare talent of philosophy, the learning of which can almost be guaranteed to bring a transformation of our own thought.

Hallo, this is Dr. Bin Song at Washington College!

Among all modern scientists who have helped to initiate and somewhat complete the Modern Scientific Revolution since the ingenious work of Copernicus, I like Galileo the most. He wrote his ground-breaking scientific works in the form of Socratic dialogue and using a fairly accessible, vernacular language, viz., Italian, in his time, which was to imitate Plato’s prototypical genre of philosophical writing. While presenting his trailblazing new science, Galileo also seriously thought about so many topics significant for the development of philosophy in general, among which God, humans, and nature are by no means trivial mentions. Most importantly, compared with Descartes and other continental philosophers in the early Modern period, Galileo was down-to-earth and always tried to embed his rigorous reasoning within experiments, observations, and hence, made sure that such reasoning does not fly too high away from humans’ common sense. If I have to express what I expect science majors at the college to become after they graduate, I wish they would be like Galileo, a gentle, well-rounded, and wise scientific soul.

Seen from the perspective of Galileo’s entire career, he had to accomplish three tasks in order to continue the scientific revolution started by Copernicus. He had to deal with two authorities which swayed a great power in the scholarly world of Galileo’s time: the authority of the Christian Bible, and the authority of Aristotle. After this, he surely needed to present his new scientific discovery in the most accessible and professional way.

His way to address the authority of the Bible on scientific matters is best represented by one letter to Castelli, which he wrote in 1613. He views that the Bible and the new science take charge of different things. Regarding salvation and other articles of Faith, the Bible has its absolute authority; however, since God the creator endows human beings with sense and reason, for Galileo, there is no reason not to use them, and therefore, the new science has its irreplaceable authority regarding the study of nature. If verses in the Bible seem to contradict what the new science discovers, we should seek “wise interpretations” of these verses so as to make the biblical truth compatible with scientific ones. In this letter, the refutation of Galileo against scholars’ use of the Joshua 10:12-13 to discredit Copernicus is a fun to read, since according to Galileo, Copernicus’s heliocentric astronomy makes more sense of the biblical verse which implies God’s command to stop the movement of the sun, and hence, this is also a great example on how a scientist can provide a “wise interpretation” of the Bible so as to square the authority of new science with the one of religious establishment.

The second authority Galileo needs to address is Aristotle, who, as we discussed before, held an absolute authority among scholastic scholars regarding the study of nature. In the “Dialogue on the Two Chief World Systems” (1632), Galileo discusses the authority of Aristotle in this way: only blind people need a guide when they walk in flat and open region; however, for anyone “who has eyes in his head and in his mind should use them as guide.” In other words, sense and reason are the genuine guide for humans to pursue science; even if Aristotle was still alive in Galileo’s time, Galileo believed that Aristotle would admit many of his mistakes in his original scientific writings in light of new evidences and demonstrations. Therefore, Galileo concludes that it is due to the lack of courage that scholars in his days stubbornly held on to the old authority of Aristotle in order to refuse new approaches of the study of nature.

Through Galileo’s writings on the two authorities, we find origins of many significant ideas of modern philosophy, such as John Locke’s separation of church and state and Kant’s definition of enlightenment as the courageous use of human reason in public. I once explained that the reason for us to study modern scientific revolution is to find origins of these ideas we initially discussed in the first section of the course on the Enlightenment. I hope you understand why this is so now.

Finally, the most important part of Galileo’s work is surely to present his new discoveries using the new scientific methodology. In this regard, I select an excerpt of Galileo’s “Dialogues concerning Two New Sciences” for your reading, and from here, we can discern such a classical use of scientific method that scientists have consistently employed it since the time of Galileo and as a consequence, such an application also caused so many profound transformations in human society.

The thinking procedure of Galileo’s work, which he called “a new science of motion,” can be summarized as follows:

Firstly (pp.334), to define the overall nature of the work. Galileo says that why such a science is new in comparison to old ones is because it cares about the exact mathematical measures and proportions that an accelerated motion indicates.

Secondly (pp. 335-336), to propose a new hypothesis about an unknown matter (viz., the uniformly accelerated motion) from the knowledge scientists already have (viz., the uniform motion). In other words, since we already know in the case of the uniform motion that space traveled by an object is proportionate to time, we can hypothesize in the uniformly accelerated motion that the increase of velocity of such an object is proportionate to time as well. As indicated in other scientific endeavors, proposing new hypotheses on unknown matters according to known ones involve genuine creativity of human thought on the basis of lots of guesses and trials. In this regard, there is really no strict method to follow, although we can discern a pattern of human thought to say a new hypothesis is proposed according to what is already known. However, this is just a pattern of thought, and how this pattern is manifested in varying cases really depends upon unpredictable human creativities, among which Galileo’s one is by no means negligible.

Thirdly (pp. 337-339), to resolve conceptual difficulties implied by the hypothesis. In this case, the difficulty is about how to envision the infinitesimal increase of speed at the initial moment of a uniformly accelerated motion.

Fourthly (pp.339-340), to disregard distracting questions which are normally more complex than the ones a newly proposed hypothesis is intended to address. So, Galileo argued with his friends that before we study the cause of a free-falling object, we need to describe the mathematical traits of its uniformly accelerated motion at first. This also speaks to a constant nature of scientific reasoning: we need to put things in order so that before tackling more difficult questions, let’s tackle easier ones at first.

Fifthly, (pp.340-342) to refute competitive hypotheses on the same matter. In this case, the alternative hypothesis that the increase of speed of a uniformly accelerated motion is proportionate to space, rather than to time, would lead to absurd consequences, and therefore, it got a quick refutation from Galileo before he argued the validity of the newly proposed one.

Sixthly, (pp. 345-346) the velocity of a freely-falling object cannot be directly measured in Galileo’s time. Therefore, in order to verify the truth of the hypothesis, Galileo deduces, using mathematical means, verifiable consequences from the hypothesis, and then, he designed experiments to check whether the observed result complies with thus predicted consequences. Here, one deduced consequence of the proposed hypothesis is expressed in Theorem 1, and Proposition 1, which says: “The time in which any space is traversed by a body starting from rest and uniformly accelerated is equal to the time in which that same space would be traversed by the same body moving at a uniform speed whose value is one-half the highest and final speed reached during the previous uniformly accelerated motion.” Here, all major magnitudes such as the equal time and the length of space can be measured in an experiment, and therefore, if this deduced consequence can be verified by the observation in a designed experiment, the proposed hypothesis would be verified to a certain extent.

In general, the scientific methodology proposed by Galileo on the new science of motion is termed by later historians as one of “hypothesis-deduction” which is featured by mathematical reasoning and experimental observation.

So, my students and readers, this is how Galileo discovered his new science, and this is also the method which scientists, in spite of not necessarily agreeing with Galileo’s concrete discoveries, have never abandoned in the scientific human endeavor of studying nature ever since. Are you familiar with this method? To what extent are you still using this method in your own work?