Thoughts on John Stuart Mill’s On Liberty

John Stuart Mill’s On Liberty presents a powerful defense of freedom of opinion, action, and individual lifestyle. Throughout the book, it is clear that he begins from a standpoint of optimism in the capacity of individuals, and a great respect of their potential to become dignified beings through developing their faculties. His entire project is devoted to the full development of the mental, moral, and physical capabilities of individuals. The main force behind his work is that individuals cannot reach their full mental and moral potential if they are uncritical and unthinking in their actions and words. For a man to reach his full potential, he must thoroughly know the reasons behind his own actions and beliefs. He must make an informed judgment, and it is impossible to make a properly informed judgment unless one knows the strongest arguments of all sides. This capacity for reasoned judgment is what elevates man above animals and machines; and through a society that encourages the development and use of this capacity, all individuals will be elevated to their fullest potential. Mill attacks the question of what type of government enable this type of society. In this sense, Mill’s work is in the same spirit as Plato’s Republic. His answer is short and clear: a democratic state that holds tightly to his refined Harm principle, which states that the State may only intervene in situations where an individual fails to fulfill a distinct and assignable responsibility to his other members of society. We can see how Mill’s project directly informs his vision for what such a state would look like. The state must be democratic as such a state enables the use of man’s capacity for rational judgment. The state must only intervene in cases where his refined Harm principle applies as in all other cases it would unjustifiably be again interfering with man’s capacity for rational judgment, limiting his development and reducing him to an automaton. From the Harm principle, freedom of opinion, action, and lifestyle trivially follow.

Despite the beautiful principles from which Mill informs his work and derives his Harm principle, he needs to defend his Harm principle from those who don’t share his founding principles and his optimism in human nature. This portion composes the bulk of his work; defending his principles against all possible objections that he has heard or he can come up with, performing a full, honest philosophical inquiry into the validity of his Harm principle. There were several particularly interesting arguments in defense of freedom of opinion. The infallibility argument argues that any state initiative to suppress a particular point of view assumes the infallibility of the state, which is clearly an incorrect assumption, as the state is composed of men and men are fallible. To the objection that there are some values of which we are so sure of that under careful consideration, so that we may be justified in using the state to censor alternative viewpoints, Mill raises the example of Marcus Aurelius. He calls Marcus Aurelius “the most Christian of the pagans”, highlighting how he was the first emperor to question how beneficial his role really was to the Roman Empire, and that he meditated deeply on the question of virtue and what is the good life, comiing to conclusions that were deeply Christian. Despite this, he still brutally oppressed and censored the Christians, despite their doctrine being a clear step forward in the moral evolution of humanity, and his own views aligning with those of the Christians. Another of one Mill’s particularly interesting arguments for the diversity of ideas and viewpoints was that in any subject in which there is permitted lively and widespread debate, the followers of a doctrine understand much more thoroughly the premises and arguments that compose and argue in favor of their doctrine. Additionally, in this state of affairs, the followers of a doctrine feel that their doctrine is much more alive and active, and more thoroughly live by its principles. He gives the example of the Christians, again: when they were persecuted, even their enemies remarked “Oh those Christians, how they love each other.” He contrasts this with the Christians of his day, who had a vague awareness of the principles of Christianity, yet rarely put into practice the doctrine that they proclaimed to adhere to so tightly. Clearly, the achievement of a hegemonic position for Christianity led to a decline in the actual practice of Christianity by Christians. The principles having diffused into the larger culture, its followers had no contrast which would allow them to become aware of its principle, to feel those principles alive in them, and have their actions driven by these principles. To the objection that, having found the “truth”, it is desirable to have it diffuse into the general culture, become hegemonic, and not have men make the mistakes of the past for the purpose of having the adherents of the truth be more thoroughly acquainted with it, Mill proposes that the system of education must step into this role. For any matters which are considered settled, citizens must be made aware of the strongest of arguments of the alternative viewpoints, such that they gain an appreciation of the difficulty of arriving to the truth of the matter considered settled, and understand the liveliness and difficulty of the debate that led to the conclusion. Having done so and understood the difficulty of arriving to the principles they have today, and thus the value of them, citizens will not only better abide by those principles, but will be more dignified in doing so, as they can now do it out of an informed, rational judgment, rather than out of mere habit. The last, most interesting, and most brutal objection to which Mill responds is the idea that truth must pass through a trial of persecution. This objection stems from the idea that truth cannot be suppressed forever, and thus persecution of the adherents of the truth will do no harm to the truth itself. Mill attacks this objection from several angles: remarking mainly that the belief that men hold that truth always triumphs over persecution is one of those pleasant falsehoods which are repeated until they are believed. He remarks that this dictum appears to be correct because there are truths which have been discovered repeatedly throughout history, and were repressed multiple times until they were discovered in more favorable circumstances. Noting that there are instances in which the repression of the truth held back humanity for centuries, he argues that we cannot let the triumph of the truth be left to mere chance.

On Liberty, after presenting its main values and principles, ends with an applications of these values and principles to real and present problems of the time. Mill recognizes the limits of his principles, and does not claim that his principles alone are sufficient to answer all questions of governance. For example, while the principle of individual liberty recognizes that it is best to leave people to come to their own agreements rather than imposing an agreement onto them, it is not sufficient to delineate the degree of control that should be exerted by the government in questions of prevention of fraud by adulteration, health and safety standards, etc. Mill recognizes that government force (beyond rational persuasion) is legitimate in these circumstances, and only wishes that the principle of individual liberty is kept in mind when answering these questions, and that the answers to these questions are rational; that the laws put in place really do have the intended effect in preventing fraud and ensuring health and safety, while not imposing too great of a burden in other respects. Recognizing the limits of his principles, Mill turns his attention to areas where his principles do have strong applicability. He uses the sale of poisons to demonstrate several important nuances of his principles, as they are a commercial good that may be used for both nefarious and beneficial purposes. First, he thinks it is just that the state mandate that all poisons are labeled as such. This is because he views it as the proper office of the state to prevent unfortunate accidents. He argues, however, that once the buyer is sufficiently informed about the dangers of what they are purchasing, the state has no right to coercion to prevent the buyer from purchasing the poison. Next, he investigates the precautions the state ought to take for the prevention of crimes perpetuated using poisons. He is very hesitant about enabling the state to prevent crimes, recognizing that this opens up practically all actions to regulation and inspection by the state. However, he admits that the prevention of crimes of this magnitude is a legitimate role of the state, and he seeks that discourages access to poison for illegitimate use while not providing a material impediment to access for legitimate use. For this, he recommends that at the sale of any poison, the details of the sale are recorded, including the time, date, amount, and purchaser, and that a third party must be present to witness the sale and the creation of the records. He argues that this provides a legitimate interference to the acquisition of poison for illegitimate purposes, while not interfering with those who wish to seek it for a legitimate reason. Another area in which he tests his principles and derives the action to be taken is those areas in which, while the harm stemming from the individual engaging in a particular action is mainly limited to the individual himself, the act of engaging in these actions is harmful to society at large. He is specifically referring to actions such as fornication and gambling. He unequivocally maintains that those that engage in these actions must be tolerated and not persecuted. However, the question of allowing the existence of those that profit from these actions – such as pimps and the owners of gambling-houses – is another question, because the incentives of these individuals are directly opposed to society’s benefit. Mill is not fully decided on this question. He acknowledges that it would be logically inconsistent to tolerate the buyer but not the seller. Yet he is not satisfied with giving the seller free reign to pursue his profit at extents that would be reasonable for other businesses. He seems to arrive at the compromise that for matters such as prostitution and gambling, neither the buyer nor seller should be persecuted, but the acquisition of these services should be limited to those that actively seek them out. Places to obtain and engage in these services should not be in the public view of society. This would imply a prohibition on all forms of advertising for these services. The authority of the state to impose such restrictions, despite it seemingly being against Mill’s previous assertions of the fallibility of the state and the right of individuals to determine best what is towards their own good, would derive from the recognition that whether these services are harmful or not is a disputable question; and that the state has the right to exclude the influence of solicitations which are not disinterested, and are for their personal gain only. It is clear that the questions Mill tackles remain real and present in current society. There are clear parallels in the debate with the sale of poisons and the gun control debate, and the legalization of certain drugs. There is one final interesting application of his principles that Mill presents that is will be highlighted. Mill tackles the question of taxation of substances which have a potentially adverse effect on society and other individuals – such as alcohol. Mill is not against these taxation when their justification does not conflict with the principles of individual liberty. He thinks the taxation of such stimulants in order to discourage their consumption is wrong. First, he notes that for some, the taxation will essentially serve as a prohibition, as the price becomes out of reach for such individuals. Thus, we should treat taxes meant to discourage consumption as a form of prohibition. Secondly, falling back on his principles, he does not see it as the place of the government to discourage individuals from a behavior through taxation. Dignified individuals must be discouraged of harmful behavior only through appealing to their rationality, thus respecting their dignity. However, this does not mean that there must be no taxation on stimulants or certain products – and that in fact, such “harmful” products such as stimulants should still be taxed. He arrives at this conclusion in the following manner. First, he notes the inevitability of taxation. Governments must enact taxes in order to fund their functions. Given this inevitability, a rational allocation of tax burden would place the largest tax burden on the least morally correct and least socially beneficial actions and goods. Thus, he approves of taxation of stimulants up to the point where they generate the largest revenue. This allows a smaller tax burden on necessary and beneficial behaviors and goods, the production of which must be encouraged. Thus, it appears that for Mill, the acceptability of a policy is not to be determined purely by its effects and actions; the chosen justification and intention of a policy, even if multiple possible justifications and intentions would lead to the same policy, must not conflict with his harm principle and individual liberty.

I think the part that I enjoyed most about On Liberty was the beautiful optimism Mill had in the capacity of individuals, and the society that would result from exploiting this capacity. He truly believed that as reading and public education became widespread, we would all be elevated and empowered in a way that would make us truly free and dignified. I think it is clear that we have not reached this state. Most citizens feel disempowered, correctly recognizing that they have little active participation in government. However, I still believe in Mill’s vision, although I think the challenges to achieving such a society are much greater than he expected. The education system he described that would train citizens ready to participate in such a society never arose, partially because it was never necessary. I think back to ancient Athens, with its radical democracy where many positions were filled by lot and the constant number of public assemblies that citizens had to attend. This was the sort of government that required for its own survival that citizens be well-informed, educated, and capable of rational thought, and thus was forced to take provisions and foster a culture in which citizens could meet these requirements. Even before being allowed to vote in assemblies, citizens would have had observed a good number of such assemblies, and would be immersed in a culture that recognizes the consequences of each person’s opinions, and the importance of factual correctness. Today’s parliamentary governments do not require those kind of citizens. The barriers to becoming a legislator are high enough such that legislators that are elected generally have the level of education and rationality to make non-disastrous decisions regardless of their voter base, and thus whether or not voters themselves hold the correct beliefs has little consequence. There is little benefit to being “right” on an issue, because one can very rarely argue for that position themselves in front of any assembly with real, actionable power. When the consequences of having an incorrect opinion on a policy has so little impact on one’s everyday life, it is not surprising that we see such a multitude of opinions that are motivated more by ideology and identity (which does have a direct impact on most individuals’ daily life) than correct opinion. This in turn explains the current state of debate seen on social media sites such as YouTube, which are more interested in “destroying” the other side instead of getting to the truth. Without a mechanism to transform belief into action, there is little incentive or consequence of getting to the truth during a debate, while “destroying” the other side can have an enormous positive effect on one’s in-group standing. Thus, the parliamentary governments which were flourishing in Mill’s time, were not sufficient to push humanity to this higher, more dignified state that Mill dreamed of. Rather, it created the conditions that impede the creation of a government which would enable this state. The increasing state of polarization and blind adherence to ideology allowed by such parliamentary governments make its citizens even more opposed to the most powerful measure which would create citizens interested in forming their beliefs to match fact, not ideology and identity. This measure would be the introduction of the powerfully democratic means of legislation, where average citizens could turn their ideas into real, enforceable policy. This would force citizens to align their beliefs with fact to a greater degree, as they would at least partially suffer the consequences for misalignment. However, as everyone at least tacitly recognizes the other side of not being based in fact but in ideology, everyone prefers the current system as opposed to seeing the current beliefs of the other side actually having some chance of being put into practice. Thus, we are stuck at an impasse where the poor state of political debate and culture makes it difficult to take any measure which would encourage a better state, and the education system that Mill dreamed of will never be possible in this state because the significant effort required to realize it will only be taken if it is necessary; but it will never be necessary so long as the beliefs of citizens have little impact on realized policy. I do think that there is hope, however, and I will also explore more of Mill’s ideas as applied to current issues in another post.

Pulp Fiction and the Unsettling Feeling

There is something a little unsettling, I think, about watching Pulp Fiction. I never felt fully at ease watching it, even during the seemingly innocent scenes. The lack of an overarching narrative is felt throughout the film. The movie opens with a scene whose conclusion remains unknown until the end of the film and remains in the back of your mind, and you wonder the significance of it. In fact, this happens repeatedly – several scenes being shown to you without explanation. As the film progresses, you get the impression that perhaps the film is not being completely honest with you, and is showing you things out of chronological order. This sets up an interesting dynamic, in which as a viewer, you know you cannot trust the film in order to best inform you of what is going on. You become suspicious of the film and focus more intensely on individual details in an attempt to orient yourself about what is really happening. Of course, many films engage in partially obscuring some of the details in order to build suspense, but built into our conception of a good film and a good story is that the movie is completely honest with you, and does not drive the plot by concealing some essential detail. In films that do this, we criticize them for relying on a deus ex machina; having another plot happening in parallel which ends up being essential to the current plot without showing this parallel plot is widely considered to be bad story-telling and leads to unsatisfying conclusions; or more precisely, conclusions that leave the viewer with some nagging sense of dissatisfaction. The viewer watches the film, and when the situation ends up being resolved by some outside force undeveloped by the film, they ask themselves “That was it? The whole time some outside army was on the way to save them?”, and so on with similar questions. The viewer ends up devaluing the dilemma the protagonist was facing as “not really a dilemma.” Pulp Fiction deconstructs this idea of Deus Ex Machina. There are many storylines in Pulp Fiction that happen in parallel and that end up colliding in an almost accidental manner. If we were only showed one of these storylines, we would be critical on the film for its overreliance on deus ex machina. Too many times, we would say, the fate of the characters we were following was determined by outside forces about which we knew nothing. Yet the film does show us these parallel lines, and we are still unsatisfied. Knowing Butch’s story and how it inevitably led to him attempting to run over Marsellus Wallace does not make their encounter seem any less deus ex machina-esque. The story remains just as incoherent and senseless. It does not make us any more satisfied with Vincent’s unceremonious death. If we were interested primarily in the robber-couple at the beginning, the fact that we knew the entire backstory of Pitt and Vincent that led them to that restaurant does not make their attempt to rob the restaurant seem any less strange and unsettling. Pulp Fiction shows us that that thing which we think is the reason we do not like deus ex machina – those storylines developed in secret and in parallel which end up being essential – is not the real reason we do not like deus ex machina. In Pulp Fiction, despite having all of those storylines shown to us, we are still unfulfilled with their conclusions.

Another unsettling element to Pulp Fiction is as a viewer, the utter lack of ability to discern what is important. The film dedicates a significant amount of time to developing the relationship between Mia and Vincent, even giving us an intense subplot in which Vincent attempts and manages to save Mia from dying from an overdose. As a viewer, one immediately thinks that the relationship between Mia and Vincent will end up being central to the film and what follows. It doesn’t – we only see one more reference to the night that Mia and Vincent shared together, and even that is in passing when Mia thanks Vincent for the dinner. For Marsellus, the event may as well have been non-existent based on what the film showed us. Even when we recognize that some event the film is showing us has significance, and we are invested in its development, we still have a difficult time recognizing exactly for whom the event would have important implications for. The subplot in which Butch is fetching his watch from his apartment ends up to our great surprise to have profound implications for Vincent’s storyline.

The lack of the viewer’s ability to discern what is important is aggravated by the film’s lack of ability to focus on things that drive the plot or develop the characters. Due to this, we have to listen to Fabienne’s desire for a potbelly. We have to listen to the discussion between Vincent and Pitt about the subtle difference between America and Europe. We are shown the little discussion between Vincent and Pitt about what counts as properly washing your hands. In doing so, the film makes an unambiguous intertextual reference to “real life.” A less mundane reference would be less clear. The films which do this by breaking the 4th wall, upon doing so, fundamentally change the nature of the film, whereas referencing some real-life event might give the viewer the impression that the film occurs in the same “timeline” instead of the intended effect of having the user think back to real life. However, by showing these little mundane, unimportant events, the film unambiguously makes a reference to something outside of film and story-telling, which focus on important events; it makes a reference to real life. Only in real life is the viewer unable to skip past these little uninspired events; only in real life does the viewer experience these events. In making this intertextual reference to real life, the film draws attention to an important factor of real life. Real life has no one editing the film and creating a narrative, eliding out the parts that are unimportant. All the unimportant parts of life are experienced just as fully as the important parts, and all of the unimportant parts are experienced just as much in passing as the unimportant parts. There is no one to divert our attention saying “here, this part of your life will end up being essential to your future; pay attention now.” This is what Pulp Fiction references, and asks us to keep in mind, by their occasional focus on the more mundane.

The most unsettling scene is the one in which Butch unceremoniously kills Vincent. Vincent, who by now is a character we are invested in and are presumably meant to like, dies because of his choice to use the bathroom at an inopportune time. When he exits the bathroom, Butch kills him without a second thought. But it is not Butch’s hesitancy in killing Vincent which is unsettling. It is the fact that Vincent was not an important character at all in Butch’s life. They was no protagonist/antagonist relationship developed between Butch and Vincent throughout the film. When Butch kills Vincent, we realize how little importance Vincent actually has in Butch’s storyline – and vice versa. Yet in an accident of fate, it is Vincent who is sent to wait for Butch as opposed to some character we are less invested in, and it is Vincent whom Butch kills and ends his story. And is this not the most real scene in the movie? Is real life not filled with these sort of encounters, in which people who do not know each other have some sort of profound impact on the other’s life? Or – and this is even more real – is real life not filled with these encounters in which two strangers who do not know each other end up having a profound asymmetrical impact on the others life – that is, one of the pair is deeply affected, and the other is not affected at all? What is particularly terrifying about these type of encounters is their utter lack of meaning. We can understand two people who know each other having some sort of important impact on each other’s lives, and we are ready to accept it; we are a little more reluctant to accept the scenario in which two strangers have such an impact on each others life, but still accept it with some willingness due to their fates now being tied together – both have been about equally affected by the event, so for both the event shares some important significance and ties them together. But the case in which one of the strangers is profoundly affected and the other is not seems to us is unacceptable; no connection between the two arises, no relationship is developed, and one of the strangers will be forever troubled by the event to which the other gave no significance to. Events like these are common in all types of applications; for college applications, essays and test scores that a student devoted hours to is simply one of many to those who work in the college admissions office, and for them the choice of whether or not to accept the student is one of little consequence to them. It is a decision that they make in passing and quickly forget; while for the student, the decision of the college admissions officer could be one that they carry throughout life. Perhaps even more far-reaching are the consequences of those who work in immigration offices, where green cards, visas, and refugee applications are decided. Yet these decisions are made with the same sort of trivial approach. And how can they not be? When reviewing so many, it is impossible to not develop some level of insensitivity to the decision being made at hand. When it is one out of thousands, such decisions easily lose their significance. Pulp Fiction lays this sort of asymmetric relationship bare, along with its terrifying consequences. The absolute reality of such a scene remains and draws attention to the asymmetric sort of relationships referenced in the scene as the viewer encounters them throughout life.

There is one last thing which unsettles me. The film intentionally draws our attention to the book that Vincent was reading right before he died. Later, at the end of the film, he is reading the same book. The book has no significance. Yet because of the way the film drew our attention to it, we intensely remember it. Why?

Descartes’ Second Meditation

After his first meditation, Descartes appears shaken. The possibility that all of his experiences are false, fed to him by an evil genius set on deceiving him, is a traumatic one, and a problem that Descartes fails to see how he will resolve. Yet nevertheless, he continues, inspired by Archimedes’ saying that he only needs one firm and immovable point from which he could move the entire Earth. In the same way, Descartes hopes to achieve great things by finding such a certain and unshakable piece of knowledge.

The Search for the Certain and Unshakable

It actually doesn’t take very long for Descartes to find this “certain and unshakable” piece of knowledge – he arrives at it within the next few paragraphs. After supposing that everything he sees, feels, remembers, sense, and so on, to be completely false – including his concept of body, shape, extension, movement, and place (all things which did not succumb to dreaming doubt but did succumb to the evil genius doubt) – he arrives at the preliminary conclusion that perhaps nothing is certain. But he is dissatisfied – perhaps he hasn’t searched hard enough. He again returns to the possibility that an evil genius is feeding him his experiences. He acknowledges again the possibility that he all of those things which he is so familiar with don’t exist. This leads him to ask himself – does he exist? Is he something? He hesitates to affirm that he is. After all, he is considering the possibility that even his own body is nothing but a false experience fed to him by the demon. But he cannot see any way to deny his existence, by the very fact that he is doing things such as questioning his own existing or persuading himself that nothing exists. Even under the case that “there is some deceiver or other who is supremely powerful and supremely sly and who is deceiving me”, then there is no doubt that he exists if he is deceiving him.

“…and let him do his best at deception, he will never bring it about that I am nothing so long as I shall think that I am something. Thus, after everything has been most carefully weighed, it must finally be established that this pronouncement “I am, I exist” is necessarily true every time I utter or conceive it in my mind.”

If you’re getting annoyed at Descartes overly-cautious approach – after all, why did it take him so long to accept the fact that he exists! – consider Descartes’ task. For one, he is working under the possibility that there could be an evil genius fabricating all of his experiences. He isn’t ready to trust anything without thoroughly investigating it and subjecting it to the most powerful doubt. Then, consider what Descartes is searching for – some knowledge that is certain and unshakable. That’s a very high criterion, and he isn’t just going to accept anything without weighing it carefully and investigating it thoroughly.

What is “I”?

Now that he has affirmed that he exists, Descartes tries to find what this mysterious “I” is. He wants to know exactly what he is affirming to exist when he says “I exist”, and what belongs to the nature of this “I”. Remember, Descartes is searching for that firm and immovable point, and the more things he is certain about, the easier it will be for him to overcome his doubt.

Here is where Descartes begins running into problems. He thought of himself as a man, but it’s not clear what a man is – he tries defining it as “rational animal”, but abandons the attempt quickly when he realizes that just leads to a rapidly growing number of questions about what “rational” means and what “animal” means. Clearly, that is not a productive avenue of exploration. Thus, he attempts to figure out what he is through what comes to him “naturally and spontaneously” – that is, the common-sense approach.

The things that immediately come to him is that he is something with a body – with hands, a face, and so on. He is also something that does things such as eating, walking, sensing, and thinking. He used to attribute these actions to the soul – which he admits he has a very poor understanding of. In fact, he recognizes that he seems to understand the nature of the body to a much higher degree. The issue is now he is supposing that some evil genius could be deceiving him and that his body doesn’t necessarily exist. So he conservatively and cautiously comes to the conclusion that he is merely “a thinking thing” – things he cannot deny since he is currently existing, which he knows because he is thinking, and he cannot deny that he is thinking for obvious reasons. He expands upon this definition a little bit by saying he is a thinking thing that “doubts, understands, affirms, denies, wills, refuses, and that also imagines and senses” – things he feels comfortable adding because he does all of these things and sees no way through which they could be separated from himself, as the body can.

But again, Descartes still has a couple misgivings. For one, all of this is very abstract. The things he is currently seeing and perceiving seem to have much more reality and obviousness to him. He cannot resist believing that corporeal things “are much more distinctly known than this mysterious “I” which does not fall within the imagination.” He has a point, and the question of what is a self is still unsettled today. Try imaging yourself – that is, the thing you refer to when you say “I”, not your body. It is something abstract, intangible, yet still real. With this in mind, Descartes decides to let himself investigate the nature of these corporeal bodies which he seems to have a much better understanding of in order to see what they can tell him about himself.

The Parable of the Wax

In this little story Descartes tells about his experience with a piece of wax (exciting, I know), Descartes wants to emphasize how we perceive bodies through our intellect, not our senses. Our senses may give us information about the body, but it is our intellect that forms a coherent idea of that thing as a body (or as a thing, rather than a disjoint set of sensory experiences). Here’s a several-paragraph story in a few sentences.

Descartes picks up a piece of wax. He observes several things; its shape, it’s smell (still smelling like the flowers it was picked from as the wax is still fresh), its taste (a hint of honey from the honeycomb it was made still remaining), its hardness, its sound (producing a dull thud when you rap on it with your knuckles, etc). Then, Descartes does something to the wax that leads to a completely different set of observations about the wax. He puts it next to the fire and the wax expands, it changes shape, it becomes hot, it loses its smell of flowers and its tastes of honey, and it no longer produces a sound when you rap on it. He is getting a completely new set of observation from his senses, yet he still perceives it as the same wax. How can this be?

For one, he concludes that his perception of the wax as such – of the wax before being the same wax as the wax now – cannot come from his senses, as they are all giving him completely different data about the wax. Then, he wonders whether his imagination is the source of him perceiving the wax as such. Yet he realizes that there are certain properties of the wax that he cannot imagine. For example, the wax is flexible. Being flexible means that wax can change shape, but Descartes cannot enumerate all of the infinite ways in which the wax can do so. Similarly, the wax has a shape, but he cannot possibly imagine all of the different shapes that the wax can have. Here, Descartes makes the point that you cannot correctly judge what the wax is without also believing that the was can take on an even greater variety of shapes then you could possibly grasp with the imagination. Thus, you cannot grasp the wax purely through the imagination – for there are essential aspects of the wax which cannot be fully grasped by the imagination. Yet this gives him a hint about the origin of his perception. Flexibility and shape is not something you can imagine – you can certainly imagine a piece of wax having a specific shape, but not having “shape.” Flexibility and shape are things that you understand. And thus, Descartes arrives at the conclusion that you perceive bodies through the mind alone. He gives a few more examples of this – one of them is of men crossing the square, of which he can only see their hats and clothes. He perceives them to be men, although his senses only show him their clothes. This perception must arrive in the understanding – for there are other cases in which his senses show him clothes yet he does not perceive them to be men – and thus, we perceive objects through the mind. It is our mind that gives objects their identity beyond the disconnected set of experiences presented to us by our senses.

The fact that we perceive objects through our mind reassures Descartes. As we use our mind to perceive corporeal objects, several facts about this mysterious “I” become much more evident. From the fact that I perceive a candle – whether through seeing, touching, hearing – it surely follows just as evidently that “I” exist as much as it follows evidently that the candle exists. In fact, because we perceive these corporeal objects through our mind, and from the fact that obviously, we can perceive nothing so clearly and evidently as our own mind, this “I” is no longer so mysterious. We are perceiving this “I” all the time, much better than we can perceive anything else, and our perceptions about ourselves are not subject to deception like our senses are. If we feel happy, we truly do feel happy, and no evil genius could deceive us into thinking we feel happy without truly feeling happy. This cannot be said about the senses.

Summary

Descartes did several important things in his second meditation. First, he finds a certain and unshakable point from which he can base his knowledge. This is the fact that he exists – a fact that is able to withstand even the evil genius doubt, for the genius cannot deceive him into thinking that he exists without him actually existing. Then, he wonders about his own nature and concludes that he is a thinking thing – that is a thing that doubts, wills, affirms, denies, senses, imagines, etc. These things are part of his essence and cannot be separated from him and his existence. There is no way for the evil genius to deceive him into thinking he is doing these things without him actually doing these things. Thirdly, he concludes that when we perceive corporeal objects – which we seem to perceive so clearly – we are not perceiving them with our senses or with our imagination, but we are perceiving them with our intellect, with our mind. While our senses may provide us sensations of that corporeal body, it is our mind that connects these otherwise disconnected sensations into our conception of the object – and thus, it is our mind that perceives the body. Lastly, given that it is our mind that perceives these corporeal bodies which we seem to perceive most clearly and evidently, and that the mind most clearly and evidently perceives itself, we can conclude that we can know this mysterious “I” which escapes our imagination even better than we can know these corporeal objects.

Descartes lays down some important groundwork here for the distinction between mind and body that he proves in the 6th meditation, while also most importantly laying down the firm and unshakable foundation for all his future knowledge; the fact that he exists.

Understanding Hessian Matrices and the Second Derivative Test

When I took Calc III (MAT 307 for me at Stony Brook), we used Hessian matrices in order to perform the multivariable equivalent of the second derivative test for determining whether a point was a maximum, minimum, saddle point, or point of inflection.

The way we did it was by finding the hessian matrix, which was the matrix of all the second partial derivatives. We would then determine whether the matrix was positive-definite, negative-definite, or neither by using the determinant of the matrix to inspect the eigenvalues.

I sort of just accepted it, because it kind of make sense to me; a “positive-definite” matrix corresponded to a positive second derivative in single-variable calculus, and a “negative-definite” matrix correspond to a negative second-derivative in single-variable calculus. It just made enough sense on the surface for me to not bother looking into it.

But then, as I learned more linear algebra, I became more curious about what positive and negative determinate meant. It turns out that if matrix H was positive definite, vTHv>0 for all v – basically, it meant that no matter what vector we put through H, we would get a vector pointing more or less in the same direction. The opposite held if H was negative definite: vTHv<0 for all v, meaning that no matter what vector we put through H, we would get a vector pointing more or less in the opposite direction.

This gave me the idea that perhaps vTHv represented some sort of directional second derivative, and after some searching online it turns out that yes, vTHv is equivalent to the directional derivative of the function.

I didn’t actually find a proof of this (then again, I didn’t search very hard), but I decided to prove it myself as it couldn’t be too difficult. It wasn’t; the only knowledge required was the definition of matrix multiplication, transposes, dot products, product rule for derivatives, and the multivariable chain rule. Once you’ve understood and know how to use all of the previous concepts, you might be interesting in seeing the proof I wrote up (attached as a PDF because as a subscriber to the free wordpress plan, I can’t use Mathjax to embed my proof into the page).

Once you understand that vTHv represents the directional second derivative, you also understand why we check that a hessian matrix is positive-definite or negative-definite. A positive-definite hessian matrix means that the second derivative is positive in every direction, and a negative-definite hessian matrix means that the second derivative is negative in every direction. If it’s neither, it means that there could be some directions where the second derivative is positive and some other directions where the second derivative is negative, indicating a saddle point.

Anyway, what’s left for me to understand is why inspecting the eigenvalues tells us whether a matrix is positive or negative definite, but hopefully that will be resolved in a future blog post.

Descartes’ First Meditation

Descartes’ synopsis accurately sums up that which he attempts to do in his first meditation:

“In the First Meditation the reasons are given why we can doubt all things, especially material things…Although the utility of such a doubt is not readily apparent, nevertheless its greatest utility lies in freeing us of all prejudices, in preparing the easiest way for us to withdraw the mind from the senses, and finally, in making it impossible for us to doubt any further those things that we later discover to be true.”

The search for a new set of axioms

Descartes starts off his first meditation by giving an architectural analogy for how knowledge is formed; you have foundations, and then you build opinions and knowledge upon those foundations, which then serve as support for the next set of opinions and knowledge, and so on.

This specific model for knowledge is important because it establishes a strong dependence of later knowledge on previous knowledge; just like when doing a mathematical proof, an falsity in a previous step will invalidate all of the dependent steps following. Realizing that he has had “numerous false opinions in my youth that I had taken to be true”, he resolves to “raze everything from the ground and begin again from the original foundations.” Thus, Descartes makes his intention explicit of basing his knowledge on an entirely new epistemological framework. As discussed earlier, Descartes was a strong rationalist, and this “razing everything to its original foundations” constitutes searching for a new set of axioms for his a priori knowledge; a new set of axioms which would be stronger (in the sense of being true) and would not lead him to make the same mistakes as he made in his youth of taking false opinions as true.

The necessity of valid reasons for doubting

Interestingly enough, Descartes doesn’t just immediately assume all of his knowledge to be false and begins right away to search for a new foundation. Rather, it’s a process he wants to “earnestly and unreservedly” apply himself to.

Descartes’ standards for what constitutes a valid foundation are high: “But reason now persuades me that I should withhold my assent no less carefully from opinions that are not completely certain and indubitable than I would from those that are patently false. “ Thus, any opinion which he has the slightest reason to doubt, he rejects – the foundations of his knowledge must be absolutely indubitable.

Returning to the architectural analogy for knowledge, Descartes doesn’t begin the general demolition of his opinions by examining each one individually; rather, he searches for the common elements on which his trust in all his opinions depends – similar to finding the load-bearing structures of a building. By finding and demolishing these, the rest of his opinions come crumbling down as well. “Rather, because undermining the foundations will cause whatever has been built upon them to crumble of its own accord, I will attack straightaway those principles which supported everything I once believed.”

At first, Descartes begins by suspecting his senses, the source of much of the material for his knowledge and opinion. He recognizes the imperfection of his senses and that they sometimes deceive him: and “it is a mark of prudence never to place our complete trust in those who have deceived us even once.” However, Descartes is not satisfied with merely rejecting the knowledge he has built up from his senses. He notes that while our senses can deceive us in “small and distant things” – ie, that we are capable of misperceiving things at the limit of our senses, there are some things that we cannot doubt that the senses are perceiving correctly – eg, that he is sitting in a chair by the fireplace, writing this meditation, etc. It is important for Descartes to find a good reason for doubting things, such that he does not engage in a fit of madness and irrationality in his search for a new foundation. Thus, he turns to an even more powerful form of doubt.

Dreaming Doubt

Recognizing that if what he is perceiving is coming from his senses, there are certain things he cannot reasonably doubt that he is perceiving correctly, he then turns to the idea that perhaps he is dreaming:

“This would all be well and good, were I not a man who is accustomed to sleeping at night, and to experiencing in my dreams the very same things…”

Thus, he is now able to doubt that he is sitting in a chair by the fireplace, writing his meditation, etc – for he could also, in fact, be dreaming. He attempts to establish whether there are any reliable signs for distinguishing whether he is awake or asleep, and realizes that there are none. It seems like he is suddenly able to call any of his opinions into doubt, as they may simply have been the result of a dream. However, looking around, Descartes concludes that there are still things he cannot doubt: “Nevertheless, it surely must be admitted that the things seen during slumber are, as it were, like painted images, which could only have been produced in the likeness of true things…” The objects in his dreams are inspired by elements of the real world, and thus they must have some element of truth in them. Even the most fantastical creature he could dream of – like satyrs and sirens – surely have some basis in reality, as they are a combination of true things he has seen. He argues that even if he were to dream something “so utterly novel that nothing like it had ever been seen before”, the colors that make it up must surely be real or composed from colors he has seen in the real world. The same can be said about concepts such as position, motion, shape, etc – these are concepts that even if he were dreaming, must exist in reality. (Here, we see a foreshadowing of Descartes’ casual adequacy principle – a topic that we’ll cover in a later post. But the inspiration for it is here: our thoughts are inspired by the real world, and thus the real world confers some of its reality into our thoughts).

Dissatisfied with the ability of his dreaming doubt to reject what remains of his knowledge, he turns to his last, most powerful form of doubt.

Evil Genius Doubt

He begins his evil genius doubt by observing that there are some truths which it does not seem possible to doubt: certain simple mathematical truths; such as the sum of two simple numbers, the number of sides that a square has, etc. Thus, to be able to reject these opinions of his, he needs a very powerful, all-pervasive sort of doubt.

Descartes then notes that he has an idea of an all-powerful God; surely this all-powerful God has it within his power to cause Descartes to deceive himself when verifying these simple facts. Yet here he runs into a problem when attempting to establish the doubt that it could be God that is deceiving him.

God is benevolent; so it is not within his nature to cause Descartes to always deceive himself (but wouldn’t it also not be within his nature to allow Descartes to be deceived even sometimes? This is a problem Descartes mentions, hinting at what will be resolved in the 5th meditation). To those atheists who would seek to escape such a doubt by denying the existence of God, he notes that the less perfect his origin (the most perfect origin being God), the more imperfect he is, and the more likely that his imperfections truly lead him to make even basic mistakes and deceiving himself. Thus, Descartes doesn’t reject God, and keeps him around as a hope that we are created by a perfect, benevolent God who in creating us made it so we don’t deceive ourselves. Descartes rejects God as a possible deceiver and a source of doubt.

Yet if Descartes rejected God as a source of doubt, will he find any being powerful enough for him to doubt the remainder of his convictions? He needs something with power far beyond his, yet at the same time evil, in order to explain this being’s devotion to constantly deceiving him. He finds this being as an “evil genius, supremely powerful and clever, who has directed his entire effort at deceiving me.” This allows him – or rather forces him – to assume that his sensory input has no basis in reality, that he might as well be a brain in a jar with wires hooked up to him feeding him a completely false reality. This allows him to doubt even his traditional notions of position, time, space, shape – as all his notions stem from what he perceived to be reality, and it is now possible that this entire reality was falsified, his doubt is effective in demolishing all of his previous convictions. Standing among the rubble, Descartes can begin searching for anything that remained standing against this most powerful doubt, allowing him to build a new foundation on this exceedingly solid material.

Summary

Upon realizing that he has built much of his knowledge on false opinions, Descartes begins razing all of his knowledge to the ground and begins the search for a new foundation. He searches for some doubt powerful enough to demolish all of his conceptions; he begins by doubting his senses, as they have deceived him before, concludes that this “sensory doubt” is not powerful enough, moves on to “dreaming doubt” – recognizing that any of his experiences and convictions could stem from dreams – also realizes that this is not powerful enough – and ends with the most effective doubt, the evil genius doubt – the assumption that all of his experiences and sensory input from the outside world were fabricated by some evil, supremely powerful, genius. Descartes needs these forms of doubt grounded in reason (rather then just assuming that all his knowledge is false for the sake of the exercise) in order to escape his prejudices, and his tendency to accept his long-held convictions as true “by their claims of intimacy and the way they take advantage of his credulity” (paraphrased). An interesting assumption driving Descartes’ demolition and rejection of his convictions is the assumption that accepting a falsity as true is much worse than not accepting a true thing as true – that it is better to reject all true things as unknown for the risk of accepting one false thing as true. Accordingly, this hyperbolic doubt serves its purpose “in making it impossible for us to doubt any further those things that we later discover to be true.” Descartes begins tackling this task in his second meditation.

Descartes’ Meditations on First Philosophy

Descartes’ Meditations on First Philosophy was a book that I may as well have chosen at random. It was one of those impulse buys, along with Angela Davis’ Are Prisons Obsolete? and Slavoj Žižek’s How to Read Lacan. Those first two I read within two weeks, and, to my credit, I did begin reading Descartes’ Meditations. However, this was interrupted as I began pledging to a fraternity, and thus it was left unread. After I finished pledging and a 2-week post-pledging recovery process, I decided to pick up Meditations again. The real reason was that I wanted to buy more books, and I don’t let myself buy more books until I finish reading the previous batch. But once I began reading it the second time, I found myself much more intrigued in Descartes’ work. He was proposing a rigorous solution to the age-old problem of skepticism, his very method being forged in the fires of extreme doubt. Along with this, he had two proofs for the existence of God, proofs that I found more interesting than the traditional “miracle-based” proofs – which required us to trust others that the miracles really happened, or to trust that there wasn’t some sort of hidden trickery happening. I was also very interested in seeing how his rationalist approach to knowledge, which implies trusting that which can be concluded by reason alone, also led him to conclude that we can trust our senses and external observations of the world – in this way, combining the best of empiricism and rationalism. His metaphysics, which allows us to conclude with certainty that we observe things as they really are, provided an interesting alternative to my belief in the distinction between the way we perceive things and the way things really are.

Descartes’ Approach

Critical to understanding Descartes’ approach is understanding that he is a rationalist. Rationalists distrust any sort of knowledge that cannot be derived from pure reason alone – i.e., a priori knowledge. An example of this is, given the premises P, and P implies Q, (alternatively, if P then Q) one can conclude Q. Or, as a mundane real-world example, given that you know if John cleaned the kitchen, he was paid $10, and you know that John cleaned the kitchen, you can safely conclude that John was paid $10. This conclusion requires no external observations of the real world, so as long as your premises are true, you can trust your conclusions to be true. The challenge that comes with being a rationalist is finding a correct set of premises. An incorrect premise would allow you to mistakenly come to incorrect conclusions, and, given that we want to have absolute certainty in our conclusions, this is unacceptable. Even more challenging in Descartes’ case is that he somehow needs to logically prove that we can trust our senses and our observations of the outside world, without using any observation of the outside world in his proof. Thus, as a Rationalist, Descartes initial task is to find a set of premises that would allow him to be absolutely certain about his conclusions, a solid set of premises which would be true in themselves, true beyond any doubt. Famously, the premise he arrives is the famous Cogito ergo sum, I think therefore I am.

Once he has his initial premise, Descartes proceeds to prove, ostensibly using pure logic, that we can trust our external observations of the world. Central to his argument is his proof for the existence of God, and that we are made by God. He has two proofs for the existence of God, also ostensibly employing only pure reason. Once he has proved he existence of God, his argument is easy to follow. God – as a supremely perfect being, did not endow us with deceptive faculties (as deception is a sign of imperfection). Thus, it logically follows that if we were given faculties that do not deceive us in their observations, we must be able to trust our observations of the outside world. However, one issue remains. Descartes observes we very obviously make mistakes. How can that be, if we were given faculties that do not deceive us? Here, Descartes gets around this by introducing the concept of proper usage of our faculties, which cannot lead us to any incorrect conclusions, and improper usage – which is the cause of our mistakes. First, he notes that (obviously) the intellect is finite, being that we are finite beings, and as we can easily imagine ourselves as having more intellect. Thus, the domain over which we can make correct judgments using our intellect is limited to the domain of things we perceive clearly and distinctly. He then notes that our will is infinite, as God bestowed us with a perfect free will, and as we cannot imagine ourselves as having more free will. Thus, the domain of the will is much larger than that of the intellect (being infinite, in fact), and our mistakes arise from judgments that occur inside the domain of the will, and outside the domain of the intellect. The will, being infinite, consents to judge anything, even those things that lie outside the domain of the intellect, leading us to make mistakes. He argues that when we properly use our faculties – that is, when we restrict our judgments to things within the domain of the intellect (in other words, to things we perceive clearly and distinctly), we cannot make mistakes, because it is a proper application of our faculties. It is important to understand that for Descartes, the fact that we have a limited intellect is simply a restriction of being a finite being, and thus having a finite intellect is not some sort of imperfection that God bestowed upon us. Thus, Descartes manages to both resolve the question of why, given that God gave us perfect faculties, we make mistakes, or, if God created us, why did he give us faculties that are capable of making mistakes. His answer to the first question is that God did give us perfect faculties and that do not make mistakes so long as we use them properly. His response to the second question is that God the faculties God gave us are as perfect as they can be in a finite being; any limitation that we find in them arise from the essence of being a finite being, not because God, as a supremely perfect being, bestowed upon us these limitations.

Descartes ties up his meditation by proving the distinction between body and soul. His main argument is that since we can clearly and distinctly conceive of the soul and body as separate concepts, there must be some real distinction between them. That is, we can easily imagine the mind existing separate from the body, and vice versa, and thus they must be distinct. This – along with Descartes proofs for the existence of God, is something we will go into more depths in future installments.

Summary

Stepping back, Descartes’ argument proceeds like so:

  1. Find an absolutely certain foundation for our knowledge.
  2. Prove logically that God exists and created us.
  3. Since God is benevolent and supremely perfect, he endowed us with faculties we must be able to trust.
  4. Thus, we can trust our outside observations of the world.
  5. Mistakes arise from improper usage of our intellect, which can be rectified by only passing judgment on things we have a good understanding of.

Overall, Descartes’ project is ambitious, and if he succeeds we would have a solid foundation for all of our knowledge, as it would all be derived from pure reason and logic, along with the added benefit of also being able to trust and use our empirical observations of the world. He would finally put an end to even the most extreme forms of skepticism. All of these would have enormous benefits to philosophy and mankind. Given the importance of such a project, I would highly encourage reading Descartes’ Meditations on First Philosophy yourself – it’s surprisingly accessible.