Sunday, January 24, 2016

The Science of Individual Existence

It is the cornerstone of my and Schopenhauer's philosophy that causality is what allows us to understand and explain reality. And that causality is ultimately responsible for the separation of ourselves from the world and a source of perpetual strife. The a priori intuitions of space and time, as borrowed from Kant, are not absolute features of the universe but are the result of a sort of division of the world into subject and object. In conjunction with experience these intuitions form our notions of cause and effect; something precedes something else spatially in succession of time and occupies different space during the same time. And yet the world is fundamentally will, known to us through the internal sense of time.

If this all holds up, why exactly is the world like this? Unfortunately this question itself involves causal thinking, and it is a mistake to apply such thinking to existence itself. The division of subject and object, space and time, and cause and effect are the conditions for knowledge as such. Without them there isnt really philosophy at all.

But perhaps one can look to science, the study of material causality, to find out what about this particular universe is responsible for our experience of events. What gives order to our understand of the universe.

The scientific reason for why we exist as individuals and understand the world causally is because particles in this universe have rest mass, which means they cannot go faster than the speed of light.

Remember Einstein's famous equation E=MC^2? Mass energy equivalence means that the inertia of a body depends on its energy content (the title of Einstein's 1905 paper). An object in motion gaining kinetic energy also gains mass. Most of the mass of our atoms is energy, not the rest mass of the quarks. Nevertheless, these particles have rest mass (now just called mass).

Because these particles have rest mass, and photons do not, it takes energy to overcome that inertia. Meaning that it would take an infinite amount of energy to go the speed of light.

The first postulate of special relativity is that the laws of physics are the same for all observers. The reason for the strange effects when objects are accelerating at very fast speeds is precisely because they must obey the "cosmic speed limit". In accordance with that limit, time from their frame of reference must be slower as they approach the speed of light.

Photons do not have rest mass, and so everything for them happens in an instant. There isn't a before and after. There are only events. This is a fundamental constant of the universe. If anything went past the speed of light, there wouldn't be anything to "bump" into. Rather, what would probably happen is backwards time travel. Effects would become causes, thus destroying any notion of causality. Knowledge would be impossible.

Since particles have rest mass, they cannot go the speed of light because that would take an infinite amount of energy to overcome that "inherent" resistance. And so events occur causally; causes precede effects. It is as if things are weighed down. Some things have more mass than others and bend space, which is responsible for Gravity according to general relativity. Mass is equivalent to energy, and so bends space. This warping of space also affects time. But if it wasn't for the "inherent" mass of some particles, there wouldn't be any matter.

What all this means is that the reason why we experience the world as we do, as individuals separate from others in space and time greater and lesser than each other, is because of the rest mass of particles which prevent them from going the speed of light where events would be instantaneous. Memories wouldn't form identity as there would be no meaningful order of things that would inherently make more sense than any other.

A current explanation for why particles have mass is the proposed Higgs field, but that's beyond the purpose of this post. Take Brian Greene's summary to help think about it.

Mass is the resistance an object offers to having its speed changed. You take a baseball. When you throw it, your arm feels resistance. A shotput, you feel that resistance. The same way for particles. Where does the resistance come from? And the theory was put forward that perhaps space was filled with an invisible "stuff," an invisible molasses-like "stuff," and when the particles try to move through the molasses, they feel a resistance, a stickiness. It's that stickiness which is where their mass comes from.... That creates the mass....

... it's an elusive invisible stuff. You don't see it. You have to find some way to access it. And the proposal, which now seems to bear fruit, is if you slam protons together, other particles, at very, very high speeds, which is what happens at the Large Hadron Collider... you slam the particles together at very high speeds, you can sometimes jiggle the molasses and sometimes flick out a little speck of the molasses, which would be a Higgs particle. So people have looked for that little speck of a particle and now it looks like it's been found.

Also watch this video, though PBS Spacetime can be hard to follow for novices.


Summed up: for some reason fundamental particles of the universe which are responsible for the fundamental forces of the universe have rest mass. The philosophy that holds that space, time, and causality are only conscious representations of phenomena holds on its own. But it's always interesting to find intersections with current physical theories.

What is interesting to think about is that everything physical has sort of stored energy in it. And as we've seen with atomic bombs and reactors, there is a lot of energy in even the smallest things. Even if not quite the level of an atomic explosion. In our lives, ponder what could be done if we could harness this immense energy. What we could accomplish.

Thursday, January 14, 2016

Final Metaphysic

The world is will and perception. Energy and idea. Matter is an idea, energy is alone substantial.

The principle of sufficient reason is the ground of all synthetic judgements. The four laws of thought.

Space and time are representations, a priori. Color, taste, smell, and touch are the product of sensations. Our body is the object known primarily.

Energy is the constant that governs all interactions, which is the potential for transformation, is what everything is made of but is not a thing.

The world outside of consciousness is what can potentially be experienced, or is omnipresent but not currently being able to be represented.

Gravity is a posteriori.

Motion is a synthetic judgement.

Wednesday, January 13, 2016

Metaphysical Drives

The aim of life is pleasure and the removal of pain. These states are not reducible to each other; pain is not the absence of pleasure and pleasure is not the absence of pain. These states exist to restore internal equilibrium, a balance which perpetuates bodily motion. 

Voluntary motion could not begin nor continue without these fundamental drives, for what "reason" or cause could there be for anything if not the prospect for more or the fear of loss from a state of balance? 

Every action is the result of a prior action and is itself the cause of future actions. This continues for the duration of our existence. 

The means of life are attraction and repulsion, love and death. Love and death are the intrinsic motivators of life as opposed to external forces which change the arrangement of things but do not determine their individual nature. 

Life is not the natural state of the universe. The unliving dominate our world. Taking an individual form requires work, a transfer of the energy of the constantly changing world to perpetuate the motion of a body complex. In a closed system this uses up the energy available for life to manifest. Thus the aim of life is death. 

‘The aim of all life is death...inanimate things existed before living ones’ -Freud
What is good is what the body attracts toward to reduce internal tension or what the body avoids for the same reason. Without hunger food wouldn't be as satisfying. As our needs are satisfied, our drives decrease. Need emerges from the fact that nothing ever ceases to truly exists and things act to preserve themselves in some way. But individual needs results from lack. Drives are driven by an imbalance, driven by external excitation. 

Instinct is the power in the inherent constitution of our being. The potential for action. Objects are the spatial/temporal expression of the universe's potential which instincts aim towards to fulfill needs and which constrain the subject. 

The instincts which promote life are opposed by the universal drive towards death. For existence is either marked by strife, action to remove tension which can result in a state of pleasure or pain, or a state of indifference where needs are satisfied.

To be something means to not be something else, thus the meaning of individual life is judged by its effects. It's essence is its continuation, it's striving. The individual will be no more, just as they were not. The continuation and extension of life's energy is the purpose of life. 

         "Happiness means ending life without being crushed by pain" Oedipus Rex

Conscious life requires an object for its existence, for it is as a living being no longer an object. A cleavage is established in the world, the creation of the subject. Which is not determined to always be a particular object but nonetheless requires an object to identify with to fulfill the prior existing needs. Life's fundamental needs which drive the individual cannot be satisfied. Thus conscious life is a constant struggle between love and death, towards and away from objects.

Sexual energy cannot be destroyed but merely channeled in different ways. In the beginning, the entire world is a source of pleasure. Sexuality is the bodily expression of pleasure, not only associated with genital stimulation. Sexuality drives everything because from the outset the entire body aims toward gratification without any other aim and by any means physically possible. Everybody is born into the world polymorphically perverse. The continuation of life is enabled when pleasure yields to the genitals as the erogenous zone and pursuit of reproduction. 

Life is the process of becoming an individual. Forming a satisfying relationship with the world. Internal balance which must act constantly to maintain itself. 

Wednesday, January 6, 2016

The Conatus: A Naturalistic Life Force

When the scientific worldview comes to predominate ones thinking, the most difficult thing to contemplate about the world I think are living things. For billions of years there was no discernible life on earth, and so far we haven't discovered much life anywhere else. Evolutionary theory explains the diversity of life, but not its origin.

Richard Dawkins' book The Blind Watchmaker gave me a simple and for the time satisfying definition of what life is.

"Left to itself-and that is what it is when it dies- the body tends to revert to a state of equilibrium with the environment. If you measure some quantity such as the temperature, the acidity, the water content or the electrical potential in a living body, you will typically find that it is markedly different from the corresponding measure in the surroundings...when we die the work stops, the temperature differential starts to disappear, and we end up the same temperature as our surroundings. Not all animals work so hard to avoid coming into equilibrium with their surrounding temperature, but all animals do some compatible work...if they fail they die. More generally, if living things didn't work actively to prevent it, they would eventually merge onto their surroundings, and cease to exist as autonomous beings."

His definition of life is quite simple and had a profound impact on me. A living thing resists its parts returning to the equilibrium conditions of its environment. A living thing is a body in motion doing work to preserve its state of motion.

This seems to necessitate some kind of life force. After all, not everything in the universe acts like this. Quite the contrary. And living things just seem qualitatively different than non living things. And yet everything described in the passage obeys the laws of physics. There isn't anything supernatural occurring.

A couple years later I started reading Thomas Hobbes' Leviathan which despite being a work on political philosophy begins with an outline of human nature from which principles of government are deduced. Hobbes' famous violent state of nature is the result of a pre-Newtonian law of inertia.

"That when a thing lies still, unless somewhat else stir it, it will lie still forever, is a truth that no man doubts. But [the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it, though the reason be the same (namely that nothing can change itself), is not so easily assented to. For men measure not only other men but all other things by themselves. And because they find themselves subject after motion to pain and lassitude, [they] think every thing else grows weary of motion and seeks repose of its own accord, little considering whether it be not some other motion wherein that desire of rest they find in themselves, consists"


An object in motion preserves its state of motion until acted upon by another object. Applying this to human psychology, humans are dominated by small internal movements (passions) which cannot be stopped and so will always conflict with each other as individual bodies unless massive force brings them together (the leviathan which is the sum of their wills).

"So that in the first place, I put for a generall inclination of all mankind, a perpetuall and restlesse desire of Power after power, that ceaseth onely in Death. And the cause of this, is not alwayes that a man hopes for a more intensive delight, than he has already attained to; or that he cannot be content with a moderate power: but because he cannot assure the power and means to live well, which he hath present, without the acquisition of more. And from hence it is, that Kings, whose power is greatest, turn their endeavours to the assuring it a home by Lawes, or abroad by Wars: and when that is done, there succeedeth a new desire; in some, of Fame from new Conquest; in others, of ease and sensuall pleasure; in others, of admiration, or being flattered for excellence in some art, or other ability of the mind."


Dawkins and Hobbes brought me closer toward a satisfying naturalistic definition of life. Several properties of living things can be explained by such a "matter in motion" hypothesis. Life is quite frustrating and complete happiness is not fully attainable, and pleasure is fleeting as is pain. Life in some way comes from the inanimate world. Life follows the same laws as anything else in the universe. And ultimately Hobbes' conclusion that social life is defined by conflict rather than harmony, contrary to Aristotle.

This however is where I don't follow Dawkins or Hobbes; that humans are only aggregations of these moving parts, however complex and interconnected.

"The behaviour of the body as a whole will then emerge as a consequence of the interactions of the parts." -Dawkins

His naturalistic definition of life doesn't capture the uniqueness, the dynamism, the wholeness of life. My consciousness isn't reducible to separate sensations. It is one unified synthetic whole. Anything that can ever be known comes to this seemingly infinite understanding, capable of comprehending the vast infinite universe.

Why can't there be a non supernatural life force, that keeps the organism in existence as a whole? And would then apply to the universe itself? No longer a dead mechanical universe, but a driven unified one.

Rejecting the supernatural explanation means several things though.

This life force isn't teleological, that is it is not purposeful.

The life force does not aim at any particular being. There is no foresight, no planning. The existence of individuals no matter how complex is contingent.

The life force isn't itself conscious, as consciousness is defined by its individual objects (as I wrote about before).

The life force isn't a thing or particular being, and as such is not represented by the causal thinking of our own minds. Only individual objects subject to cognition are represented as such.

Accordingly this life force is as practically atheistic as the mechanical explanations of Dawkins and Hobbes.

Luckily for me there was a prominent philosopher who wrote in the same early modern era of Hobbes and had a similar understanding of the universe. Baruch Spinoza, the 17th Jewish-Dutch philosopher. He wrote at about the same time as Hobbes when the Aristotlean worldview was being replaced with the mechanical universe. Spinoza was a determinist and naturalist like Hobbes, but had very important differences in his system of the universe.

Spinoza didn't think mind could be reduced to matter. But unlike Descartes didn't think mind was a separate substance either. Rather body and mind are connected, as different aspects of the same universe. Just as with Descartes, matter is defined by its extended qualities and mind by its thinking qualities.

"A mental decision and a bodily appetite, or determined state, are simultaneous, or rather are one and the same thing, which we call decision, when it is regarded under and explained through the attribute of thought, and a conditioned state, when it is regarded under the attribute of extension, and deduced from the laws of motion and rest."

The Conatus, Latin for endeavor, comes to us in Book III of the Ethics. It is something like the will to live of Schopenhauer or the will to power of Nietzsche, though its also like Newton's first law. The word conatus was used by the Stoics like Cicero and was an explanation for the passions. We want something not because it is good, but rather we think something is good because we want it. Which seems pretty Stoic to me.

"Nothing comes to pass in nature, which can be set down to a flaw therein; for nature is always the same, and everywhere one and the same in her efficacy and power of action"

Spinoza was a monist, meaning that human activity follows the same laws as nature and can be understood causally, making him also a determinist. The mind is also determined by without, but can gain knowledge of the causes of its thoughts and actions and find a sort of happiness. What is unique and sort of counter intuitive at first is that Spinoza thinks not only that body and mind are connected, but that they don't actually cause each other. "The body cannot determine the mind to think, nor the mind the body to remain in motion or at rest." The reason they do not cause each other, as in thinking about raising my arm causes my arm to rise, is that they are different aspects of the same thing. "The mind is united to the body because the body is the object of the mind."

So the Conatus is what determines the motivation of the body and what the mind desires. But determined in an individual way for self-preservation.

The Conatus is presented thus;

Prop. IV Nothing can be destroyed, except by a cause external to itself.

Prop. V Things are naturally contrary, that is, cannot exist in the same object so far as one is capable of destroying the other.

Prop. VI Everything in so far as it is in itself endeavors to persist in its own being.

Prop. VII The endeavor wherewith everything endeavors to persist in its own being is nothing else but the actual essence of the thing in question...the power or endeavour, wherewith it endeavours to persist in its own being, is nothing else but the given or actual essence of the thing in question.

Prop. VIII The endeavor whereby a thing endeavors to persist in its own being involved no finite time but an indefinite time. 

Spinoza then reiterates the Stoics. "From what has been said it is plain, therefore, that we neither strive for, wish, seek, nor desire anything because we think it to be good, but, on the contrary, we adjudge a thing to be good because we strive for, wish, seek, or desire it." This is because the mind, though it can only perceive bodies, gains knowledge by the clarity and distinctness of its ideas, thus being ignorant of the particular causes of its desires.

The argument is that something being what it is means not being able to destroy itself, which means that so long as the parts "agree" in not excluding each other, then the whole wil continue to exist. And that the birth and death of this whole does not measure its existence, but rather its actual continual existence does. The whole is greater than the sun of its parts.

If different things can exist together, they belong together in some larger sense, like how the whole world "hangs together". In individual things however, within the same space and time, existence means not becoming something else. Nothingness does exist with the individual. If something continues to persist, it does so because what is opposed to its nature is avoided and what is advantageous is attracted to. From the individual's point of view, this is not a discrete process as this constitutes the essence of the individual. Duration begins and ends with the individual.

One perseveres through change and harm simply because one perseveres as a whole. What the reductionists don't understand is that different parts can become something greater by what they share in common. The omission is that there is a principle that gives an internal nature to things. Self-preservation is that principle. By simply striving to continue to be as an individual, we determine our nature.

The form of life is a pattern, a creation of opposites. 


Sunday, December 27, 2015

Why The Dialectic?

One of the most well-known ideas introduced by Plato is "truth is justified true belief". This appears in Theaetetus as the third theory of what knowledge is which is associated with belonging to Plato. 

What is true must be known by the subject, they must believe it. The Sophists appeared to agree with that, and so would relativists today. "Man is the measure of all things" Protagoras is supposed to have said. The Sophists instead of dialectic taught rhetoric, to win the argument through appearances to change the mind of opponent, not to discover the truth or continue the discussion. They did this often for payment, seeing knowledge's value as instrumental.

But belief isn't enough says Socrates. Belief must have external support. The English word truth derives from treowth which means something like good faith. What does good mean, if it isn't just having faith? It is external. But more than that; what is external must somehow also be linked to what is good.

In The Republic book I, Socrates gets Thrasymachus the critic of the utility of justice to accept that the good for any person requires knowledge. A good doctor must have knowledge of medicine and of the human body to be a good doctor. Anything that exists has a nature to it. Living to its full potential is what defines its own good. If one hand does not move, it is not a good watch as it cannot tell accurate time which is what a watch is supposed to do. The good of something entails knowledge of what that thing is. 

For something to be good it must serve some end. The good of a watch for me is that it can prevent me from being late to work among other things. In general the end of anything, the highest good, is happiness. It must be that for the "soul" or mind that it has its own nature that defines its own good which is our highest good. The soul or mind's nature is that which superintends our own actions. All of our actions have the end of our happiness. The good of the soul is to command our actions to the fulfillment of our happiness according to the nature of what we happen to be commanding for that purpose. Thus it is that knowledge requires belief of what is true, of the nature of what we hold beliefs of. (This is essentialism, that the essence of something is the criterion of true statements). This is Plato's specific view of what makes something true. Even if one does not accept essentialism, knowledge still can scrutinize the patterns of our own thinking and the biases within.

To have knowledge is to have belief which is also justified by what is true. What is justification? It is to have a reason for a belief.

The Apology lays ground for why knowledge must be justified. Socrates tells the story of a friend who asked the Oracle of Delphi who is the wisest person. The Oracle answered that it was Socrates. Socrates was puzzled by this as surely other people know more than he does on plenty of things. But there is something that he knows that most others do not. That is he knows he knows nothing. Most people think they know something, where they really just have an opinion or prejudice. Socrates is the wisest because he admits he does not think he knows anything, which is the source of hubris.

Elsewhere in Plato's dialgogues such as Meno is the paradoxical idea that one already has to know something in order to know it. That is have the potential or capacity for knowledge. The task of philosophy is to discern whether one really does in fact already know what they assume to know. 

This need for justification is where the dialectic comes from. A belief is presented, assumed to be true. Then another proposed truth which is acknowledged to be believed by both sides. Then the principle of non-contradiction, over whether it is possible to believe these different things to be true according some common non-conflicting notion of truth. This cross examination begins with the belief and does not end until the belief stands up to asserted criticisms or is denied or changed. 

Just as with Plato's tripartite definition of knowledge as true justified belief, the dialectic asserts belief, demands justification, and ends with the truth contained within this belief which may be naught. 

Saturday, November 28, 2015

My Secret Doctrine

We humans don't live in the real world. We are trapped in our conceptions of space and time, and much of the content of our lives has been manipulated from its original meaning by language.

The real world is what comes to us via perception. Being as being. All things belonging together. Anything that can ever be "known", that is divided into the familiar categories of subject and object, is and can have as its basis only what is perception. Exempt from causal thinking, from space, time and all judgement.

Most of this is not subject to conscious thought. Self consciousness attributes to "the world" essentially what is beyond its control, its will. And yet always this self has some sort of notion of what these objects are. In reality, self-consciousness divides itself. For this knowing subject exists in a knowing relation with these objects, and itself takes an object for its existence to be real (the meaning of the cogito).

If this is true, that at all times we stand in relation to everything and in some way distance ourselves from everything, then why don't we think this way more often?

The answer is that we don't live in the real world. The self emerged from the nothingness produced by the vicissitudes of the struggle for life.

For the perpetuation of existence in its myriad animal modes, the transient individual is in a constant struggle with the world by its very nature. Being individuated in space and time, realizing this as the species gains conscious awareness, and gaining recollection of the past through memory, the individual's realization is only possible because of their impending death. This is because the individual separates from the world by its own praxis, preserving itself from a return to its undifferentiated state or a transformation into something else. This is what is common all animal life, the instinct to live.

Yet even this is not enough. Thought eventually develops to the realization of its estrangement from the world and transience. The only escape, while continuing to live, is to somehow end this alienation from the world. By either transforming it, or subverting to its "will". In either case, motivated by a desire to see itself in the world.

It is quite hard and in the end futile for the individual to transform the world in their image, so the other route is more common. To submit to the will of another (more like an-other). This necessitates on the part of who submits to identity with the master, otherwise it would pointless and death would be a more definite way of ending the alienation of individuated existence.

Thus begin the lies which inform the content of our lives. To convince ourselves and each other that our individual station in life relates to the world in a meaningful way. Using words, we can make the lesser appear the stronger and vice versa.

Philosophy can free us from the lies, but can't in my opinion give us anything positive. That is the problem. Thought takes us away from the real world of direct perception. That is the point.

The developed individual self-conscious cannot forever resist the return.

This is the real world: pain, pleasure, and the will.

Kant, Critique of Pure Reason
General Remarks Transcendental Doctrine of Elements II.

"In confirmation of this theory of the ideality of the external as well as internal sense, consequently of all objects of sense, as mere phenomena, we may especially remark, that all in our cognition that belongs to intuition contains nothing more than relations. The feelings of pain and pleasure, and the will, which are not cognitions, are excepted"

Monday, November 16, 2015

The Fourfold Root of the Principle of Sufficient Reason.

Arthur told us to read this as the introduction to The World as Will and Representation, and boy was he right. Schopenhauer explains his treatment of Kant's philosophy so succinctly that WWR is really an exposition of what is written here. The strangest thing about Schopenhauer to me when i first approached him was his fixation on causality. You don't find a lot of thinkers so fascinated with the principle of sufficient reason. It is usually taken as a given. But it does form the basis of his whole system, which is why this is the proper introduction to his thought. 

Before reading this, it is necessary to have some familiarity with Plato and Kant, as Schopenhauer also told us in the introduction to WWR. The two things that one must approach this work which are found in Plato and Kant are 1) there is a difference between how the world appears to us and how it really is (Plato) & 2) we cannot go from this appearance to the thing in itself; the division of subject and object is fundamental (Kant). 

Given these two insights, the purpose of this work is to explore what Schopenhauer thinks is the general rule governing what we can know, which manifests itself in any attempt to understand "the world". It is also helpful to read Schopenhauer's criticism of Kant's philosophy to understand how Schopenhauer's treatment of the division of subject and object differs from that of Kant. The difference is that Arthur took the idealism associated with George Berkeley seriously. That is, an object is known by a subject and cannot be considered as just "out there". Without the subject the world as object disappears. The "external" world is in some way connected to us, as we are to it. It goes both ways. 

Most importantly, it is downright foolish and misleading to say that objects "cause" our representations. For causality is something that our knowing mind projects onto reality. Again without the knowing subject this world as object disappears, and so we cannot say these objects cause our sensations. Rather they are responsible for them, we attribute to these objects a reason. But if we try that, we must then explain how it is they are responsible for these effects, and so we discover that the principle of sufficient reason is fundamental to understanding and cannot be invoked to explain "the world" or "the thing in itself". It is imparted by our own consciousness. 

What the Fourfold Root of the Principle of Sufficient Reason does is to ground sufficient reason as an explanation for various things we know, but not to invoke an explanation for it. That would require going to this noumenal world (which is dealt with in WWR). 

Sufficient reason is just that something is only explained with reference to something else. This being based on the fundamental division of subject and object. Both have no meaning without the other. It is owing to the basic relation between different things that a reason is to be provided for something, which only is in relation to what else is. 

The four classes are becoming (law of causality), knowing (reason), being (space & time), and motives (action or will). These can be thought to correspond to what are called the classical laws of thought. Schopenhauer acknowledges the four:

1) a subject is equal to the sum total of its predicates. Law of identity, a=a

2) no predicate can be attributed and denied to a subject at the same time. Law of non-contradiction, a=-a=0. 

3) one of two opposite, contradictory predicates must belong to every subject. Law of the excluded middle. A is not A and B

4) truth is the reference of a judgement to something outside of it, as its sufficient reason. 

The class of becoming corresponds to identity as like things can only be explained by like things, which shall always demand explanation. The effect is known by its cause and can contain only that. 

The class of knowing corresponds to non-contradiction. Among our representations, they may only follow from those of their type.

The class of being corresponds to excluded middle. Space and time allow for multiplicity and coexistence (space) and succession (time), thus a relation between the two as well as a difference. 

The class of motives corresponds to sufficient reason. This is because it is through the immediate object of the inner sense (time) alone that we come to know the principle of causality at first through the law of causality and then its other groundings. 

This conflation of the four laws of thought with the four roots is largely mine, though Schopenhauer does list the four laws in this way, as what he calls metalogical truths, governing the second class (of reason). I hope this conflation is accurate. If it is, then it is a splendidly easy way to understand this work. Together, the four laws of thought and the four roots explain everything. That i think Schopenhauer would assent to, even if I matched them incorrectly. 

The big point to all this is that the principle of sufficient reason and therefore all we can know is a result of the division of world into subject and object. It is that simple. Without this division, things wouldn't follow one after another, they would just be. But they could not "be" in a meaningful way without this division. 

The relevant part for his more popular ethical and aesthetic writings is the fourth class. This immediate motive power as will be shown in the World as Will and Representation is our direct access away from representation to the thing in itself.

If Schopenhauer is right about the principle of sufficient reason being "sufficient" to explain the different classes of knowing, then Kant's Procrustean table of judgements is reduced from twelve categories to one; causality. The end result of this is that it is possible to have intuitions without concepts. And thereby have access to the mysterious thing-in-itself. The route to this is the inner sense of time, where we experience an endless chain of causation where one thing becomes another, and an individual thing means nothing outside of its relation to other things. Just as the future makes no sense without a present or a past. 

We can perhaps escape our own individuated existence and learn the true nature of things. Which cannot be God, whose existence is reasoned to misapplying the principle of sufficient reason (cosmological and ontological arguments) outside of human consciousness to the universe itself. The underlying nature of reality is itself unconscious. It is not rational. Yet it is intimately connected to our conscious life. Not as a cause, but as one in the same as the world as it appears to us. 

Der Wille.