Truth lies at the end of a long, dark road. You cannot see your way along this road, or feel your way through it. You can only think your way along. Reason is the burning torch that lights the way. Humanity’s greatest geniuses are the ones who have traversed this road and their discoveries along the way can now be collected together to lead us all towards the Truth of existence.
Existence is all about the relationship between the infinite and the finite. Everything we experience seems to be finite, yet we can conceive of infinity in our minds (when we think of numbers going on forever, for example). If something is finite, it is bounded, it has an edge, an end. If something is infinite, it is unbounded, with no edge or end. A boundary is something that separates one thing from another. So, is the universe finite or infinite? Bounded or unbounded? To answer this, first we must define the word universe. By universe I literally mean everything that exists. Absolutely everything. There is nothing outside the universe, for if there were that thing would have to be included in the universe, by definition. So, if the universe was finite, there would be some sort of boundary, or edge to it. But a boundary separates one thing from another, so if the universe has a boundary at its edge, what is the universe being separated from? If there is something on the other side of this boundary, as there must be if it is to be a true boundary, then surely that something must be part of the universe, as we have defined the universe as being everything that exists. Therefore, the universe simply cannot be finite. There can never be a boundary, or an edge of the universe, for anything on the other side of that boundary would have to be included as part of the universe. Therefore, the universe must be infinite, with no boundary, edge or end. We have worked this out rationally simply by thinking. It was not necessary to perform any scientific observations, I did not have to search for the universe’s edge through a space telescope. Thus we see the power of reason over the senses. Thinking is always more powerful than seeing or feeling or touching. Scientists would search for centuries in their telescopes in an attempt to see whether or not the universe had a boundary or not. But, of course, they would never find any such thing. But I, just now, have rendered such a search pointless with a few seconds of reasoning. With reason, one needs no physical evidence. I know that the universe is infinite. If I was deaf, dumb and blind I would still know that the universe is infinite. So long as I can think rationally, I can work out everything about the universe while scientists waste their time with their space telescopes and large hadron colliders. Imbeciles!
This idea of the infinite and finite as the root of all things takes us back to root of the human search for Truth, firstly to ancient Greece and the first philosophers who undertook the momentous task of explaining existence. They called the infinite apeiron and the finite peiron.
Anaximander (610 BC – 546 BC)
The first of humanity’s greatest geniuses was Anaximander, a student of the first philosopher, Thales, and one of a group of ancient Greek thinkers known as the Pre-Socratic Philosophers (as they all lived before Socrates). The pre-Socratics were all mainly engaged in the attempt to define what they called the Arche, which was the substance from which everything in the universe is made, the most basic substance which is the basis for everything else and cannot be broken down into anything simpler. Anaximander was the genius who declared that the arche was non other than apeiron itself, the infinite. Everything else in the universe must derive from this infinite element. Anaximander’s apeiron was a kind of infinite energy in constant motion. This motion cause pieces to break away, such pieces becoming individuated things i.e. matter. If matter was something that came from apeiron, then apeiron must be something other than matter, therefore Anaximander concluded that the apeiron must be alive in some way, so that it could be the source of life as well as of dead matter. As the source of everything, apeiron must be everywhere at all times, must fill the whole universe with no gaps. Any gaps would indicate the existence of something that did not rely on apeiron for its existence therefore apeiron would not be the arche. Therefore, the arche must fill the universe with no gaps. Anaximander suggested that eventually all matter, still in motion, would eventually return to its pure state of energy, thus restoring the apeiron. Of course, Anaximander did not discover the apeiron by observing it in the scientific sense, but he used reason to know that it must exist. The apeiron is therefore a rational substance, a substance that has no physical existence but must have rational existence. Physical matter, therefore, is not the be all and end all of the universe, there is more to the universe than just matter, in fact, matter itself derives entirely from the apeiron. Matter is only secondary, whereas apeiron is primary. Prior to Anaximander, his teacher Thales had proposed that Water was the arche, the element that everything else derives from. Water, though, is physical, can be observed, touched, felt. Anaximander knew that the arche must contain the possibilities for everything that can be experienced, all of the opposites in nature must be present in the arche. Water can be hot or cold, can be still or in motion, and several other sets of opposites, but, as Anaximander realised, water can only ever be wet and never dry. So where does dryness come from? Dryness is something that exists yet is never present in water. Therefore water could not be the arche. In fact, nothing physical can be the arche as physical things always have certain characteristics that they exhibit entirely without exhibiting the opposite, like water always being wet and never dry. Therefore, the arche simply had to be non-physical, and Anaximander arrived at the idea of the apeiron purely through rationality and reason. Anaximander’s greatest use of reason is perhaps his assertion that the earth was floating in space, supported by nothing. As Thales had declared water to be the arche, he had said that the earth must be floating on water. Anaximander, having worked out that the universe was infinite, knew that this meant that the earth was in a position that was equidistant from everywhere else in the universe, as the universe was unbounded. Therefore, if the earth moved to a different position it would cease to be equidistant from everywhere else. As there was no sufficient reason for this to be, Anaximander concluded that the earth remained where it was, suspended in space with nothing required to hold it up. This was particularly ingenious as it presented a rational explanation rather than a physical explanation. Reason dictates that nothing can happen without a sufficient reason for it doing so, and Anaximander was the first genius to use this rational principle to explain things. If the earth has no reason to move, then it won’t. Anaximander also came up with the first theory of evolution. He noticed that human babies are completely helpless, and without the care of adults they would die very quickly. If humans had been created, then the first humans would have died as babies. Contrary to humans though, there are several species of animals where the adults do not care for the babies and the babies survive on their own, fish for example. Anaximander realised, therefore, that humans must have developed from earlier species whose babies needed no care. Thousands of years before Darwin, Anaximander worked out evolution rationally, just by thinking, rather than by spending years observing the behaviour of hundreds of species as Darwin did.
Pythagoras (570 BC – 495 BC)
Humanity’s next supreme genius was Pythagoras, at one time a pupil of Anaximander. Pythagoras went one step further than his teacher in his definition of the arche. Anaximander had simply declared the arche to be apeiron, an infinite, living energy from which all things arise. Pythagoras gave further definition to this idea by declaring that the arche was in fact numbers, or mathematics. Whereas most people think of mathematics as being some sort of abstract concept, Pythagoras was declaring that mathematics was, in fact, the living infinite energy that Anaximander had called apeiron. Anaximander had said that the universe comes from the motion of apeiron, but he had not explained how or why apeiron was in motion in the first place. It was Pythagoras who realised that this motion could be explained mathematically. In fact, the energy of apeiron was not just defined by numbers, but it actually was numbers and their mathematical relations. If the apeiron filled the whole universe, with no gaps, as Anaximander had realised it must, then Pythagoras realised that every point in the universe could be given its own mathematical definition, a number or co-ordinate unique to it, to differentiate it from all other points. As such, we now have a universe of mathematical points that can be thought of as a co-ordinate grid. Each of these points relates to all the others via mathematical relations and laws. Therefore, the universe is entirely mathematical and rational. Pythagoras’s insight is perhaps the most important in human history as it rationally proves that everything in the universe can be known and explained by rational minds, simply by using mathematics, of which the universe is made. Mathematics is all there is. Anaximander had said that the apeiron was the source of all life, and was therefore divine. Pythagoras had now shown that it was mathematics that was divine, the source of all life. He therefore set out to explain all of the universe using only mathematics. He founded a secret society of like minded individuals and created a religion based on reason and mathematics, a religion that explored the divinity of mathematics. Pythagoras then began to see mathematical relations everywhere he looked. He noticed that if you halved the length of a string on a lyre, it would produce a note an octave higher. This led him to work out the mathematical relations of musical notes. It transpired that simple mathematical relations produced notes that sounded harmonious together and the more complex the mathematical relation, the more dissonant the notes sounded. This led Pythagoras to declare that music was mathematics in the form of sound, and that all the universe exhibited similar harmonious mathematical relations, resulting in harmony. As every point in existence is a different number, all these numbers must be related in harmonious ways, i.e. the universe is perfectly rational. But Pythagoras also realised that, for any of this to make sense, every number had to be represented. Mathematics only works with the right numbers. For it to work you need to have all the numbers. Therefore, every possible number must exist in the universe. As the apeiron is infinite, as Anaximander said, then every number can be represented in it, as Pythagoras realised was necessary. Mathematics can only work when we have all possible numbers to use. The universe provides them. Each point in the universe corresponds to a unique number. Anaximander’s apeiron had created the concept of a kind of existence that was non-physical, non-material, and Pythagoras’s mathematics was equally non-physical and non-material. But, also, Pythagoras viewed the living aspect of humans (and all life) as also being non-physical, non-material. This living aspect, or soul, being non-physical, corresponds perfectly to the mathematical points that Pythagoras spoke of. A point has no dimensions, no measurement, therefore is also non-physical. Therefore, Pythagoras concluded, rationally, that every point in the universe was a number, and was also the root of a soul. Ultimately, all of these points, as they take up no physical space, exist all together, on top of one another. Therefore, the entire universe can be said to spring from a single, mathematical point, a point that contains all other points, all other numbers. Everything in the universe comes from these points. Two points connect to form a line, three to form a two-dimensional plane and four to form a three-dimensional solid object. Therefore, Pythagoras gave a mathematical explanation for the apeiron of Anaximander, even going so far as to declare apeiron to be mathematics. Each mathematical point that makes up apeiron is also a soul, given that the soul must be non-physical, as are these points. Therefore, Pythagoras rationally proved that the soul was immortal, in fact, each soul is part of the fundamental substance of the universe, the apeiron, pure mathematics. From this, Pythagoras realised that when the physical body dies, the soul must live on, for if the soul is a part of the apeiron, then it must be eternal and can never be destroyed. From this, Pythagoras began to teach of the transmigration of souls, or reincarnation. If the soul is a non-physical, mathematical point, then when the body dies, the soul must live on and find a new body in which to live. Pythagoras’s religious ideas were, of course, based entirely on mathematics, rather than on mystical intuition, and, as such, were revealed not to be faith-based opinions, as in other religions, but, in fact, the real, rational Truth of the universe. Pythagoras proved that the soul is immortal, that it lives on after physical death, that matter is secondary in relation to the immaterial, mathematical realm of the soul. With Pythagoras, mathematics ceases to be merely an abstract idea, and becomes True reality, it really exists, in fact it is all that exists. Rationality dictates that this must be so.
Heraclitus (535 BC – 475 BC)
Pythagoras had given a mathematical explanation to the apeiron of Anaximander, and had declared that all that existed were mathematical points, which were also souls. A student of Pythagoras, Heraclitus, redefined the apeiron as an everlasting fire, or energy, reflecting the constant motion that Anaximander had spoken of. Heraclitus said that this fire in constant motion was governed by rational laws, which he called Logos. These laws, of course, were simply the mathematics of Pythagoras. Heraclitus characterised this fire as not only being in constant motion, but being in a constant state of change. He said that there was nothing permanent except change. Just as Anaximander had stated that the apeiron was the source of all opposing forces, Heraclitus stated that the ever living fire was constantly changing as a result of the conflict of these opposing forces. All of these conflicts must be resolved, and the resolution of these conflicts produced the change that constantly takes place in the universe. As such, the universe is in a constant state of evolution, eternally changing as per the laws of Logos, and never being static or constant. Heraclitus said that the universe was constantly becoming, never simply being. As our souls are the mathematical points that make up the universe, they each contain the Logos, i.e. the mathematical laws that define existence. Through reason, Heraclitus said, we can work out the entire universe by examining these laws, contained within each and every one of us. Our pursuit through these laws is our constant becoming, constant changing. Through these laws we come across opposing forces and then we can rationally balance these opposing forces leading us on towards the next set of opposing forces. Heraclitus had rationally explained the constant motion of the apeiron as required by Anaximander and tied it to the mathematical nature of the universe as required by Pythagoras. If the arche was an ever changing fire (or energy), as Heraclitus asserted, then everything else in the universe that comes from the arche must also by ever changing. Anaximander had suggested that humans had evolved from prior species, but Heraclitus showed, rationally, that everything in the universe must be evolving, or becoming.
Parmenides (515 BC – 450 BC)
However, Heraclitus’s view was opposed by his great rival Parmenides. Where Heraclitus had said that everything in the universe was constantly changing, Parmenides, instead, stated that nothing was changing and that change was an illusion. Parmenides thought that for something to move it would first have to enter a space that was previously unoccupied, therefore empty. But if the arche fills the whole universe with no gaps then there can’t be any empty space therefore movement is impossible. From these ideas Parmenides arrived at the conclusion that there were two distinct aspects of the universe, firstly, the True, motionless, non-changing aspect, and, secondly, the illusory, moving, ever-changing aspect. From this we can see that Parmenides was an ultra-rationalist, far more so even than the greats who preceded him, for he was saying that the world we experience with our senses was purely illusory, and that the True reality was only available to reason and rationality. Before Parmenides, the philosophers had been searching for the arche, the single substance form which the entire universe is made. But with Parmenides comes the idea that there could be two substances, or two different aspects of a single substance. Anaximander had differentiated apeiron from the material world we are familiar with and Pythagoras had shown that the entire universe, mind and matter, was an expression of mathematics. But Heraclitus and Parmenides had come up with entirely opposing views of reality, Heraclitus saying that everything changes and Parmenides saying that change was an illusion.
Anaxagoras (510 BC – 428 BC)
Parmenides had created a great problem in the quest to explain the universe. He seemed to have rationally shown that nothing can ever change in the universe, yet this directly contradicts our every experience, as well as the rationality of Heraclitus. It was another great genius, Anaxagoras, who made the first progress towards solving this problem. Anaxagoras went back to Anaximander’s apeiron, the substance that contains the potential for all things that are possible in the universe. Anaxagoras realised that if all things were present in the apeiron then, no matter what thing one was examining in the universe, it too would contain everything, or at least elements of everything. For everything is made from apeiron, and apeiron contains elements of every possible thing, so every possible thing, being made from apeiron, must itself contain elements of every possible thing. Anaxagoras asserted that nothing could ever be truly isolated from apeiron because everything could always be divided further, every object could always be made smaller and smaller, always being made of apeiron and therefore containing everything. Anaxagoras then took the Logos of Heraclitus (which can be said to be the mathematics of Pythagoras) and envisaged it as the mind of the universe, which he called Nous. According to Anaxagoras, it was Nous that controlled apeiron, causing it to move and change giving rise to all the possible things in the universe. Heraclitus had spoken of the Logos as being the rational guiding force of the universe, and Pythagoras had stated that everything is an expression of mathematics i.e. the Logos is mathematics, but Anaxagoras’s concept of Nous turns the Logos into the mind of the universe, as opposed to matter. In this respect the Logos/Nous is controlling everything, causing the apeiron to form into all things. Nous obeys Pythagoras’s mathematics and Heraclitus’s rationality at all times, therefore it, itself, ] never changes, as per Parmenides. But Nous causes other things to form in the universe, being made from apeiron and containing all things within them, and this reflects the constant changing of Heraclitus. Therefore, Anaxagoras had shown how the ideas of both Heraclitus and Parmenides could be reconciled. Heraclitus was particularly vindicated as his ideas and those of Parmenides can be said to have been two opposing forces and the ideas of Anaxagoras had brought them into balance in accordance with Logos, or Pythagorean mathematics, which is exactly how Heraclitus has asserted that change takes place!
Plato (428 BC – 348 BC)
Anaxagoras had paved the way for a reconciliation of Heraclitus and Parmenides, but it was Plato who made this reconciliation his primary objective. Parmenides had suggested that the material world of change was merely an illusion, and that True reality never changes. This was the first time a philosopher had posited that there might be two aspects to reality. Plato took up this idea and asserted that there were two distinct realms of existence, one material and one immaterial. The immaterial realm was the realm of Forms. Plato states that the realm of Forms is the True reality. The Forms are perfect in every way, obeying the mathematics of Pythagoras. The material realm contains nothing but inferior copies of the Forms, hence the illusion of change that Parmenides had spoken of. It is the perfect realm of the Forms that never changes, but the material realm that does, as per the ideas of Heraclitus and Anaxagoras. Plato realised that, in the material realm, there is never any kind of perfection. For example, one can draw a circle on paper, or see something circular in nature, but none of these circles will be True circles. They won’t be perfectly circular. There will always be some kind of imperfection to them. The only True, perfect circles exist in the immaterial realm of Forms, as the Form of the circle. We can never experience a perfect circle with our senses, only with reason can we conceive of a perfect circle, for it is reason that gives us access to the realm of Forms. Plato suggested that the material realm had been fashioned by some kind of cosmic sculptor which he named the Demiurge. The Demiurge, a conscious being, was able to access the Forms with his reason, and he then proceeded to sculpt matter into copies of the Forms. Plato managed to bring together all of the ideas of the great geniuses who preceded him. His immaterial realm of Forms was derived from Parmenides, while his material realm of matter was derived from Heraclitus. His demiurge, who crafts the material realm based on the Forms, is similar to the Nous of Anaxagoras, and the Forms themselves represent mathematical perfection of the kind that Pythagoras envisaged.
Aristotle (384 BC – 322 BC)
Plato set up the Academy in Athens. His star pupil there was Aristotle. Aristotle eventually rejected a key element of Plato’s philosophy, namely, the realm of Forms itself. Whereas Plato envisaged a universe with two separate realms, the material realm of matter and the immaterial realm of Forms upon which matter was based, Aristotle only envisaged one realm, that of the physical universe. However, Aristotle didn’t reject the Forms themselves. Rather than having the Forms existing in their own separate domain, Aristotle placed the Forms in the same realm as that of matter. In his system, the Form for each thing was present within the thing itself. This idea, although in opposition to the ideas of the great geniuses prior to him, allowed Aristotle to formulate his concept of teleology. Anaximander had said that the apeiron was in constant motion and Heraclitus had embellished that idea, saying that all the motion was in accordance with the laws of Logos, which correspond to the mathematics of Pythagoras. Anaxagoras added the idea of Nous to Logos, presenting the idea that there was some kind of guiding force determining how events would proceed. By placing the Forms of things within the things themselves in the material realm, Aristotle was able to formulate a theory as to how things were guided. Aristotle said that everything contained within it, the idea or Form of the perfect or actualised way in which that thing should exist. As matter, things initially begin as potential, but the Form within them directs the matter to change and develop towards its perfect, actualised state. This idea is called teleology. Aristotle said that everything exhibits teleology, given that every thing contains its Form within it. This idea gave further embellishment to the idea that the universe was constantly in motion, as per Anaximander, constantly changing, as per Heraclitus, and being guided by a force, as per Anaxagoras, but still with the idea of perfect Forms that are unchanging, as per Parmenides. Aristotle’s teleology presents a version of evolution that is purely purposeful, there is clearly a specific aim towards which the universe is striving.
Plotinus (204 – 270)
Centuries after these great philosophers, a new school of philosophy arose based on their ideas (particularly those of Pythagoras and Plato) called Neoplatonism, founded by the great genius Plotinus. Plotinus used the ideas of the great philosophers to formulate a new philosophical religion based on their ideas. Plotinus successfully managed to combine their ideas into an elegant system. For Plotinus, everything has its source in what he called The One. The One is essentially the arche, the source of everything. But for Plotinus, The One, as the source of everything, is very similar to Pythagoras’s concept of the point that contains all other points, i.e. The One is purely dimensionless and immaterial, yet contains within it everything else in the universe. Plotinus’s system consists of a series of emanations starting from The One. The first thing that emanates from The One is The Nous, basically the same Nous as that of Anaxagoras. The Nous is the mind or the intellect of the universe, the thing that guides it and controls it. For Plotinus, the Nous contains within it all of the perfect Forms that Plato had spoken of. As the mind of the universe, the Nous knows everything about the universe and thinks all possible thoughts simultaneously. The next emanation is the Psyche or the soul, emanating from the Nous. The Psyche is equivalent to Plato’s Demiurge. Whereas the Nous thinks everything simultaneously, the Psyche thinks slowly and as a linear process. The Psyche can access the Forms present in the Nous and use them to create the next emanation which is Nature, or the physical world, which is, as Plato said, an inferior copy of the Forms in the Nous. The Psyche is also split into two parts, firstly the upper part which is the World Soul, the collective soul of the world, and secondly, the lower part which takes the form of all the individual souls in the universe. As these individual souls are only one emanation away from the physical world, Plotinus explains that these souls take the physical world to be true reality, when, in fact, True reality is mental rather than material, the true Forms in the Nous rather than the inferior copies of them in Nature. For Plotinus, the task of our souls is to leave behind the physical world and travel back up the emanations, firstly to the upper Psyche, or World Soul, then into the Nous itself where the True Forms are, and finally back to The One, which contains everything. This idea expands on Anaximander’s original concept that the universe begins as apeiron and shall return to apeiron. Unfortunately, Plotinus’s religion, based on reason, rationality and mathematics, as well as the ideas of the greatest of geniuses, failed to take hold of Europe which, instead, adopted the absurd, irrational, faith-based religion of Christianity after the fall of the Roman Empire. Christianity makes no real effort to explain the Truth of the universe, rather it tells silly stories which appeal to people’s emotions, giving them a simple satisfaction. The great rational discoveries of these ancient geniuses were almost lost thanks to this disgraceful religion.
Nicholas Of Cusa (1401 – 1464)
Fortunately, however, Roman Catholicism had retained some elements of Greek Philosophy, Aristotle in particular, and great Catholic scholars were well aware of the old philosophers and their ideas. Over a thousand years after Plotinus, his ideas were resurrected by humanity’s next great genius, Nicholas of Cusa. Nicholas made the audacious attempt to reform Catholicism by reintroducing the rational ideas of the Greek geniuses. Anaximander had said that the physical world comes from apeiron and then returns to apeiron and Plotinus had said that everything comes from the One, passes through a series of emanations before returning to the One. For Nicholas of Cusa, the One was God, the absolute maximum, pure infinity. Everything else in the universe is finite, therefore is part of God. The finite things flow out from God and then return to him. The finite things constitute God being split into small bits, each bit being a part of God and therefore containing the whole universe within them, just as Anaxagoras had said. God is made up of all of these smaller bits, yet each bit contains God within it. As God is infinite, he can be split into an infinite number of finite bits. In direct opposition to mainstream Catholicism, Nicholas declared that, as the universe was infinite, there could be no part of the universe that was at the Centre. Catholicism stated that the Earth was at the centre of the universe and Nicholas’s ideas influenced Copernicus, who stated that the Earth orbited the Sun. Catholicism also states that we are created souls alienated from God, who is the ultimate master of our fate. This is of course purely irrational and Nicholas of Cusa was making the attempt to return to rational religion by stating that we all contain God within us and we can return to God. We are therefore the masters of our own fate and eventually we will all come into contact with God within us i.e. we will all eventually become God, a radically different religious idea to Catholicism, yet one based on pure rationality and reason, i.e. one that is True. Nicholas was trying to show that Catholicism was false and the ideas of the Great greek geniuses were the real Truth.
Giordano Bruno (1548 – 1600)
A much more direct attack on Catholicism came from Giordano Bruno. Bruno destroyed the cosmology of Catholicism by rationally showing that the laws of the universe must be consistent across the whole universe. By suggesting that the sun was merely just another star, Bruno suggested that there must be other planets like the Earth orbiting other stars, some of which must have conscious life, similar to humanity. As the universe is rationally infinite, there simply must be life elsewhere on other planets. As Catholicism makes no account for this other life, Bruno had demonstrated that Catholicism was false and irrational. Bruno declared that the universe was filled with a substance called aether (like the apeiron of Anaximander) through which all of the heavenly bodies move under their own momentum. Bruno also declared that the infinite nature of the universe must apply to time as well as to space. Therefore the universe must have always existed and will continue to exist for eternity. Existence cannot come from non-existence and can never give rise to non-existence. Therefore, the universe was not created by God nor will there ever be an end to the universe, as Catholicism believed. Like Nicholas of Cusa, Bruno believed that everything in the universe was part of God, yet Bruno went further than Nicholas. He said that each part of the universe was a dimensionless point, called a monad, and everything else in the universe was formed from these monads. Souls were special kinds of monads, ones which were further on in their journey towards becoming God. Being non-physical, these monads must be mental in nature, therefore, Bruno asserted that mind was everywhere in the universe, within every bit of matter and beyond. Unfortunately, Bruno’s ideas (which destroyed the credibility of Catholicism) were considered too dangerous to the might of the Catholic Church and Bruno was found guilty of heresy and blasphemy and was burned at the stake, a great martyr of Truth killed at the hands of irrational maniacs.
René Descartes (1596 – 1650)
Nicholas and Bruno had failed to reform Catholocism from within, but reason persisted. Philosophy was ‘reborn’ thanks to the work of René Descartes, humanity’s next supreme genius. Rather than try to edit Catholocism to reflect rationality, Descartes decided to ignore any assertion about existence made by religion and start again from scratch. Just like the ancient Greeks, Descartes realised that there was a fundamental difference between mind and matter, and that they were both together, the two substances that made up the universe. Descartes formally defined these two substances more rigidly than before. He said that matter was ‘extended’, which meant that it had dimensions, was physical and could be measured. Mind, on the other hand, was ‘unextended’, which meant that it was dimensionless, non-physical and could not be measured or detected by the senses. The problem that arose from these definitions was, how could mind and matter interact with each other if they were entirely different substances defined in such a way? Having separated the universe into mind and matter, Descartes proceeded to give a primacy to mind rather than matter. He realised that one could never be sure of the existence of matter at all. One’s experience is purely mental in nature, so what is to stop matter being merely a product of mind, i.e. an illusion? Mind, however, is something one can be absolutely sure about, or at least one’s own mind, as Descartes summed up in his immortal phrase, “I think, therefore I am”. Thinking is what mind does, therefore one’s own thinking rationally proves that one’s mind exists. When it came to matter, Descartes, just like Anaximander before him, saw that the physical universe must contain no gaps, as such gaps would be unextended and therefore belong to mind rather than matter. Likewise, Descartes realised that there could not possibly be indivisible physical atoms, for anything physical, anything extended, could always be made smaller. From this, he formulated the idea of the material universe being made from basic units that obeyed strictly mathematical laws. Just like Pythagoras, Descartes realised that the universe must be purely mathematical. Descartes, therefore, envisaged the material universe as machine-like, but the mental universe as providing the element that gives rise to free will. Our minds possess will, which leads to us making free decisions, but also leads to irrational thinking. Only through pure reason can our minds understand the mathematical nature of the universe. However, the problem remained, how could mind and matter interact if they were separate substances with nothing in common?
Baruch Spinoza (1632 – 1677)
Descartes had said that the universe was made of two substances, mind and matter. Baruch Spinoza, on the other hand, said that there could only be one substance that the universe was made from, going right back to the idea of the arche, the single substance that makes the universe. Spinoza simply said that this one substance was God, although this was not the same as the God in Catholicism. For Spinoza, everything in the universe was God. All of the finite parts of the universe were simply finite parts of the infinite God, which was everything. Whereas Descartes had said that mind and matter were entirely separate, Spinoza said that mind and matter were in everything. All matter has mind and all mind has matter. They always exist together and are both attributes of the one primary substance, God. Both Descartes and Spinoza had rationally formulated their systems, yet both had come up with different ideas. Descartes’s system suffered from the problem of mind and matter interacting, a problem which was moot in Spinoza’s system as mind and matter are both aspects of one substance, yet Spinoza, like Descartes, had asserted that the universe follows mathematical laws, and is therefore like a machine. Descartes said this only applied to matter, and that the attributes of mind led to there being free will in the universe. In Spinoza’s system, however, mind and matter are always together, therefore, both mind and matter become machine-like and there is no room for free will in Spinoza’s system.
Gottfried Leibniz (1646 – 1716)
The problems of the rational systems of Descartes and Spinoza were solved by humanity’s next great genius, and perhaps the very greatest genius of them all, Gottfried Leibniz. Starting with Descartes’s definition of matter being extended, Leibniz followed the rationality of this definition and saw that matter could always be divided into smaller and smaller units. This led him to the conclusion that extended matter must somehow be derived from unextended mind. ‘Units’ of mind were unextended, therefore could not be divided further, and Leibniz realised that this made them the true units of the universe, thereby giving primacy to mind over matter. This was a synthesis of the ideas of Descartes and Spinoza. For Leibniz, mind and matter were indeed two separate substances, but one was derived from the other, namely matter was derived from mind, thereby making mind the primary substance of the universe. Matter being extended didn’t make it different from mind, but it made it simply the extended form of mind. Leibniz had presented himself with a problem, however. Just as extended matter could always be divided, becoming smaller and smaller, so unextended mind would always be unextended no matter how much of it was added together. The question was, then, how did matter come from mind, how did unextended things give rise to extended things? The answer lay in mathematics. Taking inspiration from Giordano Bruno, Leibniz envisaged the universe to be primarily made of ‘particles’ of mind called monads. Each monad was an unextended, dimensionless point and the universe constituted an infinite number of monads existing next to one another with no gaps between them. Just as Pythagoras had said, each of these monads was unique and could therefore by represented by a unique number and the universe could therefore be explained in terms of the mathematical relations between these numbers. Leibniz realised that the relations between monads were what gave rise to extended matter. The extension itself was the mathematics of the unextended monads. This was essentially the same thing that Pythagoras had said, however, Leibniz went even further. Leibniz said that each monad was an unextended, dimensionless point taking up zero physical space. Leibniz was then able to expand this definition after exploring the mathematical nature of the number zero. Leibniz realised that zero actually contained all other numbers. If one adds together every number in existence the result is zero. All numbers, both positive and negative, real and imaginary, cancel to zero when added together. Leibniz therefore realised that each monad contained an infinite amount of mathematical energy, represented by all the possible numbers, which all cancelled down to zero, maintaining the zero value of the monad. Monads, as units of mind, were all individual souls, or thinking minds, this thinking being the monad’s subjective experience of the mathematical activity of the energy contained within it. Just as an individual monad is the balance of the infinite energy contained within it, so the whole universe is a balance of the infinite energy of the infinite monads contained within it. The physical world is derived from the mathematical relations between the monads. Each monad performs mathematical operations which it experiences as thoughts. As the monad performs these operations, it begins to reflect on itself, learn about itself and the rest of the universe. Eventually, as per Aristotle’s teleology, each monad realises its potential and achieves perfect mathematical balance, meaning that, subjectively, it will know the whole universe, i.e. it will have become God, become perfect. Leibniz had provided the mathematics to support the idea that each soul was evolving towards perfection, that the universe was evolving towards perfection, governed by mathematics.
Immanuel Kant (1724 – 1804)
After Leibniz, all that remained to fully explain existence, was to provide further mathematical and philosophical rigour to his impeccable logic. Immanuel Kant was the first to add some philosophical rigour by adding to Descartes definitions of mind and matter. Where Descartes divided the universe into mind and matter, Kant divided it into the phenomenal realm and the noumenal realm. The phenomenal realm corresponds to the physical realm of matter, the realm that we experience with our senses, that we can see, hear, touch and feel. The noumenal realm corresponds to realm of mind, or Plato’s realm of the perfect Forms, the True realm of things as they are in themselves. Kant suggested that we can only ever experience the phenomenal realm and never experience the noumenal realm, as our minds only interpret the noumenal realm and it is this interpretation that creates the phenomenal realm that we experience. Kant had rigorously defined the issues philosophically but had reached the conclusion that we can never know how the universe actually is. This was due to his ignoring of the mathematical side of things. Ingenious though his philosophy was, his failure to apply mathematics to it is what resulted in his conclusion that we can never truly know the universe. Clearly, more mathematical rigour was required.
Joseph Fourier (1768 – 1830)
One of the reasons that Leibniz hadn’t entirely explained the universe was that the mathematics required to do so had not been available to him at the time. Leibniz had partially solved Descartes mind/matter interaction problem by showing that matter must be derived from mind, from the monads, and that this must be done via some mathematical operations. But it wasn’t until the work of the mathematician Joseph Fourier that these mathematical operations were discovered. As he was a mathematician and not a philosopher, Fourier himself did not realise the implications of his own discoveries, but he can nonetheless be counted among humanity’s greatest geniuses by virtue of having made the mathematical discoveries necessary to solve Descartes’s mind/matter problem. Fourier discovered that all mathematical functions can be expressed in terms of simple waves, namely sine and cosine waves. From the analysis of these waves, Fourier realised that the same mathematical information can be presented in two completely different ways. Mathematical information can be presented in terms of a frequency domain or a space/time domain. Using a mathematical operation, one can switch between the two in what is known as a transform. These mathematical ideas provide the answer to Descartes’s problem. Leibniz had shown that each monad contains infinite energy, and energy is simply a collection of simple waves. The energy within the monads, within the realm of mind, is therefore represented by Fourier’s frequency domain and this same energy can be represented by Fourier’s space/time domain, via Fourier’s transform, to form the realm of matter. Leibniz had shown that mind and matter were simply two forms of the same thing, and Fourier had provided the mathematics to show how it worked. Finally it could be shown how mind and matter can interact, by the fact that they are both presenting the same mathematical information in two different ways, related by Fourier’s transform.
Georg Hegel (1770 – 1831)
Fourier’s mathematics provided the answer to Descartes’s mind/matter interaction problem and triumphantly vindicates Leibniz’s assertion that matter is derived from mind, that the two are merely two forms of the same thing. Yet it still remained to be explained how the mathematical operations of the energy inside monads were evolving towards their teleological perfection. Enter the next great genius, Georg Hegel. To explain the evolution of monads, Hegel went back to the ideas of Heraclitus. Heraclitus had said that the universe changes due to the conflict and resolution of opposite forces. Hegel took this idea and added to it greater philosophical rigour and formed it into the idea known as the Dialectic. Hegel said that everything that exists can be called the thesis. The existence of the thesis automatically brings in to existence its opposite, the antithesis. Things are defined by what they are not, therefore nothing can exist without the thing that it is not (its opposite) also existing. The thesis and the antithesis interact and conflict arises. This conflict is eventually resolved by a new thing arising, the synthesis, which takes what is good from both the thesis and the antithesis. This higher synthesis then becomes a new thesis, the existence of which brings in to existence its antithesis causing conflict and resolution into a new, higher synthesis, which becomes a new thesis etc. This dialectical progression occurs everywhere in the universe to everything in the universe. This is how monads evolve towards their perfect state. Hegel backed up this idea by providing a philosophical reason why this should occur. Hegel defined the basic substance of the universe as Geist, meaning mind or spirit. This was the collection of monads in the Leibnizian system, God in Spinoza’s system. Geist originally exists in a purely unconscious state and strives to become fully conscious. By being split into infinite monads, Geist can begin to become conscious of itself, as the individual monads can reflect upon one another in order to become aware of themselves. Thus Hegel shows that the existence of many monads is rationally necessary in order for the universe to evolve towards its final state of full consciousness of itself. The one had to become many in order for the many to all reflect upon one another and begin the process of actualising their potential and become perfect, a process which follows the logic of the Dialectic of thesis, antithesis and synthesis.
Arthur Schopenhauer (1788 – 1860)
Disregarding Hegel and following on from Kant, Arthur Schopenhauer asserted that the universe was simply a single, mental, striving Will to exist. This will does nothing other than strive for its own continued existence. The Will as it is in itself corresponds to Kant’s noumenal domain and physical expression of the Will corresponds to Kant’s phenomenal domain, as the subjective experience of the Will. Thus was Kant’s philosophy tied to the idea of mind striving for something. However, as Schopenhauer disregarded the philosophy of Hegel, he thought that the Will was one single thing on its own, rather than being individuated into many things as Hegel (and Leibniz) would have said. Schopenhauer said that the Will strives constantly in such a way as to experience pleasure and avoid pain. However, when the Will does experience pleasure, it becomes dissatisfied with that pleasure and begins to Will pleasure of a different kind. Therefore, the Will is never ever satisfied and simply continues to Will on and on. Thus Schopenhauer’s philosophy presents the ultimate pessimistic view of reality as opposed to Hegel’s very optimistic philosophy which says that the universe will evolve to perfection eventually. Schopenhauer asserts that the Will is the very source of evil and is itself purely evil because all it does it cause us to experience only fleeting moments of pleasure as small islands in an ocean of pain and suffering. Regardless of the moral implications of Schopenhauer’s Will, his philosophy shows us that physical things have an ‘inside’ from which they are subjectively experienced, for example, our minds subjectively experience our bodies from the inside. It follows that this must be true for all physical objects, thereby proving that there is a fundamental mind that subjectively experiences all matter from the inside. Mind and matter are two sides to the same coin, just as Leibniz said.
Friedrich Nietzsche (1844 – 1900)
Following Schopenhauer, Friedrich Nietzsche added a teleological element to the Will, turning it into Will to Power. Nietzsche realised that Schopenhauer’s Will to Exist was not sufficient, as there are many occasions when one might Will something that causes pain if it then leads on to some increase in its power. Nietzsche realised that the Will wasn’t simply blindly striving to exist, but was rather striving to increase its own power, i.e. it had a teleological purpose. What the philosophies of Schopenhauer and Nietzsche do is explain the subjective experience of the evolution of monads as described by Leibniz and Hegel. Leibniz’s mathematical description of monads and Hegel’s description of the Dialectic provide the objective analysis of what is happening in the universe, as if one was looking in from the outside. Schopenhauer and Nietzsche then provided the description of what this was like from the inner point of view of an individual monad, the subjective experience of an individual within the universe. Therefore, Schopenhauer and particularly Nietzsche added a moral dimension to the explanation of existence. If existence is all about Will to Power, as Nietzsche asserted, then stronger Wills will succeed by dominating weaker Wills. For Nietzsche, morality became all about the strength of Wills. Stronger Wills who gain in power are good and weaker Wills who lose power are bad. Nietzsche realised that this gaining of power would eventually lead to the emergence of a new type of human, which Nietzsche called the Superman, individuals who had gone beyond the traditional concepts of good and evil and who had increased their power to maximum. As an atheist, Nietzsche saw the Superman as the highest level of humanity, however, if we tie in Nietzsche’s ideas with those of Leibniz and Hegel, we can say that the Superman is a human who has become God, or a monad which has dialectically solved and balanced its own internal mathematical operations. Eventually, every monad in the universe will have done this and the full monadic collective will exist at its final, perfect state, i.e. the apeiron will have returned to itself once again.
Kurt Gödel (1906 – 1978)
Leibniz and Hegel had provided the objective explanation of the universe, mathematical in nature, and Schopenhauer and Nietzsche had provided the explanation of subjective experience, yet this had not been done mathematically. Subjective experience is all about free will (or Will to Power), which had been allowed for by Descartes as for him mind was completely separate from matter, but not allowed by Spinoza who had made mind and matter two aspects of the same thing, which, being mathematical, was machine-like, obeying strict mathematical laws. What remained, therefore, was to explain free will (subjective experience) in terms of mathematics, for the whole universe had been shown (by Leibniz) to be entirely mathematical, as Pythagoras had first asserted. The genius who provided this mathematical explanation of free will was Kurt Gödel. The reason that Pythagoras’s assertion seems so strange to us, is that we are experiencing mathematics from the inside, subjectively, in the form of feelings, sensations, desires and dreams. Objective mathematics is complete, but subjective mathematics is incomplete, due to its self-referential nature. Gödel formulated his famous Incompleteness Theorem to show that for any system of logic there are always true statements that can never be proven to be so. This does not mean that mathematics itself is flawed, as mathematics, objectively, represents rational perfection, however, other systems of logic always contain self-references as they attempt to explain themselves, and it is these self-referential statements that cannot be proven by the system’s own logic, as Gödel showed. Therefore, when subjective, the system is always incomplete i.e. there is room for errors, room for choices, room for Free Will. In a brilliant twist of irony, Gödel’s Incompleteness Theorem actually completes the mathematical explanation of existence, by explaining Free Will as the unprovable statements of subjective systems of logic, i.e. when subjective, mathematics is incomplete, but when objective, it is complete and perfect. The Incompleteness Theorem is the final piece of the puzzle, filling in the gaps in all the major philosophies of Descartes, Spinoza, Kant, Hegel, Schopenhauer, Nietzsche and above all Leibniz, Gödel’s hero, who knew that his system would eventually be completed by the discovery of the relevant mathematics, which was done, firstly by Fourier, and finally by Gödel.
With the work of these geniuses, humanity’s smartest individuals, we now have everything we need to understand everything. Ignore scientists, ignore irrational religions, ignore the ignorant masses. Study the work of these nineteen geniuses, the nineteen greatest geniuses in history, and you will understand everything, you will become God.
Omega Synthesis 