Archive for December, 2008



Concepts are complex associations of simpler ideas. Regarding the ideas of physical objects, one of the most fundamental world conceptions that we make from the elements of perception, is to create a spatio-temporal picture of the world.

The notions of time, objects and space
Nature is transcendent, in the sense that it is not an object of experience on which we can have a direct knowledge. Instead, we know Nature indirectly by perceiving the physical world and interpreting its behaviour.
From perception we form mental representations of the physical world coming through our senses. On a naïve interpretation of the world we would take this representations to be real. But as we have seen, these representations are not faithful reflections of the physical world. And they were never meant to be. Our mind evolved to form useful constructions to serve practical purposes rather than truthful ones.
The form that our mental representation takes is of a spatio-temporal world full of objects. In this world, objects are taken as finite and individual elements in-themselves; and objects, space and time are considered to be three distinct entities.
In the following we are going to propose that in the physical world objects, time and space are not distinct but physically united. On our ordinary concepts of objects, time and space we find that we cannot define any one of them without including the notion of the others. The concepts of objects, time and space cannot be thought independently. They are related to one another in such a way that the definition of anyone of them depends on the definition of the others. We are going to propose that this dependence goes beyond a linguistic problem or an abstract relation. Space, time and objects are actually physically integrated. As a result of how our mind evolved to perceive the world, on our most naïve and intuitive interpretations, objects, space and time are seen as distinct entities. But although this is how we think of the world, for however useful these constructions might be, they don’t represent their physical reality. The concept of time-space for example, is little intuitive, but its a step forward towards a closer insight onto the world’s reality, for it contemplates the physical union between time and space. Nevertheless, it falls short of contemplating their union in turn with physical elements. Our representations then, are characterised by mentally dissociating object, time and space when they are actually physically united.

Imagine, for example, if we could take time out of the world. Then we would be left without variation. Without time, we would have a world of space and objects without change.
Imagine now, that if after taking time out of the world we would take the objects. Then all that remains would be an empty space. So space, in principle, could exist independently form objects and time.
But what would happen if after taking time we would try to take space rather than objects. We shall find that it is impossible. We cannot take space out of the world for objects cannot exist without space. This leads to the impression that space is a fundamental mental construction of the world. We can conceive a world without time and objects, but we cannot conceive a world without space.
This was only an imaginary exercise with a vague resemblance to the physical world. But it serves to illustrate, first the possibility of an independent space, and then the importance of the construction of space in our thought. We cannot make any mental construction without space.
But what happens in the physical world if time, objects and space are mentally dissociated but physically united? If time and objects have a physical dependence and objects are not in-themselves then time cannot be in-itself either. And bearing in mind that the only intelligible elements are those ones which can be thought as being in-themselves, then if objects and time are not in-themselves, of course, they cannot form objects of thought since they don’t have an identity of their own. And if they are not objects of thought then it would appear to be no possible thought at all. It would appear to be no possible description of the behaviour of things. And this holds some truth; the world cannot be understood in terms of what is not in-itself. But what appears to be a dead road towards unintelligibility shall be found wide opened by saving the omission that in a world where objects and time are not in-themselves, Space still exists; and Physical Space can be in-itself.  So this shall be our starting point for the study of the world: from our sole object of thought left: Space.


Mathematical truths


Mathematical truths seem to be absolute, for they seem to be universal and invariable. They seem to be objective, independent from place, culture, age, etc., and they also seem to be eternal. But mathematical truths are in the end subjective and relative.

First, mathematical truths are subjective simply because mathematics itself is humanly subjective. Mathematical systems are human constructions that don’t have any reality outside the human mind.
Mathematical spaces can be compared with a game of chess. Objectively, chess is nothing more than a squared board with pieces of different shapes and sizes. It is not the physical elements, but the mental space we create with those elements that makes the game. Algebra is for mathematics what the rules of chess is for the game. When we define the rules, we define the pieces, how they move and how they operate with each other. In both cases there is a construction of a mental space, where we define the elements, operations and functions between elements. Once the rules are defined and we are ready to play, chess, like mathematics, becomes independent from cultural, age, gender, etc. Chess and mathematics are humanly objective, but that doesn’t make them universally objective; they are just a mental spaces.

The subjectivity of mathematical truths is a sufficient condition for its relativity. In general, relative truths can be evaluated on their degree of logical consistency and consistency with experience. But since mathematics is a mental space, the validity of mathematical truths is reduced to its logical consistency (it is only in physics where it has to be complemented with consistency with experience).

So, unlike what Pythagoras, Leibnitz, Newton and many others believed, Nature is not an order written in a mathematical form, but mathematics is a human construction that we can use to explain Nature. And unlike the dominant belief during the Enlightenment that Nature is a rational order, Nature is non-rational, reason is a human faculty and we use reason to understand Nature often rationalising it. So logical consistency in mathematical truths doesn’t mean universal objectivity.

The relativity of mathematical truth not only is a necessary consequence of its subjectivity, but it has also some concrete manifestations like Gödel’s incompleteness theorems. The theorems states that mathematical systems (or at least those of any practical interest) include truths that cannot be proven within their system. Furthermore, any proof of their truthfulness would make the system inconsistent, and any attempt to prove those truths from outside the system would involve truths from another system that cannot be proven.
The consequence of Gödel’s incompleteness theorems is that, we might have a system, and truths within the system, that are logically consistent. But those truths are confined and relative to that system, and there is no way to prove them objectively. Mathematical truths then, are always relative.

The progression of truth


Ideally, an objective truth would be universal and invariable identity independent from place and time. Real concepts on the other hand, are subjective, therefore relative: they have an inherent human subjectivity on perception and conception, cultural relativity, personal subjectivity, subjectivity on social groups, subjectivity on individual experiences and subjectivity on personal development (see subjectivity). Unlike objective truths, concepts differ from person to person and they differ in time. One of the ways concepts are relative is on their variation in time. And one of the ways they can change in time is through progression. The progression of truth then, is the transition from an original state of subjectivity to higher degrees of objectivity.

We can think of progression in physical terms in its relation with complexity. Progression is a natural phenomena related with increasing levels of complexity. Complexity in turn, is the integration of differentiated parts. Concepts are mental representations formed by neurological associations out of neurological complexity. Complexity itself is relative: the higher the degrees of differentiation and integration, the higher the complexity. The degree of objectivity of our mental representations then, is related to the degree of their cognitive complexity: higher differentiation and integration in the neurological associations means mental representations with higher degrees of universality, higher degrees of internal consistency (self-consistency) and higher degrees of consistency with experience; which means higher degrees of objectivity. So subjective concepts are related with low cognitive complexity and objective concepts with high cognitive complexity. Cognitive development is the transition from an original state of low complexity and high subjectivity to higher levels of cognitive complexity and conceptual objectivity. The progression of truth then, is a natural phenomena related with increasing levels of cognitive complexity.


Note that progression is natural, but not inevitable. Things don’t progress naturally. Things change naturally, and in this change things can either progress or regress. Both progression and regression are natural occurrences, and a neutral Nature doesn’t favour any one of them over the other. What Nature does favour, is dynamic stability (see Laws of physics). And the things that progresses tends to prevail in time because they tend to be more stable (see complexity and development).

more on the relativity of truth.


The relativity of truth doesn’t mean that all truths are equally valid. Among relative truths, some are more truthful than others. And how can we measure their truthfulness? Ideally, the correspondence between the concept and the object in an absolute truth would be an identity. In the real world there is no possible identity between concepts and objects. Their correspondence instead is formed by mental associations. Associations in turn, have different degrees of consistency: consistency with experience and logical consistency. So among relative truths, the concepts that are more truthful are the ones with higher degrees of logical consistency and higher degrees of consistency with experience; that is, the ones that approximate reality with higher degrees of objectivity.

There is an apparent logical contradiction in stating that ‘truth is relative’; for it seems as if we would be stating an absolute truth. But the contradiction is not rela and the relativity of truth not only is consistent with monism and experience, but it is also self-consistent. If we think of the concept of ‘relative truth’ as an absolute, it seems to be self-contradictory. But regardless of what we think, the concept of ‘relative truth’ is itself subjective, for there are not two persons in the world with identical ideas about ‘relative truth‘; and not in any one person idea of ‘relative truth’ is ever the same. The concept of ‘relative truth’ then, is subjective therefore relative. Furthermore, it is relative and more truthful than the idea of an absolute truth, for it is self-consistent and more consistent with experience than the concept of absolute truths.

The nature of Space


In metaphysics, we defined a substance as an element that only needs itself to exist. And there are three qualities that makes an element a substance: self-containment, inalterability and unicity. We then proposed that in the universe there is only one such element: Space.  Space is the sole substance in the universe, therefore it is also its constitutive matter.

One of the difficulties about monism is how can a unitary substance explain all the diversity and change in the universe. The idea of a unitary substance might suggests an entity that is homogeneous and static. The universe on the other hand, is inhomogeneous and dynamic. How can a unitary substance sustain such a universe? The answer is that Space is not an ideal static substance but a physical substance with a physical nature.

The first quality that sets apart a physical substance from and ideal substance is that it has extension. Space is physical element with extension.

But Space doesn’t extend arbitrarily. It does so on its dimensions. So Space has dimensions; and it doesn’t have one, but many dimension (at least three. How many? we still don’t know). This multiplicity of dimensions gives Space yet another property: a geometric nature. That is, Space extends on the geometries formed by its dimensions. The geometric nature of Space is manifested in several ways in the physical world, like on the geometry of space-time, on the properties of particles (charge, spin, colours, flavours, etc.), on the properties of atoms (e.g.their place in a periodic table) and on the geometric structures of crystals, proteins, etc.

The geometric nature of Space in turn, has a particular property: it is asymmetric. We know of the asymmetric nature of Space for two reasons. First, because of the the inhomogeneity of the world around us, where there are not two things and nor two places -neither contiguous nor distant- that are exactly the same. And second, because asymmetries in Space have an inverse relation with extension and energy. Physical objects have energy and a finite extension because they are constituted by asymmetric Space. If Space would be totally symmetric, it would be infinitely extent and empty.

The combination of these qualities gives Space another property: dynamism. The dynamic nature of Space is manifested on the dynamic nature of the universe. Everything is in permanent motion and transformation: from vacuum to matter, from particles to organisms, everything in the universe is in permanent change. The universe then is dynamic, because it is constituted by a unitary space with a dynamic nature.

But how can a unitary and inalterable substance be dynamic? As we mentioned before, one of the main difficulties about monism is to explain how all the dynamics and change in the universe comes from a unitary substance. This happens because Space combines two things: the qualities of a substance (unicity and self-containment) and a physical nature. The combination of these qualities makes it dynamic. We can summarise this mutual relation in the following way:
. Space is unitary, therefore it is self-contained (i.e. it has no gaps, no discontinuities and no open ends).
. For space to remain self-contained, it has to close upon itself (i.e. its dimension have to close upon themselves).
. Space has also a geometric nature. So when space closes upon itself, it does so on its geometric structure.
. But because the geometries of space are asymmetric, when space closes upon itself it generates change.
The dynamic nature of space then, is a property that results from the combination of its unicity, with its geometric and asymmetric nature. If space would be symmetric and homogeneous the universe would be static. But because it is asymmetric and inhomogeneous we have a dynamic universe. Space itself doesn’t change. Space remains an invariable substance. But it is the change within its physical structure that makes it dynamic.

In summary, Space is a substance for being unitary, self-contained and inalterable. And it is also a physical substance for having a geometric, asymmetric and dynamic nature. The combination of these qualities explains how a monist universe can be inhomogeneous and dynamic.

The physicality of Space


We are considering a substance as belonging to the physical world. The reason for this is that the physical world is the universe’s objective reality (which is not the same than saying that the description given by physics is objective). If a substance is an element that only needs itself to exist, then it has to be independent from our thought. Any element from our conception, fancy or imagination depends on our thought, it is subjective and therefore is not a substance. The physical world on the other hand, is objective and independent from our thought. Therefore, and objective substance has to belong to the physical world (see also subjectivity and the unreality of a supernatural world).



There are different forms of monism depending on the idea of what the substance is. The four main forms of monism are: physicalism, materialism, pantheism and idealism.

 Physicalism is the idea that the nature of the universe is physical and as described by the laws of physics. Materialism is a particular form of physicalism, and is the idea that the essence of the universe is of matter. Pantheism is the idea that the nature of the universe is divine, being everything a manifestation of God. And idealism is the idea that the nature of the universe is ideal and a manifestation of the mind.

We are proposing yet another form of monism: Spatial monism. We are going to sustain that the universe’s metaphysics is of a unitary physical space.
. This differs from materialism in that we sustain that space is more fundamental than matter and that matter is constituted by physical space itself.
. With physicalism it shares the idea that the nature of the universe is physical, but it differs in the idea that it is as explained by science. Science offers useful interpretations of the physical world, but they are always practical approximations and not true reflections of it. Furthermore, they often include elements (e.g. like a background space, the dissociation of matter from space, etc.) that don’t belong to the world’s reality.
. Spatial monism differs from pantheism in that we propose a unitary substance that is physical and not divine.
. And lastly, it differs from idealism in that the world’s reality is independent from our thought. Mind and thought are natural phenomena arising from the physical world, and not the other way round.

more on particulars


To understand what Nature is we have to start from the most general and fundamental aspects of the universe, and then go down to the particular ones. The most general and fundamental aspects of the universe falls in the domain of metaphysics. Once we have presented the universe’s metaphysics, we can analyse the compatibility of this metaphysics with the physical world around us. And once we have analysed the compatibility of the universe’s metaphysics with its physics, we can analyse its compatibility with human nature and society. Man and society are natural phenomena; and as such, they have to be contemplated in the context of a universal Nature.

Particulars are usually studied presupposing the world. When we face a particular, we do so with a preconceived view of the world. And when we study them, we don’t start from scratch trying to understand the nature of the universe, we just accept our world-view and assume that the world is as we know it. And we can do this without major conflicts because we are normally interested on a practical knowledge of things rather than on their nature. Understanding the nature of things, of course, would improve their practical knowledge; but it is not a necessary condition. Practical knowledge can reach, and has reached, extraordinary degrees of perfection even under totally wrong preconceptions of the world (e.g.  the pyramids and Egyptian cosmology; Roman architecture and Roman cosmology; and in modern times, we sent a man to the moon, we sent missions to mars and to the outer solar system, and yet, we can’t agree to what the Nature of the universe is). Now, if instead of practical knowledge we are interested on understanding the nature of things, then we are forced to check our preconceptions of the world for particulars don’t exist in isolation, they exist in the universe, and the nature of all particulars are part of a universal Nature. So to understand the nature of particulars, first we have to understand the Nature of the universe.

On the evidence of Spatial Monism


There are two fundamental conditions that a theory should meet to be valid: first, a logical or internal consistency, and second, consistency with the physical world. In the case of Spatial monism, we believe that both conditions are met. Furthermore, if the theory is right, we would expect that a better understanding of the physical world would converge towards it. And we believe that this is exactly what is happening in theoretical Physics.

The general acceptance of a theory on the other hand, is an altogether different thing. There are several reasons for which a theory, despite all the evidence that might prove it right, might not be accepted (e.g. creationism and Darwin’s theory of evolution).

In the case of Spatial monism (just as for example, in Darwin’s theory of evolution ), there is no single laboratory experiment or mathematical demonstration that can prove right. The evidence of its reality instead, depends on its consistency with the physical world around us. In the following then, we are going to introduce different ways in which Spatial monism is consistent with the physical world. First of all, it is consistent with Physics. Second, it is consistent with the unification theories of Physics (which are actually converging towards monism). And then, it is also consistent with the nature of man and society (a necessary condition in a universe with a unitary and universal Nature).

1 Spatial monism and Physics

One way of showing the consistency of Spatial monism with the physical world, is to show its consistency with Physics. Science is, after all, the best interpretation we have so far of the physical world. Now, Physics is a very extensive field covering many disciplines from classical mechanics, to electromagnetism, particle physics and cosmology. So the most effective way of showing the consistency of Spatial monism would be to show its consistency with the most universal and fundamental principles in Physics. The most universal and fundamental principles in Physics, those behind all the laws of physics from the behaviour of particles to the motion of planets, are:
. Conservation laws e.g. conservation of mass, energy, momentum, etc.
. Principles of minimal variation e.g. action principle.
. Principles of maximal dynamic stability e.g. Pauli exclusion principle, second law of thermodynamics, etc.

These are not independent, but mutually related principles. The first one is probably the most familiar one. The second one is related with laws of motion e.g. Newtonian mechanics, electromagnetism, general relativity, etc. And the third one is related with the dynamics of things  e.g. thermodynamics, dynamics of fluids, and – most relevant to us- the behaviour of complex systems.
A principle, by definition, is a law that is found valid without explanation of how or why it is so. We can show, by defining the physical structure of space, that in a monist universe these mutually related principles are not whims of Nature but properties of the behaviour of Space.
It can be shown then, that the behaviour of the physical world around us is consistent with the behaviour of a unitary physical Space.
2 Unification theories
Physics tends to develop towards a gradual unification of the laws of nature. Laws that once were thought to be fundamental, are gradually found to be particular cases of even more general ones. If spatial monism is right, then the natural outcome of this tendency would be a gradual convergence towards it: and this is exactly what seems to be happening.

Currently, the two most general theories whose unification is being actively pursued are general relativity and quantum field theory. The tendency to unify them shows two things: First, it is showing the unicity of Nature: the natural world is not a world where things respond to independent laws, but everything seems to respond to a unified coherent order (and as we have seen, unicity is a necessary condition of monism); and second, their unification seems to be gradually converging to the idea that space is the fundamental substance in the universe.
For example, Einstein’s field equations, read from left to right, tells us how the geometry of space-time depends on the distribution of matter and energy in the universe. After writing them, Einstein became fixated on what the equations might be telling us if we read them the other way round. If we read the equations from right to left, they seem to suggest that, if we follow the continuity of space down to the structure of matter, this could be somehow related to the geometric structure of space itself. Nowadays, in theoretical physics, for some at least, it is becoming increasingly evident that one of the fundamental conditions for a successful unification of general relativity with quantum field theory is the elimination of background space. If this condition is ever met, it would mean that particles wouldn’t be explained as elements in space, but they would be explained as the behaviour of space itself. If this condition is ever met, it would be the most direct corroboration of physical monism yet.
3 The continuity of Nature on human nature and society.
A monist universe has a unitary Nature with no gaps and no discontinuities. The unicity and continuity of Nature means that man and society can only be natural occurrences responding to the same universal order as everything else.

To follow this continuity, we are going to follow the subject of a relatively new field in science in the study of complexity. Complexity is a link between the nature of particular occurrences (e.g. human nature or society) with universal Nature. Society arises out of human nature: human nature arises out of biological complexity: and we are going to sustain that complexity in turn, is a natural phenomena  that arises from the principles of conservation and dynamic stability; that is, complexity is a natural phenomena consistent with physical monism.

One of the characteristics of complex systems, is their non-linear dynamics where the whole is more than the sum of its parts. As a consequence of this, complex systems are also irreducible. This means that, even if unification theories were successful, the behaviour of complex systems, like life, humanity, etc, cannot be reduced to the effects of gravity or particles. And another characteristic of complexity is its universality. Due to the continuity and universality of Nature, once we know the principles governing the dynamics of complex systems, we shall find them in phenomena as diverse as protein folding, emergence of life, evolution, biological development, human nature, personal development and even society.

As we can see, in a monist universe nothing is left astray, nothing behaves in isolation, nothing is an exception, but everything responds to a coherent, unified  and universal Nature.

On the concept of Spatial Monism


1 Spatial Monism
Monism, in general, is the view that the universe is constituted by a unitary substance. It is the view that everything in the universe is made out of the same fundamental element.
In antiquity some thinkers conceived this element to be either water, air, earth or fire. Now we know that these are not fundamental elements (theoretical physics instead, is looking for them in a multiplicity of fundamental strings or loops in space).

We are going to sustain that the  universe is indeed a monist universe made out of a unitary physical substance. But we are not going to consider this substance to be any element in space; instead, we are going to consider it to be space itself.
We are going to sustain that space (that is, physical space) is a fundamental substance that is indivisible, irreducible, unalterable, imperishable and ungenerated. Furthermore, we are going to sustain that space is the sole fundamental substance constituting the universe. There is a logical and physical necessity that if there is a physical substance, it has to be all that there is in the world. So if space is this substance, then nothing exists out of space, everything can be reduced to its spatiality, and space cannot be reduced to any other element more fundamental than itself.

If spatial monism is true, then we would  expect two things form from its thesis. First, it would have to be self-consistent. And second, it would have to be consistent with the world: it would have to explain Nature, the  physical world, and the nature of man and society in this world. All these conditions we believe are met.

2 Monism and Nature
The existence of Nature in the universe is self evident… but why does Nature exist as it does is not. Monism in the universe explains why there is a Nature that is unitary, universal, immanent and invariable.

If physical space is dynamic, and there is an order on its behaviour, then one of the consequences of physical monism is that it sustains a unitary and universal order of change.
With our gradual progression on our understanding of the world, follows a gradual awareness that things don‘t have independent natures but there is only one Nature in the world.
The unicity of Nature is a necessary condition of physical monism. If the universe is constituted by a unitary space, and Nature is an order on the behaviour of space, then everything in the universe has the same Nature.
Another quality of Nature is its universality. Wherever we look in the universe we shall find the laws of Nature to be universal. Universality is another condition of monism. If the universe is constituted by a unitary space, then on every corner of the universe we shall find the same Nature.
Another quality of Nature is that it is not external to objects, but it is immanent to them. Space might be unitary but it is also dynamic. Everything in the physical world has a dynamic essence. If Nature is an order on the behaviour of space, then it is an immanent order on the dynamics of things.
And yet another quality of Nature is the invariability of its laws. And this is because space is not affected by time, therefore it is unalterable and always the same.

Monism can explain qualities which  are known, but otherwise unexplained. Nature is unitary, universal, immanent and invariable because it is an order on the behaviour of a unitary space with no gaps, no discontinuities, and which is everywhere and always the same.

3 Monism and perception
One of the main difficulties about physical monism is that, despite its essential simplicity, it is counterintuitive and opposite to ordinary perception. Monism is hard to contemplate in the physical world and this is partly due to the difference between the world as it appears to us from perception and the physical world as it is.

When we perceive physical elements we attribute them with a set of qualities that don’t belong to their  physical reality. For example, spatial discontinuity: we think of objects as if they were finite elements in space, temporal continuity: we think of objects as if they were the same in time, generalisation of ideas: with the idea of objects we treat them as if they were all the same, discontinuity in Nature: we think of objects as if they would have independent natures.
Physical elements, unlike ideal elements, exist in the continuity of space, they have a dynamic nature and they are never the same, they are all different, and in essence, they all have the same Nature.
And there is a reason for which we don’t perceive the physical world in its reality. First, because in rigour, it is unintelligible. And second, because it is useless. Our mind has a functional purpose. It didn’t evolve to form faithful representations of the world. Instead, it evolved to perceive the world and approximate it with useful mental constructions to our self-preservation (evolution in turn, is consistent with physical monism).
So monism is counterintuitive because we perceive a world of sameness, finitude and discontinuity. We only become aware of its unity, continuity and common Nature through a gradual learning process of increasing conceptual complexity (which is also a natural phenomena consistent with monism).