01 Aug

Do Life and Living Forms Present a Problem for Materialism?

This essay was written in response to the call for essays by the Royal Institute of Philosophy for their yearly essay contest. For the pleasure of readers, it is reproduced below.

Abstract

An assumption implicit in this question is that non-living objects probably don’t present a problem for materialism, because if that weren’t the case, we would be asking if materialism is a sound approach for all of science and not just the study of living forms. In this essay I will argue that: (1) the problem of materialism is not unique to living forms, but exists even for non-living things, and (2) the problem originates not in materialism per se but from reductionism which reduces big things (or wholes) to small things (or parts). Reduction has been practiced in all areas of science—physics, mathematics, and computing, apart from biology – and it makes all scientific theories either inconsistent or incomplete. This is a fundamental issue and cannot be overcome, unless our approach to reduction is inverted: rather than reduce big things to small things, we must now reduce the small things to big things. This new kind of reduction can be attained if both big and small were described as ideas: the big is now an abstract concept while the small is a contingent concept, and contingent concepts are produced from abstract concepts by adding information. This leads us to a view in which objects are also ideas—just more detailed than the abstractions in the mind; the abstract ideas precede the detailed ideas. When the reduction is inverted, a new kind of materialism emerges free from its current problems. This materialism presents a new theory of inanimate matter, not just living forms.

Introduction

There are broadly two kinds of materialism—theoretical and empirical. The empirical materialist holds that whatever I can taste, touch, smell, see, or hear must be material. The theoretical materialist holds that matter is independent objects with possessed properties, which exist even when observers don’t and these objects should therefore be described by observers in the same way as they exist independent of any observation.

It is important to make this distinction because empirical materialism may be true with or without theoretical materialism. For instance, we can observe a person’s brain and detect electrical activity corresponding to their subjective reports of perception—such as the sight of redness. This fact is indisputable. The dispute is whether the brain should be described just as inanimate objects. This dispute is problematic because if we changed the description of the brain, then we would have to change the description of inanimate objects too. Are there reasons in science why such a change would be warranted?

Objects and Collections

Science needs a change in its description of matter because it reduces collections to their parts, although in many situations this reduction is untenable. My body is indeed built up of atoms, but the collection of these atoms also constitutes an individual. This individual has new properties—such as the ability to know the world and to own a house—something that the parts of the individual’s body don’t seem to have. If we reduced the individual to the parts, we must either show how the parts also have the same properties, or discard the new properties altogether. Modern science is unable to reduce the properties associated with the individual to the parts within the individual. So, we must discard them as illusions. However, once you take away the idea of knowing and owning, then you cannot know science, and you cannot attribute any scientific theory to any particular individual. Science—as an enterprise of individuals pursuing the truth of nature and creating theories that are then attributed to them as their creations—would itself collapse.

In everyday language, we treat object collections also as objects, although in science we don’t. For instance, in everyday language, a ‘house’ is both a collection of parts, and an individual object. In science the house is reducible to its parts, which are real, although the collection itself is not. A collection draws a boundary around its parts, which is real in everyday language, but unreal in science. Objects within this boundary are real in science but the boundary is our imagination, and hence it remains in our mind, not in reality.

This basic difference between everyday intuitions and science lies at the heart of the debate about material reduction: the whole is reducible to the parts because the boundary is not considered real. Once you take out the reality of the boundary, macroscopic objects – and associated concepts – also become unreal. Collections become useful (and often essential tools for doing science – which divide the world into smaller “systems”), but since the boundary is not a real physical entity in space-time, it has no theoretical role in science. Therefore, you see a macroscopic object by your eyes and manipulate it with your hands, but you don’t admit the existence of such an object in your mind.

Living forms present a problem for materialism because they force the reality of the whole, even at the level of the mind. In fact, in the case of life, the primary individuality is at the level of the mind. If you have lost your hand or leg in an accident, you are not less of a person than you were before, even though you clearly have fewer molecules. Similarly, if you committed a crime 10 years ago and all the molecules in the body have changed since then, you must still be punished for your crimes, because you are still the same person.

The problem whittles down to a simple question: Does the collection of parts in my body also constitutes an individual? If there were no boundary, then this individual would be an epiphenomenon reducible to parts. Therefore, for the individuality to be scientifically meaningful, we need a new theoretical construct in science – that of a boundary – which aggregates material parts. This boundary is also an object, although it is a macroscopic object—conceptually more abstract than the parts. Clearly, such objects have to be described not by using the concepts applied to atomic objects—i.e. leptons and quarks—but also everyday ideas such as houses, teacups, and people.

The Reality of Collections

Can science theoretically work with the notion of a boundary? For that matter, does science even need the notion of a boundary? If yes, why? A boundary is a space-time entity, because we will draw it in space-time, and therefore it can exist objectively. However, we cannot perceive (i.e. see, taste, touch, smell, or hear) the boundary. This is important because if the boundary were objective, then empirical materialism would be false: nature would comprise things that exist but cannot be sensed.

Of course, they can be thought or imagined. All science involves some imagination or thought but we don’t consider it real unless its existence has some observable effects. In the absence of an effect, having the boundary would be indistinguishable from not having it. We might as well then—by Occam’s razor—not have it. So, can the existence of a boundary have empirical effects (which can be measured, and therefore seen, heard, tasted, touched, or smelt), even though the boundary itself is not empirical (i.e. cannot be measured)? Does the mental ability to divide the world into macroscopic systems have a real counterpart in the world? Or is that division only a convenient imagination?

This question, I believe, is central to a non-reductive, but still material understanding of living forms. In this understanding, there are physical entities—which we ordinarily call boundaries—which can have a theoretical role in science, although they cannot be measured by our senses. However, if they have effects on our measurements, they can still be real—in the same way that we cannot see an electron although we can measure its effects. We would still be within the confines of materialism, but outside the reductive—theoretical and empirical—view of materialism.

I will spend the next few sections in this essay arguing why boundaries are essential theoretical constructs for science—not just life sciences, but even physical sciences. Only when we see a reason for inducting boundaries in science will we see a real scientific reason for describing these boundaries using everyday concepts (e.g., houses and teacups), which will then enable us to talk about a living being as a single individual, irreducible to parts although comprised of parts.

The Problem of Indeterminism

Physical sciences grew out of the description of individual object properties such as mass, charge, energy, momentum, angular momentum, etc. When you aggregate many such objects, the collection too has these physical properties in the aggregate. However, if you begin in the collection, then there are many ways in which the properties of the aggregate can be divided into the parts and their properties. As an illustration, if you begin with $1 notes and aggregate 100 of them, you have $100 in total. But if you have $100 in the bank, you cannot be sure if that money exists in $1, $5, $10, or $50 denominations. All these alternatives are equally possible, which leads to the problem of money distribution—we know the total but not the parts. The same total money (and physical properties) can be divided into parts in many ways and even if we know the whole, we may not necessarily know the parts. Of course, if we knew the parts, then we will necessarily know the whole. Generally we suppose that matter is individuated into parts, and therefore the problem of matter distribution can never arise: even if we empirically do not know all the parts, there should never be a theoretical room for indeterminism if parts are real.

It would surprise many people if they realized that all fundamental physical theories of nature are (theoretically) indeterministic due to matter distributions, when they deal with object collections, and this indeterminism has been empirically confirmed. Due to indeterminism, the theory makes some predictions which can be empirically confirmed. And yet, the theory does not predict the matter distributions due to which it is incomplete. In a sense, we know that there is $100, but we don’t know the denominations. This fact can only be understood if we acknowledge that $100 can exist as an idea not converted into individual currency notes or coins. But that would entail the reality of ideas.

Delving into all the forms of indeterminism in modern physical theories would take us out of the scope of the present essay, but I will illustrate the problem with the quantum slit experiment. Quantum physics describes an ensemble of energy which can be divided into individual particles in many ways. A quantum ensemble is not a priori individuated into parts: we can say that the whole is a priori real but the parts are not. The experimenter can in fact choose to divide the ensemble into parts using a different number of slits. With every such choice, a different set of particles are detected which correspond to a different eigenfunction basis. This division is quite like $100 can be divided into currency denominations in many ways. The division remains a choice. Since this choice is not captured in any theory, the theory’s predictions remain indeterministic.

If the parts were real and the whole wasn’t, then no matter how we measured the system, we would always find the same parts. If however the whole is real but the parts are created by the experimental setup (at the point of measurement), then we can always find a new way of dividing the whole into parts. Now, it is impossible to claim that the whole is only an imagination of our minds. It is more correct to say that the whole is real, but its parts are possibilities, one of which would be realized in a particular experiment. The empirical confirmation of this theory establishes the theoretical reality of the whole, and the theoretical possibility (but the empirical reality) of the parts. The parts are real at the point of observation, but they did not exist until the observation was made.

There are similar problems of indeterminism in General Relativity and Statistical Mechanics as well, but elaborating them here would not add to the main point which is that if the parts were always real then the theories would not be indeterministic. The indeterminism of the theories entails that the whole is more real than the parts, and our measurement choices interact with the measured system to overcome that uncertainty in state, putting the system into a definite state upon observation.

It is as if the whole system (prior to observation) paints a picture of reality in the outlines but not in the details. The outline can be filled up with many different details, although not arbitrary details. Our choices of observation act upon this pre-measurement outline to complete the picture upon observation, which makes us think that the world must be just as we observe it to be. However, you can also observe the world differently and describe it accordingly, and even that alternative description of nature would be empirically confirmed. The fact that the theory permits infinitely many theoretical possible descriptions of the same system, and the fact that each of those descriptions can be empirically confirmed, entails a radical new conception about matter.

Attempts to Evade Indeterminism

Modern science deals with the multiple possible alternatives of dividing a whole in a peculiar manner: it hypothesizes (when possible) that nature has a probability of being all these alternatives, due to which one alternative randomly becomes real. Your choice of the number of slits in the quantum slit experiment must, for instance, be due to the “collapse” of a wavefunction in your brain which is then viewed as a “choice”.

If you believe that nature is a probability of many alternatives, then it is not the real “stuff” that exists independently anyway. The randomness further takes away the ability to predict what we will see upon observation. Probabilities and randomness pervade modern science in more ways than I can summarize here. This peculiar approach to scientific indeterminism juxtaposes our classical beliefs about nature as a priori individuated objects with the observed indeterminism: obviously we cannot reconcile the indeterminism with a priori reality, so let’s suppose that reality is the probabilities of all the possibilities. Probabilities undermine both predictions and explanations.

Solving the Indeterminism Problem

There is, however, a better alternative. In this alternative, we say that nature is not a priori individuated into parts. Rather, it exists as wholes which are then divided into parts at the point of measurement, quite like filling in the outline of a picture with details. The outline limits the possible fill-in alternatives, but does not identify a specific alternative. These alternatives become our choices. The outline is no less real or objective than its parts. The outline is also an object, although not as detailed. In fact, the outline can exist even when the details don’t, although the details cannot exist when the outline doesn’t (to define something as the detail of a picture, we need the outline of the picture first).

This kind of approach in science would reinstate the reality of the whole although it would not be as definite as the reality of the parts that we presently observe. We would now need a new construct in science—that of a collection—which is then divided into parts based upon our choices of perception and action. To treat this collection as an object (prior to observation) we have to treat it as a macroscopic object—like a house or a teacup. Upon observation, we could also treat it as a collection of the observed parts. The whole and the parts would now both be real; in fact, reality prior to observation would only be wholes and not their parts. Each observer can find some new, but not totally random, fact about the same world. The non-randomness indicates that there is something objective. The novelty in observation indicates that this reality is not defined as completely as we see it.

The scientific counterpart of this view is that it takes a more complex apparatus to measure the atoms than to measure a macroscopic object. From the standpoint of complexity, the outline is simpler although the details inside of it are complex. If we treated this complexity as information needed to define the object, the macroscopic object is a simple entity while the parts inside that object are the complexity that follows a choice or action.

Towards an Informational View

This approach to science requires a different view of nature in which the world is described not as things but as information. The whole system represents abstract information while the parts in that system represent the contingent details. We add details to abstract objects to create our reality, and as long as the world is abstract there can be many ways in which information can be added to transform abstractions into contingents.

When the world is already completely contingent, we can no longer add information into it, and that reality would always be described deterministically. Determinism is therefore a logical limit to adding information into abstract objects. If the universe were fully contingent, it would also be fully deterministic (as Newton envisioned in his mechanics). But the world is not completely contingent; it exists as macroscopic objects which are abstract entities that can be made contingent by adding information. This approach does not deny the possibility of determinism, but presents it only as a limiting case of choice. When all possible choices have been made, there is no more room for choices, and reality is deterministic. By assuming determinism as the paradigm of reality we preclude choices. But by assuming choice as the paradigm of reality we rediscover determinism.

Atoms are now units of information, and a measurement involves not just transfer of information from the measured system into the observer but also from the observer into the measured system via the choice of measurement apparatus. A new causal model of interaction needs to be found which involves the interaction between symbols of information rather than between blobs of energy. The laws of this causality would be quite different from how science currently describes forces between objects.

If I have transferred some information – through the act of making a choice – then my brain is in a less certain state because it compensated the uncertainty in the external world. Similarly, when I consume some food or ideas, my body regains its original level of certainty. We are still exchanging matter with the world, and my body and the external world are still material, although the matter is now described as symbols of information rather than physical things. The symbols of information can be either abstract or contingent, although physical things can be only be contingent. The uncertainty of my state is essentially that I exist in an abstract rather than contingent state, and that state can be made more (or less) certain by adding (or removing) information.

A Non-Reductive Theory of Information

The informational view is necessitated by problems of indeterminism, not merely by our desire to see ourselves differently (although such desires are not totally unfounded). The mitigation of the problem is physical and material, although not in the same sense as in modern science: matter is now information such that even a collection (without the details) can be described as an abstract object. This information would now be represented by forms in space-time; some of these forms we can see and touch, while others we cannot. The presence of the latter would however be possible by adding information that transforms the abstractions into contingents.

This approach to information is non-reductive: it does not begin in the parts and does not construct the wholes from them. It rather begins in abstract ideas and refines them through incremental additions of information. As more information is added, the abstract becomes the contingent. We perceive the contingent things by our senses, but the senses cannot perceive the abstractions. Those who cannot understand the abstractions must rely on the abstractions being illustrated through examples and material instantiations of the ideas. However, that doesn’t entail the non-reality of abstractions until the instantiation is found. Abstractions too can be modeled realistically in a new science that recognizes the objective material existence of boundaries in space-time. In a sense, we could now scientifically talk about mermaids and unicorns as ideas, although we cannot find physical instantiations of these ideas. We cannot see, taste, touch, smell, or hear the mermaids or unicorns, although we can think about them. Thought too is material and real now, even though it isn’t always translated into observable sensations.

The empirical confirmation of such a theory would involve firing photons at space-time. Rather than transparently passing through space-time, these photons will transform into observable objects, if space-time had forms that we could not previously see. Quite like CERN scientists smash particles to create measurements, it would now be possible to smash particles against space-time. That smashing – and the fact that photons do not pass through space-time transparently – would show that sometimes space-time is not empty although we cannot model its fullness as a material particle. The smashing photons fill the details within an abstraction: we could not see the abstraction before, but by smashing light into it, we have created its instantiation which we can see. In essence, we have taken the idea of a unicorn and created a unicorn out of it. The ability to create things out of ideas would change science in ways we cannot imagine right now.

Biology Needs a Revolution in Physics

If living forms contradict materialism, that contradiction has to be seen in fundamental physics before its implications can be used to revolutionize our current understanding of life. The crux of that revolution is that ensembles and collections are more real than the subatomic particles that modern physics currently studies. While these collections represent a material reality, it is not of the same kind as perceived objects. Specifically, both material objects and collections have to be described as information.

If matter is described as a priori real things, followed by the reduction of collections to their parts, then science will forever be incomplete. The alternative is to reinstate the reality of boundaries in space-time but that creates a new problem – how should we model boundaries vs. objects? If we have two kinds of things in nature, how do they interact causally? That problem can only be solved by replacing the two types with only one – information. Both objects and boundaries can be described as information, although neither can be reduced to one another physically. Current physical theories fail because they try to reduce boundaries to objects, which cannot be achieved. If, however, you discard the boundary itself, then you are not describing the system fully.

We cannot understand the reality of living forms unless we view the whole system as being something additional and logically prior to the constituent parts. We will pragmatically treat the living being as a whole, but theoretically claim to reduce it to the parts. We will assert the moral and political individuality of the person in a society but discredit that individuality as an epiphenomenon of the atoms within science. People outside science will marvel at the achievements of the scientists on one hand and feel the disillusionment of meaninglessness of life due to the reduction to atoms. Scientists themselves will struggle with the indeterminism pervading all physical theories. The artists and creative people cannot say that art, literature and music created by humans are objective, but they must say that science – also created by humans – must be objective. The dual standards – in society and in science – result from the fact that science does not acknowledge that collections are real, while society treats them as individual entities.

Biological Information

My claim is that all structures in a living body are representations of information, and the information can be abstract. The abstraction allows us to add more information in order to fill the details. One interesting way in which this incompleteness is visible in biology is that all large biomolecules have numerous possible forms that are permitted by physical theories but not predicted by them. The key problem for biological reduction is not that living beings are comprised of molecules, but how we predict which particular form a molecule takes and why. The many forms of biomolecules are many equivalent material distributions of an ensemble; i.e., they are allowed by current physical theories but not predicted by any theory. Therefore, the theory remains indeterministic.

The myriad forms a biomolecule can take are like the various sentences we can form using a set of alphabets. We can observe the different forms, but we cannot ascribe them functions quite like we can distinguish between various letter sequences but we cannot explain or predict their occurrence unless these letter sequences are viewed as expressions of meanings that existed even before the words did. The occurrence of different forms is empirical and the inability to explain their occurrence is a shortfall in the theory. The theory that can explain forms would have to recognize a property that can be associated with the whole form rather than with its parts. It should now be obvious that there cannot be a consistent and complete theory that predicts and explains which forms are real (as opposed to all the possible forms) unless we take into account the whole. This whole is now not an epiphenomenon of the parts; it is rather a fundamental construct.

Biologists can catalogue the mapping between forms and functions, but they can never predict which form (and function) will become real and never explain why a particular form is a specific function, unless an informational view of nature is adopted. For instance, geneticists can catalogue the mapping between a gene and the biological traits, but why a specific gene represents a specific trait, and why a specific kind of gene is expressed or suppressed cannot be predicted. Why a particular genotype results in a specific phenotype also cannot be explained because the mapping involves viewing both genotypes and phenotype as information. Without an informational view, biology will remain a cataloguing science, not an explanatory or predictive one.

We can enhance our catalogue through increasing experimentation, and that growth in data is called the advance in biology today. It helps us improve our predictability, as we find more patterns in the data. But those patterns are statistical correlations, not tied by any theory. These patterns are quite like our measurement of letter frequencies in the English language. We can say that the letter ‘x’ has 0.15% chance of occurrence while the letter ‘p’ has a 1.9% chance. We can even measure the probabilities of letter succession, but they will be averages over large samples. They will fail to predict the individual word sequence in a text and thereby understand what the text means. The statistical approaches to biology may work on an average but will fail in many individual cases. Essentially, biology will be an attempt to understand a book by measuring letter probabilities, unless we induct a real role for information even in the physical world.

The Doublethink in Biology

In talking about genes, biologists cut up the DNA into smaller units of code that represent different functional units, responsible for different biological traits. What is the basis of this cutting up? Why do we draw boundaries in a molecule when we don’t acknowledge the reality of boundaries in physics? Aren’t there infinitely many ways to divide the DNA into individual genes? Why is the DNA empirically partitioned in some ways when theoretically it can be divided in infinitely many ways? And doesn’t that gap between theory and experiment represent a shortfall in our understanding of the genes themselves?

Modern science has always been practiced by reducing complex systems into simpler ones. The simplicity helps us focus upon specific problems rather all of them at once. However, in focusing on specific things, we use our minds and intellects to divide the world into manageable parts, without acknowledging that there is a real material basis of that division in nature. If we, for the moment, supposed that there is no physical basis for division in nature, then the scientific method will fall apart as we would have to now find an explanation for the entire universe at once. If, on the other hand, we suppose that the division has a real basis in nature, then it must also have a real basis in science.

The pragmatic use of systems, collections, and ensembles in experiments combined with their rejection in scientific theories has created a double standard about everyday concepts in science: practically we need meters, clocks, kilograms – which are all macroscopic objects – but theoretically we believe that these entities are unreal. We can no doubt reduce a kilogram to its constituent sub-atomic particles, but there are infinite ways to do it. All these possible reductions are permitted by the theory but none of them is predicted or explained. Materialist reduction therefore leads to indeterminism.

Biology and Language

There is a profound difference between how information is treated in biology today versus how it is viewed in everyday spoken and written languages. The difference is that biology tries to correlate the occurrences of words and tries to interpret this correlation as causation, while everyday language supposes that in exchanging words we are transacting meanings and words are only methods of expressing meanings. If the occurrence of the word “STOP” causes people to stop and the occurrence of the word “GO” causes them to walk, we can correlate the words with the actions, and we would not be wrong. However, correlation is not causation. The causal explanation underlying that correlation would be missing – we can describe the fact that “STOP” causes people to stop, but we cannot explain why that happens. After all, the word “STOP” does not have enough mass, or momentum to stop a person, nor does the word “GO” have the force to make you walk.

Correlating the occurrences of the words “STOP” and “GO” with the actions that follow is not a true understanding of how languages embody meanings into words. In the same way, correlating the occurrences of genes and traits is not an explanation. If, however, you don’t want to accept that fact, you will be faced with a new problem of indeterminism: sometimes the same word has a different meaning, and the effect of that word cannot be deterministically predicted. Now, you would be faced with two choices: (a) reject that there is any universal connection between the occurrences, which leads to a collapse of biology, or (b) assert that there is a probability associated with different occurrences. This statistical view of science therefore arises because we reject a role for meanings in nature, because we cannot model nature completely based on current scientific concepts.

The problems of indeterminism that pervade physical theories are bound to recur over and over in biology. They don’t render biology impossible. But they make biology predictively incomplete. We can make our catalog of observations as large as we want. We can also use data mining to search for patterns in this catalog. None of them constitute an explanation of why something occurs, only at best a probability of its occurrence.

The Failure of Reduction in Mathematics

Most scientists will not hesitate in accepting that current science is incomplete in many ways, although they will argue that this incompleteness is the outcome of the fact that modern science is work in progress: we will eventually find a description that will be predictively complete because we have the method of reasoning and experimentation that allows us to keep progressing incrementally on the path of discovery.

To refute this type of claim, we have to demonstrate the incompleteness mathematically. All physical theories employ numbers, and numbers depend on the notion of a collection or set. While a set can be succinctly stated as an idea, it cannot always be reduced to its members. For instance, we can define the number 5 to be the collection of all possible sets that have 5 members. E.g., 5 can be defined as the collection of sets such as the set of five shoes, five flowers, five horses, etc. There are two issues in this definition: (a) the total number of possible sets that can have 5 members is so large that it cannot be practically enumerated unless we knew all the objects in the universe and were able to count them, and (b) to even count these objects, we would need to have the numbers (1, 2, 3, 4, 5, etc.) defined prior! The definition of number 5 now depends on 5 being already defined, and even with this definition we cannot know all its possible instances.

The point is that while we prodigiously use numbers in science we don’t truly have a foundation of number theory. This foundation itself depends on recognizing that 5 is an idea and not reducible to objects. If we try to reduce the idea to its members, we end up in circular reasoning, which can then be used to create many logical contradictions – including, but not limited to, the infamous Gödel’s Incompleteness theorem.

Methodological reductionism pervades not just physical theories, but also mathematics. When we try to reduce the set or collection to its parts, we can either create contradictions due to circular reasoning, or find that we can never complete the reasoning because the loop never closes. Gödel summarized this fact into the Incompleteness Theorem that all theories capable of dealing with numbers (and hence individual objects) must be either inconsistent or incomplete. The genesis of the problem lies in our inability to provide a coherent definition of numbers that begins in objects. Gödel, as a result, became a Platonist, conceiving numbers to be ideas that exist beyond this world. This is perhaps the most succinct indictment of reductionism, if there ever was a need for one.

There are better definitions of numbers that begin in collections. For example:

0 := {}
1 := {0} = {{}}
2 := {0,1} = {{},{{}}}
3 := {0,1,2} = {{},{{}},{{},{{}}}}

However, now, we can ask: How do we know that there are two braces and not three or four? The definition of 0 requires the use of two braces, but two hasn’t yet been defined. In that sense, the definition above doesn’t avoid the problem; if anything, it only exacerbates it because the problem rapidly magnifies as we try to define larger numbers: to define 0, we need to have 2, to define 1, we must have 4, to define 2, we must have 8, and so forth. As a result, we haven’t yet escaped circular reasoning, and this definition too, therefore, suffers from the same Incompleteness problem as the other definitions.

My point is that if we are to solve this problem, we must treat numbers as ideas. These ideas can be represented as things, and can be inferred from things, but they are not an epiphenomenon of things. Rather, whenever we denote ideas through things – with the honorable aim of trying to illustrate them objectively to others – and then dishonorably pretend that that illustration is itself the idea, we create either logical contradictions or incompleteness. The incompleteness manifests as probabilities in science.

The problems of indeterminism are therefore not simply about science being a work in progress; they are rather about the need for a fundamental breakaway from established dogmas where the material parts are real and their collections are epiphenomenal. The problems associated with the current scientific dogma span from mathematics to computing to physics to chemistry to biology and beyond, although they have a very simple resolution: invert the reduction. The problem is not materialism and reductionism, because even in the new approach described here, there will be matter and reduction. However, both matter and reduction are conceived differently.

Conclusion

Life too is an idea. It is a very abstract idea, which can be expressed in many living forms. We can represent the idea of life by giving birth to children. We can also infer the idea of life by observing the individual living forms. But life is not the epiphenomenon of its material representations. Materialism as it stands today has come to a dead end, not just in biology but in physics and mathematics as well. To prop materialism, science has replaced reality with chance and probability. The nature of their existence, and what we can call material about chance and probability, is deeply questionable. The loss of predictability and the limits of science that arise from this indeterminism are numerous and well-known.

Materialists, however, dishonorably pretend that this incompleteness is only a question of science perfecting itself over time by repeating the established paradigms of reducing the big to the small. One only needs to be aware of the various kinds of incompleteness, the intimate connection between them, the root cause underlying them which is the attempt to reduce the big to the small, before you will see clearly why this belief is hopeless. We can create things from ideas, but we cannot create ideas from things.

This means that the remedy is easy: we just overturn the attempts to create ideas from things to create things from ideas. We will still have ideas and things, but things would be created from ideas. This alternative requires us to think of ideas not as mysterious and otherworldly entities but simply as space-time forms, which we ordinarily call boundaries. This entails important revisions to our notions about space and time – these are no longer linear and flat, but hierarchical much like ideas are organized in a hierarchy. To envision this hierarchy we need to think about postal addresses and clock times. Like a postal address first addresses the country which is more abstract than the city that comes next, or like a clock time which addresses the year before it addresses the month, there is an inverted hierarchical way of thinking embedded in our everyday world, which science has neglected thus far. The intuitions of a new way of thinking are around us, although quite different from the way science has thought about the same world thus far.

Materialism as an empirical strategy can keep working, but as a theoretical strategy it has failed, not because there isn’t matter but because we reduce wholes to parts. We can take pride in the empirical successes of science, and point to the fact that when we speak of life we are only speaking about the body comprised of molecules. However, in making these claims we must also ask whether the theory can ever be predictively complete.

If all theories that reduce the whole to the parts are incomplete (although they make statistical predictions) we are making a fundamental mistake in our conception of nature. I believe this mistake can be corrected, not by rejecting science, but by inverting the reduction. Only with a new conception will we solve the problems of indeterminism and the problems arising from thinking of life in the present manner.