Chicken and Egg Problems in Science

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In an earlier forum response, I described some chicken and egg problems in science in describing space, time, and objects. I thought this can be elaborated in detail to illustrate the nature of the problem, and how these are solved in Sāñkhya philosophy, leading to the conclusion that whatever we call the “body” springs out of a succession of hierarchical elements that end in the soul. Science rejects the reality of the soul; however, it doesn’t solve the chicken-and-egg problems. It just assumes that the egg with the chicken in it exists.

The Chicken-and-Egg Problem of Space

A simple chicken-and-egg problem with regard to space is—Did space come before distance or did distance come before space? In our common ways of speaking about space, it is an object with a property called distance. Of course, distance is not just in space; it also exists in meters. That which exists in many things should transcend all of them, which means that distance must be prior to both space and meters. But how will we define distance without space and meters? How does a property like distance become immanent in many things?

Do Ideas Exist?

The transcendence of the concept of distance, and its immanence in space and meters, suggests a Platonic world of pure ideas that incarnate (or are reflected) in this world. Per Aristotle, concepts like distance, angle, and duration, are “theoretical” forms while concepts like beauty and justice are “practical” forms. But the incarnation of a Platonic form suggests that an idea-like reality precedes an object-like world. This claim has been disliked by all materialists.

To avoid such conclusions, science has tried to dissolve the distinction between space and distance. In geometry, we say that space is an infinite number of infinitesimal points with no length. Since length is a byproduct of points, therefore, it is fundamentally unreal and has no Platonic-world existence. But do points exist in the Platonic world? There are many points that should be incarnations of a Platonic idea called a point. Geometry responds: Each point is a number, all numbers are a priori real, hence, all points are a priori real. Words like “space”, “number”, and “line” are sets of numbers, rather than concepts. We can get rid of all Platonic concepts by substituting them with sets.

Gödel’s Incompleteness

We can show that this trick doesn’t work for mathematical statements. For example, in the sentence “even number is divisible by two”, the term “even number” should not be equated to a set because partitioning the set of even numbers into two mutually exclusive subsets of even numbers does not capture the meaning of “division” of an even number. Of course, we can prove the sentence “even number is divisible by two” by treating “even number” as a set. But that proof would not have proven the intended claim. Conversely, we can disprove the sentence “odd number is not divisible by two” by dividing the set of odd numbers into mutually exclusive sets. Thereby, all that is true is not proven (e.g., that claim about even numbers), and all that is proven is not true (e.g., the claim about odd numbers). The reduction of the Platonic concept of “number” to a set of things leads both to inconsistency and incompleteness.

The problem can be solved by rejecting the set-theoretic meaning of “odd number” and “even number” and relying only on Platonic concepts. If the need arises, we can use terms like “the set of odd numbers” and “the set of even numbers” to refer to a collection of numbers. Thus, sets are dispensable, but Platonic concepts are not. Space, distance, and point are now Platonic forms, and individual spaces, distances, and numbers are instantiations of these Platonic forms. The foundation of mathematics lies in constructing these instances from Platonic forms. If we cannot do that, then mathematics has no foundation. Since nobody knows how to create a foundation for mathematics based on Platonic forms, therefore, mathematics has no foundation.

There is still a problem with Platonism because we can construct statements such as “statement N is false”, where N is a number assigned to a statement, and Gödel showed that in any system of labeling statements, it is possible to label “statement N is false” by N. The problem is that a single word has two different meanings; N is a name and a sentence. This is just like the term “even number” could refer to a set or a concept. To get rid of the paradox, we have to get rid of one of the references, which means we cannot prove some statements.

The “Space Equals Distance” Claim

With set-theoretic problems, distance is an other-worldly Platonic concept, while meter and space are this-worldly instances of that concept. Since there is a universal Platonic world of ideas, therefore, you can still say that “distance” has a universal meaning. However, since nobody can agree on that universal meaning, therefore, we have to defer to our individual notions of “distance”. The mind enters mathematics because mathematics resurrects the Platonic world of pure ideas, which nobody can find. We still need to use concepts in science.

We can treat our minds as “this-worldly” and personal notions of “distance” as varied incarnations of the “other-worldly” Platonic idea. This view, however, leads us to three worlds, namely, matter, mind, and mathematics. The mathematical notion of distance in the Platonic world is now reflected in our minds and in matter, and the objective foundation of mathematics is based on a pure idea of distance, imperfectly known by the human mind and imperfectly applied to the measurement of the distance between material things.

A practical illustration of this problem is that we can define multiple methods of measuring length, that define what we mean by length. Based on these methods, we will produce different values of length. Thereby, length is neither a subjective nor an objective property. It is an effect produced by the combination of the two. For instance, I can look into a microscope and see things bigger than seen by the naked eye. There are two ways of measurement—one by the naked eye and the other through a microscope—that give different results.

The measured distances cannot be called real because the world looks bigger through a microscope than through the naked eye, and we don’t know what the “true length” is. Thereby, there is some factual observed length and there is some reality, but they are not the same. In fact, what we observe as length depends on our method of measurement, quite different from a universal definition of length, and quite distinct from objective length. The distinction between the Platonic world, the mind, and the real world is necessary.

The “Space Does Not Equal Distance” Claim

We solve the problems resulting from the non-objectivity of measured length by calling some length an illusion while another length a reality—e.g., we might say that the lengths seen through a microscope are illusions and those seen by the naked eye are reality. But these are unjustifiable metaphysical assertions. They arise because we try to eliminate the role of the mind in an observation to arrive at some objective reality. Such an objective reality is arbitrarily concocted by deeming a specific measurement method the definition of reality.

There would be no problem in accommodating all these alternative versions of length if the differences were attributed to the choice of different procedures of measurement of the same property. The mind will now enter an objective reality by defining what we “mean” by “distance” by defining how we want to measure the distance. It can include the naked eye and microscopes of varying resolutions. After all, who is to say that only the human naked eye defines the objective measure of spatial length, while the microscope does not?

The “Space is Prior to Distance” Claim

Einstein’s theory of special relativity took this problem of the relativity of different observations up a notch when it spoke of observed facts of “length contraction” and “time dilation” even with the same method of measurement. Different observers can now measure the distance using the same method and obtain different values. The problem of distance is disputable if we use two different methods to measure distance. But it becomes indisputable when the same method is used. Now, we must say that distance is just observation.

We can no longer say that space is an objective reality that exists prior to our measurement of distance because no two observers agree on what distance is. The claim works only if we can designate a special observer whose privileged observations define reality. The equivalence of all observers entails that any discussion of “space” or even objective length is metaphysics. The sustainable view is that all measured distances are facts even if observers disagree about them. There is hence no “space”. There are just varying distances.

The “Distance is Prior to Space” Claim

After Einstein formulated the theory of special relativity, he also adopted a Kantian stance in which space, time, object, causality, etc. are mere “goggles” through which we see the world rather than objective realities. Thereby, what we see are the combined effect of some external reality and some goggles. The fact that we cannot talk about an objective space or distance is because the distance is not “out there”. It is “in me”. Space, time, object, or causality may still exist in reality. But there is no way to know what those things in reality are.

Einstein’s difference with Kant was that everyone need not have the same standard of distance, even if they call it by the same name. My “meter” need not be the same as yours, although we both call it a “meter”. The word “meter” is a pointless label if they are not the same. By applying this concept to perceptions, we construct an external world, including that this world exists in some space. However, space has no external reality. It is rather a conceptual construct based on my chosen, private, and not identical to others’, conception of length.

This upgraded Kantian stance relies on a mind-body distinction in which my goggles are separate from reality. The problem is that these “goggles” are equated to measuring instruments, which are also in space. Hence, instead of being the goggles through which we see reality, they become the reality being seen. Instead of being pure concepts, they are things being seen.

Solution to the Chicken-and-Egg Problem

We are led to the chicken-and-egg problem because (a) of the distinction between conceptual and measured distance due to Gödel’s incompleteness, (b) space is not identical to distance because there are many methods of distance measurement, (c) we must suppose that there is an objective space out there because science works, (d) a fixed standard of measurement still leads to different results, and (e) since these results are tied to an observer, therefore, the measurement procedure, and its results, are also tied to observers.

Constructing an Experienced World

The solution to this problem is easy if we adopt a position different from both Kant and Einstein. In this solution, “distance” comes before the space of objects and it exists uniquely in each observer’s mind as the subjective concepts of “near” and “far”. These varied notions of “near” and “far” are then converted into a length measurement procedure by a choice. Finally, we use a choice to apply the procedure to measure pairwise distances between some things.

Thus, there are three kinds of choices involved—(a) our definition of “near” and “far”, (b) their translation into measurement procedures such as observation by the naked eye vs. a microscope, and (c) the observation of different objects by the naked eye or the microscope. After collecting these data points, we combine them into a mental picture of the “world”. But the picture is not the world.

Our choice of which object we measure can also be divided into an emotional and an intentional choice. For instance, you might sometimes feel lonely and wish to talk to a friend. If you have many friends, you can choose one among them. Then you use a procedure to connect to the friend—e.g., dialing a phone call. That procedure establishes a connection to the friend. Then you talk to the friend and your sense of loneliness is overcome. Since someone is making all these choices, the person who chooses is distinct from the choices.

Thereby, the “world” is constructed with six components—(a) an emotional desire for connection, (b) the intention of connecting to someone specific, (c) which causes the execution of a measurement procedure, (d) that establishes a pairwise relation, (e) the result of that connection is cognized in many ways, and (f) a self that makes a choice, different from the above five domains of choosing, namely, the emotion, intention, conation, relation, and cognition.

In a scientific experiment, the self that measures, his emotions, and his intentions are disregarded. How a procedure establishes a connection between the measured and the measuring system is ignored. After neglecting four of the six components, we get two—conation and cognition—or the execution of a measurement procedure and the result of that measurement. But still, the subjectivity in that measurement doesn’t disappear because the procedures are chosen and the results of these procedures are cognized as “near” vs. “far” and “reality” vs. “illusions”. If we consider a broader spectrum of cognitive results, then they can include words and meanings, that are also true, right, and good. The picture of our “world” gets more complicated with more details.

This “world” is an appearance constructed from a six-fold personal reality that selects and interprets the world based on our choices. Since the “world” combines both subject and object, hence, it is neither purely subjective nor purely objective. These are inseparable in the “world”. And yet, these are not identical; there is indeed something that defines us as distinct from others.

The Role of Sāñkhya Philosophy

Returning to the problem of distance, we have to construct an instrument such as a meter from the personal conceptual notion of “near” and “far”. Sāñkhya explains how conceptual “near” and “far” become a meter. The basic principle is that our personal notion of near and far creates the smallest distinction we can perceive through our senses. That personal notion translates into the smallest perceivable distinctions between tones, pitches, pushes, textures, colors, shapes, flavors, and smells, and defines the refinement of the senses. What we call a “unit length” is one aspect of seeing that corresponds to the smallest distance we can obtain perceptually, akin to a millimeter.

The objectively smallest length corresponds to the senses of an observer with the most refined sense perception. That observer is Nature. Her notion of “small” defines the objectively smallest atom; nobody can measure a distance smaller than that. In Vedic cosmology, there are many universes within the material creation that vary in the level of refinement. Hence, the smallest measurable distance—that defines the “atomic” unit of distance—is different for different universes. The present universe has the least variety, which means the coarsest capacity for discrimination. The smallest measurable length—the atomic unit of length—is the biggest for our universe among all universes.

Different species of life in a universe have different coarser discriminations based on the finest distinctions possible in a universe, which makes our sense perception incapable of any smaller distinctions. For instance, even if particle physics tries to measure subatomic particles using powerful accelerators and detectors, the measurements have to be brought to the level of the human sense perception—e.g., a hearable click or a visible dot. Thereby, we think we are perceiving subatomic particles, but we are only perceiving clicks and dots. We infer these clicks and dots into the existence of subatomic particles, but there are infinite other inferences that could be drawn from the same clicks and dots, due to which we can never be sure of what the subatomic reality is.

The Nature of Semantic Atomism

A musician has a refined sense of hearing because he can distinguish small tone and pitch differences. A chef has a refined sense of taste and smell because he can distinguish minor differences between tastes and smells. An artist has a refined sense of sight because he can distinguish minor differences in color shades. A writer has a refined grasp of the language by which he uses specific synonyms to describe different things. This refinement in sensual and mental perception depends on a person’s personal notion of atomism.

The smallest click we can hear and the smallest dot we can see is the atom for us. In Sāñkhya, it is called a trisarenu—the smallest dust particles we can see in the light pouring through a window. That trisarenu is in turn comprised of three dyads or six aspects—the six aspects are called paramānu, the three dyads are called anu, and the combination of three dyads is called a trisarenu. These six aspects are subdivisions of cognition, namely, a percept, a concept, three kinds of judgments—true, right, and good—and finally an individual.

Of course, most of us only perceive an instance of a percept and a concept of a “dust particle” and that such a thing exists. Some of us may try to imagine “What it is to be like a dust particle?” They might find the existence desirable or not. Almost nobody wonders if the movement of such a dust particle is actually righteous or unrighteous activity, although such a judgment could also be made. Accordingly, the percept is the easiest cognition, the concept of a dust particle is the next cognition, that these dust particles are not my hallucination is the next harder cognition, that being such a thing would be good is the next harder cognition, and that this existence also performs a necessary and righteous role in the universe is the hardest of all these cognitive conclusions.

Converting Concepts to Percepts

Concepts and percepts underdetermine each other. The concept table underdetermines the percepts because tables can be of varied shapes and sizes. Likewise, a shape and size can be variously called a table or a chair. Therefore, given the concept of “small”, the percepts are underdetermined. That underdetermination is overcome if “small” is qualified by a tone, pitch, push, texture, color, shape, size, color, flavor, or smell. The process by which this underdetermination is overcome is described in Nyāya, where underdetermination is called abhāva or absence or incompleteness. Overcoming it involves defining “small” in terms of sense perceptions.

We can illustrate this by asking: What do we mean by “small”? The first answer is: It is found in a small variation in tone. Then we can ask: What do we mean by a “small variation in tone”. The second answer is: It is found in a small pressure. Then we can ask: What do we mean by a “small pressure”? The third answer is: It is found in a small movement. This is how we explain the concept of “small” via examples. Sound, touch, sight, taste, and smell are just examples of “small”. Since they are examples, therefore, “small” is in the examples. But since these are just examples, therefore, “small” is not confined to these examples. We must say that “small” is both immanent in and transcendent to its examples.

This expansion of the concept into its multifarious examples will not arise unless there is someone asking the question: What is the meaning of X? Hence, a concept expands into its examples only under the presence of consciousness. Sāñkhya merely states that a subtle reality expands into a gross reality under the presence of consciousness. Nyāya however explains the role of consciousness in causing that expansion in greater detail. Those who study Sāñkhya purely as a material theory can never explain this expansion because even as “small” is incompletely defined without its examples, that incompleteness exists only if there is a person to consider it incomplete and try to complete it.

The cause of abhāva is consciousness that triggers a material expansion. If this consciousness is withdrawn, then the examples merge back into the original concept of “small”. Similarly, the fact that “small” manifests into nothing more than sound, touch, sight, taste, and smell, is also due to the fact that incompleteness is overcome by these five-fold illustrations. Since there are no more questions, therefore, there are no more answers and expansions. For instance, if someone asked “What do you mean by small?” and the answer was given in terms of something that can never be perceived, then it would not be considered a useful illustration or example. Hence, even as Sāñkhya is a theory of matter, it is inextricably tied to the nature of consciousness.

Objective and Subjective Properties

To recapitulate, distance and space are not identical; distance is prior to space. Distance is a subjective concept indicated by—(a) we cannot perceive something smaller than a select distance, and (b) we consider different things to be smaller or bigger based on personal ideas. And yet, because this subjective concept is constructed from an objectively smallest distance, therefore, “atomic length” is an objective concept. But it is not our concept; it is Nature’s perceptual ability, which means that there is something in Nature that can detect the “atomic length” and magnify it into a “measurable length” that humans can perceive. Seeing that magnified length is not the same as seeing atomic length. Thereby, there is no conflict between the subjective and the objective lengths.

Distance and Space Revisited

The fact that there is objective length doesn’t mean that we can divorce length from perception. Length is not defined by a meter or foot, although length is immanent in both meter and foot. Length is rather a transcendent property, instantiated as one of the examples of the concept “small”. The mental concept of “small” initially appears as the definition of small in terms of the sense of seeing (a measurement procedure), and then transforms into a visible object that we perceive by sight as small based on our sensual or mental concepts.

Likewise, the concept of “distance” is created by establishing a relationship between things. We can be near or far from small or big things; hence, smallness and nearness are not identical. Smallness pertains to an object while nearness pertains to a relationship with an object. They are distinct as cognition and relation. However, due to the use of modalities—i.e., the possibility of using the same word in many ways—we can loosely equate smallness to nearness in some cases although not in others. For instance, we can see a forest as a small patch of green. In this case, a big thing is seen as small due to our distance from it. The factual bigness is an objective property of the forest. But due to our distant relationship, it seems small. Thus, nearness and smallness are not identical. And yet, you can sometimes say nearness is a small distance.

All length measurements are thus subjective properties although there is an objective reality. The same thing can seem bigger or smaller to us, based on our relation to it. The perceived size and distance constitute our perceptual space, distinct from the objective reality. Thus, what we measure as space or observe as a “world” is not reality. It is an appearance of reality. But there is a reality, not identical to the observed fact. Facts are not reality. Rather, facts are byproducts of the interaction between our perceptual apparatus and reality.

Bridgman’s Operationalist View

The distinction between fact and reality cannot be altered by measuring instruments. One of the clearest illustrations of this problem comes from the fact that we cannot devise a measuring instrument that can effectively measure both small and big. For instance, the scale that weighs trucks cannot be used to weigh diamond jewelry accurately, and vice versa. We have to use two separate scales and we cannot calibrate them. This intuitively trivial problem was demonstrated by P. W. Bridgman in his measurement of gas pressures.

Bridgman found that the pressure gauges that worked for small pressures did not work for big pressures. The gauge for low pressures would break down when subjected to high pressures. New gauges had to be devised for different pressure ranges, which led to the problem of calibrating the gauges relative to other gauges. The problem with calibrating the gauges is that the lower-pressure gauges produce erroneous results near the top end of their pressure ranges, while the higher-pressure gauges produce erroneous results near the bottom end of their pressure ranges. That is just like you will not get the accurate weight of diamond jewelry using a scale that is meant to weigh trucks. So, how are you going to calibrate the low- and high-pressure gauges if you aren’t sure if the measuring instrument is giving us accurate results?

Bridgman got so flustered with this problem that he formulated a philosophy of Operationalism in which there is no meaning to a property like “pressure” other than the specific value given by a gauge that cannot be guaranteed to be calibrated with other gauges. If a gauge says that the pressure is 10 pounds per square inch, there is no way to know if this is 100 times the gauge that indicates a pressure of 0.1 pounds per square inch. All our attempts to calibrate gauges suffer from this problem. Hence, we cannot know how much these gauges are off from one another. Bridgman concluded: There is no meaning to a properly like “pressure” than what my instrument says right now. In short, science is not about objective facts if those require an extended scale because there is no universal scale and instruments cannot be calibrated. We use these numbers in some approximate theoretical models although the models don’t match the data perfectly. We don’t know if the model is wrong or if our measurements are.

The problem magnifies by orders of magnitude when we talk about small values in terms of larger scales. For example, there is no meaning to a value like 10-20 meters because we need to calibrate 20 different length scales to operate across 20 different orders of length magnitude and we cannot. If our theory rests on finding precise values and the instruments are imprecise, we have no hope.

Although Bridgman won a Nobel Prize in physics, he was attacked due to the implied pessimism of his conclusion. Eventually, he gave up trying to explain the problem, the noise died, and everyone happily went back to studying the nature of “objective reality” in science through the use of instruments.

The Problem of Measurement

Of course, to uphold any realism, Bridgman’s conclusion that “pressure” means a gauge should mean that the gauge is contained inside the gas whose pressure was being measured. This is the only way to say that gas has pressure. Since this conclusion is also untenable, therefore, to be perfectly consistent, we have to say that there is no such thing as pressure. Rather, some gas in contact with some gauge shows us some pointer values. But you cannot formulate a scientific theory with such an interpretation of scientific measurements.

Therefore, to uphold any kind of realism in science, we have to suppose that there is a property like “pressure” that transcends all measured objects and measuring instruments. We can call it a Platonic idea because is conceivable that there is the smallest measurable unit of pressure in Nature. Instruments are multiples of the unit but we cannot mutually calibrate them.

Hence, if an experiment concludes that a theoretically calculated value has been detected, there are huge assumptions involved—the gauge that measured this value was perfectly calibrated with all the other gauges that were previously used to measure all other values in all the other experiments. That calibration does not exist, and it is impossible to achieve it. A gauge could behave differently in a hot environment vs. a cold one. To accurately measure pressure, we have to align the temperatures. But the temperature gauge can also depend on the pressure in the environment. These cyclical interdependencies between various properties preclude any reliable instrument calibration.

The problem never disappears. It just gets more and more complicated as we consider more properties. For instance, to measure time using a clock, we have to define the distance between two points on a clock. If that distance expands or contracts, then the measured value of time is meaningless. In this process, time depends on space. Likewise, if you are trying to measure distance by roundtripping a light beam, what you conclude as distance depends on how much time it took the light to roundtrip. In this process, space depends on time. The clock that measures time can go slower or faster based on ambient pressure and temperature. To measure temperature using a thermometer, or pressure using a gauge, you have to be sure that the scales that indicate the numerical value on these gauges are not expanding or contracting.

All real-world measurements of properties are so inextricable from every other property that you can never be sure that the value you are measuring is a property of the world and not the measurement instrument playing tricks on you. The pointer movement can never be attributed to one property. Instead, we have to say that this pointer moves so much, under the condition that all the other property pointers moved so much, and all these pointers are somehow mutually interlinked but not identical to any other pointer elsewhere.

This general problem of inextricability is called Bhedābheda in Vedic philosophy, which means distinct but inseparable. The measurement of time, space, temperature, pressure, mass, charge, or any other property conceived in science, is inextricable from the measurement of every other property. All these properties are aspects of reality and change to one aspect can change all other properties. When properties are thus inextricable, then we cannot add or multiply these properties as if they were independent variables. That is the end of using mathematics to study nature, which relies on the assumption that the variables involved in a scientific equation are independent of each other.

Logical Necessity of Truthful Laws

The empirical method of science is deeply flawed due to the assumptions of separability. The correct method is through logical necessity. If the observation varies from that logically necessary truth, then the variations must be attributed to a problem with the observer. This method is employed in Nyāya philosophy. Just because you don’t see some reality doesn’t falsify its truth. The absence of evidence is not evidence of absence. Likewise, the presence of evidence is not evidence of presence. You might just be hallucinating a presence.

Observation is neither necessary nor sufficient to guarantee the truth if our mental and sensual instruments are flawed.  The inability to validate a logically necessary theory doesn’t invalidate the theory. It rather calls for perfecting the perceptual capacity. Such a process is called the purification of consciousness.

Meanwhile, before you pursue the purification of consciousness, you can try to become convinced of the truth based on a logical necessity. It involves questions such as—Does space equal distance? Does space not equal distance? Is distance prior to space? Is space prior to distance? Logical necessity rests on eliminating alternatives by reasoning. When all that is impossible has been eliminated, then whatever remains, however improbable, is true.

Most people cannot imagine the improbable because they have not eliminated the impossible. They may have taken the existence of space for granted without asking if distance came before space or space came before distance. For them, the truth of the idea that space emerged out of the mind seems improbable because they haven’t yet examined the problem of distance. Hence, philosophy has an important role in compelling people to ask uncomfortable questions by which they can eliminate the impossible. It is the path—prior to the purification to consciousness—to accept the improbable. Once we are convinced about the improbable, we have to realize it by perception too. But that process can take time as it requires us to perfect the instruments of perception.

Other Chicken-and-Egg Problems

The detailed discussion of the problem involved in measuring the property of length can be generalized to all kinds of measurements. We have already discussed such problems with pressure and temperature. But the issue is not limited to these properties. The problems pervade all fundamental concepts.

The Problem of Time Measurement

Time, like space, involves a conundrum: Did duration come before time or did time come before duration? The measurement of duration generally involves a clock. But for the fingers of a clock to move, time must elapse. The passing of time can move the fingers of a clock, which we can then measure as duration. The clock fingers can move slower or faster, which means everyone can have a different clock and conclude that different durations must have elapsed. Our personal notions of long and short durations, however, depend on some objective passing of time. What is the meaning of that objective time, different from the measures of duration through different personal clocks?

This problem is also solved in Vedic philosophy by describing a Causal Time. It is the choice to make the smallest amount of change defined by Nature. Time appears to pass because—(a) there is a succession of choices that make a change, and (b) each choice involves an atomic duration. Atomic time is the duration involved in making an atomic change by an atomic choice. Since atomic change can vary across universes, hence, the smallest measurable durations also vary across universes. We cannot measure a time smaller than atomic time because measurements require something to change, and the smallest change cannot occur without the passing of atomic time.

Time must pass before a duration can be measured. Hence, distance is prior to space, but time must be prior to duration. Atomic time is also a choice just like atomic distance is a choice. They are just different kinds of choices. Science has never understood time. It cannot solve this problem because calculus simply assumes that time passes. No mathematical theory can answer this question because the answer lies in the role of choice in making an atomic change. Science also cannot explain why time seems to go slower or faster, and why some people live longer because their time seems to pass slower to them.

The Problem of Object Definition

The problem of object definition is seen in set theory. To form a set of horses, one must have the idea of a horse before we can identify a horse or add that horse to the set of horses. If we don’t have the idea of a horse, then we cannot construct a set of horses. Therefore, even if we try to define the word “horse” as a set, we are still relying on the idea of “horse” as different from a set.

Similarly, to form a set of two things, you must know what “two” means. Otherwise, how will you ensure that the set has two rather than three or four members? You have to assume that there is a concept of twoness prior to forming the set of two things. And once you form the set of two things, the word “two” acquires two meanings—(a) the set of two things, and (b) the concept of twoness prior to the set. Mathematicians have tried to evade this problem in many ways unsuccessfully. For instance, one such attempt claims that we can define numbers as follows. 0:= {}, 1:= {{}}, 2:= {{}, {{}}}, and so on. Basically, 0 is an empty set; 1 is a set with one member—0; 2 is a set with two members—0 and 1. The question is: How do you represent an empty set? The simplest answer is “two braces”. So, to define 0 syntactically, we have to have the notion of 2 prior. To define 1 syntactically, we have to have the notion of 4 prior.

The Problem of Person Definition

There are even more serious issues when we try to define persons. For instance, if a person is defined as a set of objects, then any change in the set membership must change the person. Just by eating food or drinking water, you become a different person because the set membership has changed. This problem can only be avoided by saying that the person is both transcendent to and immanent in the body. If the person wasn’t immanent in the body, then hurting the body would not be hurting the person. If the person wasn’t transcendent to the body, then a minor change in the body (such as while hurting it) would change the person. Both properties are required to clearly define personhood.

How can we make a society with laws, property ownership, and rights if we cannot define what a person is? If merely drinking water changes the person, then the property purchased before drinking water is no longer owned after drinking water because the person before and after drinking water is different. Someone can commit a crime and drink water to disown all responsibility for the crime. A person can borrow money from a bank and drink water to deny that he ever borrowed money. Society cannot exist without personhood.

Similarly, unless we recognize a role for a will in a person, a bullet shot by a person under the threat of a gun to his head would be attributed not to the person who holds the gun to the head but to the shooter who actually shot the bullet. If we deny a role for will that causes action then the person who did not shoot will go unpunished while the person who shot under coercion will bear full responsibility. Laws of a society cannot exist without personhood.

The Problem of Inanimate Persons

If you buy a car, and you happen to scratch its bumper in an accident, you do not lose ownership of the car just because the material ingredients of the car are no longer what they were when you bought the car. If you buy a house, and you happen to paint it subsequently, you do not lose ownership of the house just because the material ingredients of the house are no longer what they were when you bought it. Houses and cars are given serial numbers to identify them as immutable things even when they are remodeled. That is just like a person remains immutable after eating food and drinking water. We may not ascribe will to houses and cars, and yet, their immutability requires us to treat them just like persons. Similarly, businesses are identified as immutable persons even if they move their offices, hire or fire employees, or change their logos. Cities and countries are identified as immutable persons even when people enter or leave them, even as material resources are moved in and out of them. If a country conquers a territory without changing its constitution, the new territory becomes a part of the original country, quite like a person who eats food or drinks water adds matter to his body without a change in identity.

The problems in defining objects, thus, extend to defining persons, and those problems then reflect back into the definition of personal property ownership. The problems of property ownership inherit the problems of both personhood and object definition. Unless this general problem of property ownership is solved, the problem of object definition cannot be fully solved.

The Mediocrities of Materialism

Materialism has no answer to these problems. There is no understanding of the problems in trying to define space, time, and objects. There is no understanding of the problems in defining persons and property ownership. The problems of defining space, time, and objects constitute a limited domain of truth. The problems of personhood constitute a limited domain of good. And the problems of property ownership constitute a limited domain of rightness. If we can solve these problems simultaneously, then we can solve the problems of truth, right, and good. However, since no materialistic theory solves these problems, therefore, there is no truth, right, or good within materialism.

Materialism is an intellectually weak doctrine that substitutes answers to deep questions about the origins of space, time, and objects with the axiomatization of their existence. Materialism is a morally inadequate doctrine that cannot answer the most basic questions of why a person without choice must be rewarded or punished. Materialism is an emotionally sterile doctrine that substitutes a life of great purpose with one of surviving without purpose.

Materialism is popular among the zombies who do not inquire into deep questions about reality, are not interested in developing moral character, and are unable to think of anything beyond day-to-day existence. Or, perhaps, they are incapable of such things which they rationalize by calling them non-existent or impossible. Materialism is a philosophy of the zombies, by the zombies, and for the zombies. It is a philosophy of the mediocre, by the mediocre, and for the mediocre. It is an intellectual rationalization of mediocrity.

The mediocre are relieved if they don’t have to find the truth, do their moral duties, or lead a purposeful life. An ideology that denies the possibility of truth, right, and good unburdens the mediocre mind from the guilt of not knowing the truth, right, and good, and not even trying to seek it. Materialism is that sedative that suppresses the last remnant of remorse a mediocre person may feel while comparing themselves to earnest people. Of course, since mediocrity has always existed, hence, materialism has always existed. But when it becomes a prominent dogma in society, we must understand that most of society is mediocre and getting quite comfortable with mediocrity.