Mathematics,  Overview,  Philosophy

Numbers, Truth, Morality and God

What is a Number? Is it an idea or a thing? This question has been debated since Greek times, and it still remains unanswered in philosophy and science. This post examines the nature of the problem, and what its likely resolution will look like. It illustrates how the problem of numbers leads to the problem of choice, which then results in the problem of morality, which then results in questions of happiness. The resolution of these problems requires the idea of universality—namely universal ideas, universal moral principles and universal ideas about happiness.

Russell’s Theory of Numbers

Bertrand Russell and Alfred North Whitehead—two famous British philosophers—attempted to answer this question in the early 20th century as part of their mammoth three volume work entitled Principia Mathematica. They proposed a simple scheme drawn from an everyday intuitive fact about collections—they claimed that numbers are properties of collections. They are not therefore individual objects, nor are they purely ideas (supposing that ideas were in our minds and could not be objective).

We can see that a collection of 5 horses has the property of fiveness, although it is not alone in having that property. The same property of fiveness, would, for instance, be seen even in the set of five cats. Russell and Whitehead therefore proposed that the number five is the property of all sets with five members, and to delineate this property, we would have to form a set whose members were sets with five members.

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Figure-1 Russell’s Theory of Numbers

To arrive at this definition of fiveness, we would have to find all the objects in the universe and collect them into groups of five, before we could define the idea of fiveness, which presented a practical problem. However, mathematicians aren’t concerned with such practicalities. They are more interested in theoretical definitions. For instance, mathematicians frequently deal with infinite sets—e.g. the set of all rational numbers— which is an infinite set too. So the fact that this process of defining a set could potentially involve infinite steps did not concern Russell and Whitehead.

There is, however, another theoretical problem in this definition. The problem is that to make a set of five cats, we must first count them as 1, 2, 3, 4, and 5. Before you can have a set of five cats, therefore, you must have the definition of ‘5’ already available. But this definition of fiveness is precisely what we are trying to arrive at through this procedure of collecting objects into sets of five! You can see that to define fiveness we must have already defined the idea of five, because otherwise we could not form any set of five members, and therefore collect these sets into a larger set called fiveness.

Ideas and Things

This problem in the definition of number presents a classic divide between ideas and things. We generally suppose that ideas are only in our minds—i.e. they are not real. Through science, we suppose that our mind would one day be reduced to the brain, which would then be reduced to chemistry and physics, which would then prove that the mind is nothing but matter.

Once this reduction has been achieved, we would then be able to show that matter results in chemistry, which then creates the mind (through evolution and such processes), which then comes to have ideas.

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Figure-2 The Materialist Conception of Mind and Ideas

Russell and Whitehead were trying to solve this problem for only one such idea—the idea of number. And their method of reduction essentially showed that to derive the idea of fiveness from things, the things themselves have the idea of fiveness even prior. In short, you cannot derive the idea of fiveness (or any other idea) from things without using that idea to classify and identify that thing.

For instance, if you were trying to define the idea of catness by collecting all the cats in the world, you must first collect all the cats. This might be practically very difficult, but let’s assume that you can do it. However, you still have the problem of how you distinguish a cat from a horse. If you cannot distinguish the two, then you would also have horses in your set of cats, and the definition would be wrong. However, to distinguish cats from horses you must have the ideas of cats and horses even before you collect them into the sets of cats and horses to arrive at their definition!

In short, the problem is not unique to the idea of numbers, but for any kind of idea whatsoever—if you try to derive the idea from things. To define an idea from a set of things, you must first collect the objects to which that idea can be applied, and therefore the idea must exist even prior.

This is sometimes formally called the problem of recursion: to know something you must know it beforehand. If there were only things in the world, and our minds were byproducts of the brain, which was a byproduct of chemistry, which was a byproduct of matter, we could not know anything. To know anything from the world of things, someone must know it a priori – i.e. not from the world of things. Then, that person can impart that a priori knowledge to other people, who can then see the world of things in terms of those ideas which were previously imparted to them. To begin seeing the world in terms of those ideas, you would have to accept the idea itself upon faith.

Counting = Distinguishing + Ordering

Counting involves two different mechanisms—(a) a mechanism for distinguishing things from one another, and (b) a method for ordering them into a sequence. Before you can count horses as 1, 2, 3, 4, 5, you must be able to distinguish the various horses from one another. If you could not distinguish, you could not know if there were 5 horses or just 4, 3, 2 or 1. After you have been able to distinguish the horses, you must order them into a sequence—i.e. calling them the first, second, third, fourth, and fifth horse. In each of the two steps—distinguishing and ordering—you need the ideas to exist beforehand.

Since this problem is not unique to counting, but exists for all ideas, you must have a rich repertoire of ideas before you can use them to know the world. The diversity that you can see in the world depends on the diversity of ideas by which you can categorize it. You cannot be born a blank slate such that the slate is written upon by the encounters with the world. You must rather be born wearing some goggles using which you can interpret—i.e. distinguish, divide and organize—the world in your mind.

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Figure-3 Ideological Goggles Shape Perception

John Locke—another famous British philosopher—claimed that our minds are blank slates at birth. Over time, as we encounter new facts, we acquire new ideas. In other words, Locke believed that all ideas are derived from things, and can therefore—in principle—be reduced to things. The problems that we previously spoke about and which arise in counting things (and in any cognition whatsoever) show that we cannot derive ideas from things, unless we already have those ideas in us beforehand.

We must be wearing a pair of ideological goggles of distinct ideas and categories to even see the world correctly in terms of those ideas and categories. In other words, the fact that we see ideas in the world is because we already had them (as our goggles) before we saw the world. A mind that is a blank slate at birth will never see anything at all.

Immanuel Kant—The Role of Synthetic A Priori

Immanuel Kant—an 18th century German philosopher—had a sophisticated term for this claim: he called it the synthetic a priori. The term synthetic denoted that all these ideas that exist beforehand are not trivialities—they carry very important foundations of our knowledge. The term a priori denoted that these were not derived from the external world. We had to have them if we were to know anything in the world, and therefore, we could not derive them from the world a posteriori —from experience.

It is well known that some people are tone deaf while others are musically savvy. A tone deaf person cannot appreciate music; to appreciate music you must have the tonality of music in you. The tone deaf and the musically savvy therefore don’t view music in the same way: one sees music while the other doesn’t. Music teachers will tell you: you must have some music in you before you can be taught more music. You cannot start as a blank slate and be taught music because if that were the case, then every person on earth could be a fantastic musician simply by going to school. Some of us are born wearing the googles of music, while others are not. In some people, the goggles of music are crystal clear, while in others they are hazy. Accordingly, they can be great or average musicians.

How Many Goggles?

Once you recognize that we must be wearing goggles to see the world in terms of the ideas that are ingrained in those goggles, the very next question is: How many such goggles are possible? In other words, how many ideas must we possess a priori before we can see those ideas in the world (cognize the world in terms of those ideas)?

The answer to this question is an infinity because you cannot acquire any idea from the world unless you had some preliminary form of that idea already within you. This, however, does not mean that everyone must have all the ideas beforehand. It only means that someone must have had the idea before you, who then objectivizes this idea into a thing, from which other people could also gain the idea. Before objectivizing, the creator of that object must combine the ideas themselves in his or her mind to create an abstract picture of the object to be created, which is then detailed over time to create an object.

Take the preliminary idea of a car. This idea is very abstract, and it can be refined to create other concrete ideas such as SUV, hatchback, sedan, truck, sports car, etc. Once a new variation of an idea has been created, others can look at that object and acquire the idea for themselves too.

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Figure-4 Detailed Ideas are Produced from Abstract Ideas

It is therefore correct to assume that we often acquire ideas from the external world. But that acquisition is only because someone had that idea in their minds before that idea was represented in a thing. The object you see is a vehicle or carrier of that idea, but the idea would exist (or could exist) even when all these vehicles did not. The fact that we are able to create new ideas, and then convert them into things, indicates that ideas can exist even before the things embodying them do. The ideas must therefore be logically and temporally prior to the objects in which they are embodied.

We know that we cannot reduce the ideas to particular things. For instance, we cannot reduce the idea of a hatchback to a particular instance of the hatchback because if we did that reduction nothing else (apart from that particular instance) could be a hatchback. We might claim that the idea of a hatchback is a property of all the hatchbacks (past, present and future) but this claim not only presents the practical difficulty of knowing everything that exists in the past, present and future, but also the conceptual problem that to even apply the idea of a hatchback to anything we must have that idea even beforehand. We cannot therefore reduce the idea to a particular instance, nor to a collection. We simply cannot reduce. We must accept that the idea exists even when the thing does not, and the idea is therefore logically prior to the things in which it is embodied.

It follows from here that every idea that we see in the world must exist in someone’s mind before it exists in the world. When we see something, we interpret it according to the goggles we currently wear. Upon seeing those things, we might also acquire a new pair of goggles which allows us to see that kind of thing again and again. The ideas therefore transform into things, which then convert into goggles.

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Figure-5 Three Forms of an Idea

Every idea that can exist in a creative person can potentially become goggles in another person. We first think of ideas, then we create things from ideas, and then we disseminate those things and ideas so that other people can see the world in the same way as the creative person originally saw it. Ideas become successful when they have been transformed into goggles into other people. There is hence a potentially infinite number of goggles—just as there is potentially infinite number of ideas.

The World is a Message

The conversion of our ideas into things, followed by the conversion of things into goggles by which we see those things, implies that the world exists as the embodiment of ideas. The objects we see are representations of ideas that originally just existed in our minds, but were then embodied into objects, before they became goggles.

Just as we express our thoughts through sentences—spoken or written—and these sentences are material (i.e. they are encoded using paper and ink, or uttered using sound), similarly, other material objects—like cars, horses, cats, etc., are also messages. To create the message, the meaning must exist beforehand. Similarly, to comprehend the message, the ability to understand that meaning must exist prior in us. The meaning that exists prior is the idea in our heads, and the ability in others to understand that meaning is the goggles by which they can see our meanings. Before we can communicate to each other, we must have the meanings and the goggles to read them.

In effect, we must know some language in terms of which to form ideas. If we know that language, we can use it to transform our ideas into things—e.g., words—and the listeners can then grasp those words to convert them back to meanings. The relation between the world and our mind is like that between words and meanings. The meanings exist before the words, although the meanings can be transformed into the words, and then grasped from the words. Our ability to represent the meaning in the words, and then decode them from the words, does not imply that meanings are words.

Rather, you must have the meanings before you speak words, and you must have the ability to comprehend the meaning before you listen to the words. The ability to create meanings and understand meanings is logically prior to the embodiment of meanings in material things. The world is not created as meaningless things which we interpret as meanings. The world was created with some intended meaning which we can try to understand depending on our goggles of comprehension. How well we comprehend the world depends on the quality of the goggles through which we see it.

To know the world, we don’t need to possess every idea that is possible in the world, but only the language in terms of which it is encoded. The knowledge of the language is much simpler than the knowledge of everything that can be encoded in that language. We also create ideas using a language and the listeners comprehend them if they know how to understand the language. The fundamental ingredients of the world are therefore not things; they are the memes and grammar of language. This idea is sometimes also called semiotics and it has generally been popular in continental Europe.

Not All Messages Are True

Everything you see on TV or read in a newspaper is not necessarily true. You might have the perfect understanding of language to grasp the meanings, but you don’t necessarily have a way of knowing if those meanings are also true, simply by looking at the statements themselves. How do you know if some statement is also true versus another that is false?

You can approach this problem in two ways. First, you can try to logically prove the claim based on some axioms but the truth of the claim depends on the truth of the axioms. Second, you can try to empirically prove the statement based on its conformance with the facts in the world, but the problem is that if the world is a message then you cannot simply compare two statements and infer that one is wrong and the other is right. How do you know which of the two conflicting messages is true? And even if you had two consistent messages, does their existence entail their confirmation? Could it possible that there are other contradicting facts (statements) that you haven’t yet encountered?

During medieval times, many people believed that the earth is flat and the planets go around the earth. It was one way of explaining our observations, as long as people had not discovered the fact that you can keep moving on a straight path over the seas and you will arrive back from where you started. Subsequent scientific evolution has also overturned many beliefs (and theories) in the past. How do you know that you will not encounter future such refutations of what we presently hold true?

This problem is fundamentally unsolvable. We can confirm our theories are compatible with experience, but we cannot know if they are true. In this case, confirmation truth. In the case of logical proof, we can show that if the axioms are true, then the conclusion must be logically true, but we don’t know if the axioms are true. This is therefore a fundamental problem in all forms of knowledge: namely that we can prove (logically) and confirm (empirically), but we cannot know if they are indeed true.

For instance, if all the politicians in your country were lying, and the TV and newspaper reports simply repeated those lies verbatim, all the statements that you can see and hear would appear to be mutually consistent. You could confirm that the statement reported in the newspaper is true because the politician indeed made those statements. But that doesn’t mean that that the politician is telling the truth. If one politician agrees with the other politicians, the agreement would be quite like the newspaper reporting what the politician said, and that agreement still doesn’t say if it is true. If the politicians disagree, you still have no way of knowing which one of those politicians is actually truthful, because you would simply try to find more such agreements (or disagreements) between those politicians and other observations, which may be confirmation of what one (or the other) says but as we saw above, confirmation is not equal to truth.

Truth is also A Priori

We are now led to a peculiar problem: you cannot know the truth by comparing different things to each other. You can only know the truth if you postulate something to be true. These postulates become your a priori truths; you might also call them axioms. When you look at a politician, you somehow—a priori—believe that he or she is lying. Of course, your beliefs might be wrong, but you have no way of being sure by comparing to other people or facts. This point is quite similar to the problem of meanings we saw earlier: we noted that to see an idea in the world, you must know that idea beforehand. Similarly, to know the truth of something, you must already somehow know the truth beforehand.

Rene Descartes—the founder of Cartesian geometry—struggled with this problem quite a bit. He acknowledged that he could not trust his senses, because he might be hallucinating. He could not trust his mind, because there might be an evil genius controlling his mind and leading him to false thoughts. But he argued that he could not doubt his own existence because even if he was under illusion and hallucination, he still existed. Descartes concluded—cogito ergo sum —I can think therefore I must exist. Descartes went on to build everything else from this supposition that he actually exists.

Of course, Descartes does not live anymore. If therefore we identify Descartes with the particular body and mind that was born in 1596 and died in 1650, his existence is not true anymore. Accordingly, if you take away the truth of his existence now then everything that he said previously (and which was based upon the truth of his existence) would also be false now. The only way what Descartes said at that time could be true now is if his existence was true even now, although that couldn’t be his body and mind.

The key point is that you could not know any truth unless you blindly accepted some truths. Which axioms you accept to be true are purely your choice. We cannot reduce this choice to other meanings or claims, because there is no way of knowing if these additional claims are also true. This collapse of knowledge is so fundamental that its importance cannot be overstated. However, this collapse gives us a very important starting point— namely that we have choices to decide what we accept to be true. These choices essentially constitute different theories or worldviews about reality.

What Should We Choose?

Once you realize that there are many possible axioms that you can choose, you need to ask: Which of these axioms must I choose? Each axiom set obviously works for some facts in the world, because starting with those axioms, we can derive these facts. Many of these axioms would not be consistent with the worldly facts. When you encounter such inconsistency, you are faced with a new dilemma: should I discard my assumptions and go with what the world is telling me? Or should I consider my assumptions true, and consider the facts from the world to be false? This problem is not as easy as it sounds. For instance, if you decided to simply discard your beliefs with every observation that appears inconsistent with your beliefs, then you would be easily led astray by those politicians who tell you what you don’t believe in. If, however, you decide to never discard your assumptions, and if those assumptions are faulty, then you will believe the truths to be false.

The problem of judgment involves distinguishing the truths from the lies. In comparing two statements or claims, you don’t know which one is true or false, because they are simply two statements, either of which could be true or false. If you use the worldly facts to judge the truth of your beliefs, then you might find some facts that justify your beliefs, and other facts that refute your beliefs. Should you now consider the refuting facts to be truths or lies? If you consider them true, we end up in a classic problem which we call the contention between consistency and completeness.

Assume that there are three theories—X, Y and Z—based on three different axiom sets. Assume that the theory X explains some phenomena PX, the theory Y explains some phenomena PY, and the theory Z explains some phenomena PZ. Neither theory explains all the phenomena—PX, PY, and PZ, therefore each theory (X, Y, and Z) is incomplete by itself. Together, all these theories are inconsistent because they are based on different (which might be mutually contradicting) axioms. If PX was a proper subset of PY, which was a proper subset of PZ, then we could reduce all the theories to just Z.

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Figure-6 Axiom Reduction Works for Subsets of Data

However, this reduction is not possible if each axiom set explains different domains of data. For example, it will not work if PX, PY, and PZ were mutually exclusive phenomena.

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Figure-7 Axiom Reduction Fails for Mutually Exclusive Data

Now, there are multiple independent axiom sets (X, Y, and Z) which explain mutually exclusive phenomena (PX, PY, and PZ). Each of the axiom sets is by itself incomplete. Put together, all the axiom sets are inconsistent. Each of the theories that employ an incomplete axiom set is ultimately false even though it can be empirically confirmed, because there are other phenomena where it doesn’t work. The truth of the theory has therefore nothing to do with its empirical confirmation.

It follows that if we make a choice—e.g., for an axiom set—these choices will be false, even though they will seem to work in certain limited number of scenarios. To know that these choices are false, we would have to find the phenomena where they don’t work. If you have found those phenomena, you must discard the theory as being empirically confirmed and yet false because it doesn’t always work.

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Figure-8 Different Theories Work at Different Scales

Common examples of such theories exist in modern science. E.g., quantum theory works for atomic objects, general relativity works for cosmological scales, and thermodynamic theory works for ordinary macroscopic objects. The reduction of cosmology to macroscopic objects, and the reduction of macroscopic objects to atomic objects cannot be done because they involve different theories. Reduction works only when the same theory is used to describe various phenomena. Reduction cannot work if different theories are involved at different scales – atoms, macroscopic objects and the universe. Any choice we make, we would be mistaken, although our theory can be empirically confirmed.

Truth vs. Verification

Most scientists believe that truth is that which can be verified. There are two broad ways in which we verify our claims—reason and experience. These are also therefore called methods of rationalism and empiricism. Rationalism begins with some axioms and determines if the consequences logically follow from the axioms; mathematics is a classic example of rationalism. Empiricism, similarly, starts with some given unexplained facts and tries to find the axioms. Both methods have a problem.

For rationalism, since you can begin from various axiom sets, what you can prove using those axioms depends upon your original choice of axioms. You have no way of knowing if your original choice of axioms is correct, except by finding what does not fit your axioms. For empiricism, even if you found some facts, you could explain them using many different axioms. Furthermore, you have no way of knowing if you actually have all the facts, before you can conclude that your axioms are indeed correct.

Verification is the ability to confirm facts from axioms, or axioms from facts. However, since you don’t have all the facts, you cannot know if your axioms are true (even when they are verified against a limited set of facts). Similarly, since you don’t have all the axioms, you cannot know if you have the best explanation for a set of facts (even when some facts are actually explained by the axioms).

This problem represents the classic divide between truth and verification. Verification is that which works for a given set of facts, and those facts might be quite limited. Truth is only that which works for all the facts. Something that is verified (empirically or rationally) is not necessarily true, although something that is true can always be verified. Therefore, the idea that if something has been verified it must also be true, is false. Most scientists who have not carefully undertaken a study of the scientific method and the issues in this method work under the illusion that science is about hypothesis and verification, and if something has been verified, it must also be true. They don’t recognize that science has had many theories that were previously verified but are now disproved.

If you believe that the Earth is flat, driving around your city would likely just confirm that belief. To know that the Earth is round, you must widen your experiences and test them by undertaking a sea voyage. Verification only tells you that a given fact does not refute your hypothesis. It does not tell you that the hypothesis is true, or it will never be falsified.

There are two kinds of truth—of existence and of content. For example, if a book of fiction exists, the existence of the book is true, but the content of the book is false. In a simple sense, the existence of things does not guarantee the truth of the meaning encoded in them. This fact complicates the search for truth because you don’t know a priori if a book is a work of fiction or fact. If you take the book of fiction to be fact, then you might find contradictions with other facts. How do you decide which book is a work of fiction and which one is a work of facts? You can collect all the books in the world, but you still cannot know which is fact or fiction, unless you start assuming some facts and gradually eliminate all the books that contradict those assumptions. Those assumptions will be your choices.

We are thus led to a peculiar problem—truth is not in the verifications but in our choices of axioms or hypothesis. Depending on what you choose to believe in, different observations would be deemed facts or fictions. Since we cannot use verification to know the truth, we also cannot use them to decide if our choices are correct. We must now find something beyond the empirical and the rational to know the truth.

Popper’s Falsificationism

Karl Popper—a famous philosopher of science—articulated this problem as falsificationism. The idea is that theories of science cannot be confirmed, but they can be denied. We cannot know if our theory is true, but we can tentatively know if that theory has not been disproved. However, even this claim fails if meanings are incorporated into the consideration of truth. As noted above, if you include books into the assessment of facts, then you cannot know the truths simply because some books (which are false) may contradict your claims.

We have already noted that all observable facts (including material objects) are symbols of ideas, and the world is a message with a meaning. These meanings could be true or false; e.g. a book is a message and it can carry a false meaning. Thus, when meanings are inducted into the facts, and the world is treated as a message (to solve the problem of concepts), then even falsificationism does not work, because finding a fact that contradicts your beliefs doesn’t entail that your belief is wrong, simply because that fact may have been created earlier due to a false idea.

The notion that theories are verified against facts is therefore false because you may not have all the facts. The notion that theories are disproved by the facts is also false when concepts are inducted into the world in order to address the problem of meanings. In short, the empirical-rational method of science fails both in verification and refutation. This method is supposed to work currently because science doesn’t take into account concepts or meanings. Thus, we believe that if we observe some facts, and our theories are incompatible with those facts, then those incompatibilities must disprove the theories. But this premise would fall apart when science inducts meanings, because now you can have false meanings, which exist, and are therefore facts, but their conflict with our theories doesn’t necessarily disprove the theories, just as their agreement with our theories doesn’t prove the theory.

Scientific Pragmatism

Once we have grasped this problem, you can claim that the idea of knowing the truth is overambitious. Scientific theories are not about some truth, but about some pragmatic usefulness in succinctly describing observations. Such theories are therefore our models of nature, but not necessarily how the world itself is. Within a city, the model of flat Earth works quite well, even though the Earth is round. The model isn’t therefore about reality; it is just our way of describing the world.

All such descriptions are relative to some problem we want to solve. We postulate axioms to solve these problems, and if the axioms are sufficiently good for addressing the intended goals, then they can be useful. Science is therefore not about truth; it is about usefulness. This is by far the only logically consistent view of the scientific method, because both verification and falsification are erroneous and inconsistent descriptions of how we acquire knowledge.

Nevertheless, scientific pragmatism leaves a hole in the heart: is our attempt at knowledge simply a practically useful tool to help us solve some day-to-day problems, and we cannot assert the truth of this model beyond its usefulness? And if that is indeed the case, then what if I don’t have the problems that others have considered worthy of being solved? Should I consider all such theories useless, because their existence is justified only by their usefulness relative to some problems?

This criticism of science is widespread today in the postmodern worldview in which all claims to truth can simply not be justified. Scientific theories, in this view, are simply human constructs that seem useful relative to the problems we want to solve today. If these problems changed, the models of nature created by science would change too, because the phenomena that these models explain would be different. Unlike the modern era, which led to the rise of science, and the belief in the discovery of truth through methods of experiment and reason, the postmodern worldview denies that any such method is possible.

The Big Hypothesis

I will now turn to the solution to the postmodern criticism of science. This solution foregoes the attempt to know the truth through experience and reason, but takes forward the key insight from scientific pragmatism that theories are useful tools to solve problems. The solution begins by asking: What problems are worthy of being solved? Which goals in life are worthy of being pursued? We already know that we cannot anchor the notions of truth in experience and reason, given the above problems. Can we now turn in a different direction, and anchor the truth in worthy goals?

In this solution, truth is that which is right and good, rather than which is empirically and rationally verified (since we now know that we cannot verify or disprove any such assumption to arrive at certain truth). In other words, the judgment of truth is not that which makes for practically useful material technologies, but that which involves morally correct action, and makes one happy based on that moral goodness.

The hypothesis is that every choice has two outcomes: an effect and a consequence. Consider the act of shooting with a gun. The effect of the pull of a trigger is that a bullet is ejected from the barrel. The consequence is that you will be punished or rewarded (depending on whether you were authorized and duty-bound to pull the trigger or forbidden to do so). The effect acts upon another material object, while the consequence acts upon the actor. If we had to explain the action, we can form a theory of push and pull and say that when the finger is pulled, the bullet is fired. However, this theory is incomplete because it doesn’t say why the finger is pulled. To explain that, we must say that some thoughts must occur in the brain, which causes the trigger to be pulled, which causes the gun to be fired. But why should the occurrence of a thought cause the bullet to be fired? Could you not control your thoughts, prevent their occurrences, or not translate thoughts into actions? Did you not have a choice in controlling your thoughts?

You can see that choices eventually terminate into the idea of a person who decides in a certain way although he or she could potentially have decided another way. These choices become the axioms beyond which you cannot penetrate. You can say that these choices are right or wrong, good or bad, but you cannot deconstruct them. Material objects can be reduced to theories or axioms, and these axioms must ultimately be chosen. We cannot reduce the choice to the axiom or the axiom to an object. Once you know that choices are irreducible, you can speak about causes and consequences naturally.

The hypothesis is therefore that we are not just in an empirical and rational world, but also in a moral world. In the empirical and rational world, there are causes and effects; in the moral world, we also have the consequences of our choices and actions. If we have the ability for choices—and we saw that both meanings and truths are ultimately choices—then these choices cannot be certainly verified by reason and experience, but they can be judged, if our world is not simply empirical and rational, but also moral.

The fact that you can shoot a person with a gun does not mean that your thoughts of anger which caused the shooting were correct. The thought of anger may be the cause of the shooting but that cause is wrong. The causal connection between anger and shooting is true, but the anger itself may be wrong. If we only speak about the cause and effect relation, we can never say that some cause is right or wrong. However, if we speak about the cause and consequence, we can say that some causes are wrong and that wrongness can be understood if there is a punishment that follows the cause.

An Introduction to Indian Philosophy

One of the central concepts of Indian philosophy is that the present world is not just material (empirical and rational) but also moral. This morality is, however, not imposed by God, government, or social customs. Rather, the morality is natural. Just as the cause and effect relationship is natural, the cause and consequence relationship is also natural. Therefore, it is possible to study and measure the relation between causes and consequences, just as we presently study the relation between causes and effects.

Everything we choose has an effect and a consequence. We currently make choices just thinking about their effects; for instance, we might think that if we pulled the trigger someone would die. But we must also think about the consequences of that choice: namely that we may be punished or rewarded. If this punishment or reward is natural rather than social or religious, then we could not escape it. By assessing the consequences of our choices we can know if our choices are right or wrong, and thereby correct them. These corrections can include, for instance, the choices about axioms, theories, and worldviews. By choosing different theories, we create different consequences. There is nothing to tell us which theory we must choose, if we are aware of the connection between a choice and its consequence. We are free to make any choice, and then suffer or enjoy its consequences. In one sense, there isn’t a universal truth, because every viewpoint is a choice. In another sense, every choice has a consequence, and is thus not totally free.

The universality of truth—if at all we can speak of such a thing—is therefore in the idea that we might (at some level) want similar kinds of things. E.g., we might all want to be  happy, and the same kinds of things—i.e. freedom from fear, hunger, pain—might be essential to make us happy. If some of us actually enjoy fear, hunger, or pain, then any theory would be equally true, because no matter what consequences of those choices, every theory would be liked by someone. If, however, there is a universal notion of happiness then some of the consequences would be preferred, which would then drive a preference in choices, which would then help us arrive at a universal notion of the nature of reality.

In essence, we cannot separate knowledge from choices, choices from consequences, and consequence from our notions of happiness. There is universal truth in the world only if there is a universal notion of happiness. The connection between ideas and reality is knowledge; the connection between knowledge and choices is the morality in nature; and the connection between morality and happiness is the idea of goodness. Truth, morality and goodness cannot be separated; truth is known only if there is a universal notion of happiness, and if there is a universal law of choices and consequences.

This is sometimes called satyam, shivam and sundaram in Indian philosophy. Satyam denotes the truth, shivam the rightness or morality, and sundaram the goodness or happiness. The point is that truth is morality and morality is happiness. You cannot ask what is truth, and what is morality. You must rather ask what is happiness. If you can define real happiness, then you can (through the causal connection between choice and consequence) determine what choices you must make. And if you can define your choices, then you can also choose the axioms which will make you happy.

Indian philosophy claims that there is a universal notion of happiness; we are all similar in the sense that we desire similar things—security, freedom, fearlessness, and love—which in turn dictates the right choices, which in turn determine truth. We cannot start from truth, and build it based on reason and experience, because both methods are flawed. We can, however, realize that this flaw is there because there is choice. The problem in epistemology arises simply because we can choose. These choices are in turn driven towards our own happiness. There is hence universal truth only if there is a universal choice, and there is a universal choice only if there is a universal notion of happiness.

You can know start asking the following questions: What is happiness? How do we become happy? What will make us free of fear, insecurity, and lovelessness?

Indian and Western Perspectives

Philosophy in the West has been divided into two broad categories—epistemology and ethics; the former deals with our methods of knowing the truth, and the latter with the goodness of our choices. In Indian philosophy, these two categories are joined at the hip. Our method of knowledge is never complete unless we take into account the morality of our choices. If we were only looking for the confirmation of our ideas and views in the world, many such views could be temporarily shown to be empirically and rationally confirmed, although none of them can be claimed to be true, as they could potentially be falsified in the future or even in the present in some other circumstance.

What is moral or immoral is however also a contentious problem. Societies tend to define different things as moral at different times. How do you decide what is moral? The Indian philosophical response to this problem is that every choice has a consequence, and morality is a natural connection between choices and consequences. When you perform a deed, you change the world; you have created an effect, perhaps you served someone. However, what do you get out of that action is its consequence. The moral law fixes the relation between action and it consequence. This law is different from the laws in science that model the relation between cause and effect, although this law is every bit as scientific (i.e. empirical and rational) as the laws of cause and effect.

However, the moral law is also based on premises, which must be chosen before a moral law can be chosen. Different societies choose different notions of morality. Why? They are in effect choosing different ideas about what is acceptable happiness for its members. The moral law too is therefore not universal unless you can define a universally acceptable notion of happiness. If the notion of happiness is well-defined, then the notion of morality is also well-defined, and then the nature of reality can be defined. We are therefore quickly led from the problem of which ideas are true, to which actions are right, to what we mean by good. We cannot begin in truth, then define right, and then determine happiness. We must rather first define happiness, then define rightness, and then define truth.

The Necessity of God

The universality in Indian philosophy stems from the idea that there is only one way to be happy—that which involves the happiness of a Universal Being (or God). If all truth terminates in morality and all morality terminates in happiness, and happiness is always individual, then there cannot be a universal notion of truth, morality or happiness. The very fact that we are all individuals who can think differently will preclude universality. This makes the existence of God a normative necessity; if we deny the existence of this Universal Being, then we must deny a universal notion of happiness, which will then deny the universality of moral choices, which will then deny universal truth.

Materialists don’t generally recognize this problem because they don’t understand the problem in epistemology: verification or confirmation doesn’t entail truth. In a world with meanings, contradictions only tell that one of the statement is false, not which one is false. Confirmation similarly tells us that they agree with each other, not necessarily if they are true. If false ideas in my head agree with false images on a TV screen, then their agreement doesn’t entail the truth; they only entail agreement between two facts.

If the world has meanings, then those meanings could be false. Given some set of meanings, you can never know which meaning is true, unless you postulate some truths. Those postulates are choices, which cannot be judged unless there is a moral law, the moral law cannot be defined unless there is universal notion of happiness, and the universal happiness cannot be defined unless there is a Universal Being.

The Problem of Universality

Problems in epistemology begin in the problem of universals—or ideas. If there are many things that are in essence instantiations of one idea (or law of nature) then these ideas could exist although they might be false. To know the difference between truth and falsity, we must make some choices, which are right or wrong only if there is a universal notion of morality, and that universal notion of morality can exist only if there is universal notion of happiness, which is possible only if there is a Universal Being.

The only alternative is to reject that there are universals, in which case we must give up the idea that there can be knowledge, that there is right or wrong, and good or bad. As you give up these notions one by one, you must also reject all forms of knowledge, including science. You might also claim that everyone is free to choose their theory of nature, judge by their own moral principles, and decide what is their own sense of happiness, which in turn results in chaos because of mutual disagreements in our universals.

Modern science takes a different route today. It rejects the existence of meanings, and therefore of universals, and yet postulates the existence of ideas and laws in another world of universals. How these two worlds interact remains an unsolved problem (I treat this and other problems in more depth in my two latest books Uncommon Wisdom and Moral Materialism). For instance, we can suppose that the present world is material, devoid of meanings, but the laws of nature are mathematical theories that exist in another world of ideas. It is now well-known that once you separate the world of things from that of ideas, you will create contradictions whenever these two are brought together. The world of ideas and things must therefore be two separate worlds. If we are real entities, then we cannot know the universals. If we know, then we cannot be real entities. The only alternative is to claim that we exist and we know the truth, which results in logical contradictions.

The problem of knowledge begins in the problem of universals, and the problem of universals takes us first to the problem of free will or choice, which then takes us to the problem of happiness, which then takes us to the problem of God. If we reject any of the problems, we reject all of them, and then deny knowledge, morality, happiness, and God. If we accept any of the problem, then we must accept all of them, and hence affirm the existence of knowledge, morality, happiness and God.