To find a way out

Toward that which it seeks and longs for

Travels with the hope of recovering what is lost

Travels from the reason to the heart

To bereft of power

To distinguish the hopeful

from among the hopeless causes

There’s a cold war between realities and imaginings

Dawn comes in dreams

When everything turns pale in the dead hours of the night

Dawn comes in dreams

Dreams are always vivid

Full of color

There when a man looks deep

Into unfathomed oceans

Beholds the past

The far future and what is near to come

What is old about to be replaced or renewed?

Dawn comes in dreams

When realities are too dark to endure

Dawn comes in dreams

In darkness a man suffers

The extreme of loneliness

When mouths are tight-lipped

As if zip-fastened

He wishes to sprout wings and fly

To the realms beyond and fly

Dawn comes in dreams

When events begin to drive me to give up hope

Dawn comes in dreams

The twisted grammar of the naturalistic fallacy

In assuming nature to be uniquely real, a naturalist proposes that “reality” (or “existence”) means “natural being” and nothing more. Instead of saying, “nature is real,” (or “nature exists,”) a naturalist prefers to says, “reality (or existence) is nature.” Such an utterance has an odd syntax, with the subject and predicate being strangely exchanged, thus twisting the grammar and invalidating it. It is not vague, but rather nonsensical. Such nonsense originates from the awful mistake of reducing a group (here, “beings”) into a member (“natural beings”), or, to use logical terms, equating a universal (here, “reality” or “existence”) to a particular (“natural reality” or “natural existence”). What a naturalist attempts here is to narrow the meaning of reality; this can be called “naturalistic fallacy,” borrowing G. E. Moore’s phrase. It is with this attempt that naturalism becomes unreasonable. Namely, as it is reasonable to conceive of “unnatural” beings, that is, any entities outside the world observed, it is thus unreasonable to assume nature as being unique in reality. In other words, the “world observed” is not equal to (nor does it consume the meaning of) the world of reality. The phrase “natural existence” is a necessary reference to-at least the possibility of-“unnatural existence.” Indeed, against this immediate inquiry of justification, naturalistic discourse does nothing but recede from a logical base. As the famous naturalist Kai Nielsen states, naturalism is nothing but an idea without any idea of foundation. That is to say, naturalism remains as arbitrary as any fantastic speculations about an alien world, as both share the same status of justification.

Hetoric divorced from logic

(a) “Naturalism is the view that only natural objects, kinds, and properties are real.”

As “natural” here is used to mean “of the world observed,” then the use of “only” means that “real” cannot be the proper predicate for the sentence. This statement is odd. To perceive the oddity, imagine (if possible) a man who understands the concept of “color” but is unable to perceive anything except red objects. Had such man said, “Only red is a color,” this is then equal to “All color is red.” Similarly, a naturalist suggests imagining reality as “comprising” (not “including”) nature. Can you imagine yourself answering this question: “Do you know why birds are eagles?”

(b) “Naturalism is the belief that the world is a single system of things or events, every one of which is bound to every other in a network of relations and laws, and outside this natural order there is nothing.”

If one were to ask a naturalist what convinced them to view the world as a single system that excludes unnatural things, they would answer, “The fact that I haven’t seen such things.” Responding thus, they admit the possibility of unnatural realities, which fulfills the meaning of the phrase “outside this natural order” in the statement. If a child asks this naturalist what might happen outside the natural order, how meaningful it is if they reply: “I have no idea” and how meaningless if they reply: “Nothing.” Such a conversation would demonstrate that it is impossible to place nature into “space” as a concept of physics, and that it is certainly not a childish attempt to try to squeeze reality into nature.

Groundless denial of supernatural

(c) “Naturalists reject all such notions of spirits, disembodied souls, non-material personal gods, and more-than-natural agencies. The grounds for the rejection of these notions are a lack of evidence adequate to support these notions.”

Ideas of spirits or souls are referred to as “supernatural” in that they are “ordinarily” not subject to the world observed. This means that they might be subject to the world of phenomena or of experience. There may be (reportedly, are) many experiences regarding supernatural phenomena, like spirits, angels, inspirations, revelations, etc. If this is the case then it would be unreasonable to reject all the relevant human traditions. Just as a momentary sighting of a peculiar insect is sufficient reason for the conviction that there is such a species on earth, the same is true for more peculiar entities. This indicates, as William R. Dennes clearly puts, that naturalists may have no reason to exclude intelligible reference to supernatural. Had a child reported to a naturalist that he had certainly seen a ghost, or that his dead grandfather had related a secret to him in dream, but the naturalist denies the child’s claims, accusing him of lying or dreaming, then the child’s rejection, in turn, of all the stories told and all the advice given by the naturalist that are based on experience would be meaningful.

(d) “Naturalism denies that there are any supernatural or spiritual realities. There are no purely mental substances and there are no supernatural realities beyond nature or transcendent to the world or anything of the sort, or at least we have no sound reasons for believing that there are such realities or perhaps even that there can be such realities. Physical realities, or perhaps as well realities dependent on physical realities, are the only kind of realities there are.”

The problem in the above statement is that the non-existence of supernatural entities cannot be reasonably claimed, let alone proven. Common sense commands that we not deny any possibility unless logically necessary. In logic, the denial of possibility is one of the two greatest mistakes; the other is the refusal of necessity. It seems that a naturalist cannot maintain such mistakes forever as they would necessarily encounter some form of supernatural experience, just as other fellow humans are. In other words, conjectures die away whenever phenomena manifest themselves. A naturalist then cannot be serious in his materialistic position, in denying the most manifest supernatural phenomenon, the soul, the factual manifestation of which is consciousness and the conscience. Therefore, rejecting any “purely mental substance” is a sophistic proposition. The immutable duality of “subject” and “object” always warrants the fact that “soul” is the constant interference of the supernatural into natural. Namely, if “nature” is the object that is observed, “I” am the subject that observes. Here we infer that a naturalist can only pretend to become a materialist at the expense of their own self. As Schopenhauer once wrote, materialism is the philosophy of the “subject” that forgets to give account of himself.

A pointless appeal to natural science

(e) “Naturalism is the recognition that it is within science itself, and not in some prior philosophy, that reality is to be identified and described.”

If science is claimed, in this approach, to identify reality, that is, to assign by observation what is real and what is not, then science itself is at stake as the objective study of natural reality, merely because it is the concept of reality that justifies observation. Plainly speaking, it is the sense of “real” that qualifies observation, not the opposite. This is why it is meaningful to say, “What we observe is real.” It is impossible to identify anything without having a “prior” conception of reality. In Kant’s dictionary, it is a priori concepts, the most prior of which is “reality,” that ensure all a posteriori notions, which all scientific terms are subject to. Now, upon this logical structure it is meaningful for a child to ask: “Aren’t ghosts real?” as well as for a naturalist to reply: “Certainly, not!” Similarly, natural science asks: “How is natural reality?” and answers: “It is in accordance with observation.” Thus, science admits that the reality of nature needs to be identified by a prior philosophy, a metaphysical notion. This means that natural science normally denounces (scientists must denounce) the awful illusion of scientism, the claim that science is uniquely eligible to identify the reality of the world; it is in regard with this that Wittgenstein warns that “the whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanations of natural phenomena.” What the philosopher means is that a scientist is no wiser about nature than anyone else when he steps out of his laboratory.

A final word

One may gather from this brief analysis that naturalism, in its absolute form, is destined to struggle forever, if not pass away, with the irremovable fallacy of reductionism. A naturalist may understand that to avoid from this destiny they must abandon the vacuous attempt to “invent” a logic for the world, rather maintaining the language on the grammar of possibility when assuming metaphysics, by stating, for instance, “Nature may be autonomous; who knows?” Such normalization turns naturalism, as Kai Nielsen states, into a game that might be called “fallibilism” and must be played without any confidence or hope. As a result, for anybody who wants to take metaphysics seriously for their ultimate concerns, as Michael C. Rea emphasizes, there is no such an option as naturalism.

Erkan Mazhar Kurt has a PhD in theology. He is an executive member of The Institute of Interfaith Dialog, Houston, Texas.

Notes

1. See, William Ray Dennes, Some Dilemmas of Naturalism, Columbia University Press, New York 1960, p. 80.

2. Kai Nielsen, Naturalism without Foundations, Prometheus Books, New York 1996, p. 35.

3. See, Michael C. Rea, World without Design: The Ontological Consequences

of Naturalism, Clarendon Press, Oxford 2002, p. 56. (These and the following emphases are mine for attention at conceptual relations.)

4. See, ibid, p. 55.

5. Cf. Ludwig Wittgenstein, Tractatus Logico-Philosophicus (tr. D. F. Pears & B. F. McGuinness), Routledge & Kegan Paul, London 1961, p. 149.

6. Sterling P. Lamprecht, The Metaphysics of Naturalism, Meredith Publishing

Company, New York 1967, p. 209.

7. Dennes, ibid, p. 21.

8. Nielsen, ibid, p. 25.

9. Cf. Robert Sokolowski, Introduction to Phenomenology, Cambridge University Press, New York 2000, p. 14.

10. Cf. A. D. Smith, “Non-Reductive Physicalism?” in Objections to Physicalism

(ed. Howard Robinson), Oxford 1993, p. 225.

11. Cf. Ralph Walker, “Transcendental Arguments against Physicalism” in Objections to Physicalism (ed. Howard Robinson), Oxford 1993, p. 78.

12. Arthur Schopenhauer, The World as Will and Representation (tr. E. F. J. Payne), Massachusetts 1958, II, 313.

13. See, Rea, ibid, p. 42.

14. Cf. Dallas Willard, “Knowledge and Naturalism” in Naturalism: A Critical Analysis (ed. William Lane Craig & J. P. Moreland), Routledge, New York 2000, p. 30.

15. See, Immanuel Kant, Critique of Pure Reason (tr. J. M. D. Meiklejohn), Prometheus Books, Buffalo 1990, p. 7.

16. Wittgenstein, ibid, p. 143.

17. Cf. Ian G. Barbour, Religion and Science: Historical and Contemporary Issues, HarperSanFrancisco, New York 1997, p. 87.

18. Nielsen, ibid, p. 26.

19. Rea, ibid, p. 59.

We can only speculate as to when the original man and woman appeared on Earth, which is equated with the Heavens due to the divine art it exhibits, its ontological meaning, and its value largely coming from its chief inhabitant: humanity. According to the calendar we use today, we are at the threshold of the third millennium after the birth of Jesus, upon him be peace. However, since time revolves and advances in a helicoidal relativity, there are different measures of time in the world. For example, according to the measure of time that currently enjoys global acceptance, the world is about to cross the threshold of a new thousand-year period. According to the Jewish calendar, we are already in the second half of the eighth millennium. Within the Hindu timeframe, we are living in the Kali Yuga era. If we follow the Muslim calendar, we are approaching the end of the first half of the second millennium.

We should remember, however, the fact that each measure of time is nothing more than a relative measurement. While a 100-year period is assumed to be the measure for a century, the idea of a 60-year century, based on the life span of an average person, is also worth mentioning. From this point of view, we are already in the fourth millennium after the birth of Jesus, upon him be peace, and third millennium after the hijrah, which is the starting point of the Muslim calendar. I bring up this issue due to the spiritual discomfort engendered by the terrifying auguries believed to be associated with the upcoming millennium, especially in the West.

People live in perpetual hope, and thus are children of hope. At the instant they lose their hope, they also lose their “fire” of life, no matter if their physical existence continues. Hope is directly proportional to having faith. Just as winter constitutes one-fourth of a year, so the periods in a person’s or a society’s life corresponding to winter are also small. The gears of Divine acts revolve around such comprehensive wisdom and merciful purposes that just as the circulation of night and day builds one’s hope and revivifies one’s spirit, and every new year comes with expectations of spring, and summer, so too the disastrous periods are short and followed by happy times in both an individual’s life and a nation’s history.

This circulation of the “Days of God,” which is centered in Divine Wisdom, is neither a fear nor pessimism for those with faith, insight, and genuine perceptive faculties. Rather, it is a source of continuous reflection, remembrance, and thanksgiving for those having an apprehensive heart, inner perception, and the ability to hear. Just as a day develops in the heart of night, and just as winter furnishes the womb in which spring grows, so one’s life is purified, matures, and bears its expected fruits within this circulation. Also in this circulation, God-given human abilities become aptitudes and talents, sciences blossom like roses and weave technology in the workbench of time, and humanity gradually approaches its predestined end.

Having stated this general view, which is neither personal nor subjective but rather an objective fact of human history, it should not be thought that we welcome either winter or winter-like events that correspond to sorrow, disease, and disaster. Despite the general fact that disease eventually increases the body’s resistance, strengthens the immune system, and drives medical progress, it is pathological and harmful. It is the same with terrestrial and celestial disasters. From a theological and moral point of view, they result from our sins and oppression, which are enough to shake the Earth and the Heavens, and from engaging in deeds that have been declared forbidden and despised by law and ethics (whether religious or secular). Even though they awaken people to their mistakes and negligence and provoke developments in geology, architecture, engineering, and related safety measures; even though they elevate the demolished belongings of believers to the level of charity, and the believers themselves to the level of martyrdom, these disasters cause much destruction and harm humanity.

In the same way, we read in the Qur’an: Unless God hampered some (of you) with some other (of you), the mosques, monasteries, and synagogues in which God is worshipped would have fallen into ruins (22:40). In other words, God would be so little known that men and women, who are inclined not to recognize anything superior to them and believe that their deeds will not be questioned in the Hereafter, would completely go astray, thereby making Earth unsuitable for human life. There is also the divine decree: You consider something as evil although it is good for you; you also consider something else as good although it is bad for you (2:126). For example, war is permissible. Although wars based on specific principles and with the intention of improving the existing situation may have benefits, they should not be demanded, since they bring harm; they leave behind ruined houses, destroyed families, and weeping orphans and widows.

Anyway, realities of life cannot be neglected, nor should they be ignored. Human beings are mirrors for God’s Names and Attributes, and therefore are distinguished from the rest of creation with the honor of being responsible for making Earth prosperous in His name. If they cannot grasp the wisdom and purposes behind any good or evil that is sent their way by their Creator, they cannot escape despair and pessimism. For them, as is seen in the Existentialist literature, life turns into a meaningless process, existence into a purposeless vacuity, nonsense into the only criteria, suicide into a meritorious act, and death becomes the only inevitable reality.

The Basic Nature of Humanity

After presenting the issues that constitute the basis of this subject as an introduction, we can switch to our considerations regarding the third millennium.

Human history began with two people who constituted the essence of humanity and complemented each other. People lived a tranquil life during this time of the original mother and father and the families that descended from them. They were a united society that had the same views and shared the same environment and lives.

From that day on, the essence of humanity has remained unchanged, and it will remain so. The realities surrounding their lives, their physical structure, main characteristics, basic needs, place and time of birth and death, selection of parents and physique, innate characteristics, as well as the surrounding natural environment, have not changed. All of these require some essential and vital invariable realities and values. Thus, the development and alteration of life’s secondary realities should be based on the axis of these primary realities and values, so that life will continue as a worldly paradise under the shadow of Heaven.

We mentioned above some issues that seem to be harmful and unpleasant. Similarly, there are human traits that seem to be evil at first glance, such as hatred, jealousy, enmity, the desire to dominate others, greed, rage, and egoism. A human being also has other innate drives and needs that allow the continuation of his or her worldly life, such as the need to eat and drink and the drives of lust and anger. All human drives, needs, and desires should be guided and trained in the direction of the eternal, universal, and invariable values that address the fundamental aspects of humanity. In this respect, the need to eat and drink, and the desire associated with lust and rage, can be tamed and transformed into means of absolute or relative good.

Likewise, egoism and hatred can become sources of fine attributes and goodness. Jealousy and rivalry can be transformed into competition in charitable and good deeds. The feeling of enmity can be transformed into enmity against Satan, the greatest enemy of humanity, and against the feeling of enmity itself and hatred. Greed and rage can force one to perform good deeds without tiredness. Egoism can point out the evil aspects of the carnal soul (nafs), thereby seeking to train and purify the soul by not excusing its evil actions.

All negative feelings can be transformed into sources of good by training and struggle. This is how one reaches the level of “the best of Creation,” by traveling the way of transformation from a potential human being to a real and perfected human being, to becoming the best symbol, model, and personal representative of creation and existence.

Despite this fact, the realities of human life do not always follow these guidelines. Negative feelings and attributes often defeat people, pulling them under their domination to such an extent that even the religions that guide people to goodness and kindness are abused, as well as the feelings and attributes that are sources of absolute good. Human life, at the level of the individual and of humanity as a whole, is merely the summation of internal, personal struggles and their external manifestations. These tides make the personal world of the individual, society, and history an arena of battle, struggle, war, oppression, and tyranny. As a result, it is usually human beings themselves who suffer the consequences.

Men and women always receive the fruits of their deeds. In the first period of its history, humanity lived a happy life as a single society whose members shared their joys and sorrows. But, later on they bound their necks and feet with a rusty yoke composed of chains of oppression as a result of jealousy, greed, and coveting other’s rights and properties. The consequence was Cain’s murder of Abel. As a result of this, humanity entered the path of disunity. Despite the millenniums coming one after the other like days, seasons and years, this “cycle” still continues.

The Second Millennium

The second millennium started with the Crusades and then the Mongol invasions of the Muslim world, which was like the heart of Earth and history at that time. Despite the wars and destruction, and despite the crimes committed sometimes in the name of religion and sometimes in the name of economic, political, and military supremacy, this millennium has seen the apex of the East’s civilizations, based on spirituality, metaphysical, universal, and eternal values, and the West’s civilizations, based on the physical sciences. Many significant geographical discoveries and scientific inventions have occurred.

However, the East’s and West’s civilizations existed separated from each other. This separation, which should not have occurred, was based on the former’s retiring from the intellect and science, while the latter retired from spirituality, metaphysics, and eternal and invariable values. As a result, the last centuries of this millennium have witnessed disasters that are hard to believe. Due to humanity’s growing arrogance and egoism, arising from its accomplishments, men and women have had to live through worldwide colonialism, immense massacres, revolutions that cost millions of lives, unimaginably bloody and destructive wars, racial discrimination, immense social and economic injustice, and iron curtains built by regimes whose ideology and philosophy sought to deny the essence, freedom, merit, and honor of humanity. It is partly because of this and partly because of some auguries from the Bible that many people in the West fear that the world will again be soaked by floods of blood, pus, and destruction. They are quite pessimistic and worried about the new millennium.

Our Expectations

Modern means of communication and transportation have transformed the world into a large, global village. So, those who expect that any radical changes in a country will be determined by that country alone and remain limited to it are unaware of current realities. This time is a period of interactive relations. Nations and peoples are more in need of and dependent on each other, which causes closeness in mutual relations.

This network of relations, which has surpassed the period of brute colonialism and exists on the basis of mutual interest, provides some benefits to the weaker side. Moreover, owing to the advances in technology, especially digital electronic technology, the acquisition and exchange of information grows gradually. As a result, the individual comes to the fore, making it inevitable that democratic governments that respect personal rights will replace oppressive regimes.

As each individual is like a species with respect to other species, individual rights cannot be sacrificed for society, and social rights should depend on individual rights. This is why the basic human rights and freedoms found in the revealed religions came to be considered by a war-weary West. They will enjoy priority in all relations. At the head of these rights is the right to life, which is granted and can be taken only by God. To accentuate the importance of this right in Islam, a basic Qur’anic principle is that: If one person kills another unjustly, it is the same as if he or she has killed all of humanity; if one saves another, it is the same as if he or she has saved all of humanity (5:32).

Other rights are the freedom of religion and belief, thought and expression; the right to own property and the sanctity of one’s home; to marry and have children; to communicate and travel; and the right to and freedom of education. The principles of Islamic jurisprudence are based on these and other rights, all of which are accepted by modern legal systems, such as the protection of life, religion, property, reproduction, and intellect, as well as equality of people based on the fact that all people are human beings, and the rejection of all racial, color, and linguistic discrimination. All of these will be-and should be-indispensable essentials in the new millennium.

I believe and hope that the world of the new millennium will be a happier, more just, and more compassionate place, contrary to the fears of some people. Islam, Christianity, and Judaism all come from the same root, have almost the same essentials, and are nourished from the same source. Although they have lived as rival religions for centuries, the common points between them and their shared responsibility to build a happy world for all of the creatures of God make interfaith dialogue among them necessary. This dialogue has now expanded to include the religions of Asia and other areas. The results have been positive.

As mentioned above, this dialogue will develop as a necessary process, and the followers of all religions will find ways to get closer and assist each other.

Previous generations witnessed a bitter struggle that should never have taken place: science versus religion. This conflict gave rise to atheism and materialism, which influenced Christianity more than other religions. Science cannot contradict religion, for its purpose is to understand nature and humanity, which are each a composition of the manifestations of God’s Attributes of Will and Power. Religion has its source in the Divine Attribute of Speech, which was manifested in the course of human history as Divine Scriptures such as the Qur’an, the Gospels, the Torah and others. Thanks to the efforts of both Christian and Muslim theologians and scientists, it seems that the few-century-long religion-science conflict will come to an end, or at least its absurdity will be acknowledged.

The end of this conflict and a new style of education fusing religious and scientific knowledge with morality and spirituality will produce genuinely enlightened people with hearts illumined by religious sciences and spirituality, minds illuminated with positive sciences, characterized by all kinds of humane merits and moral values, and cognizant of the socioeconomic and political conditions of their time. Our old world will experience an excellent “springtime” before its demise. This springtime will see the gap between rich and poor narrow; the world’s riches distributed most justly according to one’s work, capital, and needs; the absence of discrimination based on race, color, language, and worldview; and basic human rights and freedoms protected. Individuals will come to the fore and, learning how to realize their potential, will ascend on the way to becoming “the most elevated human” with the wings of love, knowledge, and belief.

In this new springtime, when scientific and technological progress is taken into consideration, people will understand that the current level of science and technology resembles the stage when an infant is learning how to crawl. Humanity will organize trips into space as if traveling to another country. Travelers on the way to God, those self-immolators of love who have no time for hostility, will carry the inspirations in their spirits to other worlds.

Yes, this springtime will rise on the foundations of love, compassion, mercy, dialogue, acceptance of others, mutual respect, justice, and rights. It will be a time in which humanity will discover its real essence. Goodness and kindness, righteousness and virtue will form the basic essence of the world. No matter what happens, the world will come to this track sooner or later. Nobody can prevent this.

We pray and beg the Infinitely Compassionate One not to let our hopes and expectations come to nothing.

There are two major theories about the origin or essence of mathematics. One of these theories is attributed to Plato, and the other to the so-called Formalist school. According to Plato, mathematics exists independently of man. What man does is to discover its objective reality, just as other ‘laws of nature’, which we tend to call ‘Divine laws of nature’, are discovered. The Formalist school by contrast asserts that mathematics is a product of human thinking. In order to understand the difference between these two schools, we may cite as an example their view of prime numbers (that is, numbers like 7, 17, 41 which can only be divided exactly by themselves and the number 1). Platonists argue that the prime numbers exist independently of us: before we discovered their existence, they existed in infinite number. Whereas, Formalists are of the opinion that the prime numbers exist because we have defined them as such, and it is meaningless to think about whether they are of infinite number or not.

The language of numbers

Formalists assert that numbers came into existence when human beings began to count. A well-known account of how this happened is that of a shepherd who used to put a stone in his bag for each of his sheep and by matching a stone with a sheep could find out whether any of his sheep had been lost or not. Later on, people began to call numbers each by a different name and since there were two fingers in the two hands, they found it easier to make calculations by the decimal system. This was followed by the operations of addition and subtraction.

According to the Formalists, even the simplest mathematical operations like the four basic ones consist in some logical rules based on certain axioms. They say that we do mathematics by expressing certain rules with certain symbols. That is, we take, say, 5 and 7, a couple of signs whose meaning in the physical world we do not know, and put between them the plus sign, a third sign whose meaning in the physical world we do not know, followed by an equals sign. And we know we must write 12 after the equals sign because that is a requirement of the axioms and rules of logic we are using. This is just what a calculating machine does, that is, it goes through the operation required of it without knowing what it is doing.

Let us suppose that an adding operation consists only in applying axioms or certain logical rules, and has nothing essential to do with the physical world. If we were to take our number signs and apply them to physical objects like stones and sheep, we should be surprised, amazed even, as if by a miracle, that 5 and 7 stones or sheep added together (according to the same rules as 5+7) make 12 stones or 12 sheep. We would come to know that the abstract, conceptual realities in our mind correspond to physical realities in the outer world. According to Paul Davies, the renowned physicist, if we lived in a universe where different physical realities prevailed, in a space where, for example, there were not any countable things, we would not be able to make most of the calculations we make today. David Deutsch claims that counting emerged as the result of experiences. According to him, we can do arithmetic because physical laws allow the existence of physical models convenient for arithmetics.

Richard Feynman, regarded as the greatest physicist after Einstein, says about mathematics that the problem of existence is a very interesting and difficult problem. When you take the third power of certain numbers and then add them with each other, you obtain interesting results. For example, the third power of I is 1, of 2 is 8, and of 3 is 27. The addition of these numbers gives the result of 36. The addition of 1, 2 and 3 is 6 and the second power of 6 is also 36. When you add to this the third power of 4, which is 64, the result is 100. The addition of 6 and 4 is 10 and the second power of 10 is also 100. Added to this the third number of 5, which is 125, the result is 225. 225 is the second number of 10 plus 5, i.e. 15. And so on. According to Feynman, we may not have known this typical characteristic of numbers before but when we do come to know such characteristics of numbers, we feel that they exist independently of us, and that they existed before we discovered them. However, we cannot determine a certain space for their existence. We feel their existence as conceptions only.

Let us take another example. Ibrahim Haqqi of Erzurum, a Turkish Sufi, religious scholar and scientist of the 18th century, discovered a way of checking the correctness of an operation of addition which may still be unknown to modern mathematicians. In order to check or prove the addition, we first add up the digits of each of the two numbers we are going to add up. Let us say, we are going to add 154 to 275, for which we get the answer 429. Adding the digits of each of the first two numbers, we get 1+5+4 = 10 and 2+7+5 = 14. The next step is to subtract 9 from each of these two sums, giving us 1 and 5 respectively. The third step is to add these two results together, 1+5 = 6. Now we do the same thing with the digits of the answer we are wanting to check, namely 429, and again subtract 9: 4+2+9 = 15, 15-9 = 6. The fact that we end up with the same number (i.e.6) means that our addition was correct. This way of checking an addition exists independently of us. We did not create it, we discovered it.

As water had the force of lifting objects of certain weight before Archimedes discovered it and, again, objects thrown into air or a fruit disconnected from its branch fell before Newton discovered the law of gravity so also numbers have many characteristics only some of which have been discovered.

Heinrich Herzt, a physicist, says that we cannot help but feel that the mathematical formulas discovered so far exist out there independently of us. We know that these formulas existed before we discovered them but we cannot determine a space for them. Rudy Rucker, a mathematician, is of the opinion that there is, besides the physical space, a space of mind, which he calls ‘mindspace’ and it is that that mathematician study.

Most of the distinguished mathematicians follow the view of Plato. Kurt Godel is one of them. Before Godel, it was almost a generally accepted view that mathematics is a function of the working of mans brain consisting in the collection of the logical rules which we establish between the symbols of two sets. Godel persuasively argued that there have always been correct mathematical expressions even though their correctness cannot always been proved. Another Platonist mathematician, Roger Penrose, believes that beyond the thoughts of mathematicians there are profound truths or realities in mathematical conceptions. Human thought is directed to extend into these eternal realities and they are there to be discovered as mathematical facts by any one of us. Penrose mentions complex numbers as an example for his argument. According to him, there is a profound, timeless truth in complex numbers. Penrose cites the set of Mandelbrot as another example to prove his argument. The reality this set reveals is the fact that even the lines, twists and shapes of mountains and clouds were or are formed according to certain mathematical formulas. 

What flowers reveal

Almost everyone has heard of the series of Fibonacci. This series, named after the famous mathematician, Leonardo Fibonacci, progresses as 1,1, 2,3,5,8,13,21,34,55,89,144, and so on, each term being equal to the addition of the previous two. That is, I and I make 2, and I and 2 make 3, and 2 and 3 make 5, and 3 and 5 make 8, and so on. This is the series found in nature. For example, when we count the spirals formed of the seeds in a sunflower, we find that those arranged clockwise are 55 and the others arranged anti-clockwise are 89. Both of these figures are among the consecutive terms in the Fibonacci series. These figures may vary according to the size of the sunflower: we may find the figures of 34 and 55 in a relatively small flower, and 55 and 89 in a normal sized one, but the arrangement is always as consecutive numbers in the Fibonacci series. The spirals are arranged in pine cones in 5 to 8. We may encounter the same figures in the arrangement of tobacco leaves. Another extremely interesting characteristic is found in the numbers of petals of flowers. A lily has 3 petals, while a buttercup has 5, a velvet 13, a dahlia 21, and a daisy 34 or 55 or 89, varying according to its family. It is impossible to attribute this miraculous arrangement to chance or ignorant nature. If the DNA of a sunflower or a pine cone determines random numbers for its petals or spirals, how can you explain their correspondence with the terms of the series of Fibonacci? The ratio between the consecutive terms in the series of Fibonacci is quite near what is called the golden ratio’ and known in classical art as the ratio most pleasing to human eye. In order to explain the origin of this miraculous reality, you have to either accept that flowers know what is most pleasing to human eye or that the ‘Hand’ of One, the All- Knowing, the All-Wise and the All-Beautiful, is working in nature.

In short, what Fibonacci did is to discover this characteristic in nature. This means that the universe has a mathematical order or mathematics is the branch of science studying the miraculous order of the universe, the order which the Absolute Orderer and Determiner, One Who determines a certain measure for everything, has established.