Archives for the month of: December, 2015


The modern state, which was born from the Peace of Westphalia of 1648, gave unrestricted control of the state to its rulers. This was the beginning of the concept of state sovereignty which is still dominant today The most potent shaping forces in the contemporary world are the interactions of states when enforcing their interests, capabilities and goals. However, during the latter half of the twentieth century the supremacy of the state is under challenge. Global affairs are now dominated by intergovernmental organizations that transcend national boundaries (17). Global international organizations such as the United Nations and the European Union have become independent global actors which implement their own foreign policies. Also groups of people carrying on various enterprises, such as multinational corporations, are examples of nongovernmental organizations which also transcend national boundaries and exert their influence globally.

Post Cold War, the United States has dominated world politics with the…

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Bertrand Russell famously made the argument for the non-existence of God through lack of evidence on his 90th birthday. At his party in London a woman asked him that being so close to death and an atheist what he would do if after death he found God to exist. She asked: “What will you say?” Russell gleamed at the question and, pointing his finger upwards, answered: “Why, I should say, ‘God you gave us insufficient evidence[1].’” This argument has the premises and conclusion:

  • If there were a God then we would have ample evidence of God’s existence.
  • We do not have such evidence.
  • Therefore, there is no God.

 It pragmatically objects to deism on the grounds that only evidence should regulate belief. This essay intends to question this common objection used by atheists because such premise 2 of this argument appears to ignore some of the very obvious evidence in the knowledge that humans have acquired over the past four or five thousand years; that is the role of irrationality and improbability in our reality.

Atheists argue that belief in God is irrational because there is no evidence to support it. The evidentialist argument is formulated thus:

(1) Belief in God is rational only if there is sufficient evidence for the existence of God.

(2) There is not sufficient evidence for the existence of God.

(3) Therefore, belief in God is irrational[2].

Note that the conclusion is not that God does not exist, only that if God did exist it would be unreasonable to believe in God because there is a lack of evidence to support God’s existence. Something should only be believed if it is self-evident, such as the laws of logic and arithmetic. It is argued that belief in God is not self-evident, or evident to the senses, or able to be confirmed. Therefore, as belief in God is not rational, in that it is not supported by evidence or argument, then belief in God must be irrational.

Judgments of rationality and irrationality are sometimes hard to make. Philosophers living over two and half thousand years ago reasoned that all things were made of water and used the evidence available to them to rationally speculate what comprised the main elements of the universe. To us now these ideas seem irrational and absurd when judged against contemporary knowledge and evidence. However, some of the most significant discoveries that are relevant to us today were made by ancient philosophers in mathematics and geometry, with irrational numbers being one of the main.

Irrational numbers were first realized by the Pythagorean School. It is said that Pythagoras (569-500BCE), who devoted his life to the study of mathematics, wrote on the entrance to his school “All is Number”, as Pythagoras believed the whole universe was ruled by numbers. When writing geometric proofs to find the hypotenuse of a square the Pythagorean School discovered irrational numbers. On an isosceles right triangle with a measure of one for each of the legs the hypotenuse will equal the square root of two. However this number could not be expressed as a measured length, as the answer to the square root of two can only be expressed in decimal form with an unending numerical value: 1.41421356237309504880168872420969807856967187537694807317667973799… This discovery disturbed the Pythagoreans so greatly that they refused to recognize the existence of such irrational numbers.  However, the square root of two became known as “Pythagoras’ Constant”[3]. As yet, no one has been able to find the end of this numerical value with the current record for its calculation standing at two trillion digits held by Alexander Yee in 2012[4].

Some irrational numbers are also known as transcendental numbers because they cannot be expressed as the root of any algebraic equation with rational coefficients[5]. It is common knowledge that algebraic numbers are countable while transcendental numbers are uncountable[6]. Joseph Liouville first proved the existence of transcendental numbers in 1844[7]. Transcendental numbers are uncountably infinite[8]. No rational number is transcendental and all transcendental numbers are irrational. Therefore, we assume the existence of irrational numbers whose values are uncountably infinite. While we cannot find the exact value we accept its existence because of obvious proof.

Irrational numbers are essential to humanity as they serve as a major part of industrial mathematics, in the construction of buildings and machines, chemical equations and practical physics[9]. These numbers assist human society’s understanding of our natural world and the universe that contains it. Irrational numbers such as pi or phi (the Golden Ratio) exist as an ideal that can be used in the real world. They have been essential to the development of civilization from the 3rd millenia BCE onward. Without them we would not have been able to land on the Moon. Our use of them is evidence of an intelligent life form existing on this planet.

It appears that there is a very low probability for intelligent life forms in the universe to have evolved[10]. One of the main arguments against it is that there should be many stellar systems within our own galaxy that have intelligent forms of life on them and that, considering evolutionary time frames, we should have been quite obviously visited or contacted by them up until now. In fact, it could be argued that humans are the result of an improbable set of chances. This improbability of intelligent life seems to have given rise to the concept of God, a first cause, an interventionist who created the world out of goodness and who is involved with humans in a cycle of perpetual creativity, rebellion, punishment and redemption[11]. It is this ideal cycle of creation, dissent and redemption that has preserved what some consider an irrational faith amongst those that believe in God and has allowed them to overcome adversity.

But is it irrational to believe in God when it is not irrational to believe in irrational numbers? While we can prove irrational numbers we cannot evaluate them. We assume, or have faith, that they are infinite because, as much as we have tried with the technological capacity that we have, we still have been unable to establish a finishing point. This assumption, or faith, allows us to utilize irrational numbers through approximating them to assist in our own creative output.

Humans have built and designed using the Golden Ratio such things as the Great Pyramid of Giza, Chartres Cathedral, the sculptures of Phidias, the compositions of Michelangelo, da Vinci and Rembrandt and the architecture of Le Corbusier[12], as it is used in nature to build such things as seashells, flowers and pine cones.  The irrational number e was used by Euler as the base of natural logarithms[13] and is used today as an important application in civil engineering, calculus, differential equations, probability and number theory, yet mathematicians today still cannot prove the nature of its number[14]. Again, the irrational number pi has been relevant to humans for four thousand years and its versatility is infinite being found in geometry, trigonometry, probability, statistics, complex numbers, calculus and physics[15]. These are the numbers that allow us to explore the universe and yet, after thousands of years of accumulated knowledge, we still do not understand them because of their infinite state.

The argument that Russell makes is that belief in God is irrational because of a lack of evidence, yet the existence of intelligent life in the universe is so improbable that it could be said to be the evidence of God. Like irrational numbers, there is not sufficient evidence for God but it could be argued that there is enough evidence in the improbability of the evolution of human civilization to assume God’s existence. Like irrational numbers, God is an ideal concept that profoundly assists many humans in dealing with their reality and overcoming adversity. Therefore, as it is rational for humans to accept the existence of irrational numbers, it is also rational for humans to accept the existence of God. This analogous counter argument can be set out so:

  • To believe in God is irrational because there is not sufficient evidence for the existence of God.
  • There is not sufficient evidence for the existence of irrational numbers because they have an infinite number of digits. Yet we theorize they exist as they assist us as an ideal which can be used in the real world.
  • In the same way, belief in an infinite God assists us as an ideal which can be used in the real world.
  • Therefore, God exists as irrational numbers exist.



[3]  Conway, John H.Guy, Richard K. (1996), The Book of Numbers, Copernicus, p. 25



[6] Martin Aigner and G¨unter M. Ziegler, Proofs from The Book, fifth ed., Springer-Verlag, Berlin, 2014, Including illustrations by Karl H. Hofmann. MR 3288091

[7]  Aubrey J. Kempner (October 1916). “On Transcendental Numbers”.Transactions of the American Mathematical Society (American Mathematical Society) 17 (4): 476–482. doi:10.2307/1988833. JSTOR 1988833.

[8] Weisstein, Eric W. “Uncountably Infinite.” From MathWorld–A Wolfram Web Resource.









T. Blackwell,




The Sacred Ibis (Threskionis aethiopicus) once lived in Egypt and is depicted in many ancient Egyptian wall murals and sculptures. It is also found as mummified specimens at many burial sites and played a significant religious role, in particular during the Late and Ptolemaic periods. The ibis represented the god Thoth, god of wisdom, knowledge and writing, and was considered the herald of the flood[1]. It was of practical use to villagers as it helped to rid fish ponds of water snails that contained dangerous liver parasites[2]. However, it is now extinct throughout Egypt because of gradual aridification through swamp drainage and land reclamation[3].


Ibises are waterfowl found in swamps, marshes, riverbanks and coastal lagoons on almost all the continents. They eat grasshoppers, locusts, crickets and water beetles. They also eat worms, molluscs, crustaceans, fish, eggs, carrion and refuse[4]

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Nicholas Georgouras, “Light” (2007)



Freedom can be defined as the degree to which I am not interfered with by anyone else. There exists a minimum area in which individuals must not be interfered with, a minimum area of personal freedom that on no account should be violated. Some area of human existence must remain out of the control of others because to invade such privacy would be tyrannical. The freedom of, or from, religion, opinion, expression and the protection of property from arbitrary invasion are areas of freedom that if curtailed impede civilization, prevent truthfulness and the spontaneity of ideas. It appeals to cowardice and duplicity and would, in J.S. Mill’s words, crush society ‘with the collective weight of mediocrity’[1].


Humans need a minimum area of freedom to develop their natural faculties. This is defined by a boundary between private life and public authority. This is difficult as humans are interdependent and no one’s total privacy is ever able to be so completely kept. The foundations of liberty can be said to be equality of liberty, treating others as one would wish to be treated, an obligation to those who keep my liberty or prosperity, and justice. To avoid the chaos that would come of unbounded liberty and result in great inequality and misery, one sacrifices a part of their freedom for the sake of justice and love of one’s fellow humans. Freedom is essential for agency, moral responsibility, rationality, autonomy, creativity and cooperation. It is the foundation of love and friendship.


There are three elements that are essential to upholding the rights of the individual. The first of the elements is personal rights, such as the right to a trial, freedom of thought and movement, and freedom of worship and education. The second element is political liberty, the freedom to speak, freedom of the media, and of association and the right to participate in assemblies. The third element is the ability of the individual to change the party in power through elections, this includes the freedom to dissent from the status quo and form an opposition through publicly explaining the reasons for that dissent. It is this final freedom, that of dissent, through which all the other freedoms grow.


To defend liberty there must be a constant push against the encroachment of the state, upon this area of an individual’s life. Even under the threat of persecution it is necessary to establish this area as the meaning of what it is to be human. Whether the concept of free choice is a reality or determinism found to be true, humans need to be conscious as thinking, acting beings, making choices based upon their ideas and purposes. As a society we may coerce or impose upon others some collective goal, such as for justice or public health, which becomes necessary to alleviate harm, but we cannot assume to think for the individual who is coerced or imposed upon. Society, or those who administrate it, is not a collective mental will that knows best for an individual. We cannot suppose that we know what is better for someone than they do themselves. For if we do take this view we are in danger of ignoring the autonomy of individuals and seek to oppress, bully or torture them in the name of what we believe is ‘best’ for them. Autonomy is necessary for us to act as independent agents.  For the state to control society as one made up of non-autonomous creatures that can be threatened or cajoled by their leaders would be to subject society to the worst despotism imaginable.


The ideals of justice and equality are measures with which we can resolve conflicts of will. Human societies subject themselves to such ideals so that the weak will not be prone to the strong. We can only demand of a recalcitrant human being that to which we subject ourselves also. For if we demanded others to subject themselves to that to which we would not agree we would oppress or enslave them and reserve freedom only for ourselves. By subjecting all to the ideals of justice and equality we leave room for all to make decisions in accordance with their will but also in accordance with the ideals of justice and equality. Each human has their own aspirations and abilities and they should be free to actualize their potential as long as they do not conflict with the aspirations and abilities of others. The necessity of choosing between competing claims is an inescapable element of human life. The extent of such claims must be weighed against many other claims of which equity, justice, happiness and peace are the most obvious. There is no clear or absolute answer or final solution. To demand the absolute at the expense of human life is offensive and not reconcilable with the principles of freedom. A plural system in which people are respected as ends and not means is the most humane and recognizes that freedom is part of what makes us human.


[1] ( J. S. Mill, On Liberty, chapter 3, p. 268 in Collected Works of John Stuart Mill, ed. J. M. Robson (Toronto/London, 1981- ), vol. 18.. .


Freud believed that dreams have a meaning which can be interpreted through the use of symbolic relationships[1]. Dreams can be divided into three categories in relation to their manifest and latent content[2]. The first category is dreams that are intelligible and that can be easily related to one’s mental life[3]. The second category is dreams which, although sensible and clear, have a confusing effect because they do not fit with our mental life[4]. And the third category is dreams that are incoherent, disconnected and seemingly meaningless[5]. It is the second and third categories which are significant concerning the manifest and latent content of dreams[6]. The manifest content of a dream is the fragmentary and illogical story that it tells[7]. The latent content of a dream is concerned with the ‘dream thoughts’ that occur within this dream…

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