the axiom - issue 1

Can we support that our minds exist?

Who's out on the right wing?

Which maths is 'right', and should we care?

Advice from your favourite mustachioed superman

FEATURE ARTICLE

Where theology and fi lm collide

THE

AXIOMABINGDON SCHOOL'S PHILOSOPHY MAGAZINE

SUMMER ISSUE 1• WHO IS THOMAS HOBBS?• I’M NOT FEELING MYSELF• EPICUREANISM IS FOR THE COLD HEARTED• 2001: A SPACE PHILOSOPHY • THE HILBERT BROUWER CONTROVERSY • THE PRESENT KING OF FRANCE IS BALD• ANIMAL RIGHTS AND ETHICS, AN OVERVIEW• REVIEW: A CLOCKWORK ORANGE• REVIEW: APOCOLYPSE NOW• FANTASY FOOTBALL• AGONY ÜBERMENCH• EXISTENTIAL COMICS

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Letter From the Editor

It would be silly in a covering letter to attempt to explain to anyone reading the practice of philosophy in a single side. What I hope you will find here, however, will be something to like about it, no matter from what

angle you’re picking up this magazine from. In this first issue we have made it our aim to make philosophy personable - something the geographer or the classicist or the mathematician or the historian can pick up and flip through, hopefully finding something engaging about within their own subject to take away.

We have chosen to split the publication into two halfs. In the first half of the magazine, you will find discursive articles, often tackling a single issue or topic. We have purposefully encompassed a wide range of content here; from historical approaches towards Thomas Hobbes to discussions on the nature of mathematics, as well as pieces focusing on classical philosophers and theology, we hope that most people will find something enjoyable—and maybe even useful—in this first half.

The second half we have given over to more lighthearted pieces, which should be approachable both by those who have read no philosophy and those who are fairly embroiled in the literature. With film reviews, an agony aunt, our approach to a world cup football team and even a cartoon strip, it’s something we hope everyone can have a laugh at.

This I hope will tackle a stereotype of philosophy’s—of a minor subject, ‘sweeping the room’ after the larger discoveries of the sciences (or even worse, of it being a subject of hair splitting over irrelevancies). We should all grasp that philosophy does have tangible impact and a core in most, if not all things we learn; on the quality of history’s judgements, on the foundations of mathematics, or the meanings we extract from film and literature. We hope that you enjoy this issue, and if anyone would like to contribute writings for the magazine, please contact any of the editors.

Tomas Brown

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Contents

WHO IS THOMAS HOBBS? 7I’M NOT FEELING MYSELF 10EPICUREANISM IS FOR THE COLD HEARTED 142001: A SPACE PHILOSOPHY 18INTUITIONISM, FORMALISM, AND EVERYTHING INBETWEEN 22THE PRESENT KING OF FRANCE IS BALD 26ANIMAL RIGHTS AND ETHICS, AN OVERVIEW 30

FILM REVIEWS: A CLOCKWORK ORANGE 38 APOCOLYPSE NOW 40FANTASY FOOTBALL 42AGONY ÜBERMENCH 46EXISTENTIAL COMICS 48

CONTRIBUTORS 50

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The Axiom

WHO IS THOMAS HOBBES?

Words by Liam Frahm

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Who is Thomas Hobbes?

Thomas Hobbes was born in Wiltshire in April 1588, but little is known about his early life. He attended Oxford University before extensively touring Europe in 1610, where he was exposed to European scientific and critical methods—contrasting heavily to the scholastic philosophy that he had learnt at Oxford. Before entering philosophy in 1629, Hobbes spent his time studying classical texts, which culminated in his translation of Thucydides’ History of the Peloponnesian War. Hobbes spent most of his time in Paris, where he lived during the English Civil War, which started in 1642. However, Hobbes’ most vital work is within Leviathan, in which Hobbes sets out his doctrine on government and the foundation of states.

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Who Is Thomas Hobbes?

In 1651 Hobbes published his most famous work: Leviathan, in which Hobbes shows us his inter-pretation of the human character, known as the

‘state of nature’. Within this, human life is naturally ‘sol-itary, poor, nasty, brutish, and short’, and requires some supreme power to instigate order. A common misconcep-tion of Hobbes’ work is the assumption that he merely slanders people as naturally selfish and greedy; however, this misses the real point - that in a society with no state, there is no trust between anyone. When everyone is ‘solitary’ - that is to say self interested - each person will seek to further their own means and ultimately become ‘secure against death’. The way that Hobbes suggests that this is achieved is through the arrogation of power to yourself in order to control the actions of others through the use of fear. This propagates the idea that cooperation, and ultimately, building, science, or any advanced arts, are impossible when people act naturally—we require an external power, a Leviathan, to manufacture trust in the agreements we make.

In retaliation to this, critics of Hobbes have used a number of examples in order to prove that, in fact, people trust each other and can cooperate without any interfer-ence from the state whatsoever. An example might be a group of neighbours deciding to repair a leaky roof—each one acting decidedly outside of their own interest. However, this too misses the point that Hobbes is trying to communicate; Hobbes may have had a low opinion on human nature, but to use examples of peaceful cooper-ation takes his thought out of context. Hobbes’ view on human nature also revolves around the climate of fear that would follow the breakdown of society, which would, in the eyes of Hobbes, pretty much obliterate the empa-thetic side of humanity; the side responsible for repairing the leaky roof. Hobbes’ suggests that the nicer side of humanity is resultant of the feeling of security and safety

brought about because of the protection of the society by the state itself, and without this security, we would merely descend into a state of anarchic depravity. Hobbes himself saw such a breakdown in society firsthand, with many English people fleeing to France amidst the English civil war with stories of the ensuing carnage.

Furthermore, Hobbes is a keen advocate of political authority; this is the combination of authority and forced compliance, which, when exercised, imposes require-ments that can make us materially less well off, like taxation. Hobbes’ advocacy of political authority stems from his desire for security in order to maintain trust within society. He was a strong supporter of replacing the insecurity of the state of nature with an all-powerful sovereign, who would have unrestricted and undivided authority - The Leviathan. This was, in Hobbes’ eyes, the best way to preserve and maintain the system of government and the safety that is resultant of govern-ment. Notably, Hobbes did also consider democracy as a possible system of government which, for his day, was a considerably radical idea; however, he vastly prefered the concept of a single sovereign because he believed that it was likely to be more consistent in its wishes and de-mand. The problem of multi-member sovereigns was that they were susceptible to internal divisions, which would undermine the strength of the state, thus undermining the effectiveness of the state’s protection against slipping into the state of nature.

Later, in 1666, the House of Commons published a bill against Atheism, which was used to target Hobbes’ Leviathan; however, the sole punishment of Hobbes was that he was banned from releasing material on subjects relating to human conduct. Thus, Hobbes spent the remainder of his life publishing histories, including a translation of both the Iliad and the Odyssey. Hobbes died from a stroke in December 1679.

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I'm Not Feeling Myself

I'M NOT FEELING MYSELF

Words by Tomas Brown

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and they will usually give you a very simple answer—that they are a person with a mind and a body and a number of qualities pertaining to them, such as being a boy, being a student, sitting in a room and so on. People often answer with qualities about their mental rather than physical selves - that they are creative, passionate, hardworking people for example. ‘I am a boy, I am creative, I am a student, I am hardworking’, they might say. There is a recent tradition, however, of denying this ‘I’, and questioning if there is any ‘self’ at all. Here I argue against the self, and expand upon how the misconception of its existence might have come to be.

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Asked who I am, I will say ‘I am Tomas Brown, I’m a sixth form stu-dent who enjoys philosophy and debating.’ You, most likely, will make a similar response as to what you enjoy, how you feel about things, what

your physical position is and so on. When asked who we are, we will describe our ‘self ’. We might say the thing to which all these properties belong to: the ‘mind’ in mind and body, the constituent of me which is me.

Let us, however, perform a small thought experiment. Picture your answer to that exact question: ‘who are you’. Let us make it our objective to consider ourselves, and not to consider our dispositions, our likes and dislikes, our phys-ical selves, anything our mind merely ‘participates’ in, or anything which is not the essence of our proper mental ‘self ’. Let us take my own statement:

First, lets strip away our likes or dislikes, as they are not us ourselves, merely things that our ‘selves’ participate in:

Second, let us strip away our physical position, since we are attempting to find our purely mental self:

Third, let us strip away our emotional quality and dispositions, since again, an emotion is something I participate in, not something which I myself am.

What we are left with, disappointingly, is ‘I am Tomas Brown’ - not, I admit, a very descriptive statement of my self at all given that ‘Tomas Brown’ to me is merely another term of reference for myself. What this was designed to illus-trate was that it is impossible to conceive of what the self actually is, vocalised, without reaching a contradiction - in a way which is not unrelated to Moore’s explanation of why we can’t describe good in his naturalistic fallacy. As Russell, in ‘the Problems of Philosophy’ outlines, we can have an acquaintance with our sensations, and our thoughts, but no matter how hard we attempt, we can’t have an acquaintance with our actual selves. Attempt to think of yourself without thinking of external thoughts and sensations, and you will find the attempt impossible (or at least this author does).

I would argue that without the evidence of actually being able to be ac-quainted with the self, it is highly likely that there is no ‘self ’ at all. An idealist approach (although ironic given the point I’m making) may say that because we can’t conceive of a self, it can’t exist. A slightly more convincing verificationist

(i) ‘I am Tomas Brown, I’m a sixth form student who enjoys philosophy and debating - I consider myself a calm person’.

(ii) ‘I am Tomas Brown, I’m a sixth form student who enjoys philosophy and debating - I consider myself a calm person’.

(iii) ‘I am Tomas Brown, I’m a sixth form student who enjoys philosophy and debating - I consider myself a calm person’.

(iv) ‘I am Tomas Brown, I’m a sixth form student who enjoys philosophy and debating - I consider myself a calm person’.

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approach may affirm that we can’t have positive or negative verification for the existence of a self (as we describe experiences, and not the component of us known of the self directly), it must be a meaningless and unrealisable concept.

At this point, we have two main questions to answer that stem from denying the existence of the self; First, if there is a concept of a mental ‘self’, how did such a thing arise if there is nothing (that we can be acquainted with) which relates to it; and second, what do emotions, feelings, and wills ‘happen to’ if not our self?

To the first question, I would make the reply that the mental concept of the self is merely an illusion as it derived from our physical concept of the self. I, always have immediate evidence for the conception of my physical self. I look down at my legs, and I know that they are mine; I can feel the keys of my laptop under my fingers; I control the movements of my hands as I type; I am aware of them in space and their location in relevance to me. I am aware, in other words, of the physical entity that is me, and can give an accurate description of what it is to be me right down to the atomic level. In reference to this, I propose, the term ‘self ’ was created with definite intent - to my arms, legs, torso and so on.

The concept of a mental self, I would argue, comes from an extension of this concept into the mind. As I know I have legs, arms and a torso in the physical world, I assume that I have some sort of equivalent in the mental world - the self. However, we already know from our thought experiment earlier, that we don’t have any immediate evidence for the concept of the self - we can’t be acquainted with it, only thought and sense - we find it impossible to directly describe it at all. Therefore, as we don’t have the same relation to the mental self as the physical self, the mental self becomes a referenceless condition, meaningless and correspond-ing to nothing: we proverbially look down, and we can’t see our mental legs.

The second question, of what ‘emotions and feelings’ happen to may be answered on the basis of this first reply. There is an assumption that emotions and feelings must act upon a specific mental being in order to be meaningful. The reply, given that we have taken the above as sufficient evidence against the existence of the self, is that emotions and feelings are merely events, with no particular ownership. To use my earlier example, philosophy and debating are enjoyed, but not by anything as specific as a ‘me’. They are things that happen upon a person, and perhaps happen upon a physical ‘me’ in a sense, but there is no mental ‘I’ who enjoys making a case in front of a crowd of people. The tendency to ascribe these things to a mental ‘I’ is due to the linguistic tendency to use the ‘physical’ and ‘mental’ self interchangeably.

Much of philosophy is in fact based off of this erroneous ‘mind body’ distinction. ‘I think therefore I am’ falls prey for example. It may be said that it uses ‘I’ in two distinct manners; the first ‘I’ pertaining to the physical self, that a thought might ‘happen’ to as objectively as it would any other thing; and the second a mental self, which Descartes seeks to prove is doing the thinking and hence exists. The problem here is that there is no connection between a thought and the mental self - thoughts, under our distinction, are physical entities that just ‘happen’ to the physical, and don’t need any privatised entity to take place in a mental realm. Therefore, Descartes hasn’t posited a mental self at all - merely that thoughts happen.

In conclusion, to restate; we have found that the mental self is thing which it is impossible to define and be acquainted with; from this we have concluded that ‘the mental self ’ is unverifiable; from here, we have illustrated how the physical self may lead to a concept of the mental self; and from there posited how mental events are only ‘physical events’ which happen objectively in the world. I am quite aware of the irony of having used the self reference ‘I’ roughly forty times in an article denying the self.

12

The Axiom

EPICUREANISM IS FOR THE

COLD HEARTEDWords by Giles Stratton

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Epicureanism Is For The Cold Hearted

Epicureanism, a classical take on hedonism, advises that maximizing self-pleasure is the ultimate way of experiencing life. It fundamentally

claims that in order to maximize happiness, concern for those around

you is treated as secondary to self-interest and egoistic tendencies. In the course of this article I hope to demonstrate that such a lifestyle can lead only to displeasure and

guilt, whilst also concluding that as a philosophy, it cannot be

universalized in the slightest.

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Firstly, I believe that a few myths have to be dispelled. This philosophy did not have a being or an idea that was to be worshipped, but an ideology that the sole aim of life is to be happy and content. Epicurus himself be-

lieved in gods, but not in the traditional sense of his time. Instead of them being ever watching and interfering on a whim, in Epicurus' world, they are lofty and simply don't care about the affairs

of mortals, fairly similar to us and ants. Also, when I come to talk about the idea of doing anything to become happy, this has exceptions and is not all about sensual pleasures (drink, sex, etc.).

Then, with all the misconceptions now removed, we can look at this philos-ophy idea by idea. Firstly,

the most famous quote of Epicurus in relation to his philosophy is probably 'Death is nothing to us'. This bizarre sounding statement about the inevitable becomes quite clear when you think about his overall aim as well. The basis behind this is that:

However, this still does not explain his statement; so, to answer this, he comes up with a few different perspectives with the first being the 'no subject of harm' argument. In essence, this states that while we are living, we are not dead (obviously!) and while we are dead, we are not aware that we are dead, so death is effectively not in our lives at all and is just a strange phenomenon that we have no control over—so why should we fear it?

The second is the 'non existence' argument, which simply says that death is the same as non- existence, and as we did not exist for billions of years prior to our births and it did us no harm, why should non existence at the end of life worry us?

This can be summed up as such: death is the end of sensation so cannot be physically painful, and death is the end of consciousness and so cannot be emotionally painful. A couple of replies can be brought to these ideas: The first statement about the physical element of death is true, but I believe is missing the point of why we fear death in the physical element. That is, I believe that it is not the end of sensation that scare us, but the pain that we associate having to come before it (wounds, infections, and diseases etc.) and so we have associated death with harm to us. This is why I believe Epicurus makes the perfectly un-derstandable mistake of linking our fear of death to death itself.

The second statement is a little less understandable because, as conscious minds, we strive to do anything to stop things being out of our control, explain-ing our dislike of fainting and so on. To know that there is a phenomenon which we cannot control and will shut us down permanently scares us (perfectly sensibly so). That constant worry about the impending disaster creates a fear, and so it hurts more when you are thinking about not being able to see your

The Aim of Life is Happiness •

The Main Thing Blocking This is Fear•

Our Main Fear is of Death.

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loved ones again, because of the fact that we know that this end is coming. This also has an effect on family and friends, as they know that this person in front of them is so precious to them and they are, at some point, going to be gone and they will never see them again. So it is preposterous to suggest that death involves no emotional pain, especially the for relatives and friends of the dying or dead person.

This brings us to friendships. Like a lot of other things in Epicureanism, friendships are not bad in themselves but should, primarily, be established for the rewards and benefits that they bring rather than establishing one for friend-ship's sake. This may mean that friendships are started and are destroyed when having a person as a friend is no longer beneficial, which is seen as a bad thing in modern society - the biggest example being the popular phrase 'gold-digger' - and yet is seemingly encouraged by Epicurus. However, it seems that he has not taken into account the long term with this. For as people realise that being friends with someone like this means no reciprocal feelings of companionship, but a constant feeling of being used, no-one will be friends with that person, and so all benefit is lost, as well as non- hostile human contact, something that everyone desires as we are social animals, which can be seen in the many cases of people going insane when stripped of human contact.

Finally, I bring before you the idea that while pleasure is the ultimate goal of life , not all pleasures are good for someone. Pleasure is set out to be the greatest possible state of mind, but this does not give reason to accuse this a philosophy of the sensuous; anything that is pleasurable in the short term, but could cause you pain in the long run, is forbidden as ultimate pleasure is described as not really being having a good time and enjoying yourself, but instead is the removal of all negativity, the primary one being pain. However, in this idea we come across a problem, as many innocent pleasures could give you pain in the future, for example eating chocolate or sunbathing, because chocolate could give you diabetes, and sunbathing, if not properly protected, could lead to sunburn and in extreme cases cancer, but half the fun in some things is not being fully pro-tected - but in it's defense most of this was not known about back then.

So I put to you that Epicureanism is far too idyllic and not exactly well thought-out - though some parts are true, like the greatest good is the removal of all pain and that death is nothing to us, this can only be true of a society of robots, trapped inside padded cells.

“Death is the same as non-existence, and as we did not exist for billions of years prior to our births and it did us no harm, why should non existence at the end of life worry us?”

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The Axiom

2001:A SPACE

PHILOSOPHYWords by Blake Jones

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2001: A Space Philosophy

Any film which is thought provoking or good, will have many interpretations. Some particularly odd examples of film interpretations include Toy Story 3 being about the holocaust, X-Men representing the Gay rights movement and Harry Potter as a metaphor for 9/11. Often films are thought of as being about God and religious ideas; the greatest genre for this is science fiction which deals with heavy doses of the supernatural. Yet, how much do films actually represent about God, or is it all wish fulfilment to make a good Tumblr post?

IS

THE SCI-FI EQUIVALENT OF MOSES RECEIVINGTHE TEN COMMANDMENTS?

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The philosophy of film is a very popular topic, since it can be very useful in religious teaching. Certain theological and philosophical ideas are

very hard to explain, but if they have already been shown in a film and understood there, it can be easy to apply those ideas to God. Though most interpretations of film are unlikely to have been intended by the director, they can still be used to understand God and increase enjoy-ment of the film. Stanley Kubrick once said regarding his film 2001: A Space Odyssey, ‘you're free to speculate as you wish about the philosophical and allegorical meaning of the film and such speculation is one indication that it has succeeded in gripping the audience at a deep level.’ Here, I will look into the deeper philosophical meanings of 2001: A Space Odyssey, a film which provides much opportunity for philosophical analysis. It has been the subject of several books and much speculation; probably due to how vague it is and its rather confusing ending. The film is about the progress of mankind, with the majority of the film being about a space mission to the moon. There are three elements I will study, HAL 9000, the monolith and the lack of dialogue.

When the problem of evil is raised, how is there suf-fering with an All-powerful, All- loving and All-knowing God, theists will often bring up the free-will defence in response - that God gave us free-will which we used to

cause suffering. However in response to this it could be argued that either God should not have created man if he was going to suffer or He could have created us without free-will. Yet, this argument is made due to a lack of understanding of God, to understand this better we should look at HAL 9000. HAL is an example of arti-ficial intelligence and is the computer used in the film’s space mission. Though they needed a computer, he also expresses emotions: to quote Dr. David Bowman in the film, ‘he's programmed that way to make it easier for us to talk to him.’ This shows that they chose to give him emotions, or in other words, they created him as a man in their own image and likeness and gave him free-will because it made things nicer in general. This turned out to be a mistake when HAL tries to kill them; though they may have guessed this would happen, they did so anyway. What this shows is humans themselves find it desirable to imbue things with emotions whenever they can, even if it could lead to bad consequences. Perhaps this is morally the right thing to do, and guided God in his own creation; if not, it at least helps us to understand why we were given free-will.

The monolith can be used to explain the relationship between God, science and creation. The monolith in 2001 is created by aliens to examine and manipulate minds; it appears four times in the film; first at the dawn of man,

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when it causes the apes to first begin to use tools; then on the moon to mark humans reaching space; then orbiting Jupiter; and finally at Bowman’s bed when he transforms, marking man’s next stage of evolution. The monolith could be seen as representing God and how He fits into creation. In 2001, it suggests that for man to evolve there needed to be a cause; for example, the monolith planting the idea of using tools. This could easily correspond to the moment in Genesis when animals have been created: ‘then God said, “Let us make mankind in our image, in our likeness,” Genesis 1:28. Here, evolution from animal to man needed to be caused as well, this time by God. The same idea can be transferred to original creation of the universe: the Big Bang. The chances of the Big Bang happening are incredibly small; yet it happened and we are here, but with such small chances, did the Big Bang have an extra cause? God, as is suggested in Genesis, is that cause for the Big Bang. This continues the idea in 2001 that creation needs an extra cause and shows how God, science and creation all fit together.

Additionally, I think that we can learn from the notably little dialogue in the film about the nature of revelation. In the film’s two hours and nineteen minutes, there are only forty minutes of dialogue; there is no dialogue in the first twenty five or the last twenty three minutes. Yet, much can be learnt from the film when there is no dialogue,

especially during the ending. This is because through the visuals and emotions seen in the characters, enough can be learnt about the film. In the same way, through special revelation, specifically prayer, many things can be learnt about God. People pray to God and rarely will hear anything; yet, they will have new understandings of the world and God from it. New views will come instead from experiencing certain emotions and from having the inspiration to look at things differently from prayer; a somewhat similar way to how we discover new things in 2001. However, in the same way that the ending of 2001 is vague and has been interpreted in many ways, revelation from God can be interpreted in many ways and has caused many different views about Him. Yet if there was to be dialogue throughout 2001 explaining, the film would be ruined. This applies to God: if we all had exact explana-tions of everything in prayer, we would have less personal relationships with Him and faith would cease to exist, due to God being confirmed. So the way 2001 is presented can help us see why God is presented in the way He is.

In conclusion, the complicated ideas about God can be understood through looking at them in a way easier to understand: films. In 2001: A Space Odyssey we can un-derstand the free-will defence; the relationship between God, science and nature; and special revelation through prayer with greater ease.

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The Axiom

INTUITIONISM, FORMALISM,

AND EVERYTHING INBETWEEN

Words by Tom Davy

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Intuitionism, Formalism, and Everything Inbetween

The 20th century was an enormously progressive period in mathematics,

rife with academic debate and controversy. Perhaps one of the most philosophically relevant discussions, however, existed within the ‘Hilbert-Brouwer

Controversy’, in whichBrouwer’s intuition-ism, and particularly

his denial of the “law of excluded middle”, came into immediate contention with Hilbert’s formalism, a highly dominant theory at the time.

In the course of this essay, I will attempt to illustrate the varying regions of value within the con-

flicting theories, and to what extent the two ideologies

may be synthesized for pragmatic consideration.

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In a paper entitled “The untrustworthiness of the principles of logic”, Luitzen Brouwer did swiftly away with the preceding two millennia of our logical understanding. Primarily derived from Aristotle, the highly

structural and binary approach to logic had remained enormously dominant until Brouwer’s controversial remarks. The “law of excluded middle”, a practi-cal necessity in referential logic, was condemned by Brouwer as a nuisance, and so too was total negation and other forms of certainty. In a sense, Brouwer was to logic what Descartes was to our ontology.

Brouwer’s intuitionism may be reducible to an alternative understanding of what ‘truth’ truly is. To Brouwer, ‘truth’ is that which may be proven. It would be true to claim that the three internal angles of a triangle amount to 180°, or that 2+2=4. Similarly, claiming that something is ‘false’ does not precisely deny its truth, but rather expresses that it may be refuted. This has a great deal of bearing on logic, and particularly the aforementioned law of excluded middle.

Here is an ordinary truth table, concerning whether “If he is a bachelor, he is an unmarried man” is true or false under varying circumstances. Take bachelor as P, and unmarried man as Q:

Hence the statement “If he is a bachelor, he is an unmarried man” holds false if, and only if there is an existing bachelor who is not an unmarried man1. Here we may see a visible divide between classical logic (relatively equivalent to formal-ism) and Brouwer’s intuitionism – P›Q is curiously upheld as ‘true’ even in the event that we never see a bachelor (and that we do see an unmarried man) or that we neither see an unmarried man or a bachelor. The act of non-observation or acknowledgement leaves room for potential ‘truth’, and that which is not disproven is ‘true’ for all intents and purposes. Curious religious implications aside, the very nature of this truth table is an illustration of what intuitionism is not. Brouwer would be distraught at the idea of binary truths and falsities, and would instead prefer something of an intermediary ground of realistic uncertainty. Given how popular this mentality is in epistemological fields, in-tuitionism may be concluded as rather useful, logically or not. The rejection of total truths and, by extension, the law of excluded middle, is an appreciable denial of the highly gridlocked nature of logical understanding when consider-ing the real world.

This does not, however, bode well with its validity within logical spheres. When concerning mathematics, intuitionists retreat into the use of the LoEM2

regardless of their unerring criticisms of the principle. In fact, the intuitionist may only refute the LoEM altogether - logically speaking - when concerning infinity, and the application of axiomatic principles into infinite circumstances.

1 Where P holds a truth value of T, and Q holds a truth value of F.2 Acronym for “the law of excluded middle”.

P Q P›QT T TT F FF T TF F T

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Kleene demonstrates this quite elegantly:Suppose two logicians want to prove that “there exists an n such that P(n)”

(in regards to natural numbers). There is a formalist, and there is an intuitionist. For the formalist, it is a simple task. Though expanding the premise a contradic-tion may be found in the assumption “for all n, not P(n)”. Following, via reductio ad absurdum the formalist will arrive at “not for all n, not P(n)”, which can be transformed into the original statement. For the intuitionist, however, natural numbers cannot extend into infinity. By affirmatively stating “natural numbers exist as a totality”, the intuitionist goes against his foundational belief. Brouwer instead states that infinity is in “perpetual creation”, and that by continuing upward with natural numbers, it will never reach a status of completion. Where Russell would likely dismiss this technicality in favour of affirmation, the intu-itionist cannot.

Amidst the discussion of intuitionism and formalism, Hilbert famously stat-ed that “taking the Principle of the Excluded Middle from the mathematician … is the same as … prohibiting the boxer the use of his fists”. In the formalistic or classical sense, the analogy is accurate. Only from pre-defined and consistent axioms within a constructed axiomatic system may mathematical or logical statements be verified or universalized. It is after this methodical, logical pro-cedure that meaning, or pragmatic value, may be extracted from the maths.

Although Hilbert typically sets aside the importance of ‘meanings’ in his take on formalism, we may consider it something of a bridging point between the two philosophies that have been discussed. Although we may have learned mathematics in the context of apples and other mundane items, it has shifted into its own academic circle. The implications and theory of mathematics rarely intertwine. Whether we may conclude this as a favourable situation or not, the reality is clear: the philosophical implications of mathematical understanding cannot be conjoined to the validity of its logical procedure. Intuitionism is realistic – it considers the true meaning of what affirmation is, and the dangers it presents. But as Russell has repeated time upon time, such caution is a matter of pedantry, a caution that cannot be afforded in logic or maths. Where Brouwer sought to align logic with meaning, Hilbert’s separation of the two appears, quite ironically, a far more ‘realistic’ take on the world that we inhabit.

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The Axiom

THE PRESENT KING OF

FRANCE IS BALD

Words by Tomas Brown

The Present King of France is Bald

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In Principia Mathematica, Bertrand

Russell vocalised one of the most famous objections to the law of excluded

middle there is - some propositions, whether given a truth of True or False, will always lead us to impossible conclusions. In this

article, I discuss two reactions to the criticism, exploring the logical mistake it is making, and then proceeding to consider why this

‘narrow’ approach is a dangerous way to understand a statement to be

false.

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The law of excluded middle is a fundamental instrument in knowing the truth of an argument for logicians. The law states, at first glance, a simple and tautological truth - simply stated, that;

Or, in a propositional formulation as Russell presents it;

The law is very simply applied. Say I have the proposition ‘Hesperus rotates’ Given the above law, it is either the case that (a) Hesperus rotates, because it has a truth value of True or (b) it is not the case that Hesperus rotates, because it has a truth value of False. This rather convenient bit of self evidence gives us a solid, binary basis to test the truth of an argument ‘given any interpretation’ of its premises.

However, Bertrand Russell’s Principia Mathematica vocalises a coun-terexample. Consider the proposition ‘The present King of France is bald’. According to the law of excluded middle this proposition must either have a value of True, so it is the case that the current King of France is bald; or it must have a value of False, in which it is not the case the present King of France is bald (and, it’s logical equivalent, ‘the present King of France is not bald’) - there is no third option. It’s clear, with a little thinking, that this is questionable: both positions, of the proposition being true or not true, seem to guarantee a present King of France actually exists at this moment. Here I will consider two defences to this objection, broadly in the same vein as the defences Russell himself makes.

The criticism itself I would argue is riddled with possible ambiguity in the way it treats what it means for a proposition to be true or false. In a first manner it seems to be applying the principle of a proposition being ‘not true’ or ‘negated’ selectively. Classically, negation in logic means ‘it is not the case that’ (and only means that a certain state of affairs is not so). So, it can either be the case that the current King of France is bald, or it is not the case - and it is worthy noting that the negation applies across the entire statement. I would argue that the statement ‘the present King of France is not bald’ is not the negated version of ‘the present King of France is bald’ as it doesn’t apply negation across the entire statement. Let us break the proposition into it’s elements:

or

The objection states that the statement’s negation, ‘it is not the case that the present King of France is bald’ is the same as the statement ‘the present King of France is not bald’:

or

(i) Either a proposition is true, or a proposition is not true

(ii) P ˇ ∨ ¬ P

(i) The [present King of France] is [bald]

(ii) K ^ B

(iii) The [present King of France] is not [bald]

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As we see, the ‘falsity’ or ‘negation’ has been applied only to the quality of being [bald] not to the entire statement. It may be argued that as the propositions ‘it is not the case that the present King of France is bald’ and ‘the present King of France is not bald’ are logically equivalent, the application of negation to [bald] only is an insubstantial difference. However, there is a strong case that this actually is a substantial difference as in use, ‘the present King of France is not bald’ cannot be said to be practically the same as the negation of ‘the present King of France is bald’; maintaining [the present King of France] as an unnegated element in both the True and False versions of a proposition leads us to a contradiction where there must be a France no matter the truth of the proposition. Due to this contradiction, we must affirm that only application to the whole statement as below is a valid way of applying negation:

Or

This presents the overall error of the criticism: it attempts to express a different proposition - namely ‘the King of France is not bald’ - from the negation of another proposition. We will remember that the only thing that the negation of a proposition means is that that specific state of affairs is not so. I can’t say that just because I didn’t have lamb for lunch, I must have had pasta. Yet, because ‘it is not the case that the present King of France is bald’ and ‘the present King of France is not bald’ can’t be said to be practically equivalent statements - one expressing negation, and another a whole other state of affairs - we find the argument trying to make a positive affirmation of a different state of affairs from negation.

What can we learn from this? I would argue that what we might learn is that we must create a separate proposition for each possible state of affairs we want to illustrate, and don’t rely on the assumption that the negation of a statement implies another specific state of affairs. For instance, I can’t use the negation of ‘the present King of France is bald’ to imply that the present King of France has hair. Instead, I must create a separate proposition for ‘the present King of France has hair’ to be able to use negation properly.

In conclusion, this criticism of the law of excluded middle fails - it does not apply negation thoroughly enough, and we find that the ‘narrow’ application of negation only to [bald] leads to problems of practical equivalence although the statements are logically equivalent. As the statements are not practically equivalent, the criticism attempts to express another state of affairs through negation, which is not applying the concept properly. Therefore, we find that in order to express other states of affairs, we may rely only on creating separate propositions to represent them.

(v) It is not the case that [the present King of France] is [bald]

(iv) K ^ ¬ B

(vi) ¬ ( K ^ B )

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The Axiom

ANIMAL RIGHTS AND ETHICS,

AN OVERVIEWWords by Henry Crowe

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Animal Rights and Ethics, An Overview

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Animal rights have always been a highly contested area of ethics and it is important for us to understand the views that have developed around this field. These views affect us legally, both for legislating scientific testing, captivity of creatures, and from a more human point. Our views on this issue may affect our abilities to make decisions on issues such as abortion, euthanasia and other, perhaps darker, issues. In light of that, this article seeks to shed light on current and past theories on animal rights.

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Ethics is an ever changing field, and one that reflects heavily in our legislation, generally fo-cusing on humans with respect to law. However,

in a discussion like this, perhaps it is important to talk about why these rules apply only to humans. Whether we accept the rejection animal morality in an “indirect theo-ry”; a “moral equality” theory in which animals are given equal moral status; or a “direct but unequal” theory, where animals are morally considered but humans are given higher consideration, will have a massive effect on how we approach the application of the law.

As far as indirect theories go, Aristotle is perhaps the earliest, arguing for a “hierarchy of living things”. Plants are not conscious, so they are not considered; animals are considered higher than plants, but cannot reason; humans and human interests come first. This is supported by St. Thomas Aquinas, who argues that humans are the only creatures that are rational and so capable of determining their own actions, so they are the only beings towards which we should extend concern “for their own sakes”, and non-rational organisms are instruments to be used. The common theme is that reason and autonomy are what give a creature moral status.

The indirect theories appear to fall short in a few ways.

For one, it negates the idea of sentience, or more specifical-ly: feeling, most notably pain and pleasure. Many ethicists claim this sentience, which is shared by most animals, gives us a responsibility to give them direct moral status. A fair argument - a human child can only reason about as much as a furred ape, if not less - on those grounds it should be at least a moral agent.

So perhaps we say that those without reason are direct moral agents, are they equal? On the one hand one might argue that we have a duty to protect any moral agent. However, on the other, since the reasonless cannot fulfil the same protectoral duty as us, it can be argued that they do not have “rights”. That is to say, those duties can ethical-ly be dismissed for the greater good as they are incapable of performing duties. Bentham’s word on rights - that they

“Studies have shown apes’ abilities in shape recognition and symbol based written language.”

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were “nonsense on stilts” - are fitting here, which in the author’s opinion, appears to be the case.

The other argument for the above “indirect” theories is that, to quote: “Only Human Beings are Rational, Autonomous, and Self-Conscious”, so only they can be higher moral creatures. Studies have shown apes’ abilities in shape recognition and symbol based written language. Many ape species have been known to play with toys in infancy, some even establishing ideas of “gender norms” by assigning toys by the gender of the ape. Also, dolphins have utilised pufferfish toxins as a recreational drug. These examples, and many other developments, may perhaps be hinting that a less arrogant, less human centric view of ethics is and should be on the rise.

Finally, we come to Equality theories: that animals are equal in rights to humans, and should be treated as such; ideas that are mostly supported by Peter Singer and, later, Tom Regan. Singer argued that we cannot say that humans are in some way superior to other animals as to be superior we must have a unique faculty that only humans have.

But there is no property fulfilling these conditions (as the senile or infants do not show the properties that only hu-mans have), and properties all humans have most animals have too, so the claim only we deserve full moral status can be dismissed. Further, there is a logical gap between pronouncing such a quality worthy of special recognition - if all humans had three kidneys while other mammals had two, would that make us unique beings?

If Singer’s premise is accepted, creatures (especially simian or higher intelligence sea mammals) should not un-der law or ethics be killed or harmed by humans regardless of our aims, due to the pain inflicted on our moral equals.

"All animals are created equal but some are more equal than others," as George Orwell’s oft quoted line states. Originally a commentary on the failure of Marxist states at the time, in our own age of increased understanding of the natural world, perhaps it is time to take a more literal look at this phrase. We might ask why we are “more equal” than other species of emerging intelligence and, in light of the coming dawn of artificial intelligences, if we indeed are.

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The Axiom

FILM REVIEWS

Words by Stephen Moren

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Film Reviews

(1971)

Stanley Kubrick’s ultraviolent adaption of Burgess’ novel reveals a problematic aspect of human

behaviour

In a film in which the quote-unquote ‘protagonist’ Alex and his band of ‘droogs’ spend their free time raping, thieving and assaulting whom-ever they deem fit, one would assume it is their actions that are make

this film troubling. However, whilst utterly deplorable, their actions are not the subject of this analysis; rather, the ‘cure’ to Alex’s Nihilistic tendencies, the infamous Ludovico Technique, presents a much more difficult idea. This technique involves plying Alex with a nausea-inducing drug while watching similar scenes of violence as those that he used to partake in (all the while his favourite Beethoven soundtrack blaring in his ears). This therapy renders him incapable of violence, the thought of which now makes him vomit. Alex has undergone a form of ‘Classical Conditioning’ where his free behaviour is altered by previous stimuli (i.e. the nausea the drugs made him feel whilst being forced to watch violence on screen beforehand, now re-occurs when contemplating or seeing real violence). The chaplain of the prison he is held in raises a pertinent issue, has the cure has removed Alex’s free will? His reaction to violence is now determined by something other than his own free choice. This idea is prevalent in the Behaviourism, a theory of Determinism that states we are conditioned by our past experiences (operant conditioning as B.F. Skinner called it) in a way that limits our ability to choose our actions. Applying this more broadly, are you truly free? Or are you an automaton dancing helplessly to the rhythm set by those before you? Is a freely-willed evil act more morally acceptable than forced good? Furthermore, our concept of individuality is based upon the belief in our freedom of thought and action, if these are at the very least influenced, if not actually determined by factors beyond our control, such as upbringing and even genetics, to what extent are we individuals at all?

Film ReviewsFilm Reviews

Header

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(1979)

Francis Ford Coppola’s hallucinogenic masterpiece leads us into our 'Heart of Darkness'

In your reviewer’s humble opinion this is one of the best films ever made, also inspired upon one of the greatest novellas ever written; Joseph Conrad’s Heart of Darkness. The change in setting from Belgian

Congo in the novel to the Vietnam War the film depicted gives the story a res-onance through generations; like Clockwork Orange, it reveals a disconcerting ‘truth’. We follow Captain Willard (Martin Sheen) and his crew up the Nung River on a secret mission to assassinate the rogue Colonel Kurtz (Marlon Brando). As the journey progresses we watch as the crew disintegrate mentally as they go deeper into the jungle and horrors of war become more senseless, none more so than the capture of the beach ‘Charlie don’t surf’ and Lieutenant Colonel Kilgore’s iconic Napalm speech. Kurtz captures Willard, who eventu-ally gains Kurtz’s trust and sneaks into Kurtz’s quarters in the temple and kills him. Kurtz however, has one final thing to say as he lays there dying ‘The horror, The horror’ lifted directly from Conrad’s book. The film has deeply Nietzschean overtones; most Western philosophers have clung to reason as the defining characteristic of human nature but Nietzsche rejected this idea. He believed that while the rational mind did exist, the drive behind humans was primal and that consequently civilization is a façade that is all too easily stripped away, an idea that Sigmund Freud adopted in psychoanalysis. Kurtz demonstrates the finished product of this: his own journey away from civilization makes him the uncompromisingly ruthless man we see, one who sets himself up as a demigod to the natives under his command. We also get to experience this decline in Willard and his crew, taking drugs to avoid the horror and shooting unarmed civilians to speed up the mission. The use of the ‘Ride of the Valkyries’ during the taking of the beach further cements the links with Nietzsche, whose phi-losophy in his earlier years was heavily influenced by Wagner. The film delves deeply into the darkness of the human condition; those making the film went half mad while filming - it nearly destroyed Coppola, but it produced arguably his best work, eclipsing in scope and ambition The Godfather and Godfather II, no mean feat.

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The Axiom

PHILOSOPHY FANTASY

WORLD CUP TEAM

Words by Tim McGovern

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Philosophy Fantasy World Cup Team

W ith the World Cup in full swing, I think that it is only right that

it is spoken about. Football is a sport that is part of billions of people’s lives, whether you are a die-hard fan, or you reluctantly go out with one because at the end of the day, they’re a nice guy. Philosophy is a subject affecting billions of people both out of personal interest and students who happen to have the misfortune of studying the AQA syllabus at A Level (such as myself ). So, with the some of the best players on the planet set to feature in Brazil over the next month, and Philosophy fresh in mind after exams, I got wondering who would feature in my Fantasy Philosopher’s World Cup. If I was in charge, my team would look something like this...

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1 2 34 5 6

7 8 910 11 S1

S2 S3 S4

S5 S6 S7

M AM


GK – Melvil Dewey – USADevised the squad numbering system and settled with the standard 1,2,3... A

renowned tactician of the game, he was fascinated by numbers and statistics, thus

deciding he was number 1.The keeper.

DR – John Locke – ENGExperienced full back, Locke claimed

his right to play having featured in many England lineups in the past. Locke said “You can never know how to play in a

World Cup, unless you have experienced one. Like me”.

DC – Rene Descartes – FRAHe thought he was starting at centre back,

so he was.

DC – Plato – GRC (capt)The veteran centre half at Athens Academicals has announced his

retirement from football after the tournament. He learnt the trade from

Greek Legend Socrates who spent hours giving him one to one training after hours whilst Plato tried to balance a journalistic

career by writing for Socrates as well!

DL – Baruch Spinoza – NEDEvery team needs a little Dutch flair going against the flow. Baruch “The Individual” Spinoza stood out as he defied tradition

in Philosophy by questioning why traditionalists such as Aristotle and Hume should be in the team at all. Johan Cruyff

in fact was enlightened by Spinoza to break tradition by inventing his own turn

at the 1974 World Cup finals.

MC – Ludwig Wittgenstein – AUTWittgenstein gave away his wealth due to the misleading nature of the term “I” and other linguistic reasons mentioned in his book “Tractatus Logico-Philosophicus”.

In all honesty no-one can really understand why he claims to be in the

team at all because they can’t understand what he’s saying.

MC – Immanuel Kant – DEUEligible for the Scottish team through his grand-father, Kant claimed he was eligible

for this starting eleven by a categorical imperative of deontological moral

philosophy through reason.

AMC – Aristotle – GRCFresh from his Olympic success in 356 BC,

he is considered the protégé of captain Plato having risen through the youth team

of Plato’s Athens Academicals. Using mathematics, he was able to use logic to determine why he should be in the team.

AMR – Friedrich Nietzsche – DEUNicknamed “Superman” due to his antics

on the right wing. He beat Thomas Aquinas into the starting team by claiming

he (Aquinas) was dead along with his inspiration.

AML – Karl Marx – DEU (vice capt)All about working as a collective whilst

pushing the boundaries of his power within his role as vice-captain. Chosen

ahead of fellow German Friedrich Engels as Marx claimed “It was inevitable that I, a member of the Proletariat, would be

starting at left wing”.

SC – Bertrand Russell – WALAnyone who can prove that 1+1=2 in

a proper philosophical/mathematical theory deserves a place in the line-up.

Don’t care who you are.

S1 – Noam Chomsky – USAThe substitute keeper is another linguist

in the squad. Even though he claimed that human language and grammar is innate, he was not able to put into words why he should be chosen ahead of his American

counterpart Melvil Dewey.

S2 – Jean-Paul Sartre – FRADidn’t make the cut as the first team

attacking midfielder. When asked how he felt, he said “As I said in my book, Nausea, I’m sick as a parrot”. It is thought that he was also disillusioned by the absurd and

meaningless world around him which inspired his ideologies to agree with

Existentialism.

S3 – Adam Smith - SCOThe only Economist in the team is

currently available on a free transfer which is ironic as his face is actually

worth £20 today. It came as a shock to many that the centre back missed out on the starting line-up sheet as he was

advocate for specialization in the hope for an ultimate profit.

S4 – Confucius - CHIThe only Asian member of the squad

sacrificed his chance to play at left back having admitted in an interview:

"Confucius say, Spinoza better than Confucius. It for good of team”.

S5 – George Berkeley - IRLThe Irish centre-mid missed out a chance

to play in the first team for refuting the existence of a starting line-up.

S6 – Thomas Aquinas - ITANarrowly missed out to Nietzsche after refuting him by claiming that God told

Aquinas to be in the line-up. But he took this well when he spoke about missing a chance to start: “It does not matter that I am not in the starting team due to recent performances. My reward is waiting for

me in heaven”.

S7 – David Hume - SCOHume bargained his way into the team through inductive reasoning. He said “I

am a good footballer, so I should be in the team”. This wasn’t persuasive enough to include him into the starting line-up. To cover this up, he claimed that he “chose not to be in the team as I have free will

and control over it”.

Manager – Niccolo Machiavelli - ITABe feared, or be loved? The Italian mastermind inspired Fergie to use of the “Hairdryer treatment”. Just like his question, he is either loved or hated as a manager as he produces marvellous football, but at the

same time is happy to show off immoral acts within the game such as questioning the opposition’s free will. When asked about his time in charge of Fiorentina, he answered that the State reacted badly as they didn’t agree

with his theory that “the ends justify the means”. He was actually put in prison and tortured when in the role as manager in Fiorentina. Soon after

he resigned from the post.

Asst Manager – Socrates – GRCFamous for scoring the winning goal in the 1974 Philosopher’s World

Cup Final against Germany in Munich, a match in which Aristotle, Plato, Nietzsche, Marx and (Austrian) Wittgenstein featured. Confucius and

Thomas Aquinas were the match referee and linesman respectively. No-one understands the game as well as the former Greek striker. When talking about

his knowledge of the game, he claimed it was “Innate. You can read Plato’s Meno if you want to learn more”. He is not to be confused with Brazilian

midfielder Socrates, the chain-smoking, alcoholic Doctor of Medicine who outshone the rest of the players at the 1982 World Cup Finals in Spain.

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S3

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The Axiom

AGONY ÜBERMENSCH

with Nietzsche

Words by Tom Davy & Tomas Brown(Note: The authors in no way endorse the views of Nietzsche)

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Agony Übermensch

Q: I’m too nervous to ask out the girl I like, help!A: You are a weakling, socially determined to be beta due to lack of will. Partners

only date the ubermensch. Alternatively, when considering any relationship, ask yourself the question: Do you believe that you will be able to converse with this person into your old age? Everything else in marriage is transitory.

Q: I don’t know whether to take art or drama, what should I do?!A: Neither, become a gardener of rare south american climbing plants, and

gain a thorough understanding of human nature. Alternatively, don’t pursue pesky artistic careers at all. Release your power and become a lawyer.

Q: Nietzsche, I don’t feel manly and my friends tease me, how do I make myself more masculine?

A: The true man wants for danger and play. Silence the critics and sell their organs for profit, exchange the currency with moustache wax to realise your power in the form of copious and pointy facial hair. This both asserts your manliness and improves philosophical ability - I don’t get nicknamed ‘Nietzstache’ for nothing!

Q: I keep on dropping weights on myself; any idea on safer exercise?A: Take up tightrope walking. It provides a healthy sense of balance, a familiar-

ity with horrible bone crushing danger, and a strong familiarity with ethical metaphors.

Q: I’m worried about my AS grades, how did you get over this?A: Ignore grades, nepotism works best, no matter the pesky social moral prob-

lems of inequality or fairness. I mean, I made friends with Wagner - he still sends me christmas cards.

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The Axiom

EXISTENTIAL COMICS

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Existential Comics

48

THE

AXIOMISSUE No.1

Contributors

Tomas Brown Liam Frahm Giles Stratton Blake Jones Tom Davy Henry Crowe Stephen Moran Tim McGovern

Comic by Existential ComicsDesign by Asten Yeo

THE AXIOMNo.12014

the axiom - issue 1

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