Philosophical Tangents with Ashdotman & Socrates La Funkbadger

The First in the Series

http://www.youtube.com/playlist?list=PL1A2657A4879618C5

Art by Eliza Veretilo

This weeks artist was Eliza Veretilo: http://neonsuitcase.blogspot.co.uk/

The Philosophy Takeaway 'Open Topic' Issue 34

The latest philosophical fuss in education - By Patrick Ainley

The latest philosophical fuss in education

A big philosophical row is brewing in England’s primary schools about the knowledge (sophia – or is that wisdom?) that should be taught to 5-11 year-olds in the revised national curriculum.

The existing curriculum is accused by Conservative Education Minister, Michael Gove, of being too ‘skills’ based. The argument typically centres on history which is actually developed as a subject more at secondary school but relates to conservative cultural concerns. Traditionalists – like David Cameron with his plans to ‘celebrate’ the pointless slaughter of the first world war – feel history has become too ‘skills’-based. By that they don’t mean anything practical in the way of manual skills but that history and other teachers try to encourage pupils to think about cause and effect and why things happen. Instead of this generalized knowledge, the government wants pupils learning lists of kings and queens and the dates of imperial victories – bits of information pupils can learn by rote to recite in tests!

Gove justifies his prejudice in favour of this traditional type of schooling he enjoyed(!) by borrowing from a retired US professor, ED Hirsch. (That’s not Ed’ but his initials without punctuation, the sign of a true prawn – like AC Grayling, the former-London Uni philosopher who has set up his own traditionally academic private University). Hirsch claims that he tried to teach poor Black kids in community college about their history by informing them about the American Civil War. This basic factual information would, he argues, enable them to become knowledgeable about their own past and do as well as anybody else in – guess what? – more tests!

It’s not as if nobody had ever thought of or tried this before. In the 1960s French educational sociologist, Pierre Bourdieu, advocated what he called ‘rational pedagogy’ – booster classes for working-class and minority ethnic university students to help them to catch up with upper and middle-class students who had acquired through the way they were brought up the ‘cultural capital’ recognized by higher education. In England at the same time, educationalist Basil Bernstein argued that traditionally academic ‘Education could not compensate for society’. The implication was – and Bourdieu came to accept this too – that the education system would have to change to be of any use to the majority of the population it failed.

Although there were some pioneering experiments – especially in the old polytechnics in the UK – so that many more people were encouraged by progressive primary and comprehensive schools to go on to further and higher education, education as a whole since the 1976 so-called ‘Great Debate on Education’ was narrowed to only what was useful in employment. It became training without jobs as employment collapsed and the traditional skills of apprenticeships were reduced to making students ‘competent’ in carrying out basic tasks for – once again – more tests! (Nowadays we have education without jobs and apprenticeships that

are often indistinguishable from workfare.)

Meanwhile, schools compete to cram their pupils for an academic National Curriculum. Gove confuses tests of memory under pressure – like University Challenge – with ‘intelligence’. He thinks this is inherited so that all the education system has to do is pick out the ‘bright’ Men of Gold, just like in Plato’s Republic, failing the dull Men of Silver and Bronze. So Gove thinks you don’t need to train and educate teachers, for instance, because – so long as you know your academic subject – either you can teach it or you can’t. Anyone can therefore teach in Gove’s ‘free schools’ as they can in the private schools that are the model for them.

In fact, regurgitating disconnected bits of information in traditional exams is the equivalent of training for the competence-based assessment that replaced the real skills formerly acquired on apprenticeships. (Even state school teachers are ‘trained’ like this nowadays and the government last week proposed ‘competence tests’ for NHS doctors.)

Knowledge has thus been degraded to information and skill to competence so that there is now a hopeless confusion of terms and nobody knows what they mean any longer. Clearly a job for philosophers to sort out! As we do so, we should remember that there is nothing wrong with training; it is basic to putting the components of competent performance together in the exercise of a skill but you have to go beyond training to have education. (You can train animals after all but you can’t educate them!) But training for the assessment of competence is what much of education is being reduced to.

Similarly, Hirsch’s idea of education is cramming bits of information unrelated by conceptual and generalizable knowledge. ‘Funny phonics’ even teaches reading like this – training primary children to ‘sound out’ letters in words that make no sense which predictably inhibits reading for meaning. Meaning and imagination come in at the level of knowledge which is inseparable from skill because there is no knowledge so cerebral it does not draw upon some practical skill (since the mind is not separate from the body) and you need skill to apply knowledge.

Training for unthinking performance and schooling in the rote learning of information restricts pupils / students to their place in the hierarchy of competing institutions for which largely written exams function as proxies for cultural capital. This is what reforming the national curriculum is all about. Philosophers must contribute to resisting it!

By Patrick Ainley 

The Philosophy Takeaway 'Open Topic' Issue 34

Philosophical Train Journeys- Transcendentalism - By Eliza Veretilo

Philosophical Train Journeys- Transcendentalism

Train journeys are good places to accompany mental journeys. I wonder how many brilliant theories have been thought out through the window of a train, with a beautiful open country side landscape whizzing past outside. Silence makes us pensive and the constant change in the view makes us question, makes us wonder. Seems like the perfect setting to philosophise, if only in our minds. Alone with our thoughts we can reach that place, the place beyond remembering where we left the keys or what we are going to have for lunch. That place where we become immortal in thought.

This August, I discovered American Transcendentalism in Philosophy; it’s a beautiful doctrine from the 1830’ East Coast of America which believes in the inherent goodness of both humans and nature. They also claim that it is society and its institutions, especially the influence of organised religion and political parties, what are corrupting our essentially good nature. As if as children we were programmed to forget that part of our being, in order to maintain the previously existing society/economy. Transcendentalists believe that real individuals, who are independent minded and productive, are prone to show their goodness, instead of being the victims of fear. Thus if you are free minded and self-reliant, your true nature can be expressed, in its pure estate, thus the potential of who you could be, can be actualised. And then, a true community, formed of such individuals, can exist. Beautiful. When looking out through the window to the soft, beautiful and tender landscapes, and the taciturn faces of the rest of passengers whilst looking at the sunset, I wonder... Can we do that? Could we be that? Why people are not good to each other? We could be good to each other. Let’s be good to one another!

Some philosophical theories, such as this, do speak of a direct action. Transcendentalists criticise political parties, claiming that it makes the individual ultimately uninvolved with his/her community matters and a free minded person become nothing more that a number to vote, with the illusion of a voice. Having a voice over your small community could, perhaps, work better. Same with religion, which already tells you what is waiting for you in the afterlife before you can even attempt to live this one! Well, my fellow train passenger, the declaration of Human Rights was ultimately based on this the Transcendentalist theory, which claims that life is sacred and that we are good or have some sort of moral compass, if we only care to listen. A compass that can help us to live life deliberately, even if sometimes is easier to walk around with our eyes shut. Maybe there is something, something something to Transcendentalism. The train moves, time to eat, sleep, motive, organise, raise, recognise. We all have this dormant potential, if only we could stop the rush. To appreciate it and recognise it in one another could be the first step. Transcendentalism expresses the idea of a life lived like poetry, where you appreciate yourself and nature, where awareness if a gift and nature a blessing and we can build a world, were progress doesn’t look like destruction.

By Eliza Veretilo

The Philosophy Takeaway 'Open Topic' Issue 34

Think Critically

The Philosophy Takeaway 'Open Topic' Issue 34

ANTIDOTE FOR BABY FEVER

"If the act of procreation were neither the outcome of a desire nor accompanied by feelings of pleasure, but a matter to be decided on the basis of purely rational considerations, is it likely the human race would still exist? Would each of us not rather have felt so much pity for the coming generation as to spare it the burden of existence, or at least not wish to take it upon himself to impose the burden on it in cold blood?" - Arthur Schopenhauer

 
One of the most important - arguably, the most important - of the ethical questions which a generation may consider is that of the ethical tenability of human reproduction. After all, with few exceptions, we all bear within us the desire for procreation, at least instinctually - in males, lust, and women, maternity. One's answer to the question "should we reproduce" is pivotal - from the loins resounds the exhortation "Yes!"; from reason, "No!" At any rate, every generation has answered "yes", irrespective of whether the question was ever consciously considered; for most it is an implicit goal. But whom do we serve, when not our basest animal impulses, by answering this primordial call in the affirmative; what profit have we to gain in conjuring from nothing "a weak and sin-prone race, in order to hand it over to eternal damnation"?

If "rational" considerations furnish sufficient motive (e.g. advancing evolution, colonizing space, sating the curiosity drive and the lust for the other shore), then we are at least condemning multitudes to lifelong travail and suffering in the spirit of exploration - but the argument could be made that in the context of all human venture and enterprise hitherto, insofar as we have treated the courageous investigation of unknown vistas as an end in itself, the burden of history has impelled us. Indeed, the signal from heredity to every generation is one of exploration, expansion, exploitation. This justification has at least something of nobility to it; but radically few are those who found their decisions on these thoughts. Most blindly indulge their lust, either for copulation or for its ultimate product, and these lusts are never given the analysis they demand. But the rational among us can pose the question: is this really "right"?

Since foremost in one's contemplation of this problem must be the weighing of the sufferings of which the lives of all individuals are filled, I must take this as the chief criterion by which all judging of this problem be assessed; all other considerations are in my mind subordinate to this, for the spectrum of suffering is felt more immediately and more intensely by every living organism than any other phenomena, and often by orders of magnitude.  The manner in which most individuals approach this problem will often devolve upon the peculiar nature of his character and disposition, so that from the affable and easy-going man we may expect an affirmation of the rightness of reproduction, and from the depressive and anxious man a denial. But we seek not after an emotional assessment, encumbered by years of psychic baggage, but a rational one.

Without throwing the whole edifice of philosophy into question, I wonder not at the motives of philosophers, but at the breadth of vision they ultimately serve and the conclusions towards which they strive. It has been described as an "abnormal and thus superfluous exercise of the intellect"; if logic and rationality (the intellectual outgrowths of life), when turned inward upon the beings which devised them, yield the conclusion of the intrinsic vanity and futility of life (and therefore also of reasoning - at least of reasoning designed to account for the accomplishment of man's ends), how can we justify the perpetuation of our race?

Science, philosophy and all rational inquiry seem almost of themselves idle pastimes of beings who find themselves, suddenly, existing, without ever having wished to be, and who must do something with this existence so as to distract themselves from its monotony, insipidity, the thousand fold agonies visited upon everyone regardless of fortune, and the tyrannical absurdity of the whole. In this aspect life seems to be a penal colony, wherein our enslavement is an endless expiation of the guilt of our birth - the guilt of the innumerable generations, despite the pain and abasement characterizing their lives, assenting to continue the cyclical tragedies.

If we consider the drive to exploration and conquest the guiding force of procreation - the pursuit of our species of vaster and vaster frontiers of discovery - we subordinate the importance of the lives of all individuals to its realization. Yet, since these individuals are supposedly those who this exploration is ultimately designed to benefit, for whom is their altruism ultimately intended?

If we serve no other master than tireless exploration, expansion and dominance, how do we differ fundamentally from any other opportunistic species? How dissimilar then is the human race from an ant colony? What master do we serve when we strike out for the stars, declaring as our compass "discovery"?

To the entire question "to spawn, or not to spawn", I pose a humanistic syllogism: IF evolution produces in the higher animals greater receptivity to pain ("Pain is the origin of consciousness - Dostoevsky), AND pain is bad, THEN evolution is producing greater and greater quantities and magnitudes of pain THEREFORE life ought not to exist.

It is the "net pleasure vs. net pain" concept: since the net pain potential of this world (i.e., the total ways in which one could suffer and the frequency of this suffering) overwhelmingly outweighs that of its net pleasure potential, everyone - at least, every compassionate and empathic person - must agree that life is better off not existing.

"So just because a lot of life is suffering, that means life doesn't possess its own great pleasures? Doesn't the pursuit of joy and fulfillment justify these sufferings?" That is a matter to be answered on entirely personal terms, and a person cannot answer it 'til she has been born, and lived long enough to comprehend its implications. - - But her parents will already have committed the sin of birthing her, quite without consideration of the potential tragedies they were setting in motion, on nothing more than the gamble that she would answer in the affirmative.

[Quoted liberally and lazily from Schopenhauer]

Tyler Threske

The Philosophy Takeaway 'Open Topic' Issue 34

One axiom in logic for Aristotle’s three laws of thought

Aristotle has propounded three basic laws of thought:

(i)             Law of Identity,

(ii)           Law of Non-Contradiction,

(iii)          Law of Excluded middle.

To my mind these are in fact one law, when expressed in terms of formal logic.  But firstly let me return to my contribution to the previous issue (‘Axioms or Circularity’), where I argued that we needed axioms to avoid arguments which went ‘round and round in circles’.  I stated that we need at least one new axiom if we add a new concept.  Let us informally try this out:

- Negation.  Two negatives make an affirmative.

- One proposition.  p= p, p implies itself, p and ~ p (not p) cannot be true at the same time.

- Two propositions.  If p implies q, then if q is untrue, then p must also be untrue.

- Three propositions.  If p implies q, and q implies r, then p implies r. (transitivity)

My main concern here is with item1 – one proposition – but I would to look a little at items 2 and 3 first. If we look at the question of two propositions, an important concept is that a&b is equivalent to (and indeed implies) b&a.  This is known as commutativity, and of course goes on the tree of logic.  But this is a bit of a red herring: we know that meeting the love of your life and getting married is not the same thing as getting married and meeting the love of your life.  But logicians can show that this is saying the same thing as “If p implies q, then if q is untrue, then p must also be untrue.”  And this is the important thing for reasoning.

Likewise transitivity is important for reasoning:  “If p implies q, and q implies r, then p implies r.”  But associativity is also important for logicians, and also for mathematicians (along with commutativity).  But associativity is likewise a red herring for the layman – and perhaps the non-logician philosopher – since there’s always degrees of association!  Which of course is important for ethics in matters that are not black and white.

 

So both associativity, along with double negation, go on the Tree of Logic.  … :] Well let us now get back to the question of item 1, one proposition, where a proposition is equivalent to itself, implies itself, and cannot be true at the same time as its opposite. Let us look more closely at Aristotle’s three basic laws of thought:

(i)             Law of Identity,

(ii)           Law of Non-Contradiction,

(iii)          Law of Excluded Middle.

The Law of Identity simply states that a=a, where to say p=q means that to say anything about p will always be equally true of q.  Aristotle argues in Metaphysics, Book VII, Part 17, that “the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical…”

The Law of Non-Contradiction states, according to Aristotle, that “one cannot say of something that it is and that it is not in the same respect and at the same time”, and relates to what I stated above, namely that p and ~ p (not p) cannot be true at the same time.  In formal logic this is represented by

~ (p & ~p)

But Aristotle is talking about what things are, so that we consider object x, and property A, we can never have a proposition of the form

~ (Ax & ~Ax)

i.e. x is both A and not A.

Now the Law of the Excluded Middle deals with exactly the same issue as above, but makes clear that if a reference is ambiguous, a proposition may appear to be both true and false at the same time, but there can be no contradiction in addressing the facts themselves.

But in all of this, the axiom ~ (p & ~p) is ever present, either in this form, or in the form  (p É p), p implies p.  For logicians (p É q) is by definition saying the same thing as ~ (p & ~p).  This is not so clear in natural language, since if I consider whether p implies q, then if p is in fact false, our immediate reaction is that we cannot tell.

And “p implies p” is the same thing as “p is equivalent to p” - since equivalence here means that p implies p and  vice versa!

As I said earlier, if we look at formalisms, it is useful to see how they apply to robust argumentation, and here the idea that p implies p can be expanded to the following three principles:

(i)             p is equal to and equivalent to itself,

(ii)           if we say that x is A, x cannot also be not A at the same time,

(iii)          but just to be precise, if we say that x is A, it cannot also be not A at the same time.

Note the very subtle difference between (ii) and (iii).

(iota being the affirmative operator ! )

Martin Prior

The Philosophy Takeaway 'Open Topic' Issue 34

Happy New Year

From all of us at The Philosophy Takeaway, hope you had an exciting Christmas and wishing you all a thought provoking New Year. 

Art by Eliza Veretilo

Art by Eliza Veretilo

The Philosophy Takeaway 'Open Topic' Issue 33

Use what you learn - By: Eliza Veretilo

Use what you learn

                              

                               Life is a lesson. We fall and get up, and when we do get up, we are awarded with a lesson. Every day we learn something new. So this life thing is a constant learning process in which we expand our circle of experience. Don’t agree? Well, you are entitled to it, but much evidence points to it. Our vocabulary inclines to take us from one premise to another in a succession that builds up from what was previously said thus our language and its structure are designed for instruction, for teaching and learning, sharing and listening. Our institutions are the same, we begin at school and parents want their children ‘to learn’. We then go to college, university, and there are learning courses everywhere. In my opinion this idea is somehow flawed. We assume that we learn in the first part of our life and in the second part we use that knowledge. I believe both processes are constantly going on whether we want it or not, simultaneously; but we don’t have such a big element of control. Control is gained with awareness. Planet Earth seems like a big training ground sometimes, of our chosen subjects and of life. Surviving is thus a learning activity, to hopefully, stop making the same mistakes.

                               We learn to thrive in this Universe, with its laws. The extent of our rational analysis still doesn’t change certain laws of nature, such as cause and effect, it can merely understand them. We are responsible for the consequences that stem from our actions and thus we are rational and can become more conscientious of what we do. This is why I propose that people should use all these lessons gathered in life, practically. We think we do, but do we really? We are so keen to learn from other people’s experiences, for example when we hear someone has done something terrible we say ‘Oh but I would never do that!’  Unfortunately, all our education and gathering of experiences still has not sank in deep enough; we don’t usually act on what we know.

                               My proposal is quite simple. Regardless of the economic system, the government and the weather, we could have a much better life if we lived it with awareness. If we took what we constantly learn and used it, instead of turning a blind eye on it or become lazy with our ideals. We would save ourselves and the world much loss and suffering. For example: if you think it’s unethical that when tuna are fished some dolphins get trapped in the nets, well then buy line fished tuna instead. In this world, unfortunately our money has a voice and a vote, so that is a place to apply our principles. This is a small example, but it can be applied to any aspect of life. If we do a little self evaluation, we will find that we do things that we know we know better than doing them. We can change this, by using what we have learnt and keep learning, expanding our world. Both, in how we live our practically and how we live our emotional life and most importantly, on how we treat others. Saying this, using what we have learnt doesn’t mean charity, I believe that one person living an aware life, and acting upon what they believe and have learnt, will have a lifestyle that prevents poverty in the first place. Thus a person living a life well lived is worth more than ten who live a completely upside down life, perpetuator of chaos, and then give money to charity.

                               Constantly adults tell children to apply the lesson they have taught them into their life. We say ‘didn’t you learn that at school’ we say ‘haven’t I taught you that before’ we say ‘you should know better’. But when was the last time we looked at ourselves and said the same things and actually lived by them? We constantly learn new skills; we learn how to use a new phone or how to take a bus to a new place, but our life lessons... do we apply them? Why being aware of what we do? Why are we rational? Because only awareness can reconcile chaos. Thus I say: Use what you learn.

By: Eliza Veretilo

The Philosophy Takeaway 'Open Topic' Issue 33

Let the cries of 'love' die and live - By St.Zagarus

Let the cries of 'love' die and live

I -

Philosophers are supposed to challenge everything. Not just what they know to be false, to build their esteem upon the ruins of the cardboard castles they kick down - but also what they know to be true. Yet if we took philosophers at their word we would be left with only so many hypocrites and cowards, their motives well hidden behind a smoke screen of 'objectivity' (the search for truth removed from any human, or individual bias), when in fact they know precisely where not to look, in case they face contradiction.

  Let us then dive into love, often spoken of which such bittersweet warmth, yet here so cold, as if the words were made of icicles - runes of chill!

Love, nothing could pull us further away from truth. The first love is that of a parent, a love we now call essential. For to be loved is to be able to love - or so say the psychologists! We need love now, all of us children of europe - we have been too far pulled in to christian morality to ever turn back (see the prophet-philosopher Nietzsche for more of this). This need for the parent to love the child they would like to think was universal for our species - this is not so. What of the tribe who raises their children in darkened huts without human company?

II -

Love thyself - What is there to love of the actual physical body - at worst a grotesque bag of flesh, at best a neutral beauty no more sightly than a moon or a grove, granted extra emphasis by the vanity that we too are possessed of one. Or perhaps the soul is worthy of love, that corrupt thing easily swayed, that lies to itself and those around it habitually, such that meeting an honest one is enough to make us feel like we live a charmed life! How have we allowed the soul to grow warm when there is nothing colder than it, being as it is a mere mirror with which nature may see itself.

Love thy neighbour? Where do we gain the warrant to trample on anothers individual rights to be left alone, or ignored, or generally not considered very much!

Love thy nation - so often uttered by 'hard nosed realists' - yes the same ones who adhere to invisible boundaries of law and culture, beneath their vainly fluttering flags.

Love thy god - a personal connection, a father for those hopelessly in need for the perfect parent, how desperate! A pitious grasping out into a cold cosmos in search for something all powerful and inhuman, yet human!

Love thy cola - when a capitalist is onto something, we know how easily such a thing can manipulate people - love this liquid, love this combination of metal and plastic, love this motorized car!

Love thy ruler - the captain, the duke, the charismatic general, the high-priest, the witch-doctor, himself void of character and desperate for the mass adoration of his little lovers.

And perhaps the ultimate vanity, the grandest insult to a concept that may otherwise had held some power - unconditional love. The love of dog for master, debasing even for a canine! In a human it is worse to the factor of ten times - what more is it then the need for a perfect port in which to lay anchor, a hopeless reflection of ones own need for perfection-on-earth, a desire to escape ones solitude to find solace in another person, as a foetus does a womb. Yet what a vanity it is, for who deserves to be loved without condition - no one!  And mark this - if one expects the same in return, to try and mould the other into a lover unconditional, then what utter vanity and further self-seeking, what doubled-over wretchedness!

III -

An old mood passes, replaced with the new. Can any philosopher ever escape their emotion, for the true crystal plane of reason?

  Love is incredible, irresistable. If has softened the hearts of the warrior age and brought about our expectations to protect all people - at least to a basic, realistic degree. Love of one another is all we have to cling to. Beyond each other, we can also love ideas (being moved by them in the same way as any other passion), art, music, our crafts - we can love all of these immaterial things.

  You can try and resist love - you will fail. The cold-heart melts or else it fights a constant battle against itself - even if the coldness wins, that tortured character still asks 'what would it have meant to have loved?' and this question will spin through their memory until they perish once and for all.

  The words said against love were just that; words, an interesting flight of thoughts. The great haters with their great venom were unloved, and rather than move toward the healing heat, they retreated further into the shadows by renouncing that which they never dared to grasp themselves.

By St.Zagarus

The Philosophy Takeaway 'Open Topic' Issue 33

A question from the Hat O'Wisdom - By Daniel

A question from the Hat O'Wisdom -

Is an idea more 'real' than the material?

It would be quite easy to answer this question from an existentialist point-of-view and, truth be told, that was to be the source of my initial answer. However, upon further consideration, I do not think that the question can be 'brushed aside' quite so easily.

I am of the opinion that an idea, having been created at a subconscious or conscious level, can be more real to an individual than the material. I think anything that is created by an individual will always have strong connections to its maker, be the connections tangible or intangible/material or immaterial. Such connections will make an idea real by instilling, within its creator, associated emotions and sensations. If the material is defined by signals sent to and interpreted by the brain, then signals containing idea-associated emotions and sensations can be just as real as the material. The question of being more real than the material, I believe, is entirely dependent upon the individual's need, or want, to maintain their emotive associations to their idea. For example: if a poverty-striken child has an idea that they believe could transform their poverty into financial wealth, then it is quite possible that the hope they associate with their idea could be of such a magnitude to make it, for them, more real than the material and possibly more real than their present. Similarly, a playwright creating a new script will mentally visualise their idea and obsess over it before it takes any material form: it is quite possible that, at this moment, the playwright's idea is far more 'real' to them than the physical/material staging of their play.

The area of intellectual copyright law has an interesting view on this topic. It is stated in UK law that an intellectual work is protected by copyright once it is recorded in a tangible form. However, this is merely to prove ownership of the creation, there is nothing to say that the idea/creation is not real before it is recorded.

By Daniel

The Philosophy Takeaway 'Open Topic' Issue 33

Merry christmas

Merry Christmas from all of us at the Philosophy Takeaway

Axioms or circularity - By Martin Prior

Axioms or circularity

When I was at primary school I had a special dictionary for schools and I wanted to find the meaning of a word A.  Well the dictionary told me it meant B.  But what did B mean?  Well the dictionary said that B meant A.  So I asked my parents and they were most irritated and clearly felt I should show more initiative.  Deadlock.

In an earlier Issue I argued that the purpose of life is love but that the purpose of love is life, so that anyone seeking the purpose of life would simply go round in circles:

 

Well, this won’t do for argumentation, and we have heard the accusation that certain arguments are circular.  Thus some people will say that abortion is murder.  So how do you define murder?  Oh, to include abortion.  We are in fact on a better path if we say that life is sacred, since as long as you can define life - i.e. what is the meaning of ‘life’ as opposed to what is the meaning of life – then you are on firmer ground, but nobody can argue with you.

So in logic, one builds on axioms, things we take as given.  In fact I myself spent 20 years of my life working as a statistician.  And within the various argumentations of statistics, one thing is left undefined, and that is probability itself.  Or at least that was the case nearly 50 years ago when I first studied statistics.  Such undefined  items are known as ‘primitives’.

We may note that relatable to axioms are theorems: propositions that may be proved from axioms (and/or existing theorems) .  Now if I have a formula containing expressions such as  (a+b), ab, (a Ù b), etc, we have a principle of uniform substitutability.  Because all of these operators are commutative, we can replace them with their ‘back-to-front’, i.e. commute them.  We may do this in a system which has an axiom or theorem of the form  (a.b) = (b.a), but we must do so consistently.

Another rule is that if we know (i) that A is always true, and (ii) A implies B, then B must always be true.  This is the rule of Detachment (or in Latin Modus Ponens).  Some logicians do without this rule.

Now all logicians agree that when proving things, one must build up axioms from ‘primitives’ and definitions.  One usually has two primitives, such as ‘not’ and ‘or’.  This was the starting point of Bertrand Russell and P.H. Whitehead in their Principia Mathematica.  Mordechaj Wajsberg on the other hand, produced several systems including one in which implication and falsity were taken as primitive.

But let us tabulate all this:

Tarski, Bernays, and Wajsberg, ‘basis 1’, 1937

Note that axioms may be built up depending on how many variables or separate propositions they involve: if an axiom involves one variable, generally you cannot say anything about a proposition with two variables, etc. 

But maybe we have a circularity here as well: for logic you have to turn to philosophy for its axioms and ‘primitives’.  Look at that primitive falsehood!  But philosophy cannot proceed without being logical!

By Martin Prior

References

Hackstaff, L.H. (1966)  Systems of Formal Logic. D. Reidel Publishing, 1966.

Wajsberg, Mordechaj (1937-9) “Metalogische Beiträge”  In: Wiadomości Matematyczne Volumes 43 (1937) and 47 (1939), translated by McCall and (partly) P. Woodruff  in Contributions to Metalogic (1967).

Whitehead, Alfred North and Bertrand Russell (1910)  Principia Mathematica.  Cambridge: Cambridge University Press.

The Philosophy Takeaway 'Open Topic' Issue 33

Art - By Eliza Veretilo

Art - By Eliza Veretilo


The Philosophy Takeaway 'Open Topic' Issue 32