It is said that mathematical axioms are neither true or false, but that they infers/imply their conclusions, and this is said by those with formalist leanings .


Will you not agree that if this is true, then it means that mathematics is based on unsound arguments if the axioms so used are false. And rarely do mathematical physicist check to see whether their axioms are true, rather they device a theory that fits(predicts) experiments(think Bohr model of the atom). It seem science uses this kind of reasoning a lot. There are no point particles nor isolated systems as envisioned by Newtons laws, yet these are foundations of classical mechanics. So there seem to be something false used to deduce something true. It seems unsound reasoning is pervasive in science, and I ask why should it be an issue especially in religious arguments? Why can’t we construct religious arguments using some hypothesis regardless of its truth.
–Johnson Mafoko

This is a much more interesting and complex question than your first. The basic concept is something I’ve studied for years, but unfortunately it is less straightforward than it seems at first.

You’re actually talking about two separate things, axiomatic systems and modeling.

In terms of the first, axioms are the starting point for any formal system. They are not considered “true” or “false” because truth is defined in relationship to the axioms.

When you say something is “true” in a formal system, what you really mean is that it is at least as guaranteed as the axioms.

In the case of mathematical systems such as Euclidian geometry, there is no necessary claim that the objects of the system have any physical reality, they exist only within the conceptual space defined by the axioms.

Physics, however, adds an additional claim that a given mathematical system “models” something real in the physical universe. In other words, if the mathematical system describes a certain numerical relationship between a triangle and a square, the claim is that a physical object in the shape of a triangle would have the same relationship with a physical object in the shape of a square.

It’s never a perfect match, and there is no way to definitively prove that the physical system follows all the same rules as it’s mathematical sibling. All that can be done is show by experiment that the measurements predicted by the mathematical system mirror the actual results produced by testing the physical system.

The advantage to all of this is that understanding the mathematical system allows you to make useful predictions about the physical system. For instance, the development of calculus allowed people to aim cannons with much greater accuracy. It was the practical results that convinced people of calculus’ worth, not because they had a metaphysical belief in infinitesimals. People tend to speak of scientific discoveries as if they were solid eternal truths, but what they really are is sets of tested, reliable, useful predictions.

Let me return to your query of why you can’t start from an unsure axiom and build towards a true conclusion when constructing a religious argument. You can certainly build a mathematics-like axiomatic theory of religion –many philosophers have done so. But none have had much success in showing that their system is a testable, reliable analog of the observable world.

For instance, in the Hindu religion, they believe in a system of karma where good deeds and bad deeds lead to rebirth in a better or worse existence. However, there is no good way to test the theory of karma, since one cannot –at least to my knowledge –reliably establish whether a given person is the reborn version of another one.

I myself am deeply interested in creating a testable, reliable theory of morality that aligns with my religious and metaphysical commitments. But it is far from being an easy task.

Art

Fourth in a series on ending war.

Art may seem like a odd substitute for War, but there’s reason to not dismiss the idea out of hand.  We already know that Art can be a powerful economic engine, legions of starving artists and musicians notwithstanding.  For proof just look at the movie and music industries.  What may be more of surprise is that Art has played a role on the battlefield as well.  In the days of the Roman Empire –which lasted for well over a thousand years –conquered cultures were kept in thrall to the Empire as much by the superiority of Roman art and culture as by the threat of force.  As much as having Roman overlords may have rankled, few barbarians truly wished to trade in their refined Roman existence for a return to crude tribal living.  Similarly, on the other side of the world, the Chinese Empire survived being repeatedly invaded and conquered by barbarian hordes because Chinese art and culture were so advanced that the invaders inevitably assimilated into the host culture instead of the other way around, as the physical conquerors became the culturally conquered.

But how does Art do versus our criteria?

  1. It makes jobs that challenge individuals and nations to their limits:  The answer here is both yes and no.  No, certainly, with regards to nations –no country faces its greatest challenge in maintaining itself at the cutting edge of artistic advance.   Yes, on occasion, with regards to individuals.  True, a hobbyist painter or casual guitar player isn’t experiencing much of a challenge, but dance and acrobatics challenge the physical limits of the human body, special-effects laden movies challenge the limits of technology, conceptual art challenges the intellect, “diva” songs challenge the human vocal range, and so forth and so on.  Any artist at the top of their field is probably at or near the limits of what is humanly possible in one way or another.
  2. It distributes jobs:  Here we find a deficiency.  There’s no real structure to distribute Art jobs in the way we found in other ECS candidates.  Furthermore, as with Sport, we’ve become segregated into producers and consumers with regards to Art.  Legions of musicians and artists starve while a small handful of celebrity entertainers serve as the primary artists in the lives of millions.  This is a trend that would need to be reversed before Art could actually serve as a legitimate Employment-Creation System (ECS).
  3. It makes jobs meaningful by:
    1. serving as a test of ideologies:  Here art does surprisingly well.  Didactic art, which explicitly promotes a given ideology, is rarely a success, but every piece of art, no matter how innocuous it may seem, presupposes some philosophy, some viewpoint about the world.  The way an artist solves artistic problems actually says a great deal about his or her views on how to solve general problems of life.  In addition, art cannot be as easily alienated as technology.  You can imitate a foreign art form, but you cannot create valid original work in the same vein until you internalize the ideology that gave birth to the artwork in the first place
    2. being definitive:  The killer subclause strikes again.  An artistic triumph cannot be definitive in the same way as a physical triumph, because Art is too subjective.  There is no common standard for Art, and no two observers can be relied upon to agree at all times on the merits of any piece of art.  Each region prefers its own art, yet even two siblings who grew up in the same household can have opposite artistic tastes.

Things seem bleak.  With Art, Science and Sport all striking out as potential substitutes, we are left stuck with War and Consumerism as the dysfunctional institutions that are destroying us, but that we cannot do without.

And so this is the end.  Or is it?  If a natural substitute for War and/or Consumerism existed, it would likely already be in use.  But what about a synthetic substitute?  Each of our candidates was strong in some areas, and weak in others.  Could we add together the best of each, and create a new system capable of getting the job done?

We’ll take a moment next week to explore the nature of identity, and then return in two weeks to see whether or not we can go ahead and construct a synthetic Employment-Creation System capable both of rescuing Capitalism and putting an end to War.

NEXT WEEK:  Identity

Why War Must End

War has been a feature of human existence throughout all human history.  As each war ends, each generation swears never again to beat the drums of war, and yet like any addict, the human race keeps coming back, over and over again.  And yet, something fundamental has changed, and within our own lifetimes.  This change has made it imperative that War must be ended once and for all, and in the very near future, if humanity is to have any chance of survival.

The change that has taken place in war has to do with technology.  Technology grows in power and reach at an ever increasing rate.  In particular, when it comes to weaponry and other technologies of destruction, the power to kills larger and larger numbers of people in less and less time is placed every year in the hands of a wider and wider circle of people.  With everything from biological warfare to nuclear explosives falling into the hands of terrorists, and with everything from bomb-making equipment to machine guns becoming readily available to average citizens, technology has made our world a very precarious place indeed.  And yet during the same time,  humanity has not experienced any great, worldwide moral leap forward that would allow us to shepherd such technology wisely, safely and with mercy.

“Ever-More Powerful Weapons”  X  “Neither Wiser Nor Better”  = “Inevitable Self-Annihilation”

So is there no solution?  The genie cannot be put back in the bottle, the advance of technology cannot be arrested.  But the direction of technological progress is in our hands.  As long as War remains a key feature of our mutual existence, technologies of destruction will continue to advance.  But if War can be eliminated, the development of new technology may shift towards more positive and peaceful objectives.

Given that we started this series of posts looking at the problem of unemployment, and that we’ve ended, not by solving it, but by taking on another, even more intractable problem, it may seem as though we’ve made no progress.  However, we’ve actually discovered something very important:  War is a wonderful employer, but it is killing us as a species –literally as well as figuratively.  So if can find something that will substitute for war without the downside of war, we will also have found our substitute for Consumerism –and our answer to the problem of unemployment as well.

Next week we’ll take a break to discuss the nature of reality, and then resume in two weeks with a new series on what it will take to solve the problem of war.

How can primary and secondary reflection, allow us to experience the world profoundly, and proffer a genuine sense of freedom?

“Primary” and “Secondary Reflection” are concepts from the work of Christian Existentialist Gabriel Marcel. To provide a rough and inaccurate summary, primary reflection is the initial attempt to mentally apprehend an external reality as something foreign and separate, whereas secondary reflection is considers the subject as part of the larger whole within which the observer and the observed are neither separate nor separable.

From an existential point of view, when we view the world as made up of external objects distanced from ourselves, we lose awareness of our ability to influence the reality seemingly composed by such objects. It is only when we understand the extent to which personal identity extends outwards into the world that we embrace our freedom to shape the reality in which we live.

To my regret and shame, I must admit that I am no scholar of Marcel’s work –an unforgivable omission for a Christian Existentialist such as myself –so much of what I have said may be untrue to his original vision. If this is a topic that interests you, I recommend you consult his works, of which The Mystery of Being is one of the most famous.