Axioms 

An axiom is a proposition that must be true without proof. Otherwise, nothing else can be proved. To prove anything, you need to posit an axiom that cannot be proved and that can serve as the foundation for other deductions. You can’t prove that points A and B are connected by a distinct line unless you assume the axiom:  for every two distinct points, there exists exactly one line that contains both of them. Unless you posit at least one axiom, reasoning never gets off the ground. You will land in an infinite regress, like the child wanting to know what an apple is:

It is a fruit.

What is a fruit?

A fruit is the sweet and fleshy product of a tree or other plant that contains seed and can be eaten as food.

What is a tree, plant, and food?

Etc.

There has to be something known to bring this chain to an end.

 . . .

     We have unquestioned core convictions about what the world is – more or less conscious. They function like axioms or primitive definitions in our thinking and feeling. Upon them, world versions are built. At least two sorts of axiomatic core convictions. One grounds the life world we live in. I am expressing these mostly taken-for-granted beliefs as though they were axioms in a logical system.

  The first set consists of axioms no sane human being could deny no matter from what culture or historical epoch. For example,      

• I was born and I will die.
• The world was here before me.
• If I don’t eat and drink, I will die.
• Things don’t just happen without some cause.
• I need air to breath.
• Children are conceived through sex.
• Babies grow into children; children into adults.
• Adults age and die.
• P cannot be both true and not-true in the same sense of P.
•  If p is true, then not-p cannot be true.

 A second set goes almost as deep but expresses a core understanding of what it is to be human at all.

•         We should give a newborn baby a name and not a number.
•         A pig is sentient.
•         A rock is not sentient.
•         All things being equal, it is better to be pain-free than in pain.
•         All things being equal, it is better to be alive than not be alive.
•         Death is to be feared, all things being equal.

You could keep expanding the list of axioms for a long time. Such axioms, again, are the product of being socialized in our world. They are rarely the result of conscious reflection or argument. They are like what is under the surface of the metaphorical iceberg, our consciousness being only the tip of that iceberg. They can be called into question, however. Socrates perplexed his contemporaries because he lived as though death were not to be feared, and even made arguments to back up his life. 

    Just touching the surface of the water is a third set of axioms peculiar to each one of us. These are facts and judgments, beliefs and convictions that we cannot doubt.

•         My name is Gary.
•         I was born in Owensboro, Kentucky, in 1959.
•         My parents were James and Verna.
•         They loved me.·        
•     They took care of me when I couldn’t take care of myself.
•         I regret not being a better brother.

Finally, there is a fourth set, what I consider metaphysical axioms. They are intimately connected to the first two sets, though conscious reasoning may be more active here:

•         The universe has no intrinsic value.
•         The universe is dead matter and energy.
•         The universe is indifferent to human aspirations.
•         There is no Creator of the universe.
•         The universe is an accident.
•         Human consciousness is an accident.
•         Life is a tale told by an idiot, full of sound and fury, signifying nothing.
•         Value, love – sentimental projections onto an indifferent background.
•         For every effect, there is a physical cause explainable by science.
•         Nothing is real except matter/energy as these phenomena are understood by our best science.

 There may be harmony between these sets of axioms or not, or contradictions internal to them. For example, within metaphysical axioms, the belief that the universe was without inherent value would conflict with a belief that my love for a person was not a sentimental projection. If I love a person and that love is a response to the person, then at least one thing that exists in the universe has inherent value. I cannot logically maintain both axioms. Translated, I would suffer a lack of inner peace if I believed both things at the same time.  In my examples, the entire set of metaphysical axioms would conflict with “we should give a newborn baby a name and not a number” from the first set, and “my parents loved me” from the second. We live with such contradictions, of course, but have cognitive dissonance from them at some level.

     If our world version were just coherent and nothing else, we would all still be cut off from reality, living in our own virtual reality. Our world versions must make some sense of the world, must disclose reality in some way. This is not at all clear. As I love many things, as I have known great beauty, as I have on rare occasions been visited by joy, I cannot believe the metaphysical axioms I listed above. They would make these formative experiences into illusions. To keep them, to believe that they disclose reality rather than project sentimental feelings onto it, I must reject those axioms. But I must also believe that my loves are appropriate responses to a reality that cannot be reduced to what I would like to believe. Indeed, the idea of Creation is part of a world version in which these formative experiences can  disclose reality. I might lose my belief in Creation someday, but I can’t imagine taking over beliefs that would negate my experiences, which are the most real for me. If I came to reject the Idea of Creation then only because some other Idea makes better sense of what I cannot doubt without losing myself – the axioms in the second set included.

     World versions – the sets of a person’s axiomatic convictions, beliefs, judgments, or values (always filtered through the world or form of life the person is part of) – are what we accept as given under normal circumstances. We reason based on the axioms that make up our world version.

   That implies that we do not come to our core convictions through a chain of logical reasoning.  If x is self-evident to me, but not to you, well, rationally, logically, we are stuck – but only rationally, logically, abstractly. We have a common ground to stand on – life, those axioms neither of us can deny, and those overlapping ones that we share. That makes a kind of human, finite, fallible reason possible.

      If x is an axiom for me but not for you, then we cannot reason together except in this fashion. No scientific experiment, no empirical method can prove that the universe as a whole is meaningless and without intrinsic value. No mathematical-logical proof can prove that either without assuming as axioms the very beliefs that are in question. I cannot prove to you that x is an axiom any more than you can prove that x is not an axiom. It either fits in with the massive web of axiomatic beliefs, judgments, values, etc. that informs your thinking – or not. And thus with your formative (prägende) life experiences – or not. No metaphysical starting point can be proved – though such starting points are limited by the first category of beliefs. A metaphysical starting point that denied our mortality would be a non-starter.

    Indeed, life forces most axioms on us. We wouldn’t know what to do with a person who denied that we are mortal or denied that we are born. No one is completely cut off from another, epistemologically – unless we are dealing with severe insanity.

    And as our lives are different, at the upper levels different things may be forced on us through our loves, joys, sorrows, sufferings, traumas. The axioms that go deep in us usually have their source in prägende (formative) experiences. Sublime experiences of joy or terror, for example. These may or may not be considered “subjective.” They may or may not disclose aspects of reality. For me – just like thoughts – they may tell us more about ourselves than reality. But they may also, when free of the “fat, relentless ego” (Murdoch), disclose reality. Depends on your core convictions – which must make sense of all the core axiomatic convictions as a whole, that is, of your life and world version as a whole.

 . . .

    This is important to me because if it were true –  provable – what my friend said (in a certain mood; it doesn’t represent his final thinking), then all my axiomatic convictions would be false and I would have to accept the sad truth that I have been living in a sentimental bubble. There would be no conceptual space for hope, faith, and love. There would be no conceptual space to deny what the young C. S. Lewis believed true:

Such, then, was the state of my imaginative life; over against it stood the life of my intellect. The two hemispheres of my mind were in the sharpest contrast. On the one side a many-islanded sea of poetry and myth; on the other a glib and shallow “rationalism.” Nearly all that I loved I believed to be imaginary; nearly all that I believed to be real I thought grim and meaningless.

The dark possibility expressed here is not a fact of life. It depended, as Lewis recognized, on a particular world version that elevates science and logic to the status of religion, which of course is absurd because it contradicts axioms internal to science and logic. I can believe every proposition of science and my core convictions would not be affected at all. As Wittgenstein wrote:

We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all.

If a person makes a religion out of science and logic, it is not because Reason forced that conclusion on them. It is for the same reason that I reject that possibility: namely, that it is in tune without our deepest fears, hopes, and joys; or more sadly and superficially, with the requirements of the “fat, relentless ego” to elevate itself over other egos.

     We buy hope, faith, love at the price of the necessity of believing through hope, faith, love. We may hope only because we may have no certainty in a purely logical-rational sense. A limited skepticism is our friend. We live from hope, faith, love – or die from the lack thereof. The human condition.