## Calculating. Without calculating.

Engineers have designed a metamaterial device that can solve integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the device’s unique structure manipulates the wave in such a way that it exits encoded with the solution to a pre-set integral equation for that arbitrary input. (1)

Calculating. Based on rules.

Rules imposed by humans.

Humans thinking.

Thinking based on logic.

Logic based on axioms.

Axioms based on nothing.

Calculating.

So irrational.

So wise…

## Gödel’s incompleteness theorem: The non-Cretan way out…

Gödel’s incompleteness theorem is well known for proving that the dream of most mathematicians to formulate foundations for a complete and self-consistent theory of mathematics is a futile exercise.

Gödel proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency (1).

In essence, the incompleteness syllogism by Gödel starts from talking abour logical propositions (or mathematical propositions if you like) and ends up with a proposition that talks about the validity of… itself. This proposition which we might as well call reads something like “I cannot be proved”.

If it can be proved, then it means that it cannot.

And vice versa.

So it is essentially a logically true proposition (since indeed it cannot be proved) but which cannot actually be proved within the axiomatic system at hand.

Hence, the incompleteness.

Essentially this is something the ancient Greeks have thought of thousands of years ago; something which they formulated in the famous Epimenides paradox. Epimenides was a man from Crete who said the following simple thing: “All Cretana are liars”.

Well, this ends up in the same dead-end as the proposition mentioned above. If Epimenides is truthful, then he is a liar since he is Cretan and all Cretes are liars. If he is a liar, then he is telling the truth! And, thus, he is a liar!

A self-reference paradox which essentially destroys the hope of mathematicians around the world for a consistent and full way to formulate mathematics. It is weird, but also important to mention here, that self-reference is the basis of our existence. Consciousness, our ability to speak about our self and our own existence and being, is the foundation of our essence as human beings. Without that, we would be nothing than complex machines.

But how can this dead-end be surpassed or perhaps by-passed?

Well, it cannot actually.

Unless…

You ctu right through it.

I was in a discussion the other day about the above topics and when the Epimenides paradox was mentioned, one immediate reaction that I got was the simple “So the solution is that he is not from Crete” (!)

What?! I answered. But I told you he was a Cretan.

Sure. He was.

But…

What is he wasn’t?

Then there wouldn’t be any paradox!

In the same sense…

What if the logical proposition…

“I am false”

is not a… proposition?

Then all problems would be solved!

But if it is not a logical or mathematical proposition then what is it? Well, as I said above, self-reference is not mathematics per se. It is more of a metaphysical reference to existence and being. A proposition talking about… itself is no more a proposition but an attempt to speak with the abyss. It is more God talking to humans than humans trying to talk with God. Such a thing could be many things, but ‘simply’ a logical (mathematical) proposition not.

But this is gibberish, one might counter-argue.

Sure, it can be.

(Gibberish like the Russel way out of his paradox?)

If you really think a Cretan would ever call himself a liar.

Sure, it can be.

If you accept that a proposion can ever referto itself.

But it cannot.

In a cosmos where only humans can talk for themselves.

Gibberish.

In a cosmos where mathematics cannot prove themselves.

Gibberish.

In a world where endless-loop paradoxes exist.

In a life which is full with nothing but them.

Paradoxes were the end of the hopes of mathematicians. They alone can be the ones which will instil hope in the once again.

Look around Cretan.

Tell me.

If you cannot prove that there is a sea…

Will you ever lie that you are swimming?

In all your life, have you ever seen a raven that wasn’t black? That probably leads you to conclude that all ravens are black. Of course, it’s impossible to see every raven that ever existed and ever will exist, but from the evidence you have on hand, it’s pretty fair for you to make the statement, “All ravens are black.” Put into a logical form, the argument looks like this:

Proposition 1: All ravens are black.

Evidence 1: This raven is black.

According to logic, the statement “All ravens are black” has the equivalent form “All non-black things are non-ravens” — or in regular English, “Everything that isn’t black isn’t a raven.” The same way that every black raven you see supports your first conclusion, every non-black non-raven you see (A green apple! A school bus! A Smurf!) supports it, too. This builds upon our argument like this:

Proposition 1: All ravens are black.

Proposition 2: All non-black things are non-ravens.

Evidence 1: This raven is black.

Evidence 2: This green apple is not a raven.

Though the raven example is almost absurdly simple, the paradox itself highlights a potential issue with the scientific method. Does every piece of evidence — even a piece of evidence unrelated to your topic (e.g. ravens) — really support your hypothesis, just because it doesn’t contradict it? Is the scientific method taking us into fallacious territory?

Ultimately, though, many argue the raven paradox isn’t so paradoxical. Though it doesn’t jibe with our intuition that a green apple would have a bearing on raven’s hue, that’s a problem with our intuition. A green apple does provide an almost imperceptible grain of support for the “All ravens are black” hypothesis. A black raven just provides a lot more. (1)

We all try to find evidence to support our views.

Trying to prove God exists.

But He does not need evidence.

He simply is.

And the evidence is all around us.

Even when they are not.

Or better: especially when there are not.

Oh…

Look at that raven…

Yes, there is a God.

Look at all the evidence against Him…

## Credo!

Tertullian is widely regarded as having originated the expression “Credo quia absurdum” (est) (I believe because it is absurd) and the phrase often appears in contemporary polemics about the rationality of religious belief. Patristic scholars have long pointed out that Tertullian never said this or meant anything like it. (although as I have explained many times in Harmonia Philosophica, there is nothing wrong with the irrational – it is the logical which is unfounded and full of fallacies) However, little scholarly attention has been paid to the circumstances in which this specific phrase came into existence and why, in spite of its dubious provenance, it continues to be regarded by many as a legitimate characterization of religious faith. A new paper shows how Tertullian’s original expression – “It is certain, because impossible” – was first misrepresented and modified in the early modern period. In seventeenth century England a “credo” version – I believe because it is impossible – became the common form of Tertullian’s maxim. A further modification, building on the first, was effected by the Enlightenment philosophe Voltaire, who added the “absurdity condition” and gave us the modern version of the paradox: I believe because it is absurd. These modifications played a significant role in Enlightenment representations of religion as irrational, and signal the beginning of a new understanding of faith as an epistemic vice. This doubtful maxim continues to play a role in debates about the cognitive status of religious faith, and its failure to succumb to the historical evidence against it is owing to its ongoing rhetorical usefulness in such debates. (1)

People once understood the irrationality of existence.

Then they invented Logic.

And they tried to formulate logical ways to believe in God. Let’s not forget that the founder of Logic believed in the Unmoved Mover. And the second greatest logician of all times (Gödel) formulated a renowned proof for the existence of God.

Then came “Enlightenment”.

And tried to convince people that logic has nothing to do with irrational things like religion. That rational people cannot believe in absurd things like the soul, the spirit, Jesus or God.

They were both wrong.

Logic itself is absurd and irrational. Based on axioms selected arbitrarily, without any solid foundation whatsoever. The only thing we know for sure about any set of axiomatic theories – logic included – is that it cannot prove everything.

Life IS absurd and irrational. We exist without reason, we die without reason, we love and hate with no reason, we just Are. Any attempt to rationalize life will hit the wall of reality and collapse as soon as it started.

So believe what you want.

No you are not irrational.

Because there is no such thing as “rational”…

## Why live? The irrationality of life and the futility of logic.

A liberal feminist exploded live on TV some time ago and this much hatred in one person is so rare to see. Katie Hopkins, well know British feminist crossed the line and said some awful things, including demanding euthanasia for the old people…

“We just have far too many old people. It’s ridiculous to be living in a country where we can put dogs to sleep but not people. Euthanasia vans – just like ice-cream vans – that would come to you home. It would all be perfectly charming. They might even have a nice little tune they’d play. I mean this genuinely. I’m super-keen on euthanasia vans. We need to accept that just because medial advances mean we can live longer, it’s not necessarily the right thing to do”. (1)

This is not something weird or an isolated event. We see this kind of thinking constantly. Some people are like this. Trying to find logical explanations for everything. Trying to find reason and rational arguments for anything.

Which means…

Trying to find “logical” reasons for someone to live.

Trying to find rational arguments for someone to still exist.

But there are no such arguments.

Life is not rational. Existence is not logical. Our very nature is illogical, irrational, tragic and deeply metaphysical. And you cannot uphold the miracle of life unless you actually believe it is a miracle. The rational way of thinking leads straight to death.

Ω γλυκύ μου έαρ…

Γλυκύτατο μου τέκνο…

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