Do you believe in miracles?

[Age]

It is no co-incidence that the more we understand science, the instances of reported miracles has declined.

We understand the foundations of the natural numbers completely. Still, inexplicable truths are a fundamental part of true arithmetic. No amount of better understanding of arithmetic will make them go away.

Will you please provide some actual examples, so that we have some things to actually 'look at' and 'discuss'?

To me, so-called 'inexplicable truths' sound just like an oxymoron.

https://en.m.wikipedia.org/wiki/True_arithmetic
In mathematical logic, true arithmetic is the set of all true first-order statements about the arithmetic of natural numbers.

It took until 1931 for Kurt Godel to discover the existence of inexplicable truths in true arithmetic. It is obviously not possible to derive an inexplicable truth from the theory. It is only possible to derive from the theory that they exist.

We do have a few examples, such as Goldstein's theorem, which is inexplicable in arithmetic theory.

What, exactly, do you think or believe is, supposedly, 'inexplicable' in some so-called 'arithmetic theory'?

It is provable from set theory, however, when including the axiom of infinity:

What is the 'it' word here even referring to, exactly?

https://en.m.wikipedia.org/wiki/Goodstein%27s_theorem
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944 ... This was the third example of a true statement about natural numbers that is unprovable in Peano arithmetic, after the examples provided by Gödel's incompleteness theorem and Gerhard Gentzen's 1943 direct proof of the unprovability of ε0-induction in Peano arithmetic.

Using words in such a way that they come across as 'inexplicable' to explain, is nothing new or uncommon even, well in the days when this is being written. But, that kind of usage of words is not actually saying nor proving any actual thing, actually.

A truth that is inexplicable

Again, well to me anyway, saying that, 'A truth is inexplicable', is just an oxymoron, and/or just 'moronic nonsense'.

If some thing is 'inexplicable' then how would absolutely any one know that 'that thing' is 'a truth'?

unless you introduce the axiom of infinity is actually an exceptional special case.

Do you mean 'special case', as in like a 'mental case'?

1. Provide an example of a so-called 'truth, that is, supposedly, inexplicable'.

2. After you have done this, then show how by, supposedly, introducing 'infinity', it is then a so-called 'exceptional special case' and a so-called supposed 'exceptional special case' regards to 'what', exactly?

3. Also, explain in what definition/usage of the 'axiom' word you are actually referring to and using here.

4. Then will you please explain how you are defining the 'miracle' word here, and how 'numbers', themselves, relate to your own definition of the 'miracle' word here?

The standard case is that no additional axioms could ever explain such inexplicable truth.

To me anyway, what you say here is absolutely nothing and just a form of 'circular reasoning'.

The word 'axiom', in just two of the multitude of definitions can be, an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. Which, in itself, means or says nothing at all really, again, well to me anyway.

So, if the so-called 'standard case', is that no additional, 'unprovable rule or first principle accepted as true, because it is self-evident, or because it is particularly useful', could ever explain such a so-called and self-proclaimed 'inexplicable truth', then what is 'it' that you are really trying to say and get at it here, exactly?

Again, and if you did not above, just provide what you consider to be a so-called 'inexplicable truth' to you, here now. Because for all we know what is a so-called 'inexplicable truth', to you, has already been explained, and well understood, to us already.

There are no miracles. Simple as.

It is certainly not that simple.

Inexplicable truths exist in true arithmetic.

The words, 'inexplicable truths', in so-called 'true arithmetic', sounds like some so-called "mathematician" just could not 'work out', 'figure out', nor resolve some mathematical problem or equation.

But I still wonder why they consider 'it', [whatever it is], to be 'a truth', in the first place?

Stephen Hawking concluded

you speak as though this human being is some sort of God, Allah, or Spiritual Enlightener.

you adult human beings conclude a lot of things that are False, Wrong, Inaccurate, and Incorrect. One only has to 'look into' a forum like this one here to 'see' this, very clearly.

that they therefore also exist in the physical universe.

So, some human being concluded that 'they', [so-called 'inexplicable truths'], exist in the 'physical universe', just because so-called 'inexplicable truths', supposedly, exist in some so-called 'true arithmetic'.

If you want any human being to accept 'this' here I suggest:

1. you explain what so-called 'true arithmetic' even is, exactly? And, explain how 'that' is different from 'false arithmetic'.

2. Start providing examples of so-called 'inexplicable truths'. So, we can 'look at' and 'see' if they are actually 'inexplicable' forever more, or if they are just 'inexplicable' to you, in your very tiny time of existing.

3. Start explaining how you 'know' some thing is 'true' before you can even explain 'that thing'.

4. If you are, more or less, just trying to argue that there are some things, which appear true, like, for example, that a Universe exists, or that there is some thing, existing, which is 'conscious', but which the 'why' of has not, yet, been explained to a particular group of human beings at some particular moment in Existence, Itself, then I will just say, 'Obviously'.

5. If anyone wants to consider what they have not yet become privy to, as 'a miracle', then so be it. But all so-called 'miracles', or for absolutely all things that actually happen/ed, and occur/ed, then they can all be 'explained'. And, far more easily and simply than is and was being imagined by you adult human beings, in the 'olden days', when this is/was being written.

And to prove this true, then just start listing things which, appear and seem, inexplicable to you.

Of course, Hawking could not prove his hypothesis, no matter how reasonable.

Once again, another example of how and way 'hypothesizing' was, and still is, just a waste.

The actual irrefutable Truth of things is much easier, simpler, and quicker to find, uncover, know, and understand, than it is to theorize and/or hypothesize 'about' things, and then spend hours, weeks, months, years, decades, centuries, or millennia over those 'just guesses'.

Hawking merely used the likely existence of inexplicable truths in the universe to argue that there cannot be a theory of the physical universe.

Well that human being was just another with a Truly narrowed, shallow, and/or small perspective or field of view of things.

What that human being was more or less doing was concluding things on Assumptions it was making on Past Experiences, or what I like to call APE-thinking. In other words, 'I cannot, 'currently now', imagine 'a theory of the physical universe' could exist'. Therefore, I will try to argue, 'There cannot be a theory of the physical universe'.

Which is Truly humorous to 'look at' and 'see' here 'now', especially considering that the actual GUTOE already exists.

The problem with Hawking's view is that inexplicable truths also exist in true arithmetic while we certainly do have a complete theory for the natural numbers. So, the late Hawking's view on the matter is definitely debatable.

Why would anyone really want to waste 'debating things' anyway?

Unless, of course, they think that they could 'win' some thing.

[Age]

The problem with calling things miracles is that it stops us from looking for an actual explanation.

Calling things miracles stops people from looking for actual explanations may well be very True, and let us not forget that there is an explanation for absolutely every thing that happens and occurs.

But that doesn't seem unsolvable; I think it will be explained eventually.

But no one can 'solve' what did not happen, nor occurred.

Life always exists. Life could not and did not 'just begin', just like the Universe could not and did not 'just begin'.

Consciousness is the nut we will have the most trouble cracking, I would say.

Consciousness was 'harder to crack', but still not as hard as some when this is being written might think it would be.

Life hasn't always existed on this planet, and we don't know of life anywhere else.

Here is another example of 'looking at' things from a very small, narrowed, or shallow perspective of things.

Some say earth, itself, is 'a living thing', so as long as the earth has existed, then 'life' has also existed. Therefore, 'life' has always existed, in regards to this planet and/or 'on this planet'.

And, from even a more OPEN perspective 'life' has existed for even longer, and even forever when one wants to have a Truly 'deep look' and 'delve deep into things' here.

As for consciousness; it is still a complete mystery.

When you say, 'a complete mystery', are you speaking for 'you', for 'some', or for 'everyone'?

Because what you believe is true here may well be, and/or may well not be. We will wait to see what your answer is here, first.

No one knows what it really is, or how it comes about.

Oh, so you are 'trying to' speak for absolutely EVERY one.

So, how do you know what EVERY one knows or does not know, "harbal"?

Also, are you speaking for EVERY one who has lived up to when this is being written, to those who are living when this is being written, or for absolutely EVERY one who has ever lived and will live?

Oh, and by the way, please do not forget that absolutely every thing that has come to be 'known', was once never 'known' by any one. Which, obviously, means that although you may well not, yet, 'know' what 'consciousness', itself, is others may well, already, 'know', or will become 'known' by others.

If you believe you do know, then you are badly mistaken.

Just in this one little sentence you have made two very False, Wrong, Inaccurate, and Incorrect assumptions.

But, you believe that 'this' could not even be 'possibly true', right?

And, what you are trying to say and claim here, is like telling 'the one' who was trying to say and explain how it is the earth that revolves around the sun, 'If you believe you do know, then you are badly mistaken'. And, we know how well that turned out, right?

[godelian]

To me, so-called 'inexplicable truths' sound just like an oxymoron.

What, exactly, do you think or believe is, supposedly, 'inexplicable' in some so-called 'arithmetic theory'?

If some thing is 'inexplicable' then how would absolutely any one know that 'that thing' is 'a truth'?

The mathematical term for "inexplicable truth" is "true but unprovable statement". Their existence in arithmetic theory was discovered by Kurt Godel in 1931:

https://www.theguardian.com/science/202 ... ss-theorem

In 1931, the Austrian logician Kurt Gödel published his incompleteness theorem, a result widely considered one of the greatest intellectual achievements of modern times.

The theorem states that in any reasonable mathematical system there will always be true statements that cannot be proved. The result was a huge shock to the mathematical community, where the prevailing view was an unshakeable optimism about the power and reach of their subject. It had been assumed that maths was “complete”, meaning that all mathematical statements are either provable or refutable. The 25-year-old Gödel demonstrated this was incorrect by constructing a true statement that was not provable.

In the philosophy of mathematical constructivism, you must always give an example, i .e. a "witness", if you claim that something exists.

Godel was aware of the challenge posed by constructivism ("intuitionism"):

https://en.m.wikipedia.org/wiki/Brouwer ... ontroversy

Brouwer's insistence on "constructibility" in the search for a "consistency proof for arithmetic" resulted in sensitivity to the issue as reflected by the work of Finsler and Gödel.[23] Ultimately Gödel would "numeralize" his formulae; Gödel then used primitive recursion (and its instantiation of the intuitive, constructive form of induction, i.e., counting and step-by-step evaluation) rather than a string of symbols that represent formal induction. Gödel was so sensitive to this issue that he took great pains in his 1931 paper to point out that his Theorem VI (the so-called "First incompleteness theorem") "is constructive; that is, the following has been proved in an intuitionistically unobjectionable manner ... ." He then demonstrates what he believes to be the constructive nature of his "generalization formula" 17 Gen r. Footnote 45a reinforces his point.

Technically, Godel did indeed construct a witness for his incompleteness theorem. However, his example cannot be considered to be "simple" or even particularly illustrative. In my opinion, his canonical witness just adds to the confusion.

I consider Goodstein's theorem to be the best example/witness for Godel's incompleteness theorem. Unlike the other witnesses, such as Gentzen equiconsistency theorem or Paris-Harrington theorem, it does not require a deep affinity with a particular, specialized area in mathematics. It is entirely self-contained and therefore much easier to understand.

In my opinion, there is currently no simpler example than Goodstein's theorem for Godel's incompleteness theorem.

[Age]

To me, so-called 'inexplicable truths' sound just like an oxymoron.

What, exactly, do you think or believe is, supposedly, 'inexplicable' in some so-called 'arithmetic theory'?

If some thing is 'inexplicable' then how would absolutely any one know that 'that thing' is 'a truth'?

The mathematical term for "inexplicable truth" is "true but unprovable statement". Their existence in arithmetic theory was discovered by Kurt Godel in 1931:

https://www.theguardian.com/science/202 ... ss-theorem

In 1931, the Austrian logician Kurt Gödel published his incompleteness theorem, a result widely considered one of the greatest intellectual achievements of modern times.

The theorem states that in any reasonable mathematical system there will always be true statements that cannot be proved. The result was a huge shock to the mathematical community, where the prevailing view was an unshakeable optimism about the power and reach of their subject. It had been assumed that maths was “complete”, meaning that all mathematical statements are either provable or refutable. The 25-year-old Gödel demonstrated this was incorrect by constructing a true statement that was not provable.

In the philosophy of mathematical constructivism, you must always give an example, i .e. a "witness", if you claim that something exists.

Godel was aware of the challenge posed by constructivism ("intuitionism"):

https://en.m.wikipedia.org/wiki/Brouwer ... ontroversy

Brouwer's insistence on "constructibility" in the search for a "consistency proof for arithmetic" resulted in sensitivity to the issue as reflected by the work of Finsler and Gödel.[23] Ultimately Gödel would "numeralize" his formulae; Gödel then used primitive recursion (and its instantiation of the intuitive, constructive form of induction, i.e., counting and step-by-step evaluation) rather than a string of symbols that represent formal induction. Gödel was so sensitive to this issue that he took great pains in his 1931 paper to point out that his Theorem VI (the so-called "First incompleteness theorem") "is constructive; that is, the following has been proved in an intuitionistically unobjectionable manner ... ." He then demonstrates what he believes to be the constructive nature of his "generalization formula" 17 Gen r. Footnote 45a reinforces his point.

Technically, Godel did indeed construct a witness for his incompleteness theorem. However, his example cannot be considered to be "simple" or even particularly illustrative. In my opinion, his canonical witness just adds to the confusion.

I consider Goodstein's theorem to be the best example/witness for Godel's incompleteness theorem. Unlike the other witnesses, such as Gentzen equiconsistency theorem or Paris-Harrington theorem, it does not require a deep affinity with a particular, specialized area in mathematics. It is entirely self-contained and therefore much easier to understand.

In my opinion, there is currently no simpler example than Goodstein's theorem for Godel's incompleteness theorem.

So, will you provide an example of a so-called "inexplicable truth", or, of a so-called "true but unprovable statement"?

If yes, then great.

But, if no, then why not?

Also, what has this got to do with so-called 'miracles', exactly, that is; if it does at all?

[godelian]

So, will you provide an example of a so-called "inexplicable truth", or, of a so-called "true but unprovable statement"? If yes, then great. But, if no, then why not?

In my opinion, the best example is:

Every Goodstein sequence eventually terminates at 0.

This theorem is unprovable in arithmetic. So, it is an inexplicable truth. However, this theorem is provable when you are allowed to make use of infinite ordinals. The caveat is that infinite ordinals cannot be defined in arithmetic. If you look at the proof for Goodstein's theorem, it is the following sentence that kicks the proof out of arithmetic and into set theory:

We define a function f = f ( u , k ) which computes the hereditary base k representation of u and then replaces each occurrence of the base k with the first infinite ordinal number ω.

The use of the first infinite ordinal number ω is not supported in arithmetic because the axiom of infinity is not available in that theoretical context.

Also, what has this got to do with so-called 'miracles', exactly, that is; if it does at all?

The definition of 'miracle':

A miracle is an event that is inexplicable by natural or scientific laws (and accordingly gets attributed to some supernatural or praeternatural cause)

So, a miracle is an "inexplicable truth". In mathematical lingo, it is a "true but unprovable statement". Inexplicable truths provably exist in true arithmetic. We know that they are true but only if we are able to accept infinitary notions. They may exist in the physical universe. Just like Stephen Hawking, I actually believe that they also exist in the physical universe.

[Age]

So, will you provide an example of a so-called "inexplicable truth", or, of a so-called "true but unprovable statement"? If yes, then great. But, if no, then why not?

In my opinion, the best example is:

Every Goodstein sequence eventually terminates at 0.

This theorem is unprovable in arithmetic. So, it is an inexplicable truth.

But, if every so-called "goodstein" sequence eventually terminates at 0, then 'it' cannot be refuted, and if some thing cannot be refuted, then it is, besides being irrefutable proof, it is also an irrefutable, and thus explainable, Truth, as well.

See, if some thing cannot be refuted, through 'logical reasoning', itself, then by 'logical reason', itself, that thing is just 'irrefutably True', or remains 'proved true' by the fact that 'it' cannot refuted nor disproved, anyway.

However, this theorem is provable when you are allowed to make use of infinite ordinals. The caveat is that infinite ordinals cannot be defined in arithmetic. If you look at the proof for Goodstein's theorem, it is the following sentence that kicks the proof out of arithmetic and into set theory:

We define a function f = f ( u , k ) which computes the hereditary base k representation of u and then replaces each occurrence of the base k with the first infinite ordinal number ω.

The use of the first infinite ordinal number ω is not supported in arithmetic because the axiom of infinity is not available in that theoretical context.

Also, what has this got to do with so-called 'miracles', exactly, that is; if it does at all?

The definition of 'miracle':

A miracle is an event that is inexplicable by natural or scientific laws ...

But, as I have already implied, 'There is no event that is inexplicable by natural or scientific laws'.

And, until any one provides an example of a, perceived, event, which is, supposedly, 'inexplicable by natural or scientific laws', then saying 'miracles' exist, is just one thinking or believing that not all actual occurrences and happenings happen and occur because of 'natural laws', which is obviously just insane thinking, or an insane belief.

Now, is there absolutely any one here brave enough to put up 'an, actual, event', which they think or believe happened and/or occurred outside of 'Nature', Itself?

If yes, then great and will you?

But, if no, then why even talk about 'miracles' when no one is even brave enough to provide just one thing that we can actually 'look at' and 'discuss'?

So, a miracle is an "inexplicable truth".

Well considering that there are NO so-called 'inexplicable truths', in Life, this is moot.

In mathematical lingo, it is a "true but unprovable statement".

you, personally, might call 'an event', which you think or believe is 'Naturally' inexplicable, (of which, let us not forget, as of 'now', absolutely none has ever been provided), and then just somehow relate a so-called 'inexplicable truth' as being called and/or referred to as 'a true but unprovable statement', only in mathematical lingo, however, there are no actual 'inexplicable truths', nor, 'true but unprovable statements', in Life, nor in Nature, Itself.

Well absolutely none that have been presented and put forth here for any of us to 'look at' and 'discuss' anyway.

Inexplicable truths provably exist in true arithmetic.

But the one example you gave here, I just disproved, and/or refuted.

And, what happens in some so-called 'true arithmetic', and/nor in some 'lingo' does not mean that it actually really and Truly does exist in 'Nature', Itself.

They may exist in the physical universe. Just like Stephen Hawking, I actually believe that they also exist in the physical universe.

Well PROVIDE SOME OF THEM.

What you and that other human being here 'believe', is like 'actually believing' that what 'may exist' 'actually exists', and this could apply to 'fairies', 'angels', and/or 'unicorns', as well as some 'imagined up' so-called 'inexplicable truths'.

Why do you not just say, 'I, and/or "steven hawking", believe miracles exist, in the physical universe?'

Or, have you done so already?

Now, if you want to believe 'miracles', or so-called 'inexplicable truths', exist in the so-called 'physical' only 'universe', then by all means you are absolutely free to do so.

I would and will just ask you why would you even want to start to believe that 'they' do exist?

And, have you ever come across one in your life before?

if yes, then will you present 'it' here. So, that we can 'look at' it and 'discuss' it?

If no, then why not?

[Iwannaplato]

It is no co-incidence that the more we understand science, the instances of reported miracles has declined.

And how was this measured?

History.
It's a no brainer.

Yeah, that's a non-answer. People are experiencing miracles or falsely interpreting things as miracles with regularity in the modern world. So, by what method did you draw your conclusion. If you just think it's a no brainer, and requires no justification, then you might as well be arguing
you have a revelation.

[godelian]

But, as I have already implied, 'There is no event that is inexplicable by natural or scientific laws'.
Now, is there absolutely any one here brave enough to put up 'an, actual, event', which they think or believe happened and/or occurred outside of 'Nature', Itself? If yes, then great and will you?

Some examples of phenomena that science cannot explain:

- 9 phenomena that science still can't explain
- 11 epic mysteries scientists totally can’t solve
- 25 Natural Phenomena That Science Has Yet To Explain

There is also the list of unsolved problems in physics.

Because of my personal research interests, I am much more familiar with the inexplicable truths in mathematics than with the ones in science. But then again, you can easily consult various lists of phenomena that cannot be explained by science.

[Iwannaplato]

But, as I have already implied, 'There is no event that is inexplicable by natural or scientific laws'.
Now, is there absolutely any one here brave enough to put up 'an, actual, event', which they think or believe happened and/or occurred outside of 'Nature', Itself? If yes, then great and will you?

Some examples of phenomena that science cannot explain:

- 9 phenomena that science still can't explain
- 11 epic mysteries scientists totally can’t solve
- 25 Natural Phenomena That Science Has Yet To Explain

There is also the list of unsolved problems in physics.

Because of my personal research interests, I am much more familiar with the inexplicable truths in mathematics than with the ones in science. But then again, you can easily consult various lists of phenomena that cannot be explained by science.

And those are generally recurring phenomena.
There are also 'one-shot'/occasional anomalies, which are more analogous to miracles, at least if they are larger exceptions.

It's very strange when people assume we have already explained everything. What year did we explain the last phenomenon?
Did we celebrate?
Why do scientists keep working?

[Walker]

Why do scientists keep working?

To feed the little children.

[Walker]

Logically, if conditions allow, then anything can happen.
- Science cannot explain current inexplicables.
- Science cannot explain past inexplicables.

Therefore it follows:
- Could the Red Sea have parted? Yes, because anything can happen even if every element present, or any element present, defies detection or comprehension.
- Could Lot’s wife have turned into a pillar of salt? Yes, for the same reason.
- Could water turn into wine, instantly? Same answer, same reason.
- Raised from dead? Sight restored? Cured of leprosy? Ditto.

Does science know how? No.
Does religion? Yes.
Can religion provide science with an explanation that science will accept? No.
Does this mean the religious explanation is wrong? No.

Perhaps the void of inexplicability that Dark Matter fills in for science's ignorance is in fact the nameless thing of a thousand names.

[Iwannaplato]

Why do scientists keep working?

To feed the little children.

Ah, that makes sense. I take back my objection.

[Walker]

Why do scientists keep working?

To feed the little children.

Ah, that makes sense. I take back my objection.

Given human nature and their possible politics ... they may do that by any means necessary, which means hanging onto the security of a science job.

They will sing ... "Whose bread I eat, his song I sing."

[Harbal]

Life hasn't always existed on this planet, and we don't know of life anywhere else.

Here is another example of 'looking at' things from a very small, narrowed, or shallow perspective of things.

I understand the type of life in question to be biological life, so that is the perspective from which I am looking.

Some say earth, itself, is 'a living thing', so as long as the earth has existed, then 'life' has also existed. Therefore, 'life' has always existed, in regards to this planet and/or 'on this planet'.

Well whatever "some" mean when they say that, it is not what is meant in this instance.

And, from even a more OPEN perspective 'life' has existed for even longer, and even forever when one wants to have a Truly 'deep look' and 'delve deep into things' here.

What is the point of broadening my perspective when I am referring to something specific?

No one knows what it (consciousness) really is, or how it comes about.

Oh, so you are 'trying to' speak for absolutely EVERY one.

So, how do you know what EVERY one knows or does not know, "harbal"?

I am reasonably certain that no one knows. Even those who formally study the subject of consciousness only seem to be able to arrive at vague opinions of what it might be, and where it might come from.

Oh, and by the way, please do not forget that absolutely every thing that has come to be 'known', was once never 'known' by any one. Which, obviously, means that although you may well not, yet, 'know' what 'consciousness', itself, is others may well, already, 'know', or will become 'known' by others.

I am not saying we will never understand consciousness; I am only saying that it is not understood now, in the days when etc, etc.

If you believe you do know, then you are badly mistaken.

Just in this one little sentence you have made two very False, Wrong, Inaccurate, and Incorrect assumptions.

But, you believe that 'this' could not even be 'possibly true', right?

If you think I have made false assumptions, why not just say what they are, rather than make a song and dance out of it?

And, what you are trying to say and claim here, is like telling 'the one' who was trying to say and explain how it is the earth that revolves around the sun, 'If you believe you do know, then you are badly mistaken'. And, we know how well that turned out, right?

No, this situation is not remotely like that.

[Walker]

...

I am not sure what any of this has to do with me, if it does. I was just saying that there was no 'spark of Life, Itself', and this is just because Life exists, always.

Age, science has shown that there actually is a spark when life begins.

Genesis 1:26 And God said, Let us make man in our image, after our likeness:

- I’m not a biblical scholar, and in my ignorance this indicates that because of the pronoun “our,” that God is not a singular entity.

- Would you agree? If not, why?

*

Genesis 1:3 And God said, Let there be light: and there was light.
And after that spark of life, a world begins.