Do you believe in miracles?

[Age]

What does the 'theory' word even mean or refer to, to you, exactly?

The term "theory" has three distinctive meanings.

https://en.m.wikipedia.org/wiki/Theory

In (1) science: a stubborn, observable pattern that has been experimentally tested for counterexamples.

In (2) mathematical logic: the collection of the theorems that can be deduced from a given set of axioms, given a given set of inference rules, i.e. an axiomatic system.

https://en.m.wikipedia.org/wiki/Axiomatic_system

In mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication.[1] A formal proof is a complete rendition of a mathematical proof within a formal system.

In (3) general: a body of knowledge. This was the original meaning inherited from Greek philosophy.

So, "medical theory" is a body of knowledge. It is not entirely based on experimental testing and it is also not axiomatic.

It is supposed to be clear from the context in what meaning the term "theory" is being used.

Because of my own research preferences, I mostly, but not always, use the term "theory" according to what it means in mathematical logic, i.e. an axiomatic system.

But the term 'theory' has more distinctive meanings. And, in case you are still not yet sure I was just asking what the word 'theory' means or refers to, to you.

Anyway, and in the end, medical theory, or 'medical body of knowledge', is a continually evolving and thus changing thing, so how it could be a so-called 'yardstick' for what is explicable -- and what is not -- in the medical field, I am not sure how you could actually measure that against exactly.

[godelian]

All I have been more or less pointing out here is the absurd belief that what is inexplicable 'today' does not mean that it will be inexplicable 'tomorrow'.

According to the definition for "miracle", something that is considered a miracle today could be considered not one tomorrow. Fine. I agree with that. However, this does not turn the inexplicable event into an explicable one today already.

And, this has absolutely nothing at all to do with so-called 'future improvements' of natural laws, as natural laws are, obviously, the exact same for eternity.

This assumes that we would know the true natural laws. We obviously do not. We merely have a collection of stubborn, observable patterns for which no counterexamples have been found. The collection of these patterns does not constitute a mathematical theory. We do not have the theory of everything ToE. It is a major unsolved problem:

https://en.wikipedia.org/wiki/Theory_of_everything

A theory of everything (TOE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe.[1]: 6  Finding a theory of everything is one of the major unsolved problems in physics.[2][3]

There is absolutely no guarantee that we will ever discover the Theory of Everything (ToE).

Are you under some sort of illusion that an explanation for all of those, seemingly, inexplicable events can never be found in the future?

I have never claimed that "all" such explicable events will remain inexplicable. I have merely pointed out that there is no guarantee whatsoever that an explanation for an inexplicable event will ever be found.

Example, the continuum hypothesis (CH)

https://en.m.wikipedia.org/wiki/Continuum_hypothesis
Gödel[6][2] showed that CH cannot be disproved from ZF, even if the axiom of choice (AC) is adopted (making ZFC).
Cohen[4][7] showed that CH cannot be proven from the ZFC axioms, completing the overall independence proof.

I have yet to see an actual example of absolutely any thing in mathematics that cannot be explained through and by natural laws. As I have already shown how the one example you gave can be, and was, explained through and by natural laws.

In that case feel free to prove or disprove by natural laws the continuum hypothesis (CH).

What does the word 'science' even mean or refer to, to you, exactly?

Science is the body of scientific theories. A scientific theory is a stubborn observable pattern which has been experimentally tested in order to find counterexamples.

Undecidable problems also exist in computability:

And, according to you this will last forever more, right?

Yes, Turing's Halting Problem will be unsolvable forever.

Also, how can you guarantee for the rest of eternity that the things in the field of mathematics that are inexplicable to you 'today' will be inexplicable forever more?

The definition of ZFC will never change. The definition of CH will never change. Therefore, the proof that neither CH nor the negation of CH could ever be proven from ZFC will remain valid forever. It is an eternal truth.

you speak as though some so-called 'theorem' here is absolute, unchangeable, and complete, 'today', forever more. Is this right and true?

Yes, Gödel's incompleteness theorem will forever remain provable from Peano Arithmetic theory. It is an eternal truth.

Another example. Pythagoras' theorem was discovered more than 2500 years ago. It is provable from Euclidean geometry:

https://en.wikipedia.org/wiki/Pythagorean_theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

Pythagoras' theorem has been provable from Euclidean geometry for more than 2500 years now, and it will remain provable forever. This is again, an eternal truth.

[godelian]

But the term 'theory' has more distinctive meanings. And, in case you are still not yet sure I was just asking what the word 'theory' means or refers to, to you.

I only use the term "theory" in one of the following three meanings:

- Most of the time: an axiomatic system (as defined in mathematical logic)
- Some of the time: A stubborn observable pattern that has been experimentally tested and for which no counterexamples have been found (as in science)
- Otherwise: Any body of knowledge (as in Greek philosophy)

There may be other meanings, but I do not use these other meanings.

[Age]

All I have been more or less pointing out here is the absurd belief that what is inexplicable 'today' does not mean that it will be inexplicable 'tomorrow'.

According to the definition for "miracle", something that is considered a miracle today could be considered not one tomorrow. Fine.

Great. Finally 'we' got 'here'.

And, let 'us' not forget that that was just one, of many, definitions for the word 'miracle'. It, obviously, was not 'the' definition, as you just said and claimed here.

I agree with that.

Great.

I was not sure that anyone could.

However, this does not turn the inexplicable event into an explicable one today already.

That would all depend on the claimed 'inexplicable'.

And, this has absolutely nothing at all to do with so-called 'future improvements' of natural laws, as natural laws are, obviously, the exact same for eternity.

This assumes that we would know the true natural laws.

What 'we', or at least some of 'us', do already know is that by the very 'nature' of 'natural laws', they would be the same forever.

And, even if, for example, a 'natural law' changed, then this could only happen and occur through, from, and by a 'natural law', naturally.

Again, this is the very 'nature' of 'natural laws', which 'naturally' happen and occur in 'Nature', 'naturally'.

In fact absolutely every thing that does happen and occur happens and occurs 'this way'.

We obviously do not. We merely have a collection of stubborn, observable patterns for which no counterexamples have been found. The collection of these patterns does not constitute a mathematical theory.

Okay, if you say and believe so.

We do not have the theory of everything ToE. It is a major unsolved problem:

For 'you' and some 'others' maybe. But, certainly not for 'us'. For 'we' already have this and thus have already re-solved this, literally.

https://en.wikipedia.org/wiki/Theory_of_everything

A theory of everything (TOE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe.[1]: 6  Finding a theory of everything is one of the major unsolved problems in physics.[2][3]

It has already been done. Although this is contrary to 'popular belief', in the days when this is being written.

There is absolutely no guarantee that we will ever discover the Theory of Everything (ToE).

But it has already been done.

Are you under some sort of illusion that an explanation for all of those, seemingly, inexplicable events can never be found in the future?

I have never claimed that "all" such explicable events will remain inexplicable.

Not in those words you have not. But, you have clearly stated that there are 'inexplicable events' here, right?

I have merely pointed out that there is no guarantee whatsoever that an explanation for an inexplicable event will ever be found.

But you never pointed this out, previously. Only after I pointed out that what you call an 'inexplicable event' implies a forever more.

In that case feel free to prove or disprove by natural laws the continuum hypothesis (CH).

To me, 'theories', 'hypothesis', and similar are just guesses or assumptions about what 'could be'.

So, if the so-called 'continuum hypothesis' is just 'a hypothesis', then it is not something that actually interests me at all.

I prefer to only 'look at' what is actually True and/or Right and not what is just assumed or guessed to be true and/or right.

Also, I was talking about 'explaining' through and by natural laws. And, absolutely nothing about proving nor disproving any hypothesis nor theory.

What does the word 'science' even mean or refer to, to you, exactly?

Science is the body of scientific theories. A scientific theory is a stubborn observable pattern which has been experimentally tested in order to find counterexamples.

Here 'we' have a prime example of why this one is not yet even close to uncovering, nor learning, and understanding the ToE.

And, according to you this will last forever more, right?

Yes, Turing's Halting Problem will be unsolvable forever.

Okay, if you say and believe so, then it must be so.

Also, how can you guarantee for the rest of eternity that the things in the field of mathematics that are inexplicable to you 'today' will be inexplicable forever more?

The definition of ZFC will never change. The definition of CH will never change. Therefore, the proof that neither CH nor the negation of CH could ever be proven from ZFC will remain valid forever. It is an eternal truth.

Yet 'definitions' change just about all of the time.

And, this is because of 'evolution', itself, or the 'natural law of evolution', itself.

But, "godelian" believes it knows more and better here.

you speak as though some so-called 'theorem' here is absolute, unchangeable, and complete, 'today', forever more. Is this right and true?

Yes, Gödel's incompleteness theorem will forever remain provable from Peano Arithmetic theory. It is an eternal truth.

Again, okay.

Another example. Pythagoras' theorem was discovered more than 2500 years ago. It is provable from Euclidean geometry:

https://en.wikipedia.org/wiki/Pythagorean_theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

Pythagoras' theorem has been provable from Euclidean geometry for more than 2500 years now, and it will remain provable forever. This is again, an eternal truth.

Okay, so where is the 'miracle' here, exactly?

Where, here, is an event that is inexplicable by natural or scientific laws, exactly?

[Age]

But the term 'theory' has more distinctive meanings. And, in case you are still not yet sure I was just asking what the word 'theory' means or refers to, to you.

I only use the term "theory" in one of the following three meanings:

- Most of the time: an axiomatic system (as defined in mathematical logic)
- Some of the time: A stubborn observable pattern that has been experimentally tested and for which no counterexamples have been found (as in science)
- Otherwise: Any body of knowledge (as in Greek philosophy)

There may be other meanings, but I do not use these other meanings.

Okay.

[godelian]

Only after I pointed out that what you call an 'inexplicable event' implies a forever more.

Forever inexplicable truths/facts provably exist in mathematics.

Since it is not possible to prove anything about the physical universe -- proving anything from the ToE is not possible because nobody has access to a copy of the ToE -- it is not possible to actually prove that inexplicable events in the physical universe will remain inexplicable forever.

So, if the so-called 'continuum hypothesis' is just 'a hypothesis', then it is not something that actually interests me at all.

The CH is otherwise interesting enough to have made it to the very top of David Hilbert's famous list of 23 unsolved problems in mathematics:

https://en.wikipedia.org/wiki/Continuum_hypothesis

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers,

The continuum hypothesis was advanced by Georg Cantor in 1878,[1] and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900.

The CH implies that there are growing gaps between the sequence of infinite sizes ("cardinalities"). This determines the shape of nonstandard models of arithmetic. There are reasons to believe that the universe is actually part of a multiverse with a similar shape as the collection of nonstandard models of arithmetic.

Also, I was talking about 'explaining' through and by natural laws. And, absolutely nothing about proving nor disproving any hypothesis nor theory.

In this context, "explanations" means "justification". In mathematics, "justification" means "proof".

Yet 'definitions' change just about all of the time.

No, in mathematics they don't. If you change the definition, it becomes something else. Mathematics is about 100% abstract objects only. They only exist because of their definition. There is no correspondence with physical reality. Mathematics does not change by observing anything in the physical world.

And, this is because of 'evolution', itself, or the 'natural law of evolution', itself.

That is a term from biology. It does not even apply to physics, let alone to mathematics.

Okay, so where is the 'miracle' here, exactly?
Where, here, is an event that is inexplicable by natural or scientific laws, exactly?

They clearly exist. I already gave a few examples. I also already gave several lists of inexplicable phenomena as well as a list of unsolved problems in physics. You keep asking the same question over and over again, while ignoring the answer.

[Age]

Only after I pointed out that what you call an 'inexplicable event' implies a forever more.

Forever inexplicable truths/facts provably exist in mathematics.

If this is what you want to believe and say is true, then okay.

Since it is not possible to prove anything about the physical universe -- proving anything from the ToE is not possible because nobody has access to a copy of the ToE -- it is not possible to actually prove that inexplicable events in the physical universe will remain inexplicable forever.

How do you know that no one has access to a copy of the ToE?

So, if the so-called 'continuum hypothesis' is just 'a hypothesis', then it is not something that actually interests me at all.

The CH is otherwise interesting enough to have made it to the very top of David Hilbert's famous list of 23 unsolved problems in mathematics:

https://en.wikipedia.org/wiki/Continuum_hypothesis

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers,

The continuum hypothesis was advanced by Georg Cantor in 1878,[1] and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900.

The CH implies that there are growing gaps between the sequence of infinite sizes ("cardinalities"). This determines the shape of nonstandard models of arithmetic. There are reasons to believe that the universe is actually part of a multiverse with a similar shape as the collection of nonstandard models of arithmetic.

Also, I was talking about 'explaining' through and by natural laws. And, absolutely nothing about proving nor disproving any hypothesis nor theory.

In this context, "explanations" means "justification". In mathematics, "justification" means "proof".

So what?

In this context, one thing means another. So, in truth another thing means another.

Yet 'definitions' change just about all of the time.

No, in mathematics they don't. If you change the definition, it becomes something else.

And, this is exactly what 'change' means here, in this context.

Mathematics is about 100% abstract objects only. They only exist because of their definition.

And, there are a multitude of other things that exist because of their definition only.

There is no correspondence with physical reality.

So, why then talk about it in relation to 'miracles' here?

Mathematics does not change by observing anything in the physical world.

Therefore, this, now, has less to do with what you started talking about here.

And, this is because of 'evolution', itself, or the 'natural law of evolution', itself.

That is a term from biology. It does not even apply to physics, let alone to mathematics.

Do not physical biological things have to do with physics, to you?

Okay, so where is the 'miracle' here, exactly?
Where, here, is an event that is inexplicable by natural or scientific laws, exactly?

They clearly exist. I already gave a few examples.

And, an example you gave I already showed how, exactly, it is explained by 'natural laws'.

Exactly like every other thing that actually happens and occurs.

I also already gave several lists of inexplicable phenomena as well as a list of unsolved problems in physics.

Some of which have already been explained and solved, 'today'. And, some of which are only inexplicable 'today'.

You keep asking the same question over and over again, while ignoring the answer.

No I am not.

But what you keep missing, not comprehending, and misunderstanding is that what you are just 'inexplicable' 'today' will be explained one day. As absolutely every thing you have listed and provided by example are explained with, by, and through 'natural laws'.

Now, this is irrefutable.

Did you not miss this, this time, and do you understand this, this time?

[Skepdick]

Please refer to the comments I made some time ago.

No.

[Skepdick]

In (2) mathematical logic: the collection of the theorems that can be deduced from a given set of axioms, given a given set of inference rules, i.e. an axiomatic system.

And in reverse Mathematical logic - the collection of axiom-schemas which can prove a given theorem.

The problem arises soon as one introduces the axiom of identity.

Which is sufficient to prove any theorem. By simply assuming it axiomatically true.

[godelian]

But what you keep missing, not comprehending, and misunderstanding is that what you are just 'inexplicable' 'today' will be explained one day.

I repeat my previous answer: scientific progress is not guaranteed. Moreover, no amount of progress in mathematics will ever make its provably inexplicable truths explicable.

As absolutely every thing you have listed and provided by example are explained with, by, and through 'natural laws'.

No, you keep ignoring the list of unsolved problems in physics.

[Skepdick]

No, in mathematics they don't. If you change the definition, it becomes something else.

That's not true. There are such thing as equivalent definitions. e.g different ways to define/construct any given Mathematical object.

They only exist because of their definition.

"Defining" is a verb. Definability is the central concern in Mathematical logic/model theory.

How many models of any given Mathematical object are there?

[godelian]

No, in mathematics they don't. If you change the definition, it becomes something else.

That's not true. There are such thing as equivalent definitions. e.g different ways to define/construct any given Mathematical object.

Yes, there are indeed equivalent definitions.

In fact, no object is truly unique in mathematics. Technically, they are at best unique up to isomorphism.

[godelian]

The problem arises soon as one introduces the axiom of identity. Which is sufficient to prove any theorem. By simply assuming it axiomatically true.

There are limits in doing that.

Imagine that you accept a particular logic sentence but also its opposite. The axiom of identity won't prevent this theory from not having a model at all. In that case, we have a theory in which every possible sentence becomes true. That is not a valid theory.

[Skepdick]

There are limits in doing that.

No, there aren't. Not unless you impose some limits. Once you attain Turing completeness - anything goes.

Imagine that you accept a particular logic sentence but also its opposite. The axiom of identity won't prevent this theory from not having a model at all. In that case, we have a theory in which every possible sentence becomes true. That is not a valid theory.

Do you know what a classifier is? It's an algorithm which determines category membership.
Please provide us with your classifier/algorithm which determines membership into the "valid" and "not valid" categories.

Or if you want this in the language of Mathematics.

let x be any theory.
let f(x) = { 1 if valid(x), 0 if not(valid(x)) }

Does f(x) exist?

Rinse. Repeat.

let y be any function.
let g(y) be a functor such that {1 if exists(y), 0 if not(exist(y) }

What is the value of g(f) ?

https://en.wikipedia.org/wiki/Rice%27s_theorem

[Sculptor]

According to medical theory, they do:



The benchmark for "dead" is medical theory, which could be incomplete or wrong, but that does not matter. In the end, it is sufficient for the event to be inexplicable by existing theory, which is itself not required to be perfect.

Are you trying to claim that this syndome is a "miracle" or a medical condition?

As I have indicated already, It is strictly limited to being a response to what you wrote:

These days people do not rise from the dead.

Are you trying to claim that this syndome is a "miracle" or a medical condition?