The death of Classical logic and the birth of Constructive Mathematics

[Speakpigeon]

You need to explain yourself here. Stop posting idiotic links and explain yourself.

Dimwit. In What language do you expect me to explain to you HOW to ride a bicycle? English? OK. You get on it and you pedal. Happy? The only way you are going to learn HOW formal logic works is practice, practice, practice, practice it it becomes second nature to you.
Exactly like riding a bike. Knowledge doesn't "just happen". You actually have to DO THE WORK. All by yourself. And the very first thing you need to learn to do is HOW to think. You can't read that in a book, but you can start here: https://www.learnpython.org/

Python is a programming language and as such it relies on Boolean operators in exactly the same way as any programming language.
Then you can programme whatever bullshit you want but it won't be logic.
A forum is not a place where you come to learn to programme in Python.
You come here expecting people to articulate the points they claim they have, argue their position in a rational way, and be civil enough to have a proper debate. You fail in all respect. You constantly insult people. You never properly address the points they make. You never provide any rational justification. You're a fraud and an ignoramus.
EB

[Logik]

Python is a programming language and as such it relies on Boolean operators in exactly the same way as any programming language.
Then you can programme whatever bullshit you want but it won't be logic.

So the things we build USING logic are NOT logic, how does that work?

[Scott Mayers]

He admitted it as a type of 'trick' in the programming. Read my correspondence with him.

Yes, I bet he doesn't even realise how insane his posts are.
EB

I found him reasonable to talk to here. While it may seem hard to believe of ourselves, there will always be someone who misinterprets us or our intents. I understood him, I believe, to be testing something about logic that when practiced in reality may prove to be turned upside down. Now, this may be granting too much charity of intent and I could be still misunderstanding something, but it's fair to say that at least I found some value in this thread regardless.

And I would/will of you too. So try not to be so harsh. If you don't understand something, after all, is it possible that you may just not be able to follow due to your own background. So maybe owning the misunderstanding yourself rather than insult the other of this will help prevent him from reflecting back the same charge against you.

"I don't understand" is more correct to assert than, "you must be insane since I cannot make sense of you," because it burdens the fault upon the other with certainty and closes off further discussion. How would/could you respond to this accusation by another that would improve the clarity.

I'm not saying you don't have prior reasons to draw your inference nor that I know better than you about what you believe, but that I think it might help to not be so conclusive about another's state of mind, when you can only speak about your own interpretation from your own mind alone.

Edit: P.S. If you are just jabbing each other as 'friends' may do, ignore my own misinterpretation of your style. I may be out of line in not knowing your past engagements with each other.

[Logik]

It's unrealistic to ask you to explain yourself in English and in a rational way?!

Yes. It is unrealistic to explain myself RATIONALLY in a language that is NOT rational.

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

[Logik]

I don't call myself either. I do philosophy and logic, though.
And I use whatever mathematics I need but it's really very basic because logic is formally simple. Difficult to understand, obviously, since no one has as of today, even though many great minds have given it a try, but it's simple.
If it gets complicated, you know it's no longer logic, it's mathematics, and then, who cares?

And that says it all. You seem to have drawn an arbitrary cut-off point between logic and mathematics, failing to realize it's exactly the same thing.

Failing to recognize that it has been PROVEN that it's exactly the same thing. Only your notion of "proof" is somewhat incoherent so you don't recognize it for what it is.

You say conjunction, I say f(P,Q)
f(0,0) = 0
f(0,1) = 0
f(1,0) = 0
f(1,1) = 1

You say disjunction I say g(P,Q)
g(0,0) = 0
g(0,1) = 1
g(1,0) = 1
g(1,1) = 1

You say XOR I say h(P,Q)
h(0,0) = 0
h(0,1) = 1
h(1,0) = 1
h(1,1) = 0

Absolutely EVERYTHING can be modeled as a black box with inputs and outputs! https://en.wikipedia.org/wiki/Black_box

You are doing what Marvin Minsky calls "mistaking the complex for the simple".
You are of the opinion that a complex universe such as ours can be understood with first-order logic such as the ones you can express in Boolean logic.

Boolean logic is very simplistic.
Lambda calculus is infinitely complex.

Time to open your mind a little: https://en.wikipedia.org/wiki/Complexit ... anizations

[Logik]

I believe, to be testing something about logic that when practiced in reality may prove to be turned upside down. Now, this may be granting too much charity of intent and I could be still misunderstanding something, but it's fair to say that at least I found some value in this thread regardless.

What I was doing is demonstrating that the world of logic (as studied in academic circles) is idealized and it falls for the ivory tower problem.

As you yourself mentioned that logic gates exist "without time". That's not true because nothing exists "without time". So not only is the conception of Boolean logic idealized, it's actually unrealizable in practice. EVERYTHING is a temporal phenomenon - there's not much choice in the matter.

Classical logic does not have the semantics to even express that and the more complex the topic of discussion becomes, the more this limit reasoning.

Obviously when you are dealing with phenomena which change so slowly as to be immaterial then you can abstract away the temporal dimension, but when precision begins to matter and you are using logic for real-time decision-making at the micro or millisecond scale the world looks VERY differently!

At that scale computers perform 50-100 MILLION instructions per second.

[Scott Mayers]

I believe, to be testing something about logic that when practiced in reality may prove to be turned upside down. Now, this may be granting too much charity of intent and I could be still misunderstanding something, but it's fair to say that at least I found some value in this thread regardless.

What I was doing is demonstrating that the world of logic (as studied in academic circles) is idealized and it falls for the "in theory there is no difference between theory and practice..". The ivory tower problem.

As you yourself mentioned that logic gates exist "without time". That's not true because nothing exists "without time". So not only is the conception of Boolean logic idealized, it's actually unrealizable in practice. EVERYTHING in theal world logic is a temporal phenomenon.

Classical logic does not have the semantics to even express that and the more complex the topic of discussion becomes, the more this limit reasoning.

Obviously when you are dealing with phenomena which change so slowly as to be immaterial then you can abstract away the temporal dimension, but when precision begins to matter (e.g you have to reason with temporal phenomena which change at the rate of thousands of times a second) the world looks VERY differently.

In electronics with respect to logic gates, the opposite of your assumption of mine is the case. That is, reality begs recognizing limits to the effectiveness of logic, not logic itself.

Boolean, and all first-ordered logic, is the basis for all other logic more complex. You can't appeal to some 'higher'-ordered use of reasoning when you lack the foundations they are dependent upon. You are attempting to interpret where you are on some upper floor high-rise as the 'foundation' and are explicitly denying a real foundation to which you are able to exist sustained up high in the sky.

While you may have never left your floor to know what is beneath you, you can't deny the existence of such a foundation if you refuse to leave your floor. And if I or others have personally been to the ground floors, how can you expect them but not you to default to your own asserted beliefs? You are refusing to get into the elevator with them and so forces others to have to only visit like an old bed-ridden senile relative you can only nod to when they assert things you can no longer have power to alter because they can't or won't leave their apartment.

[Logik]

In electronics with respect to logic gates, the opposite of your assumption of mine is the case. That is, reality begs recognizing limits to the effectiveness of logic, not logic itself.

Boolean, and all first-ordered logic, is the basis for all other logic more complex. You can't appeal to some 'higher'-ordered use of reasoning when you lack the foundations they are dependent upon.

Agreed! Engineering is all about understanding the limits of your tools and navigating around them.

I am perfectly familiar with the foundations. I can go right down to the physics and right up the tower of Babel.

You are attempting to interpret where you are on some upper floor high-rise as the 'foundation' and are explicitly denying a real foundation to which you are able to exist sustained up high in the sky.

Yes. This is the distinction between reductionism and holism in systems theory.
While I am perfectly happy to dive deep to the foundations, ultimately I take a holistic view on everything. Systems theory.

The building blocks for everything that is in my mind is a black box and transfer functions. Not logic gates.
Logic gates are just a special case.

While you may have never left your floor to know what is beneath you, you can't deny the existence of such a foundation if you refuse to leave your floor. And if I or others have personally been to the ground floors, how can you expect them but not you to default to your own asserted beliefs? You are refusing to get into the elevator with them and so forces others to have to only visit like an old bed-ridden senile relative you can only nod to when they assert things you can no longer have power to alter because they can't or won't leave their apartment.

You are speaking at the foundational level as if you are the only one who has been there. I got to the Penthouse via the ground floor...

What you seem to be doing is choosing to remain on the ground floor. Yes. I look at the world top-down. That is what most humans do!

On the other hand, remaining on the ground floor for most of your existence is to pretend that you experience reality at the quantum level of abstraction. You don't. And through your insistence to adhere only to foundational approaches you are applying 1st order logic to a reality that has N-th order side-effects! This IS mistaking the complex for the simple.

This is precisely why I have been able to do what I have done with Python.
At the level of human phenomenological experience of reality you can only hope for para-consistency!

You seem to grasp this concept when you spoke of a restricted universe e.g contexts
And while humans MAY be consistent in narrow and particular contexts, we are wildly inconsistent if you evaluate our behaviour outside of a 'restricted universe'.

The law of identity OR non-contradiction does not allow for para-consistency. It is too idealistic/strict given the limits of the human mind.
And the English language is not even REMOTELY consistent when looked at holistically.
So when you hold yourself to a standard that you can never achieve in practice - you have already set yourself up for failure.

[Scott Mayers]

You are speaking at the foundational level as if you are the only one who has been there. I got to the Penthouse via the ground floor...

What you seem to be doing is choosing to remain on the ground floor. Yes. I look at the world top-down. That is what most humans do!

On the other hand, remaining on the ground floor for most of your existence is to pretend that you experience reality at the quantum level of abstraction. You don't. And through your insistence to adhere only to foundational approaches you are applying 1st order logic to a reality that has N-th order side-effects! This IS mistaking the complex for the simple.

This is precisely why I have been able to do what I have done with Python.
At the level of human phenomenological experience of reality you can only hope for para-consistency!

The law of identity OR non-contradiction does not allow for para-consistency. It is too idealistic/strict given the limits of the human mind.
So when YOU hold yourself to a standard that you can never achieve in practice - you have already set yourself up for failure.

I too had to start from where I was before seeking foundations.

You appear to be denying something you refer to as "classic" logic or "first-order" logic, etc., as though this is defined uniquely by your own perspective. You falsely imply it has appropriate foundations for defining it's foundational assumptions as in error. But to assert this implies either that you lack an understanding of it or, if you do, must go down to that level to demonstrate it lacks what you claim. You can't expect me to go to the penthouse so that you can show me how the ground floor lacks existence. I could only nod with you there because we can't prove nor disprove anything from that high up.

We need to go to the ground floor together to inspect the ground floor's foundational weaknesses, if there exists any. While the penthouse may make you feel woozy as it sways in the upper atmosphere's winds, unless you prove that the penthouse is itself now AT the ground floor for the building's collapse, you can't assert the absence of some foundation's weakness. If it were non-existent, how do the upper floors even exist? So you have the burden at least take the elevator with me down to the basement so that we can see if there at least exist some cracks there before you can comment on it further. You certainly find it sufficiently comfort to stay where you are in the penthouse. So why are you trusting where you are yet not trusting there are sound floors beneath you? I'd be more worried about staying there if I think the building is about to collapse or demonstrate that I'm confident that there is no concern about a fear by willfully jumping out a window with the demonstrated faith that I can float on air.

But don't expect me to be the one to take the risk by jumping with you.

[Logik]

I too had to start from where I was before seeking foundations.

Have you found any? I haven't. It's turtles all the way down.So even in that regard our "ground floor" analogy is bullshit.

The "foundations" you seem to claim to have found are the Boolean operators. Those are just concepts. On paper - they are deterministic and have easy-to-reason properties. Till you realize the transfer function with matter and then your idealized transfer function is subject to entropy.

You appear to be denying something you refer to as "classic" logic or "first-order" logic, etc., as though this is defined uniquely by your own perspective.

Any logic that does not allow for decidability ( https://en.wikipedia.org/wiki/Decidability_(logic) )

Every complete recursively enumerable first-order theory is decidable.

Guess what recursively enumerable means? https://en.wikipedia.org/wiki/Recursive ... e_language

In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language.

How are you going to convince me that Classical logic is the 'laws" of thought when it can't even formalize/model a decision-making process?

Are you really trying to convince me that you are navigating reality using ONLY deduction and that not once have you ever needed to make a choice or a decision? You have never needed to calculate the consequences of different choices?

Pull the other one! Without the ability to make decisions your mind is paralyzed!

Or prove me wrong. Show me how you would use Classical logic to model multivariate optimization.

You falsely imply it has appropriate foundations for defining it's foundational assumptions as in error. But to assert this implies either that you lack an understanding of it or, if you do, must go down to that level to demonstrate it lacks what you claim. You can't expect me to go to the penthouse so that you can show me how the ground floor lacks existence. I could only nod with you there because we can't prove nor disprove anything from that high up.

I am not telling you the ground floor doesn't exist. I am telling you that pretending that you live on the ground floor (quantum) is an error.
Your day-to-day experience of world phenomena is more like something on the 5th floor!

So trying to interpret reality AS IF you are on the ground floor is a reductionist mistake.
Yes. You must make sure that whatever you have chosen as "foundation" behaves within some tolerance levels so as to give you some semblance of determinism but ultimately the whole is greater than the sum of its parts and you simply cannot reason about any complex system at the foundational level.

We need to go to the ground floor together to inspect the ground floor's foundational weaknesses, if there exists any.

There are always weaknesses. That's the point of limits. Understanding what the right tool for the job is.
And most importantly - understanding when a particular tool is NOT suitable for a particular task.

First order logic is NOT suitable for reasoning about temporal phenomena!
Which is a bummer since EVERYTHING becomes a temporal phenomenon once you realize the transfer function.

[Scott Mayers]

Scott Mayers wrote: ↑Mon Feb 25, 2019 2:43 pm
We need to go to the ground floor together to inspect the ground floor's foundational weaknesses, if there exists any.
There are always weaknesses. That's the point of limits. Understanding what the right tool for the job is.
And most importantly - understanding when a particular tool is NOT suitable for a particular task.

First order logic is NOT suitable for reasoning about temporal phenomena!
Which is a bummer since EVERYTHING is a temporal phenomenon.

No, you are just undefining the meaning of "first-order" to be the foundational 'first' step to reasoning. In fact, you are implicitly defining your own floor to BE the ground floor in that you think your reasoning should be considered, "first" or primary.

You presume fault of what is 'classic' based only on your own misunderstanding. You claim that the assumption of consistency as understood by first-ordered logic is inconsistent when you should be trying to prove how your own faith in your reasoning is 'consistent'.

You misinterpret the meaning of 'undecidability' somehow if you think it implies that lack of being able to determine X assures that there IS no X. The undecidable theorems are about whether we can 'decide' ahead of time what is true about ALL forms of reasoning that are BASED upon a foundation of the most simplest complete logics. They don't question that the original first -ordered logic is faulty, but that the upper-floors based upon those foundations are unpredictable. That is, you can't determine FROM the ground floor whether ALL upper floors are impossible to construct logically because in any logically sound building as a whole, there is no limits to how many floors can be built conceptually.

The 'limit' is to whether there is an ideal system of reasoning that can prove which kinds of logic systems (outside of the logic you are using to determine this) are not able to be complete without trying to reconstruct all logical systems and testing them first. That very 'theorem' itself has to be complete or its own conclusions lack validity.

If you have a 'theorem' that there is no floor above you that is MORE decidably complete above you, you still have to trust the foundation of reasoning of the system of logic you are using to propose such a theorem is correct. If your interpretation of this is ABOUT the foundations, then not even the system of logic the theorem is based on could be trusted, for it would be true about its own system of thinking.

You misunderstand what those theorems are asserting.

[Eodnhoj7]

Actually it is not, as that "lambda/type/turing" perspective you claimed you thought was original (but found out was not) is strictly an extension of your own perspective looping through itself. You have not put it into language anyone understand but you.

This is a lie.

Millions of people around the world know how to program. More and more are learning every day.

I have put it in a language so basic that a stupid machine running on 1s and 0s can understand it!
You are WAY smarter than a machine, so you should have no problem understanding it too.

The grammar/semantics of the language is public knowledge: https://github.com/python/cpython
The documentation of the language is public knowledge: https://docs.python.org/3/
Tutorials from first principles on how to learn the language are public knowledge: https://www.learnpython.org/
Global communities exist to support and beginners and experts alike if/when they run into problems: https://www.python.org/community/

To whine that I have put it in a "language that nobody understands" is to expect to be spoon-fed knowledge!
How lazy are you?

Facepalm emoji...You see the world through lambda; hence everything is a lambda loop. You loop with those who have the same language as you...and millions is a small language.

Nobody here, with "nobody" meaning a very small few as "nobody" is a general statement, is focused on computer programming as the be all end all.

If you have to "quote" someone...it just means you cannot argue it yourself. The linch pin of your argument is the continual "quotation" of a vast wikipedia page...other than that you provide no argument except maybe the word "isomorphism".

This is how backwards your thinking is! You think you have to do EVERYTHING yourself. Me? I don't have to re-invent the wheel! I will stand on the shoulders of giants instead.


The "giants" set the problems we are dealing with today.


BECAUSE Mathematical proofs are isomorphic to computer programs I don't have to "argue" anything. All I have to do is show it to you.

All of reality exists through isomorphism...you are arguing that is why computer language is justified to mathematics. I am saying "isomorphism" is a universal law which is not limited to computer programs/math.

I can literally drop the cat among the pigeons in the form of a working program and then go drink wine, while moron-philosophers figure out what the fuck happened to their "laws".

False, you pick and choose axioms to justify your stance...you ignore this basic "axiom" when dealing with concepts of "infinity" which entirely undermine your stance on "finiteness".




Logic is a constructive tool. Logic is LEGO for your mind.

False, the munchauseen trillema proves logic is subject to spatial axioms...create space without being subject to its laws.

APPLIED SCIENCE, not philosophy is the source of wisdom and knowledge. Philosophy is dead!

People are dead because they idolize the creation of there own hands...besides if philosophy was really dead...you would not have to spend all your time trying to prove it...ie "trying".

False, because applied science is producing so many divisions...the kids will not know where to go...it is the equivalent to an overpopulation resulting in a mass-die off. Look at 'overpopulation'...scientific truths will have to do the same thing...as well as programming languages.

WHEN YOU DON’T CREATE THINGS, YOU BECOME DEFINED BY YOUR TASTES RATHER THAN ABILITY. YOUR TASTES ONLY NARROW AND EXCLUDE PEOPLE. SO CREATE.
— Jonathan Gillette

Create knowledge!

If that is an absolute statement, than not all knowledge can be created. Second people create things according to their tastes, and as such the creation is subject to one's tastes.

[Logik]

You misinterpret the meaning of 'undecidability' somehow if you think it implies that lack of being able to determine X assures that there IS no X.

Huh? No. That's a strawman! Go the other way.

What I am claiming is that given the possibility of something being an X, Y, Z, P, Q, R, S and T you need SOME machine which can tell the difference between all of those things! Some machine that can sort things into categories. You are taking all of (re)cognition and binary classification for granted! To tell 2 things apart from each other you need 1 bit of information. To tell N things apart from each other you need log(N) bits of information.

The simplest experiment I can do to demonstrate this is to ask this question

Is A = А ? Yes or no.

And you are probably going to fall for the trap everybody falls for because your optical system can't tell the difference between the Latin letter A and the Cyrillic letter А. You are incapable of retrieving the information from reality to even answer the question so your logic is a non-starter because - Garbage in, Garbage out.

This is the heart of empiricism. If you don't have SOME procedure to distinguish one thing form another, they are as good as identical.

Do you believe me when I tell you that they are not the same letter?
Here is a science experiment to prove it: https://repl.it/repls/ShortLightgrayPiracy

The problem I am trying to point out (with ALL logic) is the GIGO problem.

The undecidable theorems are about whether we can 'decide' ahead of time what is true about ALL forms of reasoning that are BASED upon a foundation of the most simplest complete logics.

No. That is not what decidability is about. Decidability is STRICTLY about the capability of the machine (mind!) interpreting the logic to do data storage/retrieval and branching. Decidability is about process/procedure that can produce the correct answer.

Decidability is about the fact that where you ASSUME that something is an X, a decidable logic can determine THAT something is an X given a set of instructions.

If you don't have decidability you cannot construct a Universal Turing machine!
If you cannot construct a UTM then your mind is paralyzed to the structure of the logic which you adopted! In the most literal and absolute sense possible without decidability logic is 100% mechanical!

If that is what the "laws" of thought are about, that is an INCREDIBLY inflexible way to reason.

You are after logical completeness. I am after Turing-completeness.

They don't question that the original first -ordered logic is faulty, but that the upper-floors based upon those foundations are unpredictable. That is, you can't determine FROM the ground floor whether ALL upper floors are impossible to construct logically because in any logically sound building as a whole, there is no limits to how many floors can be built conceptually.

You don't have that problem with Lambda calculus. Because recursion a Regular language is turing complete. If it's Turing complete it can implement other Regular languages which are also Turing complete.

What Lambda calculus gives you is a language that can INTERPRET ITS OWN SYNTAX AND GRAMMAR.
That's the fundamental feature that classical logics do NOT have.

Because a language can interpret itself CONSISTENTLY you are guaranteed that the language IS consistent.
There can be no contradictions in such a system because the root-causes of contradictions (INCONSISTENCY!) has been removed BY DESIGN.

The 'limit' is to whether there is an ideal system of reasoning that can prove which kinds of logic systems (outside of the logic you are using to determine this) are not able to be complete without trying to reconstruct all logical systems and testing them first. That very 'theorem' itself has to be complete or its own conclusions lack validity.

OK. We have a fundamental misunderstanding here. Because you are talking about "outside of the logic you are using to determine this" you are necessarily appealing to Tarski's undefinability theorems and Godel's incompleteness theorems.

Wow! We exist in different paradigms!

Lambda calculus does not have 'foundations' or 'axioms'. It is 100% constructed and 100% conceptual first and foremost. The CONCEPT of computation rests simply on the abstract notion of a Universal Turing Machine.

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.

You take the Boolean operators as foundational. I don't.

There are no 'axioms' in lambda calculus. It's a universal language for describing ANY behaviour that you can conceptualize and express.
Do you want Trinary operators? Define them.
Do you want Hextenary operators? Define them.
Do you want Boolean operators? Define them.

At this point I am still speaking strictly about the conceptual/theoretical realm. No rules, no logics, no axioms.
This is what you get with Turing Completeness. Just a canvas and a Universal language to describe how each and every one of the components in your imaginary universe SHOULD behave. There are no laws of physics here - only imagination and limits of computation.

The fact that current-day computers are implemented as binary machines is just implementation detail and it is completely irrelevant.
Because Turing-Completeness is Universal.

All Turing-complete logics are Turing-equivalent!

Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P

A Quantum computer is Turing-Equivalent to a Classical computer. Just faster!
(I am mis-representing the truth here a little, we are still trying to find whether there is any class of problems that can only be solved by quantum computers). Work is currently underway to prove/disprove whether classical computers can solve BQP-class problems ( https://en.wikipedia.org/wiki/BQP ).

If you have a 'theorem' that there is no floor above you that is MORE decidably complete above you, you still have to trust the foundation of reasoning of the system of logic you are using to propose such a theorem is correct. If your interpretation of this is ABOUT the foundations, then not even the system of logic the theorem is based on could be trusted, for it would be true about its own system of thinking.

You misunderstand what those theorems are asserting.

No. You misunderstand. Theorems are the consequences of axioms and deductive rules.
I have neither axioms nor rules beyond the ones I put in my mind.

I define the axioms. I construct the models!

And that is how I see all logic - a modeling tool.

[Logik]

Facepalm emoji...You see the world through lambda; hence everything is a lambda loop. You loop with those who have the same language as you...and millions is a small language.

Nobody here, with "nobody" meaning a very small few as "nobody" is a general statement, is focused on computer programming as the be all end all.

You missed the forrest for the trees (as usual).
Lambda calculus is not about PROGRAMMING.
It's about COMPUTATION.

When you understand what the difference is, you will understand why Lambda is what you need to get your work done.

When it hits you - come say thank you.

The "giants" set the problems we are dealing with today.

How exactly is an empty canvas (a Turing machine) a "problem".
It has solved the completeness AND consistency problems in logic.

What exactly is the problem? Other than your conception of computation being the physical manifestation of a computer.

You don't actually understand the CONCEPT of computation and how universal it is.


BECAUSE Mathematical proofs are isomorphic to computer programs I don't have to "argue" anything. All I have to do is show it to you.

All of reality exists through isomorphism...you are arguing that is why computer language is justified to mathematics. I am saying "isomorphism" is a universal law which is not limited to computer programs/math.

Yes! Metamorphism is a CONCEPT. Computation is a CONCEPT.

The Mathematics is just the language in which we express our concepts so that OTHERS can understand them.
You see the mathematics, but you can't see the concept in my head so you think I don't think like you.

False, you pick and choose axioms to justify your stance...you ignore this basic "axiom" when dealing with concepts of "infinity" which entirely undermine your stance on "finiteness".

You don't even know what infinity is. You can't even express infinity in any language. How can it be an axiom?

False, the munchauseen trillema proves logic is subject to spatial axioms...create space without being subject to its laws.

Too bad that Lamba caculus doesn't deal with space. It deals with space-time. You are missing a dimension.

If that is an absolute statement, than not all knowledge can be created. Second people create things according to their tastes, and as such the creation is subject to one's tastes.

Yes. It absolutely is! We very much prefer knowledge that is USEFUL to knowledge that isn't.

We very much prefer knowledge that WORKS to knowledge that doesn't.

[Scott Mayers]

I've opened a distinct thread on the question of the meaning of the theorems themselves because you and I, as many do, disagree as to the meanings. You rely here in this thread to some backing theorems or conjectures that are essential to your thesis and so this needs to be established.

That thread will include Turing's own papers to which he attempted to describe an ideal mechanical machine that can operate unbiased to thought prior to proving things about it on a meta-logical basis.

The thread is here:

What the theorems of Incompleteness or Undecibility assert

For here,

The simplest experiment I can do to demonstrate this is to ask this question

Is A = А ? Yes or no.

And you are probably going to fall for the trap everybody falls for because your optical system can't tell the difference between the Latin letter A and the Cyrillic letter А. You are incapable of retrieving the information from reality to even answer the question so your logic is a non-starter because - Garbage in, Garbage out.

This is the heart of empiricism. If you don't have SOME procedure to distinguish one thing form another, they are as good as identical.

Do you believe me when I tell you that they are not the same letter?
Here is a science experiment to prove it: https://repl.it/repls/ShortLightgrayPiracy

The problem I am trying to point out (with ALL logic) is the GIGO problem.

....you are asking about the syntactical symbols literally and to how we read them. This requires separating the language we use to discuss some logic from the actual logic itself. What you are thinking is that the fact that we read "A = A" linearly, that what we understand them to mean within the system is unable to be true out of some practical limitations of communicating it, but implying that our lack of this ability imposes something intrinsically true about the meaning of the logical postulates.

Turing only used an idealized computer system in thought to convey the limitations about logic itself, not about physical computers. The utility of his analogy using an imaginary constructs and architecture that we today call a 'computer' is only coincidentally significant as to how it applies to actual physical computers. We call them "Turing" machines because of his unique 'design' of a simplified computer rather than to other optional designs that actual computers ended up using in reality. For instance, he treated the programs initially as lists of separate instructions that a person has to take data from a single tape, read, interpret, and alter if instructed, and then to print the outcome back onto the tape. Those are 'non-universal'. His 'universal' machine was one that has a fixed kind of BIOS hardware design that takes the first data off the tape to DEFINE a the program virtually without a need to reconfigure the hardware.

Then he used the data that defines each program before running them by a unique number, then showed that if you list all possible numbers that define new programs, when you find one that works (most do not), then you will discover your list is never complete. Thus, you cannot even use his own design of a universal computer, as completely operable as he proved it to be, to solve one kind of problem: a program that can decide if all possible programs are complete or incomplete without hanging infinitely. Since he showed that this is impossible, then it proved definitively that even an ideal universal machine could not solve all problems. [All he needed was to show that one such universal goal could not be achieved.]

You are appearing to be actually arguing something more specific about practical reality limitations, not ideal computing concepts. And so you are falsely suggesting some extended belief about what 'classical' logic itself is even suggesting.

The "law of identity" (or consistency) is stated using words about logic in an external human language. So of course we can't literally think that the symbols we used to communicate the postulates are able to be justified by some prior logic. We are begged to trust our own senses without question and so cannot expect the language we use to express something we are founded upon is able to perfectly express logic universally.

A computer nor its programs can do any better unless we trust them apart from our senses. And while you appear on the one hand to agree to its limitations about those inputting potential garbage, the architecture, while we expect it to remain relatively 'fixed' to operate without bias to our favor, the 'garbage' in also has to be attributable to the very construction of the architecture itself.