Reformulating the analytic/synthetic distinction to make it unequivocal

[PeteOlcott]

I am bypassing the need for model theory in that the semantics of an expression of language is
directly encoded in the formal system using Rudolf Carnap (1952) meaning postulates.

Pete, in what universe have you ever successfully encoded the complete semantics of your program in the program itself?

The insurmountable gap in all formal languages is that which cannot be made explicit and remains implicit: design choices, constraints, context, specifications, reasons for the decisions being made etc...

If you could make everything explicit software would not need comments/documentation!

I already defined a universal semantic language in my other reply.

[Skepdick]

I already defined a universal semantic language in my other reply.

It's not "universal" because it's not explicit about the reasons for its axiomatic choices.

You can't encode those reasons in your language.

[Sculptor]

I do and did create a new word you are incorrect when you say that I can't because I did.
The new term is {semantic tautology} It means that an expression of language that has been
defined to be true is impossibly false: 3 > 2

It will never catch on since "semantic" and "tautology" when used together suggest a different meaning based on their existing meanings. SInce the words already have a meaning you'd have to supplant their existing meaning for you to have created something new. This is not going to happen.

Since a tautology is a phrase or expression in which the same thing is said twice in different words. A tautology is already semantic. So the phrase semantic tautology is a redundancy. Since all tautologies refer to a semantic similarity a semantic tautology is itself a tautology, like a mechanical engine, or a black darkness.

https://en.wikipedia.org/wiki/Tautology ... the%20ball.

In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". A less abstract example is "The ball is all green, or the ball is not all green". This is true regardless of the color of the ball.

The modern meaning is the only relevant one.

[Skepdick]

The modern meaning is the only relevant one.

Who decides "relevance" and how?

[PeteOlcott]

I already defined a universal semantic language in my other reply.

It's not "universal" because it's not explicit about the reasons for its axiomatic choices.

You can't encode those reasons in your language.

We don't needs the reasons. We stipulate a set of relations as "given" to be true.

[Skepdick]

We don't needs the reasons. We stipulate a set of relations as "given" to be true.

I need the reasons. There is no such thing as "given" truth.

[RCSaunders]

1+1=2
1+1=10

Both are true in their respective interpretative contexts. Decimal vs Boolean.

You mean decimal vs binary.
1+1=1 boolean.

Code: Select all

char AddWithCarry(char D1, char D2, char& Carry)
{
  char SUM   = ADD_Digit[D1][D2];      
  if (Carry == '1' && SUM == '9')
  { 
    SUM   = '0'; 
    Carry = '1'; 
  }
  else if (Carry == '1' && SUM < '9')
  {
    SUM   = ADD_Digit[SUM][Carry]; 
    Carry = ADD_Carry[D1][D2];   
  }
  else // Carry == '0' 
    Carry = ADD_Carry[D1][D2];   
  return SUM; 
} 


std::string Add(std::string& OP1, std::string& OP2)
{
std::string SUM;  
  char Carry = '0'; 
  for (int N = OP1.length() - 1; N >= 0; N--)
    SUM += AddWithCarry(OP1[N], OP2[N], Carry); 
  if (Carry == '1')
    SUM += '1'; 
  std::reverse(SUM.begin(), SUM.end());
  return SUM; 
}


//
// (Proven && True) || (Unproven && Untrue)
//
bool ProveInput(std::string& OP1,std::string& OP2,
                std::string& SUM, char Relational_OP)
{
  std::string RESULT;
  RESULT = Add(OP1, OP2); 
  return (RESULT == SUM);
}
 

Like I already said the semantics of the finite string is provided by its algorithm.
The meaning of natural language words can be defined using other natural language words of this same language and type theory.
The meaning of natural language words can be defined using a universal semantic language and type theory.
The universal semantic language would simply use integer tokens in place of the Natural language words.
One unique integer token would correspond to its word in every other natural language.

Silly, but out of curiosity--

What are you going to do with natural language words which have multiple different meanings like the words bow, rock, fancy, or light (which has about 40 meanings). I also think words like transmogrify, penultimate, and autoschediastic will be a problem. The whole idea is nonsense.

[PeteOlcott]

You mean decimal vs binary.
1+1=1 boolean.

Code: Select all

char AddWithCarry(char D1, char D2, char& Carry)
{
  char SUM   = ADD_Digit[D1][D2];      
  if (Carry == '1' && SUM == '9')
  { 
    SUM   = '0'; 
    Carry = '1'; 
  }
  else if (Carry == '1' && SUM < '9')
  {
    SUM   = ADD_Digit[SUM][Carry]; 
    Carry = ADD_Carry[D1][D2];   
  }
  else // Carry == '0' 
    Carry = ADD_Carry[D1][D2];   
  return SUM; 
} 


std::string Add(std::string& OP1, std::string& OP2)
{
std::string SUM;  
  char Carry = '0'; 
  for (int N = OP1.length() - 1; N >= 0; N--)
    SUM += AddWithCarry(OP1[N], OP2[N], Carry); 
  if (Carry == '1')
    SUM += '1'; 
  std::reverse(SUM.begin(), SUM.end());
  return SUM; 
}


//
// (Proven && True) || (Unproven && Untrue)
//
bool ProveInput(std::string& OP1,std::string& OP2,
                std::string& SUM, char Relational_OP)
{
  std::string RESULT;
  RESULT = Add(OP1, OP2); 
  return (RESULT == SUM);
}
 

Like I already said the semantics of the finite string is provided by its algorithm.
The meaning of natural language words can be defined using other natural language words of this same language and type theory.
The meaning of natural language words can be defined using a universal semantic language and type theory.
The universal semantic language would simply use integer tokens in place of the Natural language words.
One unique integer token would correspond to its word in every other natural language.

Silly, but out of curiosity--

What are you going to do with natural language words which have multiple different meanings like the words bow, rock, fancy, or light (which has about 40 meanings). I also think words like transmogrify, penultimate, and autoschediastic will be a problem. The whole idea is nonsense.

An ISO standard dictionary would assign a subscript to each of the sense meanings
of a word and this would be mapped to a unique 128-bit GUID integer in the formalism.

[PeteOlcott]

We don't needs the reasons. We stipulate a set of relations as "given" to be true.

I need the reasons. There is no such thing as "given" truth.

There is created/discovered knowledge and then after this there is the
stipulated notational conventions of this brand new knowledge.

When the concept of natural numbers was first discovered someone stipulated the notational conventions:

https://en.wikipedia.org/wiki/Number#:~ ... in%20Egypt.

[Skepdick]

There is created/discovered knowledge and then after this there is the
stipulated notational conventions of this brand new knowledge.

When the concept of natural numbers was first discovered someone stipulated the notational conventions:

https://en.wikipedia.org/wiki/Number#:~ ... in%20Egypt.

It doesn't matter. The "conventions" are only conventional within a particular number system. They need not be true across systems.

Pay careful attention to the links you post:

Today, number systems are considered important special examples of much more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.

If you want an example of where your grammar fall apart simply take a look at some unusual number systems like the p-addics or the surreals.

[Skepdick]

An ISO standard dictionary would assign a subscript to each of the sense meanings
of a word and this would be mapped to a unique 128-bit GUID integer in the formalism.

What happens when you run out of GUIDs ?

[PeteOlcott]

There is created/discovered knowledge and then after this there is the
stipulated notational conventions of this brand new knowledge.

When the concept of natural numbers was first discovered someone stipulated the notational conventions:

https://en.wikipedia.org/wiki/Number#:~ ... in%20Egypt.

It doesn't matter. The "conventions" are only conventional within a particular number system. They need not be true across systems.

I have always been talking about the pure semantic meaning that exists
separately of any form of physical representation.

The concept of Successor(0) remains the same utterly immutable even if you call it {bag of dog poop}.

We could assign 0 to "no dog poop",
Successor(0) to "a bag of dog poop",
Successor(Successor(0)) to "a can of dog poop"
and the underlying semantics of Peano axioms remain immutably unchanged.

I have said this hundreds of times in many different ways and so far
no one has begun to understand that semantics exists independently of
its means of physical representation. No one has begin to understand
this in many years.

[Skepdick]

I have always been talking about the pure semantic meaning that exists
separately of any form of physical representation.

The concept of Successor(0) remains the same utterly immutable even if you call it {bag of dog poop}.

No, you aren't hearing me. You are ignoring Polymorphism.

Every function has a domain and a codomain.
In programming languages you understand this concept as the type-signature of the function. The data-type of its inputs and outputs.

If 0 is an Integer then Successor(0) => 1
If 0 is a Real number then you don't even have a Successor() function!

This happens because you are used to thinking like a computer scientist - everything is an integer (e.g discrete).

You are making the same error as all Platonists - you are trying to divorce yourself from representation. You can't do that!
Even when you speak about computation you need to be explicit about which model of computation you are using - you've been told that all models are equivalent to Turing machines, but that's a quantitative lie.

There are qualitative differences. Read this article.

[Skepdick]

The actual semantic language that I am referring to we be defined as relations between 128-bit
GUID's. We can swap out the GUID's for a different set of GUID's at any time as long as we do it
consistently the underlying semantics remains immutably unchanged.

Let me save you from yourself.

What you are looking for is called Richard's paradox

In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.

You want to read this paper

The problem is that the set of reals is uncountable, but the set of all possible
texts in English or French is countable, and so is the set of all possible
mathematical definitions or the set of all possible mathematical questions,
since these also have to be formulated within a language, yielding at most
a denumerable infinity of possibilities. So there are too many reals, and not
enough texts.

[Age]

No knowledge can be, "encoded," as strings of characters. All knowledge consists of propositions which are constructed of concepts. "Strings of characters," are only symbols which represent concepts and have no meaning in themselves. Only concepts have meaning and what they mean are those existents they identify, that is, refer to. The meaning of a concept is the actual existents, not the concept's definition.

No knowledge is provided by direct perception. All higher animals have direct perception but it does not produce knowledge for them. Empirical knowledge is only possible by the rational identification of the existents direct perception makes available to identify and study. Only human beings are capable of intellectual knowledge.

Sorry, but your dichotomy is wrong on both counts. You have apparently been influenced by Kantian nonsense, as well as linguistic analysis and logical positivism. It's not a criticism, just and observation.

Your entire rebuttal was self-contradictory in that it was knowledge encoded as strings of characters.

זה ההסבר. סמלים אינם ידע.
Also:
Tidak masalah karakter apa yang digunakan.
as well as:
2ud34kekdw80023uip.
Since, "strings of characters," are knowledge, you should have no problem understanding that explanation.

But, 'it does not matter what character is used', just as long as the character is already understood, correct?

You are confusing, "information," as in, "information theory," with, "information," meaning knowledge, which is an equivocation.