Transforming formal proof into sound deduction (rewritten)

[Logik]

Maybe to someone that fails to understand this is semantically impossible: True ↔ False

Perhaps you fail to understand? There are no semantic impossibilities.

It's called imagination.

The expression: True ↔ False is meaningless without interpretation.

That is one way of looking at it.

Alternatively an algorithm could specify its semantic meaning in terms of a set
of connected relations.

I already gave you one

https://repl.it/repls/PassionateSnowMedian

Code: Select all

↔(true, false)
=> 42

[PeteOlcott]

Perhaps you fail to understand? There are no semantic impossibilities.

It's called imagination.

The expression: True ↔ False is meaningless without interpretation.

That is one way of looking at it.

Alternatively an algorithm could specify its semantic meaning in terms of a set
of connected relations.

I already gave you one

https://repl.it/repls/PassionateSnowMedian

Code: Select all

def ↔(*args)
  return 42
end

↔(true, false)

It really seem like you are just playing head games to be annoying.
You made your point that computer programs can be liars let's get off that point
and on to the point how they can specify truth.

[Logik]

It really seem like you are just playing head games to be annoying.
You made your point that computer programs can be liars let's get off that point
and on to the point how they can specify truth.

And it really seems that the sunk cost fallacy is getting in the way of you understanding.

The computer is not "lying". The computer is evaluating the statement: ↔(true, false).
It's an algorithm. Exactly as you suggested: an algorithm could specify its semantic meaning in terms of a set
of connected relations.

Do you disagree with the semantics of the algorithm above and if so - why?

Before you can get the computer to specify "truth" first you need to know what truth is.

[PeteOlcott]

It really seem like you are just playing head games to be annoying.
You made your point that computer programs can be liars let's get off that point
and on to the point how they can specify truth.

And it really seems that the sunk cost fallacy is getting in the way of you understanding.

The computer is not "lying". The computer is evaluating the statement: ↔(true, false).
It's an algorithm. Exactly as you suggested: an algorithm could specify its semantic meaning in terms of a set
of connected relations.

Do you disagree with the semantics of the algorithm above and if so - why?

Before you can get the computer to specify "truth" first you need to know what truth is.

Truth is merely a set of expressions of language that have been assigned the
semantic value of Boolean true along with valid deductive logical inference
on the basis of these expressions.

We can talk endlessly forever in circles and you may never get this yet it
remains the fundamental basis of all truth despite your ignorance.

[PeteOlcott]

It really seem like you are just playing head games to be annoying.
You made your point that computer programs can be liars let's get off that point
and on to the point how they can specify truth.

And it really seems that the sunk cost fallacy is getting in the way of you understanding.

The computer is not "lying". The computer is evaluating the statement: ↔(true, false).
It's an algorithm. Exactly as you suggested: an algorithm could specify its semantic meaning in terms of a set
of connected relations.

Do you disagree with the semantics of the algorithm above and if so - why?

Before you can get the computer to specify "truth" first you need to know what truth is.

So it looks like you disagree with the sound deductive inference model
because this model requires true premises and according to you truth and falsity
are merely a matter of opinion so the sound deductive inference model can't
possibly be more than nonsense.

[Logik]

So it looks like you disagree with the sound deductive inference model
because this model requires true premises and according to you truth and falsity
are merely a matter of opinion so the sound deductive inference model can't
possibly be more than nonsense.

You are as ignorant as you are lazy. So you make me do all the work in pointing out counter-examples in your reasoning.

Here are two sentences that meet the: True ↔ False criterion.

There are 8 planets in the Solar system.
There are 9 planets in the Solar system.

When interpreted by astronomers circa 1830:

There are 8 planets in the Solar system ↔ False
There are 9 planets in the Solar system ↔ False

When interpreted by astronomers circa 1900:

There are 8 planets in the Solar system ↔ True
There are 9 planets in the Solar system ↔ False

When interpreted by astronomers circa 1935:

There are 8 planets in the Solar system ↔ False
There are 9 planets in the Solar system ↔ True


In 2019, would Pete Olcot assign Boolean True or False to the sentence: "There are 9 planets in the Solar system"?

[Logik]

Truth is merely a set of expressions of language that have been assigned the
semantic value of Boolean true along with valid deductive logical inference
on the basis of these expressions.

We can talk endlessly forever in circles and you may never get this yet it
remains the fundamental basis of all truth despite your ignorance.

I believe the ignorance is yours.

1. Who assigns the semantic value of Boolean True to expressions of language and why?

2. Have you ever read the definition for "validity"?

https://en.wikipedia.org/wiki/Validity_(logic)

In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (....)
A formula is valid if and only if it is true under every interpretation,

Given our interaction over last few weeks how many formulas would you say meet the criterion for it being IMPOSSIBLE for the premises to be true, but the conclusion to be false?
Given our interaction over the last few wees how many formulas would you say have been true under EVERY interpretation?

Given that it is unable to satisfy those criteria, would you care to present an example of what you deem to be a "valid" deduction?

[PeteOlcott]

So it looks like you disagree with the sound deductive inference model
because this model requires true premises and according to you truth and falsity
are merely a matter of opinion so the sound deductive inference model can't
possibly be more than nonsense.

You are as ignorant as you are lazy. So you make me do all the work in pointing out counter-examples in your reasoning.

Here are two sentences that meet the: True ↔ False criterion.

There are 8 planets in the Solar system.
There are 9 planets in the Solar system.

When interpreted by astronomers circa 1830:

There are 8 planets in the Solar system ↔ False
There are 9 planets in the Solar system ↔ False

When interpreted by astronomers circa 1900:

There are 8 planets in the Solar system ↔ True
There are 9 planets in the Solar system ↔ False

When interpreted by astronomers circa 1935:

There are 8 planets in the Solar system ↔ False
There are 9 planets in the Solar system ↔ True


In 2019, would Pete Olcot assign Boolean True or False to the sentence: "There are 9 planets in the Solar system"?

At every point in time of your examples: ¬(True ↔ False)

[PeteOlcott]

Truth is merely a set of expressions of language that have been assigned the
semantic value of Boolean true along with valid deductive logical inference
on the basis of these expressions.

We can talk endlessly forever in circles and you may never get this yet it
remains the fundamental basis of all truth despite your ignorance.

I believe the ignorance is yours.

1. Who assigns the semantic value of Boolean True to expressions of language and why?

2. Have you ever read the definition for "validity"?

https://en.wikipedia.org/wiki/Validity_(logic)

In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (....)
A formula is valid if and only if it is true under every interpretation,

"1. Who assigns the semantic value of Boolean True to expressions of language and why?"
There are a set of preexisting conventions that specify how to encode the idea that {cats} are not {dogs} as "cats are not dogs".
"cats are not dogs" is a basic fact equivalent to my specification of axiom.

[Logik]

At every point in time of your examples: ¬(True ↔ False)

You miss point. Again. In all of my examples - the assertions are made a posteriori.

A priori, what truth-value would you assign to the following sentences:

There are 6 planets in the Solar system.
There are 11 planets in the Solar system.

[Logik]

"1. Who assigns the semantic value of Boolean True to expressions of language and why?"
There are a set of preexisting conventions that specify how to encode the idea that {cats} are not {dogs} as "cats are not dogs".
"cats are not dogs" is a basic fact equivalent to my specification of axiom.

OK. You are the one who has been insisting on unique semantics. A bijection. A 1:1 relationship between symbols and meaning. Fine! I will play by your rules then.

And so I am going to map the semantics of "are" to the formal symbol "="

Cats are animals ( A = C)
Dogs are animals. (B = C)
Cats are not dogs. (A != B)

Oops! This violates transitivity!

So I will wait for you to explain why we semantically overload the meaning of "are" in English.

[PeteOlcott]

"1. Who assigns the semantic value of Boolean True to expressions of language and why?"
There are a set of preexisting conventions that specify how to encode the idea that {cats} are not {dogs} as "cats are not dogs".
"cats are not dogs" is a basic fact equivalent to my specification of axiom.

OK. You are the one who has been insisting on unique semantics. A bijection. A 1:1 relationship between symbols and meaning. Fine! I will play by your rules then.

And so I am going to map the semantics of "are" to the formal symbol "="

Cats are animals ( A = C)
Dogs are animals. (B = C)
Cats are not dogs. (A != B)

Oops! This violates transitivity!

So I will wait for you to explain why we semantically overload the meaning of "are" in English.

Example: “a cat is an animal”.
Formalized as: (cat ◁ animal)
where ◁ is the [is_a_type_of] operator adapted from UML Inheritance relation.
The only reason that we know that “a cat is an animal” is that it is defined to be True.

http://liarparadox.org/Meaning_Postulat ... p_1952.pdf

Meaning Postulates (1952) by Rudolf Carnap formalized natural language semantics:
(x) Bachelor(x) → ~Married(x)

(a) transitivity (b) for irreflexivity (c) of asymmetry
(a) (x)(y)(z) Warmer(x,y) ∧ Warmer(y,z) → Warmer(x,z)
(b) (x) ¬Warmer(x,x)
(c) (x)(y) Warmer(x,y) → ¬Warmer(y,x)

[Logik]

Example: “a cat is an animal”.
Formalized as: (cat ◁ animal)
where ◁ is the [is_a_type_of] operator adapted from UML Inheritance relation.
The only reason that we know that “a cat is an animal” is that it is defined to be True.

You are incredibly good at answering only half of the question, so I am going to shove it in your face again

I will wait for you to explain why we semantically overload the meaning of "are" in English.

roses ◁ red
cats ◁ animals
animals ◁ hungry
in-laws ◁ late for dinner
glasses ◁ broken

etc. etc. etc.

(x) Bachelor(x) → ~Married(x)

And we have already covered this in another thread: https://repl.it/repls/CruelHiddenTechnician

Code: Select all

def is_bachelor(person):
  if person.sex.lower() == 'male' and not person.marital_status:
    return True
  elif person.bachelor_degree:
    return True
  elif person.surname.lower() == "bachelor":
    return True
  else:
    return False

Thus demonstrating that the above function is still incomplete because it fails to test for the following meanings of "bachelor'

bachelor, noun, CANADIAN, bachelor apartment
bachelor, noun, HISTORICAL, a young knight serving under another's banner.

[PeteOlcott]

Example: “a cat is an animal”.
Formalized as: (cat ◁ animal)
where ◁ is the [is_a_type_of] operator adapted from UML Inheritance relation.
The only reason that we know that “a cat is an animal” is that it is defined to be True.

You are incredibly good at answering only half of the question, so I am going to shove it in your face again

I will wait for you to explain why we semantically overload the meaning of "are" in English.

Since I am ONLY defining the [is_a_type_of] aspect of "are" this is provided below:

cat ◁ mammal
mammal ◁ animal
∀x ◁ animal Breath(x)
∴ Breath(cat)

[PeteOlcott]

Example: “a cat is an animal”.
Formalized as: (cat ◁ animal)
where ◁ is the [is_a_type_of] operator adapted from UML Inheritance relation.
The only reason that we know that “a cat is an animal” is that it is defined to be True.

You are incredibly good at answering only half of the question, so I am going to shove it in your face again

I will wait for you to explain why we semantically overload the meaning of "are" in English.

roses ◁ red
cats ◁ animals
animals ◁ hungry
in-laws ◁ late for dinner
glasses ◁ broken

etc. etc. etc.

(x) Bachelor(x) → ~Married(x)

And we have already covered this in another thread: https://repl.it/repls/CruelHiddenTechnician

Code: Select all

def is_bachelor(person):
  if person.sex.lower() == 'male' and not person.marital_status:
    return True
  elif person.bachelor_degree:
    return True
  elif person.surname.lower() == "bachelor":
    return True
  else:
    return False

Thus demonstrating that the above function is still incomplete because it fails to test for the following meanings of "bachelor'

bachelor, noun, CANADIAN, bachelor apartment
bachelor, noun, HISTORICAL, a young knight serving under another's banner.

The concept of {bachelor} will have a unique place within an inheritance hierarchy knowledge ontology
so think of it as something roughly like this: Marital_State->Bachelor