The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing
Machines, and Turing Machines are a very precisely defined concept.
Unless you give an equally precise definition of a 'finite string transformation', you're not really adding anything. Can finite string transformations do something the Turing Machines cannot, or vice versa?
If not, then there's very little point in preferring your terminology
over the more standard terminology.
Perhaps if you gave some concrete examples of what you consider to be
finite string transformations and how they are implemented it would
clarify your position.
André
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
On 02/06/2026 20:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
That is not the Church-Turing thesis. The term "finite string transformatsions" includes transformations that are not
Turing computable but the Chruch-Turing thesis excludes them.
On 6/2/2026 8:39 PM, André G. Isaak wrote:
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing
Machines, and Turing Machines are a very precisely defined concept.
The Church side of the Church-Turing thesis exactly affirms my claim. Church's lambda calculus is, at its core, a system of finite symbolic rewritings on finite expressions.
On 2026-06-02 20:51, olcott wrote:
On 6/2/2026 8:39 PM, André G. Isaak wrote:
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing
Machines, and Turing Machines are a very precisely defined concept.
The Church side of the Church-Turing thesis exactly affirms my claim.
Church's lambda calculus is, at its core, a system of finite symbolic
rewritings on finite expressions.
It doesn't really affirm your claim because it isn't even clear what
your claim is.
You can conceptualize the lambda calculus as string transformation rules
if you want (though it isn't necessary to do this), but it's a very precisely defined set of string transformation rules which turns out to
be equivalent to the transformations which a Turing Machine can perform.
Given this, what possible advantage is there to replacing the usual formulation of the Church-Turing Thesis, stated in terms of Turing
Machines (or lambda calculus if you prefer) with your much more vague
statement in terms of 'finite string transformations' where you don't clearly define what you mean by this.
While TMs and lambda calculus can be thought of as string transformation operations, they aren't just arbitrary string transformations but a precisely defined set of transformations which is not captured by simply calling them 'finite string transformations'
So again, what is the advantage of your much less precise formulation of this thesis?
André
On 6/3/2026 12:24 PM, André G. Isaak wrote:
On 2026-06-02 20:51, olcott wrote:
On 6/2/2026 8:39 PM, André G. Isaak wrote:
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing
Machines, and Turing Machines are a very precisely defined concept.
The Church side of the Church-Turing thesis exactly affirms my claim.
Church's lambda calculus is, at its core, a system of finite symbolic
rewritings on finite expressions.
It doesn't really affirm your claim because it isn't even clear what
your claim is.
You can conceptualize the lambda calculus as string transformation
rules if you want (though it isn't necessary to do this), but it's a
very precisely defined set of string transformation rules which turns
out to be equivalent to the transformations which a Turing Machine can
perform.
Yet finite string transformation rules none-the-less.
Given this, what possible advantage is there to replacing the usual
formulation of the Church-Turing Thesis, stated in terms of Turing
Machines (or lambda calculus if you prefer) with your much more vague
It is generalization not vagueness. There exists an infinite
set of computationally equivalent finite string transformation rules.
statement in terms of 'finite string transformations' where you don't
clearly define what you mean by this.
There cannot possibly exist any finite string transformation
rules that transforms the finite string input DD to HHH that
derives the behavior of UTM(DD).
The halting problem never
has been any limit to computation. HHH/DD is simply outside
the scope of computation.
While TMs and lambda calculus can be thought of as string
transformation operations, they aren't just arbitrary string
transformations but a precisely defined set of transformations which
is not captured by simply calling them 'finite string transformations'
So again, what is the advantage of your much less precise formulation
of this thesis?
André
With my generalization it is much easier to directly
see the underlying foundational general principles
of the actual scope of computation.
On 2026-06-03 12:17, olcott wrote:
On 6/3/2026 12:24 PM, André G. Isaak wrote:
On 2026-06-02 20:51, olcott wrote:
On 6/2/2026 8:39 PM, André G. Isaak wrote:
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing
Machines, and Turing Machines are a very precisely defined concept.
The Church side of the Church-Turing thesis exactly affirms my claim.
Church's lambda calculus is, at its core, a system of finite
symbolic rewritings on finite expressions.
It doesn't really affirm your claim because it isn't even clear what
your claim is.
You can conceptualize the lambda calculus as string transformation
rules if you want (though it isn't necessary to do this), but it's a
very precisely defined set of string transformation rules which turns
out to be equivalent to the transformations which a Turing Machine
can perform.
Yet finite string transformation rules none-the-less.
Given this, what possible advantage is there to replacing the usual
formulation of the Church-Turing Thesis, stated in terms of Turing
Machines (or lambda calculus if you prefer) with your much more vague
It is generalization not vagueness. There exists an infinite
set of computationally equivalent finite string transformation rules.
It's not a generalization, it's an OVERgeneralization which completely misses the point of the Church-Turing Thesis. Yes, every computation can
be thought of as a finite string transformation (though they needn't be thought of this way), but it doesn't follow from that that every finite string transformation is a computation.
The point of the Church-Turing Thesis is to clarify *which* finite
string transformations are computable. By talking about finite string transformations without mentioning Turing Machines or lambda calculus,
you are completely missing this.
statement in terms of 'finite string transformations' where you don't
clearly define what you mean by this.
There cannot possibly exist any finite string transformation
rules that transforms the finite string input DD to HHH that
derives the behavior of UTM(DD).
Why not?
Unless 'finite string transformation' is constrained in some
way (i.e. those transformations which can be computed by Turing
Machines), then there is no reason you can't have a finite string transformation which performs that mapping. It's just not computable.
Unless you and I mean something different by 'finite string
transformation' which is the reason I complained earlier that you had
not defined this.
To me, a finite string transformation is simply a function which maps
finite strings to finite strings. What do you mean by this term?
The halting problem never
has been any limit to computation. HHH/DD is simply outside
the scope of computation.
While TMs and lambda calculus can be thought of as string
transformation operations, they aren't just arbitrary string
transformations but a precisely defined set of transformations which
is not captured by simply calling them 'finite string transformations'
So again, what is the advantage of your much less precise formulation
of this thesis?
André
With my generalization it is much easier to directly
see the underlying foundational general principles
of the actual scope of computation.
No. Your Overgeneralization completely misses the foundational general principle which the Church-Turing Thesis attempts to capture.
André
On 6/3/2026 1:52 PM, André G. Isaak wrote:
On 2026-06-03 12:17, olcott wrote:
On 6/3/2026 12:24 PM, André G. Isaak wrote:
On 2026-06-02 20:51, olcott wrote:
On 6/2/2026 8:39 PM, André G. Isaak wrote:
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing >>>>>> Machines, and Turing Machines are a very precisely defined concept. >>>>>>
The Church side of the Church-Turing thesis exactly affirms my claim. >>>>> Church's lambda calculus is, at its core, a system of finite
symbolic rewritings on finite expressions.
It doesn't really affirm your claim because it isn't even clear what
your claim is.
You can conceptualize the lambda calculus as string transformation
rules if you want (though it isn't necessary to do this), but it's a
very precisely defined set of string transformation rules which
turns out to be equivalent to the transformations which a Turing
Machine can perform.
Yet finite string transformation rules none-the-less.
Given this, what possible advantage is there to replacing the usual
formulation of the Church-Turing Thesis, stated in terms of Turing
Machines (or lambda calculus if you prefer) with your much more vague
It is generalization not vagueness. There exists an infinite
set of computationally equivalent finite string transformation rules.
It's not a generalization, it's an OVERgeneralization which completely
misses the point of the Church-Turing Thesis. Yes, every computation
can be thought of as a finite string transformation (though they
needn't be thought of this way), but it doesn't follow from that that
every finite string transformation is a computation.
The point of the Church-Turing Thesis is to clarify *which* finite
string transformations are computable. By talking about finite string
transformations without mentioning Turing Machines or lambda calculus,
you are completely missing this.
My system makes it much more clear that any problem
that cannot possibly be transformed into finite string
transformations of actual inputs is outside of the scope
of computation.
People have conflated the logically impossible with
the too difficult for 90 years.
statement in terms of 'finite string transformations' where you
don't clearly define what you mean by this.
There cannot possibly exist any finite string transformation
rules that transforms the finite string input DD to HHH that
derives the behavior of UTM(DD).
Why not? Unless 'finite string transformation' is constrained in some
way (i.e. those transformations which can be computed by Turing
Machines), then there is no reason you can't have a finite string
transformation which performs that mapping. It's just not computable.
There is no finite string transformation that transforms:
"What time is it (yes or no)?" into a correct yes or no
answer because the question itself has incoherent semantics.
On 2026-06-03 13:11, olcott wrote:
On 6/3/2026 1:52 PM, André G. Isaak wrote:
On 2026-06-03 12:17, olcott wrote:
On 6/3/2026 12:24 PM, André G. Isaak wrote:
On 2026-06-02 20:51, olcott wrote:
On 6/2/2026 8:39 PM, André G. Isaak wrote:
On 2026-06-02 11:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
The Church-Turing thesis is normally expressed in terms of Turing >>>>>>> Machines, and Turing Machines are a very precisely defined concept. >>>>>>>
The Church side of the Church-Turing thesis exactly affirms my claim. >>>>>> Church's lambda calculus is, at its core, a system of finite
symbolic rewritings on finite expressions.
It doesn't really affirm your claim because it isn't even clear
what your claim is.
You can conceptualize the lambda calculus as string transformation
rules if you want (though it isn't necessary to do this), but it's
a very precisely defined set of string transformation rules which
turns out to be equivalent to the transformations which a Turing
Machine can perform.
Yet finite string transformation rules none-the-less.
Given this, what possible advantage is there to replacing the usual >>>>> formulation of the Church-Turing Thesis, stated in terms of TuringIt is generalization not vagueness. There exists an infinite
Machines (or lambda calculus if you prefer) with your much more vague >>>>
set of computationally equivalent finite string transformation rules.
It's not a generalization, it's an OVERgeneralization which
completely misses the point of the Church-Turing Thesis. Yes, every
computation can be thought of as a finite string transformation
(though they needn't be thought of this way), but it doesn't follow
from that that every finite string transformation is a computation.
The point of the Church-Turing Thesis is to clarify *which* finite
string transformations are computable. By talking about finite string
transformations without mentioning Turing Machines or lambda
calculus, you are completely missing this.
My system makes it much more clear that any problem
that cannot possibly be transformed into finite string
transformations of actual inputs is outside of the scope
of computation.
People have conflated the logically impossible with
the too difficult for 90 years.
statement in terms of 'finite string transformations' where you
don't clearly define what you mean by this.
There cannot possibly exist any finite string transformation
rules that transforms the finite string input DD to HHH that
derives the behavior of UTM(DD).
Why not? Unless 'finite string transformation' is constrained in some
way (i.e. those transformations which can be computed by Turing
Machines), then there is no reason you can't have a finite string
transformation which performs that mapping. It's just not computable.
There is no finite string transformation that transforms:
"What time is it (yes or no)?" into a correct yes or no
answer because the question itself has incoherent semantics.
I think a big part of the problem is that you don't really grasp what a string is. Strings don't inherently have any semantics at all. A string
is simply a sequence of symbols.
'chat', for example, is a string
consisting of four symbols. English has semantics, and the semantics of English assigns a semantic interpretation to this string. French also
has semantics, and assigns a different interpretation to this string.
The string itself is simply an uninterpreted sequence of symbols.
To me, a finite string transformation is a function which maps one (uninterpreted) sequence of symbols to another (uninterpreted) sequence
of symbols.
You apparently have some different meaning in mind, but you
have yet to clarify what this meaning is.
Computations are purely mechanical procedures which manipulate symbols without any reference to the interpretation of those symbols. Again, I
am no longer clear on whether you perhaps have some different concept of computation in mind.
André
On 6/3/2026 2:26 PM, André G. Isaak wrote:
I think a big part of the problem is that you don't really grasp what
a string is. Strings don't inherently have any semantics at all. A
string is simply a sequence of symbols.
The actual problem is that no one knowing the theory of
computation has much more than a slight clue what semantics is.
'chat', for example, is a string consisting of four symbols. English
has semantics, and the semantics of English assigns a semantic
interpretation to this string. French also has semantics, and assigns
a different interpretation to this string. The string itself is simply
an uninterpreted sequence of symbols.
To me, a finite string transformation is a function which maps one
(uninterpreted) sequence of symbols to another (uninterpreted)
sequence of symbols.
According to some specific basis
that could include the
full semantics of natural language specified syntactically
in any combination or augmentation of these three different
ways.
Rudolf Carnap Meaning Postulates https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
The CycL language of the Cyc Project
https://en.wikipedia.org/wiki/CycL
Montague Grammar of natural language semantics https://en.wikipedia.org/wiki/Montague_grammar
I have not clarified what this meaning is more than 1000 times.
I have clarified what this meaning is many hundreds of times.
Computations are purely mechanical procedures which manipulate symbols
without any reference to the interpretation of those symbols. Again, I
am no longer clear on whether you perhaps have some different concept
of computation in mind.
André
When computation is intended to address decision problems
then there is an underlying semantics behind the mechanical
procedures which manipulate symbols.
On 2026-06-03 13:48, olcott wrote:
On 6/3/2026 2:26 PM, André G. Isaak wrote:
I think a big part of the problem is that you don't really grasp what
a string is. Strings don't inherently have any semantics at all. A
string is simply a sequence of symbols.
The actual problem is that no one knowing the theory of
computation has much more than a slight clue what semantics is.
Actually, I suspect they have a much better understanding of it than you
do. They also have an understanding of what the theory of computation is about, which is to explore the set of problems which can be solved
purely *syntactically*.
On 2026-06-03 13:48, olcott wrote:
On 6/3/2026 2:26 PM, André G. Isaak wrote:
I think a big part of the problem is that you don't really grasp what
a string is. Strings don't inherently have any semantics at all. A
string is simply a sequence of symbols.
The actual problem is that no one knowing the theory of
computation has much more than a slight clue what semantics is.
Actually, I suspect they have a much better understanding of it than you
do. They also have an understanding of what the theory of computation is about, which is to explore the set of problems which can be solved
purely *syntactically*. If you insist on dragging semantics into it then
you aren't really interested in the theory of computation, but in
something else. That other thing, whatever it is, might potentially be interesting but it isn't the theory of computation.
'chat', for example, is a string consisting of four symbols. English
has semantics, and the semantics of English assigns a semantic
interpretation to this string. French also has semantics, and assigns
a different interpretation to this string. The string itself is
simply an uninterpreted sequence of symbols.
To me, a finite string transformation is a function which maps one
(uninterpreted) sequence of symbols to another (uninterpreted)
sequence of symbols.
According to some specific basis
What exactly do you mean by 'basis'?
Here's an example of a finite string transformation. What exactly is its 'basis'?
{ 'ghjgh' -> 'fadsrr',
'psyty' -> 'zxqwiol',
'mxjwerp' -> 'lqdbvm',
'xyxl' -> 'Asgard'
'velcro' -> 'kitten',
'dfghuil' -> 'wextry' }
that could include the
full semantics of natural language specified syntactically
in any combination or augmentation of these three different
ways.
Rudolf Carnap Meaning Postulates
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
The CycL language of the Cyc Project
https://en.wikipedia.org/wiki/CycL
Montague Grammar of natural language semantics
https://en.wikipedia.org/wiki/Montague_grammar
None of the above have any relevance to the halting problem nor to the theory of computation. Montague and Carnap were concerned with the
semantics of natural language, not computation. CycL is a language for constructing encyclopaedic databases.
I have not clarified what this meaning is more than 1000 times.
I have clarified what this meaning is many hundreds of times.
You have not clarified it 1000 times but have clarified it 100 times.
Do me a favour and clarify it one more time. Exactly how do you define 'finite string transformation'. Please provide one example alongside
your definition.
Computations are purely mechanical procedures which manipulate
symbols without any reference to the interpretation of those symbols.
Again, I am no longer clear on whether you perhaps have some
different concept of computation in mind.
André
When computation is intended to address decision problems
then there is an underlying semantics behind the mechanical
procedures which manipulate symbols.
A decision problem simply determines whether a particular string is part
of a given set. Sets don't have semantics. Sets may be used to *model* semantic concepts, but this is entirely unnecessary for something to constitute a decision problem.
André
On 6/3/2026 5:30 PM, André G. Isaak wrote:
On 2026-06-03 13:48, olcott wrote:
On 6/3/2026 2:26 PM, André G. Isaak wrote:
I think a big part of the problem is that you don't really grasp
what a string is. Strings don't inherently have any semantics at
all. A string is simply a sequence of symbols.
The actual problem is that no one knowing the theory of
computation has much more than a slight clue what semantics is.
Actually, I suspect they have a much better understanding of it than
you do. They also have an understanding of what the theory of
computation is about, which is to explore the set of problems which
can be solved purely *syntactically*. If you insist on dragging
semantics into it then you aren't really interested in the theory of
computation, but in something else. That other thing, whatever it is,
might potentially be interesting but it isn't the theory of computation.
'chat', for example, is a string consisting of four symbols. English
has semantics, and the semantics of English assigns a semantic
interpretation to this string. French also has semantics, and
assigns a different interpretation to this string. The string itself
is simply an uninterpreted sequence of symbols.
To me, a finite string transformation is a function which maps one
(uninterpreted) sequence of symbols to another (uninterpreted)
sequence of symbols.
According to some specific basis
What exactly do you mean by 'basis'?
Here's an example of a finite string transformation. What exactly is
its 'basis'?
{ 'ghjgh' -> 'fadsrr',
'psyty' -> 'zxqwiol',
'mxjwerp' -> 'lqdbvm',
'xyxl' -> 'Asgard'
'velcro' -> 'kitten',
'dfghuil' -> 'wextry' }
that could include the
full semantics of natural language specified syntactically
in any combination or augmentation of these three different
ways.
Rudolf Carnap Meaning Postulates
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
The CycL language of the Cyc Project
https://en.wikipedia.org/wiki/CycL
Montague Grammar of natural language semantics
https://en.wikipedia.org/wiki/Montague_grammar
None of the above have any relevance to the halting problem nor to the
theory of computation. Montague and Carnap were concerned with the
semantics of natural language, not computation. CycL is a language for
constructing encyclopaedic databases.
I have not clarified what this meaning is more than 1000 times.
I have clarified what this meaning is many hundreds of times.
You have not clarified it 1000 times but have clarified it 100 times.
Do me a favour and clarify it one more time. Exactly how do you define
'finite string transformation'. Please provide one example alongside
your definition.
Computations are purely mechanical procedures which manipulate
symbols without any reference to the interpretation of those
symbols. Again, I am no longer clear on whether you perhaps have
some different concept of computation in mind.
André
When computation is intended to address decision problems
then there is an underlying semantics behind the mechanical
procedures which manipulate symbols.
A decision problem simply determines whether a particular string is
part of a given set. Sets don't have semantics. Sets may be used to
*model* semantic concepts, but this is entirely unnecessary for
something to constitute a decision problem.
André
In computability theory, Rice's theorem states that
all non-trivial semantic properties of programs are
undecidable. A semantic property is one about the
program's behavior.
https://en.wikipedia.org/wiki/Rice%27s_theorem
On 2026-06-03 16:57, olcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
On 2026-06-03 13:48, olcott wrote:
On 6/3/2026 2:26 PM, André G. Isaak wrote:
I think a big part of the problem is that you don't really grasp
what a string is. Strings don't inherently have any semantics at
all. A string is simply a sequence of symbols.
The actual problem is that no one knowing the theory of
computation has much more than a slight clue what semantics is.
Actually, I suspect they have a much better understanding of it than
you do. They also have an understanding of what the theory of
computation is about, which is to explore the set of problems which
can be solved purely *syntactically*. If you insist on dragging
semantics into it then you aren't really interested in the theory of
computation, but in something else. That other thing, whatever it is,
might potentially be interesting but it isn't the theory of computation. >>>
'chat', for example, is a string consisting of four symbols.
English has semantics, and the semantics of English assigns a
semantic interpretation to this string. French also has semantics,
and assigns a different interpretation to this string. The string
itself is simply an uninterpreted sequence of symbols.
To me, a finite string transformation is a function which maps one
(uninterpreted) sequence of symbols to another (uninterpreted)
sequence of symbols.
According to some specific basis
What exactly do you mean by 'basis'?
I'd really appreciate it if you would actually answer this question.
Here's an example of a finite string transformation. What exactly is
its 'basis'?
{ 'ghjgh' -> 'fadsrr',
'psyty' -> 'zxqwiol',
'mxjwerp' -> 'lqdbvm',
'xyxl' -> 'Asgard'
'velcro' -> 'kitten',
'dfghuil' -> 'wextry' }
that could include the
full semantics of natural language specified syntactically
in any combination or augmentation of these three different
ways.
Rudolf Carnap Meaning Postulates
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
The CycL language of the Cyc Project
https://en.wikipedia.org/wiki/CycL
Montague Grammar of natural language semantics
https://en.wikipedia.org/wiki/Montague_grammar
None of the above have any relevance to the halting problem nor to
the theory of computation. Montague and Carnap were concerned with
the semantics of natural language, not computation. CycL is a
language for constructing encyclopaedic databases.
I have not clarified what this meaning is more than 1000 times.
I have clarified what this meaning is many hundreds of times.
You have not clarified it 1000 times but have clarified it 100 times.
Do me a favour and clarify it one more time. Exactly how do you
define 'finite string transformation'. Please provide one example
alongside your definition.
Again, your definition would be appreciated. I suspect your definition
is different from my own and that creates a serious barrier to communication.
Computations are purely mechanical procedures which manipulate
symbols without any reference to the interpretation of those
symbols. Again, I am no longer clear on whether you perhaps have
some different concept of computation in mind.
André
When computation is intended to address decision problems
then there is an underlying semantics behind the mechanical
procedures which manipulate symbols.
A decision problem simply determines whether a particular string is
part of a given set. Sets don't have semantics. Sets may be used to
*model* semantic concepts, but this is entirely unnecessary for
something to constitute a decision problem.
André
In computability theory, Rice's theorem states that
all non-trivial semantic properties of programs are
undecidable. A semantic property is one about the
program's behavior.
https://en.wikipedia.org/wiki/Rice%27s_theorem
It's really unclear to me how the above relates in any way to the
statement which I made.
Computations are purely mechanical procedures which manipulate
symbols without any reference to the interpretation of those
symbols.
You do this quite often where, when uncertain
how to respond to something, you simple rehash something from your
previous posts. It's a very Elizaesque way of responding.
Also, I am a bit surprised that you very frequently mention Rice's
theorem. On the one hand, you want to claim that there's no such thing
as undecidability; on the other hand, you constantly cite Rice who makes
it very clear that there *are* undecidable problems.
André
On 6/3/2026 6:44 PM, André G. Isaak wrote:
On 2026-06-03 16:57, olcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
You have not clarified it 1000 times but have clarified it 100 times.
Do me a favour and clarify it one more time. Exactly how do you
define 'finite string transformation'. Please provide one example
alongside your definition.
Again, your definition would be appreciated. I suspect your definition
is different from my own and that creates a serious barrier to
communication.
See my signature line for the basis for every element
of the body of knowledge that can be expressed in language.
Computations are purely mechanical procedures which manipulate
symbols without any reference to the interpretation of those
symbols. Again, I am no longer clear on whether you perhaps have
some different concept of computation in mind.
André
When computation is intended to address decision problems
then there is an underlying semantics behind the mechanical
procedures which manipulate symbols.
A decision problem simply determines whether a particular string is
part of a given set. Sets don't have semantics. Sets may be used to
*model* semantic concepts, but this is entirely unnecessary for
something to constitute a decision problem.
André
In computability theory, Rice's theorem states that
all non-trivial semantic properties of programs are
undecidable. A semantic property is one about the
program's behavior.
https://en.wikipedia.org/wiki/Rice%27s_theorem
It's really unclear to me how the above relates in any way to the
statement which I made.
Computations are purely mechanical procedures which manipulate
symbols without any reference to the interpretation of those
symbols.
WRONG !!! non-trivial semantic properties of programs.
semantic properties of programs.
semantic properties of programs.
semantic properties of programs.
semantic properties of programs.
semantic properties of programs.
You do this quite often where, when uncertain how to respond to
something, you simple rehash something from your previous posts. It's
a very Elizaesque way of responding.
Also, I am a bit surprised that you very frequently mention Rice's
theorem. On the one hand, you want to claim that there's no such thing
as undecidability; on the other hand, you constantly cite Rice who
makes it very clear that there *are* undecidable problems.
André
On 2026-06-03 13:48, olcott wrote:
On 6/3/2026 2:26 PM, André G. Isaak wrote:
I think a big part of the problem is that you don't really grasp what
a string is. Strings don't inherently have any semantics at all. A
string is simply a sequence of symbols.
The actual problem is that no one knowing the theory of
computation has much more than a slight clue what semantics is.
Actually, I suspect they have a much better understanding of it than you
do. They also have an understanding of what the theory of computation is about, which is to explore the set of problems which can be solved
purely *syntactically*. If you insist on dragging semantics into it then
you aren't really interested in the theory of computation, but in
something else. That other thing, whatever it is, might potentially be interesting but it isn't the theory of computation.
'chat', for example, is a string consisting of four symbols. English
has semantics, and the semantics of English assigns a semantic
interpretation to this string. French also has semantics, and assigns
a different interpretation to this string. The string itself is
simply an uninterpreted sequence of symbols.
To me, a finite string transformation is a function which maps one
(uninterpreted) sequence of symbols to another (uninterpreted)
sequence of symbols.
According to some specific basis
What exactly do you mean by 'basis'?
Here's an example of a finite string transformation. What exactly is its 'basis'?
{ 'ghjgh' -> 'fadsrr',
'psyty' -> 'zxqwiol',
'mxjwerp' -> 'lqdbvm',
'xyxl' -> 'Asgard'
'velcro' -> 'kitten',
'dfghuil' -> 'wextry' }
that could include the
full semantics of natural language specified syntactically
in any combination or augmentation of these three different
ways.
Rudolf Carnap Meaning Postulates
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
The CycL language of the Cyc Project
https://en.wikipedia.org/wiki/CycL
Montague Grammar of natural language semantics
https://en.wikipedia.org/wiki/Montague_grammar
None of the above have any relevance to the halting problem nor to the theory of computation. Montague and Carnap were concerned with the
semantics of natural language, not computation. CycL is a language for constructing encyclopaedic databases.
I have not clarified what this meaning is more than 1000 times.
I have clarified what this meaning is many hundreds of times.
You have not clarified it 1000 times but have clarified it 100 times.
Do me a favour and clarify it one more time.
Exactly how do you define
'finite string transformation'. Please provide one example alongside
your definition.
On 6/3/2026 3:10 AM, Mikko wrote:
On 02/06/2026 20:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
That is not the Church-Turing thesis. The term "finite string
transformatsions" includes transformations that are not
Turing computable but the Chruch-Turing thesis excludes them.
The Church side of the Church-Turing thesis exactly
affirms my claim. Church's lambda calculus is, at
its core, a system of finite symbolic rewritings
on finite expressions.
There are no finite string transformations thatThere is a set of finite string transformations that transform the
proof theoretic semantics halt prover HHH can
apply on input finite string DD that derive the
behavior of UTM(DD) making DD out-of-the-scope of
computation for HHH.
On 03/06/2026 17:27, olcott wrote:
On 6/3/2026 3:10 AM, Mikko wrote:
On 02/06/2026 20:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
That is not the Church-Turing thesis. The term "finite string
transformatsions" includes transformations that are not
Turing computable but the Chruch-Turing thesis excludes them.
The Church side of the Church-Turing thesis exactly
affirms my claim. Church's lambda calculus is, at
its core, a system of finite symbolic rewritings
on finite expressions.
Your statement is not equivalent to the Church-Turing thesis because
it does not specify any set of finite string transformations that
cover all computations. The original thesis does.
There are no finite string transformations thatThere is a set of finite string transformations that transform the
proof theoretic semantics halt prover HHH can
apply on input finite string DD that derive the
behavior of UTM(DD) making DD out-of-the-scope of
computation for HHH.
sentence "1 + 2 = 3" to "Olcott is an idiot".
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in the
above?
You may think you are being clear, but you really are not.
Also, meaning postulates are not 'types', so you can't have a 'type hierarchy of Meaning Postulates'.
André
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in the
above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
Am 04.06.2026 um 18:06 schrieb André G. Isaak:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
It seems to me that this "transformation" may lead from true statements
to false statements (at least this may be the case concerning the
"example" mentioned above).
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy a carton of Breyer's ice cream at all (after a long day of work, say), and
may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statment would be false (in the case we considered)
even though (**) would be true.
I'd reject such "transformations". :-P
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in the
above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation called
"finite string transformation rule of reduction".
Am 04.06.2026 um 18:06 schrieb André G. Isaak:
On 2026-06-03 20:18, polcott wrote:It seems to me that this "transformation" may lead from true statements
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
to false statements (at least this may be the case concerning the
"example" mentioned above).
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy a carton of Breyer's ice cream at all (after a long day of work, say), and
may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statment would be false (in the case we considered)
even though (**) would be true.
I'd reject such "transformations". :-P
On 6/4/2026 12:00 PM, Moebius wrote:
Am 04.06.2026 um 18:06 schrieb André G. Isaak:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
It seems to me that this "transformation" may lead from true
statements to false statements (at least this may be the case
concerning the "example" mentioned above).
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of
Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy
a carton of Breyer's ice cream at all (after a long day of work, say),
and may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statment would be false (in the case we considered)
even though (**) would be true.
I'd reject such "transformations". :-P
Yet you did find a loophole.
So we translate the reduction to:
"Mary went to a store to buy some food"
On 6/4/2026 12:23 PM, André G. Isaak wrote:
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in the
above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation called
"finite string transformation rule of reduction".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
where: drove generalizes to went
Walmart generalizes to store(noun)
Breyer's ice cream generalizes to food.
thus reduces to: Mary went to the store to buy food
On 6/4/2026 12:23 PM, André G. Isaak wrote:
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in the
above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation called
"finite string transformation rule of reduction".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
where: drove generalizes to went
Walmart generalizes to store(noun)
Breyer's ice cream generalizes to food.
thus reduces to: Mary went to the store to buy food
Am 04.06.2026 um 18:06 schrieb André G. Isaak:
On 2026-06-03 20:18, polcott wrote:It seems to me that this "transformation" may lead from true statements
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
to false statements (at least this may be the case concerning the
"example" mentioned above).
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy a carton of Breyer's ice cream at all (after a long day of work, say), and
may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statment would be false (in the case we considered)
even though (**) would be true.
I'd reject such "transformations". :-P
On 2026-06-04 11:55, olcott wrote:
On 6/4/2026 12:23 PM, André G. Isaak wrote:
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please >>>>>>> provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in
the above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation called
"finite string transformation rule of reduction".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
where: drove generalizes to went
Walmart generalizes to store(noun)
Breyer's ice cream generalizes to food.
thus reduces to: Mary went to the store to buy food
You're still not providing a definition for 'finite string
transformation'. I gave you mine:
A finite string transformation is a function which maps finite strings
onto finite strings.
You still haven't given yours, which I suspect is different.
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
Since it transforms 'Walmart' into 'Store', would it transform 'I knew
Sam Walmart.' to 'I knew Sam Store.'?
On 6/4/2026 1:12 PM, André G. Isaak wrote:
On 2026-06-04 11:55, olcott wrote:
On 6/4/2026 12:23 PM, André G. Isaak wrote:
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please >>>>>>>> provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in
the above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation called
"finite string transformation rule of reduction".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
where: drove generalizes to went
Walmart generalizes to store(noun)
Breyer's ice cream generalizes to food.
thus reduces to: Mary went to the store to buy food
You're still not providing a definition for 'finite string
transformation'. I gave you mine:
"Walmart" is transformed into "the store"
You cannot get away with pretending to be so stupid
that you have no idea that "generalize" is a transformation
with "Walmart" and "the store" as the finite strings.
A finite string transformation is a function which maps finite strings
onto finite strings.
You still haven't given yours, which I suspect is different.
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
Since it transforms 'Walmart' into 'Store', would it transform 'I knew
Sam Walmart.' to 'I knew Sam Store.'?
On 6/4/2026 1:12 PM, André G. Isaak wrote:
On 2026-06-04 11:55, olcott wrote:"Walmart" is transformed into "the store"
On 6/4/2026 12:23 PM, André G. Isaak wrote:
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'. Please >>>>>>>> provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in
the above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation called
"finite string transformation rule of reduction".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
where: drove generalizes to went
Walmart generalizes to store(noun)
Breyer's ice cream generalizes to food.
thus reduces to: Mary went to the store to buy food
You're still not providing a definition for 'finite string
transformation'. I gave you mine:
You cannot get away with pretending to be so stupid
that you have no idea that "generalize" is a transformation
with "Walmart" and "the store" as the finite strings.
A finite string transformation is a function which maps finite strings
onto finite strings.
You still haven't given yours, which I suspect is different.
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
Since it transforms 'Walmart' into 'Store', would it transform 'I knew
Sam Walmart.' to 'I knew Sam Store.'?
Am 04.06.2026 um 20:17 schrieb olcott:
On 6/4/2026 1:12 PM, André G. Isaak wrote:
On 2026-06-04 11:55, olcott wrote:"Walmart" is transformed into "the store"
On 6/4/2026 12:23 PM, André G. Isaak wrote:
On 2026-06-04 10:55, polcott wrote:
On 6/4/2026 11:06 AM, André G. Isaak wrote:
On 2026-06-03 20:18, polcott wrote:
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Exactly how do you define 'finite string transformation'.
Please provide one example alongside your definition.
Reducing the finite string:
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
Where is there a definition of 'finite string transformation' in >>>>>>> the above?
"Reducing the finite string"
Is the finite string transformation rule of reduction.
So you're claiming there is some finite string transformation
called "finite string transformation rule of reduction".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
where: drove generalizes to went
Walmart generalizes to store(noun)
Breyer's ice cream generalizes to food.
thus reduces to: Mary went to the store to buy food
You're still not providing a definition for 'finite string
transformation'. I gave you mine:
You cannot get away with pretending to be so stupid
that you have no idea that "generalize" is a transformation
with "Walmart" and "the store" as the finite strings.
A finite string transformation is a function which maps finite
strings onto finite strings.
You still haven't given yours, which I suspect is different.
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
Since it transforms 'Walmart' into 'Store', would it transform 'I
knew Sam Walmart.' to 'I knew Sam Store.'?
Or, as you just explained, to 'I knew Sam the store.'
So your "transformation" will not work in a sensible way if it is based
on simply string replacement allone.
Btw. way you might be interested in the following approach:
https://en.wikipedia.org/wiki/Transformational_grammar
Am 04.06.2026 um 19:00 schrieb Moebius:
Am 04.06.2026 um 18:06 schrieb André G. Isaak:
On 2026-06-03 20:18, polcott wrote:It seems to me that this "transformation" may lead from true
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
statements to false statements (at least this may be the case
concerning the "example" mentioned above).
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of
Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy
a carton of Breyer's ice cream at all (after a long day of work, say),
and may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statment would be false (in the case we considered)
even though (**) would be true.
I'd reject such "transformations". :-P
Let's ask ChatGPT.
Q (me): Given the truth of the statement "Mary drove to Walmart to buy a carton of Breyer's ice cream." may we conlude that the statement "Mary bought food from a store." is true too?
A (ChatGPT): No, you cannot [...] conclude that. [...]
The statement:
"Mary drove to Walmart to buy a carton of Breyer's ice cream."
tells us that Mary's purpose or intention in driving to Walmart was to
buy ice cream. It does not explicitly state that she succeeded in buying
it.
Therefore:
"Mary bought food from a store."
does not logically follow [...]. Mary might have arrived and found the
ice cream out of stock, changed her mind, or left without making a
purchase.
~~~~~~~~~~~~~
Q (me): So is the following reasoning correct?
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy a carton of Breyer's ice cream at all (after a long day of work, say), and
may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statement would be false (in the case we considered)
even though (*) would be true.
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
On 6/4/2026 1:12 PM, Moebius wrote:
Am 04.06.2026 um 19:00 schrieb Moebius:I already accept your correction on this and
Am 04.06.2026 um 18:06 schrieb André G. Isaak:
On 2026-06-03 20:18, polcott wrote:It seems to me that this "transformation" may lead from true
On 6/3/2026 5:30 PM, André G. Isaak wrote:
Reducing the finite string:
Exactly how do you define 'finite string transformation'. Please
provide one example alongside your definition.
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
to "Mary bought food from a store"
on the basis of defining all of the original words in
a simple type hierarchy of Meaning Postulates.
statements to false statements (at least this may be the case
concerning the "example" mentioned above).
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of
Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to
buy a carton of Breyer's ice cream at all (after a long day of work,
say), and may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statment would be false (in the case we
considered) even though (**) would be true.
I'd reject such "transformations". :-P
Let's ask ChatGPT.
Q (me): Given the truth of the statement "Mary drove to Walmart to buy
a carton of Breyer's ice cream." may we conlude that the statement
"Mary bought food from a store." is true too?
A (ChatGPT): No, you cannot [...] conclude that. [...]
The statement:
"Mary drove to Walmart to buy a carton of Breyer's ice cream."
tells us that Mary's purpose or intention in driving to Walmart was to
buy ice cream. It does not explicitly state that she succeeded in
buying it.
Therefore:
"Mary bought food from a store."
does not logically follow [...]. Mary might have arrived and found the
ice cream out of stock, changed her mind, or left without making a
purchase.
~~~~~~~~~~~~~
Q (me): So is the following reasoning correct?
Let's assume that the statement
Mary drove to Walmart to buy a carton of Breyer's ice cream. (*)
is true, i.e. that Mary actually drove to Walmart to buy a carton of
Breyer's ice cream.
But it might have been the case that the store (the Walmart she drove
to) was closed, so she couldn't buy a carton of Breyer's ice cream
(there, "at Walmart"). Moreover she might have given up the aim to buy
a carton of Breyer's ice cream at all (after a long day of work, say),
and may not have bought any "food" at all (elsewhere).
Now by Olcott's "transformation" (don't ask!) we get the statement:
Mary bought food from a store. (**)
from (*). But this statement would be false (in the case we
considered) even though (*) would be true.
changed it to "Mary went to a store to buy some food".
"Mary drove to Walmart to buy a carton of Breyer's ice cream"
can be correctly summarized as
"Mary went to a store to buy some food".
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
There might be some "hierarchy" involved ...
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? Why
does it transform 'drove' to 'went' rather than 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define 'finite string transformation'?
On my definiion (finite string transformations are functions), a transformation must map each string to a *unique* string.
So it would appear that you don't view them as functions. What exactly do you viewUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach
them as?
A finite string transformation is a ___ (fill in the blank).
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'?
Why does it transform 'drove' to 'went' rather than 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define 'finite
string transformation'?
I'm not P. Olcott (I guess).
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'?
Why does it transform 'drove' to 'went' rather than 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define 'finite
string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a
transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic computation").
So it would appear that you don't view them as functions. What exactlyUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach
do you view them as?
A finite string transformation is a ___ (fill in the blank).
certainly would "transform" a given sentence to a "certain"
("determined") other sentence.
Counterexample: Contemporary AIs (based on LLMs). If you ask them one
end the same question repeatedly, you will get different answers (even
if you always start "from the scratch").
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change
'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'?
Why does it transform 'drove' to 'went' rather than 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define
'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a
transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. WhatUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach
exactly do you view them as?
A finite string transformation is a ___ (fill in the blank).
certainly would "transform" a given sentence to a "certain"
("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
On 2026-06-04 14:27, olcott wrote:Do you have an idea what a type hierarchy is?
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change >>>>>> 'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? >>>>>> Why does it transform 'drove' to 'went' rather than 'travelled to'? >>>>>>
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define
'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a
transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. WhatUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach
exactly do you view them as?
A finite string transformation is a ___ (fill in the blank).
certainly would "transform" a given sentence to a "certain"
("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
I have a *vague* understanding of what you seem to be saying.
On 6/4/2026 3:42 PM, André G. Isaak wrote:
On 2026-06-04 14:27, olcott wrote:Do you have an idea what a type hierarchy is?
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it change >>>>>>> 'Breyer's' to 'food' rather than to 'dessert' or 'dairy product'? >>>>>>> Why does it transform 'drove' to 'went' rather than 'travelled to'? >>>>>>>
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define
'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a
transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. WhatUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach
exactly do you view them as?
A finite string transformation is a ___ (fill in the blank).
certainly would "transform" a given sentence to a "certain"
("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
I have a *vague* understanding of what you seem to be saying.
If not then you lack simplest required basis.
Something like a Cyc knowledge ontology can encode the
entire body of general knowledge that can be expressed
in language.
On 2026-06-04 14:56, olcott wrote:
On 6/4/2026 3:42 PM, André G. Isaak wrote:
On 2026-06-04 14:27, olcott wrote:Do you have an idea what a type hierarchy is?
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string
transformation rule of reduction" actually is. Why does it
change 'Breyer's' to 'food' rather than to 'dessert' or 'dairy >>>>>>>> product'? Why does it transform 'drove' to 'went' rather than >>>>>>>> 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define
'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a
transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. WhatUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach
exactly do you view them as?
A finite string transformation is a ___ (fill in the blank).
certainly would "transform" a given sentence to a "certain"
("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
I have a *vague* understanding of what you seem to be saying.
Yes, I do. You, I suspect, do not, since you toss around expressions
like "type hierarchy of semantic entailments".
If not then you lack simplest required basis.
Something like a Cyc knowledge ontology can encode the
entire body of general knowledge that can be expressed
in language.
Which has nothing to do with what I am asking, which is how precisely do
you define "finite string transformation"?
André
On 6/4/2026 4:10 PM, André G. Isaak wrote:
On 2026-06-04 14:56, olcott wrote:
On 6/4/2026 3:42 PM, André G. Isaak wrote:
On 2026-06-04 14:27, olcott wrote:Do you have an idea what a type hierarchy is?
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string >>>>>>>>> transformation rule of reduction" actually is. Why does it
change 'Breyer's' to 'food' rather than to 'dessert' or 'dairy >>>>>>>>> product'? Why does it transform 'drove' to 'went' rather than >>>>>>>>> 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define
'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a >>>>>>> transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. WhatUsing some sort of "hierarchy" (->Cyc) and a "rule based" approach >>>>>> certainly would "transform" a given sentence to a "certain"
exactly do you view them as?
A finite string transformation is a ___ (fill in the blank).
("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
I have a *vague* understanding of what you seem to be saying.
Yes, I do. You, I suspect, do not, since you toss around expressions
like "type hierarchy of semantic entailments".
If not then you lack simplest required basis.
Something like a Cyc knowledge ontology can encode the
entire body of general knowledge that can be expressed
in language.
Which has nothing to do with what I am asking, which is how precisely
do you define "finite string transformation"?
André
Finite string transformations are specified in the CycL
language of the Cyc project.
Finite string transformations are specified in the CycL
language of the Cyc project.
Finite string transformations are specified in the CycL
language of the Cyc project.
Finite string transformations are specified in the CycL
language of the Cyc project.
Finite string transformations are specified in the CycL
language of the Cyc project.
How does CycL do this?
Look it up I am not a CycL textbook.
A google search for "CycL finite string transformation" yields no useful results. I could perform the same search five times, but it would still yield no useful results, so I'm not sure what the point of your
repetition is.
On 2026-06-04 15:29, olcott wrote:
On 6/4/2026 4:10 PM, André G. Isaak wrote:
On 2026-06-04 14:56, olcott wrote:
On 6/4/2026 3:42 PM, André G. Isaak wrote:
On 2026-06-04 14:27, olcott wrote:Do you have an idea what a type hierarchy is?
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string >>>>>>>>>> transformation rule of reduction" actually is. Why does it >>>>>>>>>> change 'Breyer's' to 'food' rather than to 'dessert' or 'dairy >>>>>>>>>> product'? Why does it transform 'drove' to 'went' rather than >>>>>>>>>> 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define >>>>>>>> 'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), a >>>>>>>> transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. What >>>>>>>> exactly do you view them as?Using some sort of "hierarchy" (->Cyc) and a "rule based"
A finite string transformation is a ___ (fill in the blank).
approach certainly would "transform" a given sentence to a
"certain" ("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
I have a *vague* understanding of what you seem to be saying.
Yes, I do. You, I suspect, do not, since you toss around expressions
like "type hierarchy of semantic entailments".
If not then you lack simplest required basis.
Something like a Cyc knowledge ontology can encode the
entire body of general knowledge that can be expressed
in language.
Which has nothing to do with what I am asking, which is how precisely
do you define "finite string transformation"?
André
Finite string transformations are specified in the CycL
language of the Cyc project.
A google search for "CycL finite string transformation" yields no useful results.
On 6/4/2026 5:10 PM, André G. Isaak wrote:
On 2026-06-04 15:29, olcott wrote:
On 6/4/2026 4:10 PM, André G. Isaak wrote:
On 2026-06-04 14:56, olcott wrote:
On 6/4/2026 3:42 PM, André G. Isaak wrote:
On 2026-06-04 14:27, olcott wrote:Do you have an idea what a type hierarchy is?
On 6/4/2026 2:12 PM, Moebius wrote:
Am 04.06.2026 um 20:59 schrieb André G. Isaak:
On 2026-06-04 12:45, Moebius wrote:
Am 04.06.2026 um 20:12 schrieb André G. Isaak:
There might be some "hierarchy" involved ...
And you still don't explain exactly what the "finite string >>>>>>>>>>> transformation rule of reduction" actually is. Why does it >>>>>>>>>>> change 'Breyer's' to 'food' rather than to 'dessert' or >>>>>>>>>>> 'dairy product'? Why does it transform 'drove' to 'went' >>>>>>>>>>> rather than 'travelled to'?
Breyer's -> ice cream -> food
dessert -> food
drive -> go (in an abstract sense)
travel to -> go (in an abstract sense)
Which takes me back to my original question. How do you define >>>>>>>>> 'finite string transformation'?
I'm not P. Olcott (I guess).
On my definiion (finite string transformations are functions), >>>>>>>>> a transformation must map each string to a *unique* string.
One might think so (especially when assuming "deterministic
computation").
So it would appear that you don't view them as functions. What >>>>>>>>> exactly do you view them as?Using some sort of "hierarchy" (->Cyc) and a "rule based"
A finite string transformation is a ___ (fill in the blank).
approach certainly would "transform" a given sentence to a
"certain" ("determined") other sentence.
André seems very motivated to pretend that he cannot
understand this.
I have a *vague* understanding of what you seem to be saying.
Yes, I do. You, I suspect, do not, since you toss around expressions
like "type hierarchy of semantic entailments".
If not then you lack simplest required basis.
Something like a Cyc knowledge ontology can encode the
entire body of general knowledge that can be expressed
in language.
Which has nothing to do with what I am asking, which is how
precisely do you define "finite string transformation"?
André
Finite string transformations are specified in the CycL
language of the Cyc project.
A google search for "CycL finite string transformation" yields no
useful results.
Google is a string matching system.
Google Gemini Pro-Extended Thinking mode
Does the CycL language perform any finite string transformations as any aspect of its inference? (Don't forget that CycL specifies semantics syntactically).
Yes, the CycL language—or more precisely, the Cyc inference engine that interprets it—performs finite string transformations as a fundamental aspect of its reasoning. Because CycL specifies semantics syntactically, these transformations occur on two distinct levels: the foundational logico-syntactic level and the literal procedural level.
On 6/4/2026 2:50 AM, Mikko wrote:
On 03/06/2026 17:27, olcott wrote:
On 6/3/2026 3:10 AM, Mikko wrote:
On 02/06/2026 20:26, polcott wrote:
The Church-Turing thesis can be greatly simplified
in saying that all computation is equivalent to
applying finite string transformations to finite strings.
That is not the Church-Turing thesis. The term "finite string
transformatsions" includes transformations that are not
Turing computable but the Chruch-Turing thesis excludes them.
The Church side of the Church-Turing thesis exactly
affirms my claim. Church's lambda calculus is, at
its core, a system of finite symbolic rewritings
on finite expressions.
Your statement is not equivalent to the Church-Turing thesis because
it does not specify any set of finite string transformations that
cover all computations. The original thesis does.
It need not. I am going form the other end.
If there does not exists a set of finite string transformations
applied to an input to derive a result than the result it
outside the scope of computation.
There are no finite string transformations that HHH
can apply to DD to derive the behavior of UTM(DD)
therefore DD is outside the scope of computation for HHH.
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