On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:Nope. Not for Formal system, which have a specific definition of
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision problems* >>>>>>>>>>
When we ask the question: What is a truthmaker? The generic >>>>>>>>>> answer is
whatever makes an expression of language true <is> its
truthmaker. This
entails that if there is nothing in the universe that makes >>>>>>>>>> expression X
true then X lacks a truthmaker and is untrue.
X may be untrue because X is false. In that case ~X has a
truthmaker.
Now we have the means to unequivocally define truth-bearer. X >>>>>>>>>> is a
truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>>>>>>>>
I have been working in this same area as a non-academician for >>>>>>>>>> a few
years. I have only focused on expressions of language that are >>>>>>>>>> {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored it is >>>>>>>>> easy to see
that self-contradictory expressions are simply not truthbearers. >>>>>>>>>
“This sentence is not true” can't be true because that would >>>>>>>>> make it
untrue and it can't be false because that would make it true. >>>>>>>>>
Within the the definition of truthmaker specified above: “this >>>>>>>>> sentence
has no truthmaker” is simply not a truthbearer. It can't be >>>>>>>>> true within
the above specified definition of truthmaker because this would >>>>>>>>> make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they can be.
Note,
When I specify the ultimate foundation of all truth then this
does apply to truth in logic, truth in math and truth in science. >>>>>>
its truth-makers, unless you let your definition become trivial
for Formal logic where a "truth-makers" is what has been defined
to be the "truth-makers" for the system.
Formal systems are free to define their own truthmakers.
When these definitions result in inconsistency they are
proved to be incorrect.
A formal system can be inconsistent without being incorrect.
*Three laws of logic apply to all propositions*
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system specifies
its own laws, which include all or some or none of those. Besides, a the
word "proposition" need not be and often is not used in the specification
of a formal system.
*This is the way that truth actually works*
*People are free to disagree and simply be wrong*
When we ask the question: What is a truthmaker? The generic answer is whatever makes an expression of language true <is> its truthmaker.
This entails that if there is nothing in the universe that makes
expression X true then X lacks a truthmaker and is untrue.
X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truthbearer. X is a
truthbearer iff (if and only if) X or ~X has a truthmaker.
People are free to stipulate the value of PI as exactly
3.0 and they are simply wrong.
But they are free to use the small greek letter pi for other purposes.
On 6/11/2024 8:44 PM, Richard Damon wrote:
On 6/11/24 12:06 PM, olcott wrote:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
Those laws do not constrain formal systems. Each formal system
specifies
its own laws, which include all or some or none of those. Besides, a
the
word "proposition" need not be and often is not used in the
specification
of a formal system.
*This is the way that truth actually works*
*People are free to disagree and simply be wrong*
Nope, YOU are simply wrong, because you don't understand how big logic
actualy is, because, it seems, your mind is to small.
Every expression of language X that is
{true on the basis of its meaning}
algorithmically requires a possibly infinite sequence of
finite string transformation rules from its meaning to X.
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker.
But logic systems don't necessaily deal with "expressions of language"
in the sense you seem to be thinking of it.
Finite strings are the most generic form of "expressions of language"
This entails that if there is nothing in the universe that makes
expression X true then X lacks a truthmaker and is untrue.
Unless it just is true because it is a truthmaker by definition.
That is more than nothing in the universe.
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:Nope. Not for Formal system, which have a specific definition of its >>>>>> truth-makers, unless you let your definition become trivial for Formal >>>>>> logic where a "truth-makers" is what has been defined to be the
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision problems* >>>>>>>>>>
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker. This
entails that if there is nothing in the universe that makes expression X
true then X lacks a truthmaker and is untrue.
X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truth-bearer. X is a >>>>>>>>>> truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>>>>>>>>
I have been working in this same area as a non-academician for a few >>>>>>>>>> years. I have only focused on expressions of language that are {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored it is easy to see
that self-contradictory expressions are simply not truthbearers. >>>>>>>>>
“This sentence is not true” can't be true because that would make it
untrue and it can't be false because that would make it true. >>>>>>>>>
Within the the definition of truthmaker specified above: “this sentence
has no truthmaker” is simply not a truthbearer. It can't be true within
the above specified definition of truthmaker because this would make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they can be.
Note,
When I specify the ultimate foundation of all truth then this
does apply to truth in logic, truth in math and truth in science. >>>>>>
"truth-makers" for the system.
Formal systems are free to define their own truthmakers.
When these definitions result in inconsistency they are
proved to be incorrect.
A formal system can be inconsistent without being incorrect.
*Three laws of logic apply to all propositions*
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system specifies
its own laws, which include all or some or none of those. Besides, a the
word "proposition" need not be and often is not used in the specification
of a formal system.
*This is the way that truth actually works*
On 6/11/2024 9:37 PM, Richard Damon wrote:
On 6/11/24 9:57 PM, olcott wrote:
On 6/11/2024 8:44 PM, Richard Damon wrote:
On 6/11/24 12:06 PM, olcott wrote:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
Those laws do not constrain formal systems. Each formal system
specifies
its own laws, which include all or some or none of those. Besides, >>>>>> a the
word "proposition" need not be and often is not used in the
specification
of a formal system.
*This is the way that truth actually works*
*People are free to disagree and simply be wrong*
Nope, YOU are simply wrong, because you don't understand how big
logic actualy is, because, it seems, your mind is to small.
Every expression of language X that is
{true on the basis of its meaning}
algorithmically requires a possibly infinite sequence of
finite string transformation rules from its meaning to X.
Unless it is just true as its nature.
Which Mendelson would encode as: ⊢𝒞
A {cat} <is defined as a type of> {animal}.
When we ask the question: What is a truthmaker? The generic answer is >>>>> whatever makes an expression of language true <is> its truthmaker.
But logic systems don't necessaily deal with "expressions of
language" in the sense you seem to be thinking of it.
Finite strings are the most generic form of "expressions of language"
And not all things are finite strings.
Every expression of language that is {true on the basis of its meaning}
is a finite string that is connected to the expressions of language that express its meaning.
This entails that if there is nothing in the universe that makes
expression X true then X lacks a truthmaker and is untrue.
Unless it just is true because it is a truthmaker by definition.
That is more than nothing in the universe.
but what makes the definition "true"? What is its truth-maker?
Not everything has a truth-maker, because it might be a truth-maker
itself.
Basic facts are stipulated to be true.
"A cat is an animal" is the same basic fact expressed
in every human language and their mathematically
formalized versions.
On 6/12/2024 2:13 AM, Mikko wrote:
On 2024-06-11 16:06:02 +0000, olcott said:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:Nope. Not for Formal system, which have a specific definition of its >>>>>>>> truth-makers, unless you let your definition become trivial for Formal >>>>>>>> logic where a "truth-makers" is what has been defined to be the >>>>>>>> "truth-makers" for the system.
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision problems* >>>>>>>>>>>>
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker. This
entails that if there is nothing in the universe that makes expression X
true then X lacks a truthmaker and is untrue.
X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truth-bearer. X is a >>>>>>>>>>>> truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>>>>>>>>>>
I have been working in this same area as a non-academician for a few
years. I have only focused on expressions of language that are {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored it is easy to see
that self-contradictory expressions are simply not truthbearers. >>>>>>>>>>>
“This sentence is not true” can't be true because that would make it
untrue and it can't be false because that would make it true. >>>>>>>>>>>
Within the the definition of truthmaker specified above: “this sentence
has no truthmaker” is simply not a truthbearer. It can't be true within
the above specified definition of truthmaker because this would make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they can be. >>>>>>>>>>
Note,
When I specify the ultimate foundation of all truth then this >>>>>>>>> does apply to truth in logic, truth in math and truth in science. >>>>>>>>
Formal systems are free to define their own truthmakers.
When these definitions result in inconsistency they are
proved to be incorrect.
A formal system can be inconsistent without being incorrect.
*Three laws of logic apply to all propositions*
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system specifies >>>> its own laws, which include all or some or none of those. Besides, a the >>>> word "proposition" need not be and often is not used in the specification >>>> of a formal system.
*This is the way that truth actually works*
As far as is empirially known. But a formal system is not limited by
the limitations of our empirical knowledge.
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
On 6/12/2024 8:41 AM, Mikko wrote:
On 2024-06-12 12:44:55 +0000, olcott said:
On 6/12/2024 2:13 AM, Mikko wrote:
On 2024-06-11 16:06:02 +0000, olcott said:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:Nope. Not for Formal system, which have a specific definition of its >>>>>>>>>> truth-makers, unless you let your definition become trivial for Formal
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision problems* >>>>>>>>>>>>>>
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker. This
entails that if there is nothing in the universe that makes expression X
true then X lacks a truthmaker and is untrue.
X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truth-bearer. X is a
truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>>>>>>>>>>>>
I have been working in this same area as a non-academician for a few
years. I have only focused on expressions of language that are {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored it is easy to see
that self-contradictory expressions are simply not truthbearers. >>>>>>>>>>>>>
“This sentence is not true” can't be true because that would make it
untrue and it can't be false because that would make it true. >>>>>>>>>>>>>
Within the the definition of truthmaker specified above: “this sentence
has no truthmaker” is simply not a truthbearer. It can't be true within
the above specified definition of truthmaker because this would make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they can be. >>>>>>>>>>>>
Note,
When I specify the ultimate foundation of all truth then this >>>>>>>>>>> does apply to truth in logic, truth in math and truth in science. >>>>>>>>>>
logic where a "truth-makers" is what has been defined to be the >>>>>>>>>> "truth-makers" for the system.
Formal systems are free to define their own truthmakers.
When these definitions result in inconsistency they are
proved to be incorrect.
A formal system can be inconsistent without being incorrect.
*Three laws of logic apply to all propositions*
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system specifies >>>>>> its own laws, which include all or some or none of those. Besides, a the >>>>>> word "proposition" need not be and often is not used in the specification
of a formal system.
*This is the way that truth actually works*
As far as is empirially known. But a formal system is not limited by
the limitations of our empirical knowledge.
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
That does not restrict what a formal system can say.
If a formal system says:
"cats <are> fifteen story office buildings"
this formal system is wrong.
On 6/12/2024 6:33 AM, Richard Damon wrote:
On 6/11/24 11:17 PM, olcott wrote:
On 6/11/2024 9:37 PM, Richard Damon wrote:
On 6/11/24 9:57 PM, olcott wrote:
On 6/11/2024 8:44 PM, Richard Damon wrote:
On 6/11/24 12:06 PM, olcott wrote:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
Those laws do not constrain formal systems. Each formal system >>>>>>>> specifies
its own laws, which include all or some or none of those.
Besides, a the
word "proposition" need not be and often is not used in the
specification
of a formal system.
*This is the way that truth actually works*
*People are free to disagree and simply be wrong*
Nope, YOU are simply wrong, because you don't understand how big
logic actualy is, because, it seems, your mind is to small.
Every expression of language X that is
{true on the basis of its meaning}
algorithmically requires a possibly infinite sequence of
finite string transformation rules from its meaning to X.
Unless it is just true as its nature.
Which Mendelson would encode as: ⊢𝒞
A {cat} <is defined as a type of> {animal}.
So, what is that statements truth-maker?
And the truth-maker of that?
You need a set of "first truth-makers" that do not themselves have
something more fundamental at their truth-makers.
I have always had that and told you about it dozens of times.
Some otherwise meaningless finite strings are stipulated to be
true thus providing these finite strings with meaning. https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
Bachelor(x) <entails> ~Married(x)
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
This covers every truth that can possibly exist, true by
definition, true by entailment, true by observation, true
by an infinite sequence of truth preserving operations.
If nothing makes X true then X is untrue.
And not all things are finite strings.
When we ask the question: What is a truthmaker? The generic
answer is
whatever makes an expression of language true <is> its truthmaker. >>>>>>>
But logic systems don't necessaily deal with "expressions of
language" in the sense you seem to be thinking of it.
Finite strings are the most generic form of "expressions of language" >>>>
Every expression of language that is {true on the basis of its meaning}
is a finite string that is connected to the expressions of language that >>> express its meaning.
And that just gets you into circles,
A tree of knowledge has no cycles. Willard Van Orman Quine
was too stupid to see this.
https://www.ditext.com/quine/quine.html
as the expression of language that expresses its meaning needs a
truth-maker too, and that need one for it, and so one.
Some expressions of language are stipulated to be true
thus giving them meaning. Rudolf Carnap may have been
the first to formalize this with his meaning Postulates.
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
Bachelor(x) <entails> ~Married(x)
You need a primative base that is accepted without proof, as there is
nothing to prove it, and that base defines the logic system you are
going to work in.
This entails that if there is nothing in the universe that makes >>>>>>> expression X true then X lacks a truthmaker and is untrue.
Unless it just is true because it is a truthmaker by definition.
That is more than nothing in the universe.
but what makes the definition "true"? What is its truth-maker?
Not everything has a truth-maker, because it might be a truth-maker
itself.
Basic facts are stipulated to be true.
"A cat is an animal" is the same basic fact expressed
in every human language and their mathematically
formalized versions.
So, basic facts do not have a truth-maker in their universe.
True by definition is their truthmaker.
But "A cat is an animal" is NOT a statement that is true in every
system, as some systems might not HAVE a concept of "cat" in it at
all, so that would be a non-sense expression, or might even define it
to be something else.
*That has already been covered by this*
When we ask the question: What is a truthmaker? The generic answer is whatever makes an expression of language true <is> its truthmaker.
This entails that if there is nothing in the universe that makes
expression X true then X lacks a truthmaker and is untrue.
YOu still keep on running into the problem that youu mind clearly
doesn't understand that expresability of logic, and you are stuck just
not understanding how abstractions work.
Not at all. The problem is that you have not yet paid
100% complete attention to ALL of my words.
On 6/12/2024 6:55 PM, Richard Damon wrote:
On 6/12/24 9:05 AM, olcott wrote:
On 6/12/2024 6:33 AM, Richard Damon wrote:
On 6/11/24 11:17 PM, olcott wrote:
Which Mendelson would encode as: ⊢𝒞
A {cat} <is defined as a type of> {animal}.
So, what is that statements truth-maker?
And the truth-maker of that?
You need a set of "first truth-makers" that do not themselves have
something more fundamental at their truth-makers.
I have always had that and told you about it dozens of times.
Some otherwise meaningless finite strings are stipulated to be
true thus providing these finite strings with meaning.
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
Bachelor(x) <entails> ~Married(x)
But that doesn't fit your defintion of a Truth having a truth maker.
OK then you disagree that cats are animals.
As I have told you many hundreds of times DEFINITION
is the foundational basis of every expression that
is {true on the basis of its meaning.
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
This covers every truth that can possibly exist, true by
definition, true by entailment, true by observation, true
by an infinite sequence of truth preserving operations.
If nothing makes X true then X is untrue.
So a "true by definition" or "stipulated truth" needs a truth maker.
DEFINITION is the foundational TRUTH-MAKER
for every expression that is
{true on the basis of its meaning.
What makes that definition or stuplation "true", what is its truth-maker?
What is it about a cat that makes it not
a fifteen story officen building?
When we ask the question: What is a truthmaker? The generic
answer is
whatever makes an expression of language true <is> its truthmaker. >>>>>>>>>
But logic systems don't necessaily deal with "expressions of
language" in the sense you seem to be thinking of it.
Finite strings are the most generic form of "expressions of
language"
And not all things are finite strings.
Every expression of language that is {true on the basis of its
meaning}
is a finite string that is connected to the expressions of language
that
express its meaning.
And that just gets you into circles,
A tree of knowledge has no cycles. Willard Van Orman Quine
was too stupid to see this.
https://www.ditext.com/quine/quine.html
And then what is at is root? Show me a word that can be "defined"
without using any other words.
The Cyc project has {thing} at its root.
as the expression of language that expresses its meaning needs a
truth-maker too, and that need one for it, and so one.
Some expressions of language are stipulated to be true
thus giving them meaning. Rudolf Carnap may have been
the first to formalize this with his meaning Postulates.
But what gives the meaning to the stipulation?
How do you know that a cat is not a fifteen story office building?
A stipulation is just a piece of language, what gives it meaning other
than the words it uses, which need definitions.
There are a set of relations that exist.
Their encoding in the various human languages is arbitrary.
That is the stipulated part.
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
Bachelor(x) <entails> ~Married(x)
You need a primative base that is accepted without proof, as there
is nothing to prove it, and that base defines the logic system you
are going to work in.
This entails that if there is nothing in the universe that makes >>>>>>>>> expression X true then X lacks a truthmaker and is untrue.
Unless it just is true because it is a truthmaker by definition. >>>>>>>>
That is more than nothing in the universe.
but what makes the definition "true"? What is its truth-maker?
Not everything has a truth-maker, because it might be a
truth-maker itself.
Basic facts are stipulated to be true.
"A cat is an animal" is the same basic fact expressed
in every human language and their mathematically
formalized versions.
So, basic facts do not have a truth-maker in their universe.
True by definition is their truthmaker.
Not by your definition.
When we ask the question: What is a truthmaker?
The generic answer is whatever makes an expression
of language true <is> its truthmaker.
When I say ALL THINGS you and most people in truthmaker theory
misinterpret EVERYTHING to mean a few things of a certain type.
But "A cat is an animal" is NOT a statement that is true in every
system, as some systems might not HAVE a concept of "cat" in it at
all, so that would be a non-sense expression, or might even define
it to be something else.
*That has already been covered by this*
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker.
This entails that if there is nothing in the universe that makes
expression X true then X lacks a truthmaker and is untrue.
But what them makes the truthmaker true? You said there were no cycles.
It is like a consistent set of axioms.
{A cat is an animal} no matter what human language
that is encoded within.
YOu still keep on running into the problem that youu mind clearly
doesn't understand that expresability of logic, and you are stuck
just not understanding how abstractions work.
Not at all. The problem is that you have not yet paid
100% complete attention to ALL of my words.
so, what makes the truthmakers true?
What makes {cats} not {fifteen story office buildings} ?
it is merely the conventions of language ?
If they make themselves true, then you have a cycle, which you said
you didn't.
There is no cycle. It is all one huge tree of knowledge.
I used to be able to link to the Cyc project's tree of
knowledge. I have an offline copy of it.
On 6/12/2024 11:45 AM, Mikko wrote:
On 2024-06-12 14:08:43 +0000, olcott said:
On 6/12/2024 8:41 AM, Mikko wrote:
On 2024-06-12 12:44:55 +0000, olcott said:
On 6/12/2024 2:13 AM, Mikko wrote:
On 2024-06-11 16:06:02 +0000, olcott said:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:*Three laws of logic apply to all propositions*
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:Nope. Not for Formal system, which have a specific definition of its
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision problems* >>>>>>>>>>>>>>>>
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker. This
entails that if there is nothing in the universe that makes expression X
true then X lacks a truthmaker and is untrue.
X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truth-bearer. X is a
truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>>>>>>>>>>>>>>
I have been working in this same area as a non-academician for a few
years. I have only focused on expressions of language that are {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored it is easy to see
that self-contradictory expressions are simply not truthbearers.
“This sentence is not true” can't be true because that would make it
untrue and it can't be false because that would make it true. >>>>>>>>>>>>>>>
Within the the definition of truthmaker specified above: “this sentence
has no truthmaker” is simply not a truthbearer. It can't be true within
the above specified definition of truthmaker because this would make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they can be. >>>>>>>>>>>>>>
Note,
When I specify the ultimate foundation of all truth then this >>>>>>>>>>>>> does apply to truth in logic, truth in math and truth in science. >>>>>>>>>>>>
truth-makers, unless you let your definition become trivial for Formal
logic where a "truth-makers" is what has been defined to be the >>>>>>>>>>>> "truth-makers" for the system.
Formal systems are free to define their own truthmakers. >>>>>>>>>>> When these definitions result in inconsistency they are
proved to be incorrect.
A formal system can be inconsistent without being incorrect. >>>>>>>>>
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system specifies
its own laws, which include all or some or none of those. Besides, a the
word "proposition" need not be and often is not used in the specification
of a formal system.
*This is the way that truth actually works*
As far as is empirially known. But a formal system is not limited by >>>>>> the limitations of our empirical knowledge.
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
That does not restrict what a formal system can say.
If a formal system says:
"cats <are> fifteen story office buildings"
this formal system is wrong.
No, it is not. If you inteprete a sentence of that language
*Correct interpretation is hardwired into the formal language*
{cats} and {office buildings} are specified by 128-bit GUIDs.
On 6/13/2024 1:17 AM, Mikko wrote:
On 2024-06-12 17:00:44 +0000, olcott said:
On 6/12/2024 11:45 AM, Mikko wrote:
On 2024-06-12 14:08:43 +0000, olcott said:
On 6/12/2024 8:41 AM, Mikko wrote:
On 2024-06-12 12:44:55 +0000, olcott said:
On 6/12/2024 2:13 AM, Mikko wrote:
On 2024-06-11 16:06:02 +0000, olcott said:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:*Three laws of logic apply to all propositions*
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision problems*
When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker. This
entails that if there is nothing in the universe that makes expression X
true then X lacks a truthmaker and is untrue. >>>>>>>>>>>>>>>>>>
X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truth-bearer. X is a
truth-bearer iff (if and only if) X or ~X has a truthmaker. >>>>>>>>>>>>>>>>>>
I have been working in this same area as a non-academician for a few
years. I have only focused on expressions of language that are {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored it is easy to see
that self-contradictory expressions are simply not truthbearers.
“This sentence is not true” can't be true because that would make it
untrue and it can't be false because that would make it true. >>>>>>>>>>>>>>>>>
Within the the definition of truthmaker specified above: “this sentence
has no truthmaker” is simply not a truthbearer. It can't be true within
the above specified definition of truthmaker because this would make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they can be. >>>>>>>>>>>>>>>>
Note,
When I specify the ultimate foundation of all truth then this >>>>>>>>>>>>>>> does apply to truth in logic, truth in math and truth in science.
Nope. Not for Formal system, which have a specific definition of its
truth-makers, unless you let your definition become trivial for Formal
logic where a "truth-makers" is what has been defined to be the >>>>>>>>>>>>>> "truth-makers" for the system.
Formal systems are free to define their own truthmakers. >>>>>>>>>>>>> When these definitions result in inconsistency they are >>>>>>>>>>>>> proved to be incorrect.
A formal system can be inconsistent without being incorrect. >>>>>>>>>>>
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system specifies
its own laws, which include all or some or none of those. Besides, a the
word "proposition" need not be and often is not used in the specification
of a formal system.
*This is the way that truth actually works*
As far as is empirially known. But a formal system is not limited by >>>>>>>> the limitations of our empirical knowledge.
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
That does not restrict what a formal system can say.
If a formal system says:
"cats <are> fifteen story office buildings"
this formal system is wrong.
No, it is not. If you inteprete a sentence of that language
*Correct interpretation is hardwired into the formal language*
{cats} and {office buildings} are specified by 128-bit GUIDs.
Both of those claims are false about typical formal systems.
When we define formal systems this way all ambiguity and vagueness is eliminated. This is best exemplified in formalized English.
When I say I am going to drive my {cat}. this could mean
Transport(pet, veterinarian) operate(earth_moving_equipment).
When each sense meaning of every term has its own GUID then we
don't have to "interpret" what is mean this is fully specified.
On 6/13/2024 1:17 AM, Mikko wrote:
On 2024-06-12 17:00:44 +0000, olcott said:
On 6/12/2024 11:45 AM, Mikko wrote:
On 2024-06-12 14:08:43 +0000, olcott said:
On 6/12/2024 8:41 AM, Mikko wrote:
On 2024-06-12 12:44:55 +0000, olcott said:
On 6/12/2024 2:13 AM, Mikko wrote:
On 2024-06-11 16:06:02 +0000, olcott said:
On 6/11/2024 2:45 AM, Mikko wrote:
On 2024-06-10 14:43:34 +0000, olcott said:
On 6/10/2024 2:13 AM, Mikko wrote:
On 2024-06-09 18:40:16 +0000, olcott said:*Three laws of logic apply to all propositions*
On 6/9/2024 1:29 PM, Richard Damon wrote:
On 6/9/24 2:13 PM, olcott wrote:
On 6/9/2024 1:08 PM, Richard Damon wrote:
On 6/9/24 1:18 PM, olcott wrote:
On 6/9/2024 10:36 AM, olcott wrote:
*This has direct application to undecidable decision >>>>>>>>>>>>>>>>>> problems*
When we ask the question: What is a truthmaker? The >>>>>>>>>>>>>>>>>> generic answer is
whatever makes an expression of language true <is> its >>>>>>>>>>>>>>>>>> truthmaker. This
entails that if there is nothing in the universe that >>>>>>>>>>>>>>>>>> makes expression X
true then X lacks a truthmaker and is untrue. >>>>>>>>>>>>>>>>>>
X may be untrue because X is false. In that case ~X >>>>>>>>>>>>>>>>>> has a truthmaker.
Now we have the means to unequivocally define >>>>>>>>>>>>>>>>>> truth-bearer. X is a
truth-bearer iff (if and only if) X or ~X has a >>>>>>>>>>>>>>>>>> truthmaker.
I have been working in this same area as a >>>>>>>>>>>>>>>>>> non-academician for a few
years. I have only focused on expressions of language >>>>>>>>>>>>>>>>>> that are {true on
the basis of their meaning}.
Now that truthmaker and truthbearer are fully anchored >>>>>>>>>>>>>>>>> it is easy to see
that self-contradictory expressions are simply not >>>>>>>>>>>>>>>>> truthbearers.
“This sentence is not true” can't be true because that >>>>>>>>>>>>>>>>> would make it
untrue and it can't be false because that would make it >>>>>>>>>>>>>>>>> true.
Within the the definition of truthmaker specified >>>>>>>>>>>>>>>>> above: “this sentence
has no truthmaker” is simply not a truthbearer. It >>>>>>>>>>>>>>>>> can't be true within
the above specified definition of truthmaker because >>>>>>>>>>>>>>>>> this would make it
false. It can't be false because that makes
it true.
Unless the system is inconsistent, in which case they >>>>>>>>>>>>>>>> can be.
Note,
When I specify the ultimate foundation of all truth then >>>>>>>>>>>>>>> this
does apply to truth in logic, truth in math and truth in >>>>>>>>>>>>>>> science.
Nope. Not for Formal system, which have a specific >>>>>>>>>>>>>> definition of its truth-makers, unless you let your >>>>>>>>>>>>>> definition become trivial for Formal logic where a >>>>>>>>>>>>>> "truth-makers" is what has been defined to be the
"truth-makers" for the system.
Formal systems are free to define their own truthmakers. >>>>>>>>>>>>> When these definitions result in inconsistency they are >>>>>>>>>>>>> proved to be incorrect.
A formal system can be inconsistent without being incorrect. >>>>>>>>>>>
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
*No it cannot*
Those laws do not constrain formal systems. Each formal system >>>>>>>>>> specifies
its own laws, which include all or some or none of those.
Besides, a the
word "proposition" need not be and often is not used in the >>>>>>>>>> specification
of a formal system.
*This is the way that truth actually works*
As far as is empirially known. But a formal system is not
limited by
the limitations of our empirical knowledge.
If there really is nothing anywhere that makes expression
of language X true then X is untrue.
That does not restrict what a formal system can say.
If a formal system says:
"cats <are> fifteen story office buildings"
this formal system is wrong.
No, it is not. If you inteprete a sentence of that language
*Correct interpretation is hardwired into the formal language*
{cats} and {office buildings} are specified by 128-bit GUIDs.
Both of those claims are false about typical formal systems.
When we define formal systems this way all ambiguity and vagueness is eliminated. This is best exemplified in formalized English.
When I say I am going to drive my {cat}. this could mean
Transport(pet, veterinarian) operate(earth_moving_equipment).
When each sense meaning of every term has its own GUID then we
don't have to "interpret" what is mean this is fully specified.
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