The truth about truth.

[keith1]

Although truth is a noun it is sort of empty without subject matter. (true) however is an adjective which refers to all those things that either have happened or will happen. There isn't really a word that explains what "truth" as we all seem to call it. But in reality there is; since we constantly check our thought processes with an imaginary figment of our perspective we call reality. Most of which hasn't happened yet and never happened in the first place. Most people call this "truth", the never-ending search for what we don't know already. Sad... No matter how hard I try I could not separate reality truth and belief as most people do these days...

It is as fair for me to ask for an alternative rendition of your thoughts here, so that the two literal renditions will give extra dimension to those thoughts.

Just as it is fair for you not to comply to that request, as if it is, in your opinion, an adequate enough explanation to satisfy your own understanding of the material, so then that is benchmark enough illumination for all.

I only ask for more, but will refrain from demanding it. I am not always so...amiable.

 

[sigurdV]

It is as fair for me to ask for an alternative rendition of your thoughts here, so that the two literal renditions will give extra dimension to those thoughts.

Just as it is fair for you not to comply to that request, as if it is, in your opinion, an adequate enough explanation to satisfy your own understanding of the material, so then that is benchmark enough illumination for all.

I only ask for more, but will refrain from demanding it. I am not always so...amiable.

Hi Keith! You seem amiable enough.
Do you agree that we should set aside some time to
clear matters up concerning the correspondence theory of truth?

The definition of truth: "x" is true if and only if x

The problem with the definition is:
1 Sentence 1 is not true (assumption to be tested)
2 "Sentence 1 is not true" is trueif and only if sentence 1 is not true (true by the definition of truth)
3 Sentence 1 is true if and only if sentence 1 is not true (true by substitution!)

 

[keith1]

The territory is huge! And our maps are slightly medieval...

Though the area is infinitely expanding, as are our maps, in an exacting cadence--the maps that are conveniently close for our observation match our own slow expansion. While the poor devils and their maps that are even an estimated fraction the infinite distances from us--seem all expanding away from us at light speeds.

Alfred Korzybski is remembered for the sentence: The Map is not the Territory.
Which in general is a truth but doesnt seem to include "This sentence contains five words.".

I'm not certain I follow. "The Map" represents the logical truth, just as the "Territory" represents the empirical truth.

http://www.sciforums.com/showthread.php?t=113956

Not a feasible venture.

http://www.sciforums.com/showthread.php?t=113940

See statements above on space expansion.

 

[keith1]

Hi Keith! You seem amiable enough.
Do you agree that we should set aside some time to
clear matters up concerning the correspondence theory of truth?

The definition of truth: "x" is true if and only if x

The problem with the definition is:
1 Sentence 1 is not true (assumption to be tested)
2 "Sentence 1 is not true" if and only if sentence 1 is not true (true by the definition of truth)
3 Sentence 1 is true if and only if sentence 1 is not true (true by substitution!)

All in good time, as that is all I have. I'll be back.

 

[sigurdV]

Lets keep this thread free from off topic debate (if possible).

Ill answer some of your statements in their appropriate channels.

By the way: Thanks for checking them out!

(1) You need to clarify ( I dont understand):

"Though the area is infinitely expanding, as are our maps, in an exacting cadence--the maps that are conveniently close for our observation match our own slow expansion. While the poor devils and their maps that are even an estimated fraction the infinite distances from us--seem all expanding away from us at light speeds."

(2) As Korzybsky (=K) meant it "The map" refers to our mental picture of... whatever it is a picture of!

PS Maybe I could reason (1) out but I must now leave for some physical exercise (=work)

 

[sigurdV]

Im postponing work and advice readers to do the same (JOKE!)

Aristoteles was the first to give a defintion of truth:

To say, of what is as it says it is, is true.

(Im simplifying, check him out:http://sv.wikipedia.org/wiki/Aristoteles#Logik)

As to that, Epimenides, a citizen of Creta had an objection which I simplify:

1 It is not as sentence 1 says!

The conundrum found its way into the bible, see Paulus letter to Titus.

Nowadays the problem has lost some actuality since methods have been given to exclude paradoxes from discourse.

I think Bertrand Russell was first with Principia Mathematica, but it was Alfred Tarski who devised (approximately the same solution) when he presented his semantic approach:

"Semantic theory of truth
The semantic theory of truth has as its general case for a given language:
'P' is true if and only if P
where 'P' is a reference to the sentence (the sentence's name), and P is just the sentence itself.

Logician and philosopher Alfred Tarski developed the theory for formal languages (such as formal logic). Here he restricted it in this way:
no language could contain its own truth predicate, that is, the expression is true could only apply to sentences in some other language. The latter he called an object language, the language being talked about. (It may, in turn, have a truth predicate that can be applied to sentences in still another language.)
The reason for his restriction was that languages that contain their own truth predicate will contain paradoxical sentences like the Liar
: This sentence is not true. See The Liar paradox.
As a result Tarski held that the semantic theory could not be applied to any natural language, such as English, because they contain their own truth predicates.

Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox. Russell and Whitehead attempted to solve these problems in Principia Mathematica by putting statements into a hierarchy of types, wherein a statement cannot refer to itself, but only to statements lower in the hierarchy. This in turn led to new orders of difficulty regarding the precise natures of types and the structures of conceptually possible type systems that have yet to be resolved to this day."

This aproach does not actually SOLVE the paradox.
The Liar Sentences are simply removed!

We should note why the method works: No self reference is allowed.

Which means paradoxes cant dissected, understood and solved...Because we are not allowed to form sentences that can produce them!

Now I make what should be considered a surprising claim:

No paradox can be produced in natural languages, since a logical error always has been done when demonstrating a paradox!

The careful and competent reader has already understood my solution but Im not sure he exists
so i will in a slow and careful manner guide the reader to it.

 

[sigurdV]

This argument is what forced Tarski to restrict the definition of truth:

1 Sentence 1 is not true (assumption to be tested)
2 "Sentence 1 is not true" is true if and only if sentence 1 is not true (true by the definition of truth)
3 Sentence 1 is true if and only if sentence 1 is not true (true by substitution!)

And hidden within the claim in blue is the mistake:

(Liar Identity!) Sentence 1 = "Sentence 1 is not true"

I already proved all Liar Identities to be logically false...

And were done

 

[Pete]

Sentence two is empirically true but logically not true!

Not under different interpretations.
There is no single interpretation of sentence two that is both empirically tryue but logically false.

Any interpretation that is empirically true has no logical truth value.

Someone asked about the sentence:

1 Sentence 1 is not empirically true.

Its slightly different from my sentence 1...

That's right, it's a different example.
Do you agree that it is logically true?

 

[NietzscheHimself]

It is as fair for me to ask for an alternative rendition of your thoughts here, so that the two literal renditions will give extra dimension to those thoughts.

Just as it is fair for you not to comply to that request, as if it is, in your opinion, an adequate enough explanation to satisfy your own understanding of the material, so then that is benchmark enough illumination for all.

I only ask for more, but will refrain from demanding it. I am not always so...amiable.

I believe I have been waiting for just such a question. I've said it twice and for once someone asks instead of demanding a third rendition.

The fact of the matter is that in reality there is always a part of "truth" that remains obscured to the observer of any event. Not to mention the fact that most reality hasn't happened yet or happened so long ago it is impossible to split and check against current reality. On the second that is to say the past is an inseparable piece of our current existence. That is to say the oldest prizes bear a striking resemblance to current realities composition.

And by now I'm sure such a person as yourself is thinking tell me something I'm not quite aware of...

 

[sigurdV]

Hi pete! Welcome

I took the liberty to edit a little,
Since it wasnt clear what you meant by "it"
it was replaced by what I think it meant.

Not under different interpretations.
There is no single interpretation of sentence two that is both empirically tryue but logically false.

Any interpretation that is empirically true has no logical truth value.


That's right, "Sentence 1 is not empirically true" is a different example.
Do you agree that it is logically true?

Now smog thickens!

What is an interpretation?
Is it the same as an understanding?

If a statement can be interpretated in several ways,
can it then really be one, and one statement only?

The laws of logic only applies to statements having only one interpretatiom,
and "interpretation" in that sense means that the statement can be understood only in one way.

Logicians first move (after deciding what logic laws to adhere to) is to decide
what they will accept as well formed sentences of the language in use,
and then they assign truth value to sentenses in a truthfunctional way...

That is that if "a" is true and "b" is true then "a and b" is also true. And this they call an "interpretation". And here its not the same as "understanding" right? Then they start examining proofs...Example:
1 a
2 b
3 a and b
And they will claim that sentence 3 follows from sentences 1 and 2.

HOW "a" gets its truth value is not considered to be a question of logic, it is said to belong to Semantics...

That is, of course, if "a" is an atomic sentence:
The sentence "a and b" is molecular and receives its value from sentences "a" and "b".

In our discussion it is of extreme importance that we understand HOW sentences gets truth values
so I dont accept a separation between Semantic and Logic!

There is a (possibly) artificial separation between statement and argument (= PROOF) Any proof consists of numbered statements and if you "add" them together you form a statement.

So far you have given no proof! Only statements, and you want me to tell if the sentence "1 Sentence 1 is not empirically true." is logically true.

Here is a truth: IF "1 Sentence 1 is not empirically true." is logically true then it follows from logical truths.

So far I have found no such proof...

But I HAVE found at least one proof that the sentence (x="x is not true") is logically false! And if x = "sentence 1" then the proof proves that there is NO sentence 1 such that Sentence 1 = "Sentence 1 is not true"!

Since Sentence 2 is (Sentence 1 = "Sentence 1 is not true) then sentence 2 is logically false! And heres the proof again:

1 x = "x is not true"
2 x is true if and only if "x is not true" is true
3 X is true if and only if x is not true

If we claim that sentence 1 IS the first sentence in the derivation of the Liar paradox (as the liar identity claims)
then we contradict ourselves!
And Logics reason for being is to save ourselves from contradiction.

So sentence 2 is (as yet) the only example of a sentence that is both empirically true and logically false!

No wonder if you believe there are no such beasts!

Heres the possibilities for any sentence:
1 empirically true (theres many)
2 logically true (theres many)
3 empirically false (theres many)
4 logically false (theres many)
5 empirically true and logically true (probably none)
6 empirically true and logically false (at least one!)
7 empirically false and logically true (probably none)
8 empirically false and logically false (probably none)

We must think through the foundations of logic and semantic...
Easier said than done

 

[sigurdV]

Not all truths are accessible.

The fact of the matter is that in reality there is always a part of "truth" that remains obscured to the observer of any event.

Ontological question: The future yet isnt,the present disappears into the past and the past is unaccessible... What exists?

Not to mention the fact that most reality hasn't happened yet or happened so long ago it is impossible to split and check against current reality.
On the second that is to say the past is an inseparable piece of our current existence. That is to say the oldest prizes bear a striking resemblance to current realities composition.

There is Reality and there are our Maps of it. Kant introduced the idea of the (inaccessible?) thing in itself. There are indeed some problems involved in observation and communication of its results. Shall we surrender?

 

[sigurdV]

On Semantics

If you looked up the article on semantics you probably missed this:

"Montague grammar
In the late 1960s, Richard Montague proposed a system for defining semantic entries in the lexicon in terms of the lambda calculus.
In these terms, the syntactic parse of the sentence "John ate every bagel" would consist of a subject (John) and a predicate (ate every bagel);
Montague showed that the meaning of the sentence as a whole could be decomposed into the meanings of its parts and relatively few rules of combination."

This seems the basic idea of semantics: The meaning of a sentence depends only of what words are in it!

Lets experiment:

1 On a paper you write: This paper is not in the waste basket.

2 What you read on the paper is true.

3 Put paper in waste basket.

5 Read paper. Now its not true!

6 What is true does NOT mean the same as what is not true. Right?

7 Then its meaning does depend on something outside the sentence!

 

[Pete]

What is an interpretation?
Is it the same as an understanding?

If a statement can be interpretated in several ways,
can it then really be one, and one statement only?

No.
That's why it is wrong for you to say that "Sentence two is empirically true but logically not true."

So far you have given no proof! Only statements, and you want me to tell if the sentence "1 Sentence 1 is not empirically true." is logically true.

See early in the thread. Post 7:

This sentence is not empirically true​

The sentence is a logical statement - it doesn't rely on any external facts - so it has no empirical truth value.
It is not empirically false. It is not empirically true.
Which is what it says.
Therefore it is logically true.

Here is a truth: IF "1 Sentence 1 is not empirically true." is logically true then it follows from logical truths.

So far I have found no such proof...

But I HAVE found at least one proof that the sentence (x="x is not true") is logically false! And if x = "sentence 1" then the proof proves that there is NO sentence 1 such that Sentence 1 = "Sentence 1 is not true"!

Since Sentence 2 is (Sentence 1 = "Sentence 1 is not true) then sentence 2 is logically false! And heres the proof again:

1 x = "x is not true"
2 x is true if and only if "x is not true" is true
3 X is true if and only if x is not true

This was fully addressed in post 6. Sentence 2 has multiple interpretations. It is not a well defined statement.
In your proof, you are assuming a particular interpretation of Sentence 2 involving only logical truth.
You seem to be considering the statement:

Sentence 1 = "Sentence 1 is logically not true"​

You also seem to be assuming that Sentence 1 is either logically true or logically false.
But that assumption relies on empirical information about Sentence 1, which might be neither logically true nor logically false. Sentence 1 might not be a statement at all.
Since your deduction relies on empirical information about Sentence 1, it is not determining a logical truth.

I maintain that since Sentence 2 referes to an external entity (Sentence 1), it is an empirical statement with no logical truth value.

Heres the possibilities for any sentence:
1 empirically true (theres many)
2 logically true (theres many)
3 empirically false (theres many)
4 logically false (theres many)
5 empirically true and logically true (probably none)
6 empirically true and logically false (at least one!)
7 empirically false and logically true (probably none)
8 empirically false and logically false (probably none)

I maintain that no unambiguous statement can have both a logical truth value and an empirical truth value.
I suggest that the possibilities are:

1. empirically true
2. empirically false
3. logically true
4. logically false
5. Neither true nor false

 

[keith1]

I believe I have been waiting for just such a question. I've said it twice and for once someone asks instead of demanding a third rendition.

The fact of the matter is that in reality there is always a part of "truth" that remains obscured to the observer of any event. Not to mention the fact that most reality hasn't happened yet or happened so long ago it is impossible to split and check against current reality. On the second that is to say the past is an inseparable piece of our current existence. That is to say the oldest prizes bear a striking resemblance to current realities composition.

And by now I'm sure such a person as yourself is thinking tell me something I'm not quite aware of...

Truth must always accompany a "delta" sign,
As uncertainty relates to position or time.

Thank you, N.

 

[sigurdV]

Now we are getting somewhere

Originally Posted by sigurdV

If a statement can be interpretated in several ways,
can it then really be one, and one statement only?

No.
That's why it is wrong for you to say that "Sentence two is empirically true but logically not true."

Sentence 2 has multiple interpretations. It is not a well defined statement.

How then can the paradox arise?

1 Sentence 1 is not true (Liar Sentence)
2 Sentence 1 = "Sentence 1 is not true" (Liar Identity)
3 Sentence 1 is true.

If you claim that the liar identity has more than one interpretation
then derivation of the liar paradox stops!
Its no longer possible to get the negation of sentence 1:

Sentences one and two no longer imply sentence three!

This solves the Liar Paradox! Great News!

In your proof, you are assuming a particular interpretation of Sentence 2 involving only logical truth.
You seem to be considering with the statement:

Sentence 1 = "Sentence 1 is logically not true"​

You also seem to be assuming that Sentence 1 is either logically true or logically false.
That assumption is unacceptable when determining logical truth - it is an empirical fact, not a logical one.

The point is to try to derive the liar paradox!
In order to do sot there MUST be a first sentence in the deduction.
That first sentence is assumed to be true.

I maintain that since Sentence 2 referes to an external entity (Sentence 1), it is an empirical statement with no logical truth value.

I accept that sentence 2 is empirically true but the sentence produces in itself a contradiction therefore it is logically false!
I accept that you dont believe it since it is an extraordinary fact!
IT HAS NEVER BEEN SUSPECTED BEFORE!

I maintain that no unambiguous statement can have both a logical truth value and an empirical truth value.
I suggest that the possibilities are:

1. empirically true
2. empirically false
3. logically true
4. logically false
5. Neither true nor false

I dont expect you to to give up your position easily... You are defending the standard view and I suspect you will get allies eventually.

But claiming that the liar identity in the derivation is ambiguous wont do you no good!
Then the paradox no longer can be derived!

Think this out: When I say that sentence two is empirically true and logically not true...Am I saying its ambiguous?
If so, aint that what you also are saying?

 

[sigurdV]

Originally Posted by Pete
I maintain that no unambiguous statement can have both a logical truth value and an empirical truth value.
I suggest that the possibilities are:
1 empirically true
2 empirically false
3 logically true
4 logically false
5 Neither true nor false

The problem here is that according to the Laws of Classical Logic any statement IS either true or false!

So IF we accept category 5 then we must abandon the Law of the Excluded Third!

That was what Brouwer did... But I stick to Classical Logic!
Its not in need of revision.

The following statement of yours is interesting (to say the least):

No unambiguous statement can have both a logical truth value and an empirical truth value.

Is the following sentence function ambiguous: x = "x is not true" ?

 

[sigurdV]

At the moment theres been 463 visits to this thread and I suspect the general visitor is thinking:

Wow! This is way over my head I better leave at once!

I would prefer if they said : Hello, what is this about?

I will honestly try to answer their questions, and here I hope I speak for ALL contributors in here!

Notice that we are arguing...But nicely! No insults! No Ad Hominem arguments! We just want to understand! Right?

 

[Kumar]

Anekāntavāda (Devanagari: अनेकान्तवाद) is one of the most important and fundamental doctrines of Jainism. It refers to the principles of pluralism and multiplicity of viewpoints, the notion that truth and reality are perceived differently from diverse points of view, and that no single point of view is the complete truth.[1][2]
http://en.wikipedia.org/wiki/Anekantavada

To a Alphanzo tree we can say;-

1. It is a big tree.

2. It is a green leaves heavy tree.

3. It is a shady tree.

4. It is a fruit bearing tree.

5. It is a mango fruit tree.

6. It is a Alphanso variety mango tree.

Though former 5 are not wrong but are partly right but no. 6 can be completely right. A painter should be able to draw right picture on the saying of no 6 but may not be on the saying of other 5. No one may be wrong but may not be right in absolute sense.

 

[Emil]

How we discover the big truths in small things ?

 

[Kumar]

By simplyfying.