The truth about truth.

[sigurdV]

On Cathegories of truth

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.

Hi Kumar, and welcome!
Your relevant contribution is refreshingly free from preaching.
I like to read more on the Jainistic viewpoint, is it complete?

[sigurdV]

That said, ill go on "preaching":

There are but two categories of derivations of the Liar Paradox:

Category 1: Using an Empirical fact.
Category 2: Using a definition.

My own example belongs to the first category:

1 Sentence 1 is not true (assumption to be tested)
2 Sentence 1 = "Sentence 1 is not true (true by an empirical fact)

For completeness i will exemplify the other way:

(The Liar Definition) Let "the Liar sentence" be a name of the expression "The Liar sentence is not true."

1 The Liar sentence is not true.(assumption to be tested)
2 The Liar sentence = "The Liar sentence is not true" (true by definition)

Its known that defining something does not autologically bring it into existence:

Let "God" be a name of the perfect being!

Now the argument goes:

A non-existent-being is not perfect, therefore God exists.

So we MUST TEST the definition:

1 The Liar sentence = " The Liar sentence is not true." (assumption)

2 The Liar sentence is true if and only if " The Liar sentence is not true." is true (true by the rule of substitutivity of identity)

3 The Liar sentence is true if and only if the liar sentence is not true.(true by simplifying 2)

Sentence three is a contradiction and therefore the assumption is false! (QED)

And the Liar Definition is NOT valid!!

[Kumar]

On Cathegories of truth



Hi Kumar, and welcome!
Your relevant contribution is refreshingly free from preaching.
I like to read more on the Jainistic viewpoint, is it complete?

We can learn from every existing knowledge, need not necessarily to follow blindly. I think Jainism suggest quality based basic things instead on entity based.

[NietzscheHimself]

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

Thank you, N.

Thank you for a fourth rendition. I was starting to think it was only me when so many philosophers from the past lead their lives from the roots of the concept we speak. We may have found words for their most subconscious thoughts. From the years I have known you and I doubt you remember I've always thought you came closest to interpreting my truest thoughts. For as you may or may not see words mean many things to many people. We all separate common and collective concepts into words which we believe "are" very different things. In actuality it is only a different perspective of the same imagery.

[wellwisher]

A good analogy for defining truth is connected to engineering. The engineer has to build real things in hard reality, at low cost and with minimal impact on the environment. Not all science is up for this task. Only what is called applied science can interact with physical reality at the level needed by the engineer. Theoretical science can touch reality, but the engineer cannot always immerse this into reality, at the level needed to build things, with minimal cost with minimal impact on the environment. There is truth but not enough for full reality immerse, unless you can improve the theory in that direction.

As such, if we compare two versions of truth, I do a practicality comparison. Only the truth can be immersed in reality with minimal cost and minimal impact. It also has to turn a profit or make reality even better.

For example, if you look at liberalism, this creates a lot of social costs and division. There is truth to this, but it is not exactly applied truth. It touches reality on the surface but its inner guts can't be fully immersed in reality.

[sigurdV]

On truth and its applications

A good analogy for defining truth is connected to engineering. The engineer has to build real things in hard reality, at low cost and with minimal impact on the environment. Not all science is up for this task. Only what is called applied science can interact with physical reality at the level needed by the engineer. Theoretical science can touch reality, but the engineer cannot always immerse this into reality, at the level needed to build things, with minimal cost with minimal impact on the environment. There is truth but not enough for full reality immerse, unless you can improve the theory in that direction.

As such, if we compare two versions of truth, I do a practicality comparison. Only the truth can be immersed in reality with minimal cost and minimal impact. It also has to turn a profit or make reality even better.

For example, if you look at liberalism, this creates a lot of social costs and division. There is truth to this, but it is not exactly applied truth. It touches reality on the surface but its inner guts can't be fully immersed in reality.

Hi! And Welcome!
I had trouble in categorising your contribution.
If you have objections let me know.

[DaveC426913]

They are both the same kind.

Logical proofs can only be constructed once we define some axioms about logic. (eg. In a binary state, if something is not true, then it is false.) That statement is not an axiom until we define it to be so. We say "this is what we mean when we use the word 'binary'." We can now build on top on that logic to form logical statements about our world.

Empirical proofs can only be constructed once we conclude that what we see with our own eyes is the only reality we really know. (eg. We cannot have any empirical truths if we posit that we are in The Matrix, where everything is fed to our senses.) We can now build on top on those sensory inputs to form empirical statements about our world.


Either way, our truths are defined by the axioms we lay down with definitions of words and processes we use.

[sigurdV]

On the foundations of logic

They are both the same kind.

Welcome DaveC! Your beginning statement probably sums up whats coming so Ill ignore its vagueness for a while.

Logical proofs can only be constructed once we define some axioms about logic.

Note to all readers: Approach DaveC with care...I can tell he is dangerous!

(eg. In a binary state, if something is not true, then it is false.)

Proof that you are wrong. (eg.In some sense):Consider the famous sentence by Lewis Carrol that is grammatically wellformed but has no sense.
Its obviously not true but if I have understood what you are saying then you want me to believe its also false!?

That statement is not an axiom until we define it to be so. We say "this is what we mean when we use the word 'binary'."

I rarely use the word, and if I do its only in its general meaning. Are you perhaps a modern logician?
As you probably already noticed I rely exclusively on Classical Logic.

We can now build on top on that logic to form logical statements about our world.

Anyway this was the best text Ive read in weeks! Ill take a brake... Maybe you are a Bobby Fischer type of player letting me wait until I lose my temper

Empirical proofs can only be constructed once we conclude that what we see with our own eyes is the only reality we really know. (eg. We cannot have any empirical truths if we posit that we are in The Matrix, where everything is fed to our senses.)

We can now build on top on those sensory inputs to form empirical statements about our world.

Either way, our truths are defined by the axioms we lay down with definitions of words and processes we use.

[DaveC426913]

Welcome DaveC! Your beginning statement probably sums up whats coming so Ill ignore its vagueness for a while.

Er sorry. This was in reference to the opening post, which ended with "there are two kinds of truth".

Proof that you are wrong. (eg.In some sense):Consider the famous sentence by Lewis Carrol that is grammatically wellformed but has no sense.

I think you missed my point. I did not make a claim, so there is nothing to be wrong about.

What I am saying is that logic requires axioms, just like math.

http://en.wikipedia.org/wiki/Axiom

A mathematical axiom is: 1+1=2. This is so because we define it to be so. The rest of our math system is based on it. We can now construct (prove) that 1+2=3.

In logic, one axiom might be that "there exists concepts that are binary. By binary we mean only and exactly two states".
It does not mean there aren't all sorts of other concepts (such as Lewis Carrol's) it simply means that we grant and acknowledge a certain kind. We then go on to say that "In such a binary system the possible results are mutually exclusive. We form an axiom such that if a concept is not true it therefore must be false. In a binary concept there are no other options (else it is not a binary concept.)"

This is a fictional example of a very basic axiom that we can establish and then use in more complex logic.

[sigurdV]

Er sorry.

I think you missed my point. I did not make a claim, so there is nothing to be wrong about.

What I am saying is that logic requires axioms, just like math.

I dont think I misunderstood. I just couldnt resist the shot:
There SOME sense in defining our words BEFORE we form the sentences that will be used to define our words.

A mathematical axiom is: 1+1=2. This is so because we define it to be so. The rest of our math system is based on it. We can now construct (prove) that 1+2=3.

The thought "1+1=2." is one of the most remarkable ideas mankind ever had!
But note that it matters WHAT things you add and HOW addition is defined:
One drop of water in space added to one drop of water still is one drop of water in space!

In logic, one axiom might be that "there exists concepts that are binary. By binary we mean only and exactly two states".
It does not mean there aren't all sorts of other concepts (such as Lewis Carrol's) it simply means that we grant and acknowledge a certain kind. We then go on to say that "In such a binary system the possible results are mutually exclusive. We form an axiom such that if a concept is not true it therefore must be false. In a binary concept there are no other options (else it is not a binary concept.)"

This is a fictional example of a very basic axiom that we can establish and then use in more complex logic.

You clearly are a modern logician
This lonely last survivor of the once widely spread Classical kind...kindly informs you that your days are numbered!
Your kind went binary to escape self reference and meaningless sentences, didnt they?

[sigurdV]

Note to the general reader:

A clash of Titans is going on!

Follow the debate on the truth about truth...

Will the only surviving Classical Logician get EXTERMINATED?

Read all about it, you can observe it...ONLY in here!

On second thought,read about it in here:http://www.sciforums.com/showthread.php?t=114077

[sigurdV]

We can learn from every existing knowledge, need not necessarily to follow blindly. I think Jainism suggest quality based basic things instead on entity based.

Our (western) view is that the joining together of an entity(=x) and a quality(=P) results in a statement(=Px).
Then we recognise a very special quality: TRUTH!

The statement "Px" is true if and only if Px!

Are you perhaps saying that we should instead begin with a quality(=P)
to form the entity (PP)? And claim:

The statement "PP" is true if and only PP

Im not saying the approach is wrong...perhaps existence is a quality like that?
But I think the matter need be explained. Our foundation must be solid so our house can be lived in.

[sigurdV]

This is so because we define it to be so. .

The complete Wittgenstein is a good example:

There is Defining and there is Using.

So (Kumar) we get:
1 defining defining
2 defining using
3 using defining
4 using using

[Kumar]

Our (western) view is that the joining together of an entity(=x) and a quality(=P) results in a statement(=Px).
Then we recognise a very special quality: TRUTH!

The statement "Px" is true if and only if Px!

Are you perhaps saying that we should instead begin with a quality(=P)
to form the entity (PP)? And claim:

The statement "PP" is true if and only PP

Im not saying the approach is wrong...perhaps existence is a quality like that?
But I think the matter need be explained. Our foundation must be solid so our house can be lived in.

No, it is Px only in jain religion in your example but it can be XX only in many other.

http://en.wikipedia.org/wiki/Dharma_(Jainism)

[DaveC426913]

You clearly are a modern logician
This lonely last survivor of the once widely spread Classical kind...kindly informs you that your days are numbered!
Your kind went binary to escape self reference and meaningless sentences, didnt they?

A clash of Titans is going on!

You seem to want to sensationalize everything. This is nothing more than a discussion about logic. If you wish to put a label on yourself as a classical logician as divide up into sides, feel free. Please avoid labeling me though.

[sigurdV]

You seem to want to sensationalize everything. This is nothing more than a discussion about logic. If you wish to put a label on yourself as a classical logician as divide up into sides, feel free. Please avoid labeling me though.

To me a discussion of logic is sensational, because it is rare! And if my manners are offensive to you ill change them. (BTW im more interested in your thinking than your manners.)

As you probably know there was much discussion going on in the early Twentieth century around paradoxes and ways to ensure mathematics and logic from contradiction was discussed. The turnout was that Classical Logic was restricted.
How does your "Binary Logic", or whatever label you prefer to give it, fit into the picture?

"Logical proofs can only be constructed once we define some axioms about logic. (eg. In a binary state, if something is not true, then it is false.) That statement is not an axiom until we define it to be so. We say "this is what we mean when we use the word 'binary'."

In classical logic something that is not true need not also be false!

The conclusion, using classic logic, is: No binary logic as defined by DaveC is a classic logic.

[sigurdV]

What is binary logic good for? Heres how you explain it:

We can now build on top on that logic to form logical statements about our world.

Its very difficult for me not to draw the conclusion that you yourself are a binary logician and therefore also a modern logician

Im not labeling you! I simply draw logical conclusions from your statements...

And when I told you that I am a classical logician then what I actually did was telling you what axioms I use!
Is it really true that you did not understand that?

[DaveC426913]

How does your "Binary Logic", or whatever label you prefer to give it, fit into the picture?

The conclusion, using classic logic, is: No binary logic as defined by DaveC is a classic logic.

Please understand that was a spurious fictional example.

I am not talking about anything so grandiose as any kind of binary logic. As you are acquainted with logic, you would recognize my example as nothing more than a garden variety true/false axiom.

In a concept where there are only two possibilities - that it is true and that it is false - the negation of one is synonymous with the other. i.e.
If (NOT true)
then (false)

If (NOT false)
then (true)

That's all. I'm simply pointing out that logic is based on axioms.

[Kumar]

No, it is Px only in jain religion in your example but it can be XX only in many other.

http://en.wikipedia.org/wiki/Dharma_(Jainism)

Hi sigurdV,
I think you have missed above.

[sigurdV]

Please understand that was a spurious fictional example.

I am not talking about anything so grandiose as any kind of binary logic. As you are acquainted with logic, you would recognize my example as nothing more than a garden variety true/false axiom.

In a concept where there are only two possibilities - that it is true and that it is false - the negation of one is synonymous with the other. i.e.
If (NOT true)
then (false)

If (NOT false)
then (true)

That's all. I'm simply pointing out that logic is based on axioms.

My first reaction on your original posting was: How nice! Here is someone displaying understanding of foundational matters!
(It is true that I have a tendency to sensationalize, but that is only because I have a sense of humour, sometimes used in excess.)

We are using Natural Language to communicate our thinking on logical matters, and it has been claimed (by Alfred Tarski) that Natural Languages are Inconsistent. Classic Logic was once considered to be a SCIENCE! The laws of logic were not just axioms to be interpretended in any way you like...
They were considered to be Natural Laws of Thinking!

When we speak...isnt there a Natural Logic governing our sentences? Thats why I shot at you at first sight!
You must use some logic while selecting your axioms! Right?

(Why not first define the words we use to form the sentences we use to define our words?)