Freethought & Rationalism Archive

Witt · 05-18-2003, 09:39 AM

Witt: Absolute truth does seem unattainable.

Darth: yes, it certainly seems so, but isn't

W: Can you provide an example of absolute truth?

D: The phrase and/or the meaning of "I Am", seems to fit the bill.

Darth exists, was not true 10M years ago..so, how can it be absolute?
If the future were knowable, how can we know that 'Darth exists' is true 10M years from now?

W: And, how do you test it?

D: Everything that exists, can if it had a mouth confirm to you that it Is

How do you know that this is absolute??

D: When you look at a stone is it not "saying" to you "I am"? Then you grab it, look at it, disect it and confirm that the stone in fact Is
Because it Is you can see it and the satement of "I Am" that follows it.

x exists, does indeed follow from, x has a particular property.

That is the essence of "I think therefore I am".

Existence is defined:

x exists, means, there is some property that x has.

Witt

Thomas Ash · 05-19-2003, 01:58 AM

Quote:

Originally posted by Witt
What do you mean by universal truth?

I take it to mean absolute truth or ultimate truth.

I think this sums up the whole "universal truth" debate in a nutshell. Self-styled opponents of "universal truth" take it to mean some grand metaphysical concept of "the One Ultimate Truth Behind the Universe(tm)" (like 42 in The Hitchhiker's Guide to the Galxy

- an answer which sums up quite neatly the whole pointlessness of what most people think of as the typical philosophy question - "What is the answer to life, the universe and everything?".) Or else they mean some necessary, unchanging absolute truth beneath the structure of the universe.
But people like me who believe in "universal truth" just think it means facts, like "I'm feeling happy today

" or "Elvis Presley really is dead

" (sorry if I offended any closet Elviphobes there...!)

T. E. Lords · 05-19-2003, 02:20 AM

Couldn't you just reword the statement to read

"The only universal truth is that, besides this statement, there are no universal truths"

Darth Dane · 05-19-2003, 02:44 AM

"The only universal truth is that, besides this statement, there are no universal truths"

God is the unmovable mover, according to some.

So teh only thing that never moves or wavers, is that fact. Everything else is relative and dependant on the situation.

Universal truth = stays the same
No universal truth = is always in motion

These two are connected. Connected by what? I say it is conciousnes, in lack of a better word.

DD - Love Spliff

Witt · 05-19-2003, 08:59 AM

Hi Witt: Thanks for your post.

You're welcome.
A=A, seems to interest many different perspectives.

quote:
--------------------------------------------------------------------------------
Originally posted by Witt
John Page: A truth is the result of comparing two entities and deeming them similar enough to be identical.

Do you mean that all truth is decided in this way?
I agree with, some truths are decided that way.
--------------------------------------------------------------------------------

John: IMO this is where all truths stem from. Of course, you are free to invent any system of divining the truth that you wish.

"divining" what is that?

I don't agree that A=A is required to prove any theorem of: propositional logic, boolean logic, syllogistic logic, etc..

Identity is introduced in first order predicate logic, with the two axioms: 1. (All x)(x=x), 2. (All x)(All y)(x=y -> (Fx <-> Fy)).

Axiom 1. (All x)(x=x), is the law of identity.

quote:
--------------------------------------------------------------------------------
Originally posted by Witt
"Let's assume that they (or what they represent) are identical (even though they're not, see LOI)."

??

--------------------------------------------------------------------------------

Law of Identity. Two things cannot have the same identity.

quote:
--------------------------------------------------------------------------------
Originally posted by Witt
Surely A=A means, the object named by A is exactly identical with the object named by A.
There is no 'similar enough' to be identical here.
They are identical because there is no difference.
--------------------------------------------------------------------------------

John: Agreed, an object can have two names - but it is not the names we are comparing.

I don't agree.
Objects have unique names.
An object with two names is not unique.
Although, it is true that objects may have many different 'descriptions'.

eg. (The current president of the US)=(The previous govenor of Texas)
(the morning star)=(the evening star)

quote:
--------------------------------------------------------------------------------
Originally posted by Witt
John=John, talks about the person named john.
"John"="John", talks about the name of John.
--------------------------------------------------------------------------------

John: Yes, this is a tautology or truism, a self-defining statement.

What does self-defining mean?

quote:
--------------------------------------------------------------------------------
Originally posted by Witt
I agree that the process of deciding truth is a mental activity.
Truth is a mental concept, ie. without minds there is no truth.

"A truth is relative to the mind that thinks it." is false, imo.

A truth is definitive only relative to the system that provides it.
--------------------------------------------------------------------------------

??

If we cannot show that a given proposition is true then we cannot know that it is true.
To know is to be able to show.

'How' we know is as important as 'What' we know.

John: I offer the following fro your consideration. The object is (literally) this "A". Note how this letter A travels through time, its form preserved through persistent pattern of electron on your screen (or some such). Let us call this letter the name a, now you can say a=a because the have the same meaning, i.e. both are a symbolic representation of the "A". Hence the Law of Identity a=a

Yes, and only when they have exactly the same meaning.

x=y, is defined, x has a property iff y has the same property..for all properties.

D1. x=y, defined, (All F)(Fx <-> Fy)

a=a, means, a has a property iff a has the same property..for all properties.
Which is tautologous. (All F)(Fa <-> Fa), is a theorem.

(which you are free to discard, and this is fun but most logicians will have an emotional reaction to because they're not logical ).

Free logics do deny, x=x for all x.
Free logics must also define identity different from D1.

John: As I see it (which could well be mistaken) the "A" that we discuss in logic is not a thing at all, it is a set of characteristics that we can recognize as "the form of the letter A". Now forms can be assumed identical hence things can appear as if they are the same as other things due to commonality of form.

Identifying 'the set of properties which an individual has' with 'the individual' may have benefits, I am not familiar with its use.

"Have I made my position clearer or not?"

I need all the help I can get.

Witt

John Page · 05-19-2003, 10:37 AM

Hi Witt,

Quote:

Originally posted by Witt
John: IMO this is where all truths stem from. Of course, you are free to invent any system of divining the truth that you wish.

"divining" what is that?

Telling, deciding, determining.

Quote:

Originally posted by Witt
I don't agree that A=A is required to prove any theorem of: propositional logic, boolean logic, syllogistic logic, etc..

How do you prove, for example P or P = P without the Law of Identity?

Quote:

Originally posted by Witt
Axiom 1. (All x)(x=x), is the law of identity.

.....Originally posted by Witt
Surely A=A means, the object named by A is exactly identical with the object named by A.
There is no 'similar enough' to be identical here.
They are identical because there is no difference.

John: Agreed, an object can have two names - but it is not the names we are comparing.

I don't agree.
Objects have unique names.
An object with two names is not unique.
Although, it is true that objects may have many different 'descriptions'.

Sorry, I don't understand. Naming an object doesn't change the object (it merely asserts that the definition associated with the name can be applied to the object). Also, regarding the predicate logic example of the LOI you give (For all x)(x=x), this implies that there may be more than one x - in which case how can they be identical.

Quote:

Originally posted by Witt
John: Yes, this is a tautology or truism, a self-defining statement.

What does self-defining mean?

Tautological.

Quote:

Originally posted by Witt
If we cannot show that a given proposition is true then we cannot know that it is true.
To know is to be able to show.

I disagree on this one, I know I exist from my own subjective experience but I cannot show this to you. (At this time, with current technology) it is not possible for you to participate directly in my mental activities.

Quote:

Originally posted by Witt
x=y, is defined, x has a property iff y has the same property..for all properties.

D1. x=y, defined, (All F)(Fx <-> Fy)

a=a, means, a has a property iff a has the same property..for all properties.
Which is tautologous. (All F)(Fa <-> Fa), is a theorem.

Agreed, but what is F? (IMO, in reality, all we're doing is comparing properties.)

Quote:

Originally posted by Witt
Free logics do deny, x=x for all x.
Free logics must also define identity different from D1.

I'll pass on this one right now - but given your familiarity with set theory do you wish to comment on my Axiom of Choice Thread?

Cheers, john

Witt · 05-19-2003, 11:28 AM

John Page:
I'll pass on this one right now - but given your familiarity with set theory do you wish to comment on my Axiom of Choice Thread?

The multiplicitive axiom, (AC) seems to me beyond doubt.

ZF(C), apparently agrees.

The axiom of choice seem too mathematical to me, at this time.

I think that: when we express extensionality and comprehension clearly enough, AC will be apparent.

Witt

John Page · 05-19-2003, 01:29 PM

Quote:

Originally posted by Witt
I think that: when we express extensionality and comprehension clearly enough, AC will be apparent.

IMO it is a mistake to assume that the term "set" can be extended over "the set of all sets".

Here's a couple of reasons.
1. A set that has the same properties does not exist at a "higher level" or category as implied by extension.
2. The set "of all sets" is not identical to "the set of all sets" - i.e. there is a category mistake.

If the logic cannot determine - who is choosing, and is this outside of logic?

Cheers, John

Witt · 05-20-2003, 05:24 AM

John Page:
IMO it is a mistake to assume that the term "set" can be extended over "the set of all sets".

Here's a couple of reasons.
1. A set that has the same properties does not exist at a "higher level" or category as implied by extension.
2. The set "of all sets" is not identical to "the set of all sets" - i.e. there is a category mistake.
-----------------------------------

The set of all sets is defined: those individuals which are self-identical.

V={x:x=x}
or
V={x:Exists(x)}
or
V={the y: Ax(x e y)}

V=V, and V is a member of V, ie. (V e V), are true.

V exists, is true by axiom. ie. EyAx(x e y) is an axiom.

V includes everything, including you and me.

How can you deny the existence of that class which contains all existent things?

Witt

John Page · 05-20-2003, 07:16 AM

Quote:

Originally posted by Witt
How can you deny the existence of that class which contains all existent things?

What you are proposing is the concept of a class that contains all things. I do not deny that the concept exists but this idea is contained within your mind - how can something within your mind (a class of things) contain all existent things? That would seem to require an idealist position.

The "set of all sets" is a way of describing all things that we define as having common properties - but the only common property they have is existence as mental concepts. The "concept(a)" of "all concepts(b)" is still a "concept(c)" but just because I'm using the word concept a lot doesn't mean the name always refers to exactly the same thing or exactly the same set of properties.

Russell's Antinomy is what occurs when you insist that a representational system is reality:

Quote:

Russell's paradox arises as a result of naive set theory's so-called unrestricted comprehension (or abstraction) axiom. Originally introduced by Georg Cantor, the axiom states that any predicate expression, P(x), which contains x as a free variable, will determine a set whose members are exactly those objects which satisfy P(x). The axiom gives form to the intuition that any coherent condition may be used to determine a set (or class). Most attempts at resolving Russell's paradox have therefore concentrated on various ways of restricting or abandoning this axiom.

With the "set of all sets" constrained to being a mental concept, reality continues unchanged. The irony is that Cantor's axiom of abstraction is a concept for abstration but Russell tried to use it to categorize "things-in-themselves" when the analysis only applies to "things-as-they-appear-to-us".

Cheers, John

05-19-2003, 08:59 AM	#25
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	A=A Hi Witt: Thanks for your post. You're welcome. A=A, seems to interest many different perspectives. quote: -------------------------------------------------------------------------------- Originally posted by Witt John Page: A truth is the result of comparing two entities and deeming them similar enough to be identical. Do you mean that all truth is decided in this way? I agree with, some truths are decided that way. -------------------------------------------------------------------------------- John: IMO this is where all truths stem from. Of course, you are free to invent any system of divining the truth that you wish. "divining" what is that? I don't agree that A=A is required to prove any theorem of: propositional logic, boolean logic, syllogistic logic, etc.. Identity is introduced in first order predicate logic, with the two axioms: 1. (All x)(x=x), 2. (All x)(All y)(x=y -> (Fx <-> Fy)). Axiom 1. (All x)(x=x), is the law of identity. quote: -------------------------------------------------------------------------------- Originally posted by Witt "Let's assume that they (or what they represent) are identical (even though they're not, see LOI)." ?? -------------------------------------------------------------------------------- Law of Identity. Two things cannot have the same identity. quote: -------------------------------------------------------------------------------- Originally posted by Witt Surely A=A means, the object named by A is exactly identical with the object named by A. There is no 'similar enough' to be identical here. They are identical because there is no difference. -------------------------------------------------------------------------------- John: Agreed, an object can have two names - but it is not the names we are comparing. I don't agree. Objects have unique names. An object with two names is not unique. Although, it is true that objects may have many different 'descriptions'. eg. (The current president of the US)=(The previous govenor of Texas) (the morning star)=(the evening star) quote: -------------------------------------------------------------------------------- Originally posted by Witt John=John, talks about the person named john. "John"="John", talks about the name of John. -------------------------------------------------------------------------------- John: Yes, this is a tautology or truism, a self-defining statement. What does self-defining mean? quote: -------------------------------------------------------------------------------- Originally posted by Witt I agree that the process of deciding truth is a mental activity. Truth is a mental concept, ie. without minds there is no truth. "A truth is relative to the mind that thinks it." is false, imo. A truth is definitive only relative to the system that provides it. -------------------------------------------------------------------------------- ?? If we cannot show that a given proposition is true then we cannot know that it is true. To know is to be able to show. 'How' we know is as important as 'What' we know. John: I offer the following fro your consideration. The object is (literally) this "A". Note how this letter A travels through time, its form preserved through persistent pattern of electron on your screen (or some such). Let us call this letter the name a, now you can say a=a because the have the same meaning, i.e. both are a symbolic representation of the "A". Hence the Law of Identity a=a Yes, and only when they have exactly the same meaning. x=y, is defined, x has a property iff y has the same property..for all properties. D1. x=y, defined, (All F)(Fx <-> Fy) a=a, means, a has a property iff a has the same property..for all properties. Which is tautologous. (All F)(Fa <-> Fa), is a theorem. (which you are free to discard, and this is fun but most logicians will have an emotional reaction to because they're not logical ). Free logics do deny, x=x for all x. Free logics must also define identity different from D1. John: As I see it (which could well be mistaken) the "A" that we discuss in logic is not a thing at all, it is a set of characteristics that we can recognize as "the form of the letter A". Now forms can be assumed identical hence things can appear as if they are the same as other things due to commonality of form. Identifying 'the set of properties which an individual has' with 'the individual' may have benefits, I am not familiar with its use. "Have I made my position clearer or not?" I need all the help I can get. Witt

05-19-2003, 11:28 AM	#27
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	The axiom of choice John Page: I'll pass on this one right now - but given your familiarity with set theory do you wish to comment on my Axiom of Choice Thread? The multiplicitive axiom, (AC) seems to me beyond doubt. ZF(C), apparently agrees. The axiom of choice seem too mathematical to me, at this time. I think that: when we express extensionality and comprehension clearly enough, AC will be apparent. Witt

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05-18-2003, 09:39 AM	#21
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	Witt: Absolute truth does seem unattainable. Darth: yes, it certainly seems so, but isn't W: Can you provide an example of absolute truth? D: The phrase and/or the meaning of "I Am", seems to fit the bill. Darth exists, was not true 10M years ago..so, how can it be absolute? If the future were knowable, how can we know that 'Darth exists' is true 10M years from now? W: And, how do you test it? D: Everything that exists, can if it had a mouth confirm to you that it Is How do you know that this is absolute?? D: When you look at a stone is it not "saying" to you "I am"? Then you grab it, look at it, disect it and confirm that the stone in fact Is Because it Is you can see it and the satement of "I Am" that follows it. x exists, does indeed follow from, x has a particular property. That is the essence of "I think therefore I am". Existence is defined: x exists, means, there is some property that x has. Witt

05-19-2003, 02:20 AM	#23
T. E. Lords Junior Member Join Date: Sep 2002 Location: El Paso Tx Posts: 66	Couldn't you just reword the statement to read "The only universal truth is that, besides this statement, there are no universal truths"

05-19-2003, 02:44 AM	#24
Darth Dane Veteran Member Join Date: Dec 2002 Location: Required Posts: 2,349	"The only universal truth is that, besides this statement, there are no universal truths" God is the unmovable mover, according to some. So teh only thing that never moves or wavers, is that fact. Everything else is relative and dependant on the situation. Universal truth = stays the same No universal truth = is always in motion These two are connected. Connected by what? I say it is conciousnes, in lack of a better word. DD - Love Spliff

05-20-2003, 05:24 AM	#29
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	John Page: IMO it is a mistake to assume that the term "set" can be extended over "the set of all sets". Here's a couple of reasons. 1. A set that has the same properties does not exist at a "higher level" or category as implied by extension. 2. The set "of all sets" is not identical to "the set of all sets" - i.e. there is a category mistake. ----------------------------------- The set of all sets is defined: those individuals which are self-identical. V={x:x=x} or V={x:Exists(x)} or V={the y: Ax(x e y)} V=V, and V is a member of V, ie. (V e V), are true. V exists, is true by axiom. ie. EyAx(x e y) is an axiom. V includes everything, including you and me. How can you deny the existence of that class which contains all existent things? Witt

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