- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Brian Tenneson <tennesb.domain.name.hidden>

Date: Mon, 12 Jan 2009 09:21:13 -0800

*The universe is not just black and white...*

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

Or another way to state that is that two truth values (true and false)

are insufficient to describe all propositions.

I propose the following:

If the universe exists and if for all things X and Y, the utterance "X

contains Y" is "proposition," then the universe must "operate" with more

than the two usual truth values, true and false.

Consequently, since the universe does exist, and if we assume that "X

contains Y" is decidable, then at least three truth values are necessary

to describe the state of all "propositions."

First the definitions and then the argument for the above proposition.

IMHO, the only room you might have for disagreement is in the

definitions, as the argument is valid.

*Definitions*

/Proposition/

Define a proposition to be something that can be decided, given enough

resources (such as computational power), and mapped to a single truth

value. An example of a proposition is "I perceive the sky to be blue" as

that is decidedly true (in good weather). Another is "I perceive the sky

to be green," which is decidedly false. A proposition is a statement

that is decidable, meaning there is a "best" truth value to assign to

that statement. If there are only two truth values then an example of a

non-proposition is "this statement is false," the liar's paradox. Later,

we will see that "If the universe exists then it operates on more than

two truth values" is a proposition as well because it will be decidedly

true.

/TV/

Let TV be a set, to be determined, consisting of truth values, possibly

such as TV = {true, false}, that represents all truth values

-sufficient- to allow for -all- propositions to have a unique,

assignable truth value, i.e., sufficient to decide all propositions.

/The universe/

For the purposes of this argument, the universe is the totality of all

that exists. Remark: what exists isn't completely clear and people

disagree on what exists; some, for example, believe that nothing exists

save themselves; this is called solipsism. Nevertheless, the definition

of universe stands as whatever that totality of all that exists is.

/Thing/

X is a thing if, and only if, X is or can be an object of thought.

(Slightly modified version of definition 3 from dictionary.com.)

/Containment/

One thing /contains/ another thing (where the 'another thing' is allowed

to be the first thing) if and only if the first thing has all of the

second thing's contents or constituent parts. In other words, all

content and/or constituent parts within the second thing is also content

of the first thing. (Slightly modified version of definition 3 from

dictionary.com.) Examples: the solar system contains the planet earth

and water molecules contain hydrogen. The primary example is the

universe: the universe contains -all- things.

*Argument*

/Overview/

The argument is an augmented form of Russell's theorem, sometimes

referred to as Russell's paradox, which proves that in Zermelo Frankel

set theory there is no set which contains every other set. The twist is,

this time, when talking about the universe, we know it exists. However,

we'll use the fact that a particular statement is a proposition except

it is neither true nor false. Recall that a proposition must have a

decidable truth value in order to be a proposition; so since this

statement is a proposition, there must be at least one extra truth value

that this proposition is most accurately mapped to in TV.

/The case for the universe operating on more than two truth values./

/Premise 1/

The universe as defined exists.

/Premise 2/

For all things X and Y, the utterance "X contains Y" is a proposition.

(Intuitively, I think the proposition "X contains Y" is 'usually' false.)

Suppose the universe exists and for all things X and Y, the utterance "X

contains Y" is a proposition. Consider the thing that contains all

things that don't contain themselves. Let's denote this thing by the

letter D. D is a thing because it is now an object of thought. The

universe, which contains all things, and itself exists by assumption,

contains D in particular as D is a thing.

Now consider the utterance "D contains D." By assumption, "D contains D"

is a proposition. (X and Y are both D in this particular case.)

/"D contains D" can't be true/

Suppose that "D contains D" is a true proposition. Then, by the

definition of D, "D does not contain D". Therefore, "D contains D" is

false. Since "D contains D" can't be both true and false, our original

assumption that "D contains D" is a true proposition is incorrect.

Consequently, "D contains D" is not a true proposition.

/"D contains D" can't be false/

A similar argument shows that "D contains D" can't be false. If we

suppose "D contains D" is false, then "D does does not contain D" is

true. However, by the definition of D, "D contains D" is then true since

D contains all things that don't contain themselves. This contradiction

implies that "D contains D" is not false.

/Conclusion/

So we've established that "D contains D" is neither true nor false. By

premise 2, "D contains D" is a proposition; by the definition of

proposition, "D contains D" must have a decidable truth value. Since

this truth value is neither true nor false, there must be a third truth

value which "D contains D" is assigned to. This completes the argument.

__________________

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden

For more options, visit this group at http://groups.google.com/group/everything-list?hl=en

-~----------~----~----~----~------~----~------~--~---

Received on Mon Jan 12 2009 - 12:21:24 PST

Date: Mon, 12 Jan 2009 09:21:13 -0800

*The universe is not just black and white...*

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

Or another way to state that is that two truth values (true and false)

are insufficient to describe all propositions.

I propose the following:

If the universe exists and if for all things X and Y, the utterance "X

contains Y" is "proposition," then the universe must "operate" with more

than the two usual truth values, true and false.

Consequently, since the universe does exist, and if we assume that "X

contains Y" is decidable, then at least three truth values are necessary

to describe the state of all "propositions."

First the definitions and then the argument for the above proposition.

IMHO, the only room you might have for disagreement is in the

definitions, as the argument is valid.

*Definitions*

/Proposition/

Define a proposition to be something that can be decided, given enough

resources (such as computational power), and mapped to a single truth

value. An example of a proposition is "I perceive the sky to be blue" as

that is decidedly true (in good weather). Another is "I perceive the sky

to be green," which is decidedly false. A proposition is a statement

that is decidable, meaning there is a "best" truth value to assign to

that statement. If there are only two truth values then an example of a

non-proposition is "this statement is false," the liar's paradox. Later,

we will see that "If the universe exists then it operates on more than

two truth values" is a proposition as well because it will be decidedly

true.

/TV/

Let TV be a set, to be determined, consisting of truth values, possibly

such as TV = {true, false}, that represents all truth values

-sufficient- to allow for -all- propositions to have a unique,

assignable truth value, i.e., sufficient to decide all propositions.

/The universe/

For the purposes of this argument, the universe is the totality of all

that exists. Remark: what exists isn't completely clear and people

disagree on what exists; some, for example, believe that nothing exists

save themselves; this is called solipsism. Nevertheless, the definition

of universe stands as whatever that totality of all that exists is.

/Thing/

X is a thing if, and only if, X is or can be an object of thought.

(Slightly modified version of definition 3 from dictionary.com.)

/Containment/

One thing /contains/ another thing (where the 'another thing' is allowed

to be the first thing) if and only if the first thing has all of the

second thing's contents or constituent parts. In other words, all

content and/or constituent parts within the second thing is also content

of the first thing. (Slightly modified version of definition 3 from

dictionary.com.) Examples: the solar system contains the planet earth

and water molecules contain hydrogen. The primary example is the

universe: the universe contains -all- things.

*Argument*

/Overview/

The argument is an augmented form of Russell's theorem, sometimes

referred to as Russell's paradox, which proves that in Zermelo Frankel

set theory there is no set which contains every other set. The twist is,

this time, when talking about the universe, we know it exists. However,

we'll use the fact that a particular statement is a proposition except

it is neither true nor false. Recall that a proposition must have a

decidable truth value in order to be a proposition; so since this

statement is a proposition, there must be at least one extra truth value

that this proposition is most accurately mapped to in TV.

/The case for the universe operating on more than two truth values./

/Premise 1/

The universe as defined exists.

/Premise 2/

For all things X and Y, the utterance "X contains Y" is a proposition.

(Intuitively, I think the proposition "X contains Y" is 'usually' false.)

Suppose the universe exists and for all things X and Y, the utterance "X

contains Y" is a proposition. Consider the thing that contains all

things that don't contain themselves. Let's denote this thing by the

letter D. D is a thing because it is now an object of thought. The

universe, which contains all things, and itself exists by assumption,

contains D in particular as D is a thing.

Now consider the utterance "D contains D." By assumption, "D contains D"

is a proposition. (X and Y are both D in this particular case.)

/"D contains D" can't be true/

Suppose that "D contains D" is a true proposition. Then, by the

definition of D, "D does not contain D". Therefore, "D contains D" is

false. Since "D contains D" can't be both true and false, our original

assumption that "D contains D" is a true proposition is incorrect.

Consequently, "D contains D" is not a true proposition.

/"D contains D" can't be false/

A similar argument shows that "D contains D" can't be false. If we

suppose "D contains D" is false, then "D does does not contain D" is

true. However, by the definition of D, "D contains D" is then true since

D contains all things that don't contain themselves. This contradiction

implies that "D contains D" is not false.

/Conclusion/

So we've established that "D contains D" is neither true nor false. By

premise 2, "D contains D" is a proposition; by the definition of

proposition, "D contains D" must have a decidable truth value. Since

this truth value is neither true nor false, there must be a third truth

value which "D contains D" is assigned to. This completes the argument.

__________________

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden

For more options, visit this group at http://groups.google.com/group/everything-list?hl=en

-~----------~----~----~----~------~----~------~--~---

Received on Mon Jan 12 2009 - 12:21:24 PST

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:15 PST
*