Let us
make a rule

There can be no negation of a single object or variable. There is no
legitimate proposition of the sort "not-x", or "not a car" or "a
non-car". Such expressions always imply a class to which, in this case,
the car belongs, such as the class of machines or red objects.

make a rule: Rule 1) Negation moves an object or variable from one group
to another group, such as moving a car from a group of red cars to a
group of differently coloured cars.

However, this leads to an asymmetry between a proposition and its
negation, for while a red car is one colour, its colour negation could
be any number of colours.

We can resolve this asymmetry by marking out another rule: Rule 2)
Negation, in moving objects from one group to another, drops the
particular case. Thus "not a red car" or more awkwardly, "a non-red car"
stipulates no more than that the car that is this colour is now that
colour. The particular colour, in this case red, drops out of
consideration.

Objection: If we describe negation in this way - voiding the particular
case, then we lose information (the fact that it was a "red" car) even
if, granted, it is at the expense of gaining symmetry between
propositions and their negations. Responding to that, we can fall back
on rule 1: singular terms cannot be negated except where such terms
entertain a suppressed property. So in this case, if we want to retain
the fact that the coloured car we have negated is red, then we must
stipulate a group to which the term red belongs. In this case, we cannot
say that the group to which red belongs is the group of cars. For then
the negation refers to car and not red - "a red non-car", rather than
the original proposition "a non-red car".

MoeBlee wrote:
On May 29, 2:11 pm, John Jones <jonescard... at (no spam) aol.com> wrote:

Let us
make a rule

No, let's not make any of your harebrained rules.

What do you do here mobly? I mean really? troll, snipe and run?

you must
be the local pain in the arse

who thinks he has a stake in the
neignbourhood.

On May 29, 2:11 pm, John Jones <jonescard... at (no spam) aol.com> wrote:

Let us
make a rule

No, let's not make any of your harebrained rules.

MoeBlee

Let us make a rule:

There is no legitimate proposition of the sort
"not-x", or "not a car" or "a non-car". Such
expressions always imply a class to which,

On 29 May, 22:11, John Jones <jonescard... at (no spam) aol.com> wrote:
There can be no negation of a single object or variable. There is no
legitimate proposition of the sort "not-x", or "not a car" or "a
non-car". Such expressions always imply a class to which, in this case,
the car belongs, such as the class of machines or red objects.


You might take 'NOT' as predicating the complement of a set or class.

Then I guess you need a distinction:

-- sets = Universe of entities (e.g. cars: "any/all cars",
enumerable);

-- classes = Universe of attributes (e.g. red: "any/all *things* red",
potential);

== atom = Any (singleton?) intersection between sets and classes,
itself its own singleton class-set under identity.(?)

An atom becomes sort of pure symbol: an unpredicated symbol retains
the whole potential across the entire domain. This is another form of
the empty-prevalence:

Empty = (unpredicated-X) = Universe

NOT-Empty = NOT-(unpredicated-X) = NOT-Universe

We do not lose any information, we rather stipulate a limit, the limit
being expressed by negating the universal notion, and the universal
symbol with it.

Informally, that limit might read: you can predicate those x's that
belong to the universe of discourse, with its given symbols and
postulated attributes. The rest is (just) not within that universe...

-LV

On Thu, 29 May 2008, John Jones wrote:

There can be no negation of a single object or variable. There is no
legitimate proposition of the sort "not-x", or "not a car" or "a
non-car".

You're absolutely right onward. 'not' is not a uniary
logical operator but a binary logical operator. For example,
Obama not Hillary.

However, this leads to an asymmetry between a proposition and its
negation, for while a red car is one colour, its colour negation could
be any number of colours.

Greatly so, there is vastly much more in the not what ever, than in the
whatever, which is just a mere whatever and not the everything else.

----

You're absolutely right onward. 'not' is not a uniary
logical operator but a binary logical operator. For example,
Obama not Hillary.

William Elliot <marsh at (no spam) hevanet.remove.com> wrote:

You're absolutely right onward. 'not' is not a uniary
logical operator but a binary logical operator. For example,
Obama not Hillary.


Interesting comment. Let's assume a discussion between two
interlocutors A and B:

A: Who are you going to vote for?
B: Obama, not Hillary.

It could look like 'not' is acting as a binary operator. But I'm not
persuaded that that's the case. Certainly in formal logics 'not' is
defined as a unary operator (is there an exception?). But even in
natural language "Obama, not Hillary" has no meaning out of context.
And when we add meaningful context, then the appearance of being a
binary-operator seems to fade away.

For example, in the context above, "Obama, not Hillary" means:

I'm voting for Obama and I'm not voting for Hillary.

So when we give it meaning (and thus make it truth valuable) it seems
we find that 'not' operates in a fashion consistent with its defined
role in classical logics. In short, it's acting as a unary' operator
applied to the statement: "Voting for Hillary." No? ~Wonderer

The significance of action of a negation will not be found in any mooted
binary or unary property. This fails to distinguish between, or makes
equivalent, x and not-x. The signifcance of a negation is that its an
action, moving from one group to another.

But even in natural language "Obama, not Hillary" has no meaning out of
context.

Bah, "Food, not bombs!"

John Jones <jonescardiff at (no spam) aol.com> wrote:
The significance of action of a negation will not be found in any mooted
binary or unary property. This fails to distinguish between, or makes
equivalent, x and not-x. The signifcance of a negation is that its an
action, moving from one group to another.

Indeed, nobody should be under the delusion that logical operators
and definitions capture the rich complexity of concepts, meaning, and
expressions in natural language (NL). The if-then operator for example
only captures a fragment of what "if...then" means in NL, and may even
violate some of our natural intuitions for such an 'operator'.

But I don't see you're view of negation as moving members of one set
to another as exactly contrary to logical negation. For example, the
definition of 'not' in type theory is a function that maps statements
to their negation.

t,t>, which is a type of expression that if applied to an expression
of type t (type t expressions are truth valuable statements) results
in an expression of type t. And <t,t> is a function. ~Wonderer

ju... at (no spam) diegidio.name wrote:
On 29 May, 22:11, John Jones <jonescard... at (no spam) aol.com> wrote:
There can be no negation of a single object or variable. There is no
legitimate proposition of the sort "not-x", or "not a car" or "a
non-car". Such expressions always imply a class to which, in this case,
the car belongs, such as the class of machines or red objects.

You might take 'NOT' as predicating the complement of a set or class.

OK. I might remove the reference to complement.

Then I guess you need a distinction:

-- sets = Universe of entities (e.g. cars: "any/all cars",
enumerable);

-- classes = Universe of attributes (e.g. red: "any/all *things* red",
potential);

== atom = Any (singleton?) intersection between sets and classes,
itself its own singleton class-set under identity.(?)

I'm not sure about the efficacy of the model of an 'intersection'. An
intersection of lines creates a point, but I can't see that as a working
model for sets.

I also have difficulty in seeing how sets are 'related'.
A set of cutlery and a set of knives are not related by virtue of being
sets.

An atom becomes sort of pure symbol: an unpredicated symbol retains
the whole potential across the entire domain. This is another form of
the empty-prevalence:

By symbol we could mean the criteria for being a certain object whether
or not that object exists. But a symbol always delivers a meaning, by
definition, so ...

Empty = (unpredicated-X) = Universe

Empty could be of course a synonym for no objects, or it could more
awkwardly be a synonym for the manifesting conditions of objects.

NOT-Empty = NOT-(unpredicated-X) = NOT-Universe

We do not lose any information, we rather stipulate a limit, the limit
being expressed by negating the universal notion, and the universal
symbol with it.

Informally, that limit might read: you can predicate those x's that
belong to the universe of discourse, with its given symbols and
postulated attributes. The rest is (just) not within that universe...

-LV-

On 31 May, 21:08, John Jones <jonescard... at (no spam) aol.com> wrote:

ju... at (no spam) diegidio.name wrote:
On 29 May, 22:11, John Jones <jonescard... at (no spam) aol.com> wrote:
There can be no negation of a single object or variable. There is no
legitimate proposition of the sort "not-x", or "not a car" or "a
non-car". Such expressions always imply a class to which, in this case,
the car belongs, such as the class of machines or red objects.

You might take 'NOT' as predicating the complement of a set or class.

OK. I might remove the reference to complement.

You are rather dropping my argument there. Anyway what I meant might
have been better said with reference to the definition of
complementation and the implied notion of universal reference domain:
~A = U \ A.

Then I guess you need a distinction:

-- sets = Universe of entities (e.g. cars: "any/all cars",
enumerable);

-- classes = Universe of attributes (e.g. red: "any/all *things* red",
potential);

== atom = Any (singleton?) intersection between sets and classes,
itself its own singleton class-set under identity.(?)

I'm not sure about the efficacy of the model of an 'intersection'. An
intersection of lines creates a point, but I can't see that as a working
model for sets.

I indeed mean intersection between sets (maybe also called
disjunction?): A /\ B. The concept of "class" is very near to that of
"set" in all theories I am aware of.

I also have difficulty in seeing how sets are 'related'.
A set of cutlery and a set of knives are not related by virtue of being
sets.

First, all sets are sets, and that's a relation of coformality. Then,
between cutlery and knives hold relations of many obvious kinds in
quite common universes of discourse.

An atom becomes sort of pure symbol: an unpredicated symbol retains
the whole potential across the entire domain. This is another form of
the empty-prevalence:

By symbol we could mean the criteria for being a certain object whether
or not that object exists. But a symbol always delivers a meaning, by
definition, so ...

Empty = (unpredicated-X) = Universe

Empty could be of course a synonym for no objects, or it could more
awkwardly be a synonym for the manifesting conditions of objects.

NOT-Empty = NOT-(unpredicated-X) = NOT-Universe

Maybe the other way round:

NOT-Empty = NOT-(unpredicated-X) = Universe
Empty = unpredicated-X = NOT-Universe

-LV

We do not lose any information, we rather stipulate a limit, the limit
being expressed by negating the universal notion, and the universal
symbol with it.

Informally, that limit might read: you can predicate those x's that
belong to the universe of discourse, with its given symbols and
postulated attributes. The rest is (just) not within that universe...

-LV