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     This lecture was given at Cornell during the evening of November
27, 2005.
 
     SYMBOLS AND REFERENTS

     Note:

     OBJECT AND EVENT
 
     In the following discussion the words object and event are
considered to be one and the same thing.  An event is either a moment
of space time bare of any other qualities, or the existence or absence
of other qualities in a space and time.
 
     Event = object = moment in space/time and what's there if
anything.
 
     In normal usage events tend to imply a CHANGE IN STATE in an
object so that if Object A remains Object A at the next moment of
time, no change has occured and thus no event has taken place.  We
find this usage to be fraught, because the very fact that Object A has
changed to a new unit of time, is a change in state, namely what time
the object is in.

     Thus Object A at 12pm and Object A at 1pm are two different
objects even though the only quality that changed between them is
their time of appearance.

     Object A at 12pm has 12pm in its quality set, and Object A at 1pm
has 1pm in its quality set, and those are two different quality sets,
and thus describe two different objects.
 
     In this sense ANY change in quality of an object dissolves that
orginal object and creates a new one in its place.
 
     We call this the candle flame principle, because in still air a
candle flame looks like the same flame from moment to moment, but
clearly its an entirely new flame every second.
 
     Thus a change in position in time is an event.  More accurately
the EXISTENCE of an object at a given time is an event.  And the
appearance of another similar object at the next moment of time is
another event.  Thus movement of an object through time is a series of
unique different events, and unique different objects.

     The only way Object A and Object B can be the same object is if
both exist at the same place and time.  Otherwise they are two
different objects, and clearly the change from Object A to Object B,
even if it is just a change in time, is an event.
 
     Since the state of any moment of time, namely an Object, is a
change from the previous moment of time, the state of any moment of
time is an event, even if all other qualities of those two moments of
time remain identical.
 
     Thus every object is an event, and every event is an object.

     An event is a state in space or a state in time or a state
in anything else that might have a state.
 
     Thus the word event includes the state of single moments of space
time, the state of two adjacent moments of space time where all that
changes was the space or time, and the state of two adjancent moments
of space time where other qualities also changed, which last is the
common language usage of the word event.

     In the common language the statement 'Object A moved along in
time for 10 minutes without changing state' is acceptable and
intuitively understandable.

     However for the purposes of this paper, if Object A has moved
along in time for 10 minutes, it is no longer Object A at the end of
the 10 minutes, nor any place in between, as it has in fact changed
state and has thus become a different object at least once for every
moment of time it has passed through.

     All Godel jails conceeded without contest.
 
#-----------------------------------------------------------------------
 
     SYMBOLS AND REFERENTS

     A symbol is an object that refers to a referent.

     A referent is an object that is referred to by a symbol.

     We know from previous discussion that there are qualities,
objects and classes.

     Objects are collections of qualities, namely the qualities that
describe the object, and classes are collections of objects, namely
all objects that have the qualities that are both common and unique to
that class.

     An object is defined by its qualities, by the qualities that it
has.  And its qualities are gathered together in what we call an
Object Quality Set.

     An object quality set could also be called a description quality
set, and is often just called a quality set.
 
     Classes are also defined by a quality set called the Pertinent
Quality set, its the quality set that is pertinent to the concept of
the class.  In other words objects in the class may have many
different qualities, but only some will be pertinent to why the object
is in the class.

     Pertinent quality sets are subsets of the qualities in an
object's quality set.  In other words any dog has a lot more qualities
than just being a dog, but its those doggy qualities that make it a
dog!

     The pertinent quality set contains all those qualities that are
both common and unique to all the objects that are in that class.

     Common means that every object in the class has those qualities,
in other words every object has the pertinent quality set as a subset
of its full object quality set.

     In other words all dogs are dogs.
 
     Unique means every object in the universe which has those
qualities in the pertinent quality set is a member of that class.

     In other words only dogs are dogs!

     Thus commonness means being in the class implies having the
pertinent quality set, and uniqueness means having the pertinent
quality set implies being in the class.
 

     NOTHING AND SOMETHING
 
     A nothing is an object with the empty quality set.

     A NOthing has NO qualities in its quality set.

     A something is an object with a non empty quality set.

     A SOMETHING has SOME qualities in its quality set.

     The empty quality set means the object has no qualities, utterly
devoid of somethingness.

     A something therefore always has SOME qualities, and a nothing
always has NO qualities at all.

     THE LAW OF ONE NOTHING.
 
     Notice there can only be one nothing.

     If there were two different nothings, then their two qualities
sets would have to be different, and thus not empty.

     Two empty quality sets can never differ from each other.

     They must therefore always be one and the same empty quality set.

     And therefore two identical quality sets must describe two
identical objects or events, namely one object or event.

     One might be tempted to ask if there can be many such nothings
all of which are identical to each other, like 101 dalmations.  But by
being two or more of them, they are no longer identical, because one
is over here, and the other is over there etc, or one is this one, and
the other is that one.

     Even if they are all piled up on top of each other on the same
point, if you can differentiate between the objects in the pile in any
way, those differentiations belong in each separate object's quality
set, and thus they are all different quality sets and thus can not be
empty, and thus not nothings.
 
     So we conclude that can be many sometings, but only one nothing.

 
     THE NATURE OF SYMBOLS AND REFERENTS
 
     Ok, so there are some important things to know about symbols and
referents.

     1.) DEFINITION OF SYMBOL AND REFERENT
 
     The first is, that a symbol is an object that is being used by
someone or something to refer to another object called the referent.

     For example, in a book, you have the word cow, and the word cow
is then used to refer to some real cow out in the real world.

     Or you have a picture of a cow in a book, and its a picture of a
cow named Daisey, with black and white spots, who lived on a
particular farm, at a particular time, and here is this complete
picture of Daisey.

     The picture is an object, and the ink on the paper is an object,
and the picture is made of paper which is an object, and this compound
object is being used to refer to the actual cow that existed in the
real world.

     The referent also is an object, it too exists in the real world,
just as the symbol does.

     Obviously, that's where milk comes from.  Moooo!
 
 
     2.) SYMBOLS AND REFERENTS ARE TWO DIFFERENT OBJECTS

     So the second most important thing to know about symbols and
referents is that they are two different objects.

     And because they are two different objects they have two
different quality sets, each one describing the object that the
quality set belongs to.

     For example the picture of the cow is made of paper, made with
ink, made with a photographic process, is basically two dimensional
and exists in a book.

     That's a symbol, it has qualities and it is an object which
exists.

     The referent is a real cow, its made out of skin and bones and
blood and teeth and eats grass and goes moo!

     So you can see that that the two different objects have two
different quality sets.
 

     3.) SYMBOLS AND REFERENTS HAVE DIFFERENT QUALITY SETS
 
     So the third thing to know about symbols and referents is that
some of the qualities of the symbol will not exist in the referent at
all.  And some of the qualities of the referent will not exist in the
symbol at all.

     For example the picture of the cow is made of paper and ink, and
yet there is no paper or ink in the real cow.
 
     The real cow is made out of blood and bone.  The picture of the
cow is not.

     So each one of these objects has qualities that are unrelated to
the other object.

     Yet the picture of the cow looks very much like the actual cow,
they have 'geometrical congruence or simiarity'.

     Technically congruence means identical in shape and size, while
similar means same shape but different size.  We use the two terms
interchangably through out this lecture.

     Also the paper that the picture is printed on has 'substance' and
so does the real cow.  Both have mass and weight etc.

     Thus there will often be qualities between symbol and referent
that belong to both symbol and referent.
 

     4.) SOME OF THE QUALITIES OF THE SYMBOL ARE MAPPED TO QUALITIES
OF THE REFERENT.
 
     The fourth thing to know about symbols and referents is that some
of the qualities of the symbol are mapped to some of the qualities of
the referent.  In other words some of the qualities of the symbol are
used to refer to some of the qualities of the referent.

     The quality in the symbol that is mapped to the quality in the
referent may be two very different qualities.  It is not the
similarity in qualities that matters but consistency of mapping and
use.
 
     In this way the symbol can be used to refer to the referent, not
just in a dumb way where symbol refers to referent, but in a more
meaningful way in which the symbol's qualities point directly to the
referent's qualities.

     For example in the picture of the cow there is a pictogram of a
cow, of Daisey in particular.  Its a space time drawing, with color,
black and white spots, outlines, projected in two dimensions, that has
a one to one general spatial correspondance to what Daisey actually
looks like.  We call this geometrical congruence between symbol and
referent.

     In this case it is pretty easy to look at the symbol and tell
what it symbolizes because a certain subset of the symbol's qualities
are very related to a subset of the referent's qualities.
 

     5.) SYMBOLS CAN HAVE PICTURE FORM AND DATA CONTENT

     The fifth thing to know about symbols and referents, is that
symbols can have pictogramness or picture form, and they can also have
data content.

     For example the word 'cow' certainly doesn't look like a cow, and
certainly doesn't have a lot of data in it that would tell you what a
cow might be.

     It's an arbitrary symbol.

     However a picture of a cow has both picture form and data
content.

     Picture form means there is a one to one correspondance between
some part of the symbol, the picture of the cow, and the actual
referent.  Picture form means the same thing as geometrical
congruency.

     Data content means that contained in the symbol either in its
picture form or in some other form is encoded data that will tell you
something specific and true about that referent.

     For example a hologram film plate of a cow has very low picture
form but very high data content about the cow.  The data content can
be extracted from the hologram film plate and in fact turned back into
picture form with lasers shining through it at just the right angle.

     A digital photograph of the cow, that is turned into one's and
zero's and then encrypted has zero picture form, but again the data
content remains very high and can be recovered from the data form.

     A scientific tome without pictures or diagrams about the cow is
also a symbol for the cow.
 
     Such a book, being all printed words, has a very high density of
symbols which in themselves have very little picture form or data
content.  The word 'cow' tells you nothing about the referent, but
once connected to a memory bank that understands what cow refers to,
the data content can again be extracted that properly decribes the
referent.

     So the word 'cow' is low picture form and low data content.
 
     A book about the cow is low picture form and high data content.

     A photographic picture of a cow is high picture form and high
data content.

     So in summary symbols can have very high picture form, very high
data content, or both or neither.

     In general however high picture form implies high data content
as long as the picture form is geometrically congruent to the
referent.

 
     6.) SYMBOLS AND REFERENTS ALWAYS HAVE A CAUSAL PATHWAY BETWEEN
THEM.
 
     The sixth thing to know about symbols and referents is that there
is always a causal pathway between them.  For example if you take a
photograph of a cow, clearly light bounces off the cow, comes into the
camera lens, affects the silver crystals on the film, and it gets
developed, and the film is a direct causal result of physical
interactions in the physical universe that can be traced back from the
film surface to the cow and the photons bouncing off the cow from the
sun.

     Even if someone a million years ago invents the word 'cow' to
refer to the general class of cows, there still had to be at some
point a causal pathway between the actual cow and the fact the person
one way or another, directly or indirectly, came up with a word 'cow'
to represent it.  If there were no causal connections between the cow
and the person, the person would never have had a need or cause to
invent a word to refer to it.

     And so that symbol 'cow' invented by the caveman still has a
causal heritage, a causal pathway, back to an actual cow or mental
imagine of a cow in the mind of the person using the symbol.

     Thus where ever there is a symbol that refers to a referent,
there must have been some causal pathway, either direct or indirect
between the original referent and the symbol.

     From this we conclude that if there is no causal pathway between
two objects, they can not be symbol and referent to each other.

     And if they are symbol and referent to each other, there
must be a casual pathway between them.

     So there we have said something very odd, and the astute reader
will notice that the following definition of symbol and referent is a
superset of the normal language usage.
 
     We are going to assert by definition that any two objects which
are causally related to each other are symbol and referent to each
other.  The referent is the earlier event and the symbol is the later
event.

     Notice that when two objects (events) are causally related to
each other, the symbol always contains some data in its final state
about that causal relationship between the symbol and the referent.
Some data content is transfered between referent and symbol everytime
there is a causal event.

     This is called a data transfer via causal imprint.

     In any two objects that are causally related to each other, the
after object is the symbol for the before object which is the
referent, and the after object contains a data 'imprint' on its state
that contains data content about the nature of before object.

     The symbol is imprinted with data content about the referent.

     In the case of arbitrarily chosen symbols chosen by man to refer
to objects, such as the word cow, the data imprint is not so obvious.
It isn't obvious that we can learn about what a cow really is by
looking at the word 'cow'.

     The data transfer has either been interrupted between referent
and symbol, lost to antiquity, or dropped below the noise floor.
 
     But in the case of symbols that are directly and intimately
causally connected to an immediately prior referent event, the data
imprint on the symbol is embodied in the very nature and state of the
symbol after the event occurs.

 
     OBJECT AND EVENT

     The definition of an object as a collection of qualities can be
broadened to mean any event in space time.

     That is, a single moment of space and a single moment of time, or
a single small conglomeration of such, form an event, and therefore
form an object.  
 
     So not only is the alarm clock on your bedroom bureau an object
but so is the fact that it is ringing at 8 o'clock in the morning on
Jan 1st, 2001.  That event of it ringing at that moment is part of the
quality set of the spacetime plus clock at that moment and thus forms
the complete object which exists at that moment.

     Thus an object is comprised of ALL the qualities that are in its
quality set at any given moment of space and time.

     Now another example of an object is a light switch on the wall.
and the wires that connect it to a light bulb via a battery, the power
source, that powers the whole system.

     The whole thing can be considered an object, or it can be broken
down into sub objects of light switch, wires, battery and light bulb.

     THE DATA CONNECTION

     Now notice that there is a causal relationship between the state
of the switch and the state of the light bulb.

     The event, the object, of the switch being off, is correlated
with the event, the object, of the light being off.

     And likewise when the switch is on, there is a correlation with
the light being on.

     Therefore the light being on is a symbol that refers to the
referent of the switch being on.

     And the light being off is a symbol for the referent of the
switch being off.

     The symbol contains data about the referent in that one can look
at the state of the light bulb and generally determine the state of
the switch.  This does not produce certainty but does produce high
dependablity if you trust the fact that the switch is connected to the
light via a proper working causal pathway as intended.

     Notice that the light being on does not give you picture form
content about the switch being on, but certainty gives you data
content about the switch being on.

     Picture form content about the switch being on would be a picture
of the switch being up (on).
 
     An likewise with the light being off doesn't give you a picture
of the switch being off, but does give you data content to the effect
that the switch is in fact off.

     The very presence of a symbol, is itself some measure of data
content indicating the presence of the referent.

     Since existence is a quality in the quality set of both the
symbol and the referent, one can say that the existence of the symbol
implies the existence of the referent with a high, although not
necessarily perfect, degree of dependability.

     Again the dependability of inference from symbol to referent
depends on one's trust in the alleged causal pathway between them.

     As another example, if the light switch were a dimmer, you could
further say that the intensity of the light was a direct correlate of
the position of the dimmer knob in the switch.
 
     In this sense the light bulb has even more data content about
nature of the light switch.
 
     Again notice that 'intensity of light' in the light bulb is a
very different quality than the 'position of dimmer' in the switch,
yet the first quality in the symbol is mapped to the second quality in
the referent, and that data content about the referent traverses that
mapping from referent to symbol via these two different qualities.

      Switch                 Light           Object
-----------------------------------------------------------------
      Referent               Symbol          Role
      Dimmer position        Intensity       Qualities mapped
      Cause             ->   Effect          Data flow

     Data content about the original referent flows along the causal
pathway from referent to symbol via these mappings between qualities
in the referent and qualities in it's chain of later symbols.

     That is HOW data is conferred across space time.
 

     RECAPITULATION

     OK, so let's recap what we have said so far.

     A symbol is an object which is used to refer to a referent.

     A referent is an object that is referred to by a symbol.

     Symbols and referents are two different objects with two
different quality sets, one for each.

     Both objects being two different objects, have qualities that do
not apply to each other.  The symbol has qualities that the referent
does not, and the referent has qualities that the symbol does not.
 
     They may however also share some common similar qualities between
them.  Both symbol and referent EXIST for example, that is a shared
common quality between them.

     The symbol has a subset of qualities that is used to map to a
subset of qualities in the referent, so that the symbol can be used to
refer to the referent, and to contain data about the referent.

     The qualities of the symbol that are used to refer to a qualities
in the referent may or may not be similar to each other.  In the case
of existence, the existence of the symbol is used to refer to the
existence of the referent and in this case they are similar.  However
in other cases they may be very different, such as position of dimmer
switch and intensity of light bulb.

     It is the consistency of the mapping and the dependable
correlation between the qualities so mapped that determine the
ultimate usefulness of such a mapping.

     Symbols can have high data content, or low data content, high
picture form or low picture form.

     There is always a causal pathway between a symbol and a referent.
 

     CONSERVATION OF DATA CONTENT

     The next most thing important thing to understand about symbols
and referents is that data content is to some extent conserved whether
in picture form or not, as the causal pathway proceeds from the
referent to its later chain of symbols.

     The further the symbol is away from the referent in causal hops,
the greater its causal distance is, the more degraded is the data
content.

     Remember that referent and symbol are releative terms relating
before events to after events.  If A B C D E are 5 events, then A is
the referent for B C D and E, and C is the referent for D and E.

     E being the last one on the line is a symbol for A B C or D.

     Since data content is conferred at each event from referent to
symbol, event E has a congolmeration of data that concerns D, C, B and
A!  The data remaining in E about A will be more degraded than the
data remaining in E about D since A is further away from E in causal
distance.

     It is also possible for data content to 'mix' in such a way that
it is no longer possible to tell at E whether its data content is
about A or about a mixture of C and B.

 
     SELF SYMBOLIZING AND SELF REFERENCING OBJECTS

     If we wish to admit that an object can symbolize itself, then the
most accurate symbol for an object would be the object itself.  Thus
as a symbol, any object has perfect picture form and perfect data
content about itself.  Since causal distance between an object and
itself is zero, there will be zero degradation of data content between
referent and symbol.

     To symbolize and to reference mean exactly the same thing, they
are the functions of a symbol pointing to a referent, thus the two
terms self symbolizing and self referencing can be used
interchangably.  As a matter of form we prefer the term self
symbolizing.

     But the minute you are looking at some OTHER object than the
original referent, some other space time event, just even a moment of
time later, then you have introduced causal distance between these two
objects and are no longer looking at something that is the original
referent and is thus only a symbol for it.

     And at that point the data content of the symbol will be somewhat
degraded, not only in detail but in certainty, from the truth of the
original referent.

     Notice that although one might be tempted to claim that an
original referent provides perfect certainty about itself, once you
have moved away from that referent to a symbol, that perfect certainty
must necessarily be degraded to something less than perfect certainty.
 
     Thus one can never get perfect certainty about the nature of a
referent by looking at a LATER DIFFERENT symbol.
 
     So we come up with the next theorem which is that the greater the
distance between referent and symbol the greater the degradation of
the data content of the symbol.

     Even if the object is simply 'moving through time' and othewise
is unchanging, one can never be sure about the nature of the apple 10
minutes ago by looking at the apple now.
 
     It may be true that the apple did not change, but the present
state of the apple does not contain certain proof of that lack of
change.  Thus if all you have is data about the apple now, then all
you have at best is conjecture about the apple 10 minutes ago, based
on your trust that it in fact did not change state.

     The last thing to say about symbols and referents is that neither
one has greater or lesser ontological status than the other.  They are
both objects, the fact that one is being used to refer to another
object, does not one make one subordinate or less important, or less
existing or less real or less actual.

     Both exist, both are actual.

     Ontology is the study of being, of what exists.

     Ontological status basically is an object's existingness.

     For example some people will tell you that good has greater
ontological status than evil, that good is real but evil is an
illusion, doesn't exist, arises from mistakes or the absence of good,
is a misperception or a hallucination.

     Other people will tell you that good and evil have equal
ontological status and they come from completely different roots with
a free willed choice to choose one or other other.

     Ontology is the study of being.

     Epistomology is the study of knowing, the nature of knowledge and
learning, of how we know, and of what can be known.

     Etiology is the study of the origins of causes, as in a medical
diagnoses, but also applies to discovering the referent that gave rise
to a symbol, and to discovery of fundamental causes.

     Etymology is the study of the origins of words, where they come
from, i.e.  their roots in earlier languages.
 
     Entymology is the study of bugs.
 
     Try not to get these confused.

     Philosophy is the precursor to science, which sets out the
framework of the game that science gets to work in by delinating the
nature of IS, definitionally, logically, observably, and intuitively.

     Homer Wilson Smith