1.0   A concept is a relation between TWO objects

    As with the word object, our philosophers have also had little luck telling us unambiguously what a concept
    is. Specifically, they still have trouble clarifying unambiguously how a concept differs from an object.

    “ A concept is an abstract idea or a mental symbol, typically associated with a corres-
       ponding representation in language or symbology, that denotes all of the objects in
       a given category or class of entities, interactions, phenomena, or relationships
       between them. Concepts are abstract in that they omit the differences of the things
       in their extension, treating them as if they were identical. They are universal in that
       they apply equally to every thing in their extension.” [1]

    “ Frege rigidly distinguished objects from functions…Frege took functional application
       ‘ƒ(x)’ as the principal operation for forming complex names of objects in his language.
       The expression ‘ƒ(x)’ denotes the object to which the function ƒ maps the object x.
       Frege called the object x the ‘argument’ of the function ƒ and called ƒ(x) the ‘value’ of
       the function. Since Frege also recognized two special objects he called truth-values
       (The True and The False), he defined a concept to be any function that always maps
       its arguments to truth-values. For example, whereas ‘x2 +3’ and ‘father-of(x)’ denote
       ordinary functions, the expressions ‘Happy(x)’ and ‘x > 5’ denote concepts. The
       former denotes a concept which maps any object that is happy to The True and all
       other objects to The False; the latter denotes a concept that maps any object that is
       greater than 5 to The True and all other objects to The False.” [2]

    “ ‘Socrates is a philosopher’ consists of ‘Socrates’, which signifies the Object Socrates,
       and ‘is a philosopher’, which signifies the Concept of being a philosopher.” [2]

    [Socrates is an object? Perhaps Man is an object or a human is an object, but 'Socrates'
     is a concept. We named this man Socrates to distinguish him from Plato and Euclid. The
     word 'Socrates' embodies a relation. When you point and say 'Socrates', the ET just sees
     Man.]

    In other words, the experts are saying that a concept is a concept! Great! What have we learned?
    If, as the philosophers argue, a concept is an abstract idea that I have in my mind, is the leprechaun I am
    thinking about at this moment an object or a concept? Isn’t a leprechaun ultimately just a little man? Doesn’t
    this little man have shape? Isn’t a centaur just a strange kind of horse? Isn’t a tribar just a weird geometric
    figure (Fig. 1)? Does the fact that I visualize them in my mind rather than have them in front of me change their
    status as objects? The definition the philosophers propose does not clarify how to distinguish an abstract
    object from an abstract concept. The listener can visualize the abstract object because it has shape. We
    cannot visualize that which doesn’t. There is no excuse for confusing objects with concepts in Science.

    What distinguishes a concept from an object is that a concept is artificial (man-made) and invokes a minimum
    of two objects (Fig. 2). All concepts, without exceptions, were invented by Man. In other words, the definition
    of the word concept is predicated on the definition of the word object. If you are marooned on an island in the
    middle of nowhere with an ET, before you can communicate concepts to him, you must teach him the name of
    the objects. You point and say 'rock,' 'tree,' 'coconut.' Before he understands verbs such as climb, knock,
    break, eat, and survive you must absolutely have a physical intermediary. Only then can you communicate to
    him sophisticated dynamic concepts, for example, that he should climb the tree and knock the coconut to the
    ground where you will break it with a rock so that you can both eat and thus survive.

    concept: A word that embodies or invokes more than one object or location.
                     (Syn.: notion, idea, mathematical object, particulars, member of a set).

    The philosophers were always hovering around the correct definitions of the words object and concept. They
    eventually came to realize somewhat vaguely that object has to do with the number 1.

    “ Natural objects are, philosophically speaking, individuals; they are involved as
       units in dynamic, causal processes.” [4]

    What they failed to realize is that a concept has to do with the number 2. So no cigar!

    A concept is a relation between two or more things or locations, and this guarantees that we can find its
    antonym or something with which it contrasts. Hot is the opposite of cold, on is the opposite of not on, and
    mass is the opposite of mass-less. Run is a comparison between two locations of one object which effectively
    amounts to a comparison between two objects: one real and one imaginary. We are considering a minimum
    of two frames, each of which contains the same object at different locations. We can just as well assume that
    we are staring at two different objects. We are also implicitly contrasting run against walk, jump, and swim,
    and thus treating it as a category of motion. You point and say ‘run’, but the ET only sees boy. The prosecutor
    must necessarily explain to an ET what run alludes to. Even the ‘categories’ object and space are themselves
    concepts, the former meaning shape and the latter meaning no shape. On the other hand, not a single
    standalone shape has an opposite. Cat is not the opposite of dog and tree is not the opposite of rock or of
    tree-less. The word cat becomes a concept when you treat it as a category of animals: when you contrast it
    against a dog or a fish. When you point to a shape and say cat, you are identifying an object. The
    extraterrestrial identifies the word cat with the designated shape. A concept is something the prosecutor of a
    theory has to explain and the jury, in the best of cases, understands. An object is a shape the prosecutor
    points to and names. The juror visualizes (i.e., sees) the object and identifies it with the sound you just
    vocalized.

    ________________________________________________________________________________________



    Last modified 02/22/08


        Copyright © by Nila Gaede 2008
QUICK! Get a bucket
of water, you
dummy! I'm just a
concept!
BUT NOT MY DRESS!

    2.0   Static versus dynamic concepts

    There are two general types of concepts, static and dynamic. For example, a ratio is a static concept. We can
    look at a circle with a line drawn down the center and conceptualize the concept π in a single image or frame.
    In order to conceptualize a dynamic concept such as a rate, we need to see the thing move for two or more
    frames. A concept such as large is also static. We don't need to see anything move to conceptualize large or
    largest. We just need to compare two or more objects within a single image. On the other hand, the concept
    inflation by its very nature invokes motion. True adjectives (flat, continuous, unbounded, straight) and
    prepositions of location (at, on, in, below/above, behind, among) are conceptually static. True adverbs
    (rectilinear, constant, perpetual, incessant) and prepositions such as  (to, under - over, forward, through,
    along, nearby) are inherently dynamic. Static concepts also include nouns of ordinary speech such as
    direction, dimension, length, and point particle. Dynamic concepts include almost all the 'mathematical
    objects' of Mathematical Physics: energy, mass, time, field, force, vector, number, volume, singularity, black
    hole, dark matter, wave, space-time. The idiots of Mathematics summarily convert these dynamic concepts
    into static objects when they inadvertently begin to move them around.

    The following words exemplify the manner in which some of these concepts embody two objects or locations:

    on (static concept): irremediably invokes two entities (e.g., a glass above and in contact with a table).
    You can’t use on unless you implicitly or explicitly allude to two objects.

    energy (dynamic concept): involves motion or a comparison (e.g., potential energy has velocity
    embedded in the equation.

    volume (dynamic concept): the mathematicians routinely confuse this concept for an object. For
    example, a cube is an object and becomes a concept when used, compared, or defined in some way. A
    volume, on the other hand, will forever remain a concept. We use units such as ‘cubic meters’ (m ³) to
    identify a volume. Now try it with a cube. What meaning would it have to append units to a cube?
    If the prosecutors want the ET to know what a cube is, they cannot present an expression such as 3 m³
    and hope that the alien ‘understands’ what they are talking about. The prosecutors have no choice but
    to point to a cube and say ‘cube.’ Only then can the ET visualize the object in question and identify it
    with the sound. If the prosecutors want the ET to understand the ‘concept’ cube, they have no choice
    but to introduce other objects such as a sphere, a square, or a chair. Conversely, a volume makes no
    provision for shape. As far as Mathematics is concerned, we can have distinct geometric figures –
    cubes, spheres and pyramids – with the same volume. A volume is all motion and no substance. The
    word volume represents a dynamic concept. A volume is ‘extension’ in space: the amount of water that
    the rubber ducky displaces inside the tub. From a conceptual point of view, the word volume means that
    the surface of a 3D object expanded to occupy a certain amount of space.

    To summarize, an object can only be illustrated and visualized. The only way to present an object is by
    pointing to Exhibit A and uttering a word. Until then, the prosecutor has done nothing with the word. He     
    hasn’t moved the object, used it in a sentence, or compared it against anything else. Only in this context are
    we dealing with objects. All the examples I gave earlier – leprechaun, centaur, tribar – are, first and foremost,
    objects. You point to a picture of a leprechaun, say “leprechaun,” and the ET just sees a man. You could have
    said “X” and it wouldn’t have made a bit of difference. It is when you categorize the green little elf and contrast
    him against other objects that the ET understands the meaning of the concept ‘leprechaun’. The concept
    'leprechaun' condenses noun, adjectives, and adverbs in a single word.

    Objects belong exclusively to the hypothesis stage of the scientific method. They form a part of the initial
    scene of a scientific theory. The jury visualizes this scene in order to understand the explanation that follows.
    Any use beyond the hypothesis summarily converts an object into a concept.

    Of course, if you buy into my definition of the word object, the pertinent question is whether space-time
    qualifies as an object. The reason a wall can exist without white is that a wall has shape. White doesn’t. So the
    question is, ‘Is it possible to paint space-time white?’ Is it possible to visualize space-time from a bird’s-eye
    perspective?’

    So now that we have the definitions in place, perhaps we can finally resolve unambiguously whether some of
    the borderline words that the philosophers have been debating for hundreds of years are objects or
    concepts. Is a hole an object or a concept? Is a shadow an object or a concept? How about fire, gas, an
    ocean? We have no trouble deciding whether a chair or a rock is an object. It is the borderline cases we have
    problems with.

Fig. 2   Object versus Concept
static

(e.g., direction, on, that)
CONCEPT     (2 objects or locations)

Fig. 1   The object ‘tribar’

The object is what you see at face value – the
outline – and that you associate with a word.
An object only has an outer perimeter or
surface. It is when you try to make sense of
the figure (i.e., understand it) that it becomes
a concept. A concept involves a relation.
dynamic

(e.g., over, infinite, energy)
Object
(shape + background)
(static)
An atom is
an abstract
concept!
You fool! Fire is
made of atoms and
is definitely a term!
The wind is just hot
air, like everything
that comes out of
your mouth!
You hard-headed
dummy! The
wind is
a substance!
GUYS! GUYS!
You can stop
fighting now!
Only a stone
such as this is
an object!
Adapted for the Internet from:

Why God Doesn't Exist
After 3000 years,
the morons of
Philosophy still
have no idea
what a concept is