Adapted for the Internet from:

Why God Doesn't Exist

    1.0   A hole, and not the object, is what has form

    Bertamini and Croucher  argue that observers tend to perceive the contour of a hole as belonging to the surrounding object,
     insinuating that a hole has no shape of its own. In their words:

    “ What is therefore the shape of a hole, if any? To resolve this apparent paradox,
       we suggest that the shape of a hole is available indirectly from the shape of the
       surrounding object. We exploited the fact that observers are faster at judging the
       position of convex vertices than concave ones.”  [1]

    “ A hole in a mathematical object is a topological structure which prevents the object
       from being continuously shrunk to a point.”  [2]

    In other words, these philosophers argue that the perceptions of observers have something to do with whether a hole is an
    object. To make their claims scientifically credible, these ‘philosophers’ carry out experiments to ‘prove’ objects and publish
    in journals which name says it all: Perception.

    In a similar vein, Casati and Varzi equate holes with objects because holes have similar properties of objects.

    “ [holes] appear to have a determinate shape, a size, and a location.” [3]

    Like Wittgenstein and Russell, they insinuate that a hole is an object because this noun may serve as the subject of a sentence.
    A hole is an object because we can talk about it. Then they ponder the chicken-or-the-egg question of whether holes are objects
    because we can make and count them or because they are part of an existing topology:

    “ I would say that the card is doubly perforated because there are two holes in it. You
       say the card with its topology is the truth-maker of our statements concerning the
       holes in it. I say the truth-makers of your statements about the card’s topology are
       the hole.” [4]

    All of these philosophers would save themselves circular discussions if they merely defined what they mean by the word object.
    Punching a hole or verifying its shape in a controlled experiment is not the way to ascertain that a hole is an object. This is the
    ‘proof’ method of defining proposed by Ramsey and Lewis and is unscientific. It is unscientific because a 'proof definition'
    cannot be used consistently in a discussion.

    In the last 2000 years, the philosophers of the world have not figured out that we don’t define objects by making them. The
    numskulls of Philosophy are comparing how they make holes (punching the card) against a still image of a hole.

    But is a hole an object merely because it has shape, size, and location?

    I believe that we now have established the foundations to answer such concerns without involving either a hands-on or a
    thought experiment. Whether a shadow or a hole or space-time is an object has nothing to do with observers or opinions. The
    word object represents a category. If a hole meets the criteria – shape – all on its own, it qualifies as an object by definition.
    Otherwise, it doesn’t. If the issue of whether a hole is an object involved the opinions of observers, half the world would
    believe that a hole is an object and the other half that it isn’t.

    I suggest rather that, like a shadow, a hole fails to meet the minimum 'shape' requirement of the definition of object. The alleged
    shape of the 'object' hole is really the inner shape of the enclosure that prevents space from serving as a backdrop to the hole
    directly. The concept ring may not do without the hole and the hole involves at least an explanation of depth, but the object ring
    stands alone without references to other objects. The ET does not need to understand what a hole is to visualize a ring and
    associate the word ring with the designated object. Should we accept the hole as an object, both definitions would become
    circular. The object ring would require that we first define the object hole and the object hole would require that we first define
    the object ring before we can classify either as an object. If a devil’s advocate proposes that a hole is an object nested within
    another object, its perimeter or surface has an infinitesimal yet finite separation from the ring and we should be able to isolate
    the hole, pull it out, and exhibit it independently. The devil’s advocate would also have to make provisions for multiple nested
    holes: a hole within a hole. These arguments can be extended to any dispute involving objects and concepts.

    The definition of object is 'that which has shape'. In the case of a doughnut-shaped object, we may have one of two situations.
    We either have a nested object or we have a single doughnut. In the first case, the devil’s advocate suggests that there are two
    objects one inside the other. However, the definition has no provisions for relations or multiple objects. Every object will be
    considered on an individual basis. In order for there to be two objects, each must be conceived as having its own surface.
    Hence, this is not a conceptual problem, but an issue of magnification. Despite all appearances, there must absolutely be an
    infinitesimal gap at the interface if the skeptic insists that there are two objects. Otherwise there would be a single object with
    no dividing surface or line. Only if each surface is delineated by space can we conceive of one object being inside the other.
    The seeming ‘common perimeter’ is an optical illusion, a question of observers and experiments and not of definitions. In the
    second situation, space serves as both the inner and outer ‘medium’. Pursuant to the scientific definition of object, the skeptic
    is now tasked to show that space has a shape of its own in order to be classified as an object. Until then, the inner hole and the
    contouring ‘medium’ are simply contrasts.

    The Wikipedia shows the drawing of a black hole: a hole surrounded by something. The picture resembles a gofer or rabbit hole
    you would find in an open field. The entry claims that the hole is the object, as if one object is encased within another. However,
    the black hole is alleged to have no structure. The black hole is wholly comprised of mass (i.e., a concept). The black hole is
    alternatively characterized as a hole in the fabric of spacetime. Some envision it as an entrance to another universe. Therefore,
    the black hole is not a physical object for the purposes of Physics.

    A hole is not an object, but an opening within an object. The word hole implies that a fragment or piece was removed.

    " we still need an explicit theory of holes" [9]

    What bumbling fools! What idiots! And these are the experts? These are the people who make the big
                   bucks working at universities and publishing in journals of Philosophy?

            After a while a rational human being loses all hope and can only be amused by the experts of Philosophy
            and Mathematical Physics. These folks have no more grey matter than what is necessary to clean latrines.

            No! We don't need a 'theory' of holes. In Science, we do not explain holes. In Science, we define them.
            What we need is an explicit and unambiguous definition of the word hole! Afterwards, you can theorize
            anything you want!
Is a hole and
object?

    Heidmann may disagree. After all, if we remove half a book, we have half the hole and half the mass. Isn’t this a way of dividing it?

    If we slide ten adjacent, 1-inch thick books to the left, the one inch thick hole that we create does not correspond to the volume of
    the ten books. The effort necessary to slide the ten books does no equate to the effort necessary to create this proportionally tiny
    hole? Therefore, the mass of one hole is not equivalent to the mass necessary to create the hole. If the bookshelf is on wheels, we
    expend less effort rolling than sliding. Again, the mass of the books is unrelated to the alleged mass of the hole. If we now slide
    the books 10 meters from the wall, the volume of the hole we create will also be larger than the volume occupied by the ten books.
    Hence, any way we look at it, Heidmann’s conclusion is wrong.

    What his example confirms, instead, is that it is misleading to define the word object through a listing of attributes or through
    measurement. As always, the analogies of relativity are misconceived and, as always, the mathematicians will defend themselves
    by trivializing the analogy they proposed as evidence of their arguments. So, again, why did they invoke the analogy in the first
    place? If Mathematics is the only route to relativity, they should not even attempt qualitative physical interpretations.

Fig. 2   A hole is not a book

If a bookshelf full of books is located
in space and we remove two books,
what is the shape of the hole?
I'm sorry, Bill! Did
you say you wanted
another nail?
No, Steve! Please
pass me a hole! The
pain is killing me!

    2.0   The book is mightier than the hole

    Heidmann  presents a different argument. He likens a hole to the region a book leaves behind when it is removed from or
    slides along a shelf.

    " Imagine a row of books on a library shelf. If you remove a book, you can consider that
       you have created two 'objects': the free book (in your hand) and the hole in the row...
       But, is the hole on the shelf really an object, just like the book that has been removed?
       It certainly has some properties in common. For example, just like a real book, the hole
       can be moved along the shelf, by the simple action of sliding neighboring books one
       by one along  the shelf. An the work needed to move a hole is the same as that needed
       to move a real book. So the hole behaves as if it had the mass of an actual book." (p. 101) [5]


    Heidmann then extrapolates the book-hole analogy to electrical charge. When we apply a voltage, an electron (the book)
    moves in one direction and the hole in the other. This is how the idiots of Mathematics explain today how a semiconductor
    works. [6] They also rely on this mechanism to explain how annihilation works. [7] Of course, all these theories are
    contingent on the assumption that the Universe is entirely comprised of discrete particles, space included. If this
    assumption is incorrect, the explanations the mechanics have been offering for the last 80 years end up in the dump.

    But let’s test Heidmann’s claim to see if it has any validity. Let's now remove two contiguous books from the shelf. We have
    two books and we can take them in two separate ways, Not so with the single hole we left behind (Fig. 2)! This experiment
    clearly shows that a hole is neither qualitatively nor quantitatively like a book. We can also slice a book in half, but not the
    hole it left behind.

    Fig. 1   The day a hole lost its doughnut


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        Copyright © by Nila Gaede 2008