Now, a hole cannot be the only identifying property (I personally preferred the term "defining attribute") of a bagel. The example for this would be the donut, which is holed, but not a bagel. However, this still does not disprove the bagel-roll proposition, as they may share defining attributes. Let's model this idea, Math Nerd-stylez:Evaluate: "A bagel without a hole is not a bagel, but a roll."
Let set R represent the set of defining attributes for rolls, {r}.
Let set B represent the set of defining attributes for bagels, {r, having a hole}.
I just like seeing it laid out like that. Anyway, this doesn't quite hold up, however, when you know further defining attributes of the bagel. A google search turned up a brief description: "Essentially, the bagel is a round piece of bread with a hole in it that's chewy on the inside and crispy on the outside. It's made with high-gluten flour, water and yeast, and is either boiled or steamed before it's baked."(Source:"Bagel Boom" Adam Djurdjulov, Arizona Daily Wildcat, September 27, 1996) this was also confirmed by pastrywiz.com, so we have a fairly solid set of definite qualities, or at least, these shall make up our attributes. The defining attributes of rolls are unknown, because some of them do fulfil almost all of these qualities, while some do not. (Suffice it to say, “the class of all rolls” is a fairly broad class.) It would appear that boiling is the breaking point, unfortunately, if we are using it as a standard. (Note: boiling may not be a universal method, but is regarded as the right way among most bagel aficionados. Einstein Bros., for instance, is reputed to not boil their bagels, another indicator of their inferior status among hardcore bagel fans.) So that would seem to settle things. So it would seem. There are several matters to be tied up.
If a bagel without a hole is neither a bagel nor a roll, what is it? The bialy appeared promising at first, as they are from similar roots, have similar appearances, except that bakers indent bialys instead of holing them. This was a promising avenue, until I learned that bialys are not boiled. Foiled again—this question seems open to investigation. Perhaps a colleague will turn over the stone I have overlooked to find the grubbing worms of Truth.
Were we logicians of the old school, this might be at an end, there might be one further path to travel. All I know is what I read in the papers, if by "papers" you mean the book "Introducing Bertrand Russell." I like how he broke a proposition down to its bare essentials. Now, if we are to decompose that proposition, we may draw some interesting conclusions. Now, my rough estimation of its decomposed form is as follows: if an entity with the property of being a bagel does not have the property of having a hole, than it does not have the property of being a bagel, and instead has the property of being a roll. When broken down (albeit by me, an amateur) the whole proposition seems shaky. It relies on something being both a bagel and not a bagel, which runs counter to one of the fundamental laws of logic. Simply put, the phrase “a bagel without a hole is not a bagel” is paradoxical. The whole house of cards comes tumbling down, roll or no roll. With some rephrasing (for instance, removing the referring expression at the beginning of the sentence, and more exact terminology), we might have something, but as it stands (or rather, as it fails to stand) this is a false proposition. Revised, it might say "Any entity that has all the properties that an entity with the property of being a bagel has, except for having a hole, has the property of being a roll." However, this takes us back to sets B and R, so while this proposition is indeed false at many levels, the question of what a bagel-like item is without a hole remains open.
Adam W. Flynn aka Bobbin Threadbare
9-1-03
Post-Script: An interesting outgrowth of all this revolves around sushi. What if the “roll” referred to was not a bread product, but in fact referred to sushi? There is such a thing as a “bagel roll” which presents linguistic oddities all its own. If we take the word at face value, it could shatter the whole of what we’ve (“we”, in this case meaning “I”) been working on.