The Class/Object Paradox confusion

You can see the problem in this diagram:

_{(source: phrogz.net)}

All object instances inherit from Object. All classes are objects, and Class is a class, therefore Class is an object. However, object instances inherit from their class, and Object is an instance of the Class class, therefore Object itself gets methods from Class.

As you can see in the diagram, however, there isn't a circular lookup loop, because there are two different inheritance 'parts' to every class: the instance methods and the 'class' methods. In the end, the lookup path is sane.

N.B.: This diagram reflects Ruby 1.8, and thus does not include the core BasicObject class introduced in Ruby 1.9.

Regarding the which-came-first criterion, there are two kinds of Ruby objects:

• Built-in objects. They exist at the start of a Ruby program and can be considered to have zero creation time.
• User created objects. They are created after the program starts via object creation methods (new/clone/dup, class-definition, module-definition, literal-constructs, ...). Such objects are linearly ordered by their time of creation. This order happens to inversely correspond to class-inheritance and instance-of relations.

A detailed explanation of the Ruby object model is available at www.atalon.cz.

In practical terms, all you need to understand is that Object is the mother of all classes. All classes extend Object. It is this relationship that you will use in programming, understanding inheritance and so forth.

Eg; You can call hash() on any instance of any object at any time? Why? Because that function appears in the Object class, and all classes inherit that function, because all classes extend Object.

As far as the idea of Class goes, this comes up much less frequently. An object of class Class is like a blueprint, it's like having the class in your hands, without creating an instance of it. There's a little more to it, but it's a difficult one to describe without a lengthy example. Rest assured, when (if ever) the time comes to use it, you'll see it's purpose.

All this excerpt is saying is that Object has a class of type Class and Class is an object, so must extend Object. Its cyclic, but it's irrelevant. The answer is buried somewhere in the compiler.

I know that my answer comes at least 3 years late, but I have learned about Ruby quite recently and I must admit that the literature sometimes presents (in my opinion) misleading explanations, even though one is handling a very simple problem. Moreover, I am (and was) surprised by such appalling phrases as:

    "The best way to deal with this paradox, at least for now, is to ignore it."

stated by the author D. Black, and quoted in the question, but this attitude seems to be pervasive. I have experienced this tendency within the physics community but I have not suspected it had also spread through the programming one. I am not stating that nobody understands what is lurking behind, but it seems at least intriguing why not providing the (indeed) very simple and precise answer, as in this case there is one, without invoking any obscure words such as "paradox" within the explanation.

This so-called "paradox" (even though it is definitely NOT such thing) comes from the (at least misleading) belief that "being an instance of (a subclass of)" should be something as "being an element of" (in, say, naive set theory), or in other terms, a class (in Ruby) is the set containing all the objects sharing some common property (for instance, under this naive interpretation the class String includes all the string objects). Even though this naive point of view (which I may call the "membership interpretation") may help understanding isolated (and rather easy) classes such as String or Symbol, it indeed PRODUCES A CLEAR CONTRADICTION with our naive understanding (and also the axiomatic one, for it contradicts Von Neumann's regularity axiom of set theory, if someone knows what I am talking about) of the membership relationship, for an object could not be an element of itself, as the previous interpretation implies when regarding the object Class.

The previously stated problem is easily avoided if one gets rid of such misleading membership interpretation with a very simply minded model as follows. I would have guess that my following explanation is well-known by the experts, so I claim no originality at all, but perhaps it was not rephrased in the (simple) terms I am going to present it: in some sense I am completely astonished that (apparently) nobody stated in these terms from the very beginning, and my intention is just to highlight what I believe is the basic underlying structure.

Let us consider a set O of (basic) objects, which consists of all the (basic) objects Ruby has, provided with a mapping f from O to O (which is more or less the .class method), satisfying that the image of the composition of f with itself has only one element. This latter element (or object) is denoted Class (indeed, what you know to be the class Class). I would be tempted to write this post using LaTeX code but I am not quite sure if it will be parsed and converted into typical math expressions. The image of the mapping f is (by definition) the set of Ruby classes (e.g. String, Object, Symbol, Class, etc). Ruby programmers (even though if they do not know it) interpret the previous construction as follows: we say that an object "x is an instance of y" if and only if y = f(x). By the way this tells us you exactly that Class is an instance of Class (i.e. of itself).

Now, we would need much more decorations to this simple model in order to get the full Ruby hierarchy of classes and functionality (imposing the existence of some fixed members on the image of the map f, a partial order on the image of the map f in order to define subclasses to get afterwards inheritance, etc), and in particular to get the nice picture that was interestingly upvoted, but I suppose that everybody can figure this out from the primitive model I gave (I have written some pages explaining this for myself, after having read several Ruby manuals. I may provide a copy if anybody finds it useful).