 The arguments above ultimately rest on the idea that every name has three functions. This assumption can also be seen, in turn, as resting on an even more basic idea, namely that in all generality ‘object’ equals ‘being capable to take up the role of object in a presentation,’ thus an object is anything that can be presented; and anything that can be named by a name (§3, 12; §5, 23; §7, 37). Yet, saying that an object is anything that can be named by a name and that a name always has the function of naming are two sides of the same coin, as are the claim that an object is anything that can be presented by a presentation and the claim that a presentation always has an object. This cluster of correlative assumptions is the core of the theory. Only when this core is accepted can the other claims put forward by Twardowski (namely (1) that ‘being presented’ is not the same as ‘existing’ and (2) that objects can possess properties even though they do not exist) become convincing parts of a cogent theory of intentionality. One might note, however, that it is a theory for which there are no non-circular arguments, for the theory is acceptable only to those who are already convinced that there are no empty names, that all categorematic terms, including ‘round square,’ ‘aether,’, ‘Pegasus,’ etc. have the function of naming something, not only the function of being meaningful.