Intuition of Quasi-Concrete Objects

In his intriguing discussion of our intuition of quasi-concrete objects Parsons focuses on a series of stroke-inscriptions (familiar from Hilbert) and their respective types. For Parsons, a perception or imagining of the inscription is not sufficient for an intuition of the type:

I do not want to say, however, that seeing a stroke-inscription necessarily counts as intuition of the type it instantiates. One has to approach it with the concept of the type; first of all to have the capacity to recognize other situations either as presenting the same type, or a different one, or as not presenting a string of this language at all. But for intuiting a type something more than mere capacity is involved, which, at least in the case of a real inscription, could be described as seeing something as the type (165).

Again, later Parons says that "intuition of an abstract object requires a certain conceptualization brought to the situation by the subject" (179).

Unfortunately, Parsons says little about what this concept is or what role it plays in the intuition of the type. The risk, to my mind, is that a clarification of the role for this concept might make the perception or imagination of the token irrelevant to the intuition. If, for example, we think of concepts along Peacocke's lines, then possessing the concept of a type is sufficient to think about the type. Some might think that acquiring the concept requires the perception or imagination of the token, but Parsons says nothing to suggest this. I would like to think this has something to do with his view that the token is an intrinsic representation of the type, but the connection is far from clear to me.

(Logic Matters has an extended discussion of the Parsons book as well.)