Changes

However, there is an obvious problem with this method of defining new notations.  It merely provides alternate signs for the same old uses.  But if the original signs are ambiguous, then equating new signs to them cannot remedy the problem.  Thus, it is necessary to find ways of selectively reforming the uses of the old notation in the interpretation of the new notation.

However, there is an obvious problem with this method of defining new notations.  It merely provides alternate signs for the same old uses.  But if the original signs are ambiguous, then equating new signs to them cannot remedy the problem.  Thus, it is necessary to find ways of selectively reforming the uses of the old notation in the interpretation of the new notation.

The invocation of higher order signs raises an important point, having to do with the typical ways that signs can become the objects of further signs, and the relationship that this type of semantic ascent bears to the interpretive agent's capacity for so called “reflection”.  This is a topic that will recur again as the discussion develops, but a speculative foreshadowing of its character will have to serve for now.

The invocation of higher order signs raises an important point, having to do with the typical ways that signs can become the objects of further signs, and the relationship that this type of semantic ascent bears to the interpretive agent's capacity for so-called “reflection”.  This is a topic that will recur again as the discussion develops, but a speculative foreshadowing of its character will have to serve for now.

Any object of an interpreter's experience and reasoning, no matter how vaguely and casually it initially appears, up to and including the merest appearance of a sign, is already, by virtue of these very circumstances, on its way to becoming the object of a formalized sign, so long as the signs are made available to denote it.  The reason for this is rooted in each agent's capacity for reflection on its own experience and reasoning, and the critical question is only whether these transient reflections can come to constitute signs of a more permanent use.

Any object of an interpreter's experience and reasoning, no matter how vaguely and casually it initially appears, up to and including the merest appearance of a sign, is already, by virtue of these very circumstances, on its way to becoming the object of a formalized sign, so long as the signs are made available to denote it.  The reason for this is rooted in each agent's capacity for reflection on its own experience and reasoning, and the critical question is only whether these transient reflections can come to constitute signs of a more permanent use.