Changes

'''Point 13.'''     A “finitely informed creature” (FIC), if it is reflective up to the point that it reflects on its own nature as such, crosses a singular threshold of reflection, whereupon it not only obeys its own capacity limitations, as it instinctively and necessarily must, but also observes and reflects on their character.

'''Point 13.'''     A “finitely informed creature” (FIC), if it is reflective up to the point that it reflects on its own nature as such, crosses a singular threshold of reflection, whereupon it not only obeys its own capacity limitations, as it instinctively and necessarily must, but also observes and reflects on their character.

'''Point 14.'''     Higher order sign relations tax the pragmatic resources of an interpretive agent to such a severe extent that they impinge on the practical limits of its representational capacity and computational ability.

Point 14. Higher order sign relations tax the pragmatic resources of an interpretive agent to such a severe extent that they impinge on the practical limits of its representational capacity and computational ability.

When it is necessary to be precise, I use the term "matriculation" to refer to the first permanent recording of a sign by an agent, the one that marks in a relatively indelible fashion the initial recognition, original declaration, or principal registration of a sign by an agent, on which every subsequent use of that sign by that agent depends, and to which every later usage of that sign by that agent implicitly or explicitly refers.

When it is necessary to be precise, I use the term “matriculation” to refer to the first permanent recording of a sign by an agent, the one that marks in a relatively indelible fashion the initial recognition, original declaration, or principal registration of a sign by an agent, on which every subsequent use of that sign by that agent depends, and to which every later usage of that sign by that agent implicitly or explicitly refers.

The feature of matriculation that is important to the present argument is that it uses up memory capacity in a monotonic way.  It is an economical strategy of memory usage to matriculate only the first token of each sign type observed and to let the observation of each subsequent token generate only a derivative reference to the primary registration.  However, the present argument does not depend on the hypothesis of such a model actually being used, since this standard is only proposed to establish a lower bound on memory usage.

The feature of matriculation that is important to the present argument is that it uses up memory capacity in a monotonic way.  It is an economical strategy of memory usage to matriculate only the first token of each sign type observed and to let the observation of each subsequent token generate only a derivative reference to the primary registration.  However, the present argument does not depend on the hypothesis of such a model actually being used, since this standard is only proposed to establish a lower bound on memory usage.

In order to reflect on sign relations, it is necessary to have signs for sign relations.  Failing this, the laws or principles that sign processes follow, even if fleetingly half intuited, remain forever semi conscious, and thus they continue to rule in a subcritical state of representation.   

In order to reflect on sign relations, it is necessary to have signs for sign relations.  Failing this, the laws or principles that sign processes follow, even if fleetingly half intuited, remain forever semi conscious, and thus they continue to rule in a subcritical state of representation.   

At this point it becomes clear that the ideals of a naive empiricism must be left behind.  The combinatorial explosion set off by the need to contemplate HO sign relations ...

At this point it becomes clear that the ideals of a naive empiricism must be left behind.  The combinatorial explosion set off by the need to contemplate HO sign relations …

If it becomes necessary to entertain hypotheses about sign transitions, then the space of HO signs that has to be matriculated is potentially as large as the space of all ordered pairs of signs from the initial domain.  If it becomes necessary to hypothesize about sign processes in general, then the space of HO signs that has to be matriculated grows like the union of the spaces of k tuples of signs from the initial domain, where k = 1, 2, 3, ..., and possibly increases with no limit in principal.

If it becomes necessary to entertain hypotheses about sign transitions, then the space of HO signs that has to be matriculated is potentially as large as the space of all ordered pairs of signs from the initial domain.  If it becomes necessary to hypothesize about sign processes in general, then the space of HO signs that has to be matriculated grows like the union of the spaces of <math>k\!</math>-tuples of signs from the initial domain, where <math>k = 1, 2, 3, \ldots,\!</math> and possibly increases with no limit in principal.

The acuteness of this point, if taken in its full generality, brings the discussion to an appreciation of the next point.

The acuteness of this point, if taken in its full generality, brings the discussion to an appreciation of the next point.

Point 15. Pragmatic incapacities have practical consequences.

Point 15. Pragmatic incapacities have practical consequences.