Changes

Notice that this depiction makes being a FIC a term of description, and thus of possible approximation, not of necessity an exact definition of the thing's essential substance.  An objective being or a real activity, even one that escapes all bounds of finite description, can be usefully represented “as” or “by means of” a FIC precisely to the extent that a particular description of it in this form succeeds in helping the agent concerned to orient toward its underlying reality and to deal with its ultimate consequences.

Notice that this depiction makes being a FIC a term of description, and thus of possible approximation, not of necessity an exact definition of the thing's essential substance.  An objective being or a real activity, even one that escapes all bounds of finite description, can be usefully represented “as” or “by means of” a FIC precisely to the extent that a particular description of it in this form succeeds in helping the agent concerned to orient toward its underlying reality and to deal with its ultimate consequences.

'''Point 12.'''     Reflection involves higher orders of sign relations.

Point 12. Reflection involves higher orders of sign relations.

As a minimum requirement, a capacity for reflection implies an ability to generate names for the elements, processes, and principles of thought.  Assuming the tenet of pragmatism that all thought takes place in signs, this is tantamount to having signs for signs, signs for sign processes, and signs for sign relations.  Further, each higher order sign that is generated in a process of reflection is required to take its place and to find its meaning within a correspondingly higher order sign relation.

As a minimum requirement, a capacity for reflection implies an ability to generate names for the elements, processes, and principles of thought.  Assuming the tenet of pragmatism that all thought takes place in signs, this is tantamount to having signs for signs, signs for sign processes, and signs for sign relations.  Further, each higher order sign that is generated in a process of reflection is required to take its place and to find its meaning within a correspondingly higher order sign relation.

In this connection, the designation "higher order" (HO) can be used as a generic adjective to describe a sign of any object whose nature it is to involve signs as a part of its being.  The use of this adjective is subject to extension in natural ways to describe not only entire classes of signs but also the kinds of sign relations that involve them.

In this connection, the designation “higher order” (HO) can be used as a generic adjective to describe a sign of any object whose nature it is to involve signs as a part of its being.  The use of this adjective is subject to extension in natural ways to describe not only entire classes of signs but also the kinds of sign relations that involve them.

In order to reflect on signs themselves, it is necessary to have signs for signs, a necessary supply of which can be generated by quotation.  But reflection on sign processes requires a much larger supply of signs.  Initially, it requires a HO sign for each sign transition that actually occurs, that is, a name for each ordered pair of signs that is observed.  Eventually, it requires a HO sign for each sign sequence that actually appears in experience, that is, a name for each k tuple of signs seen.  And reflection on sign relations requires an even larger stock of signs.  It requires, initially, a HO sign for each sign transaction of the form <o, s, i> that is observed in experience and, ultimately, a HO sign for each sign relation that is encountered in experience or contemplated in a hypothetical situation.

In order to reflect on signs themselves, it is necessary to have signs for signs, a necessary supply of which can be generated by quotation.  But reflection on sign processes requires a much larger supply of signs.  Initially, it requires a HO sign for each sign transition that actually occurs, that is, a name for each ordered pair of signs that is observed.  Eventually, it requires a HO sign for each sign sequence that actually appears in experience, that is, a name for each k-tuple of signs seen.  And reflection on sign relations requires an even larger stock of signs.  It requires, initially, a HO sign for each sign transaction of the form <o, s, i> that is observed in experience and, ultimately, a HO sign for each sign relation that is encountered in experience or contemplated in a hypothetical situation.

If reflection is to constitute more than a transient form of observation, then provision needs to be made for permanently recording its HO signs.  Under these conditions the capacity for instituting and maintaining an order of reflection is just a capacity for creating and storing HO signs.

If reflection is to constitute more than a transient form of observation, then provision needs to be made for permanently recording its HO signs.  Under these conditions the capacity for instituting and maintaining an order of reflection is just a capacity for creating and storing HO signs.

This gives a brief glimpse of the issues involved in the effort toward reflection and the roughest possible estimate of the kinds of growth rates in the population of HO signs that are engendered by the need to provide a durable and stable medium for reflection.  Further discussion of these topics can be put off to a later point.  At this point it only needs to be clear that the injunction of a reflective capacity and the injunction of capacity limitations have an acute bearing on each other.

This gives a brief glimpse of the issues involved in the effort toward reflection and the roughest possible estimate of the kinds of growth rates in the population of HO signs that are engendered by the need to provide a durable and stable medium for reflection.  Further discussion of these topics can be put off to a later point.  At this point it only needs to be clear that the injunction of a reflective capacity and the injunction of capacity limitations have an acute bearing on each other.

The combinatorial explosion engendered by reflection impinges on the capacity limitations of a FIC with such an impact that neither the standpoints of "naive empiricism" or "naive intuitionism" can continue to support viable forms of inquiry.

The combinatorial explosion engendered by reflection impinges on the capacity limitations of a FIC with such an impact that neither the standpoints of &ldquo;naive empiricism&rdquo; or &ldquo;naive intuitionism&rdquo; can continue to support viable forms of inquiry.

This is what makes the mediation of a "higher order hypothesis" (HOH), a hypothesis about the qualifications of a hypothesis, or a hypothesis about what can count as a hypothesis, so essential to the life of a FIC.

This is what makes the mediation of a &ldquo;higher order hypothesis&rdquo; (HOH), a hypothesis about the qualifications of a hypothesis, or a hypothesis about what can count as a hypothesis, so essential to the life of a FIC.

The process of generating signs that refer to things already signs is incited by a syntactic operation that is commonly called a "quotation".  Strictly speaking, the descriptive term "quotation" refers to generic class of syntactic functions, each of which maps one order of signs into the next higher order of signs.  A proper form of quotation function is required to map signs in a one to one or "injective" fashion, and thus associates each element of its source domain with a HO sign that denotes it and it alone.  In short, a quotation produces a unique "name" or a distinctive "number" to index each piece its source material.

The process of generating signs that refer to things already signs is incited by a syntactic operation that is commonly called a &ldquo;quotation&rdquo;.  Strictly speaking, the descriptive term &ldquo;quotation&rdquo; refers to generic class of syntactic functions, each of which maps one order of signs into the next higher order of signs.  A proper form of quotation function is required to map signs in a one to one or &ldquo;injective&rdquo; fashion, and thus associates each element of its source domain with a HO sign that denotes it and it alone.  In short, a quotation produces a unique &ldquo;name&rdquo; or a distinctive &ldquo;number&rdquo; to index each piece its source material.

Some sort of quotation operation has to be made available as a standard mechanism to support almost any level of theoretical discussion about syntax.  In computational settings, various types of quotation operation need to be implemented as computable functions and provided among the basic resources for almost any adequate system of symbolic computation.  Conceived as a stock device of computation, and supplied with domains of arguments already well established as signs, quotation is relatively easy to implement.

Some sort of quotation operation has to be made available as a standard mechanism to support almost any level of theoretical discussion about syntax.  In computational settings, various types of quotation operation need to be implemented as computable functions and provided among the basic resources for almost any adequate system of symbolic computation.  Conceived as a stock device of computation, and supplied with domains of arguments already well established as signs, quotation is relatively easy to implement.

But a level of genuine reflection on sign processes and sign relations exceeds the generative capacity of mere quotation.

But a level of genuine reflection on sign processes and sign relations exceeds the generative capacity of mere quotation.

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.