Changes

Any LIR is a nominal form of IR that has exactly the same level of detail as an ER, merely shifting the interpretation of primitive terms from an extensional to an intensional modality, namely, from a frame of reference terminating in ''points'', ''atomic elements'', ''elementary objects'', or ''real particulars'' to a frame of reference terminating in ''qualities'', ''basic features'', ''fundamental properties'', or ''simple propositions''.  This modification, that translates the entire set of elementary objects in an ER into a parallel set of fundamental properties in a LIR, constitutes a form of modulation that can be subtle or trivial, depending on one's point of view.  Regarded as trivial, it tends to go unmarked, leaving it up to the judgment of the interpreter to decide whether the same sign is meant to denote a point, a particular, a property, or a proposition.  An interpretive variance that goes unstated tends to be treated as final.  It is always possible to bring in more signs in an attempt to signify the variants intended, but it needs to be noted that every effort to control the interpretive variance by means of these epithets and expletives only increases the level of liability for accidental errors, if not the actual probability of misinterpretation.  For the sake of this introduction, and in spite of these risks, I treat the distinction between extensional and intensional modes of interpretation as worthy of note and deserving of an explicit notation.

Any LIR is a nominal form of IR that has exactly the same level of detail as an ER, merely shifting the interpretation of primitive terms from an extensional to an intensional modality, namely, from a frame of reference terminating in ''points'', ''atomic elements'', ''elementary objects'', or ''real particulars'' to a frame of reference terminating in ''qualities'', ''basic features'', ''fundamental properties'', or ''simple propositions''.  This modification, that translates the entire set of elementary objects in an ER into a parallel set of fundamental properties in a LIR, constitutes a form of modulation that can be subtle or trivial, depending on one's point of view.  Regarded as trivial, it tends to go unmarked, leaving it up to the judgment of the interpreter to decide whether the same sign is meant to denote a point, a particular, a property, or a proposition.  An interpretive variance that goes unstated tends to be treated as final.  It is always possible to bring in more signs in an attempt to signify the variants intended, but it needs to be noted that every effort to control the interpretive variance by means of these epithets and expletives only increases the level of liability for accidental errors, if not the actual probability of misinterpretation.  For the sake of this introduction, and in spite of these risks, I treat the distinction between extensional and intensional modes of interpretation as worthy of note and deserving of an explicit notation.

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Table 50.  Notation for Objects & Their Signs

Table 50.  Notation for Objects & Their Signs

Object Sign of Object

Object Sign of Object

"i" <i> w5 <"i"> <<i>> <w5>

"i" <i> w5 <"i"> <<i>> <w5>

"u" <u> w6 <"u"> <<u>> <w6>

"u" <u> w6 <"u"> <<u>> <w6>

Table 51.1  Notation for Properties & Their Signs (1)

Table 51.1  Notation for Properties & Their Signs (1)

Property Sign of Property

Property Sign of Property

{"i"} {<i>} {w5} <{"i"}> <{<i>}> <{w5}>

{"i"} {<i>} {w5} <{"i"}> <{<i>}> <{w5}>

{"u"} {<u>} {w6} <{"u"}> <{<u>}> <{w6}>

{"u"} {<u>} {w6} <{"u"}> <{<u>}> <{w6}>

Table 51.2  Notation for Properties & Their Signs (2)

Table 51.2  Notation for Properties & Their Signs (2)

Property Sign of Property

Property Sign of Property

"i" <i> w5 <"i"> <<i>> <w5>

"i" <i> w5 <"i"> <<i>> <w5>

"u" <u> w6 <"u"> <<u>> <w6>

"u" <u> w6 <"u"> <<u>> <w6>

Table 51.3  Notation for Properties & Their Signs (3)

Table 51.3  Notation for Properties & Their Signs (3)

Property Sign of Property

Property Sign of Property

i s3 w5 <i> <s3> <w5>

i s3 w5 <i> <s3> <w5>

u s4 w6 <u> <s4> <w6>

u s4 w6 <u> <s4> <w6>

Table 52.1  Notation for Instances & Their Signs (1)

Table 52.1  Notation for Instances & Their Signs (1)

Instance Sign of Instance

Instance Sign of Instance

["i"] [<i>] [w5] <["i"]> <[<i>]> <[w5]>

["i"] [<i>] [w5] <["i"]> <[<i>]> <[w5]>

["u"] [<u>] [w6] <["u"]> <[<u>]> <[w6]>

["u"] [<u>] [w6] <["u"]> <[<u>]> <[w6]>

Table 52.2  Notation for Instances & Their Signs (2)

Table 52.2  Notation for Instances & Their Signs (2)

Instance Sign of Instance

Instance Sign of Instance

"i" <i> w5 <"i"> <<i>> <w5>

"i" <i> w5 <"i"> <<i>> <w5>

"u" <u> w6 <"u"> <<u>> <w6>

"u" <u> w6 <"u"> <<u>> <w6>

Table 52.3  Notation for Instances & Their Signs (3)

Table 52.3  Notation for Instances & Their Signs (3)

Instance Sign of Instance

Instance Sign of Instance

i s3 w5 <i> <s3> <w5>

i s3 w5 <i> <s3> <w5>

u s4 w6 <u> <s4> <w6>

u s4 w6 <u> <s4> <w6>

Using two different stategies of representation:

 

 

Using two different strategies of representation:

1. The first strategy is called the "literal coding", because it sticks to obvious features of each syntactic element to contrive its code, or the "O(n) coding", because it uses a number on the order of n logical features to represent a domain of n elements.

1. The first strategy is called the "literal coding", because it sticks to obvious features of each syntactic element to contrive its code, or the "O(n) coding", because it uses a number on the order of n logical features to represent a domain of n elements.