Changes

Let me now illustrate what I think that a lot of our controversies about nominalism versus realism actually boil down to in practice.  From a semiotic or a sign-theoretic point of view, it all begins with a case of ''plural reference'', which occurs when a sign <math>s\!</math> is taken to denote each object <math>o_j\!</math> in a collection of objects <math>\{ o_1, \ldots, o_k, \ldots \},</math> a situation whose general pattern is suggested by a sign-relational table of the following form:

Let me now illustrate what I think that a lot of our controversies about nominalism versus realism actually boil down to in practice.  From a semiotic or a sign-theoretic point of view, it all begins with a case of ''plural reference'', which occurs when a sign <math>s\!</math> is taken to denote each object <math>o_j\!</math> in a collection of objects <math>\{ o_1, \ldots, o_k, \ldots \},</math> a situation whose general pattern is suggested by a sign-relational table of the following form:

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For example, consider the sign relation <math>L\!</math> whose sign relational triples are precisely as shown in Table&nbsp;8.

For example, consider the sign relation <math>L\!</math> whose sign relational triples are precisely as shown in Table&nbsp;8.

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I would like to diagram this somewhat after the following fashion, here detailing just the denotative component of the sign relation, that is, the 2-adic relation that is obtained by "projecting out" the Object and Sign columns of the table.

I would like to diagram this somewhat after the following fashion, here detailing just the denotative component of the sign relation, that is, the 2-adic relation that is obtained by "projecting out" the Object and Sign columns of the table.

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| [[Image:Factorization Sign Relation Piece 1.jpg|500px]]

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| <math>\text{Figure 9.  Denotative Component of Sign Relation}~ L</math>

| Denotative Component of L  |

|   Objects    |    Signs    |

o--------------o--------------o

|                             |

|  o_1  o------>             |

|              \             |

 

I would like to &mdash; but my personal limitations in the Art of ASCII Hieroglyphics do not permit me to maintain this level of detail as the figures begin to ramify much beyond this level of complexity.  Therefore, let me use the following device to symbolize the same configuration:

 

| Denotative Component of L   |

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