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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Now, should you annex <math>i\!</math> to the object domain <math>O\!</math> you will have instantly given yourself away as having ''realist'' tendencies, and you might as well go ahead and call it an ''intension'' or even an ''Idea'' of the grossly subtlest Platonic brand, since you are about to booted from Ockham's Establishment, and you might as well have the comforts of your ideals in your exile.

Now, should you annex <math>i\!</math> to the object domain <math>O\!</math> you will have instantly given yourself away as having ''realist'' tendencies, and you might as well go ahead and call it an ''intension'' or even an ''Idea'' of the grossly subtlest Platonic brand, since you are about to booted from Ockham's Establishment, and you might as well have the comforts of your ideals in your exile.

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

| <math>\text{Figure 10.  Denotative Component of Sign Relation}~ L^\prime</math>

| Denotative Component of L'  |

|  /  |  \           *        |

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