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==Nominalism and Realism==

==Nominalism and Realism==

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 happens when a sign <math>s\!</math> is quite literally taken to denote each object <math>o_j\!</math> in a whole collection of objects <math>\{ o_1, \ldots, o_k, \ldots \},</math> a situation that can be represented in a sign-relational table like this one:

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:

{| align="center" cellspacing="10" style="text-align:center; width:90%"

{| align="center" style="text-align:center; width:60%"

|

|

{| align="center" style="text-align:center; width:100%"

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

| <math>\text{Table 7. Plural Denotation}\!</math>

| Object | Sign  | Interp  |

|}

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

|-

|   o_1  |   s    |   ...  |

|

|   o_2  |   s    |   ...  |

{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:100%"

|  o_3   |   s   |  ...  |

|- style="background:#f0f0ff"

| width="33%" | <math>\text{Object}\!</math>

|  o_k  |    s    |  ...  |

| width="33%" | <math>\text{Sign}\!</math>

| width="33%" | <math>\text{Interpretant}\!</math>

|-

</pre>

|

o_1 \\ o_2 \\ o_3 \\ \ldots \\ o_k \\ \ldots

|

s \\ s \\ s \\ \ldots \\ s \\ \ldots

|

\end{matrix}</math>

|}

|}