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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:
<br>
{| align="center" style="text-align:center; width:60%"
{| align="center" style="text-align:center; width:60%"
|}
|}
For brevity, let us consider a sign relation <math>L\!</math> whose relational database table is precisely this:
<br>
For example, consider the sign relation <math>L\!</math> whose sign relational triples are precisely as shown in Table 8.
<br>
{| 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%"
| <math>\text{Table 8. Sign Relation}~ L</math>
| Sign Relation L |
</pre>
|}
|}
|-
|
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:100%"
|- style="background:#f0f0ff"
| width="33%" | <math>\text{Object}\!</math>
| width="33%" | <math>\text{Sign}\!</math>
| width="33%" | <math>\text{Interpretant}\!</math>
|-
|
<math>\begin{matrix}
o_1 \\ o_2 \\ o_3
\end{matrix}</math>
|
<math>\begin{matrix}
s \\ s \\ s
\end{matrix}</math>
|
<math>\begin{matrix}
\ldots \\ \ldots \\ \ldots
\end{matrix}</math>
|}
|}
<br>
For the moment, it does not matter what the interpretants are.
For the moment, it does not matter what the interpretants are.
