Changes

Observe, however, that here is where all the battles tend to break out, for not all factorizations are regarded with equal equanimity by folks who have divergent philosophical attitudes toward the creation of new entities, especially when they get around to asking:  "In what domain or estate shall the multiplicity of newborn entities be lodged or yet come to reside on a permanent basis?"  Some factorizations enfold new orders of entities within the Object domain of a fundamental ontology, and some factorizations invoke new orders of entities within the Sign domains of concepts, data, interpretants, language, meaning, percepts, and senses in general.  Now, opting for the "Object" choice of habitation would usually be taken as symptomatic of "realist" leanings, while opting out of the factorization altogether, or weakly conceding the purely expedient convenience of the "Sign" choice for the status of the intermediate entities, would probably be taken as evidence of a "nominalist" persuasion.

Observe, however, that here is where all the battles tend to break out, for not all factorizations are regarded with equal equanimity by folks who have divergent philosophical attitudes toward the creation of new entities, especially when they get around to asking:  "In what domain or estate shall the multiplicity of newborn entities be lodged or yet come to reside on a permanent basis?"  Some factorizations enfold new orders of entities within the Object domain of a fundamental ontology, and some factorizations invoke new orders of entities within the Sign domains of concepts, data, interpretants, language, meaning, percepts, and senses in general.  Now, opting for the "Object" choice of habitation would usually be taken as symptomatic of "realist" leanings, while opting out of the factorization altogether, or weakly conceding the purely expedient convenience of the "Sign" choice for the status of the intermediate entities, would probably be taken as evidence of a "nominalist" persuasion.

Suppose that we have a sign relation L c OxSxI,

 

where the sets O, S, I are the domains of the

Object, Sign, Interpretant domains, respectively.

 

Suppose we have a sign relation <math>L \subseteq O \times S \times I,</math> where <math>O\!</math> is the object domain, <math>S\!</math> is the sign domain, and <math>I\!</math> is the interpretant domain of the sign relation <math>L.\!</math>

Now suppose that the situation with respect to

Now suppose that the situation with respect to the ''denotative component'' of <math>L,\!</math> in other words, the projection of <math>L\!</math> on the subspace <math>O \times S,</math> can be pictured in the following manner, where equal signs written between ostensible nodes identify them into a single actual node.

the "denotative component" of L, in other words,

the "projection" of L on the subspace OxS, can

be pictured in the following manner, where equal

signs, like "=", written between ostensible nodes,

like "o", identify them into a single real node.

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The Figure depicts a situation where each of the three objects, <math>x_1, x_2, x_3,\!</math> has a ''proper name'' that denotes it alone, namely, the three proper names <math>y_1, y_2, y_3,\!</math> respectively. Over and above the objects denoted by their proper names, there is the general sign <math>y,\!</math> which denotes any and all of the objects <math>x_1, x_2, x_3.\!</math> This kind of sign is described as a ''general name'' or a ''plural term'', and its relation to its objects is a ''general reference'' or a ''plural denotation''.

This depicts a situation where each of the three objects,

x_1, x_2, x_3, has a "proper name" that denotes it alone,

namely, the three proper names y_1, y_2, y_3, respectively.

Over and above the objects denoted by their proper names,

there is the general sign y, which denotes any and all of

the objects x_1, x_2, x_3.  This kind of sign is described

as a "general name" or a "plural term", and its relation to

its objects is a "general reference" or a "plural denotation".

Now, at this stage of the game, if you ask:

Now, at this stage of the game, if you ask: ''Is the object of the sign <math>y\!</math> one or many?'', the answer has to be:  ''Not one, but many''. That is, there is not one <math>x\!</math> that <math>y\!</math> denotes, but only the three <math>x\!</math>'s in the object space. Nominal thinkers would ask:  ''Granted this, what need do we have really of more excess?''  The maxim of the nominal thinker is ''never read a general name as a name of a general'', meaning that we should never jump from the accidental circumstance of a plural sign <math>y\!</math> to the abnominal fact that a unit <math>x\!</math> exists.

"Is the object of the sign y one or many?",

the answer has to be:  "Not one, but many".

That is, there is not one x that y denotes,

but only the three x's in the object space.

Nominal thinkers would ask:  "Granted this,

what need do we have really of more excess?"

The maxim of the nominal thinker is "never

read a general name as a name of a general",

meaning that we should never jump from the

accidental circumstance of a plural sign y

to the abnominal fact that a unit x exists.

In actual practice this would be just one segment of a much larger

In actual practice this would be just one segment of a much larger

sign relation, but let us continue to focus on just this one piece.

sign relation, but let us continue to focus on just this one piece.

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==Note 2==

==Nominalism and Realism==

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