Changes

What does all of this have to do with reification and so on?

What does all of this have to do with reification and so on?

Well, suppose that the source domain <math>X\!</math> is a set of ''objects'', that the target domain <math>Y\!</math> is a set of ''signs'', and suppose that the function <math>f : X \to Y</math> indicates the effect of a classification, conceptualization, discrimination, perception, or some other type of sorting operation, distributing the elements of the set <math>X\!</math> of objects and into a set of sorting bins that are labeled with the elements of the set <math>Y,\!</math> regarded as a set of classifiers, concepts, descriptors, percepts, or just plain signs, whether these signs are regarded as being in the mind, as with concepts, or whether they happen to be inscribed more publicly in another medium.

Well, suppose that the Source domain X is a set of "objects",

that the Target domain Y is a set of "signs", and suppose that

the function f : X -> Y indicates the effect of a classification,

conceptualization, discrimination, perception, or some other type

of "sorting" operation, distributing the elements of the set X of

objects and into a set of "sorting bins" that are labeled with the

elements of the set Y, regarded as a set of classifiers, concepts,

descriptors, percepts, or just plain signs, whether these signs

are regarded as being in the mind, as with concepts, or whether

they happen to be inscribed more publicly in another medium.

In general, if we try to use the signs in the Target (Co-domain) Y

In general, if we try to use the signs in the target codomain <math>Y\!</math> to reference the objects in the source domain <math>X,\!</math> then we will be invoking what used to be called &mdash; since the Middle Ages, I think &mdash; a manner of ''general reference'' or a mode of ''plural denotation'', that is to say, one sign will, in general, denote each of many objects, in a way that would normally be called ''ambiguous'' or ''equivocal''.

to reference the objects in the Source (Domain) X, then we will be

invoking what used to be called -- since the Middle Ages, I think --

a manner of "general reference" or a mode of "plural denotation",

that is to say, one sign will, in general, denote each of many

objects, in a way that would normally be called "ambiguous",

"equivocal", "indefinite", "indiscriminate", and so on.

Notice what I did not say here, that one sign denotes a "set" of objects,

Notice what I did not say here, that one sign denotes a ''set'' of objects, because I am for the moment conducting myself as such a dyed-in-the-wool nominal thinker that I hesitate even to admit so much as the existence of this thing we call a ''set'' into the graces of my formal ontology, though, of course, my casual speech is rife with the use of the word ''set'', and in a way that the nominal thinker, true-blue to the end, would probably be inclined or duty-bound to insist is a purely dispensable convenience.

because I am for the moment conducting myself as such a dyed-in-the-wool

nominal thinker that I hesitate even to admit so much as the existence of

this thing we call a "set" into the graces of my formal ontology, though,

of course, my casual speech is rife with the use of the word "set", and

in a way that the nominal thinker, true-blue to the end, would probably

be inclined or duty-bound to insist is a purely dispensable convenience.

In fact, the invocation of a new order of entities, whether you regard

In fact, the invocation of a new order of entities, whether you regard its typical enlistee as a class, a concept, a form, a general, an idea, an interpretant, a property, a set, a universal, or whatever you elect to call it, is tantamount exactly to taking this step that I just now called the ''factoring'' of the classification function into surjective and injective factors.

its typical enlistee as a class, a concept, a form, a general, an idea,

an interpretant, a property, a set, a universal, or whatever you elect

to call it, is tantamount exactly to taking this step that I just now

called the "factoring" of the classification function into surjective

and injective factors.

Observe, however, that this is where all the battles begin to break out,

Observe, however, that this is where all the battles begin 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 sense 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.

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 "sense in general" (SIG).  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.

==Factoring Sign Relations==

==Factoring Sign Relations==