Changes

But where do the intermediate entities go?  We could lodge them in a brand new space all their own, but Ockham the Innkeeper is right up there with Old Procrustes when it comes to the amenity of his accommodations, and so we feel compelled to at least try shoving them into one or another of the spaces already reserved.

But where do the intermediate entities go?  We could lodge them in a brand new space all their own, but Ockham the Innkeeper is right up there with Old Procrustes when it comes to the amenity of his accommodations, and so we feel compelled to at least try shoving them into one or another of the spaces already reserved.

In the rest of this discussion, let us assign the label <math>{}^{\backprime\backprime} i \, {}^{\prime\prime}</math> to the intermediate entity between the objects <math>x_j\!</math> and the sign <math>y.\!</math>

In the rest of this discussion, let us assign the label "i" to

the intermediate entity between the objects x_j and the sign y.

Now, should you annex i to the object domain O you will have

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

instantly given yourself away as having "Realist" tendencies,

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.

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.

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

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

| Denotative Component of L'  |

| Denotative Component of L'  |

|                            |

|                            |

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

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

But if you assimilate i to the realm of signs S, you will

But if you assimilate <math>i\!</math> to the realm of signs <math>S,\!</math> you will be showing your inclination to remain within the straight and narrow of ''conceptualist'' or even ''nominalist'' dogmas, and you may read this <math>i\!</math> as standing for an intelligible concept, or an ''idea'' of the safely decapitalized, mental impression variety.

be showing your inclination to remain within the straight

and narrow of "Conceptualist" or even "Nominalist" dogmas,

and you may read this "i" as standing for an intelligible

concept, or an "idea" of the safely decapitalized, mental

impression variety.

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

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

| Denotative Component of L'' |

| Denotative Component of L'' |

|                            |

|                            |

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

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

But if you dare to be truly liberal, you might just find

But if you dare to be truly liberal, you might just find that you can easily afford to accommmodate the illusions of both of these types of intellectual inclinations, and after a while you begin to wonder how all of that mental or ontological downsizing got started in the first place.

that you can easily afford to accommmodate the illusions

of both of these types of intellectual inclinations, and

after a while you begin to wonder how all of that mental

or ontological downsizing got started in the first place.

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

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

| Denotative Component of L'''|

| Denotative Component of L'''|

|                            |

|                            |

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

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

To sum up, we have recognized the perfectly innocuous utility

To sum up, we have recognized the perfectly innocuous utility of admitting the abstract intermediate object <math>i,\!</math> that may be interpreted as an intension, a property, or a quality that is held in common by all of the initial objects <math>x_j\!</math> that are plurally denoted by the sign <math>y.\!</math> Further, it appears to be equally unexceptionable to allow the use of the sign <math>{}^{\backprime\backprime} i \, {}^{\prime\prime}</math> to denote this shared intension <math>i.\!</math> Finally, all of this flexibility arises from a universally available construction, a type of compositional factorization, common to the functional parts of the 2-adic components of any relation.

of admitting the abstract intermediate object i, that may be

interpreted as an intension, a property, or a quality that

is held in common by all of the initial objects x_j that

are plurally denoted by the sign y.  Further, it appears

to be equally unexceptionable to allow the use of the

sign "i" to denote this shared intension i.  Finally,

all of this flexibility arises from a universally

available construction, a type of compositional

factorization, common to the functional parts

of the 2-adic components of any relation.

==Work Area==

==Work Area==