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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.

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 regard the intermediate entity <math>i\!</math> as an intelligible concept, or an ''idea'' of the safely decapitalized, mental impression variety.

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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.

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

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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>o_j\!</math> that are plurally denoted by the sign <math>s.\!</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.

To sum up, we have recognized the perfectly innocuous utility of admitting the abstract intermediate object <math>i_o,\!</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>o_j\!</math> that are plurally denoted by the sign <math>s.\!</math>  Further, it appears to be equally unexceptionable to allow the use of the sign <math>{}^{\backprime\backprime} s \, {}^{\prime\prime}</math> to denote this shared intension <math>i_o.\!</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.

==Document History==

==Document History==