THE ANSWER
by Dennis J. Darland
August 15, 2010
Last revised 15.08.2010 01.32 time
Copyright © 2010 Dennis J. Darland

A KEY Thought

In my ideas on opacity, it may help to recognize a key idea that I am using is that of a relative product in Principia Mathematica. This is treated in *34. The relative product of rwo relations R and S is defined as:

R|S = xz{(∃ y).xRy.ySz}

The main difference is that, in my application of this, the relations have more that two terms, and products occur multiple times. This is a bit complicated, but this sort of thing is quite common in prolog programming.
First lets look as a simple example - in prolog - the definition of grand parent, in tedrms of parent:

grandparent(x,z) :- parent(x,y), parent(y,z).

For how this applies to opacity see On Opacity
There w, x, w and z occur in a manner similar to y in the examples above

Another KEY Thought

The ANSWER that recently occurred to me is this occurs throughout the philosophy of mind. There are intermediaries like y between physical objects and sensation words. And even between sensation words and our sensations (or ideas) about sensation words. Also between the components of our imaginings and our words for these imaginings etc. It is very hard to keep all this straight verbally - and completely unnecessary except when doing philosophy - where confusing these wreaks havoc!

This reminds me of a footnote in C. I. Lewis' An Analysis of Knowledge and Valuation. (page 511).
'There is a temptation for those who command the techniques of exact logical analysis to apply these to value-theory. They should be warned. On account of the complexities of our customary modes of value-predication, only three alternatives are open to such exact analysis of valuation: either it must discard common terms in their common meanings and proceed de novo in the arbitrary terminology of some 'ideal language'; or it must prove entirely inaccurate and inadequate to our common modes of speech; or it must become so inordinately complex as to serve no purpose, unless that of affording an excellent example of useless pedantry.'

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