Changes

In different lights the formula <math>[\mathrm{m,}\mathrm{b}] = [\mathrm{m,}][\mathrm{b}]\!</math> presents itself as an ''aimed arrow'', ''fair sample'', or ''stochastic independence'' condition.

In different lights the formula <math>[\mathrm{m,}\mathrm{b}] = [\mathrm{m,}][\mathrm{b}]\!</math> presents itself as an ''aimed arrow'', ''fair sample'', or ''stochastic independence'' condition.

The example apparently assumes a universe of ''things in general'', encompassing among other things the denotations of the absolute terms <math>\mathrm{m} = \text{man}\!</math> and <math>\mathrm{b} = \text{black}.\!</math>  That suggests to me that we might well illustrate this case in relief, by returning to our earlier staging of ''Othello''' and seeing how well that universe of dramatic discourse observes the premiss that "men are just as apt to be black as things in general".

The example apparently assumes a universe of ''things in general'', encompassing among other things the denotations of the absolute terms <math>\mathrm{m} = \text{man}\!</math> and <math>\mathrm{b} = \text{black}.\!</math>  That suggests to me that we might well illustrate this case in relief, by returning to our earlier staging of ''Othello'' and seeing how well that universe of dramatic discourse observes the premiss that "men are just as apt to be black as things in general".

Here are the relevant data:

Here are the relevant data:

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Thus we observe one of the more factitious facts that hold in this universe of discourse, namely:

Thus we observe one of the more factitious facts affecting this very special universe of discourse, namely:

: ''m'',''b'' = ''b''.

| <math>\mathrm{m,}\mathrm{b} ~=~ \mathrm{b}.</math>

Another way of saying that is:

This is equivalent to the implication <math>\mathrm{b} \Rightarrow \mathrm{m},</math> the content of which statement Peirce would have written in the following form:

: ''b'' –< ''m''.

| <math>\mathrm{b} ~-\!\!\!<~ \mathrm{m}.</math>

That in itself is enough to puncture any notion that ''b'' and ''m'' are statistically independent, but let us continue to develop the plot a bit more.

That in itself is enough to puncture any notion that ''b'' and ''m'' are statistically independent, but let us continue to develop the plot a bit more.