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Revision as of 02:20, 18 April 2009
, 02:20, 18 April 2009→Commentary Note 11.21
One more example and one more general observation, and then we will be all caught up with our homework on Peirce's "number of" function.
One more example and one more general observation, and then we will be all caught up with our homework on Peirce's "number of" function.
'''NOF 4.4'''
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
|
|
<p>So if men are just as apt to be black as things in general:</p>
<p>So if men are just as apt to be black as things in general:</p>
|-
| align="center" | <math>[\mathrm{m,}][\mathrm{b}] ~=~ [\mathrm{m,}\mathrm{b}]</math>
|-
<p>where the difference between [''m''] and [''m'',] must not be overlooked.</p>
|
<p>where the difference between <math>[\mathrm{m}]\!</math> and <math>[\mathrm{m,}]\!</math> must not be overlooked.</p>
<p>(Peirce, CP 3.76).</p>
<p>(Peirce, CP 3.76).</p>
The protasis, "men are just as apt to be black as things in general", is elliptic in structure, and presents us with a potential ambiguity. If we had no further clue to its meaning, it might be read as either of the following:
The protasis, "men are just as apt to be black as things in general", is elliptic in structure, and presents us with a potential ambiguity. If we had no further clue to its meaning, it might be read as either of the following:
{| align="center" cellspacing="6" width="90%"
| valign="top" | 1.
| Men are just as apt to be black as things in general are apt to be black.
|-
| valign="top" | 2.
| Men are just as apt to be black as men are apt to be things in general.
|}
The second interpretation, if grammatical, is pointless to state, since it equates a proper contingency with an absolute certainty. So I think it is safe to assume this paraphrase of what Peirce intends:
{| align="center" cellspacing="6" width="90%"
| <p>Men are just as likely to be black as things in general are likely to be black.</p>
|}
Stated in terms of the conditional probability:
Stated in terms of the conditional probability:
