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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 21:14, 19 April 2009
, 21:14, 19 April 2009→Commentary Note 11.23
Let me try to sum up as succinctly as possible the lesson that we ought to take away from Peirce's last "number of" example, since I know that the account that I have given of it so far may appear to have wandered rather widely.
Let me try to sum up as succinctly as possible the lesson that we ought to take away from Peirce's last "number of" example, since I know that the account that I have given of it so far may appear to have wandered rather widely.
'''NOF 4.4'''
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
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<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>
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| align="center" | <math>[\mathrm{m,}][\mathrm{b}] ~=~ [\mathrm{m,}\mathrm{b}]</math>
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<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>
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In different lights the formula [''m'',''b''] = [''m'',][''b''] presents itself as an "aimed arrow", "fair sample", or "independence" condition. I had taken the tack of illustrating this polymorphous theme in bas relief, that is, via detour through a universe of discourse where it fails. Here's a brief reminder of the Othello example:
In different lights the formula [''m'',''b''] = [''m'',][''b''] presents itself as an "aimed arrow", "fair sample", or "independence" condition. I had taken the tack of illustrating this polymorphous theme in bas relief, that is, via detour through a universe of discourse where it fails. Here's a brief reminder of the Othello example:
{| align="center" cellspacing="6" width="90%"
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<pre>
<pre>
B C D E I J O
B C D E I J O
B C D E I J O
B C D E I J O
</pre>
</pre>
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The condition, "men are just as apt to be black as things in general", is expressible in terms of conditional probabilities as P(''b''|''m'') = P(''b''), written out, the probability of the event Black given the event Male is exactly equal to the unconditional probability of the event Black.
The condition, "men are just as apt to be black as things in general", is expressible in terms of conditional probabilities as P(''b''|''m'') = P(''b''), written out, the probability of the event Black given the event Male is exactly equal to the unconditional probability of the event Black.