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Revision as of 04:05, 14 May 2013
, 04:05, 14 May 2013→Commentary Note 10: center figure
I will also try an alternate style of picture for the ''lifting property'', by means of which, relative to the lattice of natural (non-ad-hoc) kinds, a property ''P'', naturally predicated of ''S'', can be ''elevated'' to apply to ''M''.
I will also try an alternate style of picture for the ''lifting property'', by means of which, relative to the lattice of natural (non-ad-hoc) kinds, a property ''P'', naturally predicated of ''S'', can be ''elevated'' to apply to ''M''.
{| align="center" cellspacing="6" style="text-align:center; width:70%"
|
<font face="courier new"><pre>
<font face="courier new"><pre>
o-----------------------------o-----------------------------o
o-----------------------------o-----------------------------o
o-----------------------------------------------------------o
o-----------------------------------------------------------o
</pre></font>
</pre></font>
|}
I believe that we can now begin to see the linkage to inductive rules. When a sample ''S'' is ''fairly'' or ''randomly'' drawn from the membership ''M'' of some population and when every member of ''S'' is observed to have the property ''P'', then it is naturally rational to expect that every member of ''M'' will also have the property ''P''. This is the principle behind all of our more usual statistical generalizations, giving us the leverage that it takes to lift predicates from samples to a membership sampled.
I believe that we can now begin to see the linkage to inductive rules. When a sample ''S'' is ''fairly'' or ''randomly'' drawn from the membership ''M'' of some population and when every member of ''S'' is observed to have the property ''P'', then it is naturally rational to expect that every member of ''M'' will also have the property ''P''. This is the principle behind all of our more usual statistical generalizations, giving us the leverage that it takes to lift predicates from samples to a membership sampled.
