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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 03:48, 4 April 2009
, 03:48, 4 April 2009→Selection 8
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We may regard these fill-in-the-blank forms as being derived by way of a kind of ''rhematic abstraction'' from the corresponding instances of absolute terms.
We may regard these fill-in-the-blank forms as being derived by a kind of ''rhematic abstraction'' from the corresponding instances of absolute terms.
In other words:
In other words:
Here are the absolute terms:
Here are the absolute terms:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{*{15}{c}}
1
& = &
\mathrm{B}
& +\!\!, &
\mathrm{C}
& +\!\!, &
\mathrm{D}
& +\!\!, &
\mathrm{E}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\mathrm{b}
& = &
\mathrm{O}
\\[6pt]
\mathrm{m}
& = &
\mathrm{C}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\mathrm{w}
& = &
\mathrm{B}
& +\!\!, &
\mathrm{D}
& +\!\!, &
\mathrm{E}
\end{array}</math>
|}
Here are the 2-adic relative terms:
Here are the 2-adic relative terms:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{*{13}{c}}
\mathit{l}
& = &
\mathrm{B}:\mathrm{C}
& +\!\!, &
\mathrm{C}:\mathrm{B}
& +\!\!, &
\mathrm{D}:\mathrm{O}
& +\!\!, &
\mathrm{E}:\mathrm{I}
& +\!\!, &
\mathrm{I}:\mathrm{E}
& +\!\!, &
\mathrm{O}:\mathrm{D}
\\[6pt]
\mathit{s}
& = &
\mathrm{C}:\mathrm{O}
& +\!\!, &
\mathrm{E}:\mathrm{D}
& +\!\!, &
\mathrm{I}:\mathrm{O}
& +\!\!, &
\mathrm{J}:\mathrm{D}
& +\!\!, &
\mathrm{J}:\mathrm{O}
\end{array}</math>
|}
Here are a few of the simplest products among these terms:
Here are a few of the simplest products among these terms: