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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)

Revision as of 18:24, 6 May 2009

168 bytes added ,  18:24, 6 May 2009
→‎Selection 12
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathrm{w} ~=~ \mathrm{W}^{\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime\prime}</math>
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| height="60" | <math>\mathrm{w} ~=~ \mathrm{W}^{\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime\prime}</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathit{l}^\mathrm{w} ~=~ \mathit{l}^{(\mathrm{W}^{\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime\prime})} ~=~ (\mathit{l}\mathrm{W}^{\prime}), (\mathit{l}\mathrm{W}^{\prime\prime}), (\mathit{l}\mathrm{W}^{\prime\prime\prime}).</math>
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| height="60" | <math>\mathit{l}^\mathrm{w} ~=~ \mathit{l}^{(\mathrm{W}^{\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime} ~+\!\!,~ \mathrm{W}^{\prime\prime\prime})} ~=~ (\mathit{l}\mathrm{W}^{\prime}), (\mathit{l}\mathrm{W}^{\prime\prime}), (\mathit{l}\mathrm{W}^{\prime\prime\prime}).</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} \operatorname{proj}_1 (L \star x) ~=~ \bigcap_{x \in W} L \cdot x</math>
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| height="60" | <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} \operatorname{proj}_1 (L \star x) ~=~ \bigcap_{x \in W} L \cdot x</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathrm{J} ~\text{loves}~ \mathrm{K} ~\Leftarrow~ \mathrm{K} ~\text{is a woman}</math>
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| height="60" | <math>\mathrm{J} ~\text{loves}~ \mathrm{K} ~\Leftarrow~ \mathrm{K} ~\text{is a woman}</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} L \cdot x</math>
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| height="60" | <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} L \cdot x</math>
 
|}
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>(\mathfrak{L}^\mathfrak{W})_u ~=~ \prod_{x \in X} \mathfrak{L}_{ux}^{\mathfrak{W}_x}</math>
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| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_u ~=~ \prod_{x \in X} \mathfrak{L}_{ux}^{\mathfrak{W}_x}</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} L \cdot x ~=~ L \cdot d ~\cap~ L \cdot f ~=~ \{ c, e \} \cap \{ e, g \} ~=~ \{ e \}</math>
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| height="60" | <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} L \cdot x ~=~ L \cdot d ~\cap~ L \cdot f ~=~ \{ c, e \} \cap \{ e, g \} ~=~ \{ e \}</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>(\mathfrak{L}^\mathfrak{W})_e ~=~ \prod_{x \in X} \mathfrak{L}_{ex}^{\mathfrak{W}_x} ~=~ 0^0 \cdot 0^0 \cdot 0^0 \cdot 1^1 \cdot 1^0 \cdot 1^1 \cdot 0^0 \cdot 0^0 \cdot 0^0 ~=~ 1</math>
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| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_e ~=~ \prod_{x \in X} \mathfrak{L}_{ex}^{\mathfrak{W}_x} ~=~ 0^0 \cdot 0^0 \cdot 0^0 \cdot 1^1 \cdot 1^0 \cdot 1^1 \cdot 0^0 \cdot 0^0 \cdot 0^0 ~=~ 1</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>\mathit{s}^{(\mathit{l}\mathrm{w})} ~=~ \bigcap_{x \in LW} \operatorname{proj}_1 (S \star x) ~=~ \bigcap_{x \in LW} S \cdot x</math>
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| height="60" | <math>\mathit{s}^{(\mathit{l}\mathrm{w})} ~=~ \bigcap_{x \in LW} \operatorname{proj}_1 (S \star x) ~=~ \bigcap_{x \in LW} S \cdot x</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>(\mathfrak{S}^\mathfrak{L})_{uv} ~=~ \prod_{x \in X} \mathfrak{S}_{ux}^{\mathfrak{L}_{xv}}</math>
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| height="60" | <math>(\mathfrak{S}^\mathfrak{L})_{uv} ~=~ \prod_{x \in X} \mathfrak{S}_{ux}^{\mathfrak{L}_{xv}}</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>(\mathfrak{S}^\mathfrak{L})^\mathfrak{W} ~=~ \mathfrak{S}^{\mathfrak{L}\mathfrak{W}}</math>
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| height="60" | <math>(\mathfrak{S}^\mathfrak{L})^\mathfrak{W} ~=~ \mathfrak{S}^{\mathfrak{L}\mathfrak{W}}</math>
 
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{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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| <math>((\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_{uv} ~=~ (\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_{uv}</math>
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| height="60" | <math>((\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_{uv} ~=~ (\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_{uv}</math>
 
|}
 
|}
  
Jon Awbrey
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