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| | ===Reality at the Threshold of Logic=== | | ===Reality at the Threshold of Logic=== |
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| − | ====Original Format====
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| | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%" | | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%" |
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| | = & [\mathbb{B}^n] \\ | | = & [\mathbb{B}^n] \\ |
| | \end{matrix}</math> | | \end{matrix}</math> |
| − | |}<br>
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| − |
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| − | ====Current Format====
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| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
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| − | |+ '''Table 5. A Bridge Over Troubled Waters'''
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| − | |- style="background:ghostwhite"
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| − | ! <math>\mbox{Linear Space}\!</math>
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| − | ! <math>\mbox{Liminal Space}\!</math>
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| − | ! <math>\mbox{Logical Space}\!</math>
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| − | |-
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| − | |
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| − | <math>\begin{matrix}
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| − | \mathcal{X} \\
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| − | \{x_1, \ldots, x_n\} \\
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| − | \mbox{cardinality}\ n \\
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | \underline\mathcal{X} \\
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| − | \{\underline{x}_1, \ldots, \underline{x}_n\} \\
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| − | \mbox{cardinality}\ n \\
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | \mathcal{A} \\
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| − | \{a_1, \ldots, a_n\} \\
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| − | \mbox{cardinality}\ n \\
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| − | \end{matrix}</math>
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| − | |-
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| − | |
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| − | <math>\begin{matrix}
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| − | X_i \\
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| − | \langle x_i \rangle \\
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| − | \mbox{isomorphic to}\ \mathbb{K} \\
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | \underline{X}_i \\
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| − | \{(\underline{x}_i), \underline{x}_i \} \\
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| − | \mbox{isomorphic to}\ \mathbb{B} \\
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | A_i \\
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| − | \{(a_i), a_i \} \\
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| − | \mbox{isomorphic to}\ \mathbb{B} \\
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| − | \end{matrix}</math>
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| − | |-
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| − | |
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| − | ''X''<br>
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| − | 〈<font face="lucida calligraphy">X</font>〉<br>
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| − | 〈''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>〉<br>
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| − | {‹''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>›}<br>
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| − | ''X''<sub>1</sub> × … × ''X''<sub>''n''</sub><br>
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| − | ∏<sub>''i''</sub> ''X''<sub>''i''</sub><br>
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| − | isomorphic to '''K'''<sup>''n''</sup>
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| − | |
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| − | <u>''X''</u><br>
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| − | 〈<font face="lucida calligraphy"><u>X</u></font>〉<br>
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| − | 〈<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>〉<br>
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| − | {‹<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>›}<br>
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| − | <u>''X''</u><sub>1</sub> × … × <u>''X''</u><sub>''n''</sub><br>
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| − | ∏<sub>''i''</sub> <u>''X''</u><sub>''i''</sub><br>
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| − | isomorphic to '''B'''<sup>''n''</sup>
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| − | |
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| − | ''A''<br>
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| − | 〈<font face="lucida calligraphy">A</font>〉<br>
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| − | 〈''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>〉<br>
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| − | {‹''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>›}<br>
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| − | ''A''<sub>1</sub> × … × ''A''<sub>''n''</sub><br>
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| − | ∏<sub>''i''</sub> ''A''<sub>''i''</sub><br>
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| − | isomorphic to '''B'''<sup>''n''</sup>
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| − | |-
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| − | |
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| − | ''X''*<br>
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| − | (hom : ''X'' → '''K''')<br>
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| − | isomorphic to '''K'''<sup>''n''</sup>
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| − | |
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| − | <u>''X''</u>*<br>
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| − | (hom : <u>''X''</u> → '''B''')<br>
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| − | isomorphic to '''B'''<sup>''n''</sup>
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| − | |
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| − | ''A''*<br>
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| − | (hom : ''A'' → '''B''')<br>
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| − | isomorphic to '''B'''<sup>''n''</sup>
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| − | |-
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| − | |
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| − | ''X''^<br>
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| − | (''X'' → '''K''')<br>
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| − | isomorphic to:<br>
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| − | ('''K'''<sup>''n''</sup> → '''K''')
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| − | |
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| − | <u>''X''</u>^<br>
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| − | (<u>''X''</u> → '''B''')<br>
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| − | isomorphic to:<br>
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| − | ('''B'''<sup>''n''</sup> → '''B''')
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| − | |
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| − | ''A''^<br>
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| − | (''A'' → '''B''')<br>
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| − | isomorphic to:<br>
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| − | ('''B'''<sup>''n''</sup> → '''B''')
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| − | |-
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| − | |
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| − | ''X''<sup>•</sup><br>
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| − | [<font face="lucida calligraphy">X</font>]<br>
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| − | [''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>]<br>
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| − | (''X'', ''X''^)<br>
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| − | (''X'' +→ '''K''')<br>
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| − | (''X'', (''X'' → '''K'''))<br>
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| − | isomorphic to:<br>
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| − | ('''K'''<sup>''n''</sup>, ('''K'''<sup>''n''</sup> → '''K'''))<br>
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| − | ('''K'''<sup>''n''</sup> +→ '''K''')<br>
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| − | ['''K'''<sup>''n''</sup>]
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| − | |
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| − | <u>''X''</u><sup>•</sup><br>
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| − | [<font face="lucida calligraphy"><u>X</u></font>]<br>
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| − | [<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>]<br>
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| − | (<u>''X''</u>, <u>''X''</u>^)<br>
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| − | (<u>''X''</u> +→ '''B''')<br>
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| − | (<u>''X''</u>, (<u>''X''</u> → '''B'''))<br>
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| − | isomorphic to:<br>
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| − | ('''B'''<sup>''n''</sup>, ('''B'''<sup>''n''</sup> → '''B'''))<br>
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| − | ('''B'''<sup>''n''</sup> +→ '''B''')<br>
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| − | ['''B'''<sup>''n''</sup>]
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| − | |
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| − | ''A''<sup>•</sup><br>
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| − | [<font face="lucida calligraphy">A</font>]<br>
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| − | [''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>]<br>
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| − | (''A'', ''A''^)<br>
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| − | (''A'' +→ '''B''')<br>
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| − | (''A'', (''A'' → '''B'''))<br>
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| − | isomorphic to:<br>
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| − | ('''B'''<sup>''n''</sup>, ('''B'''<sup>''n''</sup> → '''B'''))<br>
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| − | ('''B'''<sup>''n''</sup> +→ '''B''')<br>
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| − | ['''B'''<sup>''n''</sup>]
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| | |}<br> | | |}<br> |
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