Line 5,628: |
Line 5,628: |
| Table 50 exhibits a truth table method for computing the analytic series (or the differential expansion) of a proposition in terms of coordinates. | | Table 50 exhibits a truth table method for computing the analytic series (or the differential expansion) of a proposition in terms of coordinates. |
| | | |
− | <pre>
| + | {| align="center" border="2" cellpadding="0" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%" |
− | Table 50. Computation of an Analytic Series in Terms of Coordinates | + | |+ Table 50. Computation of an Analytic Series in Terms of Coordinates |
− | o-----------o-------------o-------------oo-------------o---------o-------------o
| + | | |
− | | u v | du dv | u' v' || !e!J EJ | DJ | dJ d^2.J | | + | {| align="center" border="1" cellpadding="0" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
− | o-----------o-------------o-------------oo-------------o---------o-------------o
| + | | |
− | | | | || | | | | + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%" |
− | | 0 0 | 0 0 | 0 0 || 0 0 | 0 | 0 0 | | + | | ''u'' |
− | | | | || | | | | + | | ''v'' |
− | | | 0 1 | 0 1 || 0 | 0 | 0 0 | | + | |} |
− | | | | || | | | | + | | |
− | | | 1 0 | 1 0 || 0 | 0 | 0 0 | | + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%" |
− | | | | || | | | | + | | d''u'' |
− | | | 1 1 | 1 1 || 1 | 1 | 0 1 | | + | | d''v'' |
− | | | | || | | | | + | |} |
− | o-----------o-------------o-------------oo-------------o---------o-------------o
| + | | |
− | | | | || | | | | + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%" |
− | | 0 1 | 0 0 | 0 1 || 0 0 | 0 | 0 0 | | + | | ''u''<font face="courier new">’</font> |
− | | | | || | | | | + | | ''v''<font face="courier new">’</font> |
− | | | 0 1 | 0 0 || 0 | 0 | 0 0 | | + | |} |
− | | | | || | | | | + | |- |
− | | | 1 0 | 1 1 || 1 | 1 | 1 0 | | + | | |
− | | | | || | | | | + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
− | | | 1 1 | 1 0 || 0 | 0 | 1 1 | | + | | 0 || 0 |
− | | | | || | | | | + | |- |
− | o-----------o-------------o-------------oo-------------o---------o-------------o
| + | | || |
− | | | | || | | | | + | |- |
− | | 1 0 | 0 0 | 1 0 || 0 0 | 0 | 0 0 | | + | | || |
− | | | | || | | | | + | |- |
− | | | 0 1 | 1 1 || 1 | 1 | 1 0 | | + | | || |
− | | | | || | | | | + | |} |
− | | | 1 0 | 0 0 || 0 | 0 | 0 0 | | + | | |
− | | | | || | | | | + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
− | | | 1 1 | 0 1 || 0 | 0 | 1 1 | | + | | 0 || 0 |
− | | | | || | | | | + | |- |
− | o-----------o-------------o-------------oo-------------o---------o-------------o
| + | | 0 || 1 |
− | | | | || | | | | + | |- |
− | | 1 1 | 0 0 | 1 1 || 1 1 | 0 | 0 0 | | + | | 1 || 0 |
− | | | | || | | | | + | |- |
− | | | 0 1 | 1 0 || 0 | 1 | 1 0 | | + | | 1 || 1 |
− | | | | || | | | | + | |} |
− | | | 1 0 | 0 1 || 0 | 1 | 1 0 | | + | | |
− | | | | || | | | | + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
− | | | 1 1 | 0 0 || 0 | 1 | 0 1 | | + | | 0 || 0 |
− | | | | || | | | | + | |- |
− | o-----------o-------------o-------------oo-------------o---------o-------------o
| + | | 0 || 1 |
− | </pre> | + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 1 |
| + | |- |
| + | | || |
| + | |- |
| + | | || |
| + | |- |
| + | | || |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 1 |
| + | |- |
| + | | 0 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |- |
| + | | 1 || 0 |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 1 || 0 |
| + | |- |
| + | | || |
| + | |- |
| + | | || |
| + | |- |
| + | | || |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |- |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 1 || 1 |
| + | |- |
| + | | || |
| + | |- |
| + | | || |
| + | |- |
| + | | || |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 1 || 1 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |- |
| + | | 0 || 0 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |} |
| + | |} |
| + | | |
| + | {| align="center" border="1" cellpadding="0" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%" |
| + | | <math>\epsilon</math>''J'' |
| + | | E''J'' |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%" |
| + | | D''J'' |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%" |
| + | | d''J'' |
| + | | d<sup>2</sup>''J'' |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | || 0 |
| + | |- |
| + | | || 0 |
| + | |- |
| + | | || 1 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 |
| + | |- |
| + | | 0 |
| + | |- |
| + | | 0 |
| + | |- |
| + | | 1 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | || 0 |
| + | |- |
| + | | || 1 |
| + | |- |
| + | | || 0 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 |
| + | |- |
| + | | 0 |
| + | |- |
| + | | 1 |
| + | |- |
| + | | 0 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 0 || 0 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | || 1 |
| + | |- |
| + | | || 0 |
| + | |- |
| + | | || 0 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 |
| + | |- |
| + | | 1 |
| + | |- |
| + | | 0 |
| + | |- |
| + | | 0 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 0 || 0 |
| + | |- |
| + | | 1 || 1 |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 1 |
| + | |- |
| + | | || 0 |
| + | |- |
| + | | || 0 |
| + | |- |
| + | | || 0 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 |
| + | |- |
| + | | 1 |
| + | |- |
| + | | 1 |
| + | |- |
| + | | 1 |
| + | |} |
| + | | |
| + | {| align="center" border="0" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%" |
| + | | 0 || 0 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 1 || 0 |
| + | |- |
| + | | 0 || 1 |
| + | |} |
| + | |} |
| + | |} |
| + | <br> |
| | | |
| The first six columns of the Table, taken as a whole, represent the variables of a construct that I describe as the ''contingent universe'' [''u'', ''v'', d''u'', d''v'', ''u''′, ''v''′ ], or the bundle of ''contingency spaces'' [d''u'', d''v'', ''u''′, ''v''′ ] over the universe [''u'', ''v'']. Their placement to the left of the double bar indicates that all of them amount to independent variables, but there is a co-dependency among them, as described | | The first six columns of the Table, taken as a whole, represent the variables of a construct that I describe as the ''contingent universe'' [''u'', ''v'', d''u'', d''v'', ''u''′, ''v''′ ], or the bundle of ''contingency spaces'' [d''u'', d''v'', ''u''′, ''v''′ ] over the universe [''u'', ''v'']. Their placement to the left of the double bar indicates that all of them amount to independent variables, but there is a co-dependency among them, as described |