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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 16:04, 27 April 2009
, 16:04, 27 April 2009→Work Area
This says that a lover of every woman in the given universe of discourse is a lover of <math>\mathrm{W}^{\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math> In other words, a lover of every woman in this context is a lover of <math>\mathrm{W}^{\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math>
This says that a lover of every woman in the given universe of discourse is a lover of <math>\mathrm{W}^{\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime}</math> that is a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math> In other words, a lover of every woman in this context is a lover of <math>\mathrm{W}^{\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime}</math> and a lover of <math>\mathrm{W}^{\prime\prime\prime}.</math>
===Commentary Note 12.2===
===Commentary Note 12.2===
The term ''exponentiation'' is more generally used in mathematics for operations that involve taking a base to a power, and is slightly preferable to ''involution'' since the latter is used for different concepts in different contexts. Operations analogous to taking powers are widespread throughout mathematics and Peirce frequently makes use of them in a number of important applications, for example, in his theory of information. But that's another story.
The term ''exponentiation'' is more generally used in mathematics for operations that involve taking a base to a power, and is slightly preferable to ''involution'' since the latter is used for different concepts in different contexts. Operations analogous to taking powers are widespread throughout mathematics and Peirce frequently makes use of them in a number of important applications, for example, in his theory of information. But that's another story.