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(i) a family of actual individuals x1, x2, x3 . . . ; |
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(ii) a family of properties F,C,M . . . , attributed to individuals; |
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(iii) an 'essentiality specification' for every individual, as to whether this property is or is not essential to it; |
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(iv) relations between properties (for instance, relations of entailment). |
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Given a W1 with two individuals x1 and x2 and three properties F,C,M, the sign + means that an individual has the corresponding property, the sign - means that it does not, and the parentheses mark the essential properties, as shown in Figure 8.7. |
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Figure 8.7
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Now let us imagine a W2 in which are individuals with properties as shown in Figure 8.8. |
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Figure 8.8
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An individual in W2 is the potential variant of its prototype individual in W1 if they differ only in accidental properties (therefore y1 in W2 is a variant of x1 in W1 and y2 in W2 is a variant of x2 in W1). |
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An individual in W2 is a supernumerary in respect to the individuals in W1 if it differs from them also in essential properties (therefore y3Î W2 is supernumerary in respect to W1). |
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When a prototype in W1 has no more than one potential variant in W2, potential variance coincides with so-called transworld identity. |
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If we come back for a moment to the example given in 8.6.1, where my mother-in-law wonders what might have happened if I had never married her daughter, we see that she refers to a world structure of the sort shown in Figure 8.9, where M is the essential property of being married to her daughter and P is the accidental property of being the author of this paper. |
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On the contrary, when one wonders what might have happened if the author of this paper had never married, one refers back to a world structure of the sort shown in Figure 8.10. |
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