Goodman’s Paradox, Hume’s Problem, Goodman-Kripke Paradox: Three Different Issues


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On page 14 of "Reconceptions in Philosophy and Other Arts and Sciences" (section 4 of chapter 1) by Nelson Goodman and Catherine Z. Elgin is written: “Since ‘blue’ and ‘green’ are interdefinable with ‘grue’ and ‘bleen’, the question of which pair is basic and which pair derived is entirely a question of which pair we start with”. This paper points out that an example of interdefinability is also that one about the predicate “grueb”, which is a predicate that applies to an object if the object either is green and examined before time b, or is non-green and not examined before time b. The three predicates “green”, “grueb”, “examined before time b” are interdefinable: although the predicate “green” and the predicate “examined before time b” are interdefinable, the possibility to determine if an object is “green” without having temporal information does not imply the possibility to determine if an object is “examined before time b” without having temporal information. The interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. According to Goodman, if it is possible to determine if an object is green without needing temporal information, then it is also possible to determine if an object is grue without needing temporal information. But, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment.
Keywords induction  new riddle of induction  Goodman’s paradox  justification of induction  epistemology  philosophy of science  nominalism  undecidability  Hume's problem  Goodman’s ‘grue’ paradox
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