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This is apparently a stock example of inductive reasoning that Peiece borrows from traditional discussions, so let us pass over the circumstance that modern taxonomies may classify swine as omniverous.

This is apparently a stock example of inductive reasoning that Peirce borrows from traditional discussions, so let us pass over the circumstance that modern taxonomies may classify swine as omniverous.

In view of the analogical symmetries that the disjunctive term shares with the conjunctive case, I think that we can run through this example in fairly short order.  We have an aggregation over four terms:

In view of the analogical symmetries that the disjunctive term shares with the conjunctive case, I think that we can run through this example in fairly short order.  We have an aggregation over four terms:

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In a similar but dual fashion to the preceding consideration, there is a gap between the the logical disjunction ''u'', in lattice terminology, the ''least upper bound'' (''lub'') of the disjoined terms, ''u'' = ''lub''{''s''_''j''&nbsp;:&nbsp;''j''&nbsp;=&nbsp;1&nbsp;to&nbsp;4}, and what we might regard as the "natural disjunction" or the "natural lub", namely, ''v''&nbsp;=&nbsp;''cloven-hoofed''.

In a similar but dual fashion to the preceding consideration, there is a gap between the the logical disjunction <math>u,\!</math> in lattice terminology, the ''least upper bound'' (''lub'') of the disjoined terms, <math>u = \operatorname{lub} ( \{ s_j : j = 1 ~\text{to}~ 4 \}),</math> and what we might regard as the "natural disjunction" or the "natural lub", namely, <math>v = \text{cloven-hoofed}.\!</math>

Once again, the sheer implausibility of imagining that the disjunctive term ''u'' would ever be embedded exactly per se in a lattice of natural kinds, leads to the evident ''naturalness'' of the induction to ''v'' &rArr; ''w'', namely, the rule that cloven-hoofed animals are herbivorous.

Once again, the sheer implausibility of imagining that the disjunctive term <math>u\!</math> would ever be embedded exactly as such in a lattice of natural kinds, leads to the evident ''naturalness'' of the induction to <math>v \Rightarrow w,</math> namely, the rule that cloven-hoofed animals are herbivorous.

===Discussion===

===Discussion===