Changes

</pre>

</pre>

Aside from their common topic, the two Tables present slightly different ways of conceptualizing the operations that go to establish their maps.  Table&nbsp;14.1 records the functional associations that connect each domain with the next, taking the triplings of a sentence <math>s_j,\!</math> a cactus <math>C_j,\!</math> and a proposition <math>q_j</math> as basic data, and fixing the rest by recursion on these.  Table 14.2 records these associations in the form of equations, treating sentences and graphs as alternative kinds of signs, and generalizing the denotation bracket operator to indicate the proposition that either denotes.  It should be clear at this point that either scheme of translation puts the sentences, the graphs, and the propositions that it associates with each other roughly in the roles of the signs, the interpretants, and the objects, respectively, whose triples define an appropriate sign relation.  Indeed, the "roughly" can be made "exactly" as soon as the domains of a suitable sign relation are specified precisely.

Aside from their common topic, the two Tables present slightly different ways of conceptualizing the operations that go to establish their maps.  Table&nbsp;14.1 records the functional associations that connect each domain with the next, taking the triplings of a sentence <math>s_j,\!</math> a cactus <math>C_j,\!</math> and a proposition <math>q_j</math> as basic data, and fixing the rest by recursion on these.  Table&nbsp;14.2 records these associations in the form of equations, treating sentences and graphs as alternative kinds of signs, and generalizing the denotation bracket operator to indicate the proposition that either denotes.  It should be clear at this point that either scheme of translation puts the sentences, the graphs, and the propositions that it associates with each other roughly in the roles of the signs, the interpretants, and the objects, respectively, whose triples define an appropriate sign relation.  Indeed, the "roughly" can be made "exactly" as soon as the domains of a suitable sign relation are specified precisely.

A good way to illustrate the action of the conjunction and surjunction operators is to demonstate how they can be used to construct all of the boolean functions on <math>k\!</math> variables, just now, let us say, for <math>k = 0, 1, 2.\!</math>

A good way to illustrate the action of the conjunction and surjunction

operators is to demonstate how they can be used to construct all of the

boolean functions on k variables, just now, let us say, for k = 0, 1, 2.

A boolean function on 0 variables is just a boolean constant F^0 in the

A boolean function on 0 variables is just a boolean constant <math>F^{(0)}\!</math> in the boolean domain <math>\underline\mathbb{B} = \{ \underline{0}, \underline{1} \}.</math> Table&nbsp;15 shows several different ways of referring to these elements, just for the sake of consistency using the same format that will be used in subsequent Tables, no matter how degenerate it tends to appears in the immediate case:

boolean domain %B% = {%0%, %1%}.  Table 14 shows several different ways

of referring to these elements, just for the sake of consistency using

the same format that will be used in subsequent Tables, no matter how

degenerate it tends to appears in the immediate case:

Column 1 lists each boolean element or boolean function under its

Column 1 lists each boolean element or boolean function under its

ordinary constant name or under a succinct nickname, respectively.

ordinary constant name or under a succinct nickname, respectively.