Changes

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The easiest way to define the language <math>\mathfrak{C}(\mathfrak{P})</math> is to indicate the general sorts of operations that suffice to construct the greater share of its sentences from the specified few of its sentences that require a special election.  In accord with this manner of proceeding, I introduce a family of operations on strings of <math>\mathfrak{A}^*</math> that are called ''syntactic connectives''.  If the strings on which they operate are exclusively sentences of <math>\mathfrak{C}(\mathfrak{P}),</math> then these operations are tantamount to ''sentential connectives'', and if the syntactic sentences, considered as abstract strings of meaningless signs, are given a semantics in which they denote propositions, considered as indicator functions over some universe, then these operations amount to ''propositional connectives''.

The easiest way to define the language !C!(!P!) is to indicate the general sorts

of operations that suffice to construct the greater share of its sentences from

the specified few of its sentences that require a special election.  In accord

with this manner of proceeding, I introduce a family of operations on strings

of !A!* that are called "syntactic connectives".  If the strings on which

they operate are exclusively sentences of !C!(!P!), then these operations

are tantamount to "sentential connectives", and if the syntactic sentences,

considered as abstract strings of meaningless signs, are given a semantics

in which they denote propositions, considered as indicator functions over

some universe, then these operations amount to "propositional connectives".

Rather than presenting the most concise description of these languages

Rather than presenting the most concise description of these languages right from the beginning, it serves comprehension to develop a picture of their forms in gradual stages, starting from the most natural ways of viewing their elements, if somewhat at a distance, and working through the most easily grasped impressions of their structures, if not always the sharpest acquaintances with their details.

right from the beginning, it serves comprehension to develop a picture

of their forms in gradual stages, starting from the most natural ways

of viewing their elements, if somewhat at a distance, and working

through the most easily grasped impressions of their structures,

if not always the sharpest acquaintances with their details.

The first step is to define two sets of basic operations on strings of !A!*.

The first step is to define two sets of basic operations on strings of <math>\mathfrak{A}^*.</math>

1.  The "concatenation" of one string z_1 is just the string z_1.

1.  The "concatenation" of one string z_1 is just the string z_1.