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The concatenation <math>L_1 \cdot L_2</math> of the formal languages <math>L_1\!</math> and <math>L_2\!</math> is just the cartesian product of sets <math>L_1 \times L_2</math> without the extra <math>\times</math>'s, but the relation of cartesian products to set-theoretic intersections and thus to logical conjunctions is far from being clear.  One way of seeing a type of relation is to focus on the information that is needed to specify each construction, and thus to reflect on the signs that are used to carry this information.  As a first approach to the topic of information, according to a strategy that seeks to be as elementary and as informal as possible, I introduce the following set of ideas, intended to be taken in a very provisional way.

The concatenation <math>L_1 \cdot L_2</math> of the formal languages <math>L_1\!</math> and <math>L_2\!</math> is just the cartesian product of sets <math>L_1 \times L_2</math> without the extra <math>\times</math>'s, but the relation of cartesian products to set-theoretic intersections and thus to logical conjunctions is far from being clear.  One way of seeing a type of relation is to focus on the information that is needed to specify each construction, and thus to reflect on the signs that are used to carry this information.  As a first approach to the topic of information, according to a strategy that seeks to be as elementary and as informal as possible, I introduce the following set of ideas, intended to be taken in a very provisional way.

A ''stricture'' is a specification of a certain set in a certain place, relative to a number of other sets, yet to be specified.  It is assumed that one knows enough to tell if two strictures are equivalent as pieces of information, but any more determinate indications, like names for the places that are mentioned in the stricture, or bounds on the number of places that are involved, are regarded as being extraneous impositions, outside the proper concern of the definition, no matter how convenient they are found to be for a particular discussion.  As a schematic form of illustration, a stricture can be pictured in the following shape:

A "stricture" is a specification of a certain set in a certain place,

relative to a number of other sets, yet to be specified.  It is assumed

that one knows enough to tell if two strictures are equivalent as pieces

of information, but any more determinate indications, like names for the

places that are mentioned in the stricture, or bounds on the number of

places that are involved, are regarded as being extraneous impositions,

outside the proper concern of the definition, no matter how convenient

they are found to be for a particular discussion.  As a schematic form

of illustration, a stricture can be pictured in the following shape:

"... x X x Q x X x ..."

:{| cellpadding="8"

| <math>\ldots \times X \times Q \times X \times \ldots</math>

A "strait" is the object that is specified by a stricture, in effect,

A ''strait'' is the object that is specified by a stricture, in effect,

a certain set in a certain place of an otherwise yet to be specified

a certain set in a certain place of an otherwise yet to be specified

relation.  Somewhat sketchily, the strait that corresponds to the

relation.  Somewhat sketchily, the strait that corresponds to the

stricture just given can be pictured in the following shape:

stricture just given can be pictured in the following shape:

... x X x Q x X x ...

| <math>\ldots \times X \times Q \times X \times \ldots</math>

In this picture, Q is a certain set, and X is the universe of discourse

In this picture, Q is a certain set, and X is the universe of discourse

that is relevant to a given discussion.  Since a stricture does not, by

that is relevant to a given discussion.  Since a stricture does not, by