Changes

: In: [http://stderr.org/pipermail/inquiry/2005-October/thread.html#3104 FOLG]

: In: [http://stderr.org/pipermail/inquiry/2005-October/thread.html#3104 FOLG]

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o-----------------------------------------------------------o

o-----------------------------------------------------------o

o-----------------------------------------------------------o

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What sorts of sign relation are implicated in this sign process?  For simplicity, let's answer for the existential interpretation.

What sorts of sign relation are implicated in this sign process?  For simplicity, let's answer for the existential interpretation.

In ''Ex'', all four of the listed signs are expressions of Falsity, and, viewed within the special type of semiotic procedure that is being considered here, each sign interprets its predecessor in the sequence.  Thus we might begin by drawing up this Table:

In ''Ex'', all four of the listed signs are expressions of Falsity, and, viewed within the special type of semiotic procedure that is being considered here, each sign interprets its predecessor in the sequence.  Thus we might begin by drawing up this Table:

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o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

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That much of a sign relation is enough to cover the case before us, but of course it is only a small sample from the larger population of triples of the form <''o'', ''s'', ''i''> that is implied by the definition of the primary arithmetic.

That much of a sign relation is enough to cover the case before us, but of course it is only a small sample from the larger population of triples of the form <''o'', ''s'', ''i''> that is implied by the definition of the primary arithmetic.

Let's take another look at the semiotic sequence associated with a logical evaluation and the corresponding sample of a sign relation that we were looking at last time.

Let's take another look at the semiotic sequence associated with a logical evaluation and the corresponding sample of a sign relation that we were looking at last time.

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o-----------------------------------------------------------o

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| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |

| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |

o-----------------------------------------------------------o

o-----------------------------------------------------------o

o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

| Object` ` ` ` ` ` | Sign` ` ` ` ` ` ` | Interpretant` ` ` |

| Object` ` ` ` ` ` | Sign` ` ` ` ` ` ` | Interpretant` ` ` |

o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

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The sign of equality "=", interpreted as logical equivalence "&hArr;", that marked our steps in the process of conducting the evaluation, is evidently intended to denote an equivalence relation, and this is a 2-adic relation that is reflexive, symmetric, and transitive.  If we then pass to the reflexive, symmetric, transitive closure of the <''s'', ''i''> pairs that occur in our initial sample, attaching the constant reference to Falsity in the object domain, we will sweep out a more complete selection of the sign relation that inheres in the definition of the primary logical arithmetic.

The sign of equality "=", interpreted as logical equivalence "&hArr;", that marked our steps in the process of conducting the evaluation, is evidently intended to denote an equivalence relation, and this is a 2-adic relation that is reflexive, symmetric, and transitive.  If we then pass to the reflexive, symmetric, transitive closure of the <''s'', ''i''> pairs that occur in our initial sample, attaching the constant reference to Falsity in the object domain, we will sweep out a more complete selection of the sign relation that inheres in the definition of the primary logical arithmetic.

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o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

o-------------------o-------------------o-------------------o

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Earnest contemplation of the relationship between semiotic trajectories and the infrastructure of sign relations that is needed to support them may bring the seeker to a state of enlightenment about a motley crew of old knots in the semiotic web of maya, most pointedly the one that goes about raveling and reveiling the world in the name of infinite semiosis.

Earnest contemplation of the relationship between semiotic trajectories and the infrastructure of sign relations that is needed to support them may bring the seeker to a state of enlightenment about a motley crew of old knots in the semiotic web of maya, most pointedly the one that goes about raveling and reveiling the world in the name of infinite semiosis.

Before we leave it for richer coasts — not to say we won't find ourselves returning eternally — let's note one other feature of our randomly chosen microcosm, one I suspect we'll see many echoes of in the macrocosm of our future wanderings.

Before we leave it for richer coasts — not to say we won't find ourselves returning eternally — let's note one other feature of our randomly chosen microcosm, one I suspect we'll see many echoes of in the macrocosm of our future wanderings.

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o-----------------------------------------------------------o

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One of the things that makes this sign sequence so special, amidst the generations of other sign sequences that can be generated from the sign relation of the primary arithmetic, is that it goes from a relatively obscure and verbose sign to an optimally clear and succinct sign for the same thing.  For all its simplicity, then, it possesses a property that is characteristic of a semiotic process known as ''inquiry''.

One of the things that makes this sign sequence so special, amidst the generations of other sign sequences that can be generated from the sign relation of the primary arithmetic, is that it goes from a relatively obscure and verbose sign to an optimally clear and succinct sign for the same thing.  For all its simplicity, then, it possesses a property that is characteristic of a semiotic process known as ''inquiry''.