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, 19:06, 19 August 2011→7.2.6. Information and Inquiry: + text
====7.2.6. Information and Inquiry====
====7.2.6. Information and Inquiry====
Given my initial description of inquiry as a process that reduces the uncertainty of an inquirer (any observant agent or interpretive system) about the state of an object system, and combining this with the characterization of interpreters in concrete form as sign relations, there arises an obvious question that must be addressed by this project: How is the state of uncertainty of an agent about an object system to be defined from the data present in a sign relation?
In spite of the bare construction of the A and B dialogue it is possible to elaborate a few scenarios on its basis that illustrate the relevance of sign relations to inquiry situations. To devise motivating stories for these inquiries and still be able to obtain the needed variations from such sparce materials, I will be forced to re use many elements of the sign relations A and B in non standard ways. Because they lack most of the analytic refinements that will be needed for complete clarity, these inventions risk the introduction of a few confusions. However, the exercise of untangling potential confusions in a simple example can provide useful practice, highlighting problems before they grow too complex to tackle, and training the attention to detect what features really matter in defining a situation of inquiry.
One type of inquiry might begin with A having no idea what B will say next, except for the certain knowledge that it must be confined to the syntactic domain S = {"A", "B", "i", "u"}. I will refer to this as a "syntactic" type of inquiry, since the object system appropriate to the inquiry situation, as described, is identical to the syntactic domain S. As a rough approximation, this inquiry can be viewed as a degenerate spin off from the original dialogue, one in which the true object domain has been lost, and attention has devolved to mere banter over signs. More carefully regarded, the relationship of the syntactic inquiry to the original situation could be described as deriving new sign relations Syn (A) and Syn (B) from the old sign relations A and B, in each case replacing O with S and splitting the stock of ordered triples in a corresponding fashion, as shown in Tables ** and **.
In this sort of "syntactic inquiry", the state of uncertainty on the part of A about the state of the object system S is a condition of maximum entropy with respect to the outcomes in S and can be represented as a uniform distribution of probabilities over S. In this scenario, A has log2|S| = log2(4) = 2 bits of uncertainty about what B will say next. If A hears B say "A" next, say, then A has no remaining doubts about the issue. As a result of receiving this sign, A comes to reside in a state with 0 bits of uncertainty about the question now past. The same reasoning applies to each of the other signs in S. Altogether, each sign in S conveys 2 bits of information to the interpreter A with respect to the prior condition of maximum uncertainty about the state of the object system S. The "average uncertainty reduction per symbol", in this case 2 bits, is called the "capacity of the information channel", as this channel is defined by the entire set up of the inquiry situation.
<pre>
Table **. Sign Relation of Interpreter X
Object Sign Interpretant
"A"A A "A"A
"B"A A "B"A
"i"A A "i"A
"u"A A "u"A
"A"B B "A"B
"B"B B "B"B
"i"B B "i"B
"u"B B "u"B
Table **. Sign Relation of Interpreter Syn (B)
Object Sign Interpretant
A "A" "A"
A "A" "u"
A "u" "A"
A "u" "u"
B "B" "B"
B "B" "i"
B "i" "B"
B "i" "i"
</pre>
Another type of inquiry might begin with A wondering what object B will denote next. Here, the object system referred to as a part of the inquiry situation is identical with the object domain O of the sign relations A and B.
'''Fragments'''
To deliver the logical functionality that is required to support inquiry, a computational framework must incorporate the ability to work with both empirical and rational knowledge. To do this it needs to have signs that refer to particular experiences and symbols that represent types of experience, and it needs, not only the capacity to examine the bearings of each upon the other, but a means to express the gist of this result in an integral form.
If these references and representations are to avoid the various ways of violating the bounds of sense — something they can do either by failing to have sufficient denotation from the outset or by exceeding the bounds of consistency and tractability at any stage of attempting to process their indications — then ...
# Operating on corrupt arguments or initially senseless indications. Attempting to start out from a state of empty nonsense, from a logically pointless or impoverished point of view, and trying to pursue a moment of semantic irreference on the impulse of a direction with null import. Drawing on resources that are logically empty and following instructions that are semantically nil.
# Transgressing the bounds of consistency or tractability at any subsequent stage of computation and thereby becoming logically empty or effectively vacuous, conceptually inconsistent or computationally intractable at an intermediate stage of investigation.
Even though the present discussion is focussed on isolated cases of sign relations, it cannot illustrate the properties of these examples in an adequate way without considering extended multitudes of other relations, both those that share the same properties and those that do not. Thus, to get the comparative study of sign relations started on a casual basis, something that is helped in addition by placing sign relations within the larger field of n place relations, I will exploit a few devices of taxonomic nomenclature, intending them to be applied for the moment in a purely informal way.
dimensions of temporal evolution and deliberate evaluation
coordinating temporal evolution with directed evaluation
partial specification: approximate, deficient, imperfect, incorrect
partial satisfaction: approximate, deficient, imperfect, incorrect
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