Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems
Fragmata
- Arisbe Site, "Inquiry Driven Systems", 30 Jun 2000, Draft 8.2
- Arisbe List, "Inquiry Driven Systems", 05 Jan 2002, Drafts 8.69 – 8.70
- Inquiry List, "Reflective Inquiry" (= IDS 3.2), 13 Apr 2004
- Inquiry List, "Higher Order Signs" (= IDS 3.4.9 – 3.4.10), 24 Nov 2004
- NKS Forum, "Higher Order Signs" (= IDS 3.4.9 – 3.4.10), 24 Nov 2004
- NKS Archive, "Higher Order Signs" (= IDS 3.4.9 – 3.4.10), 24 Nov 2004
- NKS Printable, "Higher Order Signs" (= IDS 3.4.9 – 3.4.10), 24 Nov 2004
- Inquiry List, "Recurring Themes" (= IDS 1.3.10.3 – 1.3.10.7), 17 Dec 2004 (= 16 Dec 2001)
- Inquiry List, "Language Of Cacti" (= IDS 1.3.10.8 – 1.3.10.13), 13 Dec 2004 (= 06 Jan 2002)
- NKS Forum, "Language Of Cacti", 13 Dec 2004 (= 06 Jan 2002)
- NKS Archive, "Language Of Cacti", 13 Dec 2004 (= 06 Jan 2002)
- NKS Printable, "Language Of Cacti", 13 Dec 2004 (= 06 Jan 2002)
Symbol Sandbox
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- LaTeX \[< >\] \(< >\!\) \(\lessdot \gtrdot\)
\[\begin{matrix} (\ ) & = & 0 & = & \mbox{false} \\ (x) & = & \tilde{x} & = & x' \\ (x, y) & = & \tilde{x}y \lor x\tilde{y} & = & x'y \lor xy' \\ (x, y, z) & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} & = & x'yz \lor xy'z \lor xyz' \end{matrix}\]
Xj = Pj ∪ Qj , P = ∪j Pj ,
Q = ∪j Qj .
\[\begin{matrix} X_j = P_j \cup Q_j , & P = \bigcup_j P_j , & Q = \bigcup_j Q_j . \end{matrix}\]
Notes & Queries
JA: I'm in the process of merging and reconciling two slightly different versions of this paper, but it may be the end of the summer before I can finish doing that. Jon Awbrey 09:48, 29 May 2007 (PDT)
- Jon, your content soars way over my head, but I am nonetheless delighted that you're using Centiare so effectively (if at least to get #1 Google search results for inquiry driven systems — even though that's currently not happening … Google's a bit quirky as it digests our site and "learns" where to put us in the rankings). I hope that you can keep up the effort, and that we can help you from an operational standpoint. MyWikiBiz 13:26, 29 May 2007 (PDT)
JA: Thanks for the interest, and I've been "pleased as punch" with the environment so far, mostly for reasons independent of the SEO factor — the quality of the working environment is more important to me than any need to corner the market in a given subject area. As far as I know, I coined the term "inquiry driven system" back in the (19)80's — though I know as soon as I say that, it will turn out that C.S. Peirce scooped me by a century or so — anyway, it's already the case that 90% of the stuff on the web about inquiry driven systems was written by yours truly. On the other hand, when my Centiare user and directory pages depose my Wikipedia user and discussion pages from the top of the Google heap, that will be the test case for me! Jon Awbrey 14:36, 29 May 2007 (PDT)
Congratulations!
Congratulations! Someone from Missouri visited this page today as a result of this search. — MyWikiBiz 11:57, 13 October 2008 (PDT)
What do you know, it is the "Show Me" State, after all … Jon Awbrey 12:06, 13 October 2008 (PDT)
- Furthermore, someone from New York City visited the page today, via a #1 search result on Yahoo! for system inquiry examples. Congratulations, again! — MyWikiBiz 06:29, 23 October 2008 (PDT)
Propositions and Sentences
Residual Remarks
Where are we? We just defined the concept of a functional fiber in several of the most excruciating ways possible, but that's just because this method of refining functional fibers is intended partly for machine consumputation, so its schemata must be rendered free of all admixture of animate intuition. However, just between us, a single picture may suffice to sum up the notion:
| X-[| f |] , [| f |] c X
| o o o o o |
| \ / \ | / |
| \ / \ | / | f
| \ / \|/ |
| o o v
| { %0% , %1% } = %B%
Why are we doing this? The immediate reason — whose critique I defer — has to do with finding a modus vivendi, whether a working compromise or a genuine integration, between the assertive-declarative languages and the functional-procedural languages that we have available for the sake of conceptual-logical-ontological analysis, clarification, description, inference, problem-solving, programming, representation, or whatever.
In the next few installments, I will be working toward the definition of an operation called the stretch. This is related to the concept from category theory that is called a pullback. As a few will know the uses of that already, maybe there's hope of stretching the number.
I finish out the Subsection on "Propositions & Sentences" with an account of how I use concepts like "assertion" and "denial". An "expression" is a type of sign, for instance, a term or a sentence, that has a value. In forming this conception of an expression, I am deliberately leaving a number of options open, for example, whether the expression amounts to a term or to a sentence and whether it ought to be accounted as denoting a value or as connoting a value. Perhaps the expression has different values under different lights, and perhaps it relates to them differently in different respects. In the end, what one calls an expression matters less than where its value lies. Of course, no matter whether one chooses to call an expression a "term" or a "sentence", if the value is an element of %B%, then the expression affords the option of being treated as a sentence, meaning that it is subject to assertion and composition in the same way that any sentence is, having its value figure into the values of larger expressions through the linkages of sentential connectives, and affording us the consideration of what things in what universe the corresponding proposition happens to indicate. Expressions with this degree of flexibility in the types under which they can be interpreted are difficult to translate from their formal settings into more natural contexts. Indeed, the whole issue can be difficult to talk about, or even to think about, since the grammatical categories of sentential clauses and noun phrases are rarely so fluid in natural language settings are they can be rendered in artificially formal arenas. To finesse the issue of whether an expression denotes or connotes its value, or else to create a general term that covers what both possibilities have in common, one can say that an expression "evalues" its value. An "assertion" is just a sentence that is being used in a certain way, namely, to indicate the indication of the indicator function that the sentence is usually used to denote. In other words, an assertion is a sentence that is being converted to a certain use or that is being interpreted in a certain role, and one whose immediate denotation is being pursued to its substantive indication, specifically, the fiber of truth of the proposition that the sentence potentially denotes. Thus, an assertion is a sentence that is held to denote the set of things in the universe for which the sentence is held to be true. Taken in a context of communication, an assertion is basically a request that the interpreter consider the things for which the sentence is true, in other words, to find the fiber of truth in the associated proposition, or to invert the indicator function that is denoted by the sentence with respect to its possible value of truth. A "denial" of a sentence z is an assertion of its negation -(z)-. The denial acts as a request to think about the things for which the sentence is false, in other words, to find the fiber of falsity in the indicted proposition, or to invert the indicator function that is being denoted by the sentence with respect to its possible value of falsity. According to this manner of definition, any sign that happens to denote a proposition, any sign that is taken as denoting an indicator function, by that very fact alone successfully qualifies as a sentence. That is, a sentence is any sign that actually succeeds in denoting a proposition, any sign that one way or another brings to mind, as its actual object, a function of the form f : X -> B. There are many features of this definition that need to be understood. Indeed, there are problems involved in this whole style of definition that need to be discussed, and doing this requires a slight excursion.
