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Re: Michael Harris • Language About Language There is a language and a corresponding literature treating logic and mathematics as related species of communication and information gathering, na…
on Sun, 8PM
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In the development of Cactus Language to date the following two species of graphs have been instrumental. Painted And Rooted Cacti (PARCAI). Painted And Rooted Conifers (PARCOI). It suffices to beg…
on Mar 8
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In order to facilitate the use of propositions as indicator functions it helps to acquire a flexible notation for referring to propositions in that light, for interpreting sentences in a correspond…
on Mar 6
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Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sh…
on Mar 3
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A child hears it said that the stove is hot. But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold. But he touches it, and…
on Feb 27
Theory and Therapy of Representations • 5
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Re: R.J. Lipton and K.W. Regan • Legal Complexity I do not pretend to understand the moral universe; the arc is a long one, my eye reaches but little ways; I cannot calculate the curve and com…
on Feb 25
Theory and Therapy of Representations • 4
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Re: Theory and Therapy of Representations • 3 Re: Ontolog Forum • Paola Di Maio JA: What are the forces distorting our representations of what’s observed, what’s expected…
on Feb 24
Pragmatic Truth • Discussion 18
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Re: Pragmatic Truth • Discussion • (14) • (16) • (17) Re: Peirce List • Tom Gollier We do not live in axiom systems. We do not live encased in languages, formal or na…
on Feb 24
Theory and Therapy of Representations • 3
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Representation is a concept we find at the intersection of cybernetics, epistemology, logic, mathematics, psychology, and sociology. In my studies it led me from math to psych and back again,…
on Feb 24
Theory and Therapy of Representations • 2
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December 19, 2011 In a complex society, people making decisions and taking actions at places remote from you have the power to affect your life in significant ways. Those people govern your l…
on Feb 22
The Place Where Three Wars Meet
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One of the interesting things about the curse of our nation’s interesting times is the chance we have to observe how that triple threat — the War on Democracy, the War on Education, and…
on Feb 21
Theory and Therapy of Representations • 1
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Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνη…
on Feb 21
Basal Ingredients Of Society • ℞
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THE SOCIAL COMPACT If then we discard from the social compact what is not of its essence, we shall find that it reduces itself to the following terms: “Each of us puts his person and all his …
on Feb 20
Basal Ingredients Of Society • Prologue
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I settled on the acronym BIOS to suggest the vital elements of life in society, a life in association with others, and not just any association but one whose flickers of life are sustained for more…
on Feb 18
The Prime Movers of Disaster Capitalism
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☠ Obscenely Rich Corporations (ORCs) ⇒ Corporate Owned Governments (COGs) ⇒ Mercantile Engineered Social Starvation (MESS) ⇒ Corporate Owned Biosphere Wasting Earth̵…
on Feb 18
Tenacity, Authority, Plausibility, Inquiry
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Re: Peter Cameron • Mathematics and Logic My favorite polymathematician, Charles Sanders Peirce, gave a fourfold classification of what he called “methods of fixing belief”, or &ld…
on Feb 14
Theme One Program • Exposition 7
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Mathematical Structure and Logical Interpretation The main things to take away from the previous post are the following two ideas, one syntactic and one semantic. Syntax. The compos…
on Feb 13
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Theme One Program • Exposition 7 JPG Node Connective Lobe Connective PNG Logical Interpretations of Cactus Structures • En Ex $latex \text{Logical Interpretations of Cactus Structures}&am…
on Feb 13
Peirce’s 1870 “Logic of Relatives” • Comment 10.2
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Peirce’s 1870 “Logic of Relatives” • Comment 10.2 To say a relative term “imparts a relation” is to say it conveys information about the space of tuples in a cart…
on Feb 13
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Peirce’s 1870 “Logic of Relatives” • Comment 10.2 PNG Lover of a Servant of a Woman $latex \text{Figure 7. Lover of a Servant of a Woman}&fg=000000&s=1$ Giver of a Ho…
on Feb 13
Interpreter and Interpretant • Selection 10
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Transfer Returning to the scene of Dewey’s “Sign of Rain” example, let’s continue examining how the transfer of knowledge through the analogy of experience works in that cas…
on Feb 13
Charles Sanders Peirce, George Spencer Brown, and Me • 4
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Two things impacting my studies of Peirce and Spencer Brown over the years were my parallel studies in mathematics and computer science. In the overlap between those areas came courses in log…
on Feb 6
Charles Sanders Peirce, George Spencer Brown, and Me • 1
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It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to…
on Jan 30
Interpreter and Interpretant • Selection 9
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Transfer Let’s examine how the transfer of knowledge through the analogy of experience works in the case of Dewey’s “Sign of Rain” example. For concreteness, consider a frag…
on Jan 28
Interpreter and Interpretant • Selection 8
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Transfer What exactly gives the acquisition of a knowledge base its distinctively inductive character? It is evidently the “analogy of experience” involved in applying what weR…
on Jan 25
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Meaning is a privilege not a right. Not all pictures depict. Not all signs denote. Never confuse a property of a sign, just for instance, existence, with a sign of a property, for instance, existen…
on Jan 19
Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 4
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This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce. Particular attention i…
on Jan 16
Interpreter and Interpretant • Selection 7
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Learning Rules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference. For example, consider a proposition of the following form. $latex \begin{…
on Jan 16
Interpreter and Interpretant • Selection 6
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Inquiry and Induction To understand the bearing of inductive reasoning on the closing phases of inquiry there are a couple of observations we should make. Smaller inquiries are typically woven into…
on Jan 14
Interpreter and Interpretant • Selection 5
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Inquiry and Inference If we follow Dewey’s “Sign of Rain” story far enough to consider the import of thought for action, we realize the subsequent conduct of the interpreter, prog…
on Jan 12
Interpreter and Interpretant • Selection 4
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Interpretation and Inquiry To illustrate the role of sign relations in inquiry we begin with Dewey’s elegant and simple example of reflective thinking in everyday life. A man is walking on a …
on Jan 10
Interpreter and Interpretant • Selection 3
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The following selection from Peirce’s “Lowell Lectures on the Logic of Science” (1866) lays out in detail his “metaphorical argument” for the relationship between…
on Jan 9
Interpreter and Interpretant • Selection 2
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A idea of what Peirce means by an Interpretant and the part it plays in a triadic sign relation is given by the following passage. It is clearly indispensable to start with an accurate and broad an…
on Jan 8
Interpreter and Interpretant • Selection 1
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Questions about the relationship between “interpreters” and “interpretants” in Peircean semiotics have broken out again. To put the matter as pointedly as possible &md…
on Jan 6
Differential Propositional Calculus • 8
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Formal Development (cont.) Before moving on, let’s unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above. A universe o…
on Dec 7
Differential Propositional Calculus • 7
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Formal Development The preceding discussion outlined the ideas leading to the differential extension of propositional logic. The next task is to lay out the concepts and terminology needed to…
on Dec 6
Differential Propositional Calculus • 6
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Cactus Calculus Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable $latex k&fg=000000$-ary scope. A bracketed sequence of propositi…
on Dec 6
Differential Propositional Calculus • 5
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Casual Introduction (concl.) Table 5 exhibits the rules of inference responsible for giving the differential proposition $latex \mathrm{d}q&fg=000000$ its meaning in practice. $latex \text{Tabl…
on Dec 4
Differential Propositional Calculus • 4
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Casual Introduction (cont.) In Figure 3 we saw how the basis of description for the universe of discourse $latex X&fg=000000$ could be extended to a set of two qualities $latex \{q, \mathrm{d}q…
on Dec 2
Differential Propositional Calculus • 3
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Casual Introduction (cont.) Figure 3 returns to the situation in Figure 1, but this time interpolates a new quality specifically tailored to account for the relation between Figure 1…
on Dec 1
Differential Propositional Calculus • 2
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Casual Introduction (cont.) Now consider the situation represented by the venn diagram in Figure 2. $latex \text{Figure 2. Same Names, Different Habitations}&fg=000000$ Figure 2 diffe…
on Nov 30
Differential Propositional Calculus • 1
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A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of di…
on Nov 30
Differential Propositional Calculus • Overview
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The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time. W. Ross Ashby • An I…
on Nov 29
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One of my readers on Facebook told me “venn diagrams are obsolete” and we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions. In…
on Nov 26
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Introduction Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in …
on Oct 31
Information = Comprehension × Extension • Selection 2
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Over the course of Selection 1 Peirce introduces the ideas he needs to answer stubborn questions about the validity of scientific inference. Briefly put, the validity of scientific inference …
on Oct 6
Information = Comprehension × Extension • Selection 1
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Our first text comes from Peirce’s Lowell Lectures of 1866, titled “The Logic of Science, or, Induction and Hypothesis”. I still remember the first time I read these words a…
on Oct 5
Information = Comprehension × Extension • Preamble
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Eight summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems in Peirce’s semiotics and logic of science, namely, the relation between “the manne…
on Oct 4
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Re: Michael Harris • Not About Fibonacci I have often reflected on the interminglings of the main three normative sciences. In one of my earliest meditations I saw Beauty, Goodness,…
on Sep 21
Logical Graphs • Formal Development 1
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Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Formal Development Logical Graphs • First I…
on Sep 13