What is information and how does it impact the spectrum of activities that answer to the name of inquiry?

Setting out on what would become his lifelong quest to explore and explain the “Logic of Science”, C.S. Peirce pierced the veil of historical confusions enclosing the issue and fixed on what he called the “laws of information” as the needed key to solving the puzzle. This was in 1865 and 1866, detailed in his lectures at Harvard College and the Lowell Institute.

Fast forward to the present and I see the Big Question as follows. Having gone through the exercise of comparing and contrasting Peirce’s theory of information, however much it remains in a rough-hewn state, with Shannon’s paradigm that so pervasively informs the ongoing revolution in our understanding and use of information today, I have reason to believe that Peirce’s idea is root and branch more general and has the potential, with due development, to resolve many mysteries that still bedevil our grasp of inference, information, and inquiry.

- InterSciWiki • Information = Comprehension × Extension

- Blog Series • { Information = Comprehension × Extension }

- Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”. Online.

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My mind keeps flashing back to the days when I first encountered Peirce’s thought. It was so fresh, it spoke to me like no other thinker’s thought I knew, and it held so much promise of setting aside all the old schisms that boggled the mind through the ages.

I feel that way about it still but communicating precisely what I find so revolutionary in Peirce’s thought remains a work in progress for me.

Many readers of Peirce share the opinion that there is something truly novel in his thought, a difference that makes a critical difference in the way we understand our thoughts and undertake our actions in its light. The question has arisen once again, just what that difference might be.

So I’ll make another try at answering that …

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Relation Construction | Relation Composition | Relation Reduction |

Relative Term | Sign Relation | Triadic Relation |

Logic of Relatives | Hypostatic Abstraction | Continuous Predicate |

- Preliminaries
- Selection 1 • Use of the Letters
- Selection 2 • Numbers Corresponding to Letters
- Selection 3 • The Signs of Inclusion, Equality, Etc.
- Selection 4 • The Signs for Addition
- Selection 5 • The Signs for Multiplication
- Selection 6 • The Signs for Multiplication (cont.)
- Comment 6.1 • Sets as Sums

- Selection 7 • The Signs for Multiplication (cont.)
- Comment 7.1 • Proto-Graphical Syntax

- Selection 8 • The Signs for Multiplication (cont.)
- Selection 9 • The Signs for Multiplication (cont.)
- Selection 10 • The Signs for Multiplication (cont.)
- Selection 11 • The Signs for Multiplication (concl.)
- Comment 11.1
- Comment 11.2
- Comment 11.3
- Comment 11.4
- Comment 11.5
- Comment 11.6
- Comment 11.7
- Comment 11.8
- Comment 11.9
- Comment 11.10
- Comment 11.11
- Comment 11.12
- Comment 11.13
- Comment 11.14
- Comment 11.15
- Comment 11.16
- Comment 11.17
- Comment 11.18
- Comment 11.19
- Comment 11.20
- Comment 11.21
- Comment 11.22
- Comment 11.23
- Comment 11.24

- Selection 12 • The Sign of Involution
- Intermezzo

- Preliminaries
- Selections • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8)
- Comments • (7.1) • (7.2) • (7.3) • (7.4) • (7.5)

- Relations & Their Relatives • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8) • (9) • (10) • (11) • (12) • (13) • (14) • (15) • (16) • (17) • (18) • (19) • (20)

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The essential reading for answering that question — how the Protestant Ethic takes root in the hearts of those who set out merely seeking, if a bit too desperately, some assurance of personal salvation, and how they come to wander lost in the spiritual wasteland of Moneytheism that so rules our nation today — is *The Protestant Ethic and the Spirit of Capitalism* by Max Weber. There are some links on the following pages:

- Peirce and Democracy • (1)
- Readings on Moneytheism • (1) • (2)
- Theory and Therapy of Representations • (1) • (2)

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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 are your government, no matter what spheres of influence they inhabit, private or public. The only way you get a choice in that governance is if there are paths of feedback that allow you to affect the life of those decision makers and action takers in significant ways. That is what accountability, response-ability, and representative government are all about.

Naturally, some people are against that.

In the United States there has been a concerted campaign for as long as I can remember — but even more concerted since the Reagan Regime — to get the People to abdicate their hold on The Powers That Be and just let some anonymous corporate entity send us the bill after the fact. They keep trying to con the People into thinking they can starve the beast, to limit government, when what they are really doing is feeding the beast of corporate control, weakening their own power over the forces that govern their lives.

That is the road to perdition as far as responsible government goes. There is not much of anything one leader or one administration can do unsupported if the People do not constantly demand a government of, by, and for the People.

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Let me see if I can get back in the saddle on this topic, the dormitive virtues of tryptophan and a few pounds added notwithstanding.

I was addressing the following question from Jeffrey Brian Downard:

I wanted to see if anyone have might suggestions for thinking about the analogy between:

- mathematical models of the differentiation of spaces starting with a vague continuum of undifferentiated dimensions and trending towards spaces having determinate dimensions
- models for logic involving similar sorts of dimensions?

How might we understand processes of differentiation of dimensions in the case of logic?

By way of review, here are my blog posts on the discussion so far:

We can now get back to preparing the ground required to tackle Jeff’s question.

- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems

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In my mind the connection between Peirce and Democracy has long revolved around the concept of representation.

Representation in its semiotic sense has to do with signs that represent pragmatic objects to agents and communities of interpretation.

Representation in its political sense has to do with forms of government that address the *res publica*, the public concern, through elected representatives who represent, hopefully, the good will and the best information of the public at large in their stations at the rudders of the ship of state. Here the twin senses of representation converge on the common root meaning of the words *cybernetics* and *government*.

I have written a lot about this twofold sense of representation over the years but weeks of watching “The Death of a Nation” on TV have left me too dispirited to say any more on the subject.

I did happen on a recent blog post that seems to fit here:

The question for our day remains —

- What are the forces that distort our representations of what’s observed, what’s expected, and what’s intended?

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*And the founder, having shod a plough with a brazen ploughshare, and having yoked to it a bull and a cow, himself drove a deep furrow round the boundary lines, while those who followed after him had to turn the clods, which the plough threw up, inwards towards the city, and suffer no clod to lie turned outwards.*

Re: Peirce List Discussion • ET • ET • JBD • JA • JA

Our inquiry now calls on the rudiments of topology, for which I turn to J.L. Kelley.

A **topology** is a family of sets which satisfies the two conditions: the intersection of any two members of is a member of and the union of the members of each subfamily of is a member of The set is necessarily a member of because is a subfamily of itself, and every member of is a subset of The set is called the **space** of the topology and is a **topology for ** The pair is a **topological space.** When no confusion seems possible we may forget to mention the topology and write “ is a topological space.” We shall be explicit in cases where precision is necessary (for example if we are considering two different topologies for the same set ).

The members of the topology are called **open** relative to or -open, or if only one topology is under consideration, simply open sets. The space of the topology is always open, and the void set is always open because it is the union of the members of the void family. These may be the only open sets, for the family whose only members are and the void set is a topology for This is not a very interesting topology, but it occurs frequently enough to deserve a name; it is called the **indiscrete** (or **trivial**) topology for and is then an **indiscrete topological space.** At the other extreme is the family of all subsets of which is the **discrete** topology for (then is a **discrete topological space**). If is the discrete topology, then every subset of the space is open. (Kelley, p. 37).

- Kelley, J.L. (1955),
*General Topology*, Van Nostrand Reinhold, New York, NY. - Plutarch, “Romulus”, in
*Plutarch’s Lives : Volume 1*, Bernadotte Perrin (trans.), Loeb Classical Library, William Heinemann, London, UK, 1914.

- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems

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- JA:
- Trying to understand inquiry and semiosis in general as temporal processes is one of the things that forced me to develop differential logic as an extension of propositional logic, for which I naturally turned to Peirce’s logical graphs as a starting point.
- JFS:
- Yes, that’s another path to explore. For any version of logic, it’s important to determine what kinds of problems it can express and what solutions it can facilitate. What useful stories or Gedanken experiments can you explain in terms of it?

A first try at answering this question might well begin by reflecting on the analogous question in the quantitative realm:

- What kinds of situations does the differential and integral calculus serve to describe and what kinds of solutions does it help to facilitate?

Differential logic is simply the qualitative analogue of the differential and integral calculus. Both are called upon as we pass from the description of static situations to dealing with changes, differences, and transformations among multiple situations, those that occur in different modes of being or through different points in time.

- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems

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Worldly events are interfering with my concentration quite a bit this week, perhaps for days to come, but it does help to immerse myself in work. I am starting a blog series to follow out the present train of thought and trace whatever dialogue, internal or external, may ensue. Plus, the blog medium will give me better formatting if we get any further into the math.

By the way, there are a number of Facebook pages I devoted to these subjects, for anyone who makes use of that environment:

- Cybernetics
- Differential Logic
- Inquiry Driven Systems
- Logical Graphs
- Peirce Matters
- Relation Theory
- Semeiotics

- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems

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