## The Difference That Makes A Difference That Peirce Makes : 2

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 …

## Survey of Relation Theory • 3

In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of which arise quite naturally in applications.  This approach to relation theory, or the theory of relations, is distinguished from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other.

## Peirce and Democracy • 2

Re: Peirce List Discussion • GRHRJFSJA

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)

## Theory and Therapy of Representations • 2

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 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.

## Time, Topology, Differential Logic • 6

Re: Peirce List Discussion • ETJFSJAJBD

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:

1. mathematical models of the differentiation of spaces starting with a vague continuum of undifferentiated dimensions and trending towards spaces having determinate dimensions
2. 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:

• Time, Topology, Differential Logic • (1)(2)(3)(4)(5)

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

## Peirce and Democracy • 1

Re: Peirce List Discussion • GRJA

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?

## Time, Topology, Differential Logic • 5

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.

Plutarch • Life of Romulus

Re: Peirce List Discussion • ETETJBDJAJA

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

### Chapter 1. Topological Spaces

#### 1.1. Topologies and Neighborhoods

A topology is a family $\mathcal{T}$ of sets which satisfies the two conditions:  the intersection of any two members of $\mathcal{T}$ is a member of $\mathcal{T},$ and the union of the members of each subfamily of $\mathcal{T}$ is a member of $\mathcal{T}.$  The set $X = \bigcup \{ U : U \in \mathcal{T} \}$ is necessarily a member of $\mathcal{T}$ because $\mathcal{T}$ is a subfamily of itself, and every member of $\mathcal{T}$ is a subset of ${X}.$  The set ${X}$ is called the space of the topology $\mathcal{T}$ and $\mathcal{T}$ is a topology for ${X}.$  The pair $(X, \mathcal{T})$ is a topological space.  When no confusion seems possible we may forget to mention the topology and write “${X}$ 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 ${X}$).

The members of the topology $\mathcal{T}$ are called open relative to $\mathcal{T},$ or $\mathcal{T}$-open, or if only one topology is under consideration, simply open sets.  The space ${X}$ 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 ${X}$ and the void set is a topology for ${X}.$  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 ${X},$ and $(X, \mathcal{T})$ is then an indiscrete topological space.  At the other extreme is the family of all subsets of ${X},$ which is the discrete topology for ${X}$ (then $(X, \mathcal{T})$ is a discrete topological space).  If $\mathcal{T}$ is the discrete topology, then every subset of the space is open.  (Kelley, p. 37).

### References

• 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.