The Stack of Change
Overview
This is a "stack" of work in progress on this website.

This is an experiment to help me keep track of what I am working on (or perhaps more the ones I'm not actually working on but have left in mid flow to follow some other hare).

I expect it to be a stack only in the loosest sense. Which is, that the stuff at the top is what I'm working on. The stuff later I was working on before that, and the further down you go the more distant the prospect that I will ever get back to it.

I generally have so many pages in an incomplete state (most of them!) that I loose track of pages before I ever finish them. Maybe this page will help me to get things nearer to completion.
The search for a non-well-founded foundation system suited to the formal development of mathematics.
Groping for a grip on metaphysics.
Work on a synthesis of elements of rationality and romanticism, with the help of readings from Isaiah Berlin
Naïve philosophy is a collection of attitudes which underpin philosophy at RBJones.com, wwhich is naive, unscholarly, sceptical, anarchistic and utopian. It is presented in three perspectives, Taoist, Anarchist, and Sceptical.
Re-engineering the process of developing this website.
The fundamental ethos of this web site is sceptical and scepticism is the main content of the "naive philosophy" which underpins all my other philosophy. At a "higher" level my "positive" philosophy is in large part metaphysicsl positivism. The articulation both of the sceptical and the positivistic aspects of my philosophy are skeletal, and this topic concerns fleshing them out a bit.
At the extreme rationalist end of my philosophy formal methods loom large and in these logic and mathematics are crucial. This is infrastructure for formal philosophy.
Reflexive Foundations
The search for a non-well-founded foundation system suited to the formal development of mathematics.
Introduction

In September 2006 Thomas Forster announced that he would be holding meeting in 2007 for an anniversary connected with Quine's set theory NF. I decided that I would do something with NF to get myself to a level of knowledge at which it would be worth my while to go to the meeting (thinking that in my then state of ignorance too little of the proceedings would be intelligible),

I began with some attempts to formalise NF and NFU in ProofPower, and one thing lead to another. I was looking to use the formalisation of NF as a semantic domain for other (non set-theoretic) foundation systems, but as I spent time getting to understand NF better I gradually became convinced that NF was not the right starting point and decided that a non-well-founded set theory devised with my purposes in mind would be better.

That lead to the PolySets, which I made several starts at formalising some in ProofPower some in Isabelle. The formal construction was completed in Isabelle, but proof work was rather slow (I am not fluent in Isabelle proofs).

I liked the PolySets, and they seemed to do the main thing which inspired them, i.e., add to a full well-founded set ontology the graphs of (a transfinite extrapolation of) the kinds of polymorphic function definable in the programming language ML. BUT, there was something more important, which I thought might come with that but which I came to suspect would not. That is, the kind of context management similar in character to the ML let clause (which the PolySets probably are good for) but which is applied to the management of the more diverse kind of content which is needed in context for the formal development of mathematics. I here refer to the sort of thing which "Locales" are aimed at in Isabelle.

I use the category of categories as the test for this kind of context management (I know, the connection may not be obvious), and I came to feel it unlikely that the PolySets would do the trick, So I have begun to think about stretching the PolySets further, and have several ideas I am progressing.

Using ProofPower HOL
Several approaches to the formalisation of these theories are tried out here.
This was the application I started to try the best advanced formalisation of NFU.
This is an early approach to the construction of PolySets based on the non-axiomatic approach to set theory in "Membership Structures". I very quickly came to feel this not a practical way of proceeding.
This is my latest approach to the problem in which I begin with an axiomatic well-founded set theory, then construct the PolySets, as a preliminary to investigating the broadening of the ontology by adding complements.
Using Isabelle HOL
This was my first attempt at the PolySets in Isabelle, using a set theory introduced with locales. (more or less hypothesising the set theory rather than axiomatising it). The locales weren't as helpful as I had hoped and I abandoned this approach in favour of building on an axiomatic set theory.
This is the most substantial formal treatment, which gets as far as defining the representation type and the membership relationship and introducing a new type of PolySets, but not as far as proving anything useful about them.
Plain(ish) English
This is my best effort at an informal description of the PolySets. Some material on the "why"s and "wherefore"s, and some speculation about their properties,
Metaphysics
Groping for a grip on metaphysics.
There are two main objectives here. The first is to articulate a positivistic conception of metaphysics. The second is to progress certain aspects of that. The three specific aspects to progress are abstract ontology, space-time and concrete ontology.
Rationality and Romanticism
Work on a synthesis of elements of rationality and romanticism, with the help of readings from Isaiah Berlin
Introduction

This "topic cluster" gathers together links to pages concerned with a direction of development in my philosophy the purpose of which is to integrate more fully into that philosophy ideas connected with the "Romantic" tradition in philosophy.

To further this I first sketched a new philosophical posture called positive philosophy in which metaphysical positivism is counterbalanced by something of a more Romantic character provisionally named existential positivism, accompanied by some discussion of the relationship between the rationalism of the enlightenment and the Romantic reaction against it.

I quickly came to the view that I really didn't know enough about Romanticism to be able to say anything meaningful about it, decided to do a bit of background reading, and somehow concluded that reading Isaiah Berlin might help. I found Berlin readable and read several of his books. In the course of this I came up with some ideas on how to take notes (which I do very badly), and how to bridge the gap between reading, taking notes, and various degrees of more tenuously connected writing about related ideas.

None of this has worked well. My reading of Berlin is probably largely complete, at least for the time being, and my present preoccupation is with rethinking my philosophy with the "Romantic" elements having their proper influence. I am now doing this along two parallel tracks of which the original synthesis in positive philosophy is one, and the second is a completely new approach based around some new epistemological ideas and called synthetic philosophy.

The links provided are in order of decreasing distance from the reading material.

Synthetic philosophy is built around a purposive and realistic epistemology and is called synthetic because this epistemology is synthesised to be pragmatic and realistic rather than revealed as a body of philosophical dogma.
A philosophical synthesis from elements of the rational/empiricist and the romantic/existential aspects of western philosophy, overlaid on a substratum (naive philosophy) which is sceptical and expressionistic. In its less romantic elements the position is sceptical and in some respects positivistic, but the philosophy is also I hope, positive in a more ordinary sense.
Two contrasting views of the proper relationship between the logical and emotional elements of the human psyche, which may be thought representative of distinct lines of development of western philosophy are dissected with a view to a synthesis.
Isaiah Berlin was a philosopher who mainly wrote about the history of ideas and had a particular interest in the period around the French Revolution and its relevance to political thought in mid twentieth century.
Naive Philosophy
Naïve philosophy is a collection of attitudes which underpin philosophy at RBJones.com, wwhich is naive, unscholarly, sceptical, anarchistic and utopian. It is presented in three perspectives, Taoist, Anarchist, and Sceptical.
Introduction
Philosophy at this level borders on the inexpressible or the paradoxical. To help express the ideas I gather together a variety of perspectives.
Philosophical Naivety
This sceptical philosophy is naive in a manner similar to that of primitive art. The sceptic seeks wisdom but is acutely aware of the difficulties in its attainment. He is aware of his own limited ability to comprehend the world and his place in it, and naturally sceptical about received wisdom and accepted methods of attaining it, including academic institutions and the standards they impose.
Aspects of Scepticism
Our scepticism is open not closed, positive rather than negative and active rather than passive. It is open, pragmatic, creative, and even, utopian.
Open scepticism is a kind of theoretical scepticism, an anti-dogmatic philosophy in respect of knowledge, which enjoins suspension of judgement in all matters, accepting only that things appear to be as they do.
pragmatic scepticism is a variant of practical scepticism, an anti-dogmatic philosophy in relation to what should be done. It is a personally liberating philosophical position, liberating through the denial that logic (or anything else) provides conclusive grounds for any particular course of action.
Pragmatic scepticism sees uncertainty as liberating rather than paralysing, and hence is sympathetic rather than antagonistic to creative and utopian thinking, at least so far as these are openly rather than dogmatically speculative. Sceptical nescience is no barrier to the synthesis of an open-minded weltanshauung, or to the expression of that creative synthesis in some work of philosophy, of art, of life.
About Writing
Re-engineering the process of developing this website.
Very briefly in place this page is an attempt at exhibiting the dynamic of the transition from the conception of "positive philosophy" on the previous home page and something better (still not in place). It was overtaken by a more general concern with making the web site more fully express the dynamics of my philosophical thought.
My top priority just now is to get myself into a comfortable way of working, in which thinking and writing are hand in glove and the writing gets to a fair picture of the thinking.
Scepticism and Positivism
The fundamental ethos of this web site is sceptical and scepticism is the main content of the "naive philosophy" which underpins all my other philosophy. At a "higher" level my "positive" philosophy is in large part metaphysicsl positivism. The articulation both of the sceptical and the positivistic aspects of my philosophy are skeletal, and this topic concerns fleshing them out a bit.
Logic and Mathematics
At the extreme rationalist end of my philosophy formal methods loom large and in these logic and mathematics are crucial. This is infrastructure for formal philosophy.

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