Brain Retrieved

Having put aside my other intellectual enterprises to do an abstract for the ITP workshop, I came up with nothing, despite being very keen at the outset and spending three weeks tussling with the problem.

I think too much of my thinking in this area is speculative and philosophical, and the small core of relevant technical detail got simpler and less substantial the more I thought about it.

The abstract deadline is today, so I have finally thrown in the towel.
I now need to think a bit before picking up some other threads.

RBJ

Well Founded Set Theoretic Truth

In the course of failing to come up with an abstract for the upcoming ITP workshop in Cambridge, I came across something I think rather nice which is only to be found in the overheads of the last talk I gave on X-Logic.

So I thought I would post it here, to give it a better home.

First just a few words of context.

I am unusual in considering the most important role for set theory to be its role as a foundation for abstract semantics.
From this point of view it is unfortunate that mathematical logic (where set theory belongs) has a negative attitude towards semantics, and tolerates a situation  in which set theory has no definite semantics (or at least, no single generally agreed semantics, there are many possibilities).

Anyway, I came up with a neat semantics for set theory as follows.
This is a definition for the truth conditions of sentences in set theory.
It assumes understood the notion of truth in an interpretation.

• a well-founded set is a definite collection of well-founded sets
  
• an interpretation of set theory is a transitive well-founded set
  
• a sentence is false if the collection of interpretations in which it is true is definite
  
• a sentence is true if the collection of interpretations in which it is false is definite
  

This is what I wrote about this at the time.

This semantics:

• is maximally rich (large cardinal axioms are true)
  
• is definite (CH has a truth value, particular facts about cardinal arithmetic have truth values)
  
• makes ZFC neither true nor false
  
• is not limited to first order languages (will work for infinitary set theory)
  
• is self defining (conjecture)
  

This probably all needs explaining in much greater detail, I will follow up with a bit more explanation.

RBJ

Brain Hijacked

Just at the point when I am trying, almost deperately, to get movement on my X-Logic and an associated informal analytic meta-methodology, an opportunity to engage with the Theorem Proving community comes up which I can't ignore.

Workshop on Trusted Extensions of Interactive Theorem Provers


The workshop is August 11-12 2010, in Cambridge, (England!) and abstracts for contributed talks have to be in by 28 June.
I intend to submit an abstract for a talk on X-Logic.  (I have already talked about X-Logic at the Computer Labs in Cambridge, but things have moved on since then).

At the heart of X-Logic is a system assurance/trust/authority (not sure which words to use) tags which is partly inspired by the problems of trust that arise in interworking between interactive theorem provers and other software (but also by a long list of other related problems).
X-Logic is now at the heart of my thinking about analytic methods appropriate for use in philosophy (and elsewhere). Alternatively, it is a label for the formal side of my methodological thinking.

The timescales are short, so it is likely to hijack my brain between now and the event (if my abstract were accepted, otherwise up to the point of its being declined!).

Though I will be pre-occupied with getting my story straight for the workshop, I hope there will be plenty of room for discussion about the impact of X-Logic on my philosphical projects, including the Carnap/Grice conversation, and my other thing.  I will be posting on this at the X-Logic blog, and probably something at Carnap Corner, The Eternal City, and maybe other places too.

Watch these spaces.

RBJ

Speranza's Provocation

This is a rambling tribute to J.L. Speranza, muddled up with reflections on recent developments in my own philosophical thinking..

The shape of my philosophical preoccupations over the next
few years is beginning to emerge from the mists, and in
thinking of where I am and how I got here I have come to
realise how much my recent development owes to the
provocation, and to the support, which I have had from
J.L.Speranza.
I thought I would dedicate a blog post to explaining
how my dialogue with Speranza over the last 15 months has
contributed to my development.

This recent fragment of the history of my search for
philosophical fulfilment (or mere expression) begins in
January 2009, when I decided to use the hist-analytic
mailing list as a sounding board for an attempt at a
monograph on "the fundamental triple dichotomy".
Speranza and I come from opposite ends of the spectrum of analytic philosophy, and it would be natural enough to expect an unsympathetic response from him to a philosophical enterprise much closer to Logical Positivism and Rudolf Carnap than to the Oxonian ordinary language philosophy, as moderated by Paul Grice, which is dear to his heart.

Surprisingly, the resident empiricist, Bruce Aune, was
wholly unsympathetic to my enterprise, and responded with
criticisms which, if taken seriously, would surely have lead
to an immediate abandonment of the project.
Speranza on the other hand, was unfailingly supportive, and
constantly eager to engage in constructive conversation
(into which he would of course bring always the best of
H.P. Grice).

The two most important dialogues which have helped me along
are the Carnap/Grice conversation and a bit of playing with
Grice/Code on Aristotle, and I will try to explain how these
have contributed to my recent development.

It was because there was a dialogue, between myself and
Speranza, that it occurred to me that there might possibly
have been such a dialogue between Carnap and Grice, and that
exploring how that might have gone, especially if we consider how their philosophies might have developed had
they both lived to the present day, would be an interesting
and useful exercise. Having mooted this idea, we quickly
found our way into Grice's Betes Noires, demons and
perilous places.

Before we could make much progress with this conversation,
Speranza provoked me by producing a version of Code's semi-
formal Aristotelian exegesis, which originated in joint work
with Grice. This sent me scurrying off to my proof tool
(ProofPower) and an entertaining bit of formal modelling of
Aristotle.

By this time my "triple dichotomy" project had already
morphed a little, and the formal modelling set more
developments in its train.
The first change had been to broaden the scope of the
project. I had intended to place the triple-dichotomy in
historical context, and also to do something to show its
importance and significance of that fundamental distinction for the future.
I came to think that by the time the latter had been
properly addressed (without which the point of treating this
topic so seriously would be obscure), I would have an
exposition of my then present "philosophical position"
(which I called "metaphysical positivism"). So the proposed
monograph on "the fundamental triple-dichotomy" morphed into
a concise account of "metaphysical positivism".

This development was taking place at about the same time as
the venture into Aristotelian exegesis which Speranza had
provoked, and the interaction between the two had important
consequences for my philosophical outlook.
Metaphysical positivism as I then conceived it was broadly
along the lines of Carnap's philosophy in the following
respects. Carnap conceived of himself, in the
methodological work which began with his Logical Syntax and
then moved into his various more semantic works, as putting
forward "proposals", for languages (or terminology) and for
methods (for defining formal languages and their semantics
and deductive systems, and for their application in
science). Carnap was explicitly pluralistic in respect of
language, but was more of a serial monist in relation to
methods (i.e. he had an evolving conception of what methods
are appropriate, but was not as explicitly pluralistic about
the methods).

The "success" as I saw it, of the formal Aristotelian
modelling (though it is a mere foray, not close to any kind
of completeness), made me think in a different way about the
scope for application of formality in analytic philosophy,
and I though then in terms of a series of formal models
broadly parallel to the historical aspects of the
presentation of "metaphysical positivism". In this some
interesting issues arose, about how to handle the difficulty
of interpreting historical works using modern methods.
How could one avoid contamination of the analysis by the
views of the present? One of the possibilities I was
considering at that time was some modelling of Leibniz, and
in reading Russell's book on Leibniz, I was particularly
aware of how Russell's own philosophical views lead to
questionable analyses of the philosophical views of Leibniz.

The Aristotelian models show how logical systems quite
different from the logic supported by my proof tool (a
"classical!" higher order logic based on Church's simple
theory of types) could be modelled with precision using that
more modern and much more powerful system. There was here
the beginning of an idea that a strong logical system might
nevertheless have a kind of logical and metaphysical
neutrality, and might be capable of correctly modelling much
weaker logical or metaphysical systems. This is illustrated
by the Aristotelian models, in which by choice of model we
can consider the syllogism with and without the existential
fallacy and not draw incorrect conclusions arising from the
extra strength of the deductive context.

Even though I was developing there a way of working in a
strong logical system which does not interfere with the
analysis of much weaker systems, and am "proposing"
languages and methods which support this process, I was
still not happy with this device which I borrowed from
Carnap to explain the status of the languages and methods
(not facts to be established but proposals to be evaluated
pragmatically). The fact is that people with different
purposes and background will often find some alternative
system more congenial, and I have no desire to persuade them
otherwise. I use myself the languages and tools which are convenient and effective for my own work, but others must judge for themselves whether they should apply them to their own problems.

At this point, mid 2009, I decided that there was a third
alternative (what were the first two you ask?). Rather than propose particular languages and methods, on could "retreat" to analysis of their relative merits. And this is the point at which the idea of "epistemic retreat" first appears, though it now covers a broader scope than in this initial conception.
Analytic philosophy, as a whole, is, it now seems to me, an
exercise in epistemic retreat. This is certainly
conspicuous in Carnap, for he is very definite about the
scope of philosophy (at least until fairly late), Following Russell Carnap regarded philosophers as engaged in the application of logic, and any definite claims they seek to establish must be analytic, truths of logic (broadly conceived).

A second way of viewing this shift in my position is as
involving the extension of Carnap's pluralism from a
pluralism about languages (broadly conceived) to one about
methods. I also considered this to bring into philosophical
play something which I devised mainly for non-philosophical
purposes about a decade ago, "X-Logic", a bit of logical
superstructure intended to support linguistic and
methodological pluralism on the WWW in a logically coherent
way.

At this point, with the abandonment of "proposals" in favour
of more analysis, "Metaphysical Positivism" which was a
philosophical position mainly consisting of a "proposal" on
philosophical methods, is quietly dissolving,
though it didn't occur to me that it had for another six
months.

These steps, ideas for the use of logical methods for
comparative historical exegesis, methodological pluralism,
epistemic retreat, and the desire to systematise all these
in a new version of "X-Logic", have all been provoked by
considering the Grice/Code semi-formal approach to Plato and
Aristotle introduced to me by Speranza. Meanwhile the
Carnap/Grice conversation is dormant (scarcely more than
mooted), and I am spending the autumn in deep cogitation
absorbing what seemed to me quite a big change in the way in
which I think about analytic philosophy.

Come spring, I rehash my ideas on how to get this material
into words. The volume on Metaphysical Positivism is
displaced by one (not altogether dissimilar) briefly called
"HOT philosophy" (which is what happens to a book on
Metaphysical Positivism when that "system" is melting away
before your eyes). My other projected supporting large
volume(s) of formal historical exegesis go on the back
burner. Speranza and I agree to collaborate in writing
something, a short book, on the Carnap/Grice conversation.

Speranza had started The Grice Club, which is a good vehicle
for his effusive Griceeanship (?), and the Carnap/Grice
conversation begins to move forward a little. Firstly by
Speranza inventing another blog "The eternal city of truth"
which is where the Carnap/Grice conversation is leading us
we hope. For the sake of symmetry, I threw in Carnap
Corner, so the conversation is now in three blogs, and
appears in early sketch, alongside the Grice Companion (I
like to call it, Speranza prefers "appendix to the
conversation"), on a new web page for Speranza at
jls.rbjones,com.

I am thinking about this conversation in several ways,
firstly progressing a Carnap bio, mostly stolen from his
Schilpp volume, in which I try to draw even more concisely
than he does, the central thrust of his philosophy (which is
neither the Aufbau nor the verification principle, but the
logic of science).
Secondly in trying to get a grip on the
areas of concord and those of potential conflict (between
Carnap and Grice).
Thirdly, in terms of architecture, approach and method, in
considering how a conversation could possibly result in a
coherent consensus. I have to have this, partly because
these methodological questions are the ones which most
interest me (in analysis) and because I need a framework in
which to place the detail (so much that I may never get
beyond the framework into the detail, just as Austin will
never get beyond clarification of language into the tasks for
which this clarification is prerequisite).

This third item has taken a dominant position, because of my
feeling it prerequisite to the main business, and a little
history can be traced from the point of origin of the
conversation in Grice's demons. These demons were construed
as minimalisations, but interpreted as an opposition to any
kind of minimalisation they would represent a big obstacle
to the conversation, for Carnap's philosophy, possibly even
science as a whole, is minimalistic, is the search for
simplest models of reality (either because the simpler is
thought to be more likely to be true, or because it is more
readily applicable).

So we need to dig below the surface and be sure that Grice's
antagonism is quite that simplistic. And we find that he
objects to the prohibitions which the minimalisations
represent, and conclude that Grice's intolerance is an
intolerance only of dogmatic minimalisations.
This provides a route forward, for with this clarification
the demons are less obviously essential to Carnap, his
pluralism indicating tolerance and flexibility rather than
dogmatic proscription. Carnap's philosophy is ambivalent in
many of these matters, he adopts general principles and
methods (such as the principle of tolerance) which are anti-
dogmatic, but engages in many lines of investigation which
can easily slip into or be read as dogmatic. Of these the
most central is perhaps the unity of science and
physicalistic reduction (though he is more famous for the
phenomenalistic reduction, and his engagement in the unity
of science was of a more academic and less political
character than that of its principle enthusiasts).

The commutation of Grice's demons from intolerance of
minimalisations to intolerance of dogmatic minimalisations
is the first step on a slope which I have rapidly slipped down to find myself wishing to incorporate into "the conversation" my own new ideas about analytic method, in terms of epistemic retreat and X-Logic.
Whether this is feasible, or whether some kind of compromise might work, will take a while to work out.
Meanwhile my own attention, which sways gently between the Carnap/Grice conversation and my other principle project on Rationality and Deduction (which will include an exposition of epistemic retreat and X-Logic) is now mostly on the latter, and on X-Logic.

Going back to Speranza's provocation and support, which I hope I have shown to have been a big deal for me, I should say that these projects are subordinate to a kind of existential project for me, which involves arriving at a way of doing philosophy. It is this which caused me to think about "HOT philosophy", which remains unrealised, and in which Speranza's provocation has been particularly important. It is partly about "opening up", and Speranza's encouragement ought to have done the trick.
That is hasn't yet, is down to pre-requisites which noone but myself can supply. It is down to me getting clear about what kind of philosophy I want to do, and how I want to do it. I think this is all sufficiently clear in my mind, but still I am not quite there. I am looking for a process of philosophising, which ultimately, indeed steadily, delivers philosophical books and which does so in the kind of open process which one can now expect, in which the new ideas which go into the books are first exposed, and ideally discussed, immediately as they are formulated, in blogs and mailing lists. Speranza has provoked me into blogging, but discovering how to incorporate this into the book-writing process remains for me to establish.

So there you go.

Thankyou, J.L. Speranza.

RBJ

Evolution and Rationality

Another nocturnal replan and "Hot Philosophy", at least as a
book title, is gone. The new title, probably to contain the
two words "evolution" and "rationality", I need to check out
what is already out there before the final decision.
.
I was struggling yesterday to make the last plan work, and
this morning I have a new title and a new plan.
The book is now in four parts, and is one long historical
narrative with the emphasis on analysis now muted.
.
Part I Evolution as far as deduction
.
(which I take, and argue, to be
coeval with descriptive language)
.
Part II Aspects of cultural evolution to 1900
.
(not sure what to call this)
This is mostly western philosophy, logic and mathematics
with a bit of Tao.
All hanging around the concept of rationality.
.
Part III 20th century
.
Analytic Philosophy, Mathematical Logic, Computer Science.
We see the evolution of techniques and technology
for formal modelling and inference alongside some of
the most conspicuously irrational episodes in the history
of philosophy,
.
Part IV 21st century
.
This includes X-Logic but I now have a more open conception
of what I might say here.
A forward projection on the evolution of Rationality
.
Though these are all historical or futuristic, the history
is intended to be extremely selective and relates to the
development of rationality.
.
All this in a slim volume, in a short timescale, if I can
once get going.
.
RBJ

HOT philosophy warms up

I did a lot of tossing and turning last night before
eventually getting to sleep, and this morning (in a deep
frost which reminds my of Gellner's story about twigs in
salt mines), I have a new plan for my HOT Philosophy
project.
.
The changes are two.
.
The first change concerns Part I of the book, which I had
intended to be a story based around my own philosophical
odyssey covering the last 15-20 years (this possibly not a
good description, perhaps there is a better one in my last
message here?).
It is now to be a brief account of the history of analytic
philosophy in the 20th century, giving my most brutally
honest (but often highly tendentious) opinions about what
was going on, and in particular, exposing and providing the
best possible explanations for my belief that the entire
progression was highly irrational. The purpose of this part
is unchanged, only the way I intend to realise that purpose
is altered.
.
The second change is in publication timescales, on which I
had nothing definite in mind, but had thought of "HOT
philosophy" loosely as about a 1 year project.
The new plan is to make a slim first edition of the book (as
slim as it takes) which will be published on (or by) 31st
June, 2010. The expectation would then be that quite
substantial amounts of new material would be expected in
subsequent editions.
.
These two changes will both help me to raise the temperature
somewhere closer to where I want it to be, and also increase
the synergy between this an my Carnap/Grice collusion with
Speranza, which in theory is supposed to appear even faster
than that.
.
The changes will also allow me to expose (through Blogs and
mailing lists and RBJones.com) some of the most inflammatory
parts, pretty soon.
.
RBJ

What's it all about?

Since this is the first real post to my not-so-new blog I
thought I would say a few words about what I now have in
mind for it.
.
I'm trying to construct a philosophical sausage machine.
This machine will have fed in at one end philosophical ideas
and discussions from this and other blogs and internet fora,
and out of the other end will from time to time drop
perfectly formed masterpieces of insightful philosophical
prose, ready-to-publish through the amazing amazon POD
publishing machine.
.
How to achieve this is not so easy to see, but I shall give
it a go.
.
The proximate provocation (one of my favourite phrases) has
been J.L,Speranza, who lured me back to contemplating blogs
by sucking me into his Grice Club.
It was my own fault of course, because I suggested that our
conversations about the connections (or lack of them)
between the philosophies of Carnap and Grice should be
upgraded into a collaborative project to produce a small
book to try out this POD thing.
.
So Speranza made another blog for it ("The City of Eternal
Truth" which I think is a bit of Bunyon quoted by Grice in
PGRICE), and I made another "Carnap Corner" so that the
eternal city could be symmetrically flanked by the two
philosophers who would secure it.
.
A Tornado from Speranza ensued and I have yet to assimilate
the content of the dozens of messages he sent me almost
instantly as contributions to our project.
In my world things don't move quite that fast.
I like to have plenty of wide open space for deep thought.
.
That project was an ostensibly small addition to an already
inflated collection of ambitions which I was incubating
(at rbjones.com). but the new ways of working which it
brings are rather badly needed for the main project I was at
that time (and still) trying to get moving.
I had that called the "HOT philosophy" project, because I
wanted a book to pop out of the end and read as if its
writing had been an exhilarating philosophical adventure.
.
Though I had wanted the HOT philosophy project to be an open
enterprise, the process exposed to all who cared to see, I
wasn't convinced that my method of exposure would make it
easy enough to see or to get involved in.
A blog may be the answer.
.
But why stop at one?
HOT philosophy, the book, is intended to fall into three
parts. The first provides some background and clears some
ground. The ground to be cleared is primarily Quine and
Kripke so there will be some entertainment there. This is
in the search for a manner of philosophising which will suit
me (and perhaps some others). We may think of a tenuous
analogy with Hume to hint at the structure of the book.
The first part corresponds to Hume's scepticism.
What Hume then does is to offer, instead of a remedy for our
credulity, a diagnosis for it. He says its all just a bad
habit that we constantly infer from inadequate evidence
unjustified conclusions about things like material objects
and causal connections. He then proposes to model phlosophy
on the empirical sciences (something of a non-sequitur I
feel) and to undertake an enquiry into human nature.
.
In my HOT philosophy project, the discovery of the first part
is not the credulity of simple folk, but the irrationality,
particularly, of philosophers, especially when they gather
together into academic institutions. Now when this was
causing me some difficulty, I obtained my relief from an odd
place, from a book by Howard Bloom called Global Brain.
Putting aside the headline theme of the book, what it told
me about the social behaviour of life throughout the entire
history of its evolution on this planet helped me (I
imagined) to understand and come to terms with the belief
that that academic discipline which prided itself most of
all on its rationality (analytic philosophy) should be
nothing of the sort.
.
The purpose of the second part of my book is to examine the
supposed insights which came to me from Bloom (and on which
I elaborated on my own account in the years which followed).
The aim is to subject these ideas to philosophical analysis
and to see what can be made of them. So this is the
diagnostic phase of HOT philosophy, dressed up in
philosophical analysis to give it a bit more meat than
Hume's rather bald conclusion.
.
The third part is then to be more forward looking.
Whereas Hume looked forward to a philosophy undertaken after
the manner of Newtonian empirical science, I, like Rusell
and Carnap prefer a philosophy closer to Aristotle's
demonstrative science, as augmented by modern advances and
technologies. The third part addresses analytic method and
how it can be made as rigorous as can be bearing in mind
that as philosophers we habitually address just those
problems which are most difficult to pin down with the
requisite precision for formal analysis. The ideas here are
to be a melding of ideas which come from thinking about the
architecture of cognitive agents (things which know), and
ideas which come from a new approach to the resolution of
sceptical doubts. A synthesis of elements of cognitive
engineering with epistemological ideas forged in the furnace
of pyrrhonean scepticism. This is Philosophy as
Engineering, the architectural analysis of cognitive agents.
The third part of the HOT philosophy book will address this
topic in prose, but the project as a whole will include a
formal component as a project hosted by Google code and
called X-Logic. This will develop formal models and
undertake formal reasoning about these models, using modern
interactive proof tools.
.
Now back to the blogs.
The plan is that this blog will be top cover for all my
projects, but that some projects will have separate blogs.
All the blogs will be have secondary archives and discussion
lists at RBJblogs@rbjones.com.
The HOT philosophy project has such disparate parts that I
will not make one new blog for it.
The first part will be covered here, and the second and third
parts will probably each have a blog of their own,
.
The blogs are just one end of the sausage machine.
The later stages in the process will also be fully
accessible at rbjones.com and at the hosting site for
"x-logic" (http://code.google.com/p/x-logic, though you
won't find much there yet).
.
Another project is one which I once called "A Formal History
of Philosophical Logic" (and sundry variations on that
theme), but have most recently billed as "Analyses of
Analysis". This was the principle home for my attempts at
philosophically oriented formal modelling.
This I am tempted to turn into another open source project,
but will leave fallow for a while.
.
RBJ