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October 5, 2009

Shell What?

Posted by David Corfield

John kindly offered to host the contents of my old blog – The Philosophy of Real Mathematics. They are up already here. Unfortunately, the internal links to others of my pages won’t work. Where for instance they say

http://www.dcorfield.pwp.blueyonder.co.uk/2006/02/articulating-your-program.html,

they need to say

http://math.ucr.edu/home/baez/corfield/2006/02/articulating-your-program.html.

John tells me that something called a shell script might be able to perform the translation. Does anyone have an idea of how this could be achieved?

Posted at October 5, 2009 4:13 PM UTC

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Re: Shell What?

I think this command should do the trick on any Unix-like operating system:

find . -name "*.html" -print0 | xargs -n 1 -0 perl -pi'.bak' -e's#http://www\.dcorfield\.pwp\.blueyonder\.co\.uk/#http://math.ucr.edu/home/baez/corfield/#g;'

It goes through every *.html file in the current directory and all sub-directories, replacing the old URL prefix with the new one. It makes backup copies ending in .bak of every file.

But you should still make a separate backup copy of everything before you execute the command!

Posted by: Torsten Schoenfeld on October 5, 2009 5:24 PM | Permalink | Reply to this

Re: Shell What?

I guess it just means one could write a small script in Python, say, that will read each html file and then perform the necessary task of renaming all the internal links inside that particular file.

Posted by: Vishal Lama on October 5, 2009 5:25 PM | Permalink | Reply to this

Re: Shell What?

If you are using linux/unix I’d recommend using the ‘rpl’ tool, available from http://www.laffeycomputer.com/rpl.html . It can be used to do a recursive search and replace, so to update all of those links you should just need to run

rpl -R “http://www.dcorfield.pwp.blueyonder.co.uk/” “http://math.ucr.edu/home/baez/corfield/” *

from within those 2005 and 2006 directories. If those files were all that needed to be updated, I’ve already done it for you and posted new zips of those directories at

http://infimum.net/2005.zip
http://infimum.net/2006.zip

I’ve given them a once over and the links to the new the files look good, although it appears there are some other missing files, namely http://math.ucr.edu/home/baez/corfield/blog.html and http://math.ucr.edu/home/baez/corfield/htdocs/atom.xml , so until those are put in place, links to those files will be broken.

Feel free to email with questions or other rpl needs :)

Posted by: Akita on October 5, 2009 5:26 PM | Permalink | Reply to this

Re: Shell What?

Thanks very much. That’s great. Future historians of the blogosphere will now have access to a proto-Café.

And thanks everyone for the other solutions.

Posted by: David Corfield on October 6, 2009 8:48 AM | Permalink | Reply to this

Re: Shell What?

Ah, never mind, Akita has already done the needful, it seems!

Posted by: Vishal Lama on October 5, 2009 5:29 PM | Permalink | Reply to this

Re: Shell What?

It’s a bit late now I guess but my solution would have been the following, along similar lines to Torsten’s:

wget http://math.ucr.edu/home/baez/corfield/2005.zip ; unzip 2005.zip ; find ./2005 -name *.html -print0 | xargs -0 sed -i 's/http:\/\/www\.dcorfield\.pwp\.blueyonder\.co\.uk\//http:\/\/math\.ucr\.edu\/home\/baez\/corfield\//'

.. and do the same for 2006. This downloads the entire directory to a work area of your choosing, so avoiding the backup problem, until you upload it to the site again.

Posted by: Dan Hagon on October 5, 2009 5:44 PM | Permalink | Reply to this

Re: Shell What?

Oops. Missed a g in my pattern:

wget http://math.ucr.edu/home/baez/corfield/2005.zip ; unzip 2005.zip ; find ./2005 -name *.html -print0 | xargs -0 sed -i 's/http:\/\/www\.dcorfield\.pwp\.blueyonder\.co\.uk\//http:\/\/math\.ucr\.edu\/home\/baez\/corfield\//g'

Posted by: Dan Hagon on October 5, 2009 5:49 PM | Permalink | Reply to this

Re: Shell What?

of course, you can use ‘:’ instead of ‘/’ to delimit “sed s” arguments; then you needn’t escape all those directory delimiters.

Posted by: some guy on the street on October 6, 2009 2:05 AM | Permalink | Reply to this

Re: Shell What?

silly me forgot about the “:” in “http:”… ‘%’ works well.

I’m not sure escaping the “.” is really necessary; the possibility that there were many strings looking like
“http://www!dcorfield@pwp#blueyonder$co%uk”
seems a bit far-fetched, no?

Posted by: some guy on the street on October 6, 2009 5:36 PM | Permalink | Reply to this

Re: Shell What?

Looks like you need some kind of coalgebra morphism to me.

Posted by: Dan Piponi on October 5, 2009 7:14 PM | Permalink | Reply to this

Re: Shell What?

These are elegant solutions. Since you are a philosopher it’s possible that you use Windows :-). The Windows solution that I recommend to customers for web pages is XEmacs.
http://www.cse.ohio-state.edu/userguide/chapter_06.html Two kinds of Search/Replace

Posted by: Stephen Harris on October 6, 2009 8:11 AM | Permalink | Reply to this

Re: Shell What?

If it's on John's website, then it's on a Unix machine.

Posted by: Toby Bartels on October 6, 2009 8:40 AM | Permalink | Reply to this

Re: Shell What?

Editing of html files with search/replace is independent of the server OS. The two .zip files
in the index usually indicate that the files were created using Windows, then uploaded.

Posted by: Stephen Harris on October 6, 2009 1:04 PM | Permalink | Reply to this

Re: Shell What?

Thanks, Akita! David’s old blog entries with improved links are now available here (2005) and here (2006). Maybe someday we’ll make them easier to search…

… but already we can again see the famous Klein 2-geometry thread that helped lead to the formation of the nn-Café:

Someday, when we least expect it, someone is going to return to Klein 2-geometry (or nn-geometry) and knock our socks off with it.

Posted by: John Baez on October 6, 2009 4:59 PM | Permalink | Reply to this

Re: Shell What?

Here are what I thought were some of the more important omissions that could be corrected.

September 30, 2005 Grothendieck’s ‘Sketch of a Programme’ is available *here* The
URL http://www.math.jussieu.fr/~leila/EsquisseEng.pdf was not found on this server.
http://www.math.jussieu.fr/~leila/grothendieckcircle/EsquisseEng.pdf works though

This supports my *argument* October 2005 Thursday 27 The
requested URL /home/baez/corfield/HowMathematicians.pdf was not found on this server.

Monday 17, October 2005
My latest version of *How Mathematicians May Fail to be Fully Rational* The
requested URL /home/baez/corfield/HowMathematicians.pdf was not found on this server.

Thursday, November 24, 2005 R. G. Collingwood and the Historical Stance
…Mathematics look *here*. [SH: I especially liked this post.]
The requested URL /home/baez/corfield/phorem.htm was not found on this server.

Posted by: Stephen Harris on October 6, 2009 6:35 PM | Permalink | Reply to this

Re: Shell What?

1) I fixed the link to ‘EsquisseEng.pdf’.

2) We had ‘phorem.html’ in the right folder, but not ‘phorem.htm’ — now that’s fixed.

3) As for ‘HowMathematicians.pdf’, if David gives me that file I can put it in the right place. This appears among many other broken links to papers of his at ‘phorem.html’ and (same file, different name) ‘phorem.htm’. If David provides me with these papers, he should also fix this file so it knows these papers are in http://math.ucr.edu/home/baez/corfield.

4) I only do this sort of thing for people I love. I’m doing it for David because the Philosophy Department at the University of Kent at Canterbury is trying to keep up its medieval image by refusing to let its faculty have their own websites.

And next, due to budget cutbacks, they’re planning to remove the copying machines and force the faculty to serve as scribes. They’ll have to buy their own candles to work through the long gloomy winter evenings.

Posted by: John Baez on October 6, 2009 10:13 PM | Permalink | Reply to this

Re: Shell What?

You managed to shed a humorous light on a sad situation. David Corfield speculates on questions that most philosophers don’t often wonder about with profundity. Here is an Alexandrian example that you helped save:

R. G. Collingwood and the Historical Stance by David Corfield November 24, 2005

“I’m spending a lot of my time at the moment wondering what Statistical Learning Theory (see John Langford’s informative blog Machine Learning) can teach philosophy.

“Parts of philosophy concerned with empirical inference can expect to be transformed by integrating these ideas. Here, as elsewhere, this should give us pause for thought. What to do when science starts to deal with traditionally philosophical topics? Judea Pearl (Causality, CUP, 2000) integrates some of the research of philosophers (e.g., David Lewis) on causality with ideas from statistics and graphical modeling into a powerful calculus for treating causal predictions and counterfactuals. What next? Must the philosopher wishing to continue thinking about causality take on board Pearl’s work?”

SH: This question becomes much more interesting if you have read Pearl’s book.

Judea Pearl (2000) Preface
“Ten years ago, when I began writing Probabilistic Reasoning in Intelligent Systems (1988), I was working within the empiricist tradition. In this tradition, probabilistic relationships constitute the foundations of human knowledge, whereas causality simply provides useful ways of abbreviating and organizing intricate patterns of probabilistic relationships.
Today, my view is quite different. I now take causal relationships to be the fundamental building blocks both of physical reality and of human understanding of that reality, and I regard probabilistic relationships as but the surface phenomena of the causal machinery that underlies and propels our understanding of the world.”

SH: Causality has been argued about since before Hume and Kant and there is not yet a consensus description or explanation nor definition. I was not aware of Collingwood’s historical view which DC presented.

Judea Pearl quoted Einstein in his book “Causality: Models, Reasoning, and Inference” (2000)

“Develpment of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance).”

SH: I guess those monks found working by candlelight very stimulating.

Posted by: Stephen Harris on October 7, 2009 2:01 AM | Permalink | Reply to this

What The Shell !?

All through the (19)80s I worked on an AI program that had 3 modules — no, the other kind of modules — that phased through various stages of integration with each other over the decade.

There was a Learning Module (LM) called Slate that operated on empiricist principles, a Reasoning Module (RM) called Chalk that operated on rationalist principles, and an Isomorphism Module (IM) or analogy engine called Axletree.

The resource constraints of the time forced me to use a common data structure that all three modules could share, and personal time constraints occasioned my very often optimizing one module one summer, another module another summer, and trying to integrate the two during a third summer.

One of the things that I learned from these adventicities was that the most optimal algorithms and data views for the Empirical task were very often the least optimal algorithms and data views for the Rational task, and I felt that this was a clue to the trade-offs that create so much tension between diverse cognitive styles in human thinking reeds, whether between reeds or within the same reed.

Posted by: Jon Awbrey on October 7, 2009 9:08 PM | Permalink | Reply to this

Mind at the edge if chaos; Re: What The Shell !?

Maybe I oscillate between seeing a Mathematical Logic issue here, and seeing this as insight into the purpose of Consciousness in connecting and prioritizing Multiple Mind modules within one human brain.

Or maybe there’s a Lorenz-type chaotic attractor of the type that Smale missed in his initial classification of dynamical systems. And what I think that I think is merely a trajectory near a chaotic attractor, but possibly destined to move into some other basin…

What do you think?

Posted by: Jonathan Vos Post on October 8, 2009 12:33 AM | Permalink | Reply to this

I could be bounded in a nutshell …

The passage from Pearl brought to mind what Heisenberg et alea said about the trade-off between the causal picture and the spacetime picture, neither of which could be counted complete without the complement of the other.

What Pearl said about his conversion from one side of the coin to the other reminded me of how I started out saying, “Sure, I’m working proof-theoretically — model theory is dumb”, and almost as I spoke discovered the wages of that hubris would be a conversion of my own.

Posted by: Jon Awbrey on October 8, 2009 2:54 AM | Permalink | Reply to this

Inference, Information, Inquiry

Now that all that procedural monkey-business is out of the way — let us pray — maybe we can get back to the substantive issues that you so well con-silienced in David’s paper:

Way Back Here.

“Roboscience” — more prosaically known as automated or computer-assisted scientific inquiry — has been a hot and cold running topic in AI for as long as I can remember. I read a lot of HoHoNiTh, Hofstadter, Forbus, Gentner, Kuipers, Pearl, Sowa and a gadshillion et als, but also a whole lot of Peirce and even a bit of Whewell and Collingwood way back in the 80s and 90s.

Still — and I’m sure it’s no surprise to anyone by now — it is mostly Peirce that sticks to my ribs … or whatever it is I think wit.

Why is that?

I guess it was the way that Peirce always managed to vault the horns and escape the dichotomic, dualistic, dyadic impaseos of the Run of the Mill notions of scientific inquiry.

Posted by: Jon Awbrey on October 9, 2009 4:52 AM | Permalink | Reply to this

Re: Inference, Information, Inquiry

David Corfield made another post on this topic about two years later.

http://golem.ph.utexas.edu/category/2007/09/category_theory_in_machine_lea.html
September 5, 2007 Category Theory in Machine Learning Posted by David Corfield
“I was asked recently by someone for my opinion on the possibility that category
theory might prove useful in machine learning. … As for machine learning itself, perhaps one of the most promising channels is through probability theory. One advantage of working with the Bayesian approach to machine learning is that it brings with it what I take to be more beautiful mathematics.”
—————————————-

SH: I was aware of the above post when I posted the Judea Pearl quote, which seems to disagree with DC’s pov. Holland of HoHoNiTh favors a genetic algorithm or maybe a neural network approach. You suggest that Pearl’s ‘it’s Causality turtles all the way down’ may need to be balanced with a probabilistic approach perhaps like the wave/particle duality from Physics or QM and SR. Is that right?
http://www.cognitivelinguistics.org/Reviews/givon
“Context as other minds: The pragmatics of sociality, cognition and communication”
“Nevertheless, according to Givón, pragmatics “holds the key to an
integrated understanding of life, behavior, cognition and communication.
[SH:The first chapter includes an article on Charles Sanders Peirce (purse)]

The second part deals with the organization of mental categories from a bio-adaptive point of view. Chapter 2 begins with a critical approach to ‘mental categories’ through philosophy, psychology, and linguistics. Compared to Aristotelian categories which are built on necessary-and-sufficient conditions, and to Wittgensteinian ‘family resemblance’, the hybrid system of prototype-like categories turns out to best match one of the main activities of biological organisms: “sorting tokens of experience into separate categories” in order to be ready to respond to their “physical, biological, mental and social environment.” Subsequently, the prototype-like nature of categories is not a mere theoretical posture but a cognitive fact induced by information processing.”
——————————-

Not too long ago Neumaier presented his ideas for a proof-assistant which included mining data on the web. How did your Semantic Web work go? What failed?
Almost Consensually Realistic Ontology Needing Your Moral Support (ACRONYMS) :-)

Posted by: Stephen Harris on October 9, 2009 12:35 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry

Wow … questions a plenty …

Thanks for the horizontal holdlines — they’ll help me trace my impressions one horizon at a time.

Re: David Corfield (05 Sep 2007), Category Theory in Machine Learning

I was asked recently by someone for my opinion on the possibility that category theory might prove useful in machine learning. …

For other areas of computer science the task would be easier. Category theory features prominently in theoretical computer science as described in books such as Barr and Wells’ Category Theory for Computing Science. Then there’s Johnson and Rosebrugh’s work on databases.

As for machine learning itself, perhaps one of the most promising channels is through probability theory. One advantage of working with the Bayesian approach to machine learning is that it brings with it what I take to be more beautiful mathematics. …

I’d have to start out — as I did start out — agreeing about the beauty, the formidable beauty, the mathematics, the probability, and the Rule of Bayes. Those are clues to the prospective laws of information, a topic that Peirce introduced at Harvard and Lowell in 1866–1867.

“What is information that a sign may bear it?” — that pretty much signs the key of our whole unfinished symphony here, whose upshot we have yet to see.

Posted by: Jon Awbrey on October 9, 2009 3:54 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry


I discovered these notes after finding out that Causality by Judea Pearl was published as a 2nd edition.

“Identifying Dynamic Sequential Plans”by Jin Tian www.cs.iastate.edu/~jtian/papers/uai-08.pdf (2006)
“In this paper, we will formulate the sequential plan problem in the framework of causal Bayesian networks. A causal Bayesian network (CBN) consists of a DAG G over a set V = {V1, … , Vn} of variables, called a causal diagram. The interpretation of such a graph has two components, probabilistic and causal. The probabilistic interpretation views G as representing conditional independence assertions such that the joint probability function P (v) = P (v1, … , vn) factorizes according to Eq. (1). The causal interpretation views the directed edges in G as representing causal influences between the corresponding variables.”

http://www.ia-cap.org/na-cap0 /program.htm The 2009 North American Conference on Computing and Philosophy NA-CAPatIU 2009: Networks and Their Philosophical Implications “Causal Bayesian Networks: 20 Years of Philosophical Debate” Christoph Schulz
“In 1988, Judea Pearl published his “Probabilistic Reasoning in Intelligent Systems”. In chapter 8, he analysed how causal relationships can be inferred from nontemporal statistical data. Since then, researchers have designed advanced algorithms for causal discovery. However, philosophers remain skeptical about the correct interpretation of the concepts of causality and probability inherent in the model, and about the validity of the underlying assumptions.”

Pearl [1988] explicity denied that the graphs have an objective causal interpretation, on the grounds that he saw no way to distinguish associations of two variable produced by a causal relation between them from associations produced by an unobserved or unrecorded common cause. Pearl’s reservation echoed a long philosophical tradition claiming that algorithms for scientific discovery are impossible, a claim argued explicitly by Hempel from the alleged impossibility of algorithms that correctly introduce novel unobserved variable or ‘theoretical terms’. [SH: Pearl’s reservation stands in stark contrast to his description of the importance of Causality from the Preface (2000); CNB has developed since then.]
———————————————————————————

Scott Aaronson blog: June 2008 Scientific American article by Jerzy Jurkiewicz, Renate Loll and Jan Ambjorn, about the “causal dynamical triangulations approach” (CDT) to quantum gravity.

“What could the trouble be? In our search for loopholes and loose ends in the Euclidean approach [to quantum gravity], we finally hit on the crucial idea, the one ingredient absolutely necessary to make the stir fry come out right: the universe must encode what physicists call causality. Causality means that empty spacetime has a structure that allows us to distinguish unambiguously between cause and effect. It is an integral part of the classical theories of special and general relativity.”
———————————————————————————-

http://en.wikipedia.org/wiki/Fotini_Markopoulou (candidate for the Fields Medal?)
In her interdisciplinary paper “The Internal Description of a Causal Set: What the Universe Looks Like from the Inside”, Markopoulou instantiates some abstract terms from mathematical category theory to develop straightforward models of space-time. It proposes simple quantum models of space-time based on category-theoretic notions of a topos and its subobject classifier (which has a Heyting algebra structure, but not necessarily a Boolean algebra structure).”

In May 2006, Markopoulou published a paper with Lee Smolin that further popularized CDT Theory by explaining time slicing of the Ambjorn-Loll CDT model as result of gauge fixing. Their approach relaxed the definition of the Ambjorn-Loll CDT model in 1 + 1 dimensions to allow for a varying lapse.”

—————————————————————————–

SH: The philosophical evidence meshes to one beautiful grand pattern: a) CBN is the solution for Machine Learning under uncertainty; b) Category Theory can support the CDT as a unifying causal/probabilistic QG. .. A fine example of abductive reasoning.

Posted by: Stephen Harris on October 10, 2009 2:51 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry

Yikes! — too much work for a Saturday …

Let me just say what I think I learned from my own experiences over the years.

There are two sorts of experiences that come to mind — the time I had experimenting with computer facsimiles of primitive capacities for learning and reasoning, and the time I had working with real empirical data, as everything from data archivist, to particle track scanner, to statistical consultant in medical education and research settings.

Posted by: Jon Awbrey on October 10, 2009 6:20 PM | Permalink | Reply to this

Inference, Information, Inquiry, Integration

A reeder of Peirce is likely to spy a couple of catches in the rushes to Bayes’ rule and cause-effect as fundamental axes of the scientific frame of reference. I would have mentioned it before, but I didn’t want to spoil vision of beauty that we held so fastly if fleetingly before us.

Catch 1 would be that Bayes’ rule is a mathematical identity, an unimpeachable king of the hill, but only so long as it reigns in bounds of its own turf, in the chestnut shells of deductive truth.

That might be enough for some, if they think that inductive inference maintains its grounds of validity safely within the king’s preserve, but it won’t be enough for those who see an independent role for empirical reason, and far less for those who count a third something, abductive inference, as a sine qua non of the method that points the way with that fickle fingo of fête.

Posted by: Jon Awbrey on October 11, 2009 2:25 AM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

Catch 1 would be that Bayes’ rule is a mathematical identity, an unimpeachable king of the hill, but only so long as it reigns in bounds of its own turf, in the chestnut shells of deductive truth.

But reason is not three separate domains, each of which can say nothing about the others.

Bayes's theorem, when applied to inductive reasoning, is meta-reasoning. It makes perfect sense to me to use deductive meta-reasoning to reason about inductive reasoning, and also to use inductive meta-reasoning to reason about deductive reasoning. In fact, I use inductive reasoning (and abductive reasoning) often when studying deductive reasoning; whenever I draw a conclusion (however tentative) about deductive logic that I haven't proved but which I nevertheless believe due to trying out some possibilities and seeing analogies with facts that I know. And as a Bayesian and a categorist, I apply deduction to induction and abduction as well.

Not to mention, it seems to work; consider all of the examples in Jaynes's book. So by abductive and inductive meta-meta-reasoning, I conclude that applying Bayes to induction is OK!

Posted by: Toby Bartels on October 11, 2009 6:57 AM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration


JA: “Catch 1 would be that Bayes’ rule is a mathematical identity, an unimpeachable king of the hill, but only so long as it reigns in bounds of its own turf, in the chestnut shells of deductive truth.”
—————————————————————

SH: The earlier question in this thread was whether Category Theory (CT) would be helpful to Machine Learning. The learning involved is described as inductive rather than deductive. So is CT a better tool to map the inferences/inductions that children do (perhaps meta-meta reasoning) “routinely and effortlessly”? The next Toby Bartels quote seems to agree with the Gopnik remark that there seems to be an “analogy between learning in children and learning in science”. Can CT augment the creation of an algorithmic learning approach (CT -> human learning categories)?

TB: “In fact, I use inductive reasoning (and abductive reasoning) often when studying deductive reasoning; whenever I draw a conclusion (however tentative) about deductive logic that I haven’t proved but which I nevertheless believe due to trying out some possibilities and seeing analogies with facts that I know.”
—————————————————————-

web.mit.edu/cocosci/Papers/devsci07_gopnik_tenenbaum.pdf
“The papers focus on two classes of learning problems: learning causal relations, from observing co-occurrences among events and active interventions; and learning how to organize the world into categories and map word labels onto categories, from observing examples of objects in those categories. Causal learning, category learning and word learning are all problems of induction, in which children form representations of the world’s abstract structure that extend qualitatively beyond the data they observe and that support generalization to new tasks and contexts. While philosophers have long seen inductive inference as a source of great puzzles and paradoxes, children solve these natural problems of induction routinely and effortlessly.

‘Theory theorists’ in cognitive development point to an analogy between learning in children and learning in science. Causal Bayesian networks provide a computational account of a kind of inductive inference that should be familiar from everyday scientific thinking: testing hypotheses about the causal structure underlying a set of variables by observing patterns of correlation and partial correlation among these variables, and by examining the consequences of interventions (or experiments) on these variables.”

Posted by: Stephen Harris on October 11, 2009 1:06 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

Stephen,

Switch to decaff for the weekend, at least — I’m already two days behind trying to keep up with you!

What 1 or 2 points would you say are the nubs of the question here?

Posted by: Jon Awbrey on October 11, 2009 3:39 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

JA wrote: “What 1 or 2 points would you say are the nubs of the question here?”
————————————-
Causality and Probability.

I used to think Clark Glymour was the philosophical authority on statistical learning. However, David Corfied turned up in a lot of my searches. He mentioned Nils Baas which led me to the MES paper quoted below, which provides a succinct statement covering the ideas I labored over expressing in a couple of posts.
—————————————

Nils Baas
Abstract “This paper is just a comment to the impressive work by A. C. Ehresmann and J.-P. Vanbremeersch on the theory of Memory Evolutive Systems (MES). MES are truly higher order systems. Hyperstructures represent a new concept which I introduced in order to capture the essence of what a higher order structure is—encompassing hierarchies and emergence.”
—————————————

http://cogprints.org/921/0/auef.htm
“MES use Category theory not only as a language, but also as a powerful method to uncover the main processes underlying complexity. Our basic idea is that category theory is a reflection on the fundamental laws of brain functioning such as they have been determined by natural selection during Evolution: formation of relations between objects of various types allowing for the transfer and the analysis of information, formation and recognition of patterns of coordinated objects, optimization processes. We could paraphrase for this theory what Chapline [11] says about quantum mechanics:

“quantum mechanics can be regarded as a fundamental theory of distributed parallel information processing and pattern recognition… we are led to suggest that the fundamental link between mathematics and theoretical physics is the pattern recognition capabilities of the human brain”.”


Posted by: Stephen Harris on October 11, 2009 5:37 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

Thanks, Stephen, that will help me focus in the midst of a very dispersive day.

I’m guessing that all the boyz and gurls and bots in the ’hood agree that category theory is good for all things bright and mathematical, and especially computational, and so we can in all likely ’hood probably put that generality behind us.

But whether category theory adds a more specific gravitas to reasonings of a non-demonstrative ilk remains to be demonstrated, I think.

I was weaned, or over-weened, on Carlsberg beer and the Copenhagen interpretation, and I know that many another interpretation has been passed under the bridge since my froshperson year, so I have to ask: What is the current thinking with regard to that putative complementarity of causal and spacetime pictures?

Not that I’d buy it just because it’s current — but still, I think it might be worth brewing or stewing over a little while longer.

Posted by: Jon Awbrey on October 11, 2009 7:54 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

TB: But reason is not three separate domains, each of which can say nothing about the others.

Of course not. Already in Aristotle we find him analys/zing reasoning by analogy, example, or paradigm as a mixture of inductive and deductive ingredients, and Peirce — long time passing — would analys/ze analogy and the whole cycle of inquiry into a cable-istic co-operation of inferential strands that involved a con-tri-bution coming from each and every one among the Big 3.

Posted by: Jon Awbrey on October 11, 2009 2:56 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

Catch 2 would be that cause-effect is usually taken to be a 2-adic relation.

If Peirce’s analysis, couched in his logic of relatives, recommends itself to you, that would demote causal relations from serving in a genuinely fundamental capacity with regard to the composition, function, or structure of things, since the only processes or structures you can get by composing 2-adic relations are more 2-adic relations, and that falls far short of articulating or explaining the complexity of all the most phenomenal phenomena.

Of course, one could conceivably augment or extend one’s concept of causality to encompass 3-adic relations in some way or other — it’s just that very few thinkers have taken the trouble to do that, much less present a convincing case for their generalizations.

Posted by: Jon Awbrey on October 11, 2009 5:52 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

JA wrote: “Catch 2 would be that cause-effect is usually taken to be a 2-adic relation.”
—————————————-

SH: I think you are comparing apples and oranges. Cause and effect is a general belief about the nature of the physical universe. Suppose you had a lamp with 3 switches for intensity. This analogy will use each setting of the switch for illumination, to either deductive, inductive or abductive reasoning. It wouldn’t matter which setting of the switch was being used, that would be irrelevant, to conclude that in each mode of illumination/thinking, that the underlying physical process was governed by the flow or non-flow of electricity, that’s the cause, which is independent of the mode of illumination/thinking.

I tend to quote authorities because I don’t trust the understanding of various people who have opinions about sundry topics. Thus you have to dispute the authority’s understanding, not mine.
————————————

1.7.5.1 Abductive inference (Charles Sanders Peirce) CONTEXT AS OTHER MINDS by Talmy Givon
“Ever since Plato and Aristotle, empiricists have tended to emphasize induction as the prime mode of obtaining knowledge, while rationalists have tended to emphasize deduction. Echoing Kant’s rejection of both reductionist extremes, Peirce resuscitated Aristotle’s third mode, apagoge (‘reduction’), which he rechristened abduction. This is the mode by arguing by hypothesis, often by analogy. It is thus a pragmatic mode par excellence, dependent as it is on notions of similarity and/or relevance (Hanson 1958; see ch.8).

1.7.5.2 The interpretant as a third term in semiotics As noted earlier above (1.6.9), to the extent of Peirce’s notion of interpretant as the third term in the semiotic equation is distinct from Aristotle’s perfect-mirror mind, it may be interpreted as a stand in for the construed context.”
——————————————————————————————-

Section 7: Causal and Counterfactual Reasoning Chapter 29: Causal Thinking by Lance J. Rips
“Pearl is explict about the fact that an important benefit of causal models over causal networks is that the models deal correctly with counterfactual conditionals - statements of the form “If X had happened, then Y would have happened, “like if Fred had taken the trouble to fix his brakes, he wouldn’t have had an accident. It’s been recognized at least since Goodman (1955) that there’s a close connection between counterfactuals and causation. The truth of many counterfactual conditionals seems to depend on causal laws that dictate the behavior of events. These laws hold not just in our current state of affairs, but also in alternative states that differ from ours but still obey the laws in question.”
————————————

SH: Counterfactuals are often describes as ideas which that the What/If form. So there is a mathematical formalism for QM that agrees with 99.999999999~% accuracy with experimental observations. Yet, there are several Interpretations as to what these observations mean regarding the description of how the physical universe works. Each one of the Interpretations trys to fit an explanation with observed facts. This is done by hypothesizing which facts support the most consistent theory. Now whether the thinking involved at arriving at this hypothesis is deductive, inductive or abductive or a combination of all three, this provides no constraint to the goal of arriving at a causally consistent or reasonable explanation of how the universe works. Your original argument attempted to refute causality as a basic universal view with abductive reasoning, which is a mode of thinking to achieve a hypothesis often involving analogy. It wouldn’t matter if there were 17 different modes of thinking which described how or interpreted which causal relations were universally consistent -> that is the “construed context”.
QM is not yet a universal framework because it hasn’t been reconciled with SR and the human perception of time, which is called the problem of quantum gravity.
QM is still a microcosmic rather than a macrocosmic description although in the more recent era more people have started claiming that QM is universal.


Posted by: Stephen Harris on October 12, 2009 1:45 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

The discussion of “counterfactuals” in the cognitive science and philosophical literatures is horribly confused. Mathematicians and physicists have a pretty clear conception of the relevant issues, more routinely covered en passant under other names than turned into fodder for a causal cause célèbre — do math and physics folks really think of every reference to velocity or acceleration as embroiling them in quandaries over counterfactuals? … no, hardly ever.

Posted by: Jon Awbrey on October 12, 2009 3:25 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

My response which included counterfactuals disputed that cause and effect interfered in any way with abductive reasoning. Maybe you are able to remember what you posted:
JA wrote:
“Catch 2 would be that cause-effect is usually taken to be a 2-adic relation.

If Peirce’s analysis, couched in his logic of relatives, recommends itself to you, that would demote causal relations from serving in a genuinely fundamental capacity with regard to the composition, function, or structure of things, since the only processes or structures you can get by composing 2-adic relations are more 2-adic relations, and that falls far short of articulating or explaining the complexity of all the most phenomenal phenomena.”
————————————–

SH: A causal framework for generating scientific theories is already in place and can incorporate abductive reasoning. Your introduction of 2-adic relationships as inadequate to describe or compute Peirce’s third leg of human reasoning, abductive reasoning, is specious as abductive reasoning is well accounted for in the literature using a causal framework. Your Catch 2 is imaginary.
—————————————

“The classic alternative strategy for deriving causal knowledge is a form of inference to the best explanation (Harman 1965). We can start with theories about the potential causes of some phenomenon and then check to see which theory best predicts the data. The theory that provides the best fit is the one that gives the right causal picture. Of course, this form of inference doesn’t give us certainty about our causal conclusions, since it depends on the range of the alternatives we’ve considered, on the validity of the tests we’ve performed, and on the goodness of the data we’ve collected. But _no_ method yields certainty about such matters. Theoretically, there is no limit on the number or complexity of potential causal relationships, and correlation is often unable to decide among these derives causal set ups.”

“Abductive reasoning in Bayesian belief networks using a genetic algorithm” by E. S. Gelsema Abstract
“A set of computational experiments is described in which genetic algorithms are used for abductive reasoning in Bayesian belief networks. It is shown that good solutions and explanations are consistently found with high probabilities. The efficiency of genetic sampling w.r.t. random sampling is shown to increase with increasing complexity of the search space and with increasing complexity of the search goal.”

Explanation and Cognition: Chap8 - The Role of Mechanism Beliefs (pdf)
“Second, by what process do people identify a relation as causal?
These two questions roughly correspond to the distinction made by Rey (1983) with
regard to categorization. On the one hand, argues Rey, there are metaphysical questions of categorization. What do people think makes something a member of one category rather than another? Given our focus on causation, we may ask what people think distinguishes a causal relation from a noncausal one, a question that has to do with the definition of cause. In addition to metaphysical questions, Rey points out that we are often interested in epistemic questions. What do people do to decide whether or not something is a member of a category?
Again, with respect to causation, we may ask what people do when they are tryig to decide whether a relation is causal or not or to determine what is a cause in a give situation , a question that has to do with methods of identifying causes. Although these two questions are clearly linked, an answer to one does not necessarily provide an answer to the other. There may be aspects of a definition that are not (typically) used in identification and means of identifying instances that are only tenuously connected to definitions.”

Abstract Abductive reasoning involves generating an explanation for a given set of observations about the world. Abduction provides a good reasoning framework for many AI problems, including diagnosis, plan recognition and learning. This paper focuses on the use of abductive reasoning in diagnostic systems in which there may be more than one underlying cause for the observed symptoms. In exploring this topic, we will review and compare several different approaches, including Binary Choice Bayesian, Sequential Bayesian, Causal Model Based Abduction, Parsimonious Set Covering, and the use of First Order Logic.
———————————–

JA wrote: “do math and physics folks really think of every reference to velocity or acceleration as embroiling them in quandaries over counterfactuals? … no, hardly ever.”

SH: No, they do it when appropriate. Google provides a 103,000 hits to-> quantum mechanics counterfactuals, without parentheses, including titles like “Counterfactuals in Quantum Mechanics” and counterfactual definiteness. I have absorbed all that I care to learn from you.


Posted by: Stephen Harris on October 12, 2009 4:37 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

Stephen,

Just for your future reading, the best authority for Peirce’s thought is C.S. Peirce. Some people say he’s a tough nut to shell but I’ve always found him remarkably clear. There is a nice selection of his writings in the 2-volume Essential Peirce, though it’s a little thin on the mathematical side of his work it’s still pretty good for what we have been touching on here.

Posted by: Jon Awbrey on October 12, 2009 6:10 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

“The Peircean sign is a triadic relation that connects an object, O, to a representamen, R, and then to an interpretant I (some R stands for some O to some I). Peirce proved mathematically that this triadic relationship was not reducible to a dyadic relationship, i.e., an object, O, unavoidably results in an effect, E . Examples of dyadic relationships include cause and effect, functional relations ( y = f(x)), and stimulus-response (behaviorism). Dyadic relations are still applicable in mathematics and science, but when their application is extended to information processing topics, such as AI, cognitive psychology, neurosciences, and the social sciences, that the dyadic relations begin to be less effective or inapplicable altogether.”
——————————-

‘Simple dyadic relationships may be sufficient for operational learning but a learning network with shared learning features will provide for complex strategic learning.’ These didn’t exist when Peirce wrote, statistical learning networks as in a Causal Bayes Network.

‘Pearl [1988] explicity denied that the graphs have an objective causal interpretation, on the grounds that he saw no way to distinguish associations of two variable produced by a causal relation between them from associations produced by an unobserved or unrecorded common cause.
Pearl’s reservation echoed a long philosophical tradition claiming that algorithms for scientific discovery are impossible, a claim argued explicitly by Hempel from the alleged impossibility of algorithms that correctly introduce novel unobserved variable or ‘theoretical terms’. Since then [by 2000], researchers have designed advanced algorithms for causal discovery.’

Posted by: Stephen Harris on October 12, 2009 8:03 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

GAC?

IAC!

Posted by: Jon Awbrey on October 12, 2009 9:48 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

“Dyadic relations are still applicable in mathematics and science, but when their application is extended to information processing topics, such as AI, cognitive psychology, neurosciences, and the social sciences, that the dyadic relations begin to be less effective or inapplicable altogether.” wstiac.alionscience.com/pdf/GACV20N2.pdf
——————————

SH: I just realized that whoever wrote this, it was not Charles Sanders Peirce who died in 1914 long before there were terms like “AI” or “cognitive psychology” in the English language. So that means it’s an interpretation of something Peirce wrote. That makes it unreliable because of the robust confusion surrounding his writings, partly Peirce’s fault.
Writing in 1910, Peirce admits that he himself, “in almost everything I printed before the beginning of this century … more or less mixed up hypothesis and induction” [3]
Peirce, C. S. (1958). The Collected Papers of Charles Sanders Peirce, Vols. VII-VIII, Edited by AW Burks. Cambridge, MA: Harvard. [3]
I took a semester of English that emphasized semiotics so we studied Peirce. I wasn’t impressed. But I have a shorter book that I’ll glance through, looking just for this 2-adic, triadic, cause and effect discussion.

Posted by: Stephen Harris on October 13, 2009 8:36 AM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

I see that this has previously been discussed along with quoted material.
http://www.cspeirce.com/menu/people/peirce-l/11-23-02.htm

Posted by: Stephen Harris on October 13, 2009 9:06 AM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

Re: PEIRCE-L Digest for Saturday, November 23, 2002

Note. If you select the “Markdown” text filter, then you can enclose live links in the form: [Title](URL).

That’s a fragment of discussion from the Peirce List. They were recording emails that way only during a short period when their List and Archive software was out of service for a system transition. Peirce-L is an e-pendage of the Arisbe Portal, which is a pretty good resource for all things Peircean.

Posted by: Jon Awbrey on October 13, 2009 2:00 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

SH: Peirce did say logic machines of his day (Babbage) could not reason like a human but didn’t offer a prediction about the future capability. Recall that Hofstadter, made progress with the Fluid Analogy Research Group, toy model analogy program called Copycat

John F. sowa csp21st.pdf http://www.jfsowa.com/pubs/csp21st.pdf Peirce’s Contributions to the 21st Century “In addition to supporting any representation for logic, a general theory of intelligence must also support reasoning methods. The most primitive and the most general is analogy, which by itself supports case-based reasoning. Sowa and Majumdar (2003) showed how Peirce’s three branches of logic — induction, deduction, and abduction — could be defined as highly disciplined special cases of analogy. Unlike the methods of logic, which are limited to language-like symbols, analogies can relate patterns of signs of any kind: they can support the metaphors described by Lakoff and Johnson (1980), they can link abstract symbols to image-like icons, and they can relate similar patterns of percepts across different sensory modalities.”
————————————————————————-

SH: Perhaps this doesn’t capture Peirce’s “genuine” meaning but works well enough, similar to how Deep Blue plays good chess but not the same way that humans play chess. There is no evidence that 2-adic -> triadic irreducibility impedes Machine Learning.

http://nlp.stanford.edu/~manning/papers/aaai05-learnabduction.pdf
“We present a system for textual inference (the task of inferring whether a sentence follows from another text) that uses learning and a logical-formula semantic representation of the text. More precisely, our system begins by parsing and then transforming sentences into a logical formula-like representation similar to the one used by (Harabagiu et al., 2000). An abductive theorem prover then tries to find the minimum “cost” set of assumptions necessary to show that one statement follows from the other. These costs reflect how likely different assumptions are, and are learned automatically using information from syntactic/semantic features and from linguistic resources such as WordNet. If one sentence follows from the other given only highly plausible, low cost assumptions, then we conclude that it can be inferred. Our approach can be viewed as combining statistical machine learning and classical logical reasoning, in the hope of marrying the robustness and scalability of learning with the preciseness and elegance of logical theorem proving.”

Posted by: Stephen Harris on October 13, 2009 2:02 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

In computer science, abductive reasoning was already enjoying its Second Big Revival in the 80s, spurred on to a large degree by the work John Josephson at Ohio State, and partly following up on earlier work by Harry Pople in the 70s. I seem to have a memory, but not too reliable, of papers from the 60s. I abduce that the topic must be in its Third Big Revival by now, but I tend to stop following a literature when it begins to go in circles.

Posted by: Jon Awbrey on October 13, 2009 3:58 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

When I went to search on Harry Pople, the ever e-musing Google asked, “Did you mean: Hairy People?” At any rate, here’s the DBLP rap sheet on his publications.

I couldn’t find what I was thinking of from the 60s — maybe my mind’s eye blurred Pople (1973) into 1963.

Or it might have been Warren McCulloch’s Embodiments of Mind that I read back then — he knew his Peirce well and often referred to the problems of abductive reasoning.

Posted by: Jon Awbrey on October 14, 2009 12:48 AM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

This is a fairly new patent with a strong Peircian origin. She quotes quite a bit of Peirce. www.error06.econ.vt.edu/Mazzagatti.doc

Posted by: Stephen Harris on October 14, 2009 4:07 PM | Permalink | Reply to this

Re: Inference, Information, Inquiry, Integration

When it comes to what Peirce might have 4-scene of our current scene, I wouldn’t be 2-quick to limit his vision by the scope of our own.

Something we were talking about elsewhere reminded me of the prospects that I once prospected waybak at the outset of my umpteenth return to the 1-versity, and this Chapter & Peirce that I quoted then:

Thought is not necessarily connected with a brain. It appears in the work of bees, of crystals, and throughout the purely physical world; and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there. (CP 4.551).

See my Prospects For Inquiry Driven Systems, § 3.1. Propositional Calculus for a bit of additional discussion.

Posted by: Jon Awbrey on October 15, 2009 4:26 PM | Permalink | Reply to this

Re: Shell What?

We all know what can happen – legal threats, etc. – when universities allow staff to put their own material up!

Anyway thanks for doing this, John. It’s been fun looking through some old posts. Here, for instance, we get to hear about your early encounters with philosophy.

Posted by: David Corfield on October 8, 2009 8:52 AM | Permalink | Reply to this

WayBakYonder

It looks like there are WebArchive versions of some of this stuff, for example:

http://web.archive.org/web/20070701010130/http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf

Posted by: Jon Awbrey on October 8, 2009 5:19 AM | Permalink | Reply to this

Re: WayBakYonder

Taking the last available WebArchive copy for the example at the top of the thread, we get:

http://web.archive.org/web/20070811001218/http://www.dcorfield.pwp.blueyonder.co.uk/2006/02/articulating-your-program.html

The nice thing is that the WayBakMachine handles the links for you, so long as Mr. Peabody can find a contemporaneous copy.

Or was that not the problem at all?

Posted by: Jon Awbrey on October 8, 2009 5:45 AM | Permalink | Reply to this

Re: WayBakYonder

Good job finding that, I think it belongs here in the Index,
http://math.ucr.edu/home/baez/corfield/HowMathematicians.pdf
I suppose some links still won’t work like
“Applicability of mathematics: special functions”

Posted by: Stephen Harris on October 8, 2009 8:06 AM | Permalink | Reply to this

Re: WayBakYonder

Where is that?

Posted by: Jon Awbrey on October 8, 2009 8:40 AM | Permalink | Reply to this

Re: WayBakYonder

Oh, I was looking in the PDF.

No, here’s a copy that you get by clicking on the link in the archived blog page:

http://web.archive.org/web/20070811045532/www.dcorfield.pwp.blueyonder.co.uk/2006/02/applicability-of-mathematics-special.html

If you get one like that and wonder if it’s the latest edition, then put a kleene star “*” in for the date index and try that:

http://web.archive.org/web/*/www.dcorfield.pwp.blueyonder.co.uk/2006/02/applicability-of-mathematics-special.html

Posted by: Jon Awbrey on October 8, 2009 9:00 AM | Permalink | Reply to this

Re: WayBakYonder

http://math.ucr.edu/home/baez/corfield/2006/02/articulating-your-program.html

That gives a working link to “Applicability of mathematics: special functions” however,

http://web.archive.org/web/20070811001218/http://www.dcorfield.pwp.blueyonder.co.uk/2006/02/articulating-your-program.html

Clicking on the same link under Previous Posts, “Applicability of mathematics: special functions” returns a 404 error in this case. I appreciated your * workaround.

I haven’t seen or read “reed” used in the sense you employed in a long time. I doubt most Americans will ken/grok it. :-)

I thought you made a good point about Heisenberg and the complement which softened the force of Pearl’s pronouncement, and also enjoyed the account of changes in your views. Shoiman

Posted by: Stephen Harris on October 8, 2009 9:43 AM | Permalink | Reply to this

Re: Reed

I’m a Pascal hack from way back …

But Google gives 1.2×10 61.2 \times 10^6 hits for “thinking reed” and naturally there’s a blog by that name.

On to Reedy Categories

Posted by: Jon Awbrey on October 8, 2009 5:02 PM | Permalink | Reply to this

Re: Reed

JA wrote: “But Google gives 1.2×10 6 hits for “thinking reed” and naturally there’s a blog by that name.”
————————————-

My Firefox browser, which is set to Google, must be broken since I only received 39,500 hits.

Blaise Pascal Pensees
“Man is but a reed, the most feeble thing in nature, but he is a thinking reed. The entire universe need not arm itself to crush him. A vapor, a drop of water suffices to kill him.” …

So this is a famous quote from philosophy and there is also a book or two which borrowed the title. There is another word “rede” which according to Sam Johnson is pronounced the same as “reed” rarely used meaning “archaic : interpret, explain”. I think, therefore I am
sure it could include the many conflicting physical interpretations of QM.

Posted by: Stephen Harris on October 8, 2009 6:35 PM | Permalink | Reply to this

Re: Reed

1.2×10 61.2\times10^6

39,500

It depends whether you give Google the quotation marks too.

Posted by: Toby Bartels on October 8, 2009 7:36 PM | Permalink | Reply to this

Re: Reed

Urk! Am I becoming even more cognitively impaired?! I thought 1.2 x 10^6 was
1,200,000 or 1.2 million? Does your computation use some other number base.

Posted by: Stephen Harris on October 8, 2009 9:27 PM | Permalink | Reply to this

Re: Reed

Toby, I see what you mean, 1.2 million is the result of doing a google search without quotes marks for “thinking reed”, from the original Pascal quote since Jon noted that he was a Pascal hacker. It didn’t occur to me that someone would do an unquoted search of _thinking reed_ to support the use of what I will charitably describe as an extended metaphor.

JA: …” and I felt that this was a clue to the trade-offs that create so much tension between diverse cognitive styles in human thinking reeds, whether between reeds or within the same reed.”

A phrase like Pascal’s “a thinking reed” or “a broken reed” are metaphors for humans, but how does that stretch to include a human as “within the same reed.”? That construction is quite illiterate so I originally corrected it very politely, but I realize now that was a mistake.

Posted by: Stephen Harris on October 8, 2009 10:19 PM | Permalink | Reply to this

Riddle A Body !!!

I have the “advanced search page” on pull down menu and always start typing on the “exact phrase” line, but Goo-goo-google often burps (re-googletates?) my cursor back up when I’m not looking, so I get all that acid e-flux …

Anyway, I only meant that divers cognitive styles often dwell within the same breast … brain … reed … whatever it is we think wit.

Posted by: Jon Awbrey on October 8, 2009 10:48 PM | Permalink | Reply to this

Re: Riddle A Body !!!

OK, I suppose these “adventicities” are bound to happen on the information highway.
I got a copy of that Heisenberg book, “Physics and Philosophy” which you alluded to.

Posted by: Stephen Harris on October 8, 2009 11:11 PM | Permalink | Reply to this

and count myself a king of n-finite space …

Here’s a WebArchive copy of the “Selected Bibliography of Philosophical Materials Pertaining to Mathematics and Proof”, patching a missing link at the end of “Categories in Physics and the Trivium” (25 Nov 2005).

Posted by: Jon Awbrey on October 9, 2009 5:46 AM | Permalink | Reply to this

were it not that I have bad schemes …

By way of reducing clutter in the Cafe, I’ll put any new WebArchive patches I find on this thread in the Forum.

Posted by: Jon Awbrey on October 9, 2009 6:54 AM | Permalink | Reply to this

Inference, Information, Inquiry, Integration

I am going to start collecting some readings on this thread in the Forum.

Posted by: Jon Awbrey on October 11, 2009 4:40 PM | Permalink | Reply to this

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