Definition talk:Logical Graph
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Notes & Queries
Interwikis?
Does anybody know how to create interwikis? For example, so that I can link to Knol, MyWikiBiz, and PlanetMath articles by using the forms:
It should be possible to add an interwiki feature, we should probably put it to a vote to see what others think on the matter, I'll put the question up on the main page discussion.--Joe 15:10, 9 October 2008 (UTC)
Column Templates?
Another thing that might be nice to have — maybe some way to import from Wikipedia? — is the set of templates for creating evenly spaced columns:
It would be a good idea to implement these ideas here, I'm currently working on other parts of the site, so if someone else would like to set up these templates that would be awesome. --Joe 15:13, 9 October 2008 (UTC)
I've moved these discussions to the main page talk as they are fairly important.
What does it mean?
You lost me at the first line: what does it mean when two circles equal one circle, and two concentric circles equals nothing? Could we have a "translation" into standard set-theoretic language, or an internal link to an explanation of what these logical graphs mean in natural language?
JA: Don't worry too much about the present shape of that exposition as I just loaded it up there in order to have the material I need to chunk out into your local schematics, as I learn more about it. I have to be away till later today, so I will explain more when I get back. Jon Awbrey 11:06, 10 October 2008 (UTC)
JA: If you skip down to the section on Formal Development you might see stuff that looks a little more familiar. Jon Awbrey 11:10, 10 October 2008 (UTC)
JA: Matt, logical graphs are "more or less" just an alternate syntax for classical propositional calculus, but they have a number of strong advantages over the conventional syntax, especially in regard to both their conceptual efficiency and their computational efficiency.
JA: It's the "more or less" part that makes for most of the difficulties in the beginning — but if you just skip ahead to something recognizable, you can always backtrack later to see why it might have made sense to begin that way.
JA: One of the big differences between LG and the usual syntax for propositional calculus is that LG, all by itself, is an "abstract" or "un-interpreted" formal system. This means that its well-forms do not have logical meanings until they are given meanings by some interpretation or other. In the case of LG, we usually have in mind one of two interpretations that are dual to each other — much like the dual interpretations of elements in projective geometry.
JA: To be continued … Jon Awbrey 17:44, 10 October 2008 (UTC)
Wowser - okay, I'm looking forward to it. Finding a "clean" exposition of logic is a nightmare - I've been trying to teach myself it but come up against questions I can't find (or work out) the answer to. Here's to this site being the world no. 1 resource for explaining it all! --Matt Westwood 17:57, 10 October 2008 (UTC)
Update March 2010
Apologies for the bulk overwrite. It will take me a while to feather in the proof animations that I've been developing, then I'll go back and restore the edits that other people have made since the last time I was here. Jon Awbrey 18:48, 28 March 2010 (UTC)
Perfectly good page, in theory
… but utterly incomprehensible to anyone who hasn't had full grounding in the techniques. From a historical perspective, it has some minor importance, I suppose, but without the context it's quite opaque. It's littered with unexplained sesquipedalianisms (what are "entitative" and "existential" graphs?) and explanation by example is just a cop-out.
If this page is to survive on this site, it really needs the following:
- a) To be split up into several smaller, more compact, more self-contained pages;
- b) To have every technical term linked to another page explaining it;
- c) To reduce all external links to a minimum, and then only for peripheral subjects;
- d) To dispose of all pointlessly irrelevant detail (a case in point being: "Though we may note in passing such historical details as the circumstance that Charles Sanders Peirce used a streamer-cross symbol where George Spencer-Brown used a carpenter's square marker …") or at least move it into a separate page or section discussing the evolution of the symbology;
- e) To explain exactly what is being done in each of the derivations, or to provide a link (internal, of course) to an explanation of each of the operations performed (appealing to prior knowledge is unacceptable on this site). If you can't explain it, it means you don't really understand it;
- f) To write it in plain English without all the fancy academic rhetoric (this site is primarily for information — the aim is not to impress more senior academics);
- g) Cut out the foreign-language quotes unless you're prepared to translate them and (if necessary) explain why they're relevant — they make the site look pretentious.
The plan would be to keep the information on this page, but to rewrite it in the style of the rest of this site. As a piece of academic literature it may well deserve to exist somewhere - but I'm afraid probably not, in its current form, on this site. --Matt Westwood 22:22, 27 June 2010 (UTC)
Yes, it could probably stand a fresh rewrite. Getting things off the ground at the beginning has always been tough — starting out with the Laws of Form approach used to appeal to some people, but there's bound to be a less mystifying way to do that. I have travel and vacation all through July though, so it will probably be August before I can give it a serious look. Jon Awbrey 02:02, 28 June 2010 (UTC)
Notes Toward A Rewrite
- Expository Problem 1. Explaining the nature of a highly abstract formal calculus.
- This means that each formula of the system has two interpretations as a logical proposition, roughly based on De Morgan duality. The situation is similar to projective geometry, where you have the undefined primitive terms point and line and dual interpretations that switch them. As a matter of fact, Peirce would sometimes write logical theorems in parallel columns the way one does in projective geometry. I don't remember anyone giving names to the alternate interpretations of projective geometry, but Peirce gave the names "entitative graphs" and "existential graphs" to the dual interpretations of his logical graphs. The names themselves are not all that important, but the formal symmetry of the system is one of its most important properties. Jon Awbrey 12:04, 28 June 2010 (UTC)
- One of the expository choices that we have to make at the beginning is this:
- We can try to introduce the abstract calculus in a fully abstract way, with no interpretation in sight, and perhaps not even mentioning the whole issue of interpretation. This has always been a pretty tough sell, and even when we succeed at it the reader sometimes gets the wrong idea, namely, that we don't care about the meanings of our formulas at all. Much to the contrary, the whole point of seeking a highly abstract calculus is actually the opposite of that — it's more about covering the full variety of meanings than eliminating meaning altogether. Jon Awbrey 12:22, 28 June 2010 (UTC)
- We can try to introduce the abstract calculus in the presence of our favorite interpretation, only later mentioning the fact that another interpretation is possible. This is usually easier to set up on a first approach. The downside is that readers may have trouble overcoming the initial bias and seeing the full potential of the formal abstraction. Jon Awbrey 14:14, 28 June 2010 (UTC)
