From 0cd408c6a7bda2872f50a8f2f80d515c54be9d46 Mon Sep 17 00:00:00 2001 From: Ryan Reilly Date: Sun, 17 Dec 2023 21:37:26 -0500 Subject: [PATCH 1/7] Chapter 1 overview, SUMMARY update, SoA start --- src/Chapter1/SheetOfAssertion.md | 3 +++ src/Chapter1/chapter_1.md | 16 ++++++++++++++-- src/SUMMARY.md | 2 +- 3 files changed, 18 insertions(+), 3 deletions(-) create mode 100644 src/Chapter1/SheetOfAssertion.md diff --git a/src/Chapter1/SheetOfAssertion.md b/src/Chapter1/SheetOfAssertion.md new file mode 100644 index 0000000..1b120b6 --- /dev/null +++ b/src/Chapter1/SheetOfAssertion.md @@ -0,0 +1,3 @@ +# Chapter 1.1: The Sheet of Assertion + +For the truth or falsity of statements to be evaluated, one must have some way of asserting the truth or falsity of its components. diff --git a/src/Chapter1/chapter_1.md b/src/Chapter1/chapter_1.md index da4df0f..aa1bf16 100644 --- a/src/Chapter1/chapter_1.md +++ b/src/Chapter1/chapter_1.md @@ -1,3 +1,15 @@ -# Chapter 1 +# Chapter 1: Thinking Logically with AEGs -Discuss learning logic through AEGs, *without* assuming the reader knows Propositional Calculus. +Mathematical logic concerns how one determines the truth or falsity of a statement(s). In existing logics +(can be read as "systems of logic,") this involves large sets of notation and a significant amount of rewriting in proofs, +which can and does get quite annoying quite quickly. + +Logician Charles Peirce constructed the Existential Graph System to visualize several logics. For right now, we will discuss +his Alpha Existential Graph System, which we will abbreviate as AEG System in reference to the system and AEGs in reference +to Alpha Existential Graphs themselves, and we will assume you have no experience working in or understanding of other logics. + +If the object seems intimidating, please continue still. One is able to conclude logical truths as a consequence +of drawing ellipses and letters, which, while it sounds silly, is both true and good fun. If it is any motivation, +all the same conclusions reachable in other, similar logics, which concern strictly truth and falsity, are reachable through +the AEG System, even though it may seem somewhat counterintuitive at first glance that a visualization can be just as +powerful. diff --git a/src/SUMMARY.md b/src/SUMMARY.md index 942d2c0..2f9524f 100644 --- a/src/SUMMARY.md +++ b/src/SUMMARY.md @@ -3,7 +3,7 @@ [Introduction](introduction.md) - [Thinking Logically with AEGs](./Chapter1/chapter_1.md) - + - [The Sheet of Assertion](./Chapter1/SheetOfAssertion.md) - [The Propositional Calculus and AEGs](./Chapter2/chapter_2.md) - [Drawing and Proving AEGs with PMH](./Chapter3/chapter_3.md) \ No newline at end of file From 26de9f7ddead0624f5d9ee7b719046734a384e77 Mon Sep 17 00:00:00 2001 From: Ryan Reilly Date: Mon, 18 Dec 2023 10:36:23 -0500 Subject: [PATCH 2/7] sheetOfAssertion draft, README change, images --- src/Chapter1/{SheetOfAssertion.md => sheetOfAssertion.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename src/Chapter1/{SheetOfAssertion.md => sheetOfAssertion.md} (100%) diff --git a/src/Chapter1/SheetOfAssertion.md b/src/Chapter1/sheetOfAssertion.md similarity index 100% rename from src/Chapter1/SheetOfAssertion.md rename to src/Chapter1/sheetOfAssertion.md From ef185e0a7d2f34b211a76a4f3afc3419daeb9e02 Mon Sep 17 00:00:00 2001 From: Ryan Reilly Date: Mon, 18 Dec 2023 10:37:01 -0500 Subject: [PATCH 3/7] Supposed to have gone with previous commit --- README.md | 8 +++-- src/Chapter1/chapter_1.md | 8 ++++- src/Chapter1/images/JerryDiscussion.png | Bin 0 -> 5337 bytes src/Chapter1/sheetOfAssertion.md | 39 +++++++++++++++++++++++- src/introduction.md | 3 +- 5 files changed, 53 insertions(+), 5 deletions(-) create mode 100644 src/Chapter1/images/JerryDiscussion.png diff --git a/README.md b/README.md index 7b8f2b5..bc4f162 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,8 @@ # Existential Graph Theorem Proving in PMH -A book about theorem proving in [Charles Sanders Peirce's Existential Graph System](https://en.wikipedia.org/wiki/Existential_graph#The_graphs) using the [PMH](https://github.com/RAIRLab/Peirce-My-Heart) existential graph interactive theorem prover. +A book about theorem proving in +[Charles Sanders Peirce's Existential Graph System](https://en.wikipedia.org/wiki/Existential_graph#The_graphs) +using the [PMH](https://github.com/RAIRLab/Peirce-My-Heart) existential graph interactive theorem prover. Assumes that the reader has no knowledge of Propositional Calculus and no knowledge of any Existential Graphs beforehand. @@ -9,7 +11,9 @@ Made with [mdBook](https://github.com/rust-lang/mdBook). # Testing Your Changes Locally! Install rust, cargo and mdbook. -Then, run "mdbook build" in the **root directory** and ensure the message "Running the html backend" appears. +Then, run ```mdbook build``` in the **root directory** and ensure the message "Running the html backend" appears. +Then, in the newly created ./book/ directory on your machine, open "index.html" with your web browser of choice and determine +if the format is to your liking. # Root Files and Folders diff --git a/src/Chapter1/chapter_1.md b/src/Chapter1/chapter_1.md index aa1bf16..026e80f 100644 --- a/src/Chapter1/chapter_1.md +++ b/src/Chapter1/chapter_1.md @@ -6,10 +6,16 @@ which can and does get quite annoying quite quickly. Logician Charles Peirce constructed the Existential Graph System to visualize several logics. For right now, we will discuss his Alpha Existential Graph System, which we will abbreviate as AEG System in reference to the system and AEGs in reference -to Alpha Existential Graphs themselves, and we will assume you have no experience working in or understanding of other logics. +to Alpha Existential Graphs themselves, and we will assume you have no experience working in or understanding of other +logics. If the object seems intimidating, please continue still. One is able to conclude logical truths as a consequence of drawing ellipses and letters, which, while it sounds silly, is both true and good fun. If it is any motivation, all the same conclusions reachable in other, similar logics, which concern strictly truth and falsity, are reachable through the AEG System, even though it may seem somewhat counterintuitive at first glance that a visualization can be just as powerful. + +To reiterate, before going into Chapter 1.1, it is **very** important to understand the first paragraph here. There are few +numbers in these parts. While it is easy to get lost in seas of odd notation, it is helpful to remind oneself that the AEG +System and systems similar were developed to discuss and verify, strictly, the truth or falsity of some statement and its +components. diff --git a/src/Chapter1/images/JerryDiscussion.png b/src/Chapter1/images/JerryDiscussion.png new file mode 100644 index 0000000000000000000000000000000000000000..302381e5d1de6495341a03cbc3a2fab4a027cea8 GIT binary patch literal 5337 zcmeHLX;hQfy8hHE+FB5mNg!CX!chd{z!V5=4PvhXax60v0hv@l2oQzD{|DD_wJXQUEyk+mEpCe@dz3Gh955OwYVn zkY@H0+J6Z!rEPC6tz6%J9C!a>?vIt;lOd5M4)K@YKl|9M|6S;w)NOiorN7YP2VP`> zZ4KKOh=>{s%#(OofsW)^-5c{JUC8-J#j-z5@XKet2XXaClpYHUR9| zjR1g)-<9tGzT5t%2>|Thr#aX!cTZ^ncfa^tdi1Z-|6d5yP{&s!wKPKB8)Z>jmFHqT ztsuC~K(cC8$GS8c=HvP2)13e``&5oI8|N6CR_1jsYaq=Mc%j}MqOEX(!W7gn08lmj zN7txTylu+5kw~x%VLTYoxw|&ER%t}@-Qp%|6C*%4g-d+8bYBdCm=dbK6`5qybj&>e z`$D%Z`@|`Uv?S>=RxlPgwn!1uqq^qWEZ=UXX6S8Y?{NOpnDdD}Na1Z}&|k6NxjxEX z>EVrJpt;nj_|x%GKb!o|!vw5s1+^Y6*irQyP5!Wgfj5yKHqb-6$HJ}~I} zv-&sW$Wn^9d^Tu!ZTclW>VfxJq}DKM61)wlEPZNa@&2s)b62Bmk$wF{^yLOtqt+15 zvo5WxX3>i0eO5oaku>4j4`@qgYf} z+U!ay#53dCQ3J__WpQ%~Q5C{rgDW}q7Ef|+HHb8y2~lQt(U#IFah>)X@|hAZ8@R>X zw!4V^Y>TTGoSSNy{tP@HhIh&LhFmz4vHy4Ro0zjJG`_Wn3u_1*YD+SKzGC%42;+eg zE+fOqQ=B@>Jb9vPHAe8BVj)WR$A>!?k3U>8tKzO>4O@26XZxc)rBcdLV|JTRWsu## z5+q`izQYf?SU3&<0Q`J;%|&o`TK`YqmR|DQ;I6xo3HbEV?&f~ZqGGNMX%`Nn#9}DI zu!$u`iw(0y2!fjia2YM70~eozl?Y`9A3d^kj*e8fNt@}*%FUiWG2>O@t=Alr1HcOh zzpzYmrcH2Q39R zkQa^KDaxh3I#7_`@P2d$kDi=jL|o8~8&?&Pa_#;hQ?NfR>as)&*>3i-asU`RU!L_u zQu@I2pw}ZND^hqo^HohZO7*pF2N6Q{`OeI5_>&RzbXnLzruF-xJ;3~<`!WOn)nA@% za%xRpNvLRUa73uCH??^ZFT)Gt{Z<$nz{_vRZX!_zU39 ze}PoW{q##7JVWm-&bXnj*nk#)J2^7C9%tWI_^tV(dH+ef!~S0g{#F%gos+mI;hf=s zdzM|>Xa#d=6(mHlW`C#qva+dW8MF@;cEVbR8~fHN!p1sm`pem>7-JW~S%kyKP>J!- z%XneBTKu`*L{o3SsJ*dDsrKxh?NGHpIaZ$)96bD47ywL(TWkhnb(^7#P<;X5#lvGFAtpc9*jD&xbWf_cZK1vZ<7XYBv9>n zo2K3q7wCKIZf@`^{9yj*#gmkr>YLU!Md@pIj0U@k>U#@0#w~jnX=8U?oazhWI;O^n zMGN6J4?4v2tIffr41do$`K9=B0V}7R8O^J&6 zaX8K466~N0i&Q|Q=f$4Ok9W>}W?8NB@`8CyfeVYx*pt0PC30=oBIqz zO8mgY!O2>r56h&s-oh%J=E7~&7>@?EjQ2gDnX`__zqt8-g@9^Hqi60S%BjRgjFi}A zSQz#}2ph48M>rJPn!imu!$mQG=~8Ya z0@{;D4l&jZ|1fb}HLiYa^3oIm%rpLz{np?V&6?`hUh3I;YPCx_bsUSywG2H4a#aW6 z;~`sy?utmq6mzuBc&5ZKr9xd&GphbU@NY?FpY0KZf~#24uU5zlyGx$|FFM$`a%E3Z z2ri&c(<-XM6>MfAk}NLKT4js!IP>Y_tZ>Vyw-`=ca1cU#UA=}WD_E{s<;Yk4Yms8-IVZJ5`L?ma zS63oz^x+UJ!`86*nSC41#Le`c?$(u@m(rOYl^H6{yL`tBaDCG3+0n5yp6yJ1QIkwj zZ~Cn*#A`K*9yN0uvyhH#oSNAa9$7isp3fG%5LjxIMH8bZCYVspS{q#$@7V<#K~i^{t#4Q6s=+5td;U$=hp1aH z5D%x?j{CUp_3UGfPPdI3XC$g7R35zK56tg&pMV8E0vn>k9IJ*C9gEYhG^@@wr6teaV?W#^?yae94s)uqM%xu> zUiV@PiGCVu=M}uymIR_LEf(-kWqPs+ZTV?>zYiVei6WdPmhFd=j8^=8lA7J9E&8P3 zn(WiOrIpErUS+k#H|fK&w&qrEqBNirti+|SBCE3*Qd8|RAt9B|cKbblZb|F{zlMp* z>3}rLZX9?@ry(3oNh$3nS0RODol0z#os*(7m3{~6s6K{?P;{~ySFly^Nw6v+lEjt>+GU;$+j4d0J6*`v3F~; 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For example, I may say that + +```I have a cat = C``` + +```This cat's name is Jerry = J``` + +And change our Sheet of Assertion accordingly. This is allowed because we may replace C with "I have a cat" and we may +replace J with "This cat's name is Jerry" at any time. They are equal! + +![The Jerry compaction is not displayable.](./images/JerryCompaction.png) + +So are these sheets! While they look different, they really do mean the same thing. So long as one clearly states what their +atoms mean elsewhere, they may be represented as any symbol[^1], from any alphabet, or some very long +annoying string, if one so desires. + +**Why does this matter?** + +While the examples about Jerry are purposefully silly, the important part about them is that atoms can be either true +or false. Jerry may be a dog, or a cat I call Jerry +may not really be named Jerry. It is best to refer to the first sentence +in Chapter 1. We are concerned with *how* statements are determined as true or false, less so if they *are* true +or false. + +If you find yourself a bit confused, think about something as simple as addition. Adding two numbers and receiving their sum +has worked for all numbers in your head. ```1 + 1 = 2``` is never going to suddenly turn into ```1 + 1 = 43``` if you look +at the equation the wrong way. There are rules that are repeatable regardless of who is using the rule, when, how and why. +We can plug numbers into ```number + number``` for the rest of time and catalogue their sums if we choose. +Every sum received will be equal to ```number + number```. The point is that we are concerned +with forming rules that work for certain parameters, and less so with applying them. + +We say that the statement (C and J), as in, (I have a cat and This cat's name is Jerry), +is true only if both C and J are true, and false otherwise. If C is false, or J is false, or both C and J are false, +(I have a cat and This cat's name is Jerry) no longer tells the full truth, and so therefore is considered false. + +Note that that "or" is similar to the word "and" in the structure of a sentence, as in it is a grammar conjunction, +but that we cannot represent that with just The Sheet of Assertion and atoms. It still appears useful, however. +Chapter 1.3 details how we can get this, and surprisingly construct every statement you can think of, by introducing and +discussing The Cut. + +[^1] PMH supports only single-letter, English-alphabet atoms as of version 1.0.0, but in the AEG System, generally, +any one atom may be represented by any symbol(s). diff --git a/src/Chapter1/images/JerryCompaction.png b/src/Chapter1/images/JerryCompaction.png new file mode 100644 index 0000000000000000000000000000000000000000..f37eb4f95994d9ae715b85cfb92f1e7cb460f12c GIT binary patch literal 1722 zcmeAS@N?(olHy`uVBq!ia0y~yV7v*$EF5e=k(B3tpBWg~8a-VcLn`LHy=#~yohfnr zp}BWnBG19EG7dUElbKf-OPH^`x*~Xc>aLe}c9aS8yeerhVNT>*a7*IM9OY=2$aL{H zN7nqi^zKLHs)=rG+kb!beEh!p^7p^jnHavk+n&tNz!0pui9tYV6w@>eK7G5vT)>gc z``W+s^UrnLZohqe+c)^^&ELNYD&sa!e(cL`5SssM-~XyNiXM{LFYK;mZT|aGefG~y z|03p2zsB^Y|AgPQh}TD5W8eO|b!Ph4ho8RBnro9*BGdls)5~S+_POtfy!LkM1*SLM zC;YBl*t+#rNT})7J$u)EPCsSI7aLpiyWr}c)pe%UM>-fLKR>u!Q)*XL&a=;rYgbv# zT)S%a`?#FEEL*qb%oV0CWktuL?%S;MsxJ+++8q-X9C|h6YV#?kH_gktm#6&+nqO|e z@!W0knzz+Oao7J=rl~cApYkfpl6&_$I(c?gdDW9hhB(WKb7y>fm{(pJwp>n_%|dJ9 z+*QwFBTq2NOh3Wo&~d`=>bHGzeYVU8wAD8W7Z+7++r8`adt z{$Wtri(6UZ-LI}WzcfCuUwzYLZZJ=ryWnR0 z)Y#DP-E(EHn{U0X{wj5L1j7fFiE|gpe^a`*M$GuJN_ijO&$jM!F6}=0nA7I$9;;T?8`AD~eQ!m)e)srs<;L>`8P*5> zb-u|q;M@A|%Jt{FeRJ#I Date: Mon, 18 Dec 2023 14:52:01 -0500 Subject: [PATCH 5/7] Testing if the workflow detects a failed build --- src/SUMMARY.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/SUMMARY.md b/src/SUMMARY.md index a361431..67f46a4 100644 --- a/src/SUMMARY.md +++ b/src/SUMMARY.md @@ -8,7 +8,7 @@ - [The Cut](./Chapter1/chapter_1.md) - [Conjunctions between Symbols](./Chapter1/chapter_1.md) - [Rules of Equivalence](./Chapter1/chapter_1.md) - - [Rules of Inference](./Chapter1/chapter_1.md) + - [Rules of Inference] (./Chapter1/chapter_1.md) - [What AEGs Can and Cannot Model](./Chapter1/chapter_1.md) - [Conclusion](./Chapter1/chapter_1.md) From bfdfbc00163b40ced185a54a888b3f5ab0f25be5 Mon Sep 17 00:00:00 2001 From: Ryan Reilly Date: Mon, 18 Dec 2023 14:52:55 -0500 Subject: [PATCH 6/7] Excellent. Reverting previous change --- src/SUMMARY.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/SUMMARY.md b/src/SUMMARY.md index 67f46a4..a361431 100644 --- a/src/SUMMARY.md +++ b/src/SUMMARY.md @@ -8,7 +8,7 @@ - [The Cut](./Chapter1/chapter_1.md) - [Conjunctions between Symbols](./Chapter1/chapter_1.md) - [Rules of Equivalence](./Chapter1/chapter_1.md) - - [Rules of Inference] (./Chapter1/chapter_1.md) + - [Rules of Inference](./Chapter1/chapter_1.md) - [What AEGs Can and Cannot Model](./Chapter1/chapter_1.md) - [Conclusion](./Chapter1/chapter_1.md) From a3d41ef73db8f3901febcdb1982e40cd2d6131a1 Mon Sep 17 00:00:00 2001 From: Ryan Reilly Date: Thu, 21 Dec 2023 08:07:08 -0500 Subject: [PATCH 7/7] Mathjax-ifying existing equations, book config --- .vscode/settings.json | 1 + book.toml | 7 ++++++- src/Chapter1/atom.md | 10 +++++----- src/Chapter1/sheetOfAssertion.md | 2 +- 4 files changed, 13 insertions(+), 7 deletions(-) diff --git a/.vscode/settings.json b/.vscode/settings.json index a08542b..88a1a0f 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -1,5 +1,6 @@ { "cSpell.words": [ + "mathjax", "mdbook", "peaceiris", "PMH", diff --git a/book.toml b/book.toml index 4b07b6f..0dffbc7 100644 --- a/book.toml +++ b/book.toml @@ -1,6 +1,11 @@ [book] +title = "Existential Graph Theorem Proving in PMH" authors = ["James Oswald, RAIR Lab, Ryan Reilly"] +description = "For understanding and proving with AEGs and PMH." language = "en" multilingual = false src = "src" -title = "Existential Graph Theorem Proving in PMH" + +[output.html] +git-repository-url = "https://github.com/RAIRLab/EG-Theorem-Proving-in-PMH" +mathjax-support = true diff --git a/src/Chapter1/atom.md b/src/Chapter1/atom.md index bb8fe58..ac437a1 100644 --- a/src/Chapter1/atom.md +++ b/src/Chapter1/atom.md @@ -5,9 +5,9 @@ representations certainly is. An *atom* here is an indivisible component of some statement that may be true or may be false. For example, I may say that -```I have a cat = C``` +I have a cat \\( = C \\) -```This cat's name is Jerry = J``` +This cat's name is Jerry \\( = J \\) And change our Sheet of Assertion accordingly. This is allowed because we may replace C with "I have a cat" and we may replace J with "This cat's name is Jerry" at any time. They are equal! @@ -27,10 +27,10 @@ in Chapter 1. We are concerned with *how* statements are determined as true or f or false. If you find yourself a bit confused, think about something as simple as addition. Adding two numbers and receiving their sum -has worked for all numbers in your head. ```1 + 1 = 2``` is never going to suddenly turn into ```1 + 1 = 43``` if you look +has worked for all numbers in your head. \\( 1 + 1 = 2 \\) is never going to suddenly turn into \\(1 + 1 = 43 \\) if you look at the equation the wrong way. There are rules that are repeatable regardless of who is using the rule, when, how and why. -We can plug numbers into ```number + number``` for the rest of time and catalogue their sums if we choose. -Every sum received will be equal to ```number + number```. The point is that we are concerned +We can plug numbers into \\( number + number = sum \\) for the rest of time and catalogue their sums if we choose. +Every sum received will be equal to \\( number + number \\). The point is that we are concerned with forming rules that work for certain parameters, and less so with applying them. We say that the statement (C and J), as in, (I have a cat and This cat's name is Jerry), diff --git a/src/Chapter1/sheetOfAssertion.md b/src/Chapter1/sheetOfAssertion.md index a4f1d8f..0d586ad 100644 --- a/src/Chapter1/sheetOfAssertion.md +++ b/src/Chapter1/sheetOfAssertion.md @@ -25,7 +25,7 @@ would look like this on *The Sheet of Assertion*, our writable surface. ![The Jerry discussion is not displayable.](./images/JerryDiscussion.png) As a result of the statements being considered *conjuncts*, as in they are in conjunction with each other, - the *and* was removed. Otherwise, the sentence +the *and* was removed. Otherwise, the sentence "I have a cat, and this cat's name is Jerry," and the above Sheet of Assertion are equivalent in meaning. Alone, this is not too powerful[^2].