# Logicomix

Graphic novel on the history of and a gentle intro to some of the biggest ideas in logic, math and modern philosophy. It’s really not a comic and it’s a great read.

It’s a lot of things in one: - A story about the conflict between ideal rationality and the unchanging flawed fabric of reality. - A tragedy with logicians as heroes

# Authors

Haven’t looked much into:

# Plot

Autobiography of **Bertrand Russell** as a comic book.

It’s not entirely factual because it is meant to both captivate the reader but also show the kind of thought process and lives the founders of logic had because the writers feel this is vital to understanding their ideas (I feel the same way).

Starts Sept 1939 when Germany invaded Poland, (Blitzkrieg). Countdown to another world war beings UK had signed a pact of non aggression with Hitler

Sept 4 1939 Bertand Russel was meant to give a lecture on **the role of logic in human affairs** at an American uni.

Sept 4 1939 UK declared war on Germany

USA had *isolationists* who wanted the USA not to join the war

Russel had an elder brother who went to bording school but was cut from the comic.

## 1. Pembroke Lodge

His uncle was the source of the howls. He was mad and madness was Bertand’s greatest fear because it meant being the furthest from logic as a person can be. He would’ve ended his life then had it not been for the hope of **reason**. Were it not for math. He says so in greek exercises (a diary he kept to keep his grandmother from snooping).

## 2. Sorcerer’s apprentice

Met the girl who was to be his wife got first class hons at Cambridge

The atoms of logic are propositions which we combine thorugh certain laws

calculus ratiocinator by Gottfried Wilhelm Leibniz was a framework of logic Leibniz used this formal symbolic language to say such things as: a tautology added to itself is a tautology

Leibniz taught Moore about logic. Logic is using combinations of the known to reach the unknown

## 3. Wanderjahre

Bertrand went to Paris because he learned that since math rests on arithmetic they must first make arithmetic solid

## 4. Paradoxes

After returning from Paris Bertrand wanted to write a book that would solve all foundational problems this was The Principles of Mathematics published 1903. He was to use a notation invented by Giuseppe Peano

We then run into Russell’s paradox

When something refers to itself a paradox is nearby.

*A set can contain other sets or even itself. A set of all ideas is an idea. Therefore it contains itself as an element. Does the set of all sets which do not contain themselves contain itself? This subverts the notion of set as a collection defined by a common property*

This failure in set theory led to type theory. The foundations of math were like a mythical turtle supporting the cosmos yet all they did trying to create a solid ground for it was create a tower of turtles all the way down.

Set theory then felt like a foundation of systems without a foundation. See also this section on Wikipedia entry: Objections to set theory as a foundation for mathematics.

## 5. Entracte

Map makers, insanity and logic.

Logic is a map trying to map out reality. In the end they (logicians) ended up confusing reality with their maps

## 6. Logico-philosophical wars

Gottlob Frege sends Ludwig Wittgenstein to Russel. They really get into types

According to Wittgenstein, Language is a model of reality.

Bertrand Russel wrote philosophy of math in prison for protesting USA’s involvement in the war for which he got 6 months in prison. His appetite for moral duty had been satisfied. Wittgenstein wrote his total solution to problems of philosophy on the eastern front this was the Tractatus Logico-Philosophicus (TLP) published in 1922. G. E. Moore really liked it. Bertrand Russel didn’t. I haven’t yet read it to give an opinion on it.

## 6. Incompleteness

Some proofs can’t be proven according to Kurt Gödel.

## 7. Finale

I don’t have much to say here.

# Ideas

Reason is in its highest form, logic.

High rate of psychosis amongst founders of logic.

Bertrand Russel’s grandfather was former prime minister of great Britain but not of Pembroke lodge.

Logic is all about rules. Begins with definitions and continues with rules.

euclid’s proposition

Plato’s symposium is where he wrote about *finding your other half* interesting stuff btw

euclid

What is a number but the set of all sets with that number elements in it? e.g what is 3 but the set of all sets with 3 elements?

A set can contain other sets or even itself. A set of all ideas is an idea. Therefore it contains itself as an element.

The set of all birds is not a set.

Independent existence of a mathematical reality. We don’t make it up but it exists. Is there an objective reality?

Wittgenstein ideas:

- The sleep of reason produces monsters.
- Language is a corruption of pure thought.

Vienna circle’s rationalistic world view has desecrated hallowed Germanic values and for that Schlick was killed by Hitler.

# Vocabulary

stukas

panzers tank

acropolis

uncanny

wafter

cerberus

folly

diptheria

edifice

calculus rattiocinator

kindered spirit

syllogisms

occam’s razor

centaurs

Syllogism

reductio ad absurdum

austere

momento mori

pertubed

beligerence

sang froid

opus magnus

ignoramibus - we shall not know

melancholia

extant

anschluss

abberation

diatribe

tragedian

## Definitions

**tautology:** a statement that is true by virtue of its logical form e.g all red ants are red.

**logic:**

- to Aristotle: logic is new and necessary reasoning.
- new because you learn what you don’t know.
- necessary because conclusions are inescapble
- e.g all men are mortal. socrates is a man therefore socrates is mortal. new and necessary

Leibniz turned this into a symbolic system … and Boole

The international congress the world’s greatest rendezvous of mathematicians

Types save us from paradox they are essential to logic

propositional calculus invented by Leibniz is borrowed a lot from Boole’s work

**Anscluss:** Annexation of Austria by nazi Germany

**Incompleteness theorem:** The completeness of a logical system is the property that every well formed proposition in it can be proved or disproved from the system’s axioms

# Charachters

**Apostolos:**Narrator**Christos:**Theoretical computer scientist and expert in mathematical logic**Bertand Russel:**Main charachter**John Russel:**Bertand Russel’s paternal grandfather. Former prime minister of Great Braitain**Lady John:**Bertand Russel’s paternal grandmother**Alys Pearsail Smith:**John Rusell’s wife later Alys Russell**George Boole:**came up with the laws of True and False. He wrote a book called Laws of Thought.**Alfred Whitehead:**Told Bertand about people on the continent who were doing logic**Leibniz:**Had the vision of a fully logical language**Gottlob Frege:****Frau Frege:**Wife to Gottlob Frege**Gerog Cantor:**Dealt with infinity**Gauss:**warned people not to tackle infinity. It exposes the frailty of math.**Mittag Leffler:****Felix Klein:****Henri Poincare:**French believer in importance of intuition**David Hilbert:**apostle of rigourous exactness of logical proof**Bernhard Bolzano:**Czech progenitor of sets. Catholic priest**Peano:****Kurt Godel:**read all of the principia**Ludwig Wittgenstein:****Schopenhauer:****Von Neumann:****Schlick:**Killed by hitler**Adolf Hitler:**

#### Hitler

Already well known

#### Schlick

Killed by hitler

#### Bertand Russel

Pacifist activist Wrote a diary in Greek called, **greek execises**. Dreamt of a logical calculus Russel’s son got schizo granddaughter committed suicide

#### George Boole

Wrote The Laws of Thought.

Developed the idea that logical propositions can be expressed in purely symbolic lang which allows them to be manipulated by operations similar to arithmetic Worked wholly with aristotle’s method. Only had or and and not this meant it couldn’t express semantic connections between propositions. It was remedied by **predicate calculus**.

#### Gottlob Frege

Wrote the **concept script** The point of logic is not calculation but to **model** reality. Ordinary language is not suited to science. A language that is completely logical, only such a language can deal with the foundations of mathematics. Wanted to prove mathematically that jews were inferior father of modern logic invented quantifiers: universal ∀ and existential ∃

#### Leibniz

Dreamt of the calculus ratiocinator

#### Gerog Cantor

The magus of the infinite Creator of set theory He had gone crazy

Used set theory to show different kinds of infinity TODO: reread his section in the notebook section of Logicomix

#### David Hilbert

Had a talk, the problems of mathematics If a question can be rigourously stated it can be logically answered His son also was a paranoid schizo

#### Kurt Godel

The truth or falsity of every logical proposition can in theory be proven Hilbert’s second problem: the consistency and completeness of arithmetic

#### Ludwig Wittgenstein

shitty teacher got expelled by the village council What we cannot speak of we must pass over in silence. Where speak means speak logically. Wrote tractatus logico philosophicus Started becoming a mystic and wrote Philosophical Investigations

#### Aeshylus

One of the great Greek tragedians Creator of tragedy as we know it. invented dramatic dialogue

#### Euclid

Greek mathematician

# Random ideas

Wittegnstein’s Picture theory and emojis

# Notebook

## Foundations of mathematics

The program as proclaimed by David Hilbert. Creation of a formal system for math, also containing a proof that this axiomatization is: consistent - can lead to know contradiction complete - leaves no unprovable truths decidable - one is able to decide in every occassion whether a formula follows from the axioms or not thought the application of a set of algorithms

# Footnotes

## Other reviews

## Other cool places to learn about these guys

## IRC

A rough and English interpretation of what was going on in the Vienna Circle, which was HUGELY influenced/inspired by the early Wittgenstein.