temp
This commit is contained in:
parent
e596fe72d8
commit
66478400f7
32 changed files with 841 additions and 0 deletions
49
2024/documents/by-course/phil-1/paper-1/package.nix
Normal file
49
2024/documents/by-course/phil-1/paper-1/package.nix
Normal file
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@ -0,0 +1,49 @@
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{
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pkgs,
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||||
typstPackagesCache,
|
||||
typixLib,
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||||
...
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||||
}:
|
||||
let
|
||||
src = typixLib.cleanTypstSource ./.;
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||||
commonArgs = {
|
||||
typstSource = "main.typ";
|
||||
|
||||
fontPaths = [
|
||||
# Add paths to fonts here
|
||||
# "${pkgs.roboto}/share/fonts/truetype"
|
||||
];
|
||||
|
||||
virtualPaths = [
|
||||
# Add paths that must be locally accessible to typst here
|
||||
# {
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||||
# dest = "icons";
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||||
# src = "${inputs.font-awesome}/svgs/regular";
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# }
|
||||
];
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||||
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XDG_CACHE_HOME = typstPackagesCache;
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};
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# Compile a Typst project, *without* copying the result
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# to the current directory
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||||
build-drv = typixLib.buildTypstProject (
|
||||
commonArgs
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||||
// {
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inherit src;
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||||
}
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||||
);
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||||
|
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# Compile a Typst project, and then copy the result
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# to the current directory
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build-script = typixLib.buildTypstProjectLocal (
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commonArgs
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// {
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inherit src;
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}
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);
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# Watch a project and recompile on changes
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watch-script = typixLib.watchTypstProject commonArgs;
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in
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build-drv
|
99
2024/flake.lock
Normal file
99
2024/flake.lock
Normal file
|
@ -0,0 +1,99 @@
|
|||
{
|
||||
"nodes": {
|
||||
"flake-utils": {
|
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"inputs": {
|
||||
"systems": "systems"
|
||||
},
|
||||
"locked": {
|
||||
"lastModified": 1726560853,
|
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"narHash": "sha256-X6rJYSESBVr3hBoH0WbKE5KvhPU5bloyZ2L4K60/fPQ=",
|
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"owner": "numtide",
|
||||
"repo": "flake-utils",
|
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"rev": "c1dfcf08411b08f6b8615f7d8971a2bfa81d5e8a",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
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||||
"owner": "numtide",
|
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"repo": "flake-utils",
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"type": "github"
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||||
}
|
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},
|
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"nixpkgs": {
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"locked": {
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"lastModified": 1729256560,
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"narHash": "sha256-/uilDXvCIEs3C9l73JTACm4quuHUsIHcns1c+cHUJwA=",
|
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"owner": "NixOS",
|
||||
"repo": "nixpkgs",
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"rev": "4c2fcb090b1f3e5b47eaa7bd33913b574a11e0a0",
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"type": "github"
|
||||
},
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"original": {
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"owner": "NixOS",
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"ref": "nixos-unstable",
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"repo": "nixpkgs",
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"type": "github"
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}
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},
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"root": {
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"inputs": {
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"flake-utils": "flake-utils",
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"nixpkgs": "nixpkgs",
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"typix": "typix",
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"typst-packages": "typst-packages"
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}
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},
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"systems": {
|
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"locked": {
|
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"lastModified": 1681028828,
|
||||
"narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
|
||||
"owner": "nix-systems",
|
||||
"repo": "default",
|
||||
"rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "nix-systems",
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||||
"repo": "default",
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||||
"type": "github"
|
||||
}
|
||||
},
|
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"typix": {
|
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"inputs": {
|
||||
"nixpkgs": [
|
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"nixpkgs"
|
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]
|
||||
},
|
||||
"locked": {
|
||||
"lastModified": 1728290750,
|
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"narHash": "sha256-piLZT8398O69hy0e3gX8hUWqSzbCslMCt10pT8d6c8E=",
|
||||
"owner": "loqusion",
|
||||
"repo": "typix",
|
||||
"rev": "62d032735ad32a9a90225c06cb0857677fc753ee",
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"type": "github"
|
||||
},
|
||||
"original": {
|
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"owner": "loqusion",
|
||||
"repo": "typix",
|
||||
"type": "github"
|
||||
}
|
||||
},
|
||||
"typst-packages": {
|
||||
"flake": false,
|
||||
"locked": {
|
||||
"lastModified": 1729252723,
|
||||
"narHash": "sha256-xdaQYNw1GApaJnXJO4WnUTNuYeRXisxIUSuAzVXFEW4=",
|
||||
"owner": "typst",
|
||||
"repo": "packages",
|
||||
"rev": "9bcf190c85da91be6df9f5fc25a93ce5812489cc",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "typst",
|
||||
"repo": "packages",
|
||||
"type": "github"
|
||||
}
|
||||
}
|
||||
},
|
||||
"root": "root",
|
||||
"version": 7
|
||||
}
|
86
2024/flake.nix
Normal file
86
2024/flake.nix
Normal file
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@ -0,0 +1,86 @@
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{
|
||||
description = "Compiling work in 2024 in a reproducible manner";
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|
||||
inputs = {
|
||||
nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
|
||||
|
||||
typix = {
|
||||
url = "github:loqusion/typix";
|
||||
inputs.nixpkgs.follows = "nixpkgs";
|
||||
};
|
||||
|
||||
flake-utils.url = "github:numtide/flake-utils";
|
||||
|
||||
typst-packages = {
|
||||
url = "github:typst/packages";
|
||||
flake = false;
|
||||
};
|
||||
|
||||
# Example of downloading icons from a non-flake source
|
||||
# font-awesome = {
|
||||
# url = "github:FortAwesome/Font-Awesome";
|
||||
# flake = false;
|
||||
# };
|
||||
};
|
||||
|
||||
outputs =
|
||||
inputs@{
|
||||
nixpkgs,
|
||||
typix,
|
||||
flake-utils,
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||||
...
|
||||
}:
|
||||
flake-utils.lib.eachDefaultSystem (
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||||
system:
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||||
let
|
||||
pkgs = nixpkgs.legacyPackages.${system};
|
||||
in
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||||
let
|
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typstPackagesSrc = "${inputs.typst-packages}/packages";
|
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|
||||
typstPackagesCache = pkgs.stdenv.mkDerivation {
|
||||
name = "typst-packages-cache";
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||||
src = typstPackagesSrc;
|
||||
dontBuild = true;
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||||
installPhase = ''
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mkdir -p "$out/typst/packages"
|
||||
cp -LR --reflink=auto --no-preserve=mode -t "$out/typst/packages" "$src"/*
|
||||
'';
|
||||
};
|
||||
in
|
||||
let
|
||||
inherit pkgs;
|
||||
typixLib = typix.lib.${system};
|
||||
in
|
||||
{
|
||||
# checks = {
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||||
# inherit build-drv build-script watch-script;
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||||
# };
|
||||
|
||||
packages.default = import ./documents/by-course/phil-1/paper-1/package.nix {
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||||
inherit pkgs typixLib typstPackagesCache;
|
||||
};
|
||||
# apps = rec {
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||||
# default = watch;
|
||||
# build = flake-utils.lib.mkApp {
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||||
# drv = build-script;
|
||||
# };
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||||
# watch = flake-utils.lib.mkApp {
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||||
# drv = watch-script;
|
||||
# };
|
||||
# };
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||||
#
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||||
# devShells.default = typixLib.devShell {
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||||
# inherit (commonArgs) fontPaths virtualPaths;
|
||||
# packages = [
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||||
# # WARNING: Don't run `typst-build` directly, instead use `nix run .#build`
|
||||
# # See https://github.com/loqusion/typix/issues/2
|
||||
# # build-script
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||||
# watch-script
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# # More packages can be added here, like typstfmt
|
||||
# pkgs.typstyle
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# ];
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||||
# };
|
||||
}
|
||||
);
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||||
}
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1
2024/work/phil-1/paper-1-typix/.gitignore
vendored
Normal file
1
2024/work/phil-1/paper-1-typix/.gitignore
vendored
Normal file
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@ -0,0 +1 @@
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|||
result*
|
99
2024/work/phil-1/paper-1-typix/flake.lock
Normal file
99
2024/work/phil-1/paper-1-typix/flake.lock
Normal file
|
@ -0,0 +1,99 @@
|
|||
{
|
||||
"nodes": {
|
||||
"flake-utils": {
|
||||
"inputs": {
|
||||
"systems": "systems"
|
||||
},
|
||||
"locked": {
|
||||
"lastModified": 1726560853,
|
||||
"narHash": "sha256-X6rJYSESBVr3hBoH0WbKE5KvhPU5bloyZ2L4K60/fPQ=",
|
||||
"owner": "numtide",
|
||||
"repo": "flake-utils",
|
||||
"rev": "c1dfcf08411b08f6b8615f7d8971a2bfa81d5e8a",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "numtide",
|
||||
"repo": "flake-utils",
|
||||
"type": "github"
|
||||
}
|
||||
},
|
||||
"nixpkgs": {
|
||||
"locked": {
|
||||
"lastModified": 1729256560,
|
||||
"narHash": "sha256-/uilDXvCIEs3C9l73JTACm4quuHUsIHcns1c+cHUJwA=",
|
||||
"owner": "NixOS",
|
||||
"repo": "nixpkgs",
|
||||
"rev": "4c2fcb090b1f3e5b47eaa7bd33913b574a11e0a0",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "NixOS",
|
||||
"ref": "nixos-unstable",
|
||||
"repo": "nixpkgs",
|
||||
"type": "github"
|
||||
}
|
||||
},
|
||||
"root": {
|
||||
"inputs": {
|
||||
"flake-utils": "flake-utils",
|
||||
"nixpkgs": "nixpkgs",
|
||||
"typix": "typix",
|
||||
"typst-packages": "typst-packages"
|
||||
}
|
||||
},
|
||||
"systems": {
|
||||
"locked": {
|
||||
"lastModified": 1681028828,
|
||||
"narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
|
||||
"owner": "nix-systems",
|
||||
"repo": "default",
|
||||
"rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "nix-systems",
|
||||
"repo": "default",
|
||||
"type": "github"
|
||||
}
|
||||
},
|
||||
"typix": {
|
||||
"inputs": {
|
||||
"nixpkgs": [
|
||||
"nixpkgs"
|
||||
]
|
||||
},
|
||||
"locked": {
|
||||
"lastModified": 1728290750,
|
||||
"narHash": "sha256-piLZT8398O69hy0e3gX8hUWqSzbCslMCt10pT8d6c8E=",
|
||||
"owner": "loqusion",
|
||||
"repo": "typix",
|
||||
"rev": "62d032735ad32a9a90225c06cb0857677fc753ee",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "loqusion",
|
||||
"repo": "typix",
|
||||
"type": "github"
|
||||
}
|
||||
},
|
||||
"typst-packages": {
|
||||
"flake": false,
|
||||
"locked": {
|
||||
"lastModified": 1729252723,
|
||||
"narHash": "sha256-xdaQYNw1GApaJnXJO4WnUTNuYeRXisxIUSuAzVXFEW4=",
|
||||
"owner": "typst",
|
||||
"repo": "packages",
|
||||
"rev": "9bcf190c85da91be6df9f5fc25a93ce5812489cc",
|
||||
"type": "github"
|
||||
},
|
||||
"original": {
|
||||
"owner": "typst",
|
||||
"repo": "packages",
|
||||
"type": "github"
|
||||
}
|
||||
}
|
||||
},
|
||||
"root": "root",
|
||||
"version": 7
|
||||
}
|
126
2024/work/phil-1/paper-1-typix/flake.nix
Normal file
126
2024/work/phil-1/paper-1-typix/flake.nix
Normal file
|
@ -0,0 +1,126 @@
|
|||
{
|
||||
description = "A Typst project";
|
||||
|
||||
inputs = {
|
||||
nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
|
||||
|
||||
typix = {
|
||||
url = "github:loqusion/typix";
|
||||
inputs.nixpkgs.follows = "nixpkgs";
|
||||
};
|
||||
|
||||
flake-utils.url = "github:numtide/flake-utils";
|
||||
|
||||
typst-packages = {
|
||||
url = "github:typst/packages";
|
||||
flake = false;
|
||||
};
|
||||
|
||||
# Example of downloading icons from a non-flake source
|
||||
# font-awesome = {
|
||||
# url = "github:FortAwesome/Font-Awesome";
|
||||
# flake = false;
|
||||
# };
|
||||
};
|
||||
|
||||
outputs =
|
||||
inputs@{
|
||||
nixpkgs,
|
||||
typix,
|
||||
flake-utils,
|
||||
...
|
||||
}:
|
||||
flake-utils.lib.eachDefaultSystem (
|
||||
system:
|
||||
let
|
||||
pkgs = nixpkgs.legacyPackages.${system};
|
||||
in
|
||||
let
|
||||
typstPackagesSrc = "${inputs.typst-packages}/packages";
|
||||
|
||||
typstPackagesCache = pkgs.stdenv.mkDerivation {
|
||||
name = "typst-packages-cache";
|
||||
src = typstPackagesSrc;
|
||||
dontBuild = true;
|
||||
installPhase = ''
|
||||
mkdir -p "$out/typst/packages"
|
||||
cp -LR --reflink=auto --no-preserve=mode -t "$out/typst/packages" "$src"/*
|
||||
'';
|
||||
};
|
||||
in
|
||||
let
|
||||
inherit pkgs;
|
||||
typixLib = typix.lib.${system};
|
||||
|
||||
src = typixLib.cleanTypstSource ./.;
|
||||
commonArgs = {
|
||||
typstSource = "main.typ";
|
||||
|
||||
fontPaths = [
|
||||
# Add paths to fonts here
|
||||
# "${pkgs.roboto}/share/fonts/truetype"
|
||||
];
|
||||
|
||||
virtualPaths = [
|
||||
# Add paths that must be locally accessible to typst here
|
||||
# {
|
||||
# dest = "icons";
|
||||
# src = "${inputs.font-awesome}/svgs/regular";
|
||||
# }
|
||||
];
|
||||
};
|
||||
|
||||
# Compile a Typst project, *without* copying the result
|
||||
# to the current directory
|
||||
build-drv = typixLib.buildTypstProject (
|
||||
commonArgs
|
||||
// {
|
||||
inherit src;
|
||||
XDG_CACHE_HOME = typstPackagesCache;
|
||||
}
|
||||
);
|
||||
|
||||
# Compile a Typst project, and then copy the result
|
||||
# to the current directory
|
||||
build-script = typixLib.buildTypstProjectLocal (
|
||||
commonArgs
|
||||
// {
|
||||
inherit src;
|
||||
XDG_CACHE_HOME = typstPackagesCache;
|
||||
}
|
||||
);
|
||||
|
||||
# Watch a project and recompile on changes
|
||||
watch-script = typixLib.watchTypstProject commonArgs;
|
||||
in
|
||||
{
|
||||
checks = {
|
||||
inherit build-drv build-script watch-script;
|
||||
};
|
||||
|
||||
packages.default = build-drv;
|
||||
|
||||
apps = rec {
|
||||
default = watch;
|
||||
build = flake-utils.lib.mkApp {
|
||||
drv = build-script;
|
||||
};
|
||||
watch = flake-utils.lib.mkApp {
|
||||
drv = watch-script;
|
||||
};
|
||||
};
|
||||
|
||||
devShells.default = typixLib.devShell {
|
||||
inherit (commonArgs) fontPaths virtualPaths;
|
||||
packages = [
|
||||
# WARNING: Don't run `typst-build` directly, instead use `nix run .#build`
|
||||
# See https://github.com/loqusion/typix/issues/2
|
||||
# build-script
|
||||
watch-script
|
||||
# More packages can be added here, like typstfmt
|
||||
pkgs.typstyle
|
||||
];
|
||||
};
|
||||
}
|
||||
);
|
||||
}
|
2
2024/work/phil-1/paper-1-typix/main.typ
Normal file
2
2024/work/phil-1/paper-1-typix/main.typ
Normal file
|
@ -0,0 +1,2 @@
|
|||
= Lorem ipsum
|
||||
#lorem(30)
|
BIN
2024/work/phil-1/paper-1/main.pdf
Normal file
BIN
2024/work/phil-1/paper-1/main.pdf
Normal file
Binary file not shown.
302
2024/work/phil-1/paper-1/main.typ
Normal file
302
2024/work/phil-1/paper-1/main.typ
Normal file
|
@ -0,0 +1,302 @@
|
|||
#import "@preview/unequivocal-ams:0.1.1": ams-article, theorem, proof
|
||||
#import "@preview/wordometer:0.1.3": word-count, total-words
|
||||
|
||||
#import "prelude.typ": indented-argument
|
||||
|
||||
#show: ams-article.with(
|
||||
title: [The Argument for Betting on God and the Possibility of Infinite Suffering],
|
||||
bibliography: bibliography("refs.bib"),
|
||||
)
|
||||
|
||||
#show: word-count.with(exclude: (heading, <wordcount-exclude>, table))
|
||||
|
||||
#align(
|
||||
center,
|
||||
table(
|
||||
columns: (auto, auto),
|
||||
[
|
||||
Perm: A2V4847
|
||||
],
|
||||
[
|
||||
Word Count: #total-words
|
||||
#footnote[
|
||||
Figure computed programmatically during document compilation. Discounts
|
||||
content in tables and the AI contribution statement.
|
||||
]<wordcount-exclude>
|
||||
],
|
||||
),
|
||||
)
|
||||
|
||||
|
||||
= Introduction
|
||||
|
||||
The argument for Betting on God says that you should believe in God, regardless
|
||||
of other evidence, purely out of self-interest. In this paper, I challenge this
|
||||
argument by assessing the premise that believing in a particular God always
|
||||
guarantees the greatest expected utility.
|
||||
|
||||
The author's argument for belief in God #cite(supplement: [p. 38],
|
||||
<Korman2022-KORLFA>) goes as follows:
|
||||
|
||||
#indented-argument(
|
||||
title: "The Argument for Betting on God",
|
||||
abbreviation: "BG",
|
||||
[One should always choose the option with the greatest expected utility.],
|
||||
[Believing in God has a greater expected utility than not believing in God.],
|
||||
[So, you should believe in God.],
|
||||
)
|
||||
|
||||
BG1 should be uncontroversial. If you expect an action to bring you the most
|
||||
utility (i.e. be the most useful), it's rational to do it.
|
||||
|
||||
To justify BG2, the author uses a so-called "decision matrix" to compute the
|
||||
expected utility of each combination of action and possible outcome. The
|
||||
possible actions are placed on the rows, and the possible outcomes are placed
|
||||
on the columns, except for the last column, which is the calculated expected
|
||||
utility. At each intersection of a row and column, we place the utility we gain
|
||||
from that combination of action and outcome. The expected utility for a given
|
||||
action is computed by multiplying the utility of each action-outcome pair in
|
||||
that row by the probability of the corresponding outcome occurring, and summing
|
||||
up all of those values.
|
||||
|
||||
Here is the decision matrix the author proposes on #cite(supplement: [p. 38],
|
||||
<Korman2022-KORLFA>) which gives the expected utility for believing or not
|
||||
believing in God.
|
||||
|
||||
#show table.cell.where(x: 0): strong
|
||||
#show table.cell.where(y: 0): strong
|
||||
|
||||
#figure(
|
||||
caption: [Author's decision matrix],
|
||||
align(
|
||||
center,
|
||||
table(
|
||||
columns: (auto, auto, auto, auto),
|
||||
table.header(
|
||||
[],
|
||||
[God exists ($50%$)],
|
||||
[God doesn't exist ($50%$)],
|
||||
[Expected utility],
|
||||
),
|
||||
|
||||
[ Believe in God ], [$infinity$], [2], [$infinity$],
|
||||
[
|
||||
Don't believe in God
|
||||
],
|
||||
[1],
|
||||
[3],
|
||||
[2],
|
||||
),
|
||||
),
|
||||
)
|
||||
|
||||
Note that the numerical utility values themselves have no meaning, and they are
|
||||
meant to be viewed relative to each other. Utility doesn't literally provide an
|
||||
empirical measure of "usefulness" or "happiness."
|
||||
|
||||
We assign the various finite utilities as we see fit, based on how much each
|
||||
scenario benefits us. In the case where God does exist, and you believed in
|
||||
God, then you are rewarded with an eternal afterlife of bliss and pleasure in
|
||||
heaven. This reward is infinitely greater than any possible reward on earth, so
|
||||
it has a utility of $infinity$.
|
||||
|
||||
So, the expected utility for not believing is $0.5 times 1 + 0.5 times 3 = 2$,
|
||||
and the expected utility is $0.5 times infinity + 0.5 times 2 = infinity$. If,
|
||||
according to BG1, you should pick the option with greatest expected utility,
|
||||
clearly you should choose to believe in God, because the expected utility is
|
||||
$infinity$.
|
||||
|
||||
The exact utilities don't matter much, since any finite utility you could gain
|
||||
for atheism cannot possibly be greater than the infinite expected utility of
|
||||
believing in God. Also, as the author points out on #cite(<Korman2022-KORLFA>,
|
||||
supplement: [p. 40]), the exact probabilities don't matter either since
|
||||
multiplying them by $infinity$ still results in the expected utility of
|
||||
$infinity$.
|
||||
|
||||
I will show that the Argument for Betting on God fails because BG2 fails. In
|
||||
section 2, I argue you cannot determine whether or not believing in God has the
|
||||
greatest expected utility because the decision matrix approach fails when
|
||||
possible outcomes involving infinitely negative utilities are introduced. In
|
||||
section 3, I address a possible response to this objection.
|
||||
|
||||
= Possibility of Infinite Suffering
|
||||
|
||||
It is possible there are more gods than just the one that sends you to an
|
||||
eternal afterlife for believing? The author partially addresses this in
|
||||
#cite(<Korman2022-KORLFA>, supplement: [pp. 43-44]), using the example of Zeus.
|
||||
Zeus will only reward those who believe in him with an eternal afterlife of
|
||||
pleasure. So, if you believe in the wrong god, you don't go to the afterlife.
|
||||
The author concludes either believing in Zeus or the Christian God still has
|
||||
expected utilities of $infinity$, while being an atheist does has a finite
|
||||
expected utility. Therefore, it is still preferable to believe in _some_ god
|
||||
that may grant you an eternal afterlife, although no argument is made for
|
||||
_which_ god.
|
||||
|
||||
However, this leaves out the possibility of gods who punish you for some
|
||||
reason. For instance, suppose there exists an _Evil God_ who sends anyone who
|
||||
believes in any god to hell for eternity, and does nothing to atheists.
|
||||
|
||||
Let us modify our decision matrix to model an outcome where the Evil God
|
||||
exists.
|
||||
|
||||
#pagebreak()
|
||||
|
||||
#[
|
||||
#set figure()
|
||||
#figure(
|
||||
caption: [Possibility of an Evil God],
|
||||
table(
|
||||
columns: (auto, auto, auto, auto, auto),
|
||||
align: center,
|
||||
table.header(
|
||||
[],
|
||||
[Correct god exists ($33.3%$)],
|
||||
[No god exists ($33.3%$)],
|
||||
[Evil God exists ($33.3%$)],
|
||||
[E.U.],
|
||||
),
|
||||
|
||||
[ Believe in some God ], [$infinity$], [1], [$-infinity$], [$?$],
|
||||
[
|
||||
Don't believe in any God
|
||||
],
|
||||
[2],
|
||||
[3],
|
||||
[4],
|
||||
[4.5],
|
||||
),
|
||||
)
|
||||
]<other-gods-table>
|
||||
|
||||
We've added the new option to our matrix. For the sake of argument, let's say
|
||||
each option has an equally likely outcome. Again, the exact probabilities don't
|
||||
really matter when we're multiplying them by infinity.
|
||||
|
||||
The utilities are mostly the same as before. Not believing in any god and the
|
||||
Evil God existing is now the best case for the atheist since they avoided
|
||||
infinite suffering. However, the theist now faces the possibility of the worst
|
||||
case of all: eternal punishment for believing in the wrong god. If eternal
|
||||
bliss in heaven has a utility of $infinity$, then it follows that we should
|
||||
represent eternal punishment in hell with a utility of $-infinity$.
|
||||
|
||||
There is a problem: how do we calculate the expected utility of believing in
|
||||
god? We have $0.333 times infinity + 0.333 times 1 + 0.333 times -infinity$.
|
||||
What is $infinity - infinity$? A naive answer might be 0, but infinity is not a
|
||||
number in the traditional sense. It makes no sense to add or subtract infinite
|
||||
values. For instance, try and subtract the total amount of integers
|
||||
($infinity$) from the total amount of real numbers (also $infinity$)
|
||||
#footnote[Famously, this infinity is "larger" than the infinite number of
|
||||
integers in the sense of cardinality (G. Cantor). But subtracting them still
|
||||
makes no mathematical or physical sense.]. Clearly, this notion is meaningless
|
||||
and we cannot obtain a solution. So, we consider $infinity - infinity$ an
|
||||
_indeterminate form_. So, the expected utility is now _undefined_.
|
||||
|
||||
Consider the following Indeterminate Utilities argument:
|
||||
|
||||
#indented-argument(
|
||||
title: "The Indeterminate Utilities argument",
|
||||
abbreviation: "IU",
|
||||
[If the expected utility of believing in god is undefined, then we
|
||||
cannot compare the expected utilities of believing in god or not believing
|
||||
in god.],
|
||||
[The expected utility of believing in god is undefined.],
|
||||
[So, we cannot compare the expected utilities of believing in god or
|
||||
not believing in god.
|
||||
],
|
||||
[If we cannot compare the expected utilities of believing in god or
|
||||
not believing in god, then we cannot determine if believing in god has a
|
||||
higher expected utility than not believing in god.
|
||||
],
|
||||
[So, we cannot determine if believing in god has a higher expected
|
||||
utility than not believing in god. ],
|
||||
)<wordcount-exclude>
|
||||
|
||||
We just showed why the premise IU2 is true, and the conclusion IU5 is in direct
|
||||
contradiction with BG2. So, if IU5 holds, then BG2 must fail.
|
||||
|
||||
It's important to note that the Indeterminate Utilities argument doesn't say
|
||||
that the _opposite_ of BG2 is true. It doesn't argue that the expected utility
|
||||
of being an atheist is greater. In fact, it doesn't say anything about the
|
||||
expected utilities, except that they cannot be compared. If they can't be
|
||||
compared, then we can't say for certain which option has the higher expected
|
||||
utility. Since BG2 claims that believing in god must have the higher expected
|
||||
utility, it is a false premise.
|
||||
|
||||
= Addressing Objections
|
||||
|
||||
// == Believing in a god is still preferable to atheism
|
||||
//
|
||||
// One might argue that believing in a god that rewards believers is always
|
||||
// preferable to atheism since you at least have the _opportunity_ to receive
|
||||
// eternity in heaven. Perhaps there exists a god who punishes non-believers with
|
||||
// eternal damnation. Then, even without the exact expected utility calculation,
|
||||
// it's clear that the expected utility of believing in some god must be higher
|
||||
// than believing in none as you stand to gain more. Either as a theist or
|
||||
// atheist, you run the risk of eternal punishment, but you only have the
|
||||
// opportunity to go to heaven by believing in some god rather than none.
|
||||
//
|
||||
// Fair, the possibility that you are punished for believing in the wrong god
|
||||
// doesn't imply that you should be an atheist either. Indeed, there may be a god
|
||||
// that punishes atheists. However, there could also exist a god who sends
|
||||
// everyone to heaven regardless. Or perhaps they only send atheists to heaven.
|
||||
// Either way, there is also the possibility of attaining the infinite afterlife
|
||||
// in heaven by being an atheist, so it's still impossible to say that the
|
||||
// expected utility of believing in god is must be higher.
|
||||
|
||||
== The Evil God is not plausible
|
||||
|
||||
One might argue that it is not plausible there is an Evil God who punishes all
|
||||
theists, including their own believers. Many religions present a god that
|
||||
rewards believers and at most punishes disbelievers. None of the major world
|
||||
religions propose an Evil God who punishes all believers. It's much more likely
|
||||
that a benevolent god exists than an evil one.
|
||||
|
||||
I contend that it doesn't matter whether or not the Evil God is less plausible
|
||||
than a benevolent god. Surely, if a rational atheist who is unconvinced by all
|
||||
the world's scriptures can still concede that there is at least a non-zero
|
||||
chance that some god exists, the rational theist should also concede that there
|
||||
is a non-zero chance that the Evil God exists. All it takes is that non-zero
|
||||
chance, no matter how small, because multiplying it by $-infinity$ still
|
||||
results in the undefined expected utility.
|
||||
|
||||
== Finite utilities
|
||||
|
||||
One might argue that we can avoid using $infinity$ to ensure that all expected
|
||||
utility calculations are defined. Instead, suppose that the utility of going to
|
||||
heaven is just an immensely large finite number. The utility of going to hell
|
||||
is likewise a very negative number. All of our expected utility calculations
|
||||
will be defined, and given sufficiently large utilities, we should be able to
|
||||
make a similar argument for believing in god.
|
||||
|
||||
// The problem with this argument is that we now open our expected utilities up to
|
||||
// individual subjective determination. A core feature of the previous argument
|
||||
// involving infinite utilities is that they can effectively bypass numerical
|
||||
// comparison. If, instead, finite utilities were used, then each person may
|
||||
// assign different utilities to each possible outcome based on their own beliefs.
|
||||
// Also, the probabilities are no longer irrelevant, so they must be analyzed as
|
||||
// well. This greatly complicates the decision matrix.
|
||||
|
||||
The problem with this argument is that infinity has a special property the
|
||||
argument relies on. Namely, any number multiplied by $infinity$ is still
|
||||
$infinity$, so the exact probabilities we set for the existence of God don't
|
||||
matter. This is important for defending against the objection the author
|
||||
mentions on #cite(<Korman2022-KORLFA>, supplement: [p. 40]), that the
|
||||
probabilities are possibly incorrect, since the numbers don't matter anyways.
|
||||
|
||||
If, instead, only finite utilities were used, then the theist must contend with
|
||||
the concern that the probabilities in the matrix are wrong. There could
|
||||
conceivably exist a matrix with probabilities for a benevolent god and an Evil
|
||||
God such that the expected utility of atheism is actually higher. The issue is
|
||||
we cannot say for sure what the probabilities of the benevolent god and the
|
||||
Evil God existing are. If we cannot know what the actual probabilities are,
|
||||
then we cannot know the final outcome of our matrix. So, without knowing the
|
||||
final outcome of the matrix, we still cannot determine whether or not believing
|
||||
in god has greater expected utility, and BG2 still fails.
|
||||
|
||||
#pagebreak()
|
||||
|
||||
#[
|
||||
= AI Contribution Statement
|
||||
|
||||
#quote[I did not use AI whatsoever in the writing of this paper.]
|
||||
]<wordcount-exclude>
|
49
2024/work/phil-1/paper-1/package.nix
Normal file
49
2024/work/phil-1/paper-1/package.nix
Normal file
|
@ -0,0 +1,49 @@
|
|||
{
|
||||
pkgs,
|
||||
typstPackagesCache,
|
||||
typixLib,
|
||||
...
|
||||
}:
|
||||
let
|
||||
src = typixLib.cleanTypstSource ./.;
|
||||
commonArgs = {
|
||||
typstSource = "main.typ";
|
||||
|
||||
fontPaths = [
|
||||
# Add paths to fonts here
|
||||
# "${pkgs.roboto}/share/fonts/truetype"
|
||||
];
|
||||
|
||||
virtualPaths = [
|
||||
# Add paths that must be locally accessible to typst here
|
||||
# {
|
||||
# dest = "icons";
|
||||
# src = "${inputs.font-awesome}/svgs/regular";
|
||||
# }
|
||||
];
|
||||
|
||||
XDG_CACHE_HOME = typstPackagesCache;
|
||||
};
|
||||
|
||||
# Compile a Typst project, *without* copying the result
|
||||
# to the current directory
|
||||
build-drv = typixLib.buildTypstProject (
|
||||
commonArgs
|
||||
// {
|
||||
inherit src;
|
||||
}
|
||||
);
|
||||
|
||||
# Compile a Typst project, and then copy the result
|
||||
# to the current directory
|
||||
build-script = typixLib.buildTypstProjectLocal (
|
||||
commonArgs
|
||||
// {
|
||||
inherit src;
|
||||
}
|
||||
);
|
||||
|
||||
# Watch a project and recompile on changes
|
||||
watch-script = typixLib.watchTypstProject commonArgs;
|
||||
in
|
||||
build-drv
|
21
2024/work/phil-1/paper-1/prelude.typ
Normal file
21
2024/work/phil-1/paper-1/prelude.typ
Normal file
|
@ -0,0 +1,21 @@
|
|||
#set cite(style: "institute-of-electrical-and-electronics-engineers")
|
||||
#set text(fractions: true)
|
||||
|
||||
#let indented-argument(title: "", abbreviation: "", ..args) = [
|
||||
#set par(first-line-indent: 0pt)
|
||||
|
||||
#pad(left: 12pt, smallcaps(title))
|
||||
|
||||
#let arg-numbering = (..nums) => nums.pos().map(n => (
|
||||
"(" + abbreviation + str(n) + ")"
|
||||
)).join()
|
||||
|
||||
#enum(
|
||||
numbering: arg-numbering,
|
||||
indent: 16pt,
|
||||
tight: false,
|
||||
..args.pos(),
|
||||
)
|
||||
]
|
||||
|
||||
|
7
2024/work/phil-1/paper-1/refs.bib
Normal file
7
2024/work/phil-1/paper-1/refs.bib
Normal file
|
@ -0,0 +1,7 @@
|
|||
@book{Korman2022-KORLFA,
|
||||
author = {Daniel Z. Korman},
|
||||
editor = {},
|
||||
publisher = {The PhilPapers Foundation},
|
||||
title = {Learning From Arguments: An Introduction to Philosophy},
|
||||
year = {2022}
|
||||
}
|
Loading…
Reference in a new issue