main.tex

%% INDEX: logical construction; model isomorphism criterion [taking
%% stock section] and how it relates to cardinality constraint;
%% regimentation; conjunction objection; Goodmania; empirical
%% equivalence; conjunction objection; constructive empiricism;
%% implicit definition; Ramsey eliminable; Craig's theorem;
%% instrumentalism; constructive empiricism; Ramsey sentence; Beth's
%% theorem; functionalism; Nagelian reduction; new wave reduction;
%% gauge theory; ontological commitment; external question; logical
%% construction [[TO DO]]

%% TO DO

%% -- quantifier variance and Maximalism

%% MISTAKE.  Grandy 1992: "associated with each set of first-order
%% sentences is a class of models. And those models are abstract and
%% language-independent."  Compare also with statement from Psillos

%% -1. Semantics as the middle man.  Doesn't this also effect Hartry
%% Field's program -- the idea here being that ... what is this
%% nominalization strategy, as if set theory were somehow in direct
%% touch with reality ...

%% -1.5. Relative consistency.  The Frege Hilbert debate?

%% ** Neil Dewar's paper

%% ** Intended model (Suppe, Hellman)

%% ** Galilean spacetime -- symmetries.  Who is it (explicitly) that
%% advocates the quotienting strategy?  Superfluous structure??  Simon
%% Saunders??  

%% 0. Re-read what Scientific Theories could not be

%% 1. Talk about the *error* of the quotient strategy, for example, in
%% saying that there is only "one" model of Galilean spacetime.  This
%% can also be illustrated with simple examples from FOL, for example
%% the theory that says there are exactly two things

%% 2. Loose talk about reduction -- David Wallace on finding the world
%% in a wavefunction

%% 3. Loose talk about realism -- the world as isomorphic to a
%% mathematical model.

%% BE ABSOLUTELY CLEAR ABOUT why the model isomorphism criterion has
%% to go!!

%% 4. conjunction objection (Putnam, Boyd, Hawthorne1996)

%% Morita <=> Inter-trans

%% Fewster -- GTR as a category

%% Reduction, Bickle

%% 5. observation sentences; Turney; Musgrave and Dicken -- return to
%% this at least three times over, first in syntactic-1, then in
%% semantic-1, then in syntactic-2; cross reference with table in
%% introduction

%% natural properties

%% Finish intro

%% Finish Realism

%% Revise Scientific Theories


\documentclass[12pt,fleqn,toc]{book}
\usepackage{array,multirow,amsthm,amsmath,amssymb,url}
% \usepackage[osf,sc]{mathpazo}
% Helvetica for sans serif
% (scaled to match size of Palatino)
% \usepackage[scaled=0.90]{helvet}
% Bera Mono for monospaced
% (scaled to match size of Palatino)
% \usepackage[scaled=0.85]{beramono}
% \usepackage{fullpage}
\numberwithin{section}{chapter}
\numberwithin{subsection}{section}
\newcommand{\RA}{\vdash}
\usepackage{verbatim}
\usepackage{mVersion}
\usepackage{natbib}
\usepackage{bussproofs}
\usepackage{tikz}
\tikzset{node distance=1.6cm, auto}
\usepackage{tikz-cd}
\usetikzlibrary{trees}
\usetikzlibrary{decorations.markings}
\tikzset{strike through/.append style={
    decoration={markings, mark=at position 0.5 with {
    \draw[-] ++ (-3pt,-3pt) -- (3pt,3pt);}
  },postaction={decorate}}
}
\usepackage{pdflscape}
\usepackage{float}
\title{The Logic in Philosophy of Science}
\author{Hans Halvorson}
\date{Version of July 25, 2018}
% \setlength{\parindent}{0em}
% \setlength{\parskip}{1em}
\swapnumbers
\newtheorem{prop}{Proposition}
\numberwithin{prop}{section}
\newtheorem{thm}[prop]{Theorem}
\newtheorem{cor}[prop]{Corollary}
\newtheorem{lemma}[prop]{Lemma}
\newtheorem{claim}[prop]{Claim}
\newtheorem{fact}[prop]{Fact}
\newtheorem*{subthm}{Substitution Theorem}
\newtheorem*{rthm}{Replacement Theorem}
\newtheorem{conj}[prop]{Conjecture}
\theoremstyle{definition}
\newtheorem{defn}[prop]{Definition}
\newtheorem{ass}[prop]{Assumption}
\newtheorem{exercise}[prop]{Exercise}
\newtheorem{exm}[prop]{Example}
\newtheorem{question}[prop]{Question}
\newtheorem{disc}[prop]{Discussion}
\newtheorem{aside}[prop]{Technical Aside}
\newtheorem{tomt}[prop]{}
% \theoremstyle{remark}
%% what I want here is for the label to be bold (like Proposition),
%% but for the text to be regular
\newtheorem{note}[prop]{Note}

\newenvironment{example}{\begin{exm}}{\hfill $\lrcorner$\end{exm}}


\swapnumbers

% \usepackage{fbb}
\newcommand{\df}[1]{\textbf{#1}}
\usepackage{mathrsfs}
\newcommand{\2}{\mathscr}
\renewcommand{\emph}{\textbf}
\newcommand{\vp}{\phi}
\newcommand{\ol}[1]{\overline{#1}}
\newcommand{\ve}{\epsilon}
\newcommand{\tp}[2]{\mathrm{tp}^{#1}(#2)}
\usepackage{marvosym}

\usepackage[framemethod=TikZ]{mdframed}
% \newcounter{axi}\setcounter{axi}{0}
% \renewcommand{\theaxi}{\arabic{axi}}
% \newenvironment{axi}[2][]{%
%     \refstepcounter{axi}
%  \ifstrempty{#1}%
% % if condition (without title)
% {\mdfsetup{%
%     frametitle={%
%         \tikz[baseline=(current bounding box.east),outer sep=0pt]
%         \node[anchor=east,rectangle,fill=blue!20]
%         {\strut Definition};}
%     }%
% % else condition (with title)
% }{\mdfsetup{%
%     frametitle={%
%         \tikz[baseline=(current bounding box.east),outer sep=0pt]
%         \node[anchor=east,rectangle,fill=blue!20]
%         {\strut Definition};}%
%     }%
% }%
% % Both conditions
% \mdfsetup{%
%     skipabove=2em,
%     skipbelow=2em,
%     innertopmargin=10pt,linecolor=blue!20,%
%     linewidth=2pt,topline=true,%
%     frametitleaboveskip=\dimexpr-\ht\strutbox\relax%
% }
% \begin{mdframed}[]\relax}{%
% \end{mdframed}}

\newcounter{axi}\setcounter{axi}{0}
\renewcommand{\theaxi}{\arabic{axi}}
\newenvironment{axi}[2][]{%
    \refstepcounter{axi}
 \ifstrempty{#1}%
% if condition (without title)
{\mdfsetup{%
    frametitle={%
        \tikz[baseline=(current bounding box.east),outer sep=0pt]
        \node[anchor=east,rectangle,fill=blue!20]
        {\strut Axiom~\theaxi};}
    }%
% else condition (with title)
}{\mdfsetup{%
    frametitle={%
        \tikz[baseline=(current bounding box.east),outer sep=0pt]
        \node[anchor=east,rectangle,fill=blue!20]
        {\strut Axiom~\theaxi:~#1};}%
    }%
}%
% Both conditions
\mdfsetup{%
    skipabove=2em,
    skipbelow=2em,
    innertopmargin=10pt,linecolor=blue!20,%
    linewidth=2pt,topline=true,%
    frametitleaboveskip=\dimexpr-\ht\strutbox\relax%
}
\begin{mdframed}[]\relax}{%
\end{mdframed}}


\usepackage{makecell}



\newcommand{\cat}[1]{\mathbf{#1}}
\newcommand{\bax}{\begin{mdframed}\begin{axiom}}
\newcommand{\eax}{\end{axiom}\end{mdframed}}
\newcommand{\ch}[1]{\raisebox{2pt}{$\chi$}_{#1}}
\newcommand{\monic}{\rightarrowtail}
\newcommand{\epi}{\twoheadrightarrow}
\newcommand{\lra}{\leftrightarrow}
\newcommand{\cn}[1]{\mathrm{Cn}(#1)}

\newenvironment{box-thm}[1][]{%
\mdfsetup{%
    frametitle={%
        \tikz[baseline=(current bounding box.east),outer sep=0pt]
        \node[anchor=east,rectangle,fill=blue!20]
        {\strut #1};},%
    skipabove=2em,
    skipbelow=2em,
    innertopmargin=10pt,linecolor=blue!20,%
    linewidth=2pt,topline=true,%
    frametitleaboveskip=\dimexpr-\ht\strutbox\relax }
\begin{mdframed}[]\relax}{%
\end{mdframed}}

\newcommand{\7}{\mathbb}

\newtheorem{exercises}{Exercises}



% \includeonly{intro2}

% \includeonly{meta}

% \includeonly{cat-set}

% \includeonly{pred-syntactic}

% \includeonly{second-syntactic}

% \includeonly{pred-semantic}

% \includeonly{mo-semantic}

% \includeonly{science}

% \includeonly{belief}

% \includeonly{realism}

% \includeonly{putnam}


\begin{document}

\frontmatter

\maketitle



\clearpage
\vspace*{\fill}
\thispagestyle{empty} % optional -- suppress showing of page number

\begin{quotation}
  \noindent \large {\em The worse your logic, the more interesting the
    \mbox{consequences}.}

\medskip
\raggedleft
Bertrand Russell
\end{quotation}
\bigskip

\begin{quotation}
  \large {\em Philosophy of science is philosophy enough.}

\medskip
\raggedleft
W.v.O. Quine
\end{quotation}

% \bigskip

% \begin{quotation}
%   \large {\em Of making many books there is no end, and much study
%     wearies the body.}

%   \medskip
%   \raggedleft
%   Ecclesiastes 12:12 \end{quotation}

\tableofcontents

\chapter{Preface}

The 20th century's most interesting philosophers were enthralled by
the revolution in mathematical logic, and they accordingly clothed
many of their arguments in a formal garb.  For example, Hilary Putnam
claimed that the L\"owenheim-Sk{\o}lem theorem reduces metaphysical
realism to absurdity.  And Bas van Fraassen claimed that scientific
antirealism can withstand criticism only by embracing the semantic
view of theories.  And W.v.O. Quine claimed that Carnap's notion of an
``external question'' is incoherent since every many-sorted theory is
equivalent to a single-sorted theory.

Lack of knowledge of mathematical logic can be a huge obstacle to
understanding these philosophers' arguments, and this book is my
attempt to help overcome that obstacle.  However, my ideal reader is
not the casual student of 20th century philosophy, who is content to
skim along the surface of the debates.  My ideal reader is the
aspiring philosopher who wants the tools to strip these arguments down
to their logical nuts and bolts.

My original intention in writing this book was not to get across some
philosophical point.  However, a few such points emerged along the
way.  First, the distinction between realism and antirealism really
boils down to one's attitude toward theoretical equivalence.  Realists
are people with a conservative notion of equivalence, and antirealists
are people with a liberal notion of equivalence.  Second, and
relatedly, to give a philosophical account of a relation between
theories (e.g.\ equivalence, reducibility) is tantamount to
recommending certain norms of inquiry.  For example, if you say that
two theories $T$ and $T'$ are equivalent, then you mean (among other
things) that any reason for accepting $T$ is also a reason for
accepting $T'$.  Hence, you won't bother trying to design an
experiment that would test $T$ against $T'$.  Similarly, if you find
two people arguing --- one of them accepts $T$ and the other accepts
$T'$ --- then you will view them as committing a kind of mistake.  In
short, to adopt a view on relations between theories is to adopt
certain rules about how to use those theories.

I should explain one glaring omission from this book: modal logic.  I
didn't leave out modal logic because I'm a Quinean extensionalist.  To
the contrary, I've come to think that the metatheory of extensional
logic is a kind of intensional logic.  For example, the models of a
scientific theory are the nomologically possible worlds according to
the theory.  Furthermore, a scientific theory comes equipped with a
notion of ``natural properties'' (in the sense of David Lewis), and
these natural properties determine a notion of similarity between
possible worlds, which in turn licenses certain counterfactual
inferences.  So, while my goal is to theorize about the extensional
logic that is used in the sciences, I believe that doing so calls for
involvement with intensional concepts.

% I hope then that this book contributes to the recognition that, {\it
%   pace} Quine, the metatheory of scientific theories is not just more
% science.  To the contrary, metatheory can and should serve to clarify
% normative questions such as, ``when should we say that two theories
% are equivalent?''  I realize that I'm defying descriptivist orthodoxy,
% according to which there should be a fact of the matter about which
% theories are equivalent.  Instead, I follow Carnap in thinking that
% metatheory is the place to put forward proposals --- only I think,
% {\it pace} Carnap, that a ``good'' proposal is something more than a
% proposal whose implementation would lead to my desires being
% fulfilled.

\bigskip

{\it Acknowledgements:} Thanks to Bas van Fraassen for the inspiration
to pursue philosophy of science both as a science and as an art.

The idea behind this book arose during a year I spent in Utrecht
studying category theory.  I thank the Mellon New Directions
Fellowship for financing that year.  Thanks to my Dutch hosts (Klaas
Landsman, Ieke Moerdijk, and Jaap van Oosten) for their warm
hospitality.

When I returned home, I rediscovered that it's difficult to do two (or
fifty) things at once.  The project's continued life is largely due to
the efforts of four amazing students: Thomas Barrett, Neil Dewar,
Dimitris Tsementzis and Evan Washington.  They proved many of the new
results in this book.  I also found my philosophical views shaped and
sharpened by conversations with several students and colleagues,
especially John Burgess, Ellie Cohen, Robbie Hirsch, Laurenz Hudetz,
Michaela McSweeney, Alex Meehan, Gideon Rosen, Elliot Salinger, David
Schroeren, and Jim Weatherall.  I probably left somebody out, and I'm
sorry about that.  For comments and corrections on earlier versions of
the manuscript, I thank Thomas Barrett, Gordon Belot, Neil Dewar,
Harvey Lederman, Dimitris Tsementzis and Isaac Wilhelm.

Thank you to my editors at Cambridge --- Hilary Gaskin and Sophie
Taylor --- for their patience and persistence.






\mainmatter

%% little pieces to include

%% concept-index

%% observability

%% reduction


\include{intro2}
\include{meta}
\include{cat-set}
\include{cat-prop}
\include{pred-syntactic}
\include{second-syntactic}
\include{pred-semantic}
\include{mo-semantic}
% \include{science}
% \include{putnam}
\include{realism}
% \include{belief}







%% Proof: CDE iff Intertranslatable

%% Proof: Morita iff Intertranslatable

\backmatter

\bibliographystyle{apalike}
\bibliography{/Users/hhalvors/book/masterbib}






\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: