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| -rw-r--r-- | papers/1.tex | 2 | ||||
| -rw-r--r-- | papers/4.tex | 28 |
2 files changed, 15 insertions, 15 deletions
diff --git a/papers/1.tex b/papers/1.tex index 2b4704c..a5359a9 100644 --- a/papers/1.tex +++ b/papers/1.tex @@ -57,7 +57,7 @@ atheists/non-theists and theists alike.\footnote{When I say, ``God'' and omnibenevolent singular/simple creator.} He identifies a tension between two widely held theses: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \item Systemic evil: The process of natural selection necessitates diff --git a/papers/4.tex b/papers/4.tex index c554976..02a19a2 100644 --- a/papers/4.tex +++ b/papers/4.tex @@ -80,7 +80,7 @@ logic is topic neutral, because a schema abstracts from the content of the sentence, only retaining the form of the sentence. For example, take the following sentence: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \item Pigeons wear vests and cats wear hats. @@ -88,7 +88,7 @@ the following sentence: \noindent This sentence can be expressed using the following schema: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{1} \item @@ -136,7 +136,7 @@ Therefore, I define formal validity to be the following: an argument is formally valid iff it has a form which has only valid instances. An example of a formally valid argument is: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{2} \item @@ -148,7 +148,7 @@ described above. Given the use of quantifiers in (3), the schema of the argument is simply its first order formalisation (on the obvious formalisation key): -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{3} @@ -199,7 +199,7 @@ valid. Materially valid arguments are arguments in which the validity of the argument is in part due to the meaning of the non-logical terms involved. An example of a materially valid argument is: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{4} \item @@ -220,7 +220,7 @@ valid arguments. To establish the success of the interpretational account we must meet this objection. One example of a materially but not formally valid argument is (5) above, and another is: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{5} \item @@ -235,7 +235,7 @@ interpretations of (5) and (6) for which the premises are true and the conclusion false. A formalisation of these arguments in first order logic reveals their logical form: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{6} \item @@ -246,7 +246,7 @@ logic reveals their logical form: \noindent Another interpretation of each of these arguments demonstrates the point further: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{8} \item @@ -351,7 +351,7 @@ this claim will be defended further. SPS applied to the argument (5) gives: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{10} \item @@ -360,7 +360,7 @@ SPS applied to the argument (5) gives: \noindent This argument can be formalised as follows: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{11} \item @@ -467,7 +467,7 @@ different arguments, I do not need to prove that the first argument is on any argument. If the premise ``all postmen are fathers'' is added to (9) then we have a new argument: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{12} \item @@ -517,7 +517,7 @@ A counterexample to this argument has been pointed out to me.\footnote{By Owen Griffiths, in personal communication.} This is that if we take the argument: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{13} \item @@ -528,7 +528,7 @@ the argument: student then puppies are cute'' is added as a suppressed premise to (14), then we get the new valid argument: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{14} \item @@ -615,7 +615,7 @@ The final problem I shall explore in relation to SPS is the problem of modus ponens. A modus ponens is a deductive argument of the following form: -\begin{enumerate}[leftmargin=42] +\begin{enumerate}[leftmargin=42pt] \def\labelenumi{(\arabic{enumi})} \setcounter{enumi}{15} \item |