Material conditional is also called material implication

forallx-yyc-notation.tex

@@ -31,7 +31,7 @@ \section{Alternative symbols}
 \paragraph{Conjunction.}
 Conjunction is often symbolized with the \emph{ampersand}, `{\&}'. The ampersand is a decorative form of the Latin word `et', which means `and'.  (Its etymology still lingers in certain fonts, particularly in italic fonts; thus an italic ampersand might appear as `\emph{\&}'.) This symbol is commonly used in natural English writing (e.g.  `Smith \& Sons'), and so even though it is a natural choice, many logicians use a different symbol to avoid confusion between the object and metalanguage: as a symbol in a formal system, the ampersand is not the English word `\&'. The most common choice now is `$\wedge$', which is a counterpart to the symbol used for disjunction. Sometimes a single dot, `{\scriptsize\textbullet}', is used. In some older texts, there is no symbol for conjunction at all; `$A$ and $B$' is simply written `$AB$'.
 
-\paragraph{Material Conditional.} There are two common symbols for the material conditional: the \emph{arrow}, `$\rightarrow$', and the \emph{horseshoe}, `$\supset$'.
+\paragraph{Material Conditional.} There are two common symbols for the material conditional (aka material implication): the \emph{arrow}, `$\rightarrow$', and the \emph{horseshoe}, `$\supset$'.
 
 \paragraph{Material Biconditional.} The \emph{double-headed arrow}, `$\leftrightarrow$', is used in systems that use the arrow to represent the material conditional. Systems that use the horseshoe for the conditional typically use the \emph{triple bar}, `$\equiv$', for the biconditional.
 

forallx-yyc-tfl.tex

@@ -342,7 +342,7 @@ \section{Conditional}
 	\end{earg}
 If we think about it, all four of these sentences mean the same as  `If Jean is in Paris, then Jean is in France'. So they can all be symbolized by `$(P \eif F)$'.
 
-It is important to bear in mind that the connective `\eif' tells us only that, if the antecedent is true, then the consequent is true. It says nothing about a \emph{causal} connection between two events (for example). In fact, we lose a huge amount when we use `$\eif$' to symbolize English conditionals. We will return to this in \S\ref{s:IndicativeSubjunctive} and \S\ref{s:ParadoxesOfMaterialConditional}.
+It is important to bear in mind that the connective `\eif' tells us only that, if the antecedent is true, then the consequent is true. It says nothing about a \emph{causal} connection between two events (for example). In fact, we lose a huge amount when we use `$\eif$' to symbolize English conditionals. This definition of the conditional is also called the \emph{material conditional} or \emph{material implication} in the literature. We will return to this issue in \S\ref{s:IndicativeSubjunctive} and \S\ref{s:ParadoxesOfMaterialConditional}.
 
 \section{Biconditional}
 Consider these sentences:

forallx-yyc-truthtables.tex

@@ -708,7 +708,7 @@ \section{The limits of these tests}\label{s:ParadoxesOfMaterialConditional}
 	\end{earg}
 and symbolize \ref{n:GodParadox2} as `$G \eif \enot M$'.  Now, if atheists are right, and there is no God, then `$G$' is false and so `$G \eif \enot M$' is true, and the puzzle disappears. However, if `$G$' is false, `$G \eif M$', i.e., `If God exists, She answers malevolent prayers', is \emph{also} true!
 
-In different ways, these four examples highlight some of the limits of working with a language (like TFL) that can \emph{only} handle truth-functional connectives. Moreover, these limits give rise to some interesting questions in philosophical logic. The case of Jan's baldness (or otherwise) raises the general question of what logic we should use when dealing with \emph{vague} discourse. The case of the atheist raises the question of how to deal with the (so-called) \emph{paradoxes of the material conditional}. Part of the purpose of this book is to equip you with the tools to explore these questions of \emph{philosophical logic}. But we have to walk before we can run; we have to become proficient in using TFL, before we can adequately discuss its limits, and consider alternatives.
+In different ways, these four examples highlight some of the limits of working with a language (like TFL) that can \emph{only} handle truth-functional connectives. Moreover, these limits give rise to some interesting questions in philosophical logic. The case of Jan's baldness (or otherwise) raises the general question of what logic we should use when dealing with \emph{vague} discourse. The case of the atheist raises the question of how to deal with the (so-called) \emph{paradoxes of the material conditional} (aka \emph{paradoxes of material implication}). Part of the purpose of this book is to equip you with the tools to explore these questions of \emph{philosophical logic}. But we have to walk before we can run; we have to become proficient in using TFL, before we can adequately discuss its limits, and consider alternatives.
 
 \section{The double turnstile}
 In what follow, we will use the notion of entailment rather a lot in this book. It will help us, then, to introduce a symbol that abbreviates it. Rather than saying that the TFL sentences $\metav{A}_1$, $\metav{A}_2$, \dots{} and $\metav{A}_n$ together entail $\metav{C}$, we will abbreviate this by: