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\usepackage[english]{babel}
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\usepackage{times}
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\usepackage{pstricks}
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\begin{document}

\title{Episode 01 -- Syllogisms}
\author{European section -- Season 2}
\date{}

\begin{frame}
  \titlepage
\end{frame}

\section{Examples of syllogisms}

\begin{frame}
\begin{block}{Syllogism 1}
All men are mortal.\\
Socrates is a man.\\
Socrates is mortal.
\end{block}\pause

\begin{block}{Syllogism 2}
No mammal has feathers.\\
All horses are mammals.\\
No horse has feathers.\end{block}\pause

\begin{block}{Syllogism 3}
No lazy people pass exams.\\
Some students pass exams.\\
Some students are not lazy.
\end{block}
\end{frame}

\begin{frame}
\begin{block}{Syllogism 4}
All cats are black.\\
Victoria is a white cat.\\
Victoria is a black cat.
\end{block}\pause

\begin{block}{Syllogism 5}
All fruit is nutritious.\\
All fruit is tasty.\\
Some tasty things are nutritious.
\end{block}\pause

\begin{block}{Syllogism 6}
Some cats have no tails.\\
All cats are mammals.\\
Some mammals have no tails.
\end{block}
\end{frame}

\begin{frame}
\begin{block}{Syllogism 7}
Some small birds live on honey.\\
All birds that live on honey are colourful.\\
Some colourful birds are small.
\end{block}\pause

\begin{block}{Syllogism 8}
No homework is fun.\\
Some reading is homework.\\
Some reading is not fun.
\end{block}\pause

\begin{block}{Syllogism 9}
All kittens are playful.\\
Some pets are kittens.\\
Some pets are playful.
\end{block}
\end{frame}

\begin{frame}
\begin{block}{Syllogism 10}
No healthy food is fattening.\\
All cakes are fattening.\\
No cakes are healthy.
\end{block}\pause

\begin{block}{Syllogism 11}
All informative things are useful.\\
Some websites are not useful.\\
Some websites are not informative.
\end{block}\pause

\begin{block}{Syllogism 12}
All the industrious boys in this school have red hair.\\
Some of the industrious boys in this school are boarders.\\
Some boarders in this school have red hair.
\end{block}
\end{frame}

\section{What is a syllogism ?}

\begin{frame}
\begin{example}[1]
\begin{quote} 
All multiples of $12$ are multiples of $4$.\\
All multiples of $4$ are even.\\
\emph{Therefore,} all multiples of $12$ are even.
\end{quote}
\end{example}\pause

\begin{example}[2]
\begin{quote} 
No reptiles have fur.\\
All snakes are reptiles.\\
No snakes have fur.
\end{quote}
\end{example}
\end{frame}

\begin{frame}
\begin{definition}
A \emph{syllogism} is a logical argument in which one
proposition, the \emph{conclusion}, is implied by two other
propositions, the \emph{premises}.
\end{definition}
\end{frame}






\section{Different types of syllogisms}

\begin{frame}
\begin{description}
\item[A (universal affirmative) :] All S are P.\\ {\bf ``All humans are mortal.''}\pause
\item[E (universal negative) :] All S are not P.\\ {\bf ``All humans are not perfect.''} or\\ {\bf ``No humans are perfect.''}\pause
\item[I (particular affirmative) :] Some S are P.\\ {\bf ``Some humans are healthy.''}\pause
\item[O (particular negative) :] Some S are not P.\\ {\bf ``Some humans are not clever.''}
\end{description}
\end{frame}

\begin{frame}
\begin{description}
\item[S] is the subject of the conclusion ;
\item[P] is the predicate of the conclusion ;
\item[M] is the middle term.
\end{description}

The major premise links M with P. The minor premise links M with S.\pause

\begin{block}{The 4 figures}
\begin{center}
\begin{tabular}{lcccc}
 & Figure 1 & Figure 2 & Figure 3 & Figure 4 \\ \hline
Major premise & M-P & P-M & M-P & P-M \\
Minor premise & S-M & S-M & M-S & M-S \\
Conclusion & S-P & S-P & S-P & S-P \\
\end{tabular}
\end{center}
\end{block}
\end{frame}

\begin{frame}
The total number of possible types of syllogism is $4\times 4\times 4\times 4=256$.\\ \pause

\begin{block}{The 19 valid forms of syllogisms}
\begin{center}
\begin{tabular}{cccc}
Figure 1 & Figure 2 & Figure 3 & Figure 4 \\ \hline
Barbara & Cesare & Darapti & Bramantip\\
Celarent & Camestres & Disamis & Camenes\\
Darii & Festino & Datisi & Dimaris \\
Ferio & Baroco & Felapton & Fesapo \\
 &  & Bocardo & Fresison \\
 &  & Ferison  & \\		 
\end{tabular}
\end{center}
\end{block}
\end{frame}

\section{Example of analysis}

\begin{frame}
\begin{tabular}{c p{6cm}|p{0.5cm}|}
\cline{3-3}
Major premise & No reptiles have fur.\rule{0pt}{20pt}&\\
\cline{2-2}\cline{3-3}
Minor premise & All snakes are reptiles.\rule{0pt}{20pt}&\\
\cline{2-2}\cline{3-3}
Conclusion & No snakes have fur.\rule{0pt}{20pt}&\\
\cline{2-2}\cline{3-3}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{1.4cm}|l|p{1.4cm}|l|p{1.4cm}|}
\cline{2-2}\cline{4-4}\cline{6-6}
\small Subject & \rule{0pt}{20pt}& \small Middle term & & \small Predicate & \\
\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{0.6cm}|p{0.6cm}|p{0.6cm}|l|p{0.8cm}|l|p{2cm}|}
\cline{2-4}\cline{6-6}\cline{8-8}
\small Structure &&& \rule{0pt}{20pt}& \small Figure & & \small\bf Type & \\
\cline{2-4}\cline{6-6}\cline{8-8}
\end{tabular}
\end{frame}

\begin{frame}
\begin{tabular}{c p{6cm}|p{0.5cm}|}
\cline{3-3}
Major premise & No reptiles have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
Minor premise & All snakes are reptiles.\rule{0pt}{20pt}& A\\
\cline{2-2}\cline{3-3}
Conclusion & No snakes have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{1.4cm}|l|p{1.4cm}|l|p{1.4cm}|}
\cline{2-2}\cline{4-4}\cline{6-6}
\small Subject & \rule{0pt}{20pt}& \small Middle term & & \small Predicate & \\
\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{0.6cm}|p{0.6cm}|p{0.6cm}|l|p{0.8cm}|l|p{2cm}|}
\cline{2-4}\cline{6-6}\cline{8-8}
\small Structure &&& \rule{0pt}{20pt}& \small Figure & & \small\bf Type & \\
\cline{2-4}\cline{6-6}\cline{8-8}
\end{tabular}
\end{frame}

\begin{frame}
\begin{tabular}{c p{6cm}|p{0.5cm}|}
\cline{3-3}
Major premise & No reptiles have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
Minor premise & All snakes are reptiles.\rule{0pt}{20pt}& A\\
\cline{2-2}\cline{3-3}
Conclusion & No snakes have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{1.4cm}|l|p{1.4cm}|l|p{1.4cm}|}
\cline{2-2}\cline{4-4}\cline{6-6}
\small Subject & Snakes \rule{0pt}{20pt}& \small Middle term & Reptiles & \small Predicate & Fur \\
\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{0.6cm}|p{0.6cm}|p{0.6cm}|l|p{0.8cm}|l|p{2cm}|}
\cline{2-4}\cline{6-6}\cline{8-8}
\small Structure &&& \rule{0pt}{20pt}& \small Figure & & \small\bf Type & \\
\cline{2-4}\cline{6-6}\cline{8-8}
\end{tabular}
\end{frame}

\begin{frame}
\begin{tabular}{c p{6cm}|p{0.5cm}|}
\cline{3-3}
Major premise & No reptiles have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
Minor premise & All snakes are reptiles.\rule{0pt}{20pt}& A\\
\cline{2-2}\cline{3-3}
Conclusion & No snakes have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{1.4cm}|l|p{1.4cm}|l|p{1.4cm}|}
\cline{2-2}\cline{4-4}\cline{6-6}
\small Subject & Snakes \rule{0pt}{20pt}& \small Middle term & Reptiles & \small Predicate & Fur \\
\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{0.6cm}|p{0.6cm}|p{0.6cm}|l|p{0.8cm}|l|p{2cm}|}
\cline{2-4}\cline{6-6}\cline{8-8}
\small Structure &MP&SM&SP \rule{0pt}{20pt}& \small Figure & 1 & \small\bf Type & \\
\cline{2-4}\cline{6-6}\cline{8-8}
\end{tabular}
\end{frame}

\begin{frame}
\begin{tabular}{c p{6cm}|p{0.5cm}|}
\cline{3-3}
Major premise & No reptiles have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
Minor premise & All snakes are reptiles.\rule{0pt}{20pt}& A\\
\cline{2-2}\cline{3-3}
Conclusion & No snakes have fur.\rule{0pt}{20pt}& E\\
\cline{2-2}\cline{3-3}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{1.4cm}|l|p{1.4cm}|l|p{1.4cm}|}
\cline{2-2}\cline{4-4}\cline{6-6}
\small Subject & Snakes \rule{0pt}{20pt}& \small Middle term & Reptiles & \small Predicate & Fur \\
\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{0.6cm}|p{0.6cm}|p{0.6cm}|l|p{0.8cm}|l|p{2cm}|}
\cline{2-4}\cline{6-6}\cline{8-8}
\small Structure &MP&SM&SP \rule{0pt}{20pt}& \small Figure & 1 & \small\bf Type & \bf Celarent \\
\cline{2-4}\cline{6-6}\cline{8-8}
\end{tabular}
\end{frame}

\begin{frame}
\begin{tabular}{c p{6cm}|p{0.5cm}|}
\cline{3-3}
Major premise & \rule{0pt}{20pt}&\\
\cline{2-2}\cline{3-3}
Minor premise & \rule{0pt}{20pt}&\\
\cline{2-2}\cline{3-3}
Conclusion & \rule{0pt}{20pt}&\\
\cline{2-2}\cline{3-3}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{1.4cm}|l|p{1.4cm}|l|p{1.4cm}|}
\cline{2-2}\cline{4-4}\cline{6-6}
\small Subject & \rule{0pt}{20pt}& \small Middle term & & \small Predicate & \\
\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabular}

\vspace{0.7cm}

\begin{tabular}{l|p{0.6cm}|p{0.6cm}|p{0.6cm}|l|p{0.8cm}|l|p{2cm}|}
\cline{2-4}\cline{6-6}\cline{8-8}
\small Structure &&& \rule{0pt}{20pt}& \small Figure & & \small\bf Type & \\
\cline{2-4}\cline{6-6}\cline{8-8}
\end{tabular}
\end{frame}



\section{Truth and validity}

\begin{frame}
\begin{example}[Valid but not true]
\begin{quote}
All penguins have pink stripes. \\
All math teachers are penguins.\\
\emph{Therefore,} all math teachers have pink stripes.
\end{quote}
\end{example}\pause

\begin{example}[May be true, but invalid]
\begin{quote}
All equilateral triangles have angles of 60$^\circ$.\\
The triangle $ABC$ has an angle of 60$^\circ$.\\
\emph{Therefore,} the triangle $ABC$ is equilateral.
\end{quote}
\end{example}
\end{frame}



\section{Test}


\newcommand{\syll}[4]{
\begin{block}{Syllogism #4}
#1\\
#2\\
#3
\end{block}\pause}

\begin{frame}
\syll{Fish live in water.}{Monkeys are not fish.}{Therefore, monkeys do not live in the water.}{1}

\syll{No Frenchmen like plum pudding}{All Englishmen like plum pudding}{Englishmen are not Frenchmen}{2}%Valid

\syll{All lions are fierce}{Some lions do not drink coffee}{Some creatures that drink coffee are not fierce}{3}%In

\end{frame}

\begin{frame}
\syll{No pigs can fly}{All pigs are greedy}{Some greedy creatures cannot fly}{4}%Valid

\syll{Some pillows are soft}{No pokers are soft}{Some pokers are not pillows}{5}%Invalid

\syll{No emperors are dentists}{All dentists are dreaded by children}{No emperors are dreaded by children}{6}%Invalid
\end{frame}

\begin{frame}
\syll{Nothing intelligible ever puzzles me}{Logic puzzles me}{Logic is unintelligible}{7}%Valid


\syll{If war is declared, the enemy country will be invaded}{War is not declared}{The enemy country will not be
invaded}{8}%Invalid

\syll{Ninety-nine Cretans in a hundred are liars}{Epimenides is a Cretan}{Epimenides is a liar}{9}
\end{frame}

\begin{frame}
\syll{No bald creatures need a hairbrush}{No lizards have hair}{No lizards need a hairbrush}{10}
\end{frame}


\end{document}
