From d7fbd62ac0ddf8aa22d62abd13623e26ea084e90 Mon Sep 17 00:00:00 2001 From: Richard Zach Date: Wed, 1 May 2024 10:45:13 -0600 Subject: [PATCH] typos reported by W24 PHIL679 students --- .../antecedent-strengthening.tex | 2 +- .../introduction/natural-deduction.tex | 2 +- .../filtrations/examples-of-filtrations.tex | 2 +- .../normal-modal-logic/filtrations/introduction.tex | 13 +++++++------ .../syntax-and-semantics/schemas.tex | 2 +- 5 files changed, 11 insertions(+), 10 deletions(-) diff --git a/content/counterfactuals/minimal-change-semantics/antecedent-strengthening.tex b/content/counterfactuals/minimal-change-semantics/antecedent-strengthening.tex index 6fa082c5..23ea2333 100644 --- a/content/counterfactuals/minimal-change-semantics/antecedent-strengthening.tex +++ b/content/counterfactuals/minimal-change-semantics/antecedent-strengthening.tex @@ -19,7 +19,7 @@ light this match in outer space, it would light. So the following inference is invalid: \begin{quote} - I the match were struck, it would light. + If the match were struck, it would light. Therefore, if the match were struck in outer space, it would light. \end{quote} diff --git a/content/intuitionistic-logic/introduction/natural-deduction.tex b/content/intuitionistic-logic/introduction/natural-deduction.tex index a86d9dbd..409b9623 100644 --- a/content/intuitionistic-logic/introduction/natural-deduction.tex +++ b/content/intuitionistic-logic/introduction/natural-deduction.tex @@ -246,7 +246,7 @@ \subsection{Examples of \usetoken{P}{derivation}} \end{proof} \begin{prob} - Give !!{derivation}s in intuitionistic logic of the following !!{formulas}: + Give !!{derivation}s in intuitionistic logic of the following !!{formula}s: \begin{enumerate} \item $(\lnot !A \lor !B) \lif (!A \lif !B)$ \item $\lnot\lnot\lnot !A \lif \lnot !A$ diff --git a/content/normal-modal-logic/filtrations/examples-of-filtrations.tex b/content/normal-modal-logic/filtrations/examples-of-filtrations.tex index 0fc765eb..f3570c7e 100644 --- a/content/normal-modal-logic/filtrations/examples-of-filtrations.tex +++ b/content/normal-modal-logic/filtrations/examples-of-filtrations.tex @@ -139,7 +139,7 @@ i.e., $\{p, \Box p, \Box p \lif p\}$. $p$ is true at all and only the even numbers, $\Box p$ is true at all and only the odd numbers, so $\Box p \lif p$ is true at all and only the even numbers. In - other words, every odd number makes $\Box p$ true and $p$ and $\Box + other words, every odd number makes $\Box p$ true but $p$ and $\Box p \lif p$ false; every even number makes $p$ and $\Box p \lif p$ true, but $\Box p$ false. So $W^* = \{ [1], [2] \}$, where $[1] = \{1, 3, 5, \dots\}$ and $[2] = \{2, 4, 6, \dots\}$. Since $2 \in diff --git a/content/normal-modal-logic/filtrations/introduction.tex b/content/normal-modal-logic/filtrations/introduction.tex index 3c047b5b..88ba0b27 100644 --- a/content/normal-modal-logic/filtrations/introduction.tex +++ b/content/normal-modal-logic/filtrations/introduction.tex @@ -45,7 +45,7 @@ stop looking. If the !!{formula} has a finite countermodel, our procedure will find it. But if it has no finite countermodel, we won't get an answer. The !!{formula} may be valid (no countermodels at all), or it -have only an infinite countermodel, which we'll never look at. This +may have only an infinite countermodel, which we'll never look at. This problem can be overcome if we can show that every !!{formula} that has a countermodel has a finite countermodel. If this is the case we say the logic has the \emph{finite model property}. @@ -70,11 +70,12 @@ finite structures is that of ``identifying'' !!{element}s of the structure which behave the same way in relevant respects. If there are infinitely many worlds in~$\mModel{M}$ that behave the same in -relevant respects, then we might hope that there are only finitely -many ``classes'' of such worlds. In other words, we partition the set -of worlds in the right way. Each partition contains infinitely many -worlds, but there are only finitely many partitions. Then we define a -new model~$\mModel{M^*}$ where the worlds are the partitions. Finitely +relevant respects, then we may be able to collect \emph{all} worlds in +finitely many (possibly infinite) ``classes'' of such worlds. In other +words, we should partition the set of worlds in the right way, i.e., +in such a way that each partition contains infinitely many worlds, but +there are only finitely many partitions. Then we define a new +model~$\mModel{M^*}$ where the worlds are the partitions. Finitely many partitions in the old model give us finitely many worlds in the new model, i.e., a finite model. Let's call the partition a world~$w$ is in $[w]$. We'll want it to be the case that $\mSat{M}{!A}[w]$ iff diff --git a/content/normal-modal-logic/syntax-and-semantics/schemas.tex b/content/normal-modal-logic/syntax-and-semantics/schemas.tex index 805dab2f..ca2eca4d 100644 --- a/content/normal-modal-logic/syntax-and-semantics/schemas.tex +++ b/content/normal-modal-logic/syntax-and-semantics/schemas.tex @@ -48,7 +48,7 @@ We need to show that all instances of the schema are true at every world in every model. So let $\mModel{M} = \tuple{W,R,V}$ and $w \in W$ be arbitrary. To show that a conditional is true at a world we - assume the antecedent is true to show that consequent is true as + assume the antecedent is true to show that the consequent is true as well. In this case, let $\mSat{M}{\Box(!A \lif !B)}[w]$ and $\mSat{M}{\Box !A}[w]$. We need to show $\mSat{M}{\Box !B}[w]$. So let $w'$ be arbitrary such that $Rww'$. Then by the first assumption