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Diffstat (limited to 'Principia Mathematica, Volume I.tex')
| -rw-r--r-- | Principia Mathematica, Volume I.tex | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/Principia Mathematica, Volume I.tex b/Principia Mathematica, Volume I.tex index b7a0878..280fce3 100644 --- a/Principia Mathematica, Volume I.tex +++ b/Principia Mathematica, Volume I.tex @@ -1958,7 +1958,7 @@ This proposition states that, if $p$ implies its own falsehood, then $p$ is fals && & [\pmast2\pmcdot05] & &\pmthm \pmdottt q \pmimp r \pmdott \pmimp \pmdott p \pmimp q \pmdot \pmimp \pmdot p \pmimp r & && (2) \\ && & [(1)\pmdot(2)\pmdot(\pmast1\pmcdot11)]& &\pmthm \pmdottt p \pmimp q \pmdot \pmimp \pmdott q \pmimp r \pmdot \pmimp \pmdot p \pmimp r & && \end{flalign*} -In the last line of this proof, ``$(1)\pmdot(2)\pmdot(\pmast1\pmcdot11)$" means that we are inferring in accordance with $\pmast1\pmcdot11$, having before us a proposition, namely $p \pmimp q \pmdot \pmimp \pmdott q \pmimp r \pmdot \pmimp \pmdot p \pmimp r$, which, by one, is implied by $q \pmimp r \pmdot \pmimp \pmdott p \pmimp q \pmdot \pmimp \pmdot p \pmimp r$, which, by (2), is true. In general, in such cases, we shall omit the reference to $\pmast1\pmcdot11$. +In the last line of this proof, ``$(1)\pmdot(2)\pmdot(\pmast1\pmcdot11)$" means that we are inferring in accordance with $\pmast1\pmcdot11$, having before us a proposition, namely $p \pmimp q \pmdot \pmimp \pmdott q \pmimp r \pmdot \pmimp \pmdot p \pmimp r$, which, by (1), is implied by $q \pmimp r \pmdot \pmimp \pmdott p \pmimp q \pmdot \pmimp \pmdot p \pmimp r$, which, by (2), is true. In general, in such cases, we shall omit the reference to $\pmast1\pmcdot11$. \pagefirst{105} The above two propositions will both be referred to as the ``principle of the syllogism" (shortened to ``Syll"), because, as will appear later, the syllogism in Barbara is derived from them. \begin{flalign*} %2.07 @@ -2183,7 +2183,7 @@ and then ``(1)" means ``$a \pmimp d$." The proof of $\pmast2\pmcdot31$ is as fol This definition serves only for the avoidance of brackets. \begin{flalign*} %2.36 - & \mathbf{\pmast2\pmcdot32}. \quad \pmthm \pmdott (p \pmor q) \pmor r \pmdot \pmimp \pmdot p \pmor (q \pmor r) & + & \mathbf{\pmast2\pmcdot36}. \quad \pmthm \pmdott (p \pmor q) \pmor r \pmdot \pmimp \pmdot p \pmor (q \pmor r) & \end{flalign*} \pmdemi \begin{flalign*} %2.36 @@ -2487,10 +2487,10 @@ as ``Fact." \item[$\mathbf{\pmast3\pmcdot03}$.] Given two asserted elementary propositional functions ``$\pmthm \pmdot \phi p$ and ``$\pmthm \pmdot \psi p$" whose arguments are elementary propositions, we have ``$\pmthm \pmdot \phi p \pmand \psi p$. \end{description} \pmdemi -\begin{flalign*} %3.03 +\begin{flalign*} %3.03 \footnote{In the first edition, the citation of (3.01) was mistakenly given as (3.03), which would be viciously circular.} && &\pmthm \pmdot \pmast1\pmcdot7\pmcdot72 \pmand \pmast2\pmcdot11 \pmdot \pmithm \pmdott \pmnot \phi p \pmor \pmnot \psi p \pmdot \pmor \pmdot \pmnot(\pmnot \phi p \pmor \pmnot \psi p) & && (1) \\ && &\pmthm \pmdot (1) \pmand \pmast2\pmcdot32 \pmand (\pmast1\pmcdot01) \pmdot \pmithm \pmdottt \phi p \pmdot \pmimp \pmdott \psi p \pmdot \pmimp \pmdot \pmnot(\pmnot \phi p \pmor \pmnot \psi p) & && (2) \\ - && &\pmthm \pmdot (2) \pmand (\pmast3\pmcdot03) \pmdot \pmithm \pmdottt \phi p \pmdot \pmimp \pmdott \psi p \pmdot \pmimp \pmdot \phi p \pmand \psi p & && (3) \\ + && &\pmthm \pmdot (2) \pmand (\pmast3\pmcdot01) \pmdot \pmithm \pmdottt \phi p \pmdot \pmimp \pmdott \psi p \pmdot \pmimp \pmdot \phi p \pmand \psi p & && (3) \\ && &\pmthm \pmdot (3) \pmand \pmast1\pmcdot11 \pmand (\pmast1\pmcdot01) \pmdot \pmithm \pmdot \pmprop & && \end{flalign*} \begin{flalign*} %3.1 %3.11 %3.12 %3.13 %3.14 %3.2 %3.21 %3.22 |