Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Hint at future parts and note the past, e.g. Aristotle #70

Open
wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Hint at future parts and note the past, e.g. Aristotle #70

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
4 changes: 3 additions & 1 deletion forallx-yyc-tfl.tex
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -50,7 +50,9 @@ \section{Validity in virtue of form}\label{s:ValidityInVirtueOfForm}
\end{earg}
These examples illustrate an important idea, which we might describe as \emph{validity in virtue of form}. The validity of the arguments just considered has nothing very much to do with the meanings of English expressions like `Jenny is miserable', `Dipan is an avid reader of Tolstoy', or `Jim acted in lots of plays'. If it has to do with meanings at all, it is with the meanings of phrases like `and', `or', `not,' and `if \ldots, then \ldots'.

In Parts \ref{ch.TFL}--\ref{ch.NDTFL}, we are going to develop a formal language which allows us to symbolize many arguments in such a way as to show that they are valid in virtue of their form. That language will be \emph{truth-functional logic}, or TFL.
In Parts \ref{ch.TFL}--\ref{ch.NDTFL}, we are going to develop a formal language which allows us to symbolize many arguments in such a way as to show that they are valid in virtue of their form. That language will be \emph{truth-functional logic}, or TFL. Parts \ref{ch.FOL}--\ref{ch.NDFOL} will extend TFL so it can symbolize more arguments; that extended language will be \emph{first-order logic}, or FOL. Part \ref{ch.ML} will then extend FOL further into another extended language called \emph{modal logic}, or ML.

Aristotle is the first known person to have the idea of studying the general form of an argument, rather than a specific argument, by using symbols (e.g., letters) to represent parts of an argument. Aristotelian logic has been generally supplanted by more flexible modern logic systems developed by individuals such as Gottlob Frege and Bertrand Russell. That said, all such systems enable studying the validity of arguments by virtue of their form.

\section{Validity for special reasons}
There are plenty of arguments that are valid, but not for reasons relating to their form. Take an example:
Expand Down