Abstract
ABSTRACT
This part of the series has a dual purpose. In the first place we will
discuss two kinds of theories of proof. The first kind will be called a
theory of linear proof. The second has been called a theory of suppositional
proof. The term "natural deduction" has often and correctly been
used to refer to the second kind of theory, but I shall not do so here
because many of the theories so-called are not of the second kind--they
must be thought of either as disguised linear theories or theories of a
third kind (see postscript below). The second purpose of this part is 25
to develop some of the main ideas needed in constructing a comprehensive
theory of proof. The reason for choosing the linear and suppositional
theories for this purpose is because the linear theory includes only
rules of a very simple nature, and the suppositional theory can be seen
as the result of making the linear theory more comprehensive.
CORRECTION: At the time these articles were written the word ‘proof’ especially in the phrase ‘proof from hypotheses’ was widely used to refer to what were earlier and are now called deductions. I ask your forgiveness. I have forgiven Church and Henkin who misled me.