Harold R. (Hal) Foster’s Prince Valiant
© Respective copyright/trademark holders.
Apparent
variables
The
symbols “(x) . φx” denotes a definitive
proposition, and there is no distinction between “(x) . φx ” and “(y) . φy”
when they occur in the same context. Thus “x”
in “(x) . φx” is not an ambiguous constituent
in any expression in which “(x) .
φx ” occurs; and such an
expression does not cease to convey a determinant meaning by reason of the
ambiguity if the x in “φx ”.
The
range of x in “(x) . φx ”
or “($x) . φx” extends over the
complete field of the values of x for
which “φx” has meaning, and
accordingly the meaning of “(x) . φx ” or “($x) . φx” involves the supposition
that such a field is determinant. The x
which occurs in “(x) .
φx ” or “($x) . φx” is called an “apparent
variable” (after Peano). It follows from the meaning of “($x) . φx” that the x in that expression is also an apparent
variable. A proposition in which x occurs as an apparent variable is not a function of x.
Thus e.g. “(x) . x=x” will mean “everything
is equal to itself.” This is an absolute content, not a function of a variable x. This is why the x is called an apparent
variable in such cases.
As
established in the second edition, there is no need of the distinction between
real and apparent variables, nor of the primitive idea “assertion of a
propositional function.” On all occasions ahead where, in Principia Mathematica,
our authors have an asserted proposition of the form “├
. fx” or “├
. fp” this is to be
taken as meaning “├ (x) . φx”; but in “├ ($x) . φx
“ it is necessary to indicate explicitly the fact that “some” x (not “all” x’s) is involved.
Script: Gardner F. Fox Pencil and Inks: Sheldon Moldoff (signed
)Cliff Cornwall™ © Respective copyright/trademark
holders.
The text I am
working from thus far is the abridged Principia Mathematica to *56, and this
edition is drawn from the first edition. There are a number of revisions in the
second edition, which were suggested by various readers in the years between
editions. As the authors predicted this, and any metaphysical system is and
must be in in flux to be useful to its purpose. Even though it became apparent
that the distinction between real and apparent variables is not necessary
within the system of propositions described ahead, it is nonetheless useful to
understand the distinction. Even though the difference is semantic, it is still
real, and a detail that may be useful in some not yet anticipated capacity.
Script: R. D. Blackmore (original
author); Ruth A. Roche (adaptation)
Pencils and Inks: Matt Baker ©
Respective copyright/trademark holders.
BLOG
laka
Logical Philosophy In American Indian
thought and Perception
Harold R. (Hal) Foster’s Prince Valiant
© Respective copyright/trademark holders.
No comments:
Post a Comment