Harold R. (Hal) Foster’s Prince Valiant
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It is an obvious error, though one easy to commit, to assume
that cases (1) and (3) [see post 7.] are each-others contradiction. The
symbolism exposes this fallacy at once, for
(1)
is (x) . φx , which contradiction is: ~[(x)
. φx], not
(2)
(x) . φx, which contradiction is: (x) . ~
φx.
for the sake of brevity
of symbolism a definition is made, namely:
~(x)
. φx . = . ~[(x) . φx] Df.
Such definitions, of which the object is to gain advantage from
brevity are said to be of “merely symbolic import,” in contrast to those that
invite consideration of an important idea.
The proposition (x) . φx is called the “total variation” of the
function φx^.
We
do not take negation as a primitive idea when propositions of the forms (x) . φx and ($x)
. φx are concerned. But we define the
negation of (x) . φx i.e. of “(x) . φx
is always true” as being “φx is sometimes false,” i.e. “($x) . ~φx,” and
similarly we define the negation of ($x)
. ~φx as being (x) . ~φx. Thus
we put:
~{(x) . φx} . = . ($x)
. ~φx Df,
~{($x)
. φx} . = . (x). ~φx Df,
In like manner we
define a disjunction in which one of the propositions is of the form “(x) . φx”
or “($x)
. φx” in terms of a disjunction of propositions not of this form, putting:
(x)
. φx . v . p :
= . φx
v p Df
i.e. “either φx is always true or p is true” is to mean “’φx or p’ is always true,” with similar definitions in other cases. This subject will be revisited in later posts.
Script: Richard Hughes
Pencils and inks: Pete Costanza ©
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The ultimate purpose of this system is to attempt to eliminate the vagaries of
language in thinking about and expressing to others any complex and abstract thought or system of expression. In Principia Mathematica, our authors chose the broad and familiar field of mathematics to examine and express using this new metaphysical language. Another subject may have been chosen to more or less equal effect, but probably it was assumed that anyone interested in this system would already be familiar with some or much of the field.
This post demonstrates some simple
aspects of the language of propositional equations. Already it may be seen that
with familiarity of the language it is not only possible, but spotting errors
of facts become obvious, and thus future arguments are not made with these as a
foundation.
I hope to continue this blog with great
regularity, for it is truly a labor of love combining several aspects of my
favorite subjects. I am preparing to add a video aspect to hanBLOGlaka in the
near future, so look for that in coming installments!
Milton Caniff’s Steve Canyon ©
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han
BLOG
laka
Logical Philosophy In American Indian
thought and Perception
Harold R. (Hal) Foster’s Prince Valiant
© Respective copyright/trademark holders.
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