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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">Readers:<SPAN
style="mso-spacerun: yes"> </SPAN>This document will not display correctly
when read as a plain text email.<SPAN style="mso-spacerun: yes">
</SPAN>Please read it as an HTML email.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">This document is
about some very elementary concepts in logic, hence, may appear unduly
technical.<SPAN style="mso-spacerun: yes"> </SPAN>The concepts discussed
are not rocket science and the mere ability to read should make them
understandable.<SPAN style="mso-spacerun: yes"> </SPAN>Some would argue
that the below are trivial.<SPAN style="mso-spacerun: yes">
</SPAN>Perhaps.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Michael,<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">With your kind agreement with what
has so far been put forth in this thread we are nearer to discussing the problem
of evil.<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Finally, before examining your
model of the inductive process:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">The truth of a sentence or the
probability of the truth of a sentence is not always easy to
determine.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">For certain kinds of sentences, <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: blue">the truth of
those sentences is a matter of agreement of linguistic usage, or in other words,
by accepted definition and/or
axioms/postulates.</SPAN></B><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Example:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">A <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: blue">rational
number</SPAN></B> is a number that can be expressed as a fraction a/b where a
and b are integers and b <> 0 and where a and b have no common factors
which are integers. A rational number a/b is said to have numerator a and
denominator b. Numbers that are not rational are called irrational
numbers.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">For the purposes of discourse,
application, and advancement of knowledge, those who work with numbers agree
that the sentences above defining rational numbers are
true.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">There are many words and sentences
in ordinary language whose meaning and truth depend upon such agreed usage –
"all" and "none" are two such words.<SPAN style="mso-spacerun: yes">
</SPAN>The axioms of various mathematical systems such as group theory, ring
theory, point-set topology, etc are also examples of truth by agreement of usage
as are definitions in physics, chemistry, etc.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">It is <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: blue">very</SPAN></B>
important to realize contradictions can ensue and thus <B
style="mso-bidi-font-weight: normal"><SPAN
style="COLOR: red">impossibilities</SPAN></B> proposed if some object X <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: blue">is
defined</SPAN></B> in such a way which asserts that X can be described by a
particular agreed upon definition.<SPAN style="mso-spacerun: yes">
</SPAN>In such cases it is said that it is <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: red">logically
impossible</SPAN></B> for X to exist.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Example:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">Definition:<SPAN
style="mso-spacerun: yes"> </SPAN>A Steatopygous Nilsow is a positive
prime integer whose square root is a rational number.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Given the definition of rational
number above, asserting the existence of a <SPAN
style="COLOR: blue">Steatopygous Nilsow</SPAN> leads to a contradiction – given
the agreed upon definition of a rational number above, it is <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: red">logically
impossible</SPAN></B> for a <SPAN style="COLOR: blue">Steatopygous Nilsow</SPAN>
to exist.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">A simple, clear, proof of this was
given by <st1:City w:st="on"><st1:place w:st="on">Euclid</st1:place></st1:City>
and runs as follows: <SPAN style="mso-spacerun: yes"> </SPAN>(Note: <SPAN
style="mso-spacerun: yes"> </SPAN>"x squared" will be written as
"x^2".)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><st1:City w:st="on"><st1:place
w:st="on"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Euclid</SPAN></st1:place></st1:City><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">'s proof:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">1.<SPAN
style="mso-tab-count: 1"> </SPAN>Let p be a Steatopygous
Nilsow i.e. p has a rational square root.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">2.<SPAN
style="mso-tab-count: 1"> </SPAN>Then the square root of p
=a/b where a, b are integers, have no common factors, and since p > 0, then a
> b > 1.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">3.<SPAN
style="mso-tab-count: 1"> </SPAN>Observe:<SPAN
style="mso-tab-count: 2"> </SPAN>p =
a^2/b^2.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">4.<SPAN
style="mso-tab-count: 1"> </SPAN>Further:<SPAN
style="mso-tab-count: 2">
</SPAN>pb^2 = a^2.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">5.<SPAN
style="mso-tab-count: 1"> </SPAN>Notice:<SPAN
style="mso-tab-count: 2">
</SPAN>a divides a^2 evenly.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">6.<SPAN
style="mso-tab-count: 1"> </SPAN>Therefore:<SPAN
style="mso-tab-count: 1"> </SPAN>a divides pb^2
evenly.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.5in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">7.<SPAN
style="mso-tab-count: 1"> </SPAN>Notice:<SPAN
style="mso-tab-count: 2">
</SPAN>If a divides pb^2 evenly, there must be a<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1.5in; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">factor in common between a and
pb^2.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">8.<SPAN
style="mso-tab-count: 1"> </SPAN>But:<SPAN
style="mso-tab-count: 1"> </SPAN><SPAN
style="mso-tab-count: 2">
</SPAN>a and b have no common factors.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">9.<SPAN
style="mso-tab-count: 1"> </SPAN>Also:<SPAN
style="mso-tab-count: 1"> </SPAN><SPAN
style="mso-tab-count: 2"> </SPAN>p is
prime so a cannot divide p evenly.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">10.<SPAN
style="mso-tab-count: 1"> </SPAN>Hence:<SPAN
style="mso-tab-count: 2">
</SPAN>a cannot divide pb^2; hence a contradiction<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1.5in; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">has been
reached.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">11.<SPAN
style="mso-tab-count: 1"> </SPAN>Therefore:<SPAN
style="mso-tab-count: 1"> </SPAN>The square root
of p is not rational.<SPAN style="mso-spacerun: yes"> </SPAN><B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: blue">This
is<o:p></o:p></SPAN></B></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1.5in; TEXT-INDENT: 0.5in"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">a contradiction to
the assertion that a<o:p></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1.5in; TEXT-INDENT: 0.5in"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">Steatopygous Nilsow
exists.<o:p></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">This is a very simple illustration
showing that simply because some object is defined, that does not mean that the
object exists.<SPAN style="mso-spacerun: yes"> </SPAN>In the above case,
the definition of the object leads to a contradiction in an axiomatic, precisely
defined milieu, hence the <B style="mso-bidi-font-weight: normal"><SPAN
style="COLOR: red">logical impossibility</SPAN></B> that the object (<B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: blue">a Steatopygous
Nilsow</SPAN></B>) could exist is demonstrated.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">The other way the
truth of a sentence or the probability of the truth of a sentence is determined
is by some kinds of observations.</SPAN></B><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">The word "observation" in the
previous sentence means observation in an extremely broad sense.<SPAN
style="mso-spacerun: yes"> </SPAN>Examples of observations include
observations of terrestrial events such as the color of smog in Los Angeles on
July 12, 1999, observations of quantitative relationships, observations of the
meanings of words and sentences, observations of what a book says, observations
of what a person says, observations about what some alleged authority asserts,
observations about internal feelings, etc, etc.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">As we have noted above, the
probability of the truth of any observation based assertion may be extremely
close to one but the possibility that that further observations can change the
present probability must always be considered.<SPAN
style="mso-spacerun: yes"> </SPAN>Hence, any knowledge claims supported by
even one observation are not completely certain although the truth of that
knowledge claim for <SPAN style="COLOR: blue">all practical purposes</SPAN> may
be asserted as true as we noted before:<SPAN style="mso-spacerun: yes">
</SPAN>Thus we regard as true the sentence:<SPAN
style="mso-spacerun: yes"> </SPAN><SPAN style="COLOR: blue">"Barring a
high wind, a pine cone that breaks off a tree limb will always fall
earthward."<o:p></o:p></SPAN></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Just as defining an object by
definition in an axiomatic system (as above) can lead to a contradiction and
hence the <B style="mso-bidi-font-weight: normal"><SPAN
style="COLOR: red">logical impossibility</SPAN></B> of that object's existence,
a similar situation exists with definitions of objects whose real existence is
dependent upon some kind of observations or other.<SPAN
style="mso-spacerun: yes"> </SPAN>In this case, we say that the existence
of the object is <B style="mso-bidi-font-weight: normal"><SPAN
style="COLOR: red">improbable</SPAN></B> if it is not supported by
observations.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Common examples of the above
include the unicorn, Sherlock Holmes, and Saint Puce.<SPAN
style="mso-spacerun: yes"> </SPAN>In these examples, asserting the real
existence of these objects would be called an <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: red">extremely
improbable</SPAN></B> assertion or a "false" assertion in ordinary usage.<SPAN
style="mso-spacerun: yes"> </SPAN>Of course, it is logically possible for
future observations to change this, but at this point "<B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: red">extremely
improbable</SPAN></B>" is the correct description of such
assertions.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Well Michael, if we can agree on
the simple basics above, we are now in a position to examine your description of
the induction process and perhaps make one or two very minor changes to it for
the sake of clarification.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Please let me know at your
convenience whether you agree with the above or not.<SPAN
style="mso-spacerun: yes"> </SPAN>Thank you again for your
patience.</SPAN></P><SPAN style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><BR>Wayne A. Fox<BR>1009 Karen
Lane<BR>PO Box 9421<BR>Moscow, ID 83843</P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt">(208) 882-7975<BR><A
href="mailto:waf@moscow.com">waf@moscow.com</A><BR><o:p></o:p></SPAN></P></FONT></DIV></BODY></HTML>