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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.<?xml:namespace prefix = o ns =
"urn:schemas-microsoft-com:office:office" /><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">We progress laboriously toward a
meaningful discussion of the problem of evil.<SPAN
style="mso-spacerun: yes"> </SPAN>Since arguments can fail because of
faulty structure or because one or more of the premises of the argument are
false or as we will see below, one or more of the premises is more improbable
than probable, it is important for us to agree upon a few elementary things
about truth and probability.<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></FONT></DIV>
<DIV><FONT size=4></FONT> </DIV>
<DIV>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: Verdana">C.<SPAN
style="mso-tab-count: 1"> </SPAN>Brief but Important Remarks
on Arguments, Truth, Part II</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">What about the truth or
probability of sentences used as premises in an argument which result/depend
upon in some way on some kind of observation?<SPAN
style="mso-spacerun: yes"> </SPAN>Can it be said that such sentences 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">It is always possible for
observations and conclusions from obser­vations to be false for a wide
variety of reasons, hence the truth of sentences supported by observation can
never, in theory, be apodictically asserted, but only the probability range of
the truth of the sentence can be given.<SPAN style="mso-spacerun: yes">
</SPAN>I hope we can accept this without going through all the traditional
arguments supporting problems of observations – prejudice/impairment/ignorance
of the observer, conditions attendant, perspective, 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">Therefore, very technically and
very strictly speaking, it would not be proper to assert that observation based
sentences are strictly true or false.<SPAN style="mso-spacerun: yes">
</SPAN>However, an examination of the use of the words "true" and "false" in
"ordinary language" can perhaps steer us around this
difficulty.<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
sentence:<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">Barring a high wind,
a pine cone that breaks off a tree limb will always fall
earthward.<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">is a sentence that supported by
the theory of gravity, and based on (trillions and trillions of) observations
and continuing observations, hence the probability of its truth is regarded as
extremely close to 1.00 (but not exactly 1.00).<SPAN
style="mso-spacerun: yes"> </SPAN>Hence in ordinary language, we regard
such sentences as true.<SPAN style="mso-spacerun: yes"> </SPAN>In fact,
were someone to assert the above sentence is false, that person would be
regarded as delusional.<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">Therefore, for the sake of
proceeding without greatly expanding the wordage in our discussion, I hope you
will henceforth agree to regard as true those observation based sentences whose
probability of truth is extremely close to 1.00 and regard as false those
observation based sentences whose probability is extremely close to 0.00.<SPAN
style="mso-spacerun: yes"> </SPAN>Of course, the status of any particular
sentence in this regard is always open to discussion.<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">The truth or falsity of some
sentences can be sometimes quite easily determined.<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">If you say:<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; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">"It will not rain
today"</SPAN><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">but it does rain <SPAN
style="COLOR: blue">very hard</SPAN> for ten minutes at 2:00pm, your assertion
was false.<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">Of course, there may be a
disagreement of the meaning of the word "rain".<SPAN
style="mso-spacerun: yes"> </SPAN>You might argue your original sentence
is true by asserting:<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; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">"That wasn't rain at
2:00pm, it was only drizzle."<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">What the above kind of
counterargument illustrates is:<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"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; COLOR: red; FONT-FAMILY: Verdana">That it is important
for the participants in a discussion to agree on the meanings of words as close
as is necessary.</SPAN></B><B style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><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"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: Verdana">That is why we are going through
this laborious and boring set of exercises preliminary to discussing the truth
of the knowledge claims and other problems found in the consideration of problem
of evil and related problems</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"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">Likewise, suppose someone asserts
that:<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; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">"All prunes contain a
single pit."<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 falsity of that sentence is
established by </SPAN><B style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 18pt; COLOR: red; FONT-FAMILY: Verdana">one</SPAN></B><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"> confirmed observation of a prune
without a pit or a prune with two or more pits.<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">Likewise, in ancient times when it
was asserted that:<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">"All numbers are
rational." </SPAN><SPAN style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">or<SPAN
style="COLOR: blue"> "No numbers are irrational."<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">the falsity of those sentences was
established by <?xml:namespace prefix = st1 ns =
"urn:schemas-microsoft-com:office:smarttags" /><st1:place w:st="on"><st1:City
w:st="on">Euclid</st1:City></st1:place>'s proof that the square root of two is
an irrational number, a single counterexample.<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">In general:<SPAN
style="mso-spacerun: yes"> </SPAN>The falsity of general sentences such
as:<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 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">All X are
Y.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">No X is a
Y.<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">can be established by just one
confirmed observation/counter­example to the contrary.<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">More subtly, there are many
general sentences whose truth are carelessly asserted and/or taken for granted
which are actually quite false.<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">Suppose someone was under oath on
the witness stand in a secular court.<SPAN style="mso-spacerun: yes">
</SPAN>Suppose under cross examination they were asked:<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; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">"Is the sky
blue?"<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">How should they answer?<SPAN
style="mso-spacerun: yes"> </SPAN>Many would answer
"Yes."<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">They would be perjuring
themselves!<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">If you observe the sky on even on
a clear midday, there are parts of the sky that are not blue.<SPAN
style="mso-spacerun: yes"> </SPAN>For example, the part occupied by and
around the sun and the parts nearest some portions of the horizon is not
blue.<SPAN style="mso-spacerun: yes"> </SPAN>Those parts are variations of
white without any visible tinge of blue.<SPAN style="mso-spacerun: yes">
</SPAN>On a day with a few clouds in the sky, there are even more parts of the
sky that are not blue.<SPAN style="mso-spacerun: yes"> </SPAN>Normally the
sky is not blue at night.<SPAN style="mso-spacerun: yes"> </SPAN>Skillful
attorneys often make use of such erroneous assertions by a witness to
mischaracterize what a witness has said and/or to discredit the
witness.<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 above example again
illustrates how <B style="mso-bidi-font-weight: normal">important</B> for the
participants in a discussion <B style="mso-bidi-font-weight: normal">to agree as
exactly as possible or necessary on the meaning of words and sentences they are
using</B>, if that discussion is to progress toward a truthful and reliable
conclusion.<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">Building on the above, let's see
if we can agree on some other basic items.<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">Showing that an argument is not
supportive of its conclusion(s) can be done by:<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 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">[1]<SPAN
style="mso-tab-count: 1"> </SPAN>Showing the premises of the
argument are false or improbable; or<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">[2]<SPAN
style="mso-tab-count: 1"> </SPAN>Showing the structure of the
argument is defective.<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">Obvious examples of [1] and
[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 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[P1]<SPAN
style="mso-tab-count: 1"> </SPAN>All true evangelists are lean and
selfless.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[P2]<SPAN
style="mso-tab-count: 1"> </SPAN>Douglas James Wilson is a true
evangelist.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">Therefore,<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[C]<SPAN
style="mso-tab-count: 1"> </SPAN>Douglas James Wilson is lean and
selfless.<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 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[P1]<SPAN
style="mso-tab-count: 1"> </SPAN>All mathematicians can
count.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[P2]<SPAN
style="mso-tab-count: 1"> </SPAN>All those who practice the rhythm method of
contraception can count.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">Therefore,<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[C]<SPAN
style="mso-tab-count: 1"> </SPAN>All mathematicians practice the rhythm
method of contraception.<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">In practice, determining whether
an argument is correctly structured is sometimes quite
difficult.<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">Gödel's proof of the
incompleteness of the unrestricted predicate calculus is beyond the
understanding of many, and thus beyond their ability to determine if that proof
is a valid deductive argument.<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 correctness of even simple
inductive arguments is not so easily determined since the addition of other
premises to the argument may cause the probability of the outcome to change
radically.<SPAN style="mso-spacerun: yes"> </SPAN>Many inductive arguments
can be described as incomplete by nature – open ended.<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 methods of decidability
of those arguments which can be translated into the sentential calculus without
loss of fundamental cognitive import.<SPAN style="mso-spacerun: yes">
</SPAN>Likewise, there is a method of decidability for those syllogistic
arguments for which Aristotle designed a test for validity (and which method was
corrected in the 19th century by George Boole).<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">Hence, in our discussion we must
try our best to determine the structural correctness of the simple arguments
that we will be using, whether they be deductive or inductive.<SPAN
style="mso-spacerun: yes"> </SPAN>This may not always be simple.<SPAN
style="mso-spacerun: yes"> </SPAN>However, it can be simplified by noting
that certain class statements can be recast as statements amenable to treatment
in the sentential calculus or even by much simpler means.<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 0in 0pt; TEXT-INDENT: 0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">All pencil sharpeners
are really secret spy devices.<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">can be recast
as:<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">If X is a pencil
sharpener, X is really a secret spy device.<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">A further issue:<SPAN
style="mso-spacerun: yes"> </SPAN>What can be said about the conclusions
of valid deductive arguments which would be true if the premises are strictly
true, but the probability of the truth of one or more the premises <B
style="mso-bidi-font-weight: normal"><SPAN style="COLOR: red">is less
than</SPAN></B> extremely close to 1.00?<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 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[P1]<SPAN
style="mso-tab-count: 1"> </SPAN>The next President of the <st1:country-region
w:st="on">United States</st1:country-region> will visit <st1:place
w:st="on"><st1:City w:st="on">Meander River</st1:City>, <st1:State
w:st="on">Alberta</st1:State></st1:place>.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[P2]<SPAN
style="mso-tab-count: 1"> </SPAN>Bill Frist will be the next President of the
<st1:country-region w:st="on"><st1:place w:st="on">United
States</st1:place></st1:country-region>.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">Therefore,<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0.5in 0pt 1in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">[C]<SPAN
style="mso-tab-count: 1"> </SPAN>Bill Frist will visit <st1:place
w:st="on"><st1:City w:st="on">Meander River</st1:City>, <st1:State
w:st="on">Alberta</st1:State></st1:place>.<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">Suppose, the probability of P1 is
0.05 and the probability of P2 is 0.33.<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 0.5in; TEXT-INDENT: -0.5in"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana">[1]<SPAN
style="mso-tab-count: 1"> </SPAN>If the events described by P1 and
P2 <SPAN style="COLOR: blue">are independent</SPAN> of each other, then the
probability of C is (0.05)(0.33) = 0.0165.<SPAN style="mso-spacerun: yes">
</SPAN>[Notice that if two numbers are between 0 and 1, their product will
always be smaller than either number.]<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"><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">[2]<SPAN
style="mso-tab-count: 1"> </SPAN>If the events described by P1and P2
<SPAN style="COLOR: blue">are not independent</SPAN>, then the probability of C
is always less than or equal to the smallest of the probabilities of P1, P2, in
this case the probability of C is less than or equal to
0.05.<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 convenient way to say this
is:<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"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 14pt; COLOR: blue; FONT-FAMILY: Verdana">In general, the
probability of the truth of the conclusion of a valid deductive argument in the
context of the argument is less than or equal to the smallest probability of the
probabilities associated with each premise.<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"><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 whether or not
you are in agreement with the very basic fundamentals expressed above.<SPAN
style="mso-spacerun: yes"> </SPAN>If so, then I have only one other small,
but important issue to seek your agreement upon before we examine your succinct,
charming characterization 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">Thank you again for your patience
and forbearance with an aged, slow-witted codger.</SPAN></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><SPAN
style="FONT-SIZE: 14pt; FONT-FAMILY: Verdana"><BR>Art Deco (Wayne A. Fox)<BR><A
href="mailto:deco@moscow.com">deco@moscow.com</A><BR><o:p></o:p></SPAN></P></DIV></BODY></HTML>