So, the top sentence: "All men are mortal," is like a Big sentence,
which implies the two below it. As can be seen, "Socrates is mortal,"
because he is a (man), and therefore (is mortal), but this just means:
All men            are mortal.
Socrates is a               (man)               (is mortal.)
      So "All men are mortal" is like a Big sentence, that itself implies,
of its very nature, littler sentences, such as, "Socrates is mortal."
      If we look at the sentences in the opposite direction, from 'down' to
All men             are mortal.
Socrates is a               (man.)
                                     Socrates             is mortal.
<--- Induction: Start here and go up.
we see Aristotelian "induction." When we go 'up' in this way, we move
toward the Big Sentence that our littler sentence is an implication of.
      The Big Sentence "completes" or "perfects" the meaning of the
littler sentence, just because, once you find the Big Sentence, you can
see that the littler sentence is an implication of it.
      So, the Big Sentences that littler sentences are the implications of
could be called "perfections" -- completions -- of the littler sentences.
You can see -- you can only see -- the real meaning; that is, the full
meaning, of a littler sentence when you know its Perfection: the Big
Sentence that it is an implication of.
Big sentence (Perfection)
                  ( implies ) |
littler sentence
      Notice that the littler sentences themselves do not have a real, full,
settled, necessary, logical meaning on their own. The "material
singular" -- little sentences -- do not actually have meaning of their
own, because they do not have meaning on their own. Their meaning
really comes from being an implication of a Perfection, of a Big
sentence. The meaning of the little sentence, "Socrates is mortal," is
implicit in the Big sentence, "All men are mortal." The little sentence
gets its meaning only by being an implication of its Perfection.
      Here is another way of showing this. When you go 'up' (Induction),
your job is not done -- the meaning is not fully clear -- until you can
also go 'down' (Deduction) from your proposed Big sentence to your
littler one. When you can show that your littler sentence is a necessary
implication of your Bigger one, you've proved your case.
Big sentence (Perfection)
                   (implies ) |
this littler sentence
so this littler sentence is `true'
      Notice that when we go 'up' toward the Big Sentence, (which is
induction) our progress can not be as sure as when we start with the
Big Sentence and go 'down' (deduction). Going from 'down' to 'up,'
things can not be as clear.

N.B. This is an html-ized copy of a page from the pdf file, The Knucklehead's Guide to Covenantal Theology.

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