🚀 go-pugleaf

Deductive systems establish a procedure whereby one passes from a
premise or premises to a conclusion. The derivations are usually
presented as a sequence of numbered lines. For instance:

(1) Premise A
(2) Premise B
(3) Conclusion C  1,2
(4) Conclusion D  2,3
(5) ....................

The entry to the right of line (4) shows that that line was obtained
from the second and third lines, that is, that Conclusion D was
deduced from Premise B and Conclusion C.

This particular presentation of the derivations as a sequence of
numbered lines seems practical and yet it has never been and will
never be used by great deductivists raging in natural sciences. The
reason is easy to see if one first considers the bug-rivet story:

http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html
"The bug-rivet paradox is a variation on the twin paradox and is
similar to the pole-barn paradox.....The end of the rivet hits the
bottom of the hole before the head of the rivet hits the wall. So it
looks like the bug is squashed.....All this is nonsense from the bug's
point of view. The rivet head hits the wall when the rivet end is just
0.35 cm down in the hole! The rivet doesn't get close to the
bug....The paradox is not resolved."

and then tries to imagine the following sequence of numbered lines
published in both the journal Nature and the journal Science:

(1) Premise: The principle of relativity
(2) Premise: Einstein's 1905 light postulate
(3) Conclusion: Time dilation  1,2
(4) Conclusion: Length contraction  2,3
(5) Conclusion: The bug is dead  4
(6) Conclusion: The bug is alive  4

In the era of Postscientism REDUCTIO AD ABSURDUM is called "paradox"
and yet great deductivists raging in natural sciences wholeheartedly
avoid the presentation of the derivations as a sequence of numbered
lines.

Pentcho Valev
pvalev@yahoo.com