Formally correct derivations
They have the proper structure.
But an inference can be valid even though its premises are false!
Example:
A louse is bigger than a mouse.
A mouse is bigger than a house.
So, a louse is bigger than a house!
They TRANSMIT truth.
If the premises do happen to be true, then the conclusions are
guaranteed to be true.
They RETROMIT falsity.
If the conclusion turns out to be false, then at least one of
the
premises must be false.
Example from the Galileo Case Study: Venus has phases similar to the moon. Any celestial body whose apparent shape changes according to its position relative to the sun and earth does not shine by its own light. Therefore, Venus is does not shine by her own light.
Example from the Semmelweis
Case Study:
Cadaveric matter in the bloodstream increases the probablity
of childbed fever.
Ward I patients are exposed to more cadaveric matter than are
Ward II patients.
So, there should be more childbed fever in Ward I.
Example from the Galileo Case Study: If Venus were travelling in a Ptolemaic epicyclical orbit. it's illuminated face would never look like a full moon. Venus does show a full moon phase. Therefore, Venus is not travelling in a Ptolemaic epicyclical orbit. Example from the Semmelweis Case Study: Cadaveric matter is a necessary condition for childbed fever. Washing with chlorinated lime destroys cadaveric matter. All medical students in Ward I now wash with chlorinated lime after autopsies. Therefore, there is no longer childbed fever in Ward I. A false conclusion, so there are one or more false premises.
All heavenly bodies travel
in smooth curves around the earth.
The moon travels in a smooth curve around the earth.
Therefore, the moon is a heavenly body.
[It purports to be a deductive inference but it is invalid so
there is no connection between the truth/falsity of the premises
and the truth/falsity of the conclusion.
All heavenly bodies travel
in smooth curves around the earth.
The planets are heavenly bodies.
So, the planets travel in smooth curves around the earth.
[Inference is valid . When we observe retrograde motion we know
the conclusion
is false. This falsity is retromited to at least one premise.]
Any vacuum exerts a constant
inward pulling force.
A barometer column is held up by the force of the vacuum.
Mercury is thirteen times as dense as water.
Therefore, a mercury barometer will stand only 1/13 as high as
a
water barometer.
[Inference is valid; conclusion is true; but can't conclude from
that anything
about the truth of the premises. We now know, however, that there
is no force of a vacuum so the first two premises are false.]
Why science is difficult (from a logician's point of view):
FALSE hypotheses may entail TRUE conclusions.
So just because a hypothesis makes a correct prediction doesn't
PROVE that it itself is true!
(To conclude otherwise is to commit the fallacy of affirming the
consequent.)
(the logic of refutation)
Inferences with a FALSE conclusion must have at least one FALSE
premise.
So no matter how many phenomena a hypothesis explains (cf. the
force-of-the-vacuum theory), if it entails one false prediction,
then the hypothesis is false.
We say that it is refuted.
(And the logic of explanation)
We begin with a puzzle : Why P? (where we know P is true).
We dream up an explanatory hypothesis H which we hope is true
(but
may not be).
We construct a valid inference where H is the major premise and
P
is the conclusion.
We know P is the true conclusion of a valid inference but since
inferences don't retromit truth we can't conclude anything so
far about H.
(why we need an inductive
logic )
So we conduct tests of H by drawing out other predictions P* and
finding out by appropriate experiments whether each P* is true
or false.
If P* is false, we know H is false (assuming the other premises
used
in the derivations are true).
If P* is correct, we gain more confidence that H might indeed
be
true, but of course deductive logic doesn't PROVE that it is true.
However, if H passes many tests of the right sort, we use inductive
logic to say that H is confirmed to a certain degree or that it
is likely to
be true.
(and much of technology)
Once we are pretty certain that H is true, then we may use it
as the
basis for practical applications.
Namely, we use it to make inferences about how to construct useful
devices or intervene in the natural or social world in various
ways.
If H is true, then since valid inferences transmit truth, our
bridges
should not fall down and our interventions should be successful--
assuming all of the other premises in the inference were also
true.