Reasonable and rational largely indicate the
same thing: Ideas or conclusions made from good reason/reasoning/thought
process/logic/rationale. Going to college to get a better job
seems like a reasonable decision. With dark clouds looming, putting
up the tent at the new camp site before playing in the woods
is a rational ordering.
The opposite, irrational, is commonly associated with
decisions and beliefs that have no basis in fact or reason. It
is often associated with things like insanity, under the influence
of drugs, superstitions, mental problems, stupidity and ignorance.
Similarly, unreasonable is applied to ideas and judgments
that don't make sense, that don't follow accepted logic. A boss
who gives you a work load you can't possibly finish is called
unreasonable. He won't listen to reason and facts.
Reasonable, rational and logical are usually
associated with facts and truths. Reason is commonly deemed the
road to knowledge, while irrationality the road to delusions.
* * * *
The question for this page is when are objective facts unreasonable
and irrational? Under what conditions will sound reason and logic
make the truth seem false?
* * * *
Stating the obvious, much specific information is unattainable
by our reasoning powers no matter how fine tuned the reasoning
powers. How many slices of bread did President Abraham Lincoln
eat during March 1855? This is information we simply don't know,
can't know. Abe himself probably didn't keep a running total.
While our minds are able to count slices and measure bread, this
fact is beyond our reach.
There are other things we don't know even when it's present
and near. For example, we can't know for certain how other animals
psychologically perceive colors, including the ultraviolet and
infrared invisible to us. We understand and measure light, but
can't read a cat's mind. This information is beyond our powers
of reasoning.
* * * *
Logic: the innerworkings of reason
Our reason is driven by our logic. Sound reason uses sound
logic to come up with its conclusions. Logic is like the computer
language and mathematics behind a personal computer. In fact,
our logic is often is mathematical, such as below:
If a > b and b > c, then a > c
In the real world, one might use this logical equation to
deduce the following:
"If Fluffy the cat is darker more than Kitty the cat
and Kitty is darker than Snookums then, then Snookums is darker
than Fluffy."
This is an example of the real world logic and reasoning we
do every day.
* * * *
As air tight as the above logic may seem, there are a number
of weaknesses with the human logic/reasoning system.
The first is the above equation doesn't say "a > b"....
It says "If a > b" .... The logic depends
on accurate data being plugged in. If Kitty (cat b) actually
is darker more than Fluffy (cat a), the equation will produce
an incorrect answer. Garbage in is garbage out, as they say.
This brings up the question of when does good reason and logic
produce wrong answers due to bad input? When is reason made problematic
due to problematic input? I'm not talking about accidentally
typing in the wrong numbers, but problems caused fundamental
issues of perception and conception.
* * * *
Visual illusions as bad input into logic systems
Examples of bad inputs into sound logic systems include visual
illusions, where our logic, reasoning and common sense can't
make up for the viewer's non-conscious misreading of visual information:

The earlier 'cat equation' involves comparisons of darkness.
In the above visual illusion, most people misread the changes
in darkness. No matter how sound your If a > b ... logic,
your reasoning can't be more better than your ability to read
the tones.
The judgment of the tone itself was produced by an internal,
non-conscious logic system. The non-conscious brain gets the
visual information, puts it through its logic for such visual
situations and came up with a perception. Presumably, this logic
normally produces correct perceptions, but was this time fooled.
This illustrates that our mind's logic isn't always correct,
and should make one wonder about the accuracy of other non-conscious
and conscious logic systems. Can similar errors exist in mathematical
logic systems?
Duly note that the above visual logic system is designed to
make the snap decisions needed to get through life. The brain
was confronted with multiple ways to interpret the information,
and picked the wrong way. Having a small percentage of errors
is a byproduct for our need for speed.

Our non-conscious logic makes us misperceive the movement
of the barber pole.
This is why mirages can seem so real and can be so dangerous.
Normal logic tells the viewer something is a,
but it's b. People with genius
IQs can be can get killed in foreign landscapes because they
misread visual information.

For those who have never before seen or heard of the above
mirage, sound reason leads them to belief there is water in the
road. It would seem illogical that it is sky.
* * * *
Input variables due to subjective categorization and labeling
Another important input variable that causes trouble includes
how humans categorize, label and conceptualize information--
creating the a's, b's and c's for the logic equations. There
are usually many different ways to organize and label information,
and objects. In some way or other, most of our standard ways
of organizing and noting information involve our genetic tendencies,
physiological abilities, cognitive biases.
Even determining the darkness of the cats isn't as clear as
it may seem. The cats' darkness in visible light differs than
in ultraviolet and infrared light. The ordering of darkness may
depend on which light is measured. The a, b, c logic may be air
tight, but which cat is a, which is b and which is c can be debated.
When ordering the cats, 99.9 percent of humans will go by darkness
visible light, but this is merely the convention, the convenient
way. In 99.9 percent of the time the cat result of the a,b,c
equation result will be as much product of human convention as
of the soundness of the logic.
Categorizing and labeling information involves ambiguity,
meaning there are many different but equally legitimate ways
to categorize and label. Almost inevitably, humans choose the
way that means their biases, their tradition. Again, looking
at visual illusions show how choices based on bias and tradition
can result in folly.
Debatable input put through sound logic creates debatable
output. Ambiguous input creates ambiguous output.
* * * *
In the real world, humans judge information situations based
on their experience. With a story, the listener judges by how
it adds up to what they know and have been told before. Does
it seem plausible? Are there any holes in the logic or statements
you know to be false?
In this way humans are playing the odds. Implausible, or "an
unlikely story" doesn't mean it is impossible or didn't
happen-- but that it is seemingly unlikely. The story "doesn't
seem to add up." Of course, wild and seemingly implausible
stories have turned out to be true, so, without full knowledge
of what really happened, you never say never.
Propagandists know that a seemingly plausible lie, matching
the listener's experience, biases and reason, is more readily
believed than a implausible sounding truth. Truth can be stranger
than fiction, as they say.
* * * *
Duly note that rationality can and should comment on reliability,
or lack thereof. A rational statement would acknowledge degrees
of error, or potential degrees of error, in the logic and perception
system. It would be unreasonable for you or I to boldly state
we never make errors.