Hey, sub. Interesting choice of topic. I wonder how much mileage we'll be able to get out of it?
Part of the problem is that you are confusing
deductive logic, the type that is studied in philosophy and mathematics courses, with
inductive logic, which is more relevant to science.
To take your example, what we start with is (a slight modification of) your hypothesis,
It has rained.
So to test this, we say,
If it has rained, the roof will be wet.
The roof is wet.
Therefore, it may indeed have rained.
What we are really doing is testing the
contrapositive:
If the roof is not wet, then it has not rained.
The roof is wet.
Therefore, we cannot conclude that it is false that it has rained.
The hypothesis that it has rained has been tentatively confirmed, pending further studies.
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Let's look at another example:
Hypothesis: All ravens are black.(I like this one, because I try to expose my Math Concepts students to
the raven paradox.)
So how do we determine this is true? We certainly cannot examine all ravens. The only thing we can do is,
If all ravens are black, then the very next raven I see will be black.
So then I examine the next raven. It is black. Well, this sure as heck does not prove that all ravens are black in a deductive sense, but it does increase my confidence (a little) that maybe all ravens are black.
So then I look at the next raven. And then the next. After examining 1000 random ravens from different areas from two different continents, I find that each and every one of them is black. Now, from a purely deductive standpoint, I have proved nothing. However, I think that we can see that it is becoming quire reasonable to believe that maybe all ravens are black after all. In fact, we can even begin to put error bars on our conclusion; using relatively simple statistics, we can use the observed fact that, to date, all 1000 ravens that we have seen are black to estimate a maximum for the proportion of ravens that are not black.
Now suppose that we come across a white raven. So now we have a scientific falsification of our simple hypothesis that all ravens are black. We now have to do one of three things:
(1) Find out whether we made an experimental or observational error:
That's not a raven, moron, that's a swan
!
(2) Modify the original theory (and then test the modifications):
All ravens are black except those that suffer from white fungus albinism
.
(3) Abandon the theory altogether under the weight of contrary evidence:
Out of 1000 ravens in the sample, 700 were black, and 300 were white. I guess that not all ravens are black after all.
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Now, getting back to the former example.
If it has rained, the roof will be wet.
The roof is wet.
Therefore, we can tentatively retain the theory that it has rained.
Now, a Biblical anti-precipitationalist can object to this by, for example, positing,
the roof is wet because the owner hosed it down. Well, this hypothesis can, itself, be tested. Would the owner have a motivation for hosing the roof (say, as protection of an approaching wild fire)? Do we still see a hose connected to the outdoor tap?
Also, we can further test the original hypothesis:
If it has rained, the neighbor's roof will also be wet.
Also, the trees across the street will be dripping.
And the rutted road on the next block will have mud puddles.
And so forth.
Now these predictions are confirmed, and the anti-percipitationalist offers counter-explanations: the neighbor installed a fire-sprinker system in the ceiling that burst, soaking through to the roof; the trees aren't dripping rain water, they are dripping sap, and the puddles in the next street are because someone on that street has overfilled their swimming pool.
Well, we note a few things here. First, we then go and test each and every one of these counter-explanations to try to find whether they are plausible. Second, we note that the anti-precipitationalist has to come up with
ad hoc explanations for a wide variety of data, while the Theory of Recent Precipitation is a single explanation that unites this seemingly unrelated variety of phenomena (this is called conscilience, a good word -- I am currently reading Stephen Jay Gould's
The Structure of Evolutionary Theory).
And of course the anti-precipitationalist then points out that the basketball court is not wet. Oops! A potential falsification. Now the precipitationalist must try to come up with an explanation that fits the theory: is the basketball court covered? Is the ground composed of a material that dries out quickly?
Of course, in sight of the bulk of data that supports the Theory of Recent Precipitation, one seemingly contradiction is not going to discount the theory immediately. But it does open up a line of further investigation: can we determine why the basketball court is dry? We might discover something exciting about basketball courts! Or, are there other phenomena that falsify the Theory of Recent Precipitation? Once contradicting data becomes too numerous to ignore, people will start to look for an alternate hypothesis to explain the phenomenon of Widespread Wetness.
----
Heh. This went a bit long. Summary: there is a difference between
deductive and
inductive logic.
Edited by Chiroptera, : Typos. More than one.
I have always preferred, as guides to human action, messy hypothetical imperatives like the Golden Rule, based on negotiation, compromise and general respect, to the Kantian categorical imperatives of absolute righteousness, in whose name we so often murder and maim until we decide that we had followed the wrong instantiation of the right generality. -- Stephen Jay Gould
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