Tuesday, April 24, 2012

Affirming the consequent and predictive value

In the hard sciences, the ability of a theory to make accurate predictions is taken to count in favour of that theory.  Let's use gravity as an example.  Although on earth, nobody had ever dropped a feather at the same time they dropped a heavy dense object and observed them falling at the same rate, the theory of gravity predicted that they should fall at the same rate if you eliminate all the forces (especially air friction) and drop them in a vacuum.  Since then, the theory has been tested by dropping feathers and bowling balls together in vacuums and found to be true.  The feather and the bowling ball do drop at the same rate in a vacuum where there is no air resistance.  That counts in favour of the theory of gravity.

Criminal investigators use this kind of reasoning, too.  For example, when somebody flees, that's taken as evidence of their guilt because fleeing is exactly what we'd expect from somebody who's guilty.

Historians also use this kind of reasoning.  I can't think of an example off the top of my head, but if I did, the scenario would be pretty much just like the criminal investigator scenario above.

This type of reasoning appears to commit one of the most basic formal fallacies called "affirming the consequent."  It takes this form:

1.  If P, then Q.
2.  Q
3.  Therefore, P.

In the case of gravity, the reasoning would look like this:

1.  If the theory of gravity is true, then a feather and a bowling ball should drop at the same rate in a vacuum.
2.  A feather and a bowling ball DO drop at the same rate in a vacuum.
3.  Therefore, the theory of gravity is true.

This whole principle of predictive value seems to depend on this fallacy:

1.  If theory X is true, then effect Y should be observed.
2.  Effect Y is observed.
3.  Therefore, theory X is true.

Don't get me wrong, though.  I'm not trying to argue that the predictive value of a theory does not count in its favour.  What I suspect, instead, is that it's not a deductive argument, and it's a mistake to characterize it as such.

4 Comments:

At 4/26/2012 12:19 AM , Anonymous Boz said...

I think this argument should be reversed, because scientific observations attempt to falsify the hypothesis.

1. If the theory of gravity is FALSE, then a feather and a bowling ball should NOT drop at the same rate in a vacuum.
2. A feather and a bowling ball DO drop at the same rate in a vacuum.
3. Therefore, the theory of gravity is NOT FALSE.

1. If P, then Q.
2. ~Q
3. Therefore, ~P.


I'm not sure if this logical example works, because with logic, NotFalse = True, and NotTrue = False.

But with an experiment, 'Not Falsified' = 'A tiny bit more likely to be true'

What do you think?

 
At 4/26/2012 2:54 PM , Blogger Sam said...

Boz, I think the way you characterize has problems, too. Your first premise is problematic because if the theory of gravity were false, that wouldn't necessarily mean a feather and bowling ball would NOT drop at the same rate (they may do so for a different reason). I think it's the other way around. If a bowling ball and feather did NOT drop at the same rate, THEN the theory of gravity would be false. Notice the contrapositive:

If the theory of gravity is true, then a feather and a bowling ball should drop at the same rate.

If a feather and a bowling ball do not drop at the same rate, then the theory of gravity is not true.

The second statement is the contrapositive of the first.

So the argument should look like this:

1. If a feather and a bowling ball do not drop at the same rate, then the theory of gravity is not true.
2. A feather and a bowling ball DO drop at the same rate.
3. Therefore, the theory of gravity is true.

But this argument commits another fallacy. It commits the fallacy of denying the antecedent.

I agree that a theory that is given a negative test (i.e. a test that could disprove the theory) but that passes the test is a tiny bit more likely to be true. I just don't think you can construct a deductive argument to make that case.

 
At 4/26/2012 7:26 PM , Anonymous Boz said...

thanks for the correction.

It looks like it is impossible to put this test in to the form of a syllogism. (?)

 
At 4/26/2012 9:37 PM , Blogger Sam said...

I think it's possible to put inductive arguments in the form of a syllogism as long as you put all the induction into one of the premises. For example:

1. If every time I drop objects, they behave exactly like the theory of gravity predicts, then the theory of gravity is likely to be true.
2. Every time I drop objects, they behave exactly like the theory of gravity predicts.
3. Therefore, the theory of gravity is true.

All the induction is in the first premise. The more objects behave according to Fg = G(m1*m2/r^2), the more likely it is that the formula for Fg is true.

 

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