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Separating true theories from TruthLike ones

Post of the Month: March 2010


Subject:    | Pagano's blather
Date:       | 07 Mar 2010
Message-ID: |

Tony Pagano asserts:
> It is what Hume---the rabid atheist----warned us of in the mid-1700s.
> Corroborative evidence tells us not one twit about the truthlikeness
> of our theories. It doesn't even tell us whether our theories are
> probably true. And as Karl Popper pointed out (in the mid-1900s)
> every false theory has some (or many) true consequences making
> corroborative evidence readily found for all FALSE theories.

Bill Rogers begins:
We'll show just what pretentious nonsense this all is in a moment. But first, let's stop to enjoy just one of Pagano's favorite words. Truthlikeness....Say it several times. Roll it on your tongue. How tasty! How strong and masculine and Germanic it sounds compared to its weak, Latinate cousin, verisimilitude. Truthlikeness. It's easy to imagine Kant or Heidegger including it in their limpid, transparent prose style. I say it again and again. Slowly I feel profound and wise, able to see past all sorts of Enlightenment claptrap. I say it again, "truthlikeness, truthlikeness," and slowly my shirt morphs into a well worn tweed coat with patches at the elbows, a lit pipe appears in my mouth, leather bound books appear on the walls. Ah, truthlikeness, I feel so much smarter already, I'm going into a deep trance of complacent self-satisfaction.....

Oh, but to the nonsense at hand.

Let's look at this bit here ..."And as Karl Popper pointed out (in the mid-1900s) every false theory has some (or many) true consequences making corroborative evidence readily found for all FALSE theories."

First of all, theories do not have consequences; theories make predictions. [Well, that's not quite true. One consequence of the theory of evolution is that a subset of religious people have their panties in a twist, but that's clearly not what Pagano means by the consequences of a theory.] That the apple falls is not a consequence of the theory of gravity. The theory predicts that the apple will fall as a consequence of gravity.

So what does it mean to say that "corroborative evidence is found for all false theories?" Pagano also likes to claim that theories are underdetermined by the evidence and that therefore there are an infinite number of theories that can explain any set of evidence, a related but slightly different point.

What does it mean for there to be corroborative evidence for a false theory? It must mean that the "false" theory makes a correct prediction. How could this work? I won't try to come up with an infinite number of theories to explain this evidence, but let's start with three. The observation is that a 98 gram apple falls to earth with an acceleration of 9.8 m/s/s. Consider three theories:

  1. a mass falls under the influence of gravity at an acceleration equal to its mass in grams divided by 10
  2. Newtonian gravitation
  3. General relativity.
Our Paganoesque scientist likes the first theory. He finds two dozen apples, each one weighing 98 grams. He drops them and finds that they all fall at 9.8 m/s/s. He's thrilled. Corroborative evidence! This theory is TRUTHLIKE. But, he's not a fool. He knows he should test the theory under other conditions. He drops a few 98 gram pears and peaches. Once again they fall at the predicted acceleration. He's identified the deep principle of Gravitational Fruit Invariance. He tries 98 g cantaloupe, plums, oranges. He goes for 98 gram rocks - my God, it's true beyond the domain of fruits! He's hit the big time.

OK. This seems to be what Pagano means by a false theory with many bits of corroborative evidence. But the theory is indeed making correct predictions. It's just that a few better thought out experiments would show that its ability to make correct predictions is restricted to objects with a mass of 98 grams. It's not really a false theory, just one that is only true in a very, very limited domain. Newton's gravity is similar, true in a restricted domain, except that the restricted domain is wide enough that it's actually a useful theory for many, many applications. Einstein's gravity makes correct predictions in an even wider domain. It's a bit hard to work with, though, so if you want to predict the gravitational acceleration of a 98 gram apple, you can stick with theory number one.

There are several points here. First, what distinguishes a smart scientist from Pagano is the ability to find situations in which different theories make different predictions - gee, lets drop a 2 kg watermelon instead of a 98 gram apple - see, it doesn't fall at 200m/s/s. Wow. Second, a theory which makes correct predictions in all the situations you can think of is as "truthlike" as a theory gets. Third, pace Popper, good scientists do not attempt to confirm or reject single theories in isolation; they develop alternative theories and then look at situations where the alternative theories make different predictions. Fourth, rambling on about Popper and Hume and the scientific method in the absence of specific examples just makes you look silly.

If you do feel silly and foolish, though, all you need do is repeat to yourself over and over "Truthlikeness, truthlikeness, truthlikeness," and you'll feel much better.

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