Livelogic: The rule of two consequents

[mns2012]

Preface to Russian readers:

• Мой перевод записки livelogic: "Правило двух". Разрешение автора на перевод было получено мной уже давно, правда, не помню, когда именно. При желании это можно установить.

mns2012: Below is my English translation of the original post entitled "The rule of two consequents" by livelogic.

Here is my modest contribution to the scientific method in the form of the Rule of Two Consequents which posits that each statement of a scientific theory should yield at least two independent and testable consequents.

The principle is easy to understand. If only one consequent follows from some initial theoretical proposition, then we can accept that consequent as our new proposition, while the original one can be discarded as unnecessary. Another way to look at this is as follows: If we have an unexplained fact F1, and we try to explain it through assumptions A1 and A2, such an explanation is not parsimonious: we start with one unexplained fact, but end up with two unexplained assumptions, which increases the amount of the unexplained. And, of course, another important point to mention is that facts/observations do not fall under this rule; they may not participate in any reasoning at all.

Let's consider a simple example. We've lost a slipper and need a theory to explain it, preferably a scientific one. First, let's try to explain it using the aliens:

The slipper was taken by the aliens.

What do we know about the peculiarities of alien theft? Perhaps, nothing except that whatever is taken by the aliens is not here anymore. Not much... but an explanation can be constructed nonetheless.

So in our theory we have:
* Hypothesis: The slipper has been stolen by the aliens.
* Postulate: X has been stolen by the aliens therefore X is not here.
* Consequent: The slipper is not here.


With our tentative theory, using two theoretical propositions we have managed to derive a practical consequent. Is it helpful? Not really. Indeed, there was one unexplained point, and now there are two. So, while trying to explain one thing we ended up increasing the amount of explanandum to two things.

Okay, if this is not the way to build explanations, how should we build them?

It would be better if we could make a prediction that follows from our hypothesis. The idea is clear: apart from its main job to explain what we want, our hypothesis should yield at least one more consequent that could be tested independently.

How does it work? Let's return to our example and see if we can improve our theory. This time though we will use a pet dog instead of the aliens.

The trick is that we know much more about dogs than about the aliens. E.g. a dog drags its favorite things behind the wardrobe and a stolen item is usually wet with dog's drool.



Our hypothesis "the slipper is stolen by the dog" turned out to be a very fruitful starting idea: it has a total of three consequents. Looking at this carefully, "The slipper is behind the wardrobe" and "the slipper is not here" are dependent, which may be interpreted as problematic. At any rate, there are definitely two independent consequents.

However, we can see another problem here, namely that our postulates have only one consequent each. Can we fix it?

Yes, we can. Let us use a sock as an additional item. Our theory now looks like this.



So, everything looks correct now: the postulates and the hypotheses explain what we want to explain, and they provide at least two consequents each. Our theory is becoming a scientific one while the introduction of additional explanatory entities becomes justified.

Evolutionary theories

All evolutionary explanations are akin to explanations through the aliens. Indeed, the rule of the two consequents is not satisfied. Explanatory entities multiply faster than the explanations they provide. For example, how can the presence of multicellular organisms on Earth be explained from an evolutionary standpoint?



The structure of the theory is exactly like our alien theory above: two explanatory items are used to explain one observation.

Can we fix it? Let's bring in organism diversity. What do we have now?



Is the situation better now? No, because we now have two postulates each yielding only one conclusion, and we use three explanatory items to explain two observations. Moreover, there are no predictions. The patent for such explanations have long belonged to religion: everything is according to God's will [and expectedly so since religion is inherently different from scientific inquiry; while being true, this statement has a tad bit of pardonable friendly humor -- mns2012].

What can help us here? To some extent, the discovery of a second diverse and multicellular life, for example, on Mars. Then our evolutionary postulates will sprout second shoots and become alive.

There is another problem here as well. Evolutionary theories come up with statements like this: "Natural selection is the main driving force of evolution" or "All life descends from LUCA". The logical chains will have to be built involving such statements. Can it be done? Maybe, but I've never encountered any examples of such chains. The well-known philosopher of science Karl Popper was skeptical of evolutionary explanations at one time:

"Suppose we find life on Mars, consisting strictly of three types of bacteria with a genetic structure similar to that of three Earthly species. Would this refute Darwinism? By no means. We would say that these three species are just forms among other mutants that happened to be well adapted for survival. And we would say the same if there were only one species (or none). Thus, Darwinism does not actually predict the evolution of changes. Therefore, it is unable to explain this evolution."

Karl Popper. "Darwinism as a Metaphysical Research Program"

Later, he, however, renounced this position, but that's another story...

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[mns2012]

Fame at long last. But all credit goes to livelogic.