d

Grue

In experiments on 29/06/2011 at 9:32 am

Not many people have heard of Alfred North Whitehead’s (yes, the coauthor of the Principia Mathematica!) 1922 theory of gravitation. It’s an interesting theory, not just for its content, but for its historical significance: for the longest time, both Einstein’s theory of gravitation and Whitehead’s theory of gravitation predicted “not only for the three classic tests of light bending, gravitational redshift and the precession of the perihelion of Mercury, but also for the Shapiro time delay effect,” (See Gary Biggons, On the Multiple Deaths of Whitehead’s Theory of Gravity) and subsequently both theories were equally corroborated by the data.

As of now, there exist several refuting instances of Whitehead’s theory, but for close to half a century both theories were viable candidates.

The question might be, then, is why was Einstein’s theory preferred over Whitehead’s when both predicted the same phenomena? In fact, Whitehead’s theory was rejected half a century before a crucial test could be conducted between the two theories.

I’m simplifying a great deal. A large number of philosophers and scientists adopted Whitehead’s theory and argued in favor of it for decades. There were pros and cons for both theories, and depending on the context, Einstein’s or Whitehead’s theory preformed better than the other. In that case, there was a period of time where two rival theories successfully competed against each other for survival in much the same way as two competing species fought it ought over the same ecological niche.

But forget all that. Assume for a moment that Whitehead’s theory was rejected outright by the scientific community without any prior testing. Treat Whitehead’s theory as an imaginary case-study of why a scientist rejects a theory before it has been tested.

There are other possible criticisms of theories besides refuting instances: we cannot test every theory that comes to our attention. There are some basic rules that go beyond simply “do not adopt a theory if there exists a refuting instance to it”: does it not cohere with other assumed body of knowledge? Is it logically inconsistent? Is the theory more complex compared to other theories? Is it too ad hoc? If a theory does not survive these criticisms, then we may choose not to prefer that theory.

Yet, what does the scientist do when both theories are coherent, logically consistent, and simple in form/not ad hoc? What else is there available?

I think there is no rational choice to be made between either theory in that case, but there may be non-rational choices. This is a real-world example of Goodman’s new riddle of induction: just as Einstein’s and Whitehead’s theories were at one time equally corroborated, the the terms ‘green’ and ‘grue’ are equally corroborated.

In the case of ‘green’ and ‘grue’, however, I can say that I will prefer the term ‘green.’ There are two ways of viewing Goodman’s new riddle of induction: in the first, observed emeralds retain their characteristics and do not change over at a certain time t; in the second, observed emeralds physically change their color after a certain time t.

The first interpretation expresses–in what I think is a very poor thought experiment–the underdetermination of our theories: no matter the number of corroborations, they equally supports a great number of viable theories. We can’t get out of this by positing a priori a uniformity of nature, for the expression ‘green’ is translatable into “grue before time t and bleen after time t,” so the term ‘green’ is no more uniform than ‘grue’ or ‘gred’ or ‘grack.’ If such a problem were solved, this still wouldn’t solve the problems of whether or not we witness an actual case of law-abiding behavior (think of Hume) and preferring one non-grue-predicate theory over another when both are equally corroborated.

The second interpretation, while more radical than the first, is of interest: there could be a physical switch of observed emeralds from ‘green’ to ‘blue’ after a single point in time. Imagine how strange this would be, to look at the Chalk Emerald Ring and see it change its composition right before your eyes! There’s no trickery taking place; no subtle shifts in lighting or a visual illusion, but a real shift in the frequency of light given off by emeralds.

This would look to us as a miracle, following rules that are wholly alien to the way we understand the world. Of course, this is possible: emeralds may mature over time, so that after a certain period of time, all emeralds ‘birthed’ at a specific time ‘age.’

Suppose that this will take place tomorrow without my knowledge. There is no way for me to influence this outcome. The emerald could change its physical makeup in just the same way as I could be struck by a comet, or my town could be instantly turned to ash by an atom bomb: I cannot make preparations for situations that are out of my control.

In cases of practical action, rather than theory-preference, if the physical switch from green to blue of emeralds has been a serious financial problem for emerald owners, then perhaps I ought to seek out some sort of insurance, just as I would take fire or earthquake insurance out on my house, even though the chances of houses burning down or suffering from an earthquake (depending on where you live) are relatively small.

In that case, we want decision making to be a case of satisficing rather than maximizing. We need only be successful enough for present needs. I then want to buy information in the form of insurance. If I insure against my emeralds turning blue (say, my $1,000 emerald would be devalued to a mere $100 if this should take place), then just as with fire insurance, I will be fully compensated if my emeralds should in fact be grue and not green.

Assume that the chances of emeralds turning blue, or gold turning into silver, or money turning into parchment is a pressing problem for me. Assume that these physical transformations take place quite often. I am making decisions under uncertainty, since while one course of action (‘behave as if emeralds will always be green’) has been subjected to criticism and survived in what appears to be our world, there remain other proposals for action (‘behave as if emeralds might turn blue, or gold will turn into silver, or paper into parchment’) that have not been effectively criticized, for there exist possible worlds quite close to ours where the switch is just around the corner.

Yet, since we cannot predict if our emeralds will turn blue, or our gold will turn into silver, we naturally diversify of investments. What I am saying about ontology is translatable to economic theory: you can never know if your investment will lose its value. So what do the economic gurus say we should do? Don’t put all your eggs in one basket!

If, however, the universe should engage in this change-over with all manner of things (eggs turning into tulips), then investment–in general, attempts to make decisions about the future–would be far more difficult than it is now.

But what of it? The clincher: I should not invest too much in scientific theories, even if they should appear to be extremely supported.

Deutsch’s solution to Goodman’s new riddle, however, is strong enough to dismiss grue-predicates, yet it does not address Whitehead’s theory: some sort of explanation for the grue-like behavior is necessary before they are treated as viable. Why ought I spend my time on theories that say the sidewalk may turn into tapioca pudding? Yes, it may occur, but many things–from Flying Spaghetti Monsters to teapots orbiting Mars–may occur.

In science, rather than finance, there’s very little riding on our decisions. False conjectures, for the most part, do little harm. We can afford to make mistakes. If emeralds should be ‘grue’ in the future (‘grue’ as understood in either context explained in IV.), I will own up to my error in judgment, for I will have made a conjecture that turns out to have been false. In the first case, I’ll shrug my shoulders and move on; in the second case, something is very wrong in the way we understand the ‘maturing’ of emeralds over time.

In order for make a decision of which of the two equally-successful theories to adopt for experimentation or notation, just as Buridan’s ass, one must simply choose. Flip a coin or go with what’s more computationally convenient. A scientist can search for any possible case where the two theories do not predict the same phenomena, but presently they look equally tasty. No one will lose a great deal of money over the failure of Whitehead’s theory.

If there are possible test-cases, then try to test them the moment you can. If there are no possible test-cases, then perhaps the two theories are in fact expressions of the same theory, or like the corpuscular and wave theories of light, each may be incorporated into/superseded by QED.

And with that, Goodman’s new riddle of induction is dissolved: if both theories should survive criticism, prefer whatever of the two theories you want. It won’t be a rational preference, like between a glass of cold water and a glass of poison; it will be a nonrational preference, like between chocolate or vanilla ice cream. If the two ice creams or theories are incompatible in their predictions, seek out the crucial tests!

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