Published on: 2020-04-05
Truth value as magnitude of predictions
The best way to discern truths from lies is to see if they have a probability and a margin of error attached to them.
The second best way to do so is to ask when the people holding those potential truths were able to bring them to bear to alter the course of the world.
Once you get past the silly phenomenological and metaphysical layers (i.e. “Do chairs exist ?" Style questions) the problem of truth becomes rather interesting.
In that “truth”, as we commonly use it, will always be dependent on the context, the individual thinking or saying it and the inherent errors in the ways we determine it.
Sometimes (usually) we consider the errors or the probability of it being “true” as being negligible, other times we go to great lengths to determine them.
When looking at a chair it’s rather obvious that the mental map we have for any given chair will differ between individuals. If two people were to strive towards perfectly describing a chair there might be some amount of difference between their description, but the difference would be of no consequence. Thus, we don’t ascribe any error bars to the truth of an object being a chair.
When looking at the data resulting from the collision between some particles, the instruments will have collected certain things that we consider to be truthful insights into the events… and indeed, one could argue they differ much less than the mental pictures two individuals have of a given chair.
However, we still try our best to determine the potential errors our instruments might induce and account for them, thus attaching a margin of error and a probability to the observation, because even minute errors in particle physics are going to be much more consequential than even glaring errors in two individual’s conception of a chair.
That’s also why discussions around gathering and interpreting data from particle accelerators is a much more pertinent subject than a discussion between a myope and a hyperope regarding their mental image of a chair. In a way both of these discussions involve truth claims, but the former is a “truth” that’s worth defining more clearly. I would argue that, the very reason why we might feel like this is so, is how we can end up creating a better definition for its truth value.
But I digress, let’s look at scientific truth for examples, it seems that the two main features of generating scientific truth are:
1. Comparison with other scientific truths via Occam’s Razor.
Entities should not be multiplied without necessity.
If you have the equation
y = x^2 * ((b – 1) * (b + 1) - b^2) and the equation
y = -(x^2), both formulations are true, both purport to model the behavior of
y in relation to
x and both succeed at doing so. But the second formulation postulates the simplest equation and only a subset of the variables in the first one, so the second would be considered “true” in the scientific sense and, I’d argue, in the colloquial sense as well.
To give one example, we can have the statements:
a) Objects attract other objects towards them with an acceleration linearly correlated to their mass.
b) Objects contain primordial gremlins that use the forgotten magic of the fae lords in order to attract other objects towards them with an acceleration linearly correlated to the mass of the object they reside in.
Both would have been equally correct at the time Newton made his speculations about gravity, since objects large enough for him this effect included only the planets, star and moons of our Solar system. The existence of primordial gremlins skilled in fae magic at the center of these entities is not something that cannot be easily disproved to this day.
But, alas, Occam’s razor tells us that, if a) and b) model the same phenomenon (gravity) and we can reach a) by just removing a bunch of entities (the primordial gremlins and the fae magic) from b), “a)” is what we’d define as “the truth”, at least until future evidence arises.
On the other hand, our good pre-scientific philosopher friar William of Ockham himself might postulate:
c) Objects attract other objects towards them at a given acceleration because God willed the world to be so.
Ockham might even astutely point out that the mass-proportional theory of gravity seems to have a few flaws in it, e.g. the fact that Mercury’s trajectory doesn’t seem to abide by the rules of gravity as stipulated by Newton. On the other hand, the heavenly and earthly bodies moving in the exact way we observed them because of divine ordinance perfectly accounts for these various abnormalities.
2. Popper’s falsifiability
A hypothesis is falsifiable if some observation might show it to be false
Going back to our model of gravity, suddenly, we have an answer to give to Ockham, something along the lines of: “Hey, what this Newton fellow postulated seems like something that could be disproved based on observations about the movement of the planets and even of objects here on Earth, however, I see no particular way of disproving the existence of a predetermined divine order”.
Even if Newton’s theory has some observations disproving it and the divine predeterminism theory doesn’t, the former is still “closer to the truth” because it is able to explain some observations while admitting a way to be disproven.
We can even go further and say something like: The truth-value of the hypothesis is proportional to how easy the observation[s] that can disprove it would be to make.
Under this model, even a truth which upon attempt to falsify reveals cases where it is untrue, is still fundamentally “true-er” than a truth which doesn’t admit falsification, or for which falsification would be unreasonably hard to engage in.
However, the combination of these two criteria still leaves us with a few problems.
Namely the vast amount of truths that can be generated and which, by applying these two criteria, we should consider to be valid until further disproof.
This is indeed a problem, because truth is something we use to make claims about the world we live in, so the fewer truths there are out there, the easier it becomes to think clearly about the world.
I am by no means a fan of the idea that unified theory of everything is worth pursuing, I’m inclined to believe that any such theory would be either so complex or so difficult to apply as to render it impotent. Even if by a stroke of luck this wouldn’t be so, coming up with one would render our lives terribly boring.
However, there is something appealing about the idea that you can, in any given zeitgeist, agree upon a finite list of models that, if fully understood, would basically allow one access to the sum of human knowledge.
Having too many theories about the going-ons in the world, even if they are not contradicting, leads us into an epistemic swamp. Where one could spend their whole life learning truthful things about the world yet be rendered completely unable to help his fellow men or even sublimate his own sorrows via this knowledge.
So ultimately, I think there must be a way to rank two true statements or theories, to say that even though they are both based on observation, even though Occam’s razor can cut neither of them, even though they are both falsifiable, one is nonetheless fundamentally “truer” than the other one.
This seems like a rather difficult task, but conveniently enough our collective actions would indicate such a criterion already exists, but I’ve seen nobody bother to spell it out, at least not in a way that I found to be satisfactory.
Truth value as magnitude of predictions
Let’s take as our competing example a recent psychological experiment on trash-talking in competitive video games) and the series of experiments that lead to the discovery of fission in the late 30s.
In short, the psychology experiment involves taking two people, making them play an american football video game on a PS2, instructing them either to stay silent or to trash-talk their opponent. Based on this some observations were made about the effect of talk talking vs silence in the player’s own performance and in that of this opponent.
The physics experiments that lead to the discovery of fission, involved bombarding a mass of uranium with neutrons, and theorizing as to the nature of the particles emanating from them. From this a hypothesis came about that uranium atoms could become so unstable due to this bombardment as to actually split into two separate atoms, which would be repelled by each other due to their charge, resulting in the release of a massive amount of energy. Finally, this led to experiments proving this, providing to us the key to nuclear energy and an entry point into how one might exploit the generative nature of this process to cause an explosive chain reaction.
I can’t find the original papers for the physics experiments, but provided that this was being done in the 30s, I wouldn’t even be surprised if their statistical apparatus was less advanced than that of the psychologists. Furthermore, whilst they had “the gist of it”, it took much longer for their observation to materialize into concrete theories that could be applied to produce nuclear energy and fission chain reaction.
Nor is there any noticeable qualitative difference under Occam’s razor or looking through the lens of falsifiability between these two experiments. Indeed, based on falsifiability alone one could argue that the truth claims of the trash-talking experiment are much narrower and much easier to disprove in terms of the experimental apparatus and prior knowledge required.
Yet it seems obvious that the theory of fission is one of those “key truths” that underlies our understanding of the world.
It seems equally obvious that the reaction of an adult playing a sports video game when his opponent insults his play-style is so irrelevant to anything or anyone as to only be called “truth” or “knowledge” under an imperfect or outright useless definition of those terms. It is indicative of a bug in our language.
There're two problems that stem from this example, one is related to treating the kind of mental illness that drives someone to run an experiment yielding such trivial, uninteresting and useless results no matter it’s outcome. Alas, I think that for now that might be best left to the psychologists’ own colleagues.
The other problem is one of differentiating clearly between these two pieces of “truth” in order to give our intellect and funding to the kind of endeavour that would generate the later and give our compassion and care to those afflicted with the madness that would lead them to generate the former.
The obvious differentiating factor between these fragments of truth, at the time they were discovered, is their predictive magnitude.
If asked about the potential predictions one could make based on the discovery of fission, the European physicists of the 30s might answer something like:
“Under a best case scenario this could potentially lead to us producing amounts of energy which would make all current electrical plants obsolete and solve the problems of pollution and cost for all our energy needs, it might also lead to weapons so powerful as to destroy our very planet. Under a more probable scenario, it could lead to a source of energy that would be less polluting and more efficient than our current power plants and to weapons so powerful as to allow us to wipe entire capitals from the face of the earth in a mere second”.
The magnitude of the prediction consists in the number of inductive steps required to go from “This is how a bit of uranium expels particle when bombarded with neutrons” to “This is how you could blow up an entire cities within a second with a device the size of a small car” compose a rather impressive chain. It also consists in the sheer importance it’s final conclusion.
Nuclear energy and nuclear chain reactions are two of the things that one can infer from the possibility of fission in uranium atoms, but are not in any way the only ones. These kinds of observations, when integrated into the greater model of physics, have the power of explaining and generating most of the objects in the modern world that we would view as making our condition superior compared to the generations that came before us.
On the other hand, if we are to ask the psychologists about what predictions their experiment might entail, they might answer: “Under a best case scenario, where more similar studies are realized, it might tell us whether or not trash talking your opponent is usually useful in competitive games. Under the current circumstances, it confirms and disconfirms some people’s intuition about trash-talking in this very constrained setting and might prescribe some optimal behaviors to… ahm, people people that want to win more often at playing pretend sports”.
If we associate predictive magnitude to truth values, the distinction is immediately obvious. But predictive magnitude is hard to quantify. To some extent, it depends on one’s personal values.
However, when it comes to comparing fields and subfields more closely related in terms of impact, the answer to the question of “which is the prediction with a greater magnitude” might become less obvious.
That is not necessarily a problem, at the end of the day my purpose here is to describe a criteria under which to discard some truths as completely irrelevant. The purpose here is to think about how to make the set of truths that one must concern himself with smaller, rather than reach the smallest possible set.
Indeed, if we come to disagree on the value of specific predictions, that just means that we end up concerning ourselves with different fields of inquiry and funding or helping with different projects. This in itself is a good thing, as long as it’s not taken to the extremes that generate our modern pseudosciences.
Predictive magnitude as a way of discerning personal truth
Indeed, I think that predictive magnitude as a way of determining the relevance of a certain truth is not only useful in science or engineering, but could be generalized as the model we commonly used to judge all truth, including those of interpersonal relationships.
Take for example our customs regarding monogamous relationships, these involve:
Sacrificing sexual relationships with all other people
Spending an exorbitant amount of money on a wedding ring and wedding
Putting yourself at great risk of having to deal with financial loss, social shunning and legal issues in the case of a divorce
It seems like a traditional monogamous relationship has a lot of downsides and the upsides (a small tax cut, in certain countries) is rather tiny.
One could think of them as a remnant of ages past, where e.g.they made for the only way to raise kids safely and they avoided the spreading of STDs which were much more deadly back then. But I think this is a rather reductive view and none of these reasons apply to our modern world.
I would argue that the monogamous relationships endured in this format, exactly because of their many potential downsides. Especially because the downsides are much more poignant if one ends the relationship and even more so if they engage in a new one afterwards.
Let’s look at all the 4 items listed above and try to analyze them through the lens of the kind of predictions that lead to them.
Sacrificing sexual relationships with all other people, is partially equivalent to saying “I predict that I like you so much, I would rather have sex with you than anyone else for the rest of my life”.
Spending an exorbitant amount of money on a wedding ring and wedding, is partially equivalent to saying “I predict that even though this amount of spending is beyond my means, it won’t harm me in the long run because it’s a one-time thing”.
Risking financial, social and legal distress in the case of a divorce, is partially equivalent to saying “I predict that we can safely ignore the probability of this horrible event, since we get along so well I can’t see it ever happening”.
In other words, you are making predictions about how much you love the person you are in a relationship with. While all these things might not be beneficial on their own, they are beneficial in that they reinforce the truth value behind the claim of love. Or, to put it even more disgustingly corny way, they are an attempt at showing true love.
Indeed, that statement can be made about a lot of inter-personal truths, such as friendship, which usually becomes stronger if the people go through some sort of hardship together.
In a sense, friendship as we define it should involve more than just grabbing a beer with someone every weekend, friendship is a prediction of being able to rely one someone, so when that prediction comes true (i.e. when you help them or when you provide mutual help in a hard situation), the truth value of the friendship itself is reinforced.
This way of thinking about things also provides a framework of thinking about the truth values in culture and religion. Cultures and religion make claims without backing them up with any evidence, “You should give your kids gifts for Christmas and pretend a jolly magical fat bearded man bought them” or “You should not kill and you should love thy neighbour”. These are implicit and explicit truth claims made by religion and culture about how one should behave.
These sorts of claims stand un-backed by evidence, but within these claims is the implicit assumption of “If you act as if though they are true, society will prosper”. The only thing that does assign a truth value to them is the fact that most members of society went along with them for a long time and the implicit prediction they made came true (since here we are).
Granted, this paradigm does not provide a way to think about the kind of religious or cultural truths one should discard. Stick too closely to the paradigm and you will end up defending slavery or the unjust persecution of various groups purely out of conservative reasons, out of fear of experimenting with anything new.
Generators of truth
Lastly, there comes the question of what this kind of thinking would have to say about generating new truths.
After all, asking “What kind of predictions can this theory make ?” is all well and good once you’ve got a complete theory, but most promising theories are incomplete. Even once a theory is complete, putting it in practice might involve a significant investment.
One may initially see little value in classifying and studying wild animals and plants, but give that area of study the thousands of years necessary to get from Aristotle to Darwin and you get a theory about how life changes and propagates itself. Give it a hundred and a few more years and you can start building modern genetics upon it,that certainly has a lot of useful predictions it can bring to the table.
But ask Aristotel what’s the point of trying to find traits that separate animals, and not in his wildest dreams will he be able to say “Well, it could lead to recombinant DNA vaccine being created to prevent deaths from Dengue and JE”. At most he might make a claim such as “Well, we might be able to figure out which animals can be easily domesticated”… but if that was his predictive scope, although it might have had a huge impact, it would have horribly failed. All animals that we could easily domesticate and put to use have been domesticated since way before his time.
To take a more current example, various flavors of string theory are yet unable to make any meaningful predictions. While I don’t know enough physics to comment definitively on this one, it seems to me that most of the people involved in it wouldn’t stick their hand in the fire about any potential near-future predictive power either.
Even more so, some areas of study might never produce predictions of any magnitude and yet we still consider them to be important.
So why should one study astronomy ? After all the vast majority of inquiry into the subject matter have yielded nothing directly. What little it has yielded, e.g. the ability to navigate based on the positions of the stars, is no longer of use to us.
But obviously, the indirect results from the study of astronomy have been astonishing. As mentioned before, gravity itself was postulated as a result of trying to explain the movement of the planets.
Furthermore, a lot of modern physics, the kind that leads to the creation of amazing things here on Earth, seems to stem from the mathematical and conceptual apparatus that appeared from the study of astronomy.
A very pessimist answer here would be something like “It doesn’t really matter”, after all for every well of truths that ended up being useful there’s probably a thousand others that amounted to very little.
Aristotels writing might have sown the seeds of natural science, but Aristotle had no way of knowing that Pyrrho’s skepticism or Epicurius’s philosophy of mind were inferior paradigms from which to seek the truth.
I expanded a bit on my thoughts on this idea here.
But overall I don’t think this answer holds much sway, neither with myself and I’d think even less so with you.
A better answer might be that the generation of new truths without any predictive value could be guided by the subject under which they reside. For example, studying animals and plants seems to be generally more fruitful of an endeavour than inquiries into the idea that all perception is illusory. So Aristotle could gather his ideas under that rallying cry as being somehow “superior” to that of an ancient skeptic.
The same could be said for comparing string theory to any number of other systems of “understanding everything” proposed by quacks all over the world. In that one could say, that the very fact that string theory takes a line of thought which has previously yielded results, trying to deconstruct processes into ever smaller components, increases it’s chances of yielding useful predictions.
Indeed, this seems to be the reason why experimental psychology, which nowadays concerns itself with theories which I’d view as utterly devoid of meaningful truth, is still regarded as something worth doing. Because experimental psychology in its original form, stemming from Amos Tversky and Daniel Kahneman’s theories about cognitive biases, proved to reveal things with tremendous predictive power in areas where making those predictions is tremendously useful.
An answer which allows for even more room would be putting more trust into argument from authority and argument from people with skin in the game.
If someone or some organization that has produced valuable truths before claims it’s working towards producing similar new truths, that is the best we can do to judge it’s progress until the discoveries and theories amount to a truth of an acceptable predictive magnitude.
One could say that the truth claims are correlated with how invested their makers are into their predictive ability.
For example, let’s say that back in 1992, a group of economists fromUCL compose a theory that says, given current monetary policy, the pound sterling will be able to meet the currency exchange limits for staying in the ERM.
The economists make this theory, but have no particular stake in it being true, they don’t throw away all their money towards investment strategies that would benefit from it being true, they don’t stake their tenure or their salary on the prospects of their theory’s predictive power. At most, they have their reputation to lose, but it’s the custom for economic theories to fail, so even that hit wouldn’t be so harsh.
Let’s say that back in 1992, George Soros also makes a theory as to how the pound won’t be able to meet the currency exchange limits to stay in the ERM, he proceeds to throw billions of dollars at this prediction, a tremendous chunk of his wealth, and to call all his investor friend telling them to do the same. He is actively trying to prove his theory true, by causing the event it predicts. Staking a tremendous sum of money and a lot of his reputation and business relations on this theory.
Should we assume that he is more correct ? Well, provided that both his theory and the economists’ theory are equally valid in all other aspects, and neither of them have made any meaningful predictions yet, I would say that our answer should be that, given the amount of skin in the game Soros’s theory has, it should be the correct one.
But, this is all post factual interpretations of events, it’s making no predictive claims, so it’s arguably kind of empty in terms of truth value under this very theory of mine.
Alas, I do actually use this view in order to dictate my actions. For example, I ignore most modern psychology based on it’s lack of predictive power. I stake both my investments and a huge chunk of the time I spend learning new facts, working, looking at experiments and understanding theories into machine learning (and into auto-ml in particular) and into the biology and medicine involved in extending lifespan and healthspan.
These two fields I’ve named as my favorite, have tremendous predictive magnitude associated with them and seem to rely on validation methods much more focused on predicting the future in unknown ways, rather than simply fitting past data.
I would be as brash as to claim that, in the future, those two fields will end up producing more truths which we can all agree are meaningful than experimental psychology and sociology, behavioral biology or investment banking.
But that’s a fairly weak claim, a stronger claim would be that these two fields will prove to be much more relevant to our future than, say, string theory or the pursuit of symptom-treating evidence based medicine. I would venture as far as to give a high probability to that claim, but if I had to stake my life on it, I would not venture that far.
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