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The raven



                        I believe all this is redundant but nonetheless it keeps me amused



In these notes "falsifiability" refers to a theory of scientific method, developed by Karl Popper, asserting (amongst other things) that a proposition or hypothesis is not scientific unless it is falsifiable. This rests on the belief that scientific method is not inductive, but proceeds by formulating general hypotheses which must then be tested by attempting to find instances which falsify them. This is supposed to form the basis for scientific progress. Theories that are not open to testing in this way are non-scientific (the "principle of demarcation") and by the same token the verification principle of the the European positivists fails in its role as a guardian of science. This is the naïve or popular version of falsifiability. Popper recognised certain limitations with the naïve theory and subsequently developed a considerably more sophisticated account. This will not concern us, however, as it is the elementary basis of the entire theory which is questioned here. I do not for one moment believe that Popper would have considered such basic matters (which probably have little bearing on scientific method) to cast a shadow over his demarcation principle, but, if not, it's difficult to understand how the principle maintains any semblance of rigour. The only other account of scientific progress to gain any popularity in the 20th century, Thomas Kuhn's The Structure of Scientific Revolutions, approached the topic from an entirely different angle and encountered much criticism. It is only marginally relevant to the current discussion.

The naïve version of falsifiabilty, then, derives from the view that there is a problem of induction ("inferring a general law from particular instances"), especially evident when the problem is articulated in terms of either traditional (Aristotelian) or classical (Russelian) logic. These logics include universal propositions of the form "All A's are B", which, when negated, yield existential propositions of the form "Some A's are not B". For example, "All ravens are black" is rebutted by "Some ravens are not black" or more exactly "At least one raven is not black" (given that ravens exist). The problem of induction arises from the widely held opinion that "All ravens are black" cannot be confirmed by observing black ravens, since no matter how many ravens are found to be black, the possibility of a non-black raven turning up will always remain. However, if a single instance of a non-black raven is discovered, then the proposition "All ravens are black" is allegedly shown to be false. Thus the proposition (on this score) qualifies as "scientific" because, while not verifiable, it is falsifiable. And according to Popper, it is a requirement of all scientific hypotheses that they be falsifiable; indeed this is the only way they can be decisively tested. The primary task of scientists is therefore to search, not for supporting evidence, but for occurrences that are incompatible with the current body of hypotheses.

I will call statements like "All ravens are black" material universals. But first let us take note of some kinds of general proposition which are frequently represented in the standard universal ("All A's are B") format, but which are not material universals because, amongst other things, they do not meet the proposed criterion of being falsifiable by producing just one contrary instance (propositions of pure mathematics are excluded because, according to the prevailing view, they do not deal with events in the real world).

1. Defining or diagnostic statements such as "All mammals have bones and hair" are not open to falsification in this way, since the predicate (the possession of bones and hair) is part of the meaning of the subject (mammal). Such statements are definitions (complete or partial) of a species or class, so the proper contradiction of this example (in the same kind of language) is "No mammal has bones or hair".

2. In "normal" contexts, intrinsic propositions such as "All soccer balls are able to move only up or down, frontwards or backwards, left or right" and "No soccer ball can be both red and blue all over" cannot be falsified by producing contrary instances, since in the real world no such instances are possible or even imaginable. Propositions of this type differ from type 1 in that they are not "purely verbal" conventions, as their truth is determined by the nature of experience and not (for example) by a decision to call creatures with certain characteristics "mammals".

3. Sometimes probability statements are loosely expressed in this format, for example the statement "All matches ignite when struck" presumably means no more than that in normal circumstances the probability of finding a match that does not ignite is small (I wouldn't hedge any bets on this!) Finding a single dud match would not disprove the theory. Of course, at this mundane level one would not expect either scientists or philosophers to mistake a probability statement for a universal. But on a higher plane it's arguable that many do just that.

There are also various kinds of proposition which are frequently represented in the standard universal format but which are excluded from this class for reasons other than their resistance to one-off falsifiability (NB - here we're still going along with the myth that material universals are in fact falsifiable). Most important among these are (what one might call) "restricted universals":

4. A restricted universal is not really a universal at all, but a variety of existential proposition, exemplified by "All current residents of the Redland shire are licensed drivers". Clearly this statement implies the existence of a countable collection of objects (residents). It would indeed be falsified by the discovery of just one resident without a driving licence, but it could also be verified by checking that every resident is licensed. In practice the two procedures are virtually identical and their outcomes are equally cogent.

An unwary person might be misled by a variant of this type of statement in which the assumption of a countable collection is not made explicit in the statement itself, but is pre-supposed. For example "All B-class submarines carry nuclear weapons" is simply a statement of fact, given that no more B-class submarines will be built.

We must recognise, of course, that the boundaries between the various kinds of general proposition are fuzzy and flexible, due to the ever-changing rules of play affecting different language-situations. We assume that in a given context the basic logical properties of every relevant proposition are constant, otherwise the context itself must change. Also note that, regardless of any terminology used in this article, I would argue that there are no genuinely analytic propositions, not even in the realm of pure mathematics - see "Six kinds of proposition and the edges of normality" and/or "The physical nature of mathematics".

None of the above kinds of proposition equate to the material universal type, as represented by statements such as "All ravens are black". A thoroughgoing verificationist, however, would probably argue that this statement is meaningless, precisely because there's no way of verifying it. And although I find the verificationists' philosophy wanting, nevertheless I'd be inclined to agree with them that the statement is meaningless or absurd, though largely for other, more straightforward reasons. The main reason, outlined in "Six kinds of proposition ...", §2: Propositions, is the inviolable relationship between truth, meaning and plain speaking (i.e. making a declarative statement). Essentially:

Every statement purports to be true
Every meaningful, grounded* statement contains the possibility of being true
Every meaningful, grounded statement contains the possibility of being properly falsified
      (see the above reference and *Footnotes 1 and 2)

I take these to be fundamental facts about ordinary language (though you might have noticed they look for all the world like material universals! - so we'll probably have to be content with calling them definitions instead). I believe every meaningful "scientific" proposition contains within it the possibility of being verified - and verified in a certain kind of way, depending on the kind of proposition. And I believe we should be able to show that material universals are not only unverifiable, but that they are incapable of being corroborated, refuted or subjected to statistical evaluation.

A convenient way of approaching the refutability question is via the supposed paradox pointed out by Hempel (whose example of black ravens we are using here) and others. It is commonly held that the (pseudo-) proposition "All ravens are black" is corroborated by observations of black ravens. But in standard logic All ravens are black is equivalent to All non-black things are non-ravens. Therefore (it is alleged) every observation of a non-black non-raven, such as a red bus, a blue wig or a green Martian, corroborates the statement All ravens are black. This is patently absurd (seemingly more so when we realise that these observations also allegedly support the statement All ravens are white), but the elementary mistake here lies in the no less absurd belief that some observations do corroborate that statement. This mistake can perhaps be more easily understood if we rephrase the All ravens... pseudo-statement as There's an infinite number of ravens and they are all black. Clearly not one, not two not any number of observations of black ravens support this statement. For no matter how many black ravens are observed, there always remains an infinite number of unobserved ravens. The pursuit of the problem of this kind of induction is pointless, and it's difficult to understand why it still preoccupies some philosophers.

But rephrasing the pseudo-statement this way tends to refresh the belief that a single contrary instance (a non-black raven observation) would suffice to disprove the hypothesis. The error here is to suppose that mathematical infinities can somehow be matched to real-world sets of objects. There are no such real-world sets. But suppose that there were. A single exception, indeed any number of exceptions, would never be enough to refute the hypothesis, since there would still be an infinite number of black ravens remaining and thus the hypothesis would remain intact (in this fantasy land of nonsense statements).

Consider how you might attempt in practice to falsify a material universal such as "All fine art collectors make a profit". If the statement is well founded, you might have to interview, say, 20,000 fine art collectors before you found one that made a loss. Then you'd be able to announce to the world that the hypothesis "All fine art collectors make a profit" is false. But what would be the practical utility of that finding? Far from pronouncing the hypothesis dead, most people would probably rush out to grab some fine art, because the chances appear to be at least 20,000 to 1 that they'd make a profit. Of course, if lots of people seize this opportunity, the odds might change dramatically, but that's besides the point. The point is, rather, that the falsification excercise, even if successful, might strengthen rather than weaken one's faith in the concept which the material universal is supposed to articulate. I am not suggesting that the structure of scientific theories is anything like this (far from it - see below), but if they differ very markedly from this, one might well wonder why any philosopher of science would even bother giving the falsifiability proposal a second glance.

The falsifiability illusion, therefore, revolves around the absurdity of thinking of "All...." as an empirical statement. There are no genuine statements that are both universal and empirical, since those which are supposed to belong in this category cannot be verified, corroborated, refuted or statistically analysed, and those who trust in them harbour a peculiarly misguided view of reality. You can talk about all of a finite number of instances, such as all the ravens living in a given area, or all the ravens so far observed (by western philosophers, at least!), but not about all of an open-ended set (such as ravens in general including those that haven't yet been and perhaps never will be observed by anyone anywhere) unless your statement is intended to express a defining feature of ravens. To put it another way: if an observation against All ravens are black is not particularly startling, why would you ever want to make that statement in the first place, and if it's really startling why would you still want to maintain that the observed creatures be called ravens?

A normal "scientific" hypothesis about ravens might go along the lines "90% of ravens are black and 10% are not black" and the validation of this kind of proposition does not involve searching for contrary instances. However, one can keep observing ravens in order to corroborate the theory, but no such theory is ever considered "gospel". At best, by increasing the number of observations and employing statistics (or, for that matter, intuition) one can gain confidence that the 90:10 ratio is more or less correct. If, as many have argued, most scientific theories are like probability statements, it is clear that the evidence which could weaken or strengthen a theory does not exhibit the extreme imbalance (between falsification and verification) which characterises the notion of falsifiability. Most important theories, however, are yet more complicated than this, and often receive support from a wide variety of hard data which do not readily yield to statistical analysis.

The belief that scientific theories are logically similar to universal propositions is thus far removed from the true state of affairs. While collectively theories don't fit any exclusive pattern, many appear to satisfy the following simplistic description:

A theory is a unified body of facts
The "theoretical" part of a theory consists in the unification
Facts include relationships among facts
Unification consists largely in modelling these relationships
Sometimes the model may require the existence of facts not yet observed

Of course, there are many kinds and purposes of models, most apparently having been constructed especially to predict "facts not yet observed", and many of them are rather poor predictors. But the more serious scientific models often appear to be essentially similar to those used in the life sciences and reflect the scientists' relative lack of interest in falsification. In practice scientists tend to positively seek regularities in nature, and the occasional irregularity might not faze them: they simply tweek their models a bit. (Or else build enormous - and enormously expensive - machines to hunt for hypothetical particles, gravitational waves or missing dark matter.)

Returning to the subject of material universals, one could of course force them into the "restricted universal" mold by setting arbitrary limits on the numerical size of the sets concerned. One could speculate that there are now, have been in the past and will be in the future a total of, say, a billion ravens, and that a million of them have already been observed and every one of them was black. (The question of who does the observing is significant. Take the case of black swans: unheard of in Europe until relatively recently, but presumably familiar to Australian aborigines and New Zealand maories for thousands of years. See Footnote 3 for remarks on Nassim Taleb's book "The Black Swan".) Now, I understand very little about probability theory, other than through intuition, but it's just possible that on the basis of these numbers one could estimate the probability of discovering a non-black raven at some time in the future. I don't know how, because intuitively one would need to have already recorded at least one non-black raven to be able to deliver an estimate, and it would be a very poor estimate at that (the margin of error would be high). Anyway, what use would it be? For consider these points:

(1) Whatever estimate one produced would be an estimate of the probability of discovering, not only (say) a white raven, but a raven of any colour whatsoever other than black. But since the naming of colours is quite arbitrary, the number of colours is arbitrary too, and this circumstance would apparently play havoc with the estimate.

The raven (2) Supposing at some time in the future there's a genetic mutation in ravens that has a high survival value: for example, say some white ravens suddenly appear and this colour is favoured over black, so that eventually all the black ravens die out and only white ravens become established. What would one make of the probability estimate then?!  (This comment bypasses the fact that, although extremely rare, a few white ravens do currently exist, as this photo shows. No, it's not an albino! And there are very good reasons for classifying them as ravens rather than a new species.)

Clearly, the restriction of "All ..." to a finite collection hardly makes the concept of induction any more intelligible. One might wonder, too, what value there is in the idea of attempting to refute a theory by seeking a contrary instance. Suppose, for example, that an enthusiastic ornithologist discovered a green raven, thus "disproving the hypothesis" All ravens are black. So be it, but it doesn't add anything to our make-believe future scenario that most ravens are in fact white. A more astute ornithologist, with an enlightened hunch, might well go hunting for white ravens - not because of a desire to knock the black raven theory on the head, but possibly because he anticipates that most ravens at some time in the future will be white. He's not interested in falsifying, only in collecting positive evidence for his own theory (for an interesting aside see Footnote 4). At the experimental level this is surely the way of science, unless one thinks of scientists as a bunch of zombies with no imagination.

It's arguable that, in the context of an open-ended universe, particularising statements too cannot be verified and, assuming they have a sound basis, must stand (though in semi-limbo) until falsified. For example, the "hypothesis" There is one and only one red gremlin in existence cannot be known to be true with certainty, but the discovery of two or more red gremlins would disprove it. (And much the same argument applies to any numerically specific statement of this kind.) In attempting to refute this, however, you'd go looking for more red gremlins, not for non-red gremlins (or non-red anythings or non-gremlins). The methodological distinction between overthrowing There is one and only one red gremlin and confirming There are two or more red gremlins is insignificant.

This kind of proposition draws attention to a problem of observation - more exactly, a problem of recognition. The statement "There is one and only one red gremlin" implies: "All observations of a red gremlin are observations of the same red gremlin". Now, if the single known red gremlin is in captivity, a high degree of assuredness attaches to the assumption that observations of red gremlins at large will be observations of a different red gremlin. But if the known red gremlin is, so to speak, feral (and has escaped implantation with a tracking device) we have to deal with the problem of recognition - possibly not an acute problem in the case of gremlins, but often puzzling in the world of scientific entities. An important property of recognition is that it entails repeated observations in order to identify or confirm the existence of the object under scrutiny. So the identification of an exception to "All ravens are black" (supposing the proposition were sensible) seems to require a verification-type procedure after all. (At least we can say that a proposition such as "There exists at least one white raven" might well be in need of confirmation, depending on circumstances and the expected utility of the proposition.)

I shall not enter into further discussion of the problem of recognition here, but simply point out that it is one of several problems bugging the notion that falsifying a theory by observing a particular (contrary) instance is a more robust exercise, and leads to greater certainty, than the verification route. Both rely on generalities that one might be tempted to put in the material universal category.

It's more important to trivialise “logical” theories of induction: the continuous stream of silly attempts to formalise this concept is becoming irksome (as is the growing number of “theories” about how science is supposed to advance):  all the more so because the ultimate basis of deduction is itself inductive. Continuity and regularity are just essential elements of experience. Even the simplest statement of fact involves induction: you see a fig tree over there, to be sure of what you see you need either to keep on seeing it for awhile (continuity) or maybe to come back next day and take another look (regularity, recognition). Induction is simply a half-blind* trust that the tree will be there day after day, that the days keep on coming, that life goes on. There's always a possibility that someone will chop down the tree, a cyclone will remove it, or, worse, the sun will explode leaving no tomorrows. Only breadth of experience and knowledge can tell us which extraneous possibilities are worth taking into account. There seems to be no rationale for induction - it is largely subjective. Most of us are not even good at it, not wise enough. The poor man who survives by hand-to-mouth, day to day, is wiser than the philosopher. He accepts what comes, verifying nothing, and his theory of falsification can be explained in one word - death. We who have time to live and think can be sure of only one thing: in nature, anything can happen and logic and maths cannot be relied upon to help us. (*See Footnote 4B).

Scientists, perhaps, believe themselves to have more control over nature - a belief that receives some justification from the exponential growth in technological innovation. The input of philosophers into this revolution has been very disappointing, and largely descriptive. It really doesn't matter at all what "theories" (descriptions) of scientific progress and methodology they come up with. What, exactly, is their value, apart from entertaining other philosophers? All that matters, one would think, is that scientists maintain objectivity, integrity and a sufficient degree of open mindedness to expect the unexpected, whether in reality or in theoretical developments. And, these days, most of them do.

Despite these misgivings, I will somewhat reluctantly offer my "theory" of scientific theories (though doubtless it has been offered by many others before in one form or another). Roughly speaking, this theory says that the sense (life, substance, essence or content) of every scientific theory lies entirely in its practical utility - in the successful technology it propagates, the useful discoveries and inventions that follow from it. Any theory or part thereof with no demonstrable effects is dead wood. The hardware of a theory constitutes its verification, and since there is no more to a theory than its hardware, the verification of a theory equals the theory. More or less. A theory "needs" inventions and discoveries, but inventions and discoveries don't "need" a theory. In theories there's an element of openness or anticipation that does not exist in the hardware alone, and for this reason inventions and discoveries may exist independently of any theory, and indeed may be used in the construction of theories. But a theory is only meaningful to the extent that it says "we should be able to do such and such" or "we should be able to find such and such", and it is the "such and such's" that we manage to do or find that give life to the theory. In this sense, verification is of the essence, and falsification, as a scientific undertaking, drops out of the picture. (For a short, simplistic account of how this applies to the theory of evolution, see the end of Footnote 24 of Central Humanism. Evolutionism is a good example of a "descriptive" theory, which depends heavily on factual knowledge, while the relativity theory, at its inception, was an example of a "predictive" theory which needed a relatively small number of new, accurate observations to back it.)

So how does science make progress? Not à la Kuhn, not à la Popper, but simply through the efforts of people who work things out. They take whatever interests them in the knowledge base developed so far, then re-arrange, find new patterns, extrapolate, calculate, experiment, make new observations and so forth, hopefully with practical consequences always in mind, for, if there are none, the theory must be branded pseudo-scientific pie in the sky (regardless of how much effort has been put into it by mathematicians and astronomers - see Footnote 6). Of course, following publication of a theory or experimental result, final judgement of its worth must be left to others. No big deal really.

Finally, getting back to where we started, I will offer an informal definition of induction that doesn't beg quite so many questions:

Induction is an expectation, based on past observations of instances of X in respect of certain thusfar constant contingent characteristics of X, that any future observation of an instance of X in similar circumstances will disclose the same characteristics in X.

(The word "contingent" is included because X has both defining and contingent characteristics, and induction only concerns the latter. "X-like" qualities are excluded for the sake of simplicity. "Circumstances"? - a grey area! Also see Footnotes 4B and 5 and "Six types of proposition and the edges of normality", §9.4: Preservation of type - universals and quantification and §8.6: Logic as inductive thinking.)

Footnote 1 - What you say is what you mean. You don't need to append that you mean it is true. But of course just making a statement does not make it right or true. And if the statement turns out to be "wrong", it might be wrong because it's false (what the statement says is incorrect) or because there's something wrong with the statement itself, e.g. it is actually meaningless or irrelevant in the current context ("ungrounded").

Footnote 2 - My position on the meaning and truth of empirical propositions is far from robust. It's largely pragmatic, organic and sharply dismissive of scientism, semantic and coherence theories. I make no ultimate distinction between deductive and inductive argument, believing both to be grounded in natural processes. (See e.g. op. cit. §6.6: Personal interactivity and op. cit. §9.3: Theories of truth and "My philosophical outlook" Footnote.

Footnote 3 - How untoward was Nassim Taleb in choosing the title (and theme) for his book The Black Swan, since the traditional problems employing this metaphor are quite different to the issues he raises. While it's true the traditional problems would not have been couched in "swan" terms had the black swan (discovery) event already occurred, nevertheless his predilection for this avian species tends to cause confusion. Having said that, I really can't find much of interest in Taleb's book and wonder how it could have caused such a stir. His tale expands the trivial observation that unpredictable events may cause more havoc (or fortune) than rather predictable ones, hence (according to him) undermining the application of statistical methodology in social and economic domains. So let's all adopt the scouts' motto "Be prepared"! For what? Still, his practical advice on handling the unpredictable may be of greater value than the background theory, such as it is.

Footnote 4 - The science historian George Dyson has a more entertaining and scientifically more challenging theory about ravens. He has observed that ravens in different regions of Alaska and Canada "speak in distinct dialects" and these divisions correspond to the divisions between indigenous human language groups. His theory is that the languages of ravens and humans have "coevolved".

Footnote 4B - However, I would add my support to the belief that inductive thinking is, at least, “not unreasonable” (depending what you mean by "reason", I suppose). It is "justifiable" because future expectations are based, not merely on past observations, but on past expectations having become fulfilled.

Footnote 5 - I can hardly leave without mentioning Goodman's "new paradox" of inductive thinking, the catalyst for the title of this website. Briefly, an object may be called "grue" if it looks green up to some future time, t, or if it looks blue after t. Emeralds have all looked green up till now, so one can say (in conventional terms) "All emeralds are green". But one can also say "All emeralds are grue", and this supposedly creates the paradox that emeralds could just as well look blue after t. Intuitively this enigma, which soon came to exist in many more complicated versions, is just a clever piece of nonsense, and I accept most of the standard objections to it (as initially offered by Swinburne, Quine and others). To my mind, however, the problem lies entirely with language - not merely the misuse of language (a criticism which others have brought against Goodman, in particular that "grue" is not a projectable predicate), but the intrinsic properties of language that shape our interpretation of reality. I have touched upon this subject here. Returning to the "projectable predicate" argument, however, my interpretation of this is that the "old" concept of induction has been internalised, i.e. included within a statement which would otherwise itself exemplify the unadulterated paradox.

But my gripes precede all this stuff, both temporally and logically, with the underlying claim that material general (All X's are Y's) propositions are inadmissible entities (see here) unless intended as current definitions ("current" I add because even definitions are open to revision). So if the notion of "generalisation" is itself flawed why bother with all the downstream wrangling? I very much doubt whether the vast majority of scientists, even those working in areas of fundamental physics and cosmology, believe that any concept or state of affairs is sacred until overturned by new evidence. Truth is not inviolable.

Footnote 6 - Stephen Hawking's most useful theory is not about cosmology but about the obesity epidemic in the western world: It's not rocket science. Eat less, move more!

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