obs: this is a corrected rough draft for an Appendix of the book Philosophical Semantics: Towards a New Orthodoxy to be published by Oxford Scholars Publishing in 2016.
Appendix to chapter 5
THE KEY TO SOLVING HUME’S PROBLEM OF INDUCTION
It would be impossible to say truly that the universe is a chaos, since if the universe were genuinely chaotic there could not be a language to tell it. A language depends on things and qualities having enough persistence in time to be identified by words and this same persistence is a form of uniformity.
J. Teichman & C. C. Evans
I will first reconstruct Hume’s skeptical argument against the possibility of induction in the clearest way possible. Then I will sketch what I believe to be the best way to answer it, in order to re-establish the credibility of inductive reasoning, which is assumed throughout this book.
The Humean argument
According to Hume, our inductive inferences require metaphysical principles of uniformity of nature to support them. Although induction can be not only from the past to the future, but also from the future to the past and from one spatial region to another in the present, for the sake of simplicity I will limit myself here to the first case. The principle of uniformity from the past to the future can be stated as:
PF: the future will resemble the past.
If this principle is true, it ensures the truth of inductive inferences from the past to the future. Consider the following very simple example of an inductive argument justifying the introduction of PF as a first premise:
1. The future will resemble the past. (PF)
2. The Sun has always risen in the past.
3. Hence: The Sun will rise tomorrow.
This seems at first glance a natural way to justify the inference that if the Sun rose each day in the past, it will also rise tomorrow, an inference which could be extended as the generalization ‘The Sun will always rise in the future.’
It is at this point that the problem of induction begins to be delineated. It begins with the observation that the first premise of the argument – a formulation of PF – is not a true reason characterized by the inconsistency of its negation, i.e. it is not an analytic proposition. According to Hume, it is perfectly imaginable that the future could be very different from the past, for example, that trees will bloom in the depth of winter and snow will burn like fire!
We can still try to gain the certainty that the future will resemble the past based on the past permanence of uniformities that once belonged to the future: past futures. This is the inference that at first glance seems to justify PF:
1. Already past futures were always similar to their own pasts.
2. Hence: The future of the present will also resemble its past.
The problem with this inference is that it is also inductive. That is: in order to justify the induction we need to use PF, the principle that the future will resemble the past; but PF itself needs to be justified. However, when we try to justify PF, we need to appeal to induction again, which will require PF again. Consequently, the above justification is circular.
From such considerations Hume concludes that induction cannot be justified. Therefore, there is no rational justification either for the expectations created by the laws of empirical science, or for our own expectations of everyday life, since both are based upon induction.
It is true that we are very willing to believe in our inductive inferences. But for Hume, this disposition is only due to our psychological constitution. We are by nature inclined to acquire habits of having inductive expectations. Once formed, they constantly make us obey them, like moths flying towards bright lights. This is an extremely skeptical conclusion, and it is not without reason that only a few philosophers followed Hume’s lead. Most think that something must be wrong somewhere in the argumentation.
There have been many unsatisfactory attempts to solve Hume’s problem. I believe that the strategy that I follow, although only sketched out, has the virtue of facing the central core of the problem. I want to first present a general argument and then try to show how it could influence PF.
My general thesis has a mildly Kantian flavor, but without its indigestible synthetic a priori. It is the idea that any concept of a world (nature, reality) that we may have must be open to induction. I see this as a conceptual truth in the same way as, say, the truth of our concept that the empirical world must in some way be accessible to perception.
Understanding any maximal set of entities compatible with each other (a minimal condition) as a world, our thesis can be unpacked as follows.
For us an external world can only exist if it is at least conceivable. But we cannot conceive of an external world without any degree of uniformity or regularity. Now, as we can only experience what we are able to conceive, it is clear that we cannot experience any world completely devoid of regularity. However, the existence of regularity is all that is needed for at least some inductive procedure to be applicable. But if this is the case, then it is not possible for us to conceive of any experienceable world that is not open to induction. Hence, it is a conceptual fact that if a world is given to us, then some inductive procedure should be applicable to it.
There is a predictable objection to this thesis: why should we assume that a chaotic world cannot be imagined to exist? – a world devoid of any regularity and therefore closed to induction? In my view, the widespread belief in this possibility has been a great mistake, and David Hume is to blame for this. His error was to choose causal regularity as the focus of his discussion, strengthening it with selected examples. This was misleading and in what follows I want to explain why.
Causal regularity is what I would call a form of diachronic regularity, that is, one in which a given kind of phenomenon is regularly followed by another kind of phenomenon. Such patterns constitute what we could call ‘becoming’ in a world or regular sucessions.
However, induction applies not only to diachronic regularities, but also to something that was never considered by Hume: synchronic regularities. Synchronic regularities are what we could also call structures: states of affairs that endure over time in the constitution of anything we can imagine. Their patterns constitute the ‘remaining’ in a world that includes permanence. We can make this concept clear by conceiving of a world without any diachronic regularity, causal regularities included. This world would be devoid of change, static, frozen. It still seems as though it could be properly called a world. But even a frozen world must have regularities in order to be conceivable; it must have synchronic regularities. But if this frozen world were constituted of synchronic regularities, then it would still be open to induction: we can foresee that its structural regularities would endure for some period of time, the period of its existence, and this already permits inductive reasoning.
Considerations like this show the weakness in Hume’s argument. By concentrating on diachronic patterns and thinking of them as if they were the only regularities that can be to be inductively treated, it becomes quite easy to imagine the real existence of a world to which induction does not apply or cannot be applicable, but still remains a world.
Try now to imagine a world destitute of both synchronic and diachronic structures. Something close to that can be illustrated when we think of a world as made up of irregular or temporally random repetitions of a single point of light or sound. However, even if the light or sound occurs irregularly, they will have to be repeated at times (as long as the world lasts), which demonstrates that it still has the regularity of randomly intermittent repetition. Hence, it turns out that induction could be applied even to such a minimalist world as long as it lasts.
Indeed, a world absolutely destitute of both species of regularity is inconceivable, and therefore not accessible to experience. We cannot conceive of any set of empirical elements without giving some kind of structure to them. But if that’s the case, if a world without regularities is unthinkable, whereas the existence of regularities is all we need for some kind of inductive inference to be applicable, then it is not possible that there is for us a world closed to induction. And since the concept of a world is nothing but the concept of a world for us, there is no world at all closed to induction.
Summarizing my argument: by focusing on causal relationships, Hume invited us to ignore the fact that the world is made up not only of diachronic but also of synchronic regularities, which in turn leads us to the illusion that we can conceive of a world inaccessible to inductive inference. If we take into account both general types of regularity to which induction is applicable, we realize that a world that is entirely unpredictable, chaotic, devoid of any regularity, is impossible, because any possible world consists of regularities, being therefore intrinsically open to induction.
I am by no means the first to grasp this point. For example, Keith Campbell has developed an argument for the inevitability of applying inductive procedures, which is another way to say the same thing. As he noted, in order cognitively to experience a world – an objectively structured reality – we must continually reapply empirical concepts, which, in turn, if they are to be postulated, learned and used, require a re-identification of the designata of their applications as being identical. However, he thinks this is only possible if there is a certain degree of uniformity in the world, one sufficient to allow re-identification. Indeed, if the world could lose all the synchronic and diachronic regularities implicitly referred to in Campbell’s argument, no concept would be re-applicable, and the experience of a world would cease.
But could there not be at least a partially chaotic world with a minimum of structure or uniformity, which would therefore be insufficient for the purposes of our inductive procedures? I guess that this is a theoretical impossibility. And the reason for this is that induction has a self-adjusting nature, i.e. the application of its principles must always be calibrated in accordance with the nature of what they apply. The requirement of an inductive basis, of a repeated and varied inductive attempt, can always be made greater if greater improbability of uniformity is expected. Hence, even a system with a minimum of uniformity requiring a maximum inductive search would always end up enabling the success of induction.
These general considerations suggest a thread of conceptual inferences, such as the following:
Possible cognitive-conceptual experience of a world ↔ applicability of inductive procedures ↔ existence of regularities in the world ↔ existence of a world ↔ possible cognitive-conceptual experience of a world…
These things are internally related to each other in order to derive each other extensionally, so that their existence already implies these relations. By this means, contrary to what Hume believed, when properly understood the principles of uniformity should be analytic-conceptual truths, i.e., they must be truths of reason applicable to any possible world.
Reformulations of PF
To show how the just offered proposal could be applied to the reformulation of the principles of uniformity or induction, I will reconsider in some detail PF, the principle that the future will be like the past. If my suggestion is correct, then it must be possible to turn this principle into analytic-conceptual truths constituting our only possibilities of conceiving and experiencing the world. I understand an analytic conceptual proposition to be one whose truth depends only on the combination of its semantic constituents. This truth does not widen our knowledge (in opposition to synthetic propositions), and isn’t such that its denial implies a contradiction or inconsistency.
To show how the aforementioned suggestion could be applied to the reformulation of the principles of uniformity or induction, I would like to redefine PF. If my suggestion is correct, then it must be possible to turn this principle into an analytic-conceptual truth, constituting our way of conceiving and experiencing the world. Here is my first attempt to formulate PF in this way:
PF *: The future must have some resemblance to its past.
Unlike PF, PF* can be more easily accepted as expressing an analytic-conceptual truth, for PF* can be seen as satisfying the above characterization of analyticity. Without doubt, it belongs to the concept of the future to be the future of its own past. It cannot be the future of another past belonging to some alien world. If a future had nothing to do with its past, we couldn’t even recognize it as being the future of its own past, because it could be the future of any other past... In other words: the future of our present world as Fw can only be the future of w, of the past of w, that is, of Pw; It cannot be the future of numerous other possible worlds, w1, w2, w3... that have as their past respectively Pw1, Pw2, Pw3... It is necessary, therefore, that there is something that identifies Fw as being the future of Pw, and this something can only be some degree of similarity.
Against this we can try to illustrate the possibility of complete changes of the world by means of examples, showing that this isn’t possible. Suppose, in an attempt to imagine a future totally different from its past, a ‘complete transformation of the world’, as foretold in the New Testament book of Revelations. It is hard to imagine more drastic changes than those described there. Here is the biblical passage describing the locusts sent by the fifth angel:
In appearance the locusts were like horses equipped for battle. And on their heads were what looked like golden crowns; their faces were like human faces and their hair like women’s hair; they had teeth like lions’ teeth and they wore breastplates like iron; the sound of their wings was like the noise of horses and chariots rushing to battle; they had tails like scorpions with stings in them, and in their stings lay their power to plague mankind for five months.
The problem with this example is that there is nothing in this report that puts PF* at risk. In fact, accurate examination of the example demonstrates that even PF isn’t seriously challenged. Although these biblical locusts are indeed strange creatures, they consist of combinations of parts with which we are already very familiar, horses, women, men, heads, teeth, scorpion tails with stings, faces of persons, etc. Both internally and externally they include a vast quantity of synchronic regularities, of structural associations, together with familiar diachronic associations, like the sequential causal relationship between the noise produced by wings or the sting of the scorpion and the effects of its poison on humans.
In fact, were it not for these uniformities, the Revelation of John would not be understandable, conceivably able to be subjected of any linguistic description, and consequently it would be impossible to imagine. The future, at least proportionally to its greater proximity to the present, must maintain sufficient similarity to its past to allow an application of inductive procedures in the recognition of the continuity of the same world.
Now one could object that maybe it is possible that at some time in a remote future we could find a dissimilarity so great between the future and our past that invalidates all reasonable inductive procedures; a future that would be radically different from its past. Indeed, it is conceivable that a continuous sequence of small changes could in the course of a very long period of time give way to something if not totally different, at least extremely different. This would not destroy PF* because its formulation is too weak, requiring only that some similarity remains. But it is clear that this weakness of PF*, though not destroying its analytic-conceptual character, makes it poor as a way to assure the accuracy of inductive forecasts.
However, precisely this weakness of PF* indicates a way to improve it. We see that the closer we get to the point of junction between the future and the past, the greater must be the similarity between future and past, becoming both identical in their limit, which is the present. This point can be approximated when we remember the Aristotelian analysis of change as assuming the permanence of something that remains identical in a continuous way, without gains or losses. In other words, the suggestion is that every change must occur upon some basis of permanence.
This leads us to another principle, namely, that the measure of permanence must be inversely proportional to the period of time in which the change occurs. In other words: if a sequence of changes is given that are parts of a more complete change, the changes that belong to the smaller parts presuppose more permanence than the more complete change.
This principle can be illustrated by many examples. Consider one of them: the changes resulting from heating a piece of wax. The change from the solid state to the liquid state assumes the permanence of the same wax-like material. But the next change, of the liquid wax to carbon ash, assumes only the permanence of carbon atoms. If then the heat is much more intense, carbon will lose its atomic configuration, giving place to a superheated plasma of neutrons, protons and electrons. We have here four periods of time in a row: regarding the shortest period of time from t1 to t2, we assume as remaining (i) the same wax, made up of (ii) the same carbon atoms, which in turn are composed of (iii) their same subatomic constituents, protons, neutrons and electrons. In the longer period of time from t1 to t3 we assume as identical only (ii) and (iii). And in the still longer period of time from t1 to t4 the only thing that remains the same are (iii) the subatomic constituents.
Note that this model is not restricted to changes in the physical and material world! As Leibniz saw: Natura non facit saltus. And this can be generalized: the same examples repeat in every domain that you can imagine, psychological, social, economic, historical… with the same patterns: the closer the future is to its junction with its past, the more identities must be assumed. Thus, it belongs to the very structure of the experienceable world that the changes that take place in a shorter period of time tend to presuppose more permanence than the most comprehensive changes in which they take part. One consequence of this is that the future closer to its present should in more aspects be similar to its past than the more distant futures (which, as already noticed, may become nearly unrecognizably different). Regarding induction, this principle ensures that inductive predictions become more likely, the closer the future is to which they relate. On this basis principle PF* can be improved here as:
PF**: The closer the future is to the junction point with its own past, the more it will tend to resemble its past, the two being indifferentiable at the point of junction (the present).
For a correct understanding of PF** we need to add that this principle should be applied to a future that is sufficiently close to its past and not to an indefinitely distant future. Moreover, we need to safeguard the possibility of anomalous but possible cases in which we find sequential moments in which states of affairs of a more distant future are closer to the present than those of an earlier future. A clause clause excluding these anomalies must be added to PF**.
This shows that PF** should be considered more carefully, allowing the addition of formal methods. But it seems to me that with the addition of the above remarks this principle already meets our understanding of analyticity.
Moreover, it is the truth of PF** which makes it natural to think that the more distant the future, the less probable our inductive forecasts will be. This explains why our inductive generalizations about the future cannot be applied to the too distant future. When we say, for example, that induction allows us to infer that the Sun will ‘always’ rise, the word must be placed in quotation marks. It makes sense to affirm, on the basis of induction, that the sun will rise tomorrow or a thousand years from now. But it doesn't make any sense (and is astronomically false) to use the same inductive basis to say that the Sun will rise in seventeen billion years.
Finally, PF** can ensure restricted applications of PF: If the future is sufficiently close to its junction with the past, then the future is unavoidably similar to its past. The problem, of course, is that we need to establish criteria for knowing how close we have to expect that the future to be to its past so that PF applies. We can imagine, if the response does not depend on the domain of regularities in which the change is being considered, a domain of regularities to which a whole system of sufficiently well entrenched beliefs applies.
Looking for an example: the inductive conclusion that the Sun will rise tomorrow belongs to the domain of regularities implicated in the changes studied by astronomy, which includes a very distant future in which broader changes, such as the death of the Sun, are possible. Moreover, it is always possible that the Sun will not rise tomorrow. But this is only conceivable at the price of an immense loss of other well entrenched beliefs on regularities and, subsequently, the loss of the current intelligibility of a considerable part of the physical world that surrounds us. Still, what makes us consider as highly likely the future occurrence of regularities such as that the sun will rise tomorrow? The ultimate answer seems, based on the inevitable assumption of the world we experience, that our world as a whole will continue for a long time to exist as a system of regularities. And this assumption – I am forced to admit – is a real and inevitable gamble. There is nothing preventing that our whole world disappear in the next second. But once we make this general assumption – that our world as a whole will remain in existence – it looks as though the rest will take place: we are inevitably forced to admit how likely the existence of certain fields of cohesive regularities remain. Conversely, if we decide to reject arbitrarily more central future regularities, we will need to put in question the future of the whole system of regularities constituting our world, something fairly improbable.
There is no reason that makes it improbable or probable that the whole world will disappear a moment from now. But we can find reasons that make it improbable that a dependent part of the world will disappear in a moment, while others continue to exist, since this already presupposes the permanence of the world as an inductive basis.
The crude arguments I have just presented were developed only for a single form of induction: from the past to the future. But it would not be difficult to generalize them, even if they need further development. Still, they indicate a path to be open which may be of some relevance regarding a problem that from any other angle seems to remain disorienting and intangible.
 Curiously the idea of a chaotic world to which induction isn’t applicable was uncritically assumed as possible in the literature on the problem from P. F. Strawson to Wesley Salmon.
 Keith Campbell: “One Form of Scepticism about Induction”, in Richard Swinburne (ed.): The Justification of Induction (Oxford: Oxford University Press 1974), pp. 80-83.
 New English Bible: The Revelation of John, sec. 9. 7.
 Aristotle: Physics, 200b, 33-35.
 Maybe not in quantum mechanics, though I have my doubts.