Draft in english of an article published in
portuguese.
THE MOST REASONABLE
RESPONSE TO THE HUMEAN PROBLEM OF INDUCTION
It would be impossible to truly say that the universe is chaotic, for if
the universe were genuinely chaotic there could be no language with which to
say so. Language depends on things and qualities that have sufficient
persistence in time to be identified by words, and that very persistence is a
form of uniformity.
Jenny Teichman
I would like to discuss here the apparently
insoluble problem of the justification of induction introduced by David Hume.
To do so, I want to begin by reconstructing Hume’s famous critique of the
possibility of grounding our inductive inferences. Then I will outline, in
very general terms, a solution to the problem that seems to me the only truly
viable one.
1. The Humean Argument
I begin by briefly reconstructing Hume’s
argument. He presented the problem through a critique of causal necessity, but
in the reconstruction that follows I detach Hume’s anti‑inductivist argument
from that critique, in order to make clearer what concerns us. According to
Hume, our inductive inferences—that is, those that amplify our knowledge by
moving from the observed to the unobserved—require metaphysical principles of regularity
or uniformity of nature that guarantee them. Although induction may proceed
not only from past to future but also from future to past, or from one spatial
region to another, whether in the present or not, for the sake of simplicity I
will restrict myself here to the first case, whose principle of uniformity can
be stated as:
PF: the future will
resemble the past.
If this principle is true, it will guarantee
inductive inferences from the past to the future. Consider the following very
simple example of justifying an inductive argument by introducing PF as the
first premise:
1. The future will
resemble the past (PF).
2. The sun has
always risen every day.
3. Hence: the sun
will rise tomorrow.
This seems at first sight a natural way to
justify the inference that if the sun has always risen every day, it will also
rise tomorrow—an inference that could also be extended in the form of the
generalization “The sun will always rise.” Here the problem of induction begins
to take shape. It starts with the observation that the first premise of the
argument, the formulation of PF, is not a relation of ideas (Hume) or a truth
of reason (Leibniz), characterized by the contradictory or inconsistent nature
of its negation; that is, it is not an analytic proposition (Kant). It is
perfectly conceivable, Hume writes, that the future might become very different
from the past—for example, that trees bloom in winter and that snow burns like
fire. Even so (although Hume did not present it this way), it seems that we can
acquire the conviction that the future will resemble the past based on our
experience of past futures, which were similar to their own pasts. Here is the
inference that seems to justify PF:
1. Past futures have
always resembled their own pasts.
2. Hence: the
future will resemble the past.
The whole problem is that this is an inductive
inference. In other words: to justify induction we appeal to PF, the principle
that the future will resemble the past, and to justify PF we again appeal to
induction. The attempted justification of induction thus proves circular, since it
depends on a principle that itself ends up depending on induction in order to
be established.
Hume’s well-known
conclusion is that no rational justification for induction is possible;
therefore, there is no rational justification either for the expectations
created by empirical scientific laws or even for our everyday common‑sense
expectations, since both clearly rely on induction. It is true that we possess
a very strong disposition to believe in our inductive inferences. But for Hume
this disposition has no rational basis; it is due only to our psychological
constitution. We are instinctively disposed to acquire certain habits that
produce inductive expectations, and once formed, these habits make us act much
like moths, which are naturally disposed to fly toward light. This is an
extremely skeptical conclusion, and it is not surprising that only a few
philosophers have followed Hume on this point. Most think that something must
be wrong somewhere.
2. Proposal of an analytic-conceptual solution
The strategy that I believe to be able to solve the Humean problem
of induction in its very foundations, admits a priori inductive principles; however, they are not something with the
strength of synthetic a priori principles. Rather, they are
analytic–conceptual principles, in the sense that they are said to be true by
virtue of what they mean — more precisely, by virtue of the combination of the
meanings of their semantic constituents — such that their denial would involve
contradiction or incoherence with our common rules of reasoning. My strategy
also preserves something of a common‑sense solution, insofar as it turns much
of Hume’s argument into a pseudo‑problem. I want first to present my general
thesis and then show how it would apply to a chosen inductive principle.
The general thesis has a faint Kantian
flavor, though without an indigestible seasoning of the synthetic a
priori. It is the
idea that it is part of our very capacity to conceive a world of any kind —
indeed part of the concept of experiencing any world whatsoever — that the
world to which the concepts constitutive of it apply must be open to induction.
I want to argue that this is a conceptual truth (analytic, since obtained
a priori).
Defining a possible world as a world like
ours, though also conceivable as in greater or lesser degree different from
ours, the argument can be formulated more carefully as follows:
A world can possibly exist only if it is at least
conceivable. But one cannot conceive a world with no degree whatsoever of
uniformity or regularity. Now, since one can only experience what one can
conceive, one cannot experience any world completely devoid of uniformity or
regularity. And since the existence of regularity or uniformity is sufficient
for some inductive procedure to be applicable, it follows that no conceivable
or experienceable world can be closed to induction. It is, therefore, a conceptual truth that if a world
is given to us, then some inductive procedure must be applicable to it. (A
world that is in principle non‑experienceable or inconceivable, cannot qualify
as such.)
The objection to this thesis is predictable:
what authorizes anyone to suppose that a chaotic world cannot exist — a world
devoid of any regularity and therefore closed to induction? After all, the
hypothesis of a world inaccessible to induction has traditionally been
accepted.
Nonetheless, the widespread belief in this
possibility has, in my view, been a major mistake, one whose responsibility
lies with David Hume himself. This
mistake was introduced at the very beginning by the fact that Hume mixed the
problem of induction with the problem of causation. He chose causal regularity
as the focus of his discussion of induction and selected his examples
accordingly, which was from begin misleading. What follows is meant to justify
this claim.
Causal regularity is what I would call a diachronic
regularity, that is, one
in which we think that a given thing is regularly followed by another thing
different from the first, often in a way deeply entrenched in our belief
system. Note also that not all diachronic regularities are causal; some are
merely sequencial. After night there always comes a new day, but night does not
cause day. Still, this is a diachronic regularity. Diachronic regularities
constitute what might be called the becoming of the world.
Yet it is a fact that we can conceive a
world without becoming, without diachronic regularities, including causal
regularity. This would be the case of a world without change: a static, frozen
world. Even so, it seems it could still be correctly called a world. After all,
worlds without diachronic regularities are conceivable and even in principle
knowable, although things like the induction of causal laws would not apply to
them. (I am abstracting here from any causal interaction between a frozen world
and the epistemic subject.) The problem with Hume’s argumentative focus
restricted to causal inductive inference — which is diachronic — is that it
diverts our attention from the fact that an empirical world is equally
constituted by synchronic regularities, which, just like diachronic regularities, can only
be known through inductive procedures.
But what, after all, are these synchronic
regularities? We can define them as the relations simultaneously holding among things
differently located in space, insofar as these relations endure through time. In
contrast to becoming, they are responsible for what we could call the permanence of the world. This is the case of the relations that exist among
the faces of a crystal, to take a distinctive example. It is induction that
must justify the persistence of synchronic relations, leading us to believe,
for instance, that the crystal will remain recognizable as having the same form
when observed again in the future. The domain of synchronic regularities is extremely
broad, since not only any object but any complex property and any recognizable
state of affairs possesses constitutive relations among its parts — relations
that must endure as long as the object, property, or state of affairs exists. The
most interesting form of synchronic regularity is what could be called a structure. Synchronic regularities are often structures in
the sense of possessing an internal identity that persists over time. A Gothic
cathedral, with its pointed arches, large stained‑glass windows, ornaments, and
statuary, can serve as an illustrative example of synchronic structurality. But
a pile of books, although constituting a synchronic regularity while it remains
the same, does not have what we more properly call a structure.
A frozen world is a world only because,
although it lacks diachronic regularities, it still possesses synchronic
regularities, and it is expected to possess some structure. Moreover, induction
is certainly applicable to this structure, since it is always applicable to
synchronic regularities in predicting their persistence in the future. If the
frozen world has the exagonal structure of a snow crystal, this structure must
endure, and after a while, one could inductively predict that in the following
moment, this structure will remain. What makes the frozen world knowable are its
synchronic regularities.
Let us now try to imagine a world without synchronic
or diachronic regularities, without permanence or becoming. At first sight,
this minimalist world seems illustrable if we think of it as consisting of
irregular repetitions of a single luminous point or a single sound. However,
even if the luminous point or the sound occurs irregularly, it must repeat at
least once (as long as the world lasts), which already demonstrates at least
the diachronic regularity of repetition; hence, induction applies to such
minimalist worlds as long as they endure. But what about a world absolutely
devoid of both kinds of regularity, without permanence and without becoming —
is it conceivable? The answer is clear: a world without any regularity cannot
be genuinely conceivable, and therefore cannot be accessible to experience. We
cannot think of any set of compatible empirical elements without giving it some
permanence or becoming. But if this is so — if a world without regularities is
inconceivable — and since the existence of regularities is all we need for some
inductive inference to be applicable, then it is impossible for there to exist
a world that is not open to induction. Wherever there is a world, there must be
some regularity; and wherever there is some regularity, some inductive access
will be logically possible. To conceive a world to which induction does not
apply would amount to conceiving a world without any regularity, which
contradicts our very concept of a world.
To
summarize: by concentrating on causal relations, Hume leads us to ignore that
the world is also constituted by synchronic regularities, which in turn leads
us to believe that we can conceive the existence of a world whose becoming is
devoid of diachronic regularities — that is, an entirely chaotic world and
therefore inaccessible to inductive inference. When we properly take into account
both kinds of regularity to which induction applies, we realize that an
entirely chaotic world, without any regularity, is inconceivable and therefore
impossible, since any possible world is made of its regularities and is thus
intrinsically open to induction.
Searching in the literatur, I discovered that I am
not the only person to have noted that any conceivable world must be open to
induction. According to Keith Campbell, in order for us to cognitively
experience a world — an objectively structured reality — we must always be
reapplying empirical concepts, which, in turn, in order to be fixed, learned,
and used, require a reidentification of their designations as being identical;
but this is only possible if there is a degree of uniformity in the world
sufficient to allow reidentification. Indeed, if the world could completely
lose its regularities (not only diachronic ones, but also synchronic ones),
then no concept could be reapplied, the experience of the world would cease,
and it would, for us, cease to exist. Such considerations only corroborate what
has already been suggested.
Another
reason why people tend to admit the possibility of a world whose degree of
irregularity would make induction impossible is the neglect of the fact that
induction has a self‑adjusting nature; that is, the application of the
inductive procedure must always be calibratable in accordance with the
nature of that to which it is applied. The requirement of inductive basis —
repeated and varied inductive experimentation — can theoretically always be
increased, the more improbable the expected uniformity is; consequently, even a
world with minimal uniformity would still end up making inductive success
possible, since it would require a maximized inductive search. In other words:
it is enough that there be some uniformity for some requirement of inductive basis to ideally allow us
to find it.
To
illustrate, imagine that in a nearby possible world a team of zoologists is
searching for wild camels in the Gobi Desert in the final of the last century. This
desert is immense, covering northern China and all of Mongolia. Moreover, these
shy camels were are extremely difficult to find. The zoologists would have to
visually inspect, with binoculars, a vast expanse of desert, climbing and
descending dunes until they eventually find, with some luck, this almost
mythical animal. Here the
pressure of inductive calibration must be very much increased.
The general considerations made so far
suggest the following interwoven set of conceptual inferences: effective
cognitive‑conceptual experience of the world ↔ applicability of empirical
concepts ↔ applicability of inductive procedures ↔ existence of a world
intrinsically possessing regularities.
These concepts are internally related in the
sense that they can be intrinsically inferred from one another. By this means,
contrary to what Hume believed, when adequately formulated the principles of
uniformity should reveal themselves as analytic‑conceptual truths understood as
truths applicable to any possible world and which cannot be denied without
contradiction. Thus, my goal now is to establish at least one formulation of these
principles in a way that makes it sound like the analytic‑conceptual truths
they must be.
3. UNIFORMITY OF NATURE IN A NEW FORM
To show
how the thesis just presented could be applied to the reformulation of the
principles of uniformity or induction, I would like to reconsider PF in some
detail. Could it be transformed into an analytic‑conceptual truth? As I have
already noted, I understand an analytic‑conceptual proposition as one whose
truth depends only on the combination of its semantic constituents. This truth
is characterized by not being ampliative of our knowledge (as opposed to
synthetic propositions), possessing as its criterion of identification the
feature that its negation is contradictory, incoherent, or impossible to
conceive.
The first question that arises is whether
PF, stating that the future will be similar to the past, can satisfy this usual
characterization of analyticity. Hume thought not. As we have seen, he
considers that we can conceive of snow beginning to burn like fire and trees
beginning to blossom in winter… But
these examples of Hume are as suggestive as they are illusory. For since a
multitude of other regularities, especially synchronic ones, would continue to
remain, these examples are far from making the future so dissimilar from the
past as to invalidate inductive procedures. Nevertheless, it is still clearly
conceivable that if some unpredictable cosmic cataclysm were to profoundly
modify the future, making it different from the past, this shows us that PF is
conceivably deniable and therefore non‑analytic. However, we can redo PF.
Consider the following reformulation:
PF\*: The future must have some
similarity with its past.
Unlike
PF, PF* can clearly be understood as expressing an analytic‑conceptual truth.
After all, PF* seems to satisfy the characterization of analyticity presented
above. Here is how this can be shown: understanding the notion of future in
terms of successive sets of regularities constituting the world to be given at
times later than the present, and clarifying the concept of past in terms of
successive sets of regularities at times earlier than the present, we can say
the following: it belongs to the concept of future that it is the future of its
own past. It cannot be the future of any other past. But if a future had
nothing to do with its past, we could not even recognize it as being the future
of its own past, for it could then be the future of some other past. In other
words: the future F of the actual world m can only be the future of m, that is, Fm, which can only be the future of the
past of m, that
is, Pm; it cannot be the future of the many other possible worlds m1, m2, m3…
which had as pasts the sequences Pm1, Pm2, Pm3… There must, therefore, be something that identifies
Fm as being the future of Pm. Now, that something can only be some margin of
similarity. That is: the notion of future must be in some way conceptually
linked to the notion of its past as being to some extent, in some manner,
similar to it — at least to the extent and in the manner that allow the
temporal association of Fm with Pm. This is why PF* satisfies our
characterization of analyticity: to deny it is to render the words “future” and
“past” meaningless by making it impossible to relate them in the way
conventionally done; if I deny PF, then it seems
clear that the future no longer needs to be distinguished from its past as
being the future of its past. Moreover, PF does not seem to enlarge our knowledge. PF*
satisfies the criterion for identifying analytic propositions, for we are not
capable of coherently denying it; we are not capable of thinking that the
future has no similarity whatsoever with its past without inconsistency.
Indeed, it seems that, in an attempt to reject PF, whenever
we try to conceive a dissimilarity so great between future and past that it
invalidates all inductive procedures, we fail to conceive any objective
structure and even any possible world. This point can be easily illustrated
through examples. Imagine, in an attempt to conceive a future completely
different from its past, a “complete transformation of the world” such as that
narrated in the biblical text of Revelation. It is difficult
to imagine more drastic alterations than those described there. After
all, it is the narration of the very end of the world as we know it! But it is
a mistake to think that the destruction of our world described in Revelation
would imply a negation of PF, since the idea of a “complete transformation” is not
understood here in a literal sense. If we examine the text more closely, we
will see that the great majority of things with which we are familiar — that
is, the basic synchronic regularities and even most diachronic regularities —
remain unchanged after the transformation, although they have been bizarrely
combined, as in the biblical passage describing the locusts sent by the fifth
angel:
The appearance of these locusts was like horses prepared for battle. On
their heads they wore something like crowns with golden reflections. Their
faces were like human faces. Their hair was like women’s hair, and their teeth
were like lions’ teeth. Their chests seemed to be covered in iron, and the
sound of their wings was like the noise of chariots with many horses rushing
into battle. They had tails like scorpions, with stingers, and the power to
afflict human beings for five months.
Now,
nothing in this account puts PF* into question. In fact, a careful examination
of the example shows that it does not even challenge a loose understanding of
PF! For although these biblical locusts appear deliriously strange to us, they
are composed of combinations of parts with which we are already very familiar —
such as hair, women, men, teeth, scorpions, stingers — which internally and
externally include a vast sum of regularities, of structural associations (such
as those that form locusts, those that form crowns, those that form human
faces…) and sequential associations (such as the causal relation between crowns
and their golden reflections, between the scorpion’s sting and the effects of
its venom on human beings for five months, between the beating of wings and the
noises they produce…), all of which remain preserved and inductively accessible
despite the alterations. Indeed, if this were not so, the Apocalypse would not
be comprehensible, thinkable, conceivable, or capable of linguistic description
— and what is none of these is also impossible to experience. The account
illustrates the idea already mentioned: that the future world must, at least
insofar as it remains sufficiently close to the present, continue sufficiently
similar to its past so that it can be conceived as the future of that same
past; that is, it must remain sufficiently similar to its past to warrant the
application of inductive procedures in recognizing its continuity as a world.
But what should we say of a future immensely
later than the present? Could it not be totally different from the past? It
seems that it could. If we interpreted PF* as referring not to the future as a
whole from the present onward, but to a very remotely distant future, detached
from all those that preceded it, then it seems clear that PF* could be
falsified, for it is not inconceivable that a continuous sequence of small
alterations in regularities could, over a very long period of time, give rise
to completely different regularities. But this is not the sense in which I
intended PF*, for when I presented it, it was already implicit that it
concerned the continuation of its own past, including at least the future that
immediately follows the present.
This last consideration reminds us of another
conceptual truth already observable in the relation considered by PF*. The
closer we approach the point of junction between future and past — that is, the
present — the greater the similarity between them must be, with future and past
becoming identical at their limit, which is the present. This point can be
approached when we recall Aristotle’s analysis of the concept of change as
presupposing the permanence of something that remains identical and that
continuously gains or loses. The suggestion is that all change presupposes some
basis of permanence, that is, some synchronic regularity, which not only allows
inductive inference but requires it in order to be known.
But that is not all. There is a relevant observation that still needs to
be made, now concerning the measure of the permanence presupposed. While change
occurs, the measure of permanence as a whole must be inversely proportional to
the period in which the change occurs. This means that if we are given a
sequence of changes that are part of a more complete change, then, compared to
the whole, the changes that are part of the sequence presuppose more permanence
than the more complete change.
The
principle I have just presented may at first seem somewhat obscure, but it can
be well illustrated through an example: consider the changes resulting from
heating a piece of wax starting at T0. First we have the change from solid to
liquid at T1. With greater heating we have the change from liquid wax to carbon
ash at T2. If this ash is heated to many millions of degrees Celsius, we
finally have the dissolution of the carbon atoms and the formation of a plasma
of subatomic particles at T3. Here is a scheme showing how changes typically
presuppose greater permanence the more partial and brief they are:
PHYSICAL COURSE OF TIME:
ENTITY:
T0 T1 T2 T3
Solid wax X
Liquid wax X X
Carbon ashes X X X
Subatomic X X X X
Particles
(plasma)
Notice
how synchronic regularities are lost over time. From T0 to T1, what is
presupposed as permanent is the wax and its atomic constituents — carbon,
oxygen, and hydrogen atoms — as well as subatomic constituents. From T1 to T2,
only the carbon atoms and their subatomic constituents remain presupposed as
permanent. Finally, from T1 to T3, all that remains are certain subatomic
constituents. The change here
is gradual in its loss of regularities.
The model of change suggested above is not
restricted to cases such as the chemical structure of a compound. It applies to
physical, biological, psychological, social, economic alterations — in short,
to any empirical domain we can conceive. Consider, for example, the Industrial
Revolution. It began in the eighteenth century with the introduction of weaving
machines, division of labor, and a small rural exodus. The social and economic
structure of England remained practically the same at first. In the course of
the nineteenth century, however, the changes deepened. Ironworks appeared,
steam locomotives, a railway network, a large rural exodus… English society
ceased to be the same, although many uniformities remained. There are
successive losses and gains of regularities here. But the alterations can only
be identified on the basis of permanence.
What I am suggesting is that this model of
change applies to everything for the simple reason that it constitutes part of
the metaphysical structure of reality, as it is conceptually conceivable. It is
constitutive of the very structure of the world of real or conceivable
experience that changes occurring over a shorter period typically presuppose
more permanence than the more complete changes of which they are part: natura
non facit saltus. Even the
abrupt change of an electron’s orbit only occurs under a structure of
permanence, which in this case is the atom.
The metaphysical model of change just
suggested has consequences for our epistemological understanding of induction.
The future closest to us must, by necessity, if taken as a sufficiently
proximate whole, be more similar to its past than more distant futures (which,
as we have already noted, may become even unrecognizably different from the
present). This should already have been clear when we examined the example of
the heated wax: if T0 is the present, T1 retains more similarities with T0 than
T2, and T2 retains more similarities with T0 and T1 than the more distant T3.
With respect to induction, this principle
guarantees, given a certain frame of reference, that inductive predictions
become all the more probable the closer the future to which they refer is. On
this basis we can replace the excessively weak principle PF* with:
PF**: A sufficiently proximate future
must retain some similarity with its sufficiently proximate past such that the
closer it is to the point of junction with its own past (the present), the more
it must tend to resemble that past, becoming identical to it at the point of
junction.
For the
correct understanding of PF**, ir ia important to consider that the futures
must be sufficiently close to their pasts, since it is necessary that something
in them contain situations belonging to the past or the continuation of changes
arising from the past. After all, we can conceibe a longinquous future where
there is nothing or nearly nothing that wouldd be similar to its past.
Firthermore, it is important to emphasize the tendential aspect of the process: we must add that nothing
prevents the anomaly that part of this sufficiently proximate future may remain
the same or even be more diverse from the present than a part of it that is
more distant, provided that at its point of junction with the past the future
becomes identical to the present. (Consider, for a simple example, the cyclical
crises that occur in the economy, despite its long‑term ever‑increasing
pattern. For instance: the U.S. GDP of 1930 returned to that of 1920, although
overall, from 1900 to 2000, it was increasing…)
I belive that PF** could be considered in greater
detail and even formally. But it seems to me that this principle already
clearly satisfies the characterization of analyticity defended here, for it
shows that it belongs to the very concept of a future sufficiently close to the
present that, taken as a whole, it tends to resemble its past exponentially
more, the closer it is to its point of junction with that past,
converging toward identity at the very point of junction, which is the present.
We may even attempt the Fregean strategy of showing that PF** can be
transformed into a tautology, where x may be occupied by any event or by a variety of
events, Fa = …what
belongs to the sufficiently proximate future, Pa = …what belongs to the sufficiently proximate past,
≈a≈ = tend,
in proportion to their proximity to the present, to be identical to one another.
Here is how this relation may be presented:
PF**: (x) (Fax ≈a≈ Tax)
Something
like this could be understood as a tautology within a temporal logic, insofar
as it seems to be part of what we understand and can define as the flow of
events in time; something reminiscent of a logarithmic scale which, indicating
the present, runs from past to future within a given frame of reference.
A consequence of admitting PF** is that it
becomes natural to think that the more distant from its point of junction with
the past a future period is, the less probable the inductive predictions
concerning it will be. This
explains why our inductive generalizations about the future are never truly
about an indefinitely remote future, as might seem at first glance. When we
say, for example, that induction allows us to infer that the Sun will always
rise, the word “always” should be placed in quotation marks. It makes sense to
affirm, on the inductive basis that the Sun has always risen, that it will rise
tomorrow and even a thousand years from now. But it makes no sense at all (and
in fact astronomy asserts it to be predictively false) to use the same
inductive basis to say that the Sun will rise seventeen billion years from now.
There is, of course, the case of scientific
laws such as those of general relativity or quantum mechanics, which
hypothetically apply to the entire universe. These laws generally result from inferences to the
best explanation. An inference to
the best explanation is inductive because ampliative, resting surreptitiously
on an immense volume of prior enumerative inductions. Even so, it is questionable whether PF** would not
be valid even for them. The field equations of general relativity apply well to
known regions of the universe. Would they truly apply to everything in the
universe? Suppose, for
example, that multiple universes exist. In that case we would no longer feel so
secure about the scope of their application.
Finally, PF** can guarantee restricted
applications of PF, making PF analytic when understood as restricted to the
domain of those applications: if the future in question is sufficiently close
to its point of junction with the past, then that future will necessarily tend
to resemble its past. The problem, naturally, is that we
lack criteria for determining how close a future must be to its past for PF to
apply to it. We may speculate that the answer depends on assuming a domain of
regularities to which the change under consideration belongs — a domain of
regularities understood as one to which an entire system of well‑entrenched
beliefs applies. Thus, the inductive conclusion that the Sun will rise tomorrow
belongs to the domain of regularities implicated in the changes investigated by
astronomy, which includes a future distant enough for the broader changes to
occur, such as the death of the Sun. It is possible, although highly
improbable, that the Sun will not rise tomorrow, as the inductive procedure
itself predicts. But this would only be conceivable at the cost of an immense
loss of other regularities and, subsequently, of our present intelligibility of
a considerable part of what surrounds us.
Still, what
leads us to consider highly probable the future permanence of particular
regularities, such as the Sun rising each day? The answer seems to begin with
the inevitable assumption of the brute fact that the world exists as a system
of regularities, since we can conceive it and experience it. Along with this,
it seems that we also assume that this system of regularities that is our world
will continue to exist. But are we not once again falling into the Humean
abyss? After all, what guarantees that our world will not suddenly cease to
exist five seconds from now, along with everything within it, including
ourselves?
The answer is that although we may find
reasons that make it improbable that part of our world will disappear in the
near future while other parts remain, it makes no sense at all to suppose that
the entire world could vanish in an instant. The reason for this is
verificationist. According to a reasonable principle of verification, a
statement that cannot be verified or refuted in any way cannot have cognitive
meaning. Statements such as (i) “My brother died after tomorrow” and (ii)
“During this night the entire world doubled in size along with everything
belonging to it” may have grammatical meaning — that provided by grammatical
rules — but they do not have the much more important and proper cognitive
meaning of being capable of saying something about the world, a meaning to be
given by verification rules. (Obviously, someone might object here that
verificationism is a doctrine refuted by the later development of much of
analytic philosophy of language and even by its main defenders, the logical
positivists… However, this would be a serious mistake! Semantic verificationism
was first proposed by Wittgenstein to the logical positivists in 1929 and, as I
tried to show in the first chapter, it was a commonsense proposal, far more
flexible and plausible than theirs, and not open to the same objections.)
Now, in the same way as with statements (i)
and (ii), we may suggest that the statement (iii) “The entire world will
disappear five seconds from now” is unverifiable. (Note that a statement such
as (iv) “Possibly the entire world will disappear five seconds from now” is verifiable, for it will be verified after five
seconds, since what is certain is also possible. But statement (iv) is
different from assertion (iii), which has no justificatory basis.) We can
easily deceive ourselves on this point by imagining ourselves outside the
world, perceiving its disappearance. But since we ourselves belong to the
world, it is simply impossible to verify such an event, for the epistemic
subject capable of verifying it would also disappear, and, no longer existing,
would be logically incapable of performing such verification. We conclude,
therefore, that the statement above only seems to possess cognitive meaning,
but does not truly possess it. But what about its negation? What about the
statement (v) “The entire world will not disappear five seconds from now” or
(vi) “The entire world will continue to exist five seconds from now”? The
negation of a meaningless statement must also be meaningless: the negation of
“My brother died after tomorrow,” which is “My brother did not die after
tomorrow,” is equally meaningless. Consequently, statements (v) and (vi) must
also lack cognitive meaning. However, one might suggest that (v) and (vi)
escape this rule, since after the five seconds have elapsed these statements
will have been verified. What is certain? I prefer to think that (v) and (vi)
truly make no sense as such, for these statements assert the inassertible —
that the world will continue to exist — unlike a statement such as (vii) “It is
possible that the world will continue to exist five seconds from now,” which
can be verified by the fact of the world’s non‑disappearance after the five
seconds, since existence implies possibility. That we have the disposition to
continue acting as if the world will continue to exist seems to be a purely
dispositional matter. Apart from this natural disposition, we are not capable
of finding any reason to believe that everything will exist or cease to exist
in the near future. This is why this dispositional fact cannot lead us into
skepticism: it remains cognitively unredeemable.
Such considerations do not prevent us from
admitting as probable the existence of certain cohesive domains of
regularities, and of the particular regularities inferred within these domains
as being of probable permanence, following PF**. The consequence of conceiving
things in this way is that if we reject the future permanence of a regularity —
such as the Sun rising each day — we must reject the future permanence of the
entire domain of regularities in which it is included. But since the very
probability of the regularity in question is measured on the basis of admitting
the permanence of that domain of regularities (a point demonstrable by Bayes’
theorem), it ceases to be rational for us to put it into question.
The solution I have just sketched is
schematic and inconclusive, limited to a single form of induction.
Nevertheless, it has the advantage of not approaching the Humean problem
equivocally, as seems to me to be the case with all others. It approaches the
Humean problem head‑on, in the condition in which it presents itself, without
reducing it to something else, which may already be of some help for a problem
that, viewed from any other angle, has appeared disorienting and intangible.
