This is a draft for the last chapter of the book to be called BASIC EPISTEMOLOGY.
IV
LIMITS OF
KNOWLEDGE
The difficulty is
to realize the groundlessness of our believing.
Wittgenstein
Scepticism is
doubt regarding the indubitable. Philosophers have constructed arguments that
lead us to questioning things we normally consider certain, like knowledge by
testimony, existence of other minds, existence of the external world, inductive
knowledge, and even the existence of any knowledge – with the exception of
their own knowledge that there is no knowledge, of course, in order to save
them from self-contradiction. These arguments are important for epistemology, not
as much because they seem to be sound, but mainly because they offer a
challenge to the epistemologist – and much philosophical progress is
dialectically tributary to challenges like these. Moreover, they help us to
establish the limits of our meaningful language and knowledge. Answering the
sceptics might allow us to distinguish real questions that can be rationally answered
from pseudo-questions that only invite us to produce pointless pseudo-answers.
They are only apparently meaningful, because they transcend the limits of what
can be cognitively questioned and answered. In what follows, I will restrict
myself to the discussion of two such cases: scepticism about induction and
scepticism about the external world.
1. Scepticism about induction
Scepticism about
induction was introduced by David Hume, entangled with his analysis of
causation. Since I am interested here in scepticism about induction, I will
strongly reconstruct the argument, separating it from his analysis of
causation.
First, you probably know the form of an
enumerative inductive argument: we have a thing[1]
A that is associated with a thing B on all occasions, for instance, fire is
always associated with heat, which serves as the premise for the conclusion
that the next time there is a fire it will heat its surroundings, or even for the
generalization that fire will always produce heat. Inductive inferences can be
not only from the past to the future (as in the case above), but also from a
recent past to a distant past (fire has always heated its surroundings, dinosaurs once inhabited the
earth), and from different locations to new ones, actual or not (like fire in
Europe, fire in Burma will heat its surroundings, as much as a fire in
Kamchatka heated its surroundings during the last Ice Age). There are other
important forms of inductive reasoning, like the inference to the best
explanation (abduction). We came to the conclusion that the moon is illuminated
by the sun, causing its different phases, because we always see the sun on the
side of the sky opposed to the illuminated side of the moon. More than any
other hypothesis, this is the best explanation for the phases of the moon.
Since premises can be true and despite this the conclusion false, this
inference is inductive. Moreover, it seems clear that this kind of inductive
inference is based on numerous previous enumerative inferences, like the view
that rightly placed luminous physical bodies illuminate non-luminous bodies.
The Humean question was: how do we know that
the premises of a strong inductive argument make the conclusion probable? His
answer was the appeal to a metaphysical principle of the regularity or uniformity of nature, which concerning the causal
relation can be expressed in the statement that the future will be like the
past. We can express the argument as follows:
A
1. The future will be like the past.[2]
2. Fire has always heated its surroundings.
3. The next fire will heat its surroundings.
Since we wish to
contemplate the different extensions of induction in time and space, we can
state the principle of uniformity more broadly as follows:
PU: (i) The future must be like its past, (ii)
the less recent past must be like its more recent past, (iii) the next location
of space must be like the already known ones.[3]
If PU(i) is
correct, then the inductive force of the argument is warranted. A first problem
with PU(i) is that this principle is not analytic-conceptual. One can deny it
without contradiction or incongruency. “The future will not be like its past”
is a perfectly meaningful sentence. If it is so, then PU(i) must be a synthetic
statement. But this seems to mean that it is based on experience. Reflecting on
this, a Humean sceptic could pose against PU(i) the following question: how do
we know the principle of uniformity? The answer concerning PU(i) seems to be
the following:
1. All the futures of our pasts were
like their own pasts.
2. Hence (probably) the future (of
our present) will be like its past.
There is,
however, a serious problem with this argument: it is an inductive one. That is,
we are trying to warrant our inductive arguments by means of a principle based
upon induction, and this is circular. We are committing a petitio principii by trying to justify something using what we
intend to justify in the justification. The same can be said regarding the two
other parts of PU. Concerning PU(ii) we have the following example:
1. The less recent past must be like
its more recent past. (PU(ii))
2. In the recent past fire has always
heated things.
3. Hence (probably) in the remote
past fire also heated things.
Concerning PU(iii)
(plus PU(ii)) we have also a similar example:
1. The next region of space must be
like the already known region of space. (PU(iii))
2. The less recent past must be like
its more recent past. (PU(ii))
3. In the recent past fire has always
heated things in all regions of earth.
4. Hence (probably) fire heated things
in Kamchatka during the Ice Age.
Hume’s
conclusion, based on an analysis restricted to PU(i), was downright sceptical:
we cannot warrant our inductive arguments. And this conclusion must be
obviously extended to PU(ii) and PU(iii), since these parts of our version of
the principle of uniformity also depend on inductive reasoning to be
established.
The conclusion is that we have no reason to
believe that the sun will rise tomorrow or that in the remote past fire heated things
or that it heated things in Kamchatka during the last Ice Age… Neither our
empirical science nor our common sense knowledge of the world have any rational
warrant.
According to Hume, we have only a
psychological disposition to believe in our inductive results, since they form
a habit or custom for us: we have the habit to expect that the next fire will
heat things or that the sun will rise tomorrow in the same way insects have the
instinctive tendency to follow light (1764: 75). However, with the queer
exception of Karl Popper, few philosophers have followed Hume on this point.
2. A general answer
There have been many
intelligent attempts to solve Hume’s problem of induction, all of them in one
way or another disappointing. There is, however, one that seems to me to touch
the very heart of the problem, though it has never been sufficiently developed.
It is suggested in the words of Jenny Teichman and C. C. Evans (1999), in their
short introduction to philosophy:
It would be impossible to say
truly that the universe is a chaos, since if the universe were genuinely
chaotic there would 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.
The philosopher
Keith Campbell made the same point earlier. As I understand him, he noted that
the world must have sufficient order to allow us to reapply a concept, since if
our concepts could not be reapplied, they could not be interpersonally checked,
and therefore could not be established as concepts (1974: 80-83). Indeed, concepts
could not turn out to be intersubjectively granted and consensually associated
with conceptual words.
Although emphasizing language, what these
authors grasped is that it doesn’t matter how disorderly a world is, if it is
recognizable as a world, it must have enough order (spatial and temporal) to be
open to some kind of inductive access. That is, a possible world is only
conceivable if it is open to induction. Openness to induction is a condition of
possibility for the cognition of any possible world.
We can order these intuitions about the
relationship between world (or universe), and induction in the form of the
following argument:
1. Any possible world must be at least
conceivable.
2. Any conceivable world should have
at least some degree of regularity.
3. Any world that has some degree of
regularity is open to some kind of inductive procedure.
4. (1-3) Any conceivable world must
be open to some kind of inductive procedure.
5. Any world must be conceivable.
6. (4,5) Hence, any world must be
open to some kind of inductive procedure.
7. Corollary to 6: our world is open
to some kind of inductive procedure;
The central idea
in this argument is that the existence of a fully chaotic world is impossible,
since such a world would be inconceivable and we cannot speak meaningfully of
worlds that are inconceivable, that is, in no sense imaginable, since this does
not belong to the concept of world (or universe) as we are able to understand
it.
One reason why this idea can meet some
resistance is that the literature on the problem of induction is full of
references to chaotic worlds which are inaccessible to inductive procedures.
This is, however, a tragic mistake, and I am sorry to say that that the person
most responsible for this mistake was Hume himself. This mistake arose from his
objection against the justifiability of induction restricted to his analysis of
causality, which is based on UP(i). Causality is typically what we could call a
case of diachronic regularity, which
occurs when in a regular way an event A occurs temporally earlier than an event
B. This is clear in Hume’s counter-inductive examples, which go from Adam, who
seeing a lake for the first time did not know that the water could drown him,
to falling snow that unexpectedly burns and flowers that unexpectedly bloom in
the middle of winter (1764: 35). If induction were restricted to diachronic
regularities, it would suffice to imagine a frozen world – a world without any
diachronic regularity – and it would be a world impervious to induction.
However, focusing on diachronic regularities leads us to forget another,
equally important form of regularity also assumed by UP, namely, synchronic regularity. The state of
affairs that Notre Dame is on the Ille de France, the situation that the Tower
of Pisa leans and the supposed fact that Cleopatra had a big nose are all
synchronic regularities. These synchronic regularities are often called structures. A gothic cathedral has a
very complex synchronic structure and has usually existed over a long period of
time. Synchronic regularities are, however, objects of induction as much as diachronic
regularities, since only induction allows us to foresee that synchronic
regularities perceived in the past will endure in the future. Notre Dame will
remain on the Ille of France, the Tower of Pisa will continue to lean,
Cleopatra supposedly had a big nose until her death, the gothic Cathedrals are
expected to preserve their structures through the centuries, all this we
believe as result of induction.
When we realize that our world is made up as
much of diachronic regularities as also of synchronic regularities, then it
becomes clearly impossible to think that we are able to conceive a world
without regularities. Consider, for instance, one among the many attempts to
imagine a world so completely chaotic that it would be a world without
regularities. We can appeal to ‘complete transformations of the world’ as
described in many fictional books. I choose the following passage from Sartre’s
novel Nausea. It reminds us of
surrealistic art, such as the paintings of Dali:
It can happen any time, perhaps right now: the omens are present.
For example, the father of a family might go out for a walk, and, across the
street, he’ll see something like a red rag, blown towards him by the wind. And
when the rag has gotten close to him, he’ll see that it is a side of rotten
meat, grimy with dust, dragging itself along by crawling, skipping, a piece of
writhing flesh rolling in the gutter, spasmodically shooting out spurts of
blood. Or a mother might look at her child’s cheek and ask him: "What's
that – a pimple?" and see the flesh puff out a little, split, open, and at
the bottom of the split an eye, a laughing eye might appear. Or they might feel
things gently brushing against their bodies, like the caresses of reeds to
swimmers in a river. And they will realize that their clothing has become
living things. And someone else might feel something scratching in his mouth.
He goes to the mirror, opens his mouth: and his tongue is an enormous, live
centipede, rubbing its legs together and scraping his palate. He’d like to spit
it out, but the centipede is a part of him and he will have to tear it out with
his own hands. And a crowd of things will appear for which people will have to
find new names—stone-eye, great three-cornered arm, toecrutch, spider-jaw. And
someone might be sleeping in his comfortable bed, in his quiet, warm room, and
wake up naked on a bluish earth, in a forest of rustling birch trees, rising
red and white towards the sky like the smokestacks of Jouxtebouville, with big
bumps half-way out of the ground, hairy and bulbous like onions. And birds will
fly around these birch trees and pick at them with their beaks and make them
bleed. Sperm will flow slowly, gently, from these wounds, sperm mixed with
blood, warm and glassy with little bubbles. (…)
At first glance,
these changes are extreme. Nonetheless, there is nothing in this report (or in
any report of the kind) that makes it really chaotic. Although the living
rotten meat crawling to the family father is indeed a strange creature, its
unexpected properties are all already well-known. Moreover, even the
individuals suffering changes, like the child, an eye, a man, a tongue, birch
trees, birds, can be also identified, although their also well-known new
properties are unexpected and frightening. The centipede behaves like a
centipede and human beings react desperately as expected in the such
situations. What Sartre describes is based on a considerable number of
well-known synchronic and diachronic regularities combined in unexpected ways,
and the only reason why we are able to fully understand the description and
react to it is because of our acquaintance with all these well-known
regularities. In fact, if all regularities could be erased, the text would lose
any intelligibility. The future, at least in proportion to its greater
proximity to the present, must maintain sufficient similarity to its past to
allow an application of inductive procedures, making us recognize the
continuity of the same world we know today, notwithstanding how many unexpected
and undesirable changes come to pass.
We can do some thought-experiments in order
to reinforce these conclusions. Imagine a frozen world without any diachronic
regularities. This world would still have the regularity of the permanence of
its form or structure, once we apply inductive reasoning to foresee that it
would remain the same world in the next moment or over the whole period of its
existence. Imagine by contrast a world formed by a note of a single pitch or a
blinking red light that repeats itself at aleatory intervals. Once it ceases to
repeat, this world ceases to exist. But this minimalist world still has the
regularity of repetition. Hence, one could inductively expect this repetition.
One can complain that it may be difficult to
apply induction when the regularities are few. But this remark ignores a
logical point. Induction is theoretically flexible. The required inductive
search can be calibrated in conformity with circumstances. When the probability
to find a regularity is lower, we expand the inductive search. Consider, for
instance, the wild camels of the Gobi desert. The expanse of the Gobi desert is
immense. It includes the north of China and the whole of Mongolia. And these
shy camels are rare, supposing they have not yet become extinct. You can visually
survey a vast expanse of desert, searching up and down the hills with powerful
binoculars until you find a Gobi camel, if you have luck. The pressure of inductive
calibration must be very high in this case.
The general conclusion is that some
principle of uniformity must be applicable, insofar as we might assume
cognitive access to the world. As we will see, we lack a formulation of this
principle that is sufficiently precise and adequate instead of vague and
misleading.
3. Searching for more appropriate answers
When we more
carefully consider the temporal dimensions (i) and (ii) and the spatial
dimension (iii) of PU, within which we apply inductive reasoning, we see that
much more must be taken into consideration.[4]
Consider PU(i): the principle that the future will be like its past. What is
meant with PU(i) is vague. Suppose we take it literally (like Hume) and deny
this by saying that the future will not be like its past. This denial
does not seem to contain any contradiction, which means that PU(i) is not
analytical. This is not desirable, since PU(i) cannot be synthetic a posteriori
or empirical, and since we do not wish to accept a principle of uniformity that
is synthetic a priori; such a principle would go against the very plausible
view according to which all (or almost all) our empirical knowledge is
fallible. Moreover, the literal reading of PU(i) as telling us that all of the
future will be similar to its past is obviously wrong. Not only does nothing
prevent great unexpected changes (a great meteor collides with the earth,
etc.), but considering the infinitude of time, the distant future can be
utterly different from our past. Suppose, for instance, you could observe the
world some micro-seconds after the big-bang. The future in which there would be
myriads of galaxies with stars and planets, some of them with life and
consciousness like we find on the earth, would be utterly different from what
was going on at that moment.
However, there is something analytically
right in PU(i). Although the future can be different from its past, it cannot
be completely different from its past, or at least the near future cannot be.
For in this case, how could we identify a future as the future of its own past? We must interpret PU(i) as
saying that the future, insofar as it approaches the present, must be
sufficiently similar to its past in order to be the future of its own past.
Call the future of our world FW0. It must, at least insofar as it
approaches the present, be more like its past, in order to be identified with
the future of the past W0 or PW0. If it were not so, it
could be identified with the past of any possible future world, say, of FW1,
FW2, FW3… and we would lose the proper way of distinguishing
it. (Moreover, this related transition from past to future must be spatially
located: imagine, for instance, that the near past of a sunny day in London is
suddenly replaced by the near future on Calisto, a satellite of Jupiter.)
If we wish to warrant induction, we must
read the principle that the future must be like its past in a more precise and
adequate way. We must refine PU(i) so that it shows itself as something
analytic-conceptual and a priori in this harmless sense. In order to show that
such a reading is possible, consider the following example:
Presently, at time T0,
there is a piece of wax. This piece of wax is warmed and in T1 it changes
from a solid to a liquid state. Until now, most things have remained the same,
not only the atomic constitution of the wax, but also the molecular
constitution that makes up what we commonly call wax. Then, in T2
the wax is warmed much more, so that what remains are only ashes. The chemical
constitution of the wax is now lost, the atoms of oxygen have disappeared, only
the atoms of carbon are still there. Now, suppose that the process of heating
continues and that the carbon ash is heated by hundreds of millions of degrees,
so that in T3 the atoms disintegrate and all that remains is a
plasma of sub-atomic particles.
It is easy to
understand what this progression shows: the nearer the future is to the
present, the more properties it still has in common with the present, until the
point of junction of the future and the past – which is the present – a point
of complete identity, where all properties are the same. The same rule is valid
considering the relation between the present and its past. Furthermore, the
example with the piece of wax can be generalized. It can be applied to any
domain of our world. On any level, this same pattern repeats itself: Natura non facit saltus. For instance,
the industrial revolution began in the second half of the XVIIIth century. But
if we consider the changes in a short period of time, such as from 1760 to
1800, we can find only a few changes, like the introduction of mechanized weaving
machines in England and a small rural exodus in England. Large-scale iron and
steel production, steam power, steamships, locomotives and railways, the great
rural exodus and serious social tensions… had to wait until the next century.
Certainly, there are anomalous progressions in which a near future can for a
while be more different from the present than a more distant future, but in
this case, you can consider only the nearest future, or you can consider a
broader interval that includes this kind of anomaly but makes it irrelevant. To
give an analogy, consider the following anomalous progression: {1, 2, 3, 2, 3,
4, 3, 4, 5…}. The fact that some numbers are unexpectedly nearer to 1 does not
change the fact that this is a positive numerical progression, and many
variants, also anomic ones, can be added. Looking for a real empirical example,
consider the continued economic development of a country, with all its booms and
busts.
Using the word ‘tendency’ to discard
possible anomalies, the principle that the future will be similar to its past
can be improved as follows:
UP(i)* Tendentially, the nearer
the future is to its point of junction with its past (i.e., the present), the
more similarities will be held with its past, being both the same at the point
of junction.
I would
understand this reading of UP(i) as analytic-conceptual. We cannot deny it
without saying something incongruent, if not contradictory. We cannot deny that
there is a tendency to the annulation of the differences between future and
past the nearer they approximate to the present. Now we can warrant inductive
probability by means of an analytic-conceptual (a priori) principle:
1. Tendentially, the nearer the
future is to its own past, the more similarities it will have with its past.
2. In the past fire always heated things.
3. The next fire will (probably) heat
things.
This seems to me
sufficient to inductively warrant that the next fire will probably heat things.
Consider now the other sub-principles of
uniformity. Sub-principle UP(ii) represents no problem, since it is UP(i)
projected onto the past. But sub-principle (iii) still requires some
explanation. The principle that one region of space must be like another, taken
strictly, is certainly false. The region of the Côte d’Azur must be very
different from the region of a black hole. We are in fact speaking of proximal
regions. Thinking in this way we can state the principle of spatial uniformity
in a way that is analogous to the above principles of temporal uniformity:
UP(iii)*: Tendentially, the nearer
one spatial region is to the spatial region we have already considered, the
more similar this spatial region will be to the spatial region we are
considering, both being the same in their point of junction (i.e., the spatial
limit).
For instance:
suppose that we can see part of a checkerboard surface. You can be fairly sure that
the next segment we see of the same surface will also have a checkerboard pattern.
We expect based on experience that unknown space will preserve regularities in
the same way as time. UP(iii)* is also analytic-conceptual: you cannot deny
this tendency without contradiction.[5]
Indeed, if this principle is constitutive of the way we are able to access any
possible world in its temporal dimension, it cannot be logico-conceptually
refuted.
Outflanked, the sceptic could appeal to a
drastic objection. Even if we concede that a world, in order to be a world,
must have enough uniformity to make possible the use of inductive procedures,
there is nothing that absolutely warrants the continuity of anything. Suppose
that our whole world disappears five seconds from now. Nothing in our principle
of uniformity PU(i)* would prevent this possibility! To this consideration one
has the inclination to answer in the affirmative, admitting that there is
nothing to warrant the permanence of our world. Hume was, after all, right!
Nonetheless, when we think about this
sceptical objection more carefully, we see that the true answer is a different
one. The truth is that this sceptical objection makes no sense, because it
requires a completely unverifiable answer. If the universe disappears in five
seconds, there will be no one to verify this disappearance.[6]
In this regard, it makes no sense to speak about what you logically cannot
know. The situation seems to be possible because we can imagine the world
disappearing with us as if we could be transcendent observers of this dissolution.[7]
In other words, we have arrived at the limits of what we can meaningfully think
and know. The sentence “We and our whole world could disappear in the next five
seconds” is like the sentence “The whole world doubled its size last night”. It
might be dizzying, but it has only a grammatical sense and an emotional effect
– not a cognitive sense.
4. Scepticism about the external world
The second famous
sceptical argument aims to show that we cannot know the existence of the
external world. I call it the argument
for ignorance about the external world. This argument makes use of
sceptical hypotheses about the external world. Hence, in order to explain it I
begin by giving three examples of this kind of sceptical hypotheses:
h1: The external world is a dream.
h2: I am a soul being deceived by
a malign genie that produces in me
the coherent hallucination of an external world.
h3: I am a brain-in-a-vat with all
afferent and efferent neuronal bundles linked to a supercomputer on the planet
Omega; the program of this supercomputer makes me believe that I am living a
normal life on the planet earth.
The argument for
ignorance is based on the fact that it seems impossible to prove that the
sceptical hypotheses are false. This might seem strange, but it is at least
logically possible, a possibility that is explored in science fiction films like
Matrix or The Real Thing. Now, applying hypothesis h3[8],
the sceptic can argue as follows. If I cannot know that I am a brain-in-a-vat,
then I cannot know that I really have two hands or that I am typing on a real
computer keyboard; hence, since I cannot know that I am not a brain-in-a-vat, I
cannot know that I have two hands or that I am typing… Putting this argument in
conventional form we have the following modus
ponens:
Instance of AI:
1. I do not know that I am not a
brain-in-a-vat.
2. Since I do not know that I am not
a brain-in-a-vat, I cannot know that I have two hands.
3. Hence, I cannot know that I have
two hands. (MP 1, 2)
Indeed, if I
cannot know whether or not I am a brain-in-a-vat, then I cannot know if I have
two hands, since a brain-in-a-vat does not have two hands (but only imagines
having them). Hence, if I do not know that I am not a brain-in-a-vat, I cannot
know that I have two hands.
Now, replacing any trivial proposition about
the external world by p, and using K as a knowledge-operator applied by
some epistemic subject a, we can
symbolize in a generalized form the argument for ignorance, aiming to show that
in fact we know nothing about the external world:
AI:
1.
~a(K~h)
2.
~a(K~h) → ~aKp
3.
~aKp (MP 1, 2)
The argument of
ignorance seems to show that since we cannot know that the sceptical hypothesis
is false, we cannot acquire any substantive knowledge about the external world.
This shares with other sceptical arguments a property noted by Hume: they do
not admit of answers and do not produce conviction (1748: 155).
There is a contrapositive to this argument,
made famous in an article by the English philosopher G. E. Moore. His approach was
to begin by acknowledging that we at least know with certainty that many trivial
things around us do exist. As he wrote:
I can
prove that two human hands exist. How? Raising my two hands and making a
certain gesture with my right hand: “Here is a hand”. And then making the same
gesture with the left: “Here is another hand”. (1939)
We can modify Moore’s statements a bit, from an argument to prove the
existence of the world to an anti-sceptical argument – call it the argument for knowledge regarding the
external world. The conventional form of this argument will be the following modus ponens:
Instance of AC:
1. I know that I have two hands.
2. If I know that I have two hands,
then I know that I am not a brain-in-a-vat.
3. I know that I am not a
brain-in-a-vat. (MP 1, 2)
Or, in a
generalized symbolic form:
AC:
1.
aKp
2.
aKp → ~a(K~h)
3.
~a(K~h)
The two arguments
seem to have the same force. The question, however, persists, since it is contradictory
that we have two equally powerful arguments leading us to opposite results.
5. Some attempted ways of answering
There are many
attempts to answer the argument of ignorance about the external world. Hilary
Putnam’s answer, for instance, would be that we cannot be brains in vats
because according to his externalist theory of meaning we would need to have causal
experience of things in the world in order to know their meaning. Now, if we
can imagine that we are brains in vats seeing trees, then we must have had the
experience of real external things like trees and vats and even brains, which
means that we cannot be brains-in-vats. In the end, all that the brain-in-a-vat
causally experiences are electrical patterns of trees, or images he may produce
of vats, which are also originated from electrical patterns produced by the
supercomputer. One could answer that at least the people who manufactured the
supercomputer and created its programs had the causal experience of trees and
vats and brains. In this case, they would be caused by these things to create
the programs that indirectly caused our pattern images and our false idea that
we could be brains-in-vats. Putnam’s answer to this would be that the
brain-in-a-vat and the supercomputer could be created by a mere cosmic
accident, without any living beings producing the brain, the computer and its
program!
There are several objections to Putnam’s
argument. One is that it only works against the brain-in-a-vat sceptical
hypothesis; one could instead use the dream hypothesis. Another is that one can
accept Putnam’s argument, but retain the hypothesis by considering recently
envatted brains (these brains would already have causally experienced our
world) (DeRose 1999). A third objection is that Putnam disregards the flexibility of language.
If it is possible that the cosmic accident produces a brain-in-a-vat powered by
the program of a supercomputer, then it is also possible that the electrical pattern
that causes the vision of the tree and the idea that we are brains in vats are,
by pure coincidence, the same patterns that cause in us the illusion that we
are seeing a tree and the ideas that we are brains-in-vats, while we really are
brains-in-vats. Why not?
A different answer to the sceptical problem
consists in denial of the so-called principle of closure. According to this
principle, if person a knows p and also knows that p entails q, then a also knows q. Symbolically, we can state the
principle of closure as:
[aKp & aK(p →
q)] → aKq
This principle is
very intuitive, except in cases where the conclusion is a shortcut for many
intermediary steps (say, [aKp & aK(p → p1 → … →pn→q)]
→ aKn), which we might leave out of consideration.
However, objecting to the sceptic, one can
say that according to the context the principle can be flawed. This is the case
of answers appealing to the principle of relevant alternatives. According to
them, one alternative possibility should only respect closure when it is
sufficiently relevant. For instance, suppose you are in a zoo and you see a
zebra. Then a sceptic comes to you and says that you cannot really know that
you are seeing a zebra, since it is possible that it is only a donkey cleverly
painted in a way that makes it seem to be a zebra. However, the context of a
serious zoo would make it almost impossible that people would paint donkeys so
that they would seem to be zebras. (Dretske 1970) According to this view, “I am
seeing a zebra” does not entail “This is not a donkey cleverly painted in order
to be mistakenly regarded as a zebra” and does not need to entail this. Here
the principle of closure does not work.
The problem with this argument is that it is
not clear that I cannot apply the closure principle. If I know that this is a
zebra, and I know that if it is a zebra then it is not a donkey, then I know
that it is not a donkey. Indeed, I know that it is not a donkey because I am supported
by contextual information: I know that this is a serious zoo and not a circus.
I know that because it is a zebra the proposed irrelevant alternative is false.
With the help of his argument, the defender
of the relevant alternatives answer to the sceptic usually argues that it is
very implausible to think that the statement “I cannot know that I am not a
brain-in-a-vat” would entail something so distant from this as “I cannot know
that I have two hands”. The context that would allow this possibility is too
strange and remote. The answer that could be given is that we cannot make such
kinds of considerations. The hypothesis that I am a brain-in-a-vat is not
improbable in comparison with the hypothesis that I have two hands. We simply
do not have means to attest to its probability or improbability.
Another attempt to deal with the sceptical
argument is contextualism. As we have already noted, according to contextualism
the word ‘knowledge’ can be used with different degrees of precision when
placed in different contexts. With this idea at hand, the contextualist will
say that in the context of daily life standards of knowledge are very low,
which means that we can claim knowledge of things around us, like our hands. But
in sceptical contexts we cannot say that we know that we have two hands, since
the standards of knowledge are too high. Consequently, both are right, the
sceptical and the anti-sceptical views, since they claim different things.
A first problem with this argument is that
it is not clear that the sceptical view does demand very high standards of
knowledge. Clearer is that the sceptical hypothesis cannot be probabilistically
approached. It is only a logical possibility.
A second problem with this argument resides
in the contextualist thesis. It is not clear that contextually different
knowledge-claims really demand different standards of empirical precision.
Repeating the objection that I made in chapter II, if I buy the ticket for a
plane flight, I can say that I know
my aircraft will not crash, because the probability of this occurrence is very
low (1 in 5.4 million). But if I buy a lottery ticket, I am not allowed to say
that I know I will not win, even if the probability of winning a lottery is
much lower than the probability that my aircraft will crash (1 in 13 million
for the lottery). Why don’t I say I know I will not win a lottery prize? The
contextualist answer is that in the lottery context the demands of probability
are much higher.
Nevertheless,
it seems to me that a better answer would be that the linguistic expression of
thought is often too inexplicit, although the thought is what the sentence
really means, and the sentence is the truth-bearer of the thought. In the first
case, what is demanded is practical certainty, while in the second case what is
demanded is logical certainty. What really changes is the thought, which is too
vaguely expressed by the declarative sentence. The thought expressed in the
first case is: “I know [with practical certainty] that my aircraft will not
crash”, while in the second case the thought must be expressed as “I do not
know [with probability 1] that I will not win the lottery”, since it is a
statistic inference that demands formal certainty.
6. A more convincing answer
The solution I
will propose takes as its assumption the notion that problems and their
solutions are more complex than they seem at first view. Consequently, the
above suggested answers, despite their originality, do not really solve the
problems, since their formulations contribute to hiding complexities invisible
on the argumentative surface.
Now, the solution I intend to present is
based upon a demonstration that the two arguments – for ignorance and for
knowledge – implicitly contain two different concepts of external reality. These
concepts, however, change their meaning from the premises to the conclusion, which
makes both arguments equivocal and consequently fallacious. This solution is
motivated by Rudolph Carnap’s distinction between internal and external
questions of existence. According to him, internal questions are those
regarding elements of a system and are answered by placing the elements
adequately within the system. For example: “Is there a number 2?” is internal
regarding the system of natural numbers. “Are there physical objects?” is
internal regarding the system of physical things (the Thing-World). These
questions are legitimate. External questions are ones regarding the existence
of systems in themselves. These questions only allow pragmatic answers. We
decide to accept the system of natural numbers. We decide to accept the system
of physical things. These decisions arise from a pragmatic fiat. Philosophers such as P. F. Strawson (1974) and Barry Stroud
(1984) have with reason criticized Carnap on the grounds that our decision of
accepting a system, in particular the system of physical things, obviously does
not arise from a pragmatic decision. The external world simply imposes itself on
us, independently of any wish or advantage its acceptance gives us. The
analysis I will propose circumvents this kind of objection, though maintaining
that there are two kinds of attributions of external existence or reality.
The first thing to do in order to reach our
goal is to show that the arguments for ignorance and knowledge have implicit
commitments to attributions and disattributions of reality. This is easy to
show. Comcerning the argument for ignorance, we can give the following
paraphrase:
Instance of AI:
1. I do not know that I am not in reality
a brain-in-a-vat.
2. Since I do not know that I am not in reality a brain-in-a-vat, I cannot
know that I have two real hands.
3. Hence, I cannot know that I have
two real hands. (MP 1, 2)
While with the
argument for knowledge the paraphrase is:
Instance of AC:
1. I know that I have two real hands.
2. If I know that I have two real hands, then I know that I am not in reality a brain-in-a-vat.
3. I know that I am not in reality a brain-in-a-vat. (MP 1, 2)
There is no doubt
about this: any statement concerning an external world contains a commitment to
the assumption of the external reality for what it affirms or the assumption of
a lack of external reality for what it denies.
What should be noted, however, is that the
expression ‘external reality’ in our most common uses has a sense very
different from the expression ‘external reality’ as used in sceptical
scenarios. To show this, all we need is to note that after being liberated from
a life as a brain-in-a-vat, a person will presumably not say that her earlier
world was not real. She will probably say that in a sense her earlier world was
very real for her or “had a perfect degree of reality” for her at the time,
although in another sense it was indeed not the ultimately real world, as she
subsequently discovered. This means that the person is using the word ‘real’ in
two very different senses: in the first one she affirms the existence of the
previous real world of the supercomputer, in the second she denies its existence.
I call the first the inherent sense
of external reality, a sense that allows the attribution of external reality to
the contents of experience of the brain-in-a-vat when it still was a
brain-in-a-vat, while the second I call the adherent
sense of external reality, a sense that does not allow the attribution of
external reality to the contents of experience of the brain-in-a-vat when it
still was a brain-in-a-vat. In order to make the distinction clear I will separately
examine the criteria of application constitutive of each of these senses of
‘external reality’. After all, by knowing the criteria of application of these
words, we can better understand their meanings. Or, as Wittgenstein once said,
criteria “give our words their common meaning” (1958: 57).
Consider, first, the inherent sense of
external reality. It is the usual sense which is applied when we
attribute/disattribute external existence in everyday life. For instance, when
we ask about the existence or reality of something we are looking for. This
sense is made by a group of criteria that ordinarily must be experienced
together, and it was frequently and in various ways considered by modern
philosophers like Descartes, Locke, Berkeley, Hume, and even by analytic
philosophers like Frege. G. E. Moore wrote an article about these criteria,
summarizing them in the following sentence:
The real is something independent
of the mind that is verifiable by others, continuously connected with other
things, and in this way has certain causes, effects and accompaniments (I would
say that it ‘displays regularities’) with the highest degree of reality. (1953)
I think I can
summarize the most fundamental criteria as follows:
a. The sensory experience of them has
the greatest intensity (normally this experience is co-sensorial),
b. They are independent of our will
(typically),
c. They are interpersonally checkable
by anyone in the right position,
d. They display regularities imposed
by natural laws (on various different levels).
Separately, these
conditions are not sufficient for the attribution of inherent reality to objects
outside us. (Laurence Bonjour was right when he wrote that Locke’s criteria
were insufficient to warrant external reality (2002: 130-35)). However, my
point is that if you join together all those criteria, they are sufficient to confer inherent reality on
what they apply to during the time when they are applicable. They are
sufficient for a simple reason: they define
what we all understand by external reality in the inherent sense of the word.
Consider, for example, my computer. I can
see it, touch it, and hear it with the maximum expected intensity, differently
from the images I can form in my mind when I close my eyes. Moreover, its
existence and properties are not directly dependent on my will (my mental image
of it is directly dependent on my will). My hand-held computer can be an object
of interpersonal experience: others can come to me, see it, and agree about its
existence and properties. Finally, my computer obeys the laws of nature. It
needs electrical energy to work, to respond to my commands, it will break if it
is dropped from a high place, etc. If we join these four criteria of external
reality together, it is impossible to imagine a situation where we cannot say
that the object of experience is (inherently) real. Even if I were a
brain-in-a-vat or if I were subjected to a very highly developed experience of
artificial reality, my hand-computer would be very real in this sense of the
word.
What about things too small or too distant
to be presently observed by us? Could we say that they are real in the inherent
sense? Yes, of course, and by means of a very common mechanism of semantic extension of the three above
given criteria. In an indirect way, a thing that is too small is said to be
real because it is causally related to other things with which we can have
sensory-perceptual contact (like tracks left by electrons in a cloud chamber).
Things that are too far distant, either because they were once objects of
perception and are retained in our memories (like my great-father’s house), or
that were once objects of sensory perception by others (like Angkor Wat, a
religious site I have never visited), satisfy the four criteria considered
above, because we know that these things would satisfy those criteria to us,
given the right circumstances of access. Finally, since we have always
experienced new things in such ways, we inductively expect that we will
continue to have new experiences of new things (the world is open). We can even
join all these things in order to produce a proof of the external world as a
whole, insofar as we understand it as possessing inherent reality. Indeed, this
is in my view the long sought proof of the external world’s existence! This is
the reason why people say that only philosophers and madman deny that our world
exists. They all have implicitly made such inferences, and what they mean is that
the external world is nothing but the sum of all these implicit extensions of
applications of the concept of inherent reality.
These inherent attributions/disatributions
of reality are the usual ones: without perceiving this we apply them all the time.
But there is another attribution/disatribution of reality that is sometimes
made, which concerns what I called the adherent
sense of reality or existence. This is the sense of reality that we
attribute/disattribute to things like fictional reality and sceptical
scenarios. We can say that the sense is different because the criteria of
application have nothing to do with the four criteria of inherent reality
considered above. Suppose, for a moment, that the world is a dream or that you
are a brain-in-a-vat. In this case, the world continues to exist for you in the
inherent sense of the word. If you fall from a tree and break a leg, your pain
is as real as any other, and the leg is really broken and in need of immediate medical
attention. All things appear to you with maximum sensory intensity,
interpersonally and following the laws of nature (since the supercomputer program
is the best on the market), which warrants the inherent existence of things around
you. But in some other sense, these things are not real, and this sense is that
of adherent reality. Although the world of the dreamer or the brain-in-a-vat
has no adherent reality, in the inherent sense it continues to be perfectly
real.
The question now is about criteria for adherent
reality. How can one know that a world is adherently unreal? The answer is: comparatively and by reasons of coherence.
The concept of adherent reality is a comparative
(or relative) one. A comparative concept changes its applicability in
conformity with the context. For instance, the words ‘small’ and ‘big’: a baby
elephant is small compared with an adult elephant; however, it is a big animal compared
with a mouse (Copi). Now, suppose that you have lived your whole life as a
brain-in-a-vat and that now you are liberated. Your brain was inserted in the
head of a person on the planet Omega and you awake in your new world, meeting
other people who resemble you as you now appear. They reveal that the
experiment was motivated by the desire to create cultural diversity on the
planet. Moreover, they show you the empty vat and the supercomputer, together
with other fellow brains-in-vats being nourished and formatted. Surely, if all
this does not drive you mad, you will compare and see that the world where you
lived was a kind of sub-product of the truly real world, the world of the
planet Omega, since this is the best way you have to make the information you
have received until now seem coherent.
Knowledge of adherent reality is, I think,
only comparative. Before you were liberated from the vat, it would have made no
sense to ask if you were a brain-in-a-vat or not. The same is true concerning
ourselves and our world. To question its adherent reality makes no sense
without the advent of a sceptical scenario that endows us with the expected
comparative criteria. Furthermore, the comparative sense of the adherent
attributions/ disattributions of reality is defeasible. You cannot be sure that
the new world of the planet Omega is the ultimate one: there is no criteria for
this. It is even possible that you are once more being deceived. It is possible
that they only changed the program. As you awoke, the program running in the
supercomputer was “being awakened from a brain-in-a-vat experiment”.
I believe it is important to see that there
is no absolute sense for adherent
reality, but only a comparative one. Because of this, the question “Is our
world adherently real? – is it the ultimate world?” is strictly considered
meaningless if taken in a literal sense, since the comparative criteria are not
at our disposal. What the question “Is our world adherently real?” means is to
ask whether our world is the ultimately real one, but this is a pseudo-question
that can only work as a metaphysical trap that could have and has often led to
many pseudo-answers. It sounds like the question, “Why
(for what reason) does the world exist?”, which has a grammatical sense and an
emotive effect, but lacks cognitive sense, as much as any attempt to answer it.
Then,
why does it seem to make sense? Well, because we confuse it with another
question that lurks in our imagination, namely: “Could our world in opposition
to a sceptical scenario be comparatively classified as the adherently non-real
one?”, and this question makes full sense. For this reason, “I know that our
world is adherently real” is a senseless pseudo-affirmation, unless it is
understood as “If I were liberated in a sceptical scenario, I would (comparatively)
know that the actual world is the adherently real one”. Wittgenstein considered
claims of knowledge that make no sense, for instance, if in the presence of another
person one suddenly says, “I know that you are in front of me” without any
purpose (1984a), and I think we have such a case here. With pseudo-questions
like “Can we know if our world is real?”, intending to use the word ‘real’ in
an adherent absolute sense – whích philosophers have often meant – we have
already transgressed the limits of what can be meaningfully known.
Now, having understood the two senses of the
word ‘external reality’ (or ‘existence’), we are prepared to see why both the
sceptical argument of ignorance and the anti-sceptical argument of knowledge
are equivocal and consequently fallacious. It is because in both cases we
imperceptibly pass from a commitment to one sense of ‘external reality’ to a commitment
to the other sense of ‘external reality’. In order to make the point clear,
definitely breaking down the arguments, all we need to do is to make explicit
the commitments to reality/non-reality implicit in each argument.
The first sentence of the argument of
ignorance will be as follows:
Instance of AI:
1. I cannot know that I am not an adherently real brain-in-a-vat.
2. Since I cannot know that I am not an adherently real brain-in-a-vat, I
cannot know that I have two adherently
real hands.
3. Hence, I cannot know that I have
two inherently real hands. (MP 1, 2)
This is the most
natural way to interpret the argument, choosing the sense of reality in
accordance with the statements’ semantic context. In the first two sentences we
have a sceptical scenario, and the senses of external reality contextually
suggested are adherent ones. In the conclusion, however, the sceptical wish is
to convince us that we cannot attribute inherent reality to anything. The
sceptic intends to give us the comforting sense that our hands, like all other
external things, are ethereal objects like ghosts in haze and that we are
living in a fictive world without material reality. If the conclusion were,
“Hence, I cannot know that I have two adherently real hands,” the argument
would be sound, but trivial. Indeed, this we cannot know, since outside the
sceptical comparative scenario we have no way to use comparative attributions
of reality or non-reality. Obviously, this result can be extended to the
generalized formal version of the argument of ignorance.
Curiously, a similar fallacy plagues the
argument of knowledge. Once we expose the implicit assumptions of reality, it
looks like this:
Instance of AC:
1. I know I have two inherently real hands.[9]
2. If I know that I have two adherently real hands, then I know that
I am not an adherently real
brain-in-a-vat.
3. Hence, I know that I am not an adherently real brain-in-a-vat. (MP 1,
2)
The anti-sceptic
makes an equivocal step from the first to the second premise of the argument in
his attempt to prove that he knows that this is our ultimate world, resistant
to sceptical doubts. But his equivocal conclusion lies beyond the limits of our
knowledge. It makes no sense to ask for something that lacks any verifying
criteria, since the statement requires an absolute attribution of adherent
reality.
In conclusion, scepticism about induction
and scepticism about the external world have something in common. Both are
fallacious arguments based on disregard for the limits of our knowledge, which
is reflected in the limitations of meaningful language and thought.
BIBLIOGRAPHY
Almeder, Robert F. 1974. “Truth and
Evidence”. Philosophical Quarterly,
24, pp. 365-68.
Alston, William P., 1989. Epistemic
Justification: Essays in the Theory of Knowledge. Ithaca, NY: Cornell
University Press.
Armstrong, David, 1973. Belief, Truth, and Knowledge.
Cambridge: Cambridge University Press.
Attwood, Thomas. 2007. A Complete Guide to Asperger’s Syndrome. London: Jessica Kingsley
Publishers.
Audi, Robert. 1998. Epistemology:
A Contemporary Introduction to the Theory of Knowledge. London: Routledge.
Audi, Robert. 1993. The
Structure of Justification. Cambridge: Cambridge University Press.
Ayer, A. J. 1956. The
Problem of Knowledge (London:
Macmillan).
Boghossian, Paul. (2006) Fear of Knowledge: Against
Relativism and Constructivism. Oxford: Oxford University Press.
Bonjour, Laurence & Ernest Sosa. 2003. Epistemic
Justification: Internalism vs. Externalism, Foundations vs. Virtues. Oxford:
Blackwell.
BonJour, L. (2002).
Epistemology: Classic Problems and Contemporary Responses. Lanham, MD: Rowman
& Littlefield.
Bonjour, Laurence. 1998. In Defense of Pure Reason. Cambridge:
Cambridge University Press.
- 1985. The Structure of Empirical Knowledge. Cambridge: Harvard University
Press.
Bosanquet, Bernard. 1920. Implication
and Linear Inference. London: McMillan.
Casullo, Albert.
2003. A Priori Justification. New York: Oxford University
Press.
Chisholm, Roderick M. (1977). Theory of Knowledge. Englewood Cliffs, NJ: Prentice Hall.
Chomsky, Noam. 1965. Aspects of the Theory of Syntax. Cambridge: MIT-Press.
Clark, H. I. 1963. “Knowledge
on Grounds: A Comment on Mr. Gettier’s Paper”. Analysis 24, 46-8.
Costa, Claudio. 2018. Philosophical
Semantics: Reintegrating Theoretical Philosophy. Newcastle upon Tyne:
Cambridge Scholars Publishing.
Costa, Claudio. 2014. Lines of Thought: Rethinking Philosophical
Assumptions, Chap. 5, Newcastle
upon Tyne: Cambridge Scholars Publishing. First published as “A Perspectival
Definition of Knowledge”, in Ratio 23, 2010, 151-167.
Cottingham, J. 1984. Rationalism. Paladi/Granada.
Dancy, Jonathan. 1995. Introduction to Contemporary Epistemology.
Oxford: Blackwell.
DeRose, Keith. 2018. The Appearance of Ignorance: Knowledge,
Skepticism, and Context. Oxford: Oxford University Press.
Dretske, Fred. 1981. Knowledge and the Flow of Information.
Cambridge: MIT Press.
- 1970.
“Epistemic Operators.” The Journal of Philosophy, 67: 1007-23.
- 1971.
“Conclusive Reasons.” Australasian Journal of Philosophy, 49: 1-22.
De Rose, Keith., and Warfield,
Ted., 1999. Skepticism: A Contemporary
Reader. Oxford: Oxford University Press.
Dennett, Daniel. 2018. From Bacteria to Bach and Back. W. W. Norton & Company.
Dennett, Daniel. 1984. Elbow Room: The Varieties of Free Will Worth Wanting. Cambridge:
MIT Press.
DeRose, K. 2005. “The Ordinary Language Basis for
Contextualism, and the New Invariantism”. The Philosophical Quarterly,
55, 172-98.
DeRose, Keith & Ted A. Warfield. 1999. Skepticism: A Contemporary Reader. Oxford:
Oxford University Press.
Devitt, M. 2010. “No Place for the A Priori”. In Putting Metaphysics First: Essays on Metaphysics
and Epistemology, chap. 13. Oxford: Oxford University Press.
Feldman, R. 2003. Epistemology. Englewood Cliffs, NJ: Prentice Hall.
Feldman, R. Earl Conee. 1985. “Philosophical Studies”,
48, 15-34.
Feldman, Richard. 1974. “An Alleged Defect in
Gettier’s Counter-Examples”. The
Australasian Journal of Philosophy, 52, pp. 68-9.
Fogelin, R. J. 1994. Pirrhonian Reflections on Knowledge and Justification. Oxford:
Oxford University Press.
Gettier, E. L., 1963. “Is Justified True Belief
Knowledge?” Analysis 23; 121-3.
Ginet, Carl. 1975. Knowledge, Perception, and
Memory. Dordrecht and Boston:
Reidel Pub. Co.
Goldman, Alan H. 1988. Empirical Knowledge. Berkeley & Los Angeles: University of
California Press.
Goldman, Alvin I., 1986. Epistemology and
Cognition. Cambridge: Harvard University Press.
Goldman, A. I., 1979. “What is Justified Belief?” In Justification and Knowledge, ed. George
S. Pappas. Dordrecht: Reidel.
Goldman, A. I. 1976. “Discrimination and Perceptual
Knowledge”. Journal of Philosophy 73:
771-91.
Goldman, A. I. 1967. “A Causal Theory of Knowing”. Journal of Philosophy 64: 357-72.
Goldman, A. I. & Matthew McGrath: Epistemology:
A Contemporary Introduction. Oxford: Oxford University Press.
Haack, Susan. 1993. Evidence and Inquiry. Oxford: Basil Blackwell.
Habermas, Jürgen. 1976. ‘Was heißt Universal
Pragmatik?’ in K. O. Apel (ed.), Sprachpragmatik und Philosophie.
Frankfurt: Suhrkamp.
Harman, Gilbert. 1968. “Knowledge, Inference and
Explanation”, American Philosophical Quarterly, 5, 164-173.
Hume, David. 1955 (1748). Enquiry Concerning Human Understanding. Ed. Charles W. Hendel,
Indianapolis, IN: Bobbs-Merrill.
Hume, David. 1739-1740. A Treatise of Human Nature.
Kant, Immanuel. 1929 (1787). Critique of Pure Reason. Translated by Norman Kemp Smith, London:
Macmillan.
Lehrer, Keith. 1990. Theory of Knowledge. London: Routledge.
Lehrer, Keith & Thomas Paxon. 1969. “Knowledge:
Undefeated Justified True Belief”. The Journal of Philosophy 66, pp.
225-37.
Leibniz, Gottfried Wilhelm. 1981 (1704). New Essays on Human Understanding.
Cambridge: Cambridge University Press.
Lewis, C. I. 1946. An Analysis of Knowledge and Evaluation. LaSalle,
IL: Open Court.
Lewis, C. I. 1995 (1923). “A Pragmatic
Conception of the A Priori”. Rep. in P. Lewis, David, 1996. “Elusive
Knowledge”. Australasian Journal of Philosophy, 74, pp. 549-567.
K. Moser, Arnold van der Nat, Human Knowledge: Classical and Contemporary Approaches. Oxford:
Oxford University Press.
Lockard, R. B., American
Psychologist 1971, 26, 168-179.
Locke, John. 1975 (1689). An Essay Concerning Human Understanding. Ed. P. H. Nidditch.
Oxford: Oxford University Press.
Martin, R. M. 2010. Epistemology. London: Oneworld.
Markie, Peter. 2017. “Rationalism
vs. Empiricism”. The Stanford Encyclopedia of Philosophy, ed.
Edward N. Zalta.
Moser, Paul K. 1985. Empirical Justification. Dordrecht and
Boston: Reidel.
Mellor, D. H. 1971. The Matter of Chance. Cambridge: Cambridge University Press.
Mittag, D. M. “Evidentialism”. The
Internet Encyclopedia of Philosophy (internet resources).
Moore, G. E. 1953. “The Meaning of
Real”, in his Some Main Problems of Philosophy. London: George Allen
& Unwin.
Moore, G. E. 1939. “Proof of an External
World”. Proceedings of the British
Academy 25, pp. 273-300.
Nagel, Jennifer. 2014. Knowledge: A
Very Short Introduction. Oxford: Oxford University Press.
Nietzsche, Friedrich 2009 (1889). Twilight of the Idols: How to Philosophize with a Hammer. Oxford:
Oxford University Press.
Nozick, Robert 1981. Philosophical Explanations. Cambridge: Harvard University Press.
O’Connor, D. J. and Brian Carr. 1984. Introduction to the Theory of Knowledge
(Brighton, UK: The Harvester Press).
Pappineau, David. 2012. Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets.
Oxford: Oxford University Press.
Plato. 1997. Plato: Complete Works, ed. John M.
Cooper (Indianapolis, IN: Hackett Publishing).
Pollock, John L. 1987. Contemporary Theories of Knowledge. Lanham, MD: Rowman &
Littlefield.
Popper, Karl. 1994. The Myth of the Framework. London: Routledge.
Popper, Karl. 1974. Objective Knowledge. London: Oxford University Press.
Popper, Karl. 1963. Conjectures
and Refutations: The Growth of Scientific Knowledge. London: Routledge.
Putnam, Hilary. 1984. Reason, Truth, and History. Cambridge:
Cambridge University Press.
- 1975. ‘The Meaning of
‘Meaning’’, in Mind, Language, and
Reality. Cambridge: Cambridge University Press.
Quine, W. V. O. 1969. From
a Logical Point of View. 2nd
ed. Cambridge: Harvard University Press.
Radford, Collin. 1966. “Knowledge – by Examples”. Analysis
27, 1-11.
Russell, Bertrand. 2016 (1912). The Problems of
Philosophy. CreateSpace.
Russell, Bruce. 2017.
“A Priori Justification and Epistemology”. The
Stanford Encyclopedia of Philosophy, ed.
Edward N. Zalta.
Sacks, Oliver. 30 August 2010. “Prosopagnosia: The
Science Behind Face Blindness”. The New
Yorker.
Sosa, Ernest. 1980. “The Raft and the Pyramid:
Coherence versus Foundations in the Theory of Knowledge”. Midwest Studies in
Philosophy, 5, 3-26.
Shope, R. K. 1983. The
Analysis of Knowing: A Decade of Research. Princeton: Princeton University
Press.
Stanley, Jason. 2005. Knowledge
and Practical Interest, Oxford: Oxford University Press.
Strawson, P. F. 1974. Freedom
and Resentment and other Essays. London: Methuen.
Stroud, Barry. 1984. The
Significance of Philosophical Skepticism. Oxford: Oxford University Press.
Teichman, J., C. C. Evans.
1999. Philosophy: A Beginners Guide.
Oxford: Willey-Blackwell.
Shor, Eran, Simchai, Dalit. 2009. “Incest Avoidance,
the Incest Taboo, and Social Cohesion: Revisiting Westermark and the Case of
the Israeli Kibbutzim”. American
Journal of Sociology. 114 (6),
1803-1842.
Steup, M. Ernst Sosa. 2005. Contemporary Debates in Philosophy. Oxford: Willey Blackwell.
Williams, Michael. 2001. Problems of Knowledge: A
Critical Introduction to Epistemology. Oxford: Oxford University Press.
Williams,
Michael. 1999. Groundless Belief. Princeton: Princeton
University Press (first published 1977).
Williamson,
Timothy. 2005. Contextualism, Subject-sensitive Invariantism and Knowledge
of Knowledge.
Wuketits, Franz M. 2010. Evolutionary
Epistemology. Albany: State
University of New York Press.
Wittgenstein, Ludwig. 1984. Über Gewissheit (On Certainty)
Frankfurt: Suhrkamp.
Wittgenstein, Ludwig. 1984. Philosophische
Untersuchungen (Philosophical Investigations). Frankfurt: Suhrkamp.
Wittgenstein, Ludwig. 1958. The Blue and
the Brown Books. Oxford: Basil Blackwell.
Wittgenstein, Ludwig. 1984. Tractatus
Logico Philosophicus. Frankfurt: Suhrkamp.
[1] Hume used the word ‘object’; most authors
use the word ‘event’. I prefer to use the word ‘thing’ in a wide sense for
reasons that will be made clear later.
[2] By reasons of simplicity of exposition, I
am abbreviating what should be rather said: “The conjunctions of things found
in the past must be approximately like the conjunctions of things to be found
in the future”.
[3] For
reasons of simplicity of exposition, I am also using abbreviated language in
PU(ii) and PU(iii). What I mean is rather “The conjunctions of things in the
recent past must be like the conjunctions of things in the more recent past”
(PU(ii)), and “The conjunctions of things in a next location in space must be
like the conjunctions of things in the already known space” (PU(iii)).
[4] I always keep in mind a sufficiently
unified system of reference. I need to say this because relativity theory has
shown that present, past and future vary according to systems of reference
moving at great speeds in relation to each other.
[5] What we could do is to search for a still
more precise treatment. It seems plausible to think that the approximation of
future and past tends to have a form of two opposed exponential curves that touch
at the point called the present, etc.
[6] One could object that the principle of
verification was long since been debunked, first by the positivists of the
Vienna Circle and then by philosophers like W. V-O. Quine and even Saul Kripke.
One can, however, maintain Wittgenstein’s earlier suggestion that the
(cognitive) meaning of a statement is in some way given by the group of
procedures we use to verify it, some more central, others not. (For a detailed
rebuttal of straw man objections to semantic verificationism, see Costa 2018,
Ch. V.)
[7] In On Certainty Wittgenstein gives
several examples of how our imagination can betray us, making us see meaning
where there is none.
[9] Note that I cannot interpret 1 as “I know that
I have two adherently real hands”, since this cannot be true.
