UNSOLVABLE PROBLEMS AND PHILOSOPHICAL PROGRESS
American Philosophical Quarterly 19 (1982) 289–298
William J. Rapaport
Department of Computer Science and Engineering,
Department of Philosophy,
and Center for Cognitive Science
State University of New York at Buffalo
Buffalo, NY 14260
rapaport@cse.buffalo.edu
http://www.cse.buffalo.edu/∼rapaport
ERRATA
Missing epigraph, p. 289: Commitment is not an outcome, but a process. (Cited in Perry 1981b: 5.)
p. 289,
col. 1,
p. 291,
p. 294,
col. 1,
col. 1,
para. 2, L. –4:
L. –2:
L. –3:
L. 10:
L. –3:
L. 3:
p. 295,
col. 2,
para. 0, L. –2:
col. 2,
‘metaphyhsical’
‘psuedo-’
‘÷’
‘miles’
‘define’
‘ontoloico-’
‘coint’
‘superceded’
1
should be
should be
should be
should be
should be
should be
should be
should be
‘metaphysical’
‘pseudo-’
‘×’
‘feet’
‘defend’
‘ontologico-’
‘coin’
‘superseded’
American
Philosophical
19, Number
Volume
Quarterly
1982
4, October
Winning Entry in the 1982APQ Prize Essay Competition
I. UNSOLVABLE
PROBLEMS AND
PHILOSOPHICAL
PROGRESS
WILLIAM J. RAPAPORT
I. Problems
and Solutions
there unsolvable
problems?
Philosophy
as a field
sometimes been characterized
are
at
unsolvable
least, whose
problems
(or,
are
and this, in
unsolvable),
important problems
turn, has often been taken to mean that there can
in philosophy.
It might
indeed
be no progress
ARE
whose
ones, for surely all problems,
merely
purported
even pseudo-problems,
can have purported
solu?
tions. So: When
is a purported
solution a real or
correct
has
a set of purported solutions to a problem,
first eliminate the clearly wrong or irrele?
vant ones. But one must still find a way to choose
the correct one from the remainder. Consider
the
one must
of determining
the length of a side of a
square plot of land whose area is 4 square miles,
so that one might know how much fencing to pur?
chase. The following might be a set of purported
this if the only measure of progress in a field
(over a period of time) is the number of problems
I shall
that have been solved (during that period).
but
argue that there can be progress in philosophy,
problem
is an overly
answers:
mean
that such "success"
one?
Given
{5 feet, 2 feet, -2 feet). Now, as a simple
calculation
shows, 5 feet is wrong?mathematical?
is -2 feet wrong; but
ly wrong. So, for that matter
it is physically
wrong (indeed, physically nonsen?
so. Of course, itmight
sical), not mathematically
simplistic measure
of it.
Let us consider
kind of unsolvable
the problem of problems. One
problem would be unintelligi?
or otherwise
ill
ble, poorly
stated, nonsensical,
that it is even mathematically
formed ones; these would
be objected
be unsolvable
in the
wrong,
sense
assumes
was
that
not
that
it
the
lack
solutions.
Of
course,
//one
they
problem
simple
merely to
to *2 = 4, but rather to: *2 = 4
find the solution(s)
is not always a trivial matter to show that a given
is of this kind, as a consideration
we shall see, are
and x>0.
of the
Such assumptions,
problem
on
un
essential to identifying
attack
the apparent
solutions.
logical-positivist
of metaphyhsical
As another example, consider '42' as the answer2
reveals.
solvability
problems
to "the Ultimate
the unsolvability
of ill-formed
of Life, the Universe,
But, of course,
Question
as in Douglas
does not guarantee
and Everything,"
the solvability
of
Adams's
The
problems
ones.
well-formed
to the Galaxy
Hitch-Hiker's
Guide
(1979: 135).
Are there, then, intelligible,
of course, the humor of this answer lies in
clearly stated, sen? Now,
its very
its category
sible, or otherwise well-formed
problems
inappropriateness,
("real"
one might say, as opposed to "pseudo-"
But as Adams
mistakenness.
problems,
cleverly goes on to
that are unsolvable?
an
it
Some philosophers
be
may
problems)
observe,
only
apparent
inap?
for example)
have argued that
(Benson Mates,
there are, that "the traditional problems
of phil?
...
... ab?
are
but
osophy
intelligible
enough,
insoluble"
1981:
cf.
solutely
3;
(Mates
ix, x).1
Before
this position
of "solvability
examining
it will prove worthwhile
to consider
skepticism,"
the nature of solutions.
Just as we need to talk of real, not psuedo-,
so we must speak of real solutions, not
problems,
for it may well be the question
propriateness,
that's at fault. Perhaps some ill-formed problems
can be restated. But a restatement
(or questions)
should preserve
the intentions
of the original
x
"What
is
7?"
not be an
6
would
problem. Thus,
restatement
case.
in
this
appropriate
Nor, for that
matter should "What is 6 + 9?" be-yet
'42' is ac?
in the story as the answer
(Adams 1980: 184)! And itmakes
cepted
289
to that question
perfect sense (as
290
far as anything can)
i.e., both question
in the context of that story;
and
and answer ?problem
sense
//one accepts the assump?
the story. So, to object that a restated
isn't the original problem may be as un?
solution?make
tions of
AMERICAN PHILOSOPHICAL QUARTERLY
problem
fair as the attitude
of the child who wants
to know
the largest number is and whose father says
he can't answer that because there is no largest: the
but still want to know the
child may acquiesce
what
answer
to the original
can lead
persistence
of
discovery
arithmetic?but
question.
(Of course, such
to new insights ?e.g.,
the
or
transfinite
of modular
such an insight is probably not an
answer
intended
to
the
question
as
originally
stated.)
II. The Solvability
On
to have
Skeptic
'sArgument
the surface,
appears
solvability
skepticism
a point. (A student once told me that he
did was to give
philosophers
the
to unanswerao/e
Surely,
questions.)
Free Will problem does not seem to have a solu?
or even scien?
tion the way,
say, mathematical,
thought
answers
that what
tific,
problems
and
mathematical
Even
do.
as-yet-unsolved
have solu?
problems
we
we
haven't found
like to believe: while
tions,
them yet, we believe that (with a few exceptions)
we will find them, given enough time and more
evidence.
The exceptions,
though, are not insignificant.
Perhaps
we will
scientific
never
know
the solutions
to the
problems of the origin of life or of what happened
before the Big Bang, simply because the necessary
One tends to feel,
evidence has been destroyed.
however,
tion?that
that
that
a practical
limita?
are not unsolvable
in
is merely
such problems
a well-formed
problem would be un?
Roughly,
for solving it
if the procedure
solvable in practice
a virtually
what
called
be
either
might
(a)
requires
amount
of
resources
space,
(time,
requiring 10100 seconds to
(b) information which once was but
perform?or
an irretrievably
lost
is no longer available?e.g.,
etc.) ?e.g.,
a calculation
?or
(c) information which is exceeding?
to obtain?e.g.,
the exact
(impractical)
ly difficult
time at which
I began writing
this sentence. That
but we cannot
have
such
solutions,
is,
problems
reasons as these.
know them, for such practical
a well-formed
And,
roughly,
problem would
in principle
if there is no solution
unsolvable
be
for
us to know.
Are
there,
are unsolvable
which
then, well-formed
problems
in principle? Well, perhaps the Big
is unsolvable
in principle,
but that
Bang problem
that it can well serve as an exam?
issue is so muddy
In
of unsolvable
problem.
ones
do exist, notably in logic
principle unsolvable
the problem of whether
the con?
and mathematics:
ple
of
both
kinds
But
tinuum
is true, for instance.
hypothesis
so
that
that
mathematicians
say
stated,
problem,
Is
is ill-formed. Restated,
becomes:
the problem
or
the continuum
hypothesis
logically implied by,
with, the axioms of (say) ZF set
answer is: Neither.4
the
And
theory?
we
But
can't come up with even an
philosophers
is it inconsistent
to the Free Will
solution
analogous
problem, et al.
do seem to be
in general,
Philosophical
problems,
of unsolvable
while mathe?
problems,
paradigms
are
as para?
in
taken
matical
general,
problems,
ones.
digms of solvable
that there is no
This is not to say, of course,
to the Free Will problem.
On the con?
solution
solutions. Why
trary, there are lots of (purported)
seem to accept (correct) solutions
does everybody
but not everybody
to mathematical
problems,
agrees on a correct solution to the Free Will prob?
lem? The solvability
skeptic's point, roughly put,
to philosophical
is that there are no solutions
problems
solutions:
What
principle.3
infinite
document
because
makes
there are no generally
... the
philosophical
accepted
problems
so
in?
teresting, and what keeps them going, is the fact that,
although each possible point of contact [i.e., defini?
tion
of
a term,
meaning
and
truth-value
of
a premise,
step in an argument, etc.] is identified by somebody as
the source of the difficulty, each is also exonerated by
the great majority; and consequently no purported
solution
ever
comes
(Mates 1981: 5.)
close
to
general
acceptance.
UNSOLVABLE PROBLEMS AND PHILOSOPHICAL PROGRESS 291
is not a sufficient
But being generally accepted
solution to count as a
for a purported
condition
a proposition
may be generally
as
true
and
being the solution
accepted
it is either
even though (unknown to the accepters)
Nor
is general
false or true-but-not-the-solution.
correct
solution:
as being
can be true,
a proposition
necessary:
acceptance
or a purported
solution correct, even if it is not
of mis- or
perhaps because
accepted,
generally
(or any number of other acciden?
pre-conceptions
The history of science is largely
tal circumstances).
the story of such cases: Newtonian
physics may
serve as an example of the former; the case of
in geology as an ex?
and plate tectonics
Wegener
ample of the latter.
That there are lots of
sources
in
of difficulty
solution
purported
agreeing to accept a particular
to
as the solution?lots
of options
and choices
and
make
about
terms,
logical
premises,
to (or
the commitment
that
steps ?suggests
acceptance
of) a
choices one makes
solution
depends
the options
among
"points of contact."
by the various
The stucture of Mates's
upon
the
presented
of the skeptical
solu?
is to show that for each purported
argument
there are some
tion to a philosophical
problem,
we just don't want to make or prin?
assumptions
ciples we don't want
purported
definition,
accepted,
solvable.
version
to give up ?that
to accept any
solution,
(a
unacceptable
something
a premise, etc.) would also have to be
is un?
the problem
yet isn't. Hence,
mean
in
But surely this must
unsolvable
not unsolvable
in principle;
and not
practice,
but because
because of any lack of information,
of a lack of general acceptability.
is an
Yet, as we have just seen, acceptability
true
criterion
of
solutionhood,
being
unacceptable
nor sufficient
It is
neither necessary
therefor.
possible
perhaps,
Let me
to get a solution,
though at the price,
a
of
cherished belief. But so what?
illustrate my analysis of the solvability
a brief con?
with
argument-structure
skeptic's
sideration of purported
solutions to the Free Will
I wish to define a certain
In so doing,
problem.
thesis,
tion:
to which
the following
is a first approxima?
Any purported solution, S, to a problem, P, is really
the consequent of an implicit conditional solution,
A-+S, where A is a conjunction of principles which,
once
accepted,
make
S a correct
solution
to P.
un?
an in-principle
to this thesis,
According
there
solvable problem would be one for which
were no principles, A, which allowed or entailed a
solution.
Following Mates's analysis, there are four possi?
to the usual statement of the
ble opening moves
of
the notion
Free Will
(1) Replace
problem:
or
causation by that of a functional
relationship,
else (2) deny the principle of universal causation,
or
else
that
(3) claim
statistically
events are
or
true,
less caused
is only
principle
that
claim
mental
(4)
ones. And
than physical
the
else
that (l)-(4) in?
objections:
distinctions
(b) untenable
or
to explain
fail
that
events,
among
(l)-(4)
(c)
are
some
free
human
actions
(Mates
why only
there are three possible
(a) ad hoc or
volve
1981: 600
a
can always
be met:
objections
the back?
distinction
is ad hoc (a) only against
a
if
ad hoc
of
theory;
apparently
given
ground
But
such
can be made to work elsewhere,
they
to be (merely) ad hoc. There is no a priori
reason why the distinctions made
in (l)-(4) could
to work elsewhere,
not be made
though at the
distinctions
cease
doubt too great?of
other
reshuffling
price?no
well-established
categories.
distinctions
refer to
"Untenable"
(b) could
a
incorrect
solution
mak?
ones;
merely
purported
a
distinction
be
such
wrong,
might
simply
ing
But
'untenable'
incorrect
really means:
our
we
are
theory; if
willing to
against
background
pay the price of giving up our background
theory,
we can make the distinctions
tenable.
period.
if the explanatory
insight or ingenuity,
And
of
failure
failure
then
(c) is due to lack
it is a contingent
If it is a necessary
and possibly reparable.
failure, then the solution is either wrong or?more
is only relatively
failure
necessary:
likely?the
relative to a background
theory which could be
given up, at a price.
Such replies take the form of further premises
or assumptions
(which the skeptic rejects) having
292
AMERICAN PHILOSOPHICAL QUARTERLY
features:
the following
(I) They "straighten out"
thus fitting the solution
the knot of the problem,
in with (some) background
theory; and (II) they
the
become
skeptic's next objec?
to a different
is moved
loca?
for
focus
the knot
tion?i.e.,
tion, but
that a knot which
to a different
point on an open
keeps moving
ended (or infinite)
string eventually
disappears;
can
the
i.e., enough premises
replace (become)
a
To
continue
the metaphor,
theory.
background
if it could not
problem would be truly unsolvable
be unknotted;
but (A) the skeptical
argument
doesn't show that, and (B) such a situation is very
and the problem
ill-formed.
likely inconsistent,
we
should
be
for
the
that
(But
prepared
possibility
even the ultimate (Peircean) complete theory is in?
be a
may
inconsistency
have to accept in order to gain
that
consistent,
i.e.,
premise we would
at all.)
solutions
III. Solvability
structure
of the dialectic
fault with all pur?
finding
But
the
solution
ported
solutions.)
purported
if these further principles were ac?
would work
universal
objector,
that
solution
claim
proposers
Indeed,
cepted.
these principles must be accepted because they ac?
solution.5
cept the proposed
The thesis of the last section
more
it is not merely
but that
conditional,
general:
always
which "grow" background
Any purported
part
of
a
theory,
can now be made
that solutions
they
theories:
are
solution, 5, to a problem, P,
among
Are
whose
other
there
no
solutions
simpliciter,
uncondi?
tional
solu?
solutions, non-theory-laden
solutions,
tions without
As the skeptic might
commitments?
Arche
put it, are there any solvable problems?
as
we've
mathematical
and
noted,
typically,
(to a
are solvable.
lesser degree) scientific problems
In?
Mates
discusses
Zeno's
deed,
(1981: 7f)
paradoxes
as paradigms
of solvable problems
because
they
have a unique "locus": a "point of contact" which
a generally
enables
solution
accepted
to come
forth.
is there a locus in Zeno's
case? There
is,
a
a
locus
solution
that does min?
perhaps,
enabling
imal damage to (and coheres well with) our world
not necessarily
view. But notice: our world-view,
But
Zeno's!
If this
between
can be
solvable
seen
is paradigmatic
and unsolvable
the
that
of
difference
the difference
then it
problems,
concerns
the
of the purported
solution and its atten?
dant commitments
with our (current) world-view.
That is, the structure of the problem/solution
dialectic
is the same both for so-called
solvable
coherence
vs. Unsolvability
is always this: A
is posed, and a purported
is of?
solution
problem
solution comes with strings
fered; the purported
or implications which an ob?
attached?premises
jector rejects. (The solvability
skeptic is simply the
The
the problem,
e.g.,
which
has
the
theory
entire
problem.6
the
it's still there. Note
to "dissolve"
may be necessary
to give up the
parts
are
(e.g., mathematical
unsolvable
(e.g.,
or scientific)
and for so-called
All
philosophical)
problems:
are
solutions
conditional
upon certain premises.
The solutions of so-called solvable problems have
are
further commitments
which
(e.g., axioms)
more
acceptable
(more coherent with our other
than those of philosophical
commitments)
prob?
But even they
lems; that's the only real difference.
don't have to be accepted;
in fact, the more
in mathematics
and the
philosophical
problems
sciences are usually unsolved precisely because of
over assumptions.
disagreement
"seeds"
IV.
is really
are
Epistemological
the
background principles entailing 5 and the further
principles (or commitments) entailed by 5.
un?
to this thesis, then, an in-principle
According
no
solvable
would
be one for which
problem
this is the case, it
theory contains a solution. When
Intellectual
Development
and
Progress
A.
Perry's Theory.
The hardened skeptic may
as support for his position:
saying
take these observations
after all, haven't
solutions
that there are no absolute
I been
to any
UNSOLVABLE PROBLEMS AND PHILOSOPHICAL PROGRESS 293
I think we may get a clearer picture of
problems?
the solvability
skeptic's place in the epistemol
to
ogical scheme of things if we turn for a moment
a striking parallel offered by William
G. Perry's
theories about college students' attitudes towards
knowledge.7
form?
Perry describes a sequence of "positions"
a
"scheme of cognitive
and ethical develop?
ing
ment" that college students progress through. You
will
see how appropriate
also
appropriate
larger scale.
Position
and,
1 is Basic
it is for them; I think it is
on a
at least, illuminating
Duality:
There
are
answers
to all questions,
engraved in tablets
sky, to which the teacher has access, and to which,
through hard work, we (the students) will, too.
(Cf. Plato,
Position
perhaps.)
results when we realize
2, Dualism,
authorities
teachers,
(notably English
will do nicely) disagree on cor?
but philosophers
rect answers,
while
others
and
(mathematics
that
some
the former must
teachers) agree. Hence,
their vi?
clouds over their heads, obscuring
sion of the tablets. But all is known; we just have
to follow the right authorities.
science
have
we take the
In Position
3, Early Multiplicity,
view that only most knowledge
is known, but all is
knowa?te.
The answers are there, but we haven't
found them all yet. (Positions 2 and 3, by the way,
are said to be the positions
of most
college
freshmen.)
In Position
4 (4a, in Perry 1981a), Late Multi?
it is felt that "Where Authorities
don't
plicity,
know the Right Answers,
everyone has a right to
his own opinion; no one is wrong" (Perry 1981a:
79). "In some areas we
knowedge
[e.g.,
mathematics].
we really don't
[e.g., philosophy]
for sure" (Cornfield
The
which
holds
still have
certainty
In most
about
areas
know
anything
and Knefelkamp,
1979).
next
Contextual
position,
Relativism,
is viewed as a more
"mature" position,
that uAll knowledge
is disconnected
from
any concept of Absolute
Truth," though there are
of adequacy" ?that
standards?"rules
theories
must adhere to (Cornfeld and Knefelkamp
1979;
my emphasis).
"mature"
positions,
we
in which the
Position
6, Commitment
Foreseen,
seeker of knowledge
realizes that he must make
some commitments
among
theories;
competing
in Position
this is accomplished
ment;
Position
7, Initial Commit?
in Implications
of Com?
8, Orientation
in which one balances
the several com?
mitment,
mitments
in 6 and 7; and
made
in
9, Developing
Commitment(s),
it is seen that one must retrace "this whole
Position
which
right
in the
to the most
Progressing
next find:
journey over and over" (Perry 1970, 1981a).
There are, in addition,
three paths of "deflec?
tend to occur before
tions from growth," which
5 or 6, of which
Position
only one need concern
us
here:
Alienation,
"Escape.
sibility.
Relativism
Exploitation
for avoidance
abandonment
of
of
Multiplicity
of Commitment"
respon?
and
(Perry
1981a: 80, 90).8
B. The Skeptic's Position.
to Mates,
"traditional
According
...
skepticism
held that we can only know how things seem to be;
of how things really are is impossi?
knowledge
the skeptic considers
ble.... Hence
that the right
attitude
nature
towards
of
the true
questions
concerning
of judgment...."
is suspension
things
(Mates 1981: ix). This is somewhere around Posi?
tion 4, but it is also a form of Escape. According
to the Perry scheme, a more "mature" Position
would hold that all we can know is how things
to certain
would be were we to commit ourselves
assumptions,
theory-relative
Solvability
of
problems
i.e., to hold to a conditional
view of solutions to problems.
or
"doubts that [the major
... are solvable or even
[philosophy]
and ... it argues that the reasons giv?
skepticism
'dissolvable';
en on both sides of the issues are equally good
(Mates 1981: ix). This is more than suspension
..."
of
a
it is clearly to refrain from making
judgment;
For if 'judgment' is to be understood
commitment.
as elliptical
for "rational judgment,"
then surely
one could suspend that, yet make a commitment
nonetheless.
If, indeed,
the "reasons
... on both
AMERICAN PHILOSOPHICAL QUARTERLY
294
... are equally good," then it doesn't seem ir? distinction,
if any, is that the assumptions
in the
case are (almost)
ac?
in such a case on
mathematical
rational to make a commitment
universally
case.
the basis of, say, the toss of a coint or ontoloico
cepted, unlike the philosophical
no dif?
are there: At the very least,
If it really makes
But the assumptions
aesthetic
preferences.
= 5' is true
we
one
+
'2
2
could
that
solution and attendant
ference which
say
theory
//one assumed
sides
to ?because
each solution is ac?
ourselves
a
and
consistent
by
complete
(or, at
companied
worst, equally incomplete and inconsistent) world
commit
view?then
matter
it shouldn't
what
of
method
choice we use.
claim that the skeptical position
is Perry
Position
4a. At best, it is 5; more
likely, it is an
4; cf.
Escape
(which happens at around Position
the chart in Perry 1970). The skeptic is correct to a
point: there are no right answers. There are only
to some of which,
relative
ones,
(conditional)
we
should
commit
ourselves, moving
eventually,
to Position
6, and beyond.
one: there
then, is an anti-skeptical
but they are all theory-laden,
hence
And this is not Position 4, because
theory-relative.
I also claim that we must
to
commit ourselves
My thesis,
are solutions,
some
theory (thus siding with James's Will to Be?
lieve, rather than Clifford's
duty to suspend judg?
ment).9
a philosopher
be thus commited? After all,
all
is it not the philosopher's
duty to question
It
all
would
commitments?
examine
assumptions,
that we are stuck at Position
appear
4, at
Can
But
Philo?
can
which
be
9,
really
a
we
can
For
for
false multiplicity.
mistaken
(in?
while remain?
deed, must) question
assumptions,
to them (at least pro temp?re), as in
ing committed
Neurath's
deceive:
boat metaphor.
V.
Let
appearances
dit Position
Problems,
us
return
and
ments
to (or assumptions
or
properties,
to
distinction
the
the nature
about)
negation,
of ob?
etc. ?witness
the
1978:
Russell-Meinong
(cf. Rapaport
disputes
is that
165f). But perhaps of most
significance
are
theorems
in
conditional
virtually
always
form ?a particular
to a problem)
claim (solution
is true under
certain
"unconditional"
axioms
And
and
axioms
the nature
of
the underlying
logic.
upon philosophical
the nature of mathematical
ob?
are conditional
about
assumptions
Even apparently
conditional
upon
conditions.
are
theorems
jects.
claim parity be?
(On the other side, one might
on
tween mathematics
and philosophy
the
are
that
there
that
truths
grounds
philosophical
are assumption-free:
such first-person
observation
reports as "it seems to me that I am now experienc?
ing red," say; but surely this claim is laden with
theories about experiences,
colors, the nature of
"seeming," etc.)
in mathematics
There are, of course, problems
which
lack solutions because of a lack of agree?
ment on assumptions
these are
(though, arguably,
problems
in the more
philosophical
The difference
between
ematics).
of problems
areas of math?
these two kinds
may be described by adapting
of Kuhn's
distinction
between
solutions;
the ter?
"prob?
Ch.
have
Puzzles
(1962,
IV).
have
lots
of
problems
possible,
solutions.
(un-)acceptable,
purported
are, roughly, what problems become when
they are treated within a given "paradigm"; other?
wise they are alike, for researchers within a given
equally
Puzzles
between
wherein
the former
and mathematics,
philosophy
the
is viewed as presenting
unsolvable
problems,
am
a
ones.
is
I
solvable
This,
latter,
suggesting,
and mathe?
false dichotomy;
both philosophical
but they are all
matical
have solutions,
problems
conditional
example
formulation
(unique)
Paradigms
does. A better
of Non-Contradiction,
any
of which
involves one in commit?
minology
lems" and "puzzles"
Puzzles,
'4' ordinarily
what
is "the" Law
jects,
Iwould
Multiplicity.
sophers are
that '5' denoted
theory-relative
solutions.
The
have agreed to accept the assumptions
paradigm
to have a solu?
which allow the erstwhile problem
Puzzles play the role in "normal"
tion simpliciter.
science
science.
that
problems
do
in
"revolutionary"
UNSOLVABLE PROBLEMS AND PHILOSOPHICAL PROGRESS 295
of all those premises
the conjunction
Thus,
to become
whose
acceptance
permits problems
whose
acceptance
prob?
permits
(i.e.,
puzzles
have solu?
I used the term earlier ?to
lems?as
activity consists in the develop?
Sym-philosophical
ment
of philosophical
theories,
i.e., systematic
hypotheses about the general structure of the world
of
and
The
experience....
ultimate
com?
is the
aim
tions)
theories in order to
parative study of maximal
establish, through isomorphisms among them, a
orientation.
establishment of such isomorphisms and invariences
is dia-philosophy.
(1980: 14f.)
is the fundamental
axioms, as it were, of a
or
of
the
theory "grown" by the solu?
paradigm
tion?what
Rescher
(1978) calls a methodological
Rescher's
Indeed,
philosophical
ment about
analysis
disagreement
the conditional
and my Perrian
of
the structure
of
is in substantial
structure
agree?
of solutions
analysis:
A philosophical position thus always has the implicit
conditional form: given a certain set of commitments
regarding the relevant cognitive values, such and such
a position on the question at issue is the appropriate
one. (Rescher 1978: 229.)
[A] locally optimal (or adequate)
for
those
to
committed
a
certain
solution...is
cogent
probative-value
orientation. And given that...[this is the] perspective
[which] is apposite, it follows that such "demonstra?
tions" as there are in philosophy...[i]n
effect take the
form: IF you are prepared tomake certain procedural
commitments..., THEN you will arive at a particular
solution. A rational constraint is clearly at issue here,
rather
but it is basis-relative (or orientation-relative),
than absolute. Yet it is not a matter of "anything
(Rescher
goes...."
1978:
232f.)
Since "All that one can do in philosophy,"
or, I
would add, in any field, "is to view the issues from
one or another of a limited number of 'available'
of
system
that entail the solu?
assumptions
And this is impossible,
for there is
to know that we have considered
every
question-begging
tion simpliciter.
no way
to problems.
more
developed
solutions
all
be
Varying
or less
"Carnapian principle of tolerance: Let everybody
in the system of his choice" must
work
be
turns
that is, "dia-philosophy
to
be
feasible"
out, empirically,
(1980: 21).
It is thus feasible, in a simple fashion, as soon as
"if,"
superceded,
there are a finite number
theories.
But
of completed
if one wants
(or nearly
complete
results, then the reasons I have
dia-philosophical
given for the skeptic's failure to show that philo?
are unsolvable?and
hence to
sophical problems
completed)
show
that there cannot
also
theory?are
complete
be even one philosophical
for thinking
that such
reasons
dia-philosophical
results
cannot
be
forthcoming.
VI.
On Progress
in Philosophy
to my discus?
is a potential
objection
I have missed
the solvability
skeptic's
the thesis ismerely
that there are
point. Possibly,
philosophical
problems which don't, or will never,
There
sion?that
accepted solutions, with no fur?
about unsolva?/7/Yy
intended.
ill
does
bode
for
this
the hopes of "success"
admit of generally
ther implications
Casta?eda's
tinctions
According
the
to major
each
simultaneously,
susceptible
And he
criticism only when completed
20).
(1980:
as
view
with
the
Perrian
he
calls
agrees
it, the
that,
Surely
or progress
to Casta?eda,
and
comparisons
sees the task of philosophy
theories which,
then, can yield
theory-relative
theories must
or set of assumptions.10
orientation,
paradigm,
This suggests, by the way, that there might be
some
a priori
on Hector-Neri
limitations
It sug?
program of "dia-philosophy":
not
but
entail
does
this
because
his
gests
program
does not assume that all theories be considered.
Such
also
Thus, Casta?eda
as constructing
orientations"
methodological
(Rescher 1978: 232),
it follows
that truly to defend
solvability
skep?
ticism, one would have to show that within each
the issue at hand has
orientation,
methodological
no resolution?i.e.,
each paradigm,
that within
the puzzle
is unsolvable,
that there are no non
invariences.
But
Mates's
ix-x);
in philosophy,
and supports the dis?
between
and mathematics.
philosophy
this thesis is not as astounding
as, e.g.,
claims
and
about
"don't"
absolute
insolubility
seems too parochial,
(1981:
while
AMERICAN PHILOSOPHICAL QUARTERLY
296
too pessimistic,
though closer to
not
"there
does
appear to have
position:
one iota of progress
toward a generally ac?
is surely
"never"
Mates's
been
solution"
of any major
philosophical
1981:
7).
(Mates
problem
If so, why
Can there be progress in philosophy?
ceptable
not appear
and science
does philosophy
do mathematics
to progress,
appear to?
and why
etc., by another. Science, though,
paradigm,
to be more
than philosophy,
revolutionary
lending support to the belief that science
doesn't.
philosophy
at its lower levels,
Mathematics,
Position-2
discipline?its
"puzzles"?because
at the higher
pore
tends
thus
"pro?
is a Perry
are really all
"problems"
the assumptions
pro tem
levels. Thus, all solutions are
of
or theory-relative
at the lower
to
not
do
be:
appear
they
really
conditional
level,
though
[G]iven the lengths of the sides of a rectangle, how
one
does
find
its area?
A...better
is, does
problem
every plane rectangle have associated with it a
numerical quantity which can meaningfully be called
an
area?...[T]he
problem
previous
cannot
be
solved
unless the answer to this one is yes. Yet very little em?
is put
phasis
mathematics.
granted....
this
last question
upon
seems obvious:
Its answer
[M]athematicians
have
in elementary
it is taken
for
become
extremely
wary of taking anything at all for granted. Accepting
something as 'obviously true* has led them astray too
often. (Ogilvy 1972: 5.)
At
its higher
levels,
as philosophy:
mathematics
is as
"open
happens when
makes a great advance, new insights
mathematics
are achieved
regarding concepts which had long
been taken for granted" (Wilder 1973: 175).
On the other hand, philosophy,
by its self
ended"
"As usually
is
nature,
constantly
questioning
seem
at
makes
it
its
This
levels.
all
"open-ended"
as if philosophy
cannot progress because all at?
but
blocked;
tempts at progress are immediately
of "doing philosophy" ?of
the process
constantly
conscious,
challenging
of progress.
the very essence
and questioning?is
there being pro
of
the
illusion
Thus,
in mathematics
is due both
philosophy
nature of mathematics
while
there
to a too-narrow
is none
in
view of the
and to the refusal
to con?
sider progress as other than "success."
in philosophy,
There can be (and is) progress
the ap?
for the central stumbling
block?viz.,
of philosophical
parent
unsolvability
prob?
lems?
There is a simple reason in the case of science.
to which
There is a sense of "progress" according
to replace one
to be "progress"
it is viewed
gresses" while
gress
is illusory.
non-negative,
sort
Surely,
of
there can be a trivial, or
an
progress:
out-and-out
er?
ror can be found
in someone's
theory, or one can
one's own earlier writings.
(Of course, the
In a more
earlier work might have been better!)
correct
whenever
sense, philosophy
progresses
anyone builds upon or extends one's own work or
turn
the work of others. True, this may ultimately
out to have been a wild-goose
but
until
that
chase,
positive
is known,
it counts as progress:
"the philosopher
to
who refines the Kantian
imperative contributes
to
if
that
of
the
that
shares
group
progress,
only
his premises" (Kuhn 1962: 161). And even if it has
been a wild-goose
chase, there may have been pro?
senses
in
that we understand
the
the problem
gress
better and that we may have gotten interesting
from our study of it.
useful by-products
and
there is progress even if the only sense
Finally,
in which we understand
the problem better is the
we
one
know what won't work;11
that
important
was
for
learned about Hilbert's
consider what
inmathematics
from G?dePs
in?
program
there
is progress
theorem.
But
if we learn as a result what premises we
especially
have to accept if we want a solution.12
malistic
completeness
For
would
to know what won't work
work
// we were willing
whose
is to know what
to accept those
a solution.
forestalls
principles
rejection
to be
such principles
allows problems
Accepting
to
the number of solutions
solved (thus allowing
of progress).
be a measure
must be for us
what our commitments
Knowing
for philosophy
to have solutions
is progress,
is
con?
are
in
the
that
its
solvable
such
only
problems
or theory-relative
sense, not in any ab?
sense. But philosophy
is not alone in this; in
science,
any discipline where there is progress?in
as well as in philosophy?solu
in mathematics,
ditional
solute
UNSOLVABLE PROBLEMS AND PHILOSOPHICAL PROGRESS 297
and so all "progress" in
tions are theory-relative,
the same way, namely, within the framework of a
of New
State University
at Fredonia
York, College
or
a paradigm,
orientation,
set of commitments.13
methodological
held
commonly
Received
a
27,1982
January
NOTES
1. I shall not distinguish
articles:
"insoluble,"
between
"unsolvable"
and "insoluble,"
though
and Fowler
1965: 272f,
"unsolvable;"
"insolvable,"
a useful
possibly
distinction
be made.
could
(on "in- and un-,"
666
and
p. 273;
esp.
Cf.
the OED
"unsolvable,"
resp.).
2. Nor
I distinguish
shall
distinctions
teresting
assume
that
some
4. Alternatively,
1981: 470):
solutions
5. As Wesley
"mathematical
Salmon
have
problems
it, one man's MT
has put
and
problems
questions
cf. Ogilvy
one
(inducing
see Stent
problem,
ther principles
feature
of
the theory
not of itself
Casta?eda
answers,
on
depending
or background
by assumptions
any other
it would
hence,
of predication
the model
(MacLane
of eliminating
the apparent
in?
correspond
or in conjunction
with
fur?
open
separately
to
sentences
such principle
could solve the problem.
In this case, the
that there are two (distinct) modes
of predication
which are such that a
in two
object
(Meinongian)
do not permit
cf. the two modes
for set theory"
used
that no
be to give up the theory
which
answers)
theory.
by this one either
entailed
suppose
the principles
of a single
and
solutions
in?
I shall
man's MPonens.
principles
But
theory.
by rejecting
lead to inconsistency;
itself,
the predication
of predication
This
ways.
(distinct)
the theory?the
to a given
property
and?along
of a given
discussed
in Dicker
to the more
accessible
be to give up an essential
would
with
1981 or, more
problem
it spawned.
item in both ways
does
in
those discussed
relevantly,
1972.
7. The
locus
classicus
is Perry
1970, but
I shall
refer mainly
versions
in Perry
1981a and Cornfeld
and
1979.
Knefelkamp
are also Transitions
8. There
Randall
if there were
10. Even
11. As Morton
between
out
pointed
Dipert
tent orientations,
12. To
and,
two modes
(There being
9. As
the revised Meinongian
can be predicated
property
with
together
be "dissolved"
could
problem
single
of
1981),
there are
3, 5), but
1981: 36.
the revised Meinongian
1978 appears
to be inconsistent.
The problem
theory of Rapaport
can
a
to
solved
not
be
the
effect
that
all
well-formed
consistency
(I believe)
by adopting
principle
(cf. Rapaport
1972:
between
6. E.g.,
properties
no doubt,
Here,
"question."
"question";
purpose.
different
is another
and
than a mere
rather
the former
or are determined
upon
depend
of
the unsolvability
or "problem"
"answer"
for the present
unimportant
twist on
interesting
and
project,"
between
correspondence
these distinctions
an
3. For
"solution"
as "research
"problem"
is a natural
there
makes
which
either
between
(e.g.,
some way
paraphrase
to ensure
has often
the famous
while
which,
that all theories
or assumptions
paradigms,
Schagrin
the Positions,
to the scheme,
essential
I have
omitted
for ease of exposition.
to me.
out
pointed
financier's
had been
classical
?plus
itmight
considered,
still be impossible
if one accepts
inconsis?
logic!
to me.
"Do you
question,
sincerely
want
to be rich?", we may
ask: Do
you
want
sincerely
solution?
13. The
idea for this paper
Component
ment
Staff
neth Lucey,
of General-Liberal
Symposium
arose
from discussions
Education"
in December
Tibor Machan,
David
during my
(Summer
1981; I am grateful
Palmer,
to Carol
and Morton
in an NEH
participation
1981). An
Schagrin
draft was
earlier
Brownson,
Randall
Pilot Grant
presented
Dipert,
Stephen
for their comments.
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