Prev: [Port%d] \\.\HCD%d
Next: On The Question of Absolute Undecidability
From: cplxphil on 21 Oct 2009 19:44
On Oct 21, 7:32 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote:
> On Oct 21, 8:34 am, Future_News <future_n...(a)brew-master.com> wrote:
>
>
>
>
>
> > What does the statement `P=NP' mean? A good way to understand it is to
> > look at an illustrative example. Suppose I secretly choose two prime
> > numbers p and q, tell you their product n=pq and ask you to tell me
> > what p and q are. In principle you can work this out, since by the
> > fundamental theorem of arithmetic p and q are uniquely determined.
> > However, in practice it is not easy to come up with a systematic way
> > of finding them other than to look at all primes up to n1/2 and see
> > whether they are factors of n. If n has 500 digits, this takes much
> > too long to be feasible on even the fastest computers, and this
> > difficulty is the basis of much of modern cryptography. Actually, more
> > efficient methods have been discovered than straightforward trial and
> > error, but, even after decades of intensive research, it is still out
> > of the question to factorize a 500-digit number. At the end of the
> > last century there was a great deal of excitement when Peter Shor
> > discovered that quantum computers could factorize large numbers far
> > more efficiently, but, despite several well-publicized announcements
> > to the contrary, nobody has managed to build such a computer.
>
> I have an issue with the number encoding schema. Somewhere in the
> introduction section Gary-Johnston textbook describes how numbers are
> encoded in the computer and asserts that exponential notation
> (regardless of base) is the most natural way to go. Objection, your
> honor! There is no genuine mathematical reason why to exclude unary
> number system.
>
> Factorization problem is not hard in unary system. Any other NP-
> complete problem that doesn't depend on number encoding? Let's try the
> subset sum problem. On the first sight, the subset property looks hard
> to check by the virtue of the fact that we have to analyze the
> powerset which size is exponential (in any number encoding schema).
> Let's look into the problem little closer. Consider the following
> naive algorithm where we keep track of all the sums, and when adding a
> number to the list we just go through the list and add the number to
> each element. The list would double at each step,- you may say. Not
> really. In unary number system there is just not enough room: one has
> to have big numbers in order to accommodate all possibilities. So the
> subset sum problem appears to be of cubic complexity in unary number
> system.
>
> So my question is: are there any genuinely "hard" problems that don't
> depend on (rather arbitrary) choice of number system?

I'm fairly certain that any NP-complete problem can be solved in
polynomial time if you encode in unary.

Unfortunately, the P vs. NP problem requires that we encode in an
alphabet with at least two elements; this is simply the definition of
the problem. See the first page of http://claymath.org/millennium/P_vs_NP/pvsnp.pdf
if you do not believe me.

Also, I'm curious...is Future_News Musatov? A Google search revealed
that this text is from another website: http://www.dpmms.cam.ac.uk/~wtg10/future.news2.html

-Phil
From: Tegiri Nenashi on 21 Oct 2009 19:50
On Oct 21, 3:44 pm, cplxphil <cplxp...(a)gmail.com> wrote:
> On Oct 21, 7:32 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote:
>
>
>
> > On Oct 21, 8:34 am, Future_News <future_n...(a)brew-master.com> wrote:
>
> > > What does the statement `P=NP' mean? A good way to understand it is to
> > > look at an illustrative example. Suppose I secretly choose two prime
> > > numbers p and q, tell you their product n=pq and ask you to tell me
> > > what p and q are. In principle you can work this out, since by the
> > > fundamental theorem of arithmetic p and q are uniquely determined.
> > > However, in practice it is not easy to come up with a systematic way
> > > of finding them other than to look at all primes up to n1/2 and see
> > > whether they are factors of n. If n has 500 digits, this takes much
> > > too long to be feasible on even the fastest computers, and this
> > > difficulty is the basis of much of modern cryptography. Actually, more
> > > efficient methods have been discovered than straightforward trial and
> > > error, but, even after decades of intensive research, it is still out
> > > of the question to factorize a 500-digit number. At the end of the
> > > last century there was a great deal of excitement when Peter Shor
> > > discovered that quantum computers could factorize large numbers far
> > > more efficiently, but, despite several well-publicized announcements
> > > to the contrary, nobody has managed to build such a computer.
>
> > I have an issue with the number encoding schema. Somewhere in the
> > introduction section Gary-Johnston textbook describes how numbers are
> > encoded in the computer and asserts that exponential notation
> > (regardless of base) is the most natural way to go. Objection, your
> > honor! There is no genuine mathematical reason why to exclude unary
> > number system.
>
> > Factorization problem is not hard in unary system. Any other NP-
> > complete problem that doesn't depend on number encoding? Let's try the
> > subset sum problem. On the first sight, the subset property looks hard
> > to check by the virtue of the fact that we have to analyze the
> > powerset which size is exponential (in any number encoding schema).
> > Let's look into the problem little closer. Consider the following
> > naive algorithm where we keep track of all the sums, and when adding a
> > number to the list we just go through the list and add the number to
> > each element. The list would double at each step,- you may say. Not
> > really. In unary number system there is just not enough room: one has
> > to have big numbers in order to accommodate all possibilities. So the
> > subset sum problem appears to be of cubic complexity in unary number
> > system.
>
> > So my question is: are there any genuinely "hard" problems that don't
> > depend on (rather arbitrary) choice of number system?
>
> I'm fairly certain that any NP-complete problem can be solved in
> polynomial time if you encode in unary.
>
> Unfortunately, the P vs. NP problem requires that we encode in an
> alphabet with at least two elements; this is simply the definition of
> the problem.  See the first page ofhttp://claymath.org/millennium/P_vs_NP/pvsnp.pdf
> if you do not believe me.

Right. I see that for SAT we have the same decision problem if
variables are encoded in alphabet of one ore more than one symbol.

> Also, I'm curious...is Future_News Musatov?  A Google search revealed
> that this text is from another website:http://www.dpmms.cam.ac.uk/~wtg10/future.news2.html

Who cares? (Although a certain full of garbage reply in this thread
indicates that probably he is)
From: cplxphil on 21 Oct 2009 20:04
On Oct 21, 7:50 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote:
> On Oct 21, 3:44 pm, cplxphil <cplxp...(a)gmail.com> wrote:
>
>
>
>
>
> > On Oct 21, 7:32 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote:
>
> > > On Oct 21, 8:34 am, Future_News <future_n...(a)brew-master.com> wrote:
>
> > > > What does the statement `P=NP' mean? A good way to understand it is to
> > > > look at an illustrative example. Suppose I secretly choose two prime
> > > > numbers p and q, tell you their product n=pq and ask you to tell me
> > > > what p and q are. In principle you can work this out, since by the
> > > > fundamental theorem of arithmetic p and q are uniquely determined.
> > > > However, in practice it is not easy to come up with a systematic way
> > > > of finding them other than to look at all primes up to n1/2 and see
> > > > whether they are factors of n. If n has 500 digits, this takes much
> > > > too long to be feasible on even the fastest computers, and this
> > > > difficulty is the basis of much of modern cryptography. Actually, more
> > > > efficient methods have been discovered than straightforward trial and
> > > > error, but, even after decades of intensive research, it is still out
> > > > of the question to factorize a 500-digit number. At the end of the
> > > > last century there was a great deal of excitement when Peter Shor
> > > > discovered that quantum computers could factorize large numbers far
> > > > more efficiently, but, despite several well-publicized announcements
> > > > to the contrary, nobody has managed to build such a computer.
>
> > > I have an issue with the number encoding schema. Somewhere in the
> > > introduction section Gary-Johnston textbook describes how numbers are
> > > encoded in the computer and asserts that exponential notation
> > > (regardless of base) is the most natural way to go. Objection, your
> > > honor! There is no genuine mathematical reason why to exclude unary
> > > number system.
>
> > > Factorization problem is not hard in unary system. Any other NP-
> > > complete problem that doesn't depend on number encoding? Let's try the
> > > subset sum problem. On the first sight, the subset property looks hard
> > > to check by the virtue of the fact that we have to analyze the
> > > powerset which size is exponential (in any number encoding schema).
> > > Let's look into the problem little closer. Consider the following
> > > naive algorithm where we keep track of all the sums, and when adding a
> > > number to the list we just go through the list and add the number to
> > > each element. The list would double at each step,- you may say. Not
> > > really. In unary number system there is just not enough room: one has
> > > to have big numbers in order to accommodate all possibilities. So the
> > > subset sum problem appears to be of cubic complexity in unary number
> > > system.
>
> > > So my question is: are there any genuinely "hard" problems that don't
> > > depend on (rather arbitrary) choice of number system?
>
> > I'm fairly certain that any NP-complete problem can be solved in
> > polynomial time if you encode in unary.
>
> > Unfortunately, the P vs. NP problem requires that we encode in an
> > alphabet with at least two elements; this is simply the definition of
> > the problem.  See the first page ofhttp://claymath.org/millennium/P_vs_NP/pvsnp.pdf
> > if you do not believe me.
>
> Right. I see that for SAT we have the same decision problem if
> variables are encoded in alphabet of one ore more than one symbol.
>

I'm not sure if you're disagreeing. If you are, my response is that
you could argue that it preserves the same structure of the decision
problem, but expressed as a formal language, it's technically
different. It has to be proven that languages are basically
equivalent (in terms of decidability, time complexity, and space
complexity) and independent of encoding scheme, and this proof only
applies to encoding schemes that use at least two symbols in the
alphabet.

I guess something I should have mentioned earlier is that Cook's
theorem would not be true if you use a unary alphabet, meaning that
SAT would not be NP-complete in that case. If you think you can prove
Cook's theorem for a unary alphabet, please share this proof.



> > Also, I'm curious...is Future_News Musatov?  A Google search revealed
> > that this text is from another website:http://www.dpmms.cam.ac.uk/~wtg10/future.news2.html
>
> Who cares? (Although a certain full of garbage reply in this thread
> indicates that probably he is)

I suppose it is just interesting to note that Musatov seems to be
changing strategies in an attempt to draw more attention to his posts.
From: Gordon Stangler on 21 Oct 2009 22:58
On Oct 21, 6:50 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote:
> On Oct 21, 3:44 pm, cplxphil <cplxp...(a)gmail.com> wrote:
>
[snip]
>
> > Also, I'm curious...is Future_News Musatov?  A Google search revealed
> > that this text is from another website:http://www.dpmms.cam.ac.uk/~wtg10/future.news2.html
>
> Who cares? (Although a certain full of garbage reply in this thread
> indicates that probably he is)

What is so wrong about that? Taking the work of others without
attribution is stealing, like it or not. And some people, myself
included, are deeply disturbed by stealing.
From: Future_News on 22 Oct 2009 00:42
On Oct 21, 4:32 pm, Tegiri Nenashi <tegirinena...(a)gmail.com> wrote:
> On Oct 21, 8:34 am, Future_News <future_n...(a)brew-master.com> wrote:
>
>
>
> > What does the statement `P=NP' mean? A good way to understand it is to
> > look at an illustrative example. Suppose I secretly choose two prime
> > numbers p and q, tell you their product n=pq and ask you to tell me
> > what p and q are. In principle you can work this out, since by the
> > fundamental theorem of arithmetic p and q are uniquely determined.
> > However, in practice it is not easy to come up with a systematic way
> > of finding them other than to look at all primes up to n1/2 and see
> > whether they are factors of n. If n has 500 digits, this takes much
> > too long to be feasible on even the fastest computers, and this
> > difficulty is the basis of much of modern cryptography. Actually, more
> > efficient methods have been discovered than straightforward trial and
> > error, but, even after decades of intensive research, it is still out
> > of the question to factorize a 500-digit number. At the end of the
> > last century there was a great deal of excitement when Peter Shor
> > discovered that quantum computers could factorize large numbers far
> > more efficiently, but, despite several well-publicized announcements
> > to the contrary, nobody has managed to build such a computer.
>
> I have an issue with the number encoding schema. Somewhere in the
> introduction section Gary-Johnston textbook describes how numbers are
> encoded in the computer and asserts that exponential notation
> (regardless of base) is the most natural way to go. Objection, your
> honor! There is no genuine mathematical reason why to exclude unary
> number system.
>
> Factorization problem is not hard in unary system. Any other NP-
> complete problem that doesn't depend on number encoding? Let's try the
> subset sum problem. On the first sight, the subset property looks hard
> to check by the virtue of the fact that we have to analyze the
> powerset which size is exponential (in any number encoding schema).
> Let's look into the problem little closer. Consider the following
> naive algorithm where we keep track of all the sums, and when adding a
> number to the list we just go through the list and add the number to
> each element. The list would double at each step,- you may say. Not
> really. In unary number system there is just not enough room: one has
> to have big numbers in order to accommodate all possibilities. So the
> subset sum problem appears to be of cubic complexity in unary number
> system.
>
> So my question is: are there any genuinely "hard" problems that don't
> depend on (rather arbitrary) choice of number system?

The closest person to me calls me 'Martian'... :)

Keeping in the 'spirit' of things it has to be interesting and topical
or it's out the window, so here goes: (*da_bing*) ROUND TWO:

WHAT IS IT LIKE TO BE A HUMAN (INSTEAD OF A BAT)?

My purpose in this paper is to discuss and defend an objection to
physicalist or materialist accounts of the mind—one that I believe to
be essentially conclusive.[1] The argument in question is not new. A
version of it seems to be lurking, along with much else, in Thomas
Nagel's famous paper "What Is It Like to Be a Bat?"[2]; and a somewhat
more explicit version is to be found in a well-known paper by Frank
Jackson.[3] Despite the efforts of Nagel and Jackson (and some
others), however, I believe that the most compelling version of the
argument has not emerged clearly, with the result that responses that
in fact fail to speak to its central point are widely taken to be
adequate. Thus one purpose of the present paper is to offer what I
regard as a more perspicuous restatement of the Nagel-Jackson
argument, one which shows clearly why the responses in question do not
work. A second purpose is to suggest that the application of the
argument is in fact very much wider than the case of phenomenal
properties or qualia upon which both Nagel and Jackson focus, that it
in fact applies just as well to the content of intentional mental
states like thoughts and indeed to the general phenomenon of
consciousness itself.

i

I begin with a brief and selective recapitulation of Nagel's and
Jackson's presentations of the argument and of some of the critical
responses they evoked, focusing on those raised by Paul Churchland.

Though, as we will see, there are several other balls in the air, the
strand of Nagel's argument upon which I wish to focus goes at least
approximately as follows: It is reasonable to assume that bats have
conscious experience of some kind, that as Nagel puts it "there is
something it is like to be a bat" [423]. But such experience is
surely enormously different from our own in many ways, due to the very
different "range of activity and sensory apparatus" [423] possessed by
bats, in particular their well-known capacity of perceiving the world
and navigating through it via a kind of sonar resulting from the
reflection of their own high-pitched cries. Nagel's question is
whether we could ever come to know "what it is like to be a bat," and
in particular whether we could do this on the basis of a thoroughgoing
knowledge of the physical or material facts pertaining to bat
physiology. His claim is that we could not, and the suggested
conclusion, which he himself never quite draws, is that physicalism is
false.

As will emerge, I believe that the foregoing argument is essentially
sound. I also believe that it is present in Nagel. But it is very
hard to be sure of the latter claim, because so many other ideas and
suggestions are present in the paper as well, ideas and suggestions
that seem in some cases to be incompatible with the foregoing argument
and in other cases to point in at least rather different directions.
There is, first, the idea of a "point of view," with the suggestion
that certain kinds of facts may be knowable only from a certain point
of view and the accompanying distinction, suggestive but also quite
elusive, between various "subjective" points of view and the
"objective" point of view characteristic of physical science.
Secondly, there is the concern with conceptual limitations, and the
suggestion that the main problem with regard to bats is that we may
not have and may not be able to acquire the right concepts to capture
bat experiences. Third, there is the suggestion that the right
conclusion is not so much that physicalism is false as that we do not
understand how it could be true—which might still be compatible, Nagel
suggests, with having good or even compelling reasons to think that it
is true. And, fourth, even the formulation that I have echoed in my
title in terms of "what it is like to be a bat" is at least
potentially misleading, in that it (along with the employment of the
objective/subjective dichotomy) might suggest that the knowledge that
we are lacking with respect to bats is not so much knowledge of facts
as knowledge of what it would "feel like from the inside" to be a bat—
thereby inviting the reasonably plausible response that this is not a
sort of knowledge that physicalism could be expected to provide even
if it were true.[4]

I do not mean to suggest that some or all of these ideas may not be
valuable on their own. In particular, the idea of subjective and
objective points of view may well yield a much deeper insight into the
mysterious nature of consciousness than could ever be derived from the
argument that I mean to focus on here. My point is merely that these
elements are quite inessential to the argument that is my present
concern, an argument that I believe to be more immediately and
unproblematically compelling as an objection to physicalism or
materialism, even if perhaps ultimately less insightful in other
ways. By diverting attention, those other elements tend to prevent
that argument from emerging clearly and also to invite irrelevant
responses.

Jackson's version of the argument focuses more clearly on the central
point. In the most compelling version, it imagines a brilliant
neurophysiologist, Mary, who lives her entire life, acquires her
education, and does all of her scientific work in a black-and-white
environment, using black-and-white books and black-and-white
television for all of her learning and research. In this way, we may
suppose, she comes to have a complete knowledge of all the physical
facts in neurophysiology and related fields, together with their
deductive consequences, insofar as these are relevant—thus arriving at
as complete an understanding of human functioning as those sciences
can provide. In particular, Mary knows the functional roles of all of
the various neurophysiological states, including those pertaining to
sense perception, insofar as these are reflected in their causal
relations to sensory inputs, behavioral outputs, and other such
states. But despite all of this knowledge, Jackson suggests, Mary
does not know all that there is to know about human mental states: for
when she is released from her black-and-white environment and allowed
to view the world normally, she will, by viewing objects like ripe
tomatoes, "learn what it is like to see something red,"[5] and
analogous things about other colors. "But then," comments Jackson,
"it is inescapable that her previous knowledge was incomplete. But
she had all the physical information. Ergo there is more to have than
that, and Physicalism is false."[6]

While this version of the argument is certainly less burdened with
other distractions than Nagel's and is also once again, I believe,
essentially sound, there are still problems. These may be examined by
considering two objections to the Jackson version offered by
Churchland.[7]

Churchland's first objection is that while Mary undoubtedly learns
something new when she is released from her black-and-white
environment, what she acquires is not knowledge in the same sense of
that term in which it is a consequence of the truth of physicalism
that she already knows all there is to know. The sense of "knowledge"
in which physicalism guarantees that Mary's knowledge is complete is
"a matter of having mastered a set of sentences or propositions,"
while the sort that Mary acquires is:

a matter of having a representation of redness in some prelinguistic
or sublinguistic medium of representation for sensory variables,
or . . . a matter of being able to make certain sensory
discriminations, or something along these lines. [23]

Churchland's point may perhaps be put somewhat more clearly by saying
that it is not the case, according to him, that what Mary is initially
lacking and then later comes to acquire is a knowledge of certain
facts or truths about human mental states, but that knowledge of facts
or truths is all that the physical account could be expected to
supply, even if physicalism were correct. I believe that Churchland's
claim that Mary does not come to know any new facts or truths is
mistaken, but this point is difficult to establish clearly within the
context of Jackson's formulation of the argument: if she learns new
facts or truths, what exactly are they? Thus Jackson, in his
response, is reduced to arguing in a very indirect fashion for the
existence of such facts (by appealing to the genuineness of the
problem of other minds).[8]

Churchland's second objection turns on the intriguing suggestion that
Mary, once she has learned to employ the concepts of a completed
neuroscience in introspection, might be able to imaginatively
extrapolate from her introspective awareness of her black-and-white
experiences to the experiences she would have if she were in the
neurophysiological states corresponding to color experience and thus
might come to know "what it is like to see something red." Jackson's
response[9] is that if physicalism were true, Mary should know what
the experience is like, rather than merely having to imagine it. But
I do not see why Churchland, if his point were otherwise sound, could
not claim that Mary might indeed come to know in this way what the
experience is like, albeit via a kind of imaginative inference rather
than direct experience. Again, I believe that Churchland is mistaken
here: both about what Mary would be able to do and, more importantly,
about the relevance of this issue to the central point of the
argument. But the way in which Jackson has formulated the argument
makes it hard to clearly establish either of these things.

ii

What is needed, in my judgment, is a version of the argument that (i)
makes it clear that there are facts or truths about human mental
states that someone in Mary's position does not and cannot know on the
basis of purely physical and neurophysiological knowledge, however
complete that may be, and (ii) avoids relatively intractable issues
about what Mary might be able to imagine or imaginatively infer on the
basis of her own experience. And the way to do this, I suggest, is in
effect to invert Nagel's original example, in a way that he himself
suggests in passing but does not develop [425]: instead of imagining
ourselves trying to know or comprehend the experiences of an alien
form of life, we need instead to imagine an alien form of life trying
to know or comprehend our experiences.

Suppose then that a brilliant Martian scientist comes to earth to
investigate, with our full cooperation, the nature and makeup of human
beings. Being a Martian, he has, we may suppose, a quite different
sensory apparatus from ours, but one which is still quite adequate,
given his complete mastery of the standard sorts of inductive and
explanatory reasoning, to arrive at a complete knowledge of any purely
physical phenomenon. Thus, in time, the Martian arrives at an ideally
complete knowledge of the physical and neurophysiological facts
concerning human beings, including those pertaining to causally
defined functional roles. Does he thereby come to know all of the
facts about human mental states such as experiences of color?

Suppose that I am one of the subjects studied by the Martian. On a
particular occasion, I look at a newly mowed, well-watered, and
healthy lawn and thereby have an experience of a certain specific
phenomenal or sensuous property, one which is somewhere toward the
middle of the range of such properties that I am accustomed to call
"green." On another occasion, I look at a newly painted fire engine
and thereby have an experience of a second specific phenomenal or
sensuous property, one which is somewhere toward the middle of the
range of properties that I am accustomed to call "red." It is, I
submit, simply a fact about me in the most straightforward possible
sense that on the first occasion I experience the first property and
that on the second occasion I experience the second property. The
Martian is present on both occasions and is carefully monitoring my
physical and neurophysiological states with an elaborate set of
instruments that he has devised for this purpose. He thereby comes to
know everything about those states, including their causal relations
to other states, to as fine a level of detail as could possibly be
relevant.[10] Does he thereby know that I am experiencing the first
property on the first occasion and the second property on the second
occasion?

I have stipulated that the Martian does not possess senses like ours.
In particular, he does not possess eyes and a faculty of vision like
ours. Thus one thing that he cannot do is determine what property I
am experiencing by looking at the relevant objects himself. Nor
should he need to do this, since facts about his own experiences are
of course no part of his supposedly complete physical and
neurophysiological account of humans in general and of me in
particular. (The same thing is in fact true of Mary: Though she
happens to be a member of the species that she is investigating, her
introspective awareness of her own experiences is still not a part of
the ideally complete physical and neurophysiological account of humans
at which she arrives by the methods of physical science. This is why
Churchland's speculations about her imaginative extrapolations are
strictly irrelevant.)

The Martian does not experience colors in the way and in the contexts
that we do. But it is still possible that he is familiar in some
other way with the specific phenomenal or sensuous properties at
issue, and it will help to focus the essential point if we suppose
that this is so. Thus suppose that he does experience those very
properties, albeit in some quite different causal context. Perhaps he
experiences colors when he hears or otherwise senses vibrations in the
air corresponding to music. Or, less fancifully, perhaps he does have
something like eyes and vision, but in relation to a quite different
range of electromagnetic radiation, and experiences all of the colors
that we experience (and perhaps others?) in that connection. Thus, we
may suppose, he has a perfectly good grasp of the concepts of having
an experience of each of the two properties in question, and the issue
is only whether he can apply those concepts correctly to me.[11]

We may even concede to the Martian one more useful piece of
information, albeit one that he almost certainly could not in fact
arrive at on his own. Let us stipulate not only that he is familiar
with color properties and possesses the concepts of having such
experiences, but even that he somehow knows[12]—perhaps God whispers
it in his ear or appropriate alternative sense organ—that two specific
color properties out of the ones with which he is familiar are in fact
the two that I am experiencing on the two occasions in question (but
not of course which is which). In addition, we may suppose that the
Martian has solved the difficult but probably not entirely intractable
problem of isolating the specific features of my neurophysiology that
are relevant to the issue we are concerned with, so that he is able to
focus on two relatively restricted neurophysiological states that are,
supposing that physicalism is true, identical to my experiencing of
the two colors. Thus he is able to formulate to himself two pairs of
propositions, one pair identifying the first of these restricted
states with an experiencing of the first of the two properties and the
second restricted state with an experiencing of the second of the two
properties, and the other pair reversing these ascriptions. He thus
knows, we are supposing, that the propositions in one pair are true
and those in the other pair false, but not which is which. Can he
tell, solely on the basis of his complete physical and
neurophysiological knowledge, which is the correct pair?

In thinking about this question, it is important to be quite clear
about the exact shape of the issue. If physicalism is true, I submit,
then the Martian should not have to extrapolate or surmise or guess,
in however educated a fashion, in order to determine which pair of
propositions is the correct one. If the ideal physical and
neurophysiological account is indeed a complete account of all the
facts concerning humans and their mental states, and if one of the two
pairs of propositions is true and the other false in relation to that
subject-matter, then it seems to follow that the propositions of the
true pair must be already included in some way in that account, and
that the propositions in the other pair must be in some way
incompatible with that account—where the inclusion and incompatibility
in question can apparently be only logical or analytic inclusion or
incompatibility. And this would apparently mean in turn that the
ideas or concepts of the two phenomenal or sensuous properties in
question would have to be either already present in the
neurophysiological account or somehow strictly definable on the basis
of neurophysiological ideas or concepts. The former of these
alternatives seems clearly mistaken, which is just to say that
neurophysiology does not explicitly invoke the idea of sensuous or
phenomenal color. And the latter alternative is no more palatable.
One way to argue this point is to appeal to the familiar view that
color concepts are primitive or indefinable, a view that I believe to
be correct albeit somewhat elusive. But even apart from this sort of
appeal, the idea that the concepts of the various sensuous or
phenomenal colors are strictly definable on the basis of
neurophysiological primitives has, if anything, even less plausibility
than the old phenomenalist idea that physical object concepts are
definable in purely sensory terms. I do not know how to strictly
prove that no such definition is possible, but I know of no one who
has ever seriously defended such a view, nor of any way to make it
even minimally plausible.[13]

Thus it seems utterly plain that the answer to our original question
is "no." All that the Martian's physical and neurophysiological
knowledge can give him is increasingly complicated accounts of the
structure of the two restricted neurophysiological states and of their
structural and causal relations to each other and to other states and
processes of the same kind. But all of this knowledge, however
detailed and elaborate we may suppose it to be, would still be
entirely compatible with the truth of either of the two pairs of
propositions. The indicated conclusion is that although the Martian
scientist knows all the physical and neurophysiological facts there
are, he does not know all of the facts there are, and hence that
physicalism or materialism is false.

I want to conclude this section by considering briefly two possible
rejoinders on behalf of the physicalist, both of them attempts to
evade the argument in the only way that might still seem open to him:
via a denial that it is a consequence of the truth of physicalism that
all of the facts about a given sort of thing must be logically
contained in a complete physical account of that thing. It is obvious
that many physicalists, at least since the death of logical
behaviorism, have wanted to avoid such a requirement, indeed that this
has been much of the point of the various physicalist positions. But
it seems to me very doubtful that any adequate rationale for rejecting
this requirement, as opposed to qualifying it in minor and ultimately
irrelevant ways, has ever been given.

First. The most obvious rejoinder is that there are at least two
conspicuous sorts of facts about a thing, one of them perhaps a
subclass of the other, that need not, even if physicalism is true, be
thus contained in a complete physical account that is confined to that
thing. One sort of fact pertains to the function or purpose of the
thing: thus I could know all of the purely physical facts about a
certain sort of object and still not know that it is a chair, because
being a chair has to do with its function for human beings and not
with its purely physical description. The other sort of fact pertains
to classifications that are relative to human needs or purposes and
perhaps also to some degree conventional or even arbitrary: thus,
e.g., I could know all of the physical facts about a thing, including
the precise mean kinetic energy of its molecules, and still not know
that it was hot rather than lukewarm, as classified by common sense,
because the difference here has to do with a fuzzy and relatively
arbitrary line that humans draw, for reasons having to do with their
own bodily temperature, within an essentially continuous range of
physical temperatures.

But what makes facts of these kinds (and perhaps others of similar
sorts as well) unknowable on the basis of a complete physical
description of the thing is that they implicitly have to do with
relations between the thing in question and other things, in this case
humans and their purposes and classifications, and it is obviously no
surprise that a relational fact cannot be known via a complete
description of one of the relata alone (where it is now obvious that
by a complete description is meant a complete description of the
intrinsic or non-relational properties of the thing). And the reason
that this point is irrelevant to the argument against physicalism,
forcing at most a minor clarification, is that it seems abundantly
clear that having an experience of one phenomenal property rather than
another on a given occasion is an intrinsic property of a person, not
one that is in any way relational.[14] (To say that such a fact was
relational would be to say roughly that it could be altered by
altering something about the external relata, while leaving the
intrinsic properties of the original thing unchanged.[15])

Second. The other possible rejoinder is an appeal to views about the
relations between different "conceptual schemes" or "levels of
description" and to related doctrines in the philosophy of science,
especially views about reduction. The suggestion, very roughly, is
that the Martian scientist might in fact know the very phenomenal
facts in question, i.e. that certain propositions within his body of
physical and neurophysiological knowledge might describe the very same
facts that are described by the correct pair of propositions
formulated in phenomenal terms, even though the Martian is entirely
unable to tell, even in principle, that this is so. And the view
which underlies this suggestion is the idea that descriptions of the
same fact in different and perhaps incommensurable conceptual schemes
need not be logically or analytically or even recognizably equivalent
to each other.[16] A full consideration of the complicated issues in
the vicinity of this suggestion is obviously impossible within the
confines of the present paper, but the following brief remarks may
suffice to indicate why I do not find it at all plausible as a
response to the present argument.

It is obvious and uncontroversial that particular, concrete entities
(objects, states, events) can be picked out or specified in different
and not obviously equivalent ways: thus, e.g., Venus as the morning
star or as the evening star. It is also obvious that properties can
be specified in non-equivalent ways where these specifications are
indirect or accidental, i.e. where they pick out the property by
invoking a contingent description of it: thus, e.g., one of the
phenomenal properties in question might be specified as Joe's favorite
color or as the color experienced in connection with a certain
standard sort of object. (Indeed, my specifications in this paper
were of this sort, which does not of course mean that my own grasp of
the properties in question depended on such a specification.) Or, to
take a somewhat more interesting case, heat might be specified as the
property causally responsible for certain kinds of effects, such as
the melting of ice and the cooking of food. But it seems clear that
not all property specifications can be thus indirect or accidental,
that properties are often specified in a way that reflects or captures
their essential or intrinsic character. And it seems abundantly clear
that both the property of having an experience of a certain sensuous
color and the various physical and neurophysiological properties, as
these are understood by the Martian scientist, are specified in this
essential or intrinsic way.[17]

In these terms, the present suggestion is that there could be two
different property specifications, each of which captures or
represents the essential or intrinsic nature of the very same property
rather than picking it out via some sort of indirect or accidental
description, but which nonetheless still fail to be logically or even
recognizably equivalent to someone who fully understands them both.
It seems to me very doubtful that this suggestion is even
intelligible, the reason being roughly that properties, unlike most
kinds of particulars, simply do not have the right kind of logical
depth or complexity to make non-equivalent essential specifications
possible. If there are two non-equivalent essential property
specifications, I suggest, then there are two properties—however
closely related in other ways they may be.

But while I think that the foregoing point is correct as a matter of
general metaphysics, I do not want to rely entirely on it here. Thus
I propose to grant the physicalist the intelligibility of the present
suggestion, at least for the sake of the argument, and see whether it
really does him any good. What we are supposing then, applying it to
the specific sort of case in question, is that the property specified
as being in a certain neurophysiological state and the property
specified as having an experience of one of the color properties
originally in question are in fact the very same property, even though
neither the Martian scientist nor anyone else can tell directly that
this is so. But then, as long both specifications are conceded to be
intrinsic, it seems to follow that the single property in question
nonetheless has a kind of internal duality or complexity: it has, we
may say, two different aspects or dimensions, one reflected in one
specification and one in the other. And now the knowledge that the
Martian scientist has no access to will be the knowledge that the
latter, experiential aspect or dimension of the property is present on
the occasions when the former, neurophysiological aspect or dimension
is. Thus as long as the presence or absence of this experiential
aspect or dimension in a particular case is conceded to be a genuine
fact, which is something that only the most radical and implausible
sort of eliminativism could deny, it will still be the case that the
complete physical account leaves out some of the facts and hence, once
again, that physicalism is false.[18]

III

My conclusion so far is that the physicalist or materialist view of
human mental states is false, on the grounds that certain entirely
obvious facts about the qualitative character of phenomenal experience
are not captured by any imaginable physical account. I claim no great
originality for the argument to this point, for I think that it is
very close to what Nagel and especially Jackson had in mind, even
though their specific formulations opened the door to irrelevant
responses. But unlike Jackson and probably Nagel, I do not think that
the force of the argument is restricted to phenomenal experiences, and
I will devote the final two sections of the paper to a consideration
of how it can be more widely applied, focusing in the present section
on states such as propositional attitudes that have intentional
content.

Even among those who are doubtful about the case of phenomenal qualia,
it has often been supposed that a physicalist account of intentional
states like beliefs and desires is on a much sounder footing. This
discussion has tended to focus on states of belief, and unfortunately
has almost always failed to adequately distinguish the issue of our
public belief attribution practices from that of the private or
subjective content of the states in question. In the present
discussion, I will avoid those complexities by focusing on a simpler
sort of state, but one that is still clearly intentional: the state of
simply thinking about or envisaging something, of having it in mind.

Suppose then that on a particular occasion I am thinking about a
certain species of animal, say dogs—not some specific dog, just dogs
in general (but I mean domestic dogs, specifically, not dogs in the
generic sense that includes wolves and coyotes). The Martian
scientist is present and has his usual complete knowledge of my
neurophysiological state. Can he tell on that basis alone what I am
thinking about? Can he tell that I am thinking about dogs rather than
about cats or radishes or typewriters or free will or nothing at all?
It is surely far from obvious how he might do this. My suggestion is
that he cannot, that no knowledge of the complexities of my
neurophysiological state will enable him to pick out that specific
content in the logically tight way required, and hence that
physicalism is once again clearly shown to be false.

Before examining this issue, however, it is important to be somewhat
clearer than has been necessary so far about the scope of the
knowledge that the Martian is allowed to draw on for this purpose. It
is natural and, I believe, essentially correct, to regard my having a
thought about dogs as a purely internal property of me, one that does
not depend in a constitutive way on external objects and situations or
on my relations to them (though it may of course be a causal result of
such things). This is reflected in the fact that I am able in general
to tell “from the inside,” simply by reflection, what I am thinking
about, without needing to know anything about these external matters.
Thus the Martian should apparently be able to tell on the basis of my
internal physiology alone that I am thinking about dogs.

Before arguing specifically that he cannot, I want to consider briefly
some possible objections to this construal of the issue, growing out
of recent work in the philosophy of language, which challenge the very
idea that having a thought with a certain content is an internal
property of the person. A full consideration of the various ideas and
doctrines involved in these objections is once again obviously
impossible within the confines of this paper. But I believe that it
will nonetheless be relatively easy to see that they have no serious
effect on the main line of argument being advocated here.

Consider, first, the idea of "the division of linguistic labor." In
various papers, Putnam has suggested that I need not have any very
clear and determinate conception of, e.g., dogs in order to be
thinking about them. It is enough, he seems to suggest, if I merely
employ in my thinking the word "dog," with the reference of the word
being determined by "the relevant group of experts."[19] Thus, it
might be suggested, it would not be at all surprising if the Martian
scientist is unable to determine on the basis of my internal
neurophysiology alone that I am thinking about dogs, for this fact
depends on facts about the experts and not merely on my internal
properties.

I think that it is far from obvious that someone who has no conception
at all of what sort of thing a dog is, not even that it is an animal
as opposed to a vegetable or an inanimate or even an abstract object,
is nonetheless thinking about dogs solely by virtue of employing the
word. I also doubt that the Martian scientist would find it any
easier to determine that I am indeed employing, in the relevant sense,
a certain word. But it is enough for present purposes to focus on
someone like myself who has a much more detailed conception of a dog.
I am not one of the relevant experts (though that would be a possible
case too), so it is possible that there are actual non-dogs that I
could not distinguish from dogs. And even if I were one of the
experts, there would surely be creatures that are at least possible,
e.g. perhaps Twin-Earth dogs, that I would be unable to distinguish
from real dogs. This is to say that my conception, and probably
anyone's conception, of dogs fails to be completely determinate. But
this does nothing to solve the main problem, for we can still ask
whether the Martian can tell what this somewhat indeterminate thought
content is, and the correct answer, I suggest, will still be negative.

Another idea in the same vicinity is the causal theory of reference or
perhaps of thought content generally. Again it is suggested that what
I am thinking about is not determined by my internal state alone, but
depends also on external relations, in this case causal relations,
including the causal history of the words I employ. Here too we may
concede that there is something right about the point in question. It
is at least plausible to think that part of what makes my thoughts
pertain to dogs, the earthly species, rather than to Twin-Earth dogs
which might be indistinguishable even by the experts at the time in
question, is that I am causally related, partly or perhaps even
entirely via the causal history of the word, to earthly dogs and not
to Twin-Earth dogs. The only thing that we must resist is a
completely externalist account of content, according to which my
internal state possesses by itself no content at all and thus nothing
that the Martian could fail to know. And here it is enough, I think,
to point out that a completely externalist view of content would be
incompatible with the obvious fact pointed out earlier: on a
completely externalist view, I would have from the inside no grasp at
all of what I was thinking about, since I have in general no access to
the relevant causal relations—a result that I take to be obviously and
indeed monumentally absurd.[20]

Despite the enormous complexity and subtlety of the recent work in
this area, the foregoing is, I think, enough to show that the specific
instance of the argument against physicalism that is under discussion
in this section cannot be plausibly met by denying that the content of
my thoughts is, to a sufficient degree to pose the problem, an
internal property of me. Any account of content that makes it
accessible enough from the inside to avoid clear absurdity will also
make it to that same degree internal, thereby posing a clear challenge
to the Martian and hence to physicalism. It may be conceded that
there is quite possibly no simple and non-misleading way to specify
such purely internal content, thus showing once again the degree to
which ordinary language and common sense are insensitive to
philosophically significant but practically unimportant (or at least
seemingly unimportant) distinctions. But while this may make the
argument somewhat more difficult to formulate, it does nothing at all
to affect its basic cogency.[21]

Suppose then, as seems undeniable, that when I am thinking about dogs,
my state of mind has a definite internal or intrinsic albeit somewhat
indeterminate content, perhaps roughly the idea of a medium-sized
hairy animal of a distinctive shape, behaving in characteristic ways.
Is there any plausible way in which, contrary to my earlier
suggestion, the Martian scientist might come to know this content on
the basis of his neurophysiological knowledge of me? As with the
earlier instance of the argument, we may set aside issues that are
here irrelevant (though they may well have an independent significance
of their own) by supposing that the Martian scientist has an
independent grasp of a conception of dogs that is essentially the same
as mine, so that he is able to formulate to himself, as one
possibility among many, that I am thinking about dogs, thus
conceived. We may also suppose that he has isolated the particular
neurophysiological state that either is or is correlated with my
thought about dogs. Is there any way that he can get further than
this?

The problem is essentially the same as before. The Martian will know
a lot of structural facts about the state in question, together with
causal and structural facts about its relations to other such states.
But it is clear that the various ingredients of my conception of dogs
(such as the ideas of hairiness, of barking, and so on) will not be
explicitly present in the neurophysiological account, and extremely
implausible to think that they will be definable on the basis of
neurophysiological concepts. Thus, it would seem, there is no way
that the neurophysiological account can logically compel the
conclusion that I am thinking about dogs to the exclusion of other
alternatives.

There is, however, one possibility here that is worth brief
exploration. A number of philosophers have at least flirted with the
idea of what might be called a relational or coherence theory of
conceptual content: the idea that concepts are defined entirely by the
formal structure of their inference relations to each other. The
further suggestion is then roughly that any system of states that
realizes the appropriate formal structure will thereby come to be a
genuinely representational system with the concepts in question as the
represented content. And if this were so, then the Martian scientist,
by knowing the causal structure of my various neurophysiological
states, might be able to identify the corresponding contents. (This
assumes, obviously and more than a little problematically, that a
transition can be made from causal structure to inferential structure,
i.e. that causal relations or some appropriately arrived at subset of
them can be taken to reflect inference relations.)

There is much that could be said about this sort of picture and a good
deal more that would have to be done to make it even minimally
plausible. For present purposes, however, two points will suffice.
First, even if the coherence theory of concepts is correct, having a
structure isomorphic to a given set of concepts will be at most a
necessary, not a sufficient condition for a system of states to
actually represent those concepts. There simply is no reason why a
system of states could not accidentally happen to have the right
structure while in fact representing nothing at all. And thus no
structural knowledge on the part of the Martian would show
definitively that I was thinking about dogs.

Second, the coherence theory of concepts is in fact very implausible,
because it is very implausible that a particular set of concepts can
ever be identified on the basis of formal inferential structure
alone. On the contrary, there appears to be no reason at all why lots
of different sets of concepts could not possess completely parallel
and hence indiscernible inferential structures. And this possibility,
which is already very serious for concepts considered in the abstract,
becomes more serious still when we are dealing with a particular
system of concrete states which can plainly never embody all of the
possible concepts and inference relations that are abstractly
possible, so that two or more systems of concepts that were abstractly
discernible might be equally plausible interpretations of a system of
concrete states that did not perfectly embody any of them.[22]

Thus the idea that the Martian scientist would be able to determine
the intrinsic or internal contents of my thought on the basis of the
structural relations between my neurophysiological states is extremely
implausible, and I can think of no other approach to this issue that
does any better. The indicated conclusion, once again, is that the
physical account leaves out a fundamental aspect of our mental lives,
and hence that physicalism is false.

IV

I want to consider one more application of our general line of
argument, in some ways the most fundamental of all, but one that is
fortunately capable of being dealt with very briefly. It is obvious
that on any plausible version of physicalism, only some of our
neurophysiological states will be identified with conscious mental
states. There is no consciousness associated with those states, for
example, that control breathing and heartbeat. But this suggests the
issue of whether our Martian scientist, on the basis of his complete
physical and neurophysiological knowledge, can tell which
neurophysiological states are conscious and which are not. My
suggestion, once again, is that there is no way that he can do this in
the logically tight way that is required.

We may suppose, reasonably enough, that there is some structural
difference between states that are conscious and states that are not,
and hence that the Martian can divide our states into two groups,
corresponding to this difference. But even if he can get this far,
how can he possibly determine, as opposed to merely surmise or
conjecture, that the states in one group involve consciousness and
that those in the other do not? It is, if anything, even more obvious
that consciousness is not explicitly mentioned as such in his complete
neurophysiological account, nor definable in terms of things that are
mentioned. And again, as with the case of phenomenal properties, I
know of no one who has ever seriously suggested otherwise.



My conclusion, which could, I believe, be extended to many other sorts
of mental states as well, is that the Martian scientist, in spite of
possessing complete physical and neurophysiological knowledge of me,
could not know many important facts about my conscious mental life,
nor indeed even that I have a conscious mental life at all. This
means that the physical and neurophysiological account is radically
incomplete as an account of my complete personal makeup and hence that
physicalism or materialism, as an account of human beings, is surely
and irredeemably false.


Laurence BonJour


University of Washington




--------------------------------------------------------------------------------

NOTES

[1] The argument in question may well be a decisive objection to
"naturalism" as well, but my understanding of that popular doctrine is
too uncertain to warrant very much confidence in such a claim.

[2] Thomas Nagel, "What Is It Like to Be a Bat?" Philosophical Review,
volume 83 (1974), pp. 435-50; reprinted in David M. Rosenthal (ed.),
The Nature of Mind (New York: Oxford University Press, 1991), pp.
422-28. References in the text to Nagel are to the pages of this
reprint.

[3] Frank Jackson, "Epiphenomenal Qualia," Philosophical Quarterly,
volume 32 (1982), pp. 127-36. The argument in question is what
Jackson calls "the knowledge argument." It receives some useful
elaboration in Jackson's note, "What Mary Didn't Know," Journal of
Philosophy, volume 83 (1986), pp. 291-95; reprinted in Rosenthal
(ed.), pp. 292-4. (Subsequent references to this latter article will
be to the reprint in Rosenthal.)

[4] See Jackson, "Epiphenomenal Qualia," p. 132, for a bit more
discussion of this point. I don't mean to suggest that it is clear
that a true physicalist account should not be expected to provide such
knowledge, and still less that it is clear why this is supposed to be
so. But the issue is difficult at best, so that it is better to find
a version of the argument that does not require resolving it.

[5] Jackson, "What Mary Didn't Know," p. 392.

[6] Jackson, "Epiphenomenal Qualia," p. 130.

[7] Paul M. Churchland, "Reduction, Qualia, and the Direct Inspection
of Brain States," Journal of Philosophy, volume 82 (1985), pp. 8-28.
(References in the text to Churchland are to the pages of this paper.)

[8] See Jackson, "What Mary Didn't Know," p. 394.

[9] Jackson, "What Mary Didn't Know," p. 394.

[10] If there is no limit to the levels of detail, if the facts about
my states are, as it were, infinitely fine-grained, then the Martian,
being finite, does not know absolutely everything about my states.
But we may surely stipulate that his knowledge is sufficiently fine-
grained to capture everything that is relevant to the issue with which
we are concerned here.

[11] One suggestion that has been made in discussion is that it is
question-begging against the materialist to assume that it is possible
for the Martian to have the same phenomenal experiences even though
both his neurophysiological states and their functional roles are
presumably different from ours. Actually, it would be quite possible,
for all that has been said, to stipulate that the Martian's
neurophysiological states are essentially the same as ours, even
though hooked up in different ways to sensory mechanisms—and hence
different in functional role. Since even many functionalists concede
that phenomenal properties are not captured by functional role, this
does not seem to beg any serious questions. But the main point is
that allowing the Martian to have such phenomenal experiences makes
his task easier, not harder, so that it is hard to see on what basis
the materialist can object to it. If this is in fact not genuinely
possible, then so much the worse for materialism.

[12] Actually it would be somewhat less problematic, and still
adequate for my purposes here to suppose merely that the Martian
correctly believes this to be the case. But it will be simpler and
less distracting to speak of knowledge.

[13] Churchland, in his discussion of Mary, suggests as a part of his
account of her imaginative extrapolation that color sensations might
turn out to be "structured sets of elements" rather than
"undifferentiated wholes" [26-7]. I take it that this would mean that
color properties were somehow complex, rather than simple, thus at
least opening the possibility that they might somehow be definable in
terms of neurophysiological primitives. But while it seems clear that
something in this direction would be needed to defend the view that
the propositions about color experience are indeed logically contained
in the neurophysiological account, I can see no real hope that any
such view will turn out to be tenable—nor is it clear that even
Churchland means to suggest it, given his heavy reliance on the idea
that introspective knowledge must first be formulated in
neurophysiological terms.

[14]Unless, of course, it involves a relation to a non-physical
particular, perhaps a sense-datum or sensum. But it is obvious that
this possibility is no help to the physicalist.

[15] David Lewis seems to hold a view according to which the
phenomenal character of experience would be in this way relational, by
virtue of depending on a choice of an "appropriate" population, in
relation to which a person's state is to be classified. See his "Mad
Pain and Martian Pain," reprinted in David Rosenthal (ed.), The Nature
of Mind (Oxford: Oxford University Press, 1991), pp. 229-35. Here I
will simply assume that such a view is too implausible to require
serious consideration.

[16] See Churchland, op. cit., for one attempt in this direction.

[17]It would in fact be easier to question this claim in the case of
the physical and neurophysiological properties, but this would
obviously not help the physicalist.

[18] The eliminativist possibility is suggested somewhat obliquely by
Churchland in his discussion of Jackson (ibid.) and, of course, more
explicitly elsewhere. The basic idea that a description in a reducing
theory might fail to logically entail a description in a theory being
reduced because the theory being reduced is strictly false, albeit
close enough to the truth to be regarded as having glimpsed the truth
through a glass darkly. Churchland is, of course, quite right that
this sort of case is possible in general, as illustrated by various
episodes in the history of science. But what is, I believe, too
implausible to be taken seriously is the idea that the phenomenal
description of my experience is false to the degree that would be
required to accommodate in this way the Martian's inability to know
which color experience I was having.

[19] See, e.g., Hilary Putnam, "The Meaning of 'Meaning'," in his
Mind, Language and Reality (Cambridge: Cambridge University Press,
1975).

[20] A philosopher who shall remain nameless once conceded to me in
the course of a discussion of this sort of issue that on his view, he
could not tell from the inside that we were not discussing quantum
mechanics rather than the philosophy of language. It should be easy
to see why this made it seem futile to go on with the discussion.

[21] For a somewhat fuller discussion of these recent ideas in the
philosophy of language and their bearing on the idea of internally
accessible thought content, see my paper "Is Thought a Symbolic
Process?" Synthese, vol. 89 (1991), pp. 331-52, especially pp. 337-40.

[22] For a somewhat fuller consideration of the coherence theory of
content and its implications for thought content in particular, see
the paper referred to in the preceding note, pp. 340-45.
First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4
Prev: [Port%d] \\.\HCD%d
Next: On The Question of Absolute Undecidability