Objections to Objectivism 1/3
Lawrence M. Sanger
edited it much since then. I am posting it reluctantly, only because many
people have been asking for instances of the "minor errors" in Objectivism
that I wrote of in my "Sixteen Theses about Objectivism." (Well, here's a
few.) Before going shooting your mouths off about this, please (1) read
what you are replying to very carefully, and remember that it was not
written by an idiot, and (2) take note that I _will not_ be responding to
replies to it. I am not trying to start a debate about the contents of
this long post. I don't have time for that. I am just trying to support
my claim that there are minor errors in Objectivism. (And some of the
errors seem to me not so minor, actually.) Also, please note that many of
these "objections" are not actually objections -- in many of these points I
am merely stating that there are some glaring omissions in Objectivism, and
of course hardly anyone disputes that.
I have discovered, over the years, several errors and omissions of
some import in Objectivism. Since many of these errors seem to me quite
glaring, I often find myself disgusted at the seeming dogmatism with which
Rand’s ideas are repeated. In this post I will present a selection (it is
not exhaustive) of these errors and omissions. Most of them are not merely
nit-picks, in my opinion; most are serious and deep objections, and they
cannot be taken lightly. My target here, however, is not (what I take to
be) the essence of Rand’s thinking, for this I admire. I admire, for
example, her insistence that axioms are not arbitrary. My target is what
is mistaken about her thinking, and moreover the dogmatism with which it is
propounded. Those who call themselves Objectivists should, I think, stand
back and take stock of their consistent adherence to Rand’s philosophy; one
part of this stock-taking might be actually to try to formulate clear and
convincing answers to my objections. I doubt that anyone can do so,
because I think that at least several of these objections are completely
successful. But I will have achieved my purpose if I simply cause some
Objectivists to become more critical and careful thinkers, while remaining
true to the cause of reason and individualism.
If in answer to any of these objections you wish to direct me to
other of Rand’s works, or other Objectivist works, then _please_ tell me
page numbers -- and before you do this, please look at what Rand says and
make sure that you are persuaded that what she says there does indeed
permit a successful response to _my particular_ objection.
Notice that I have criticisms only of the more fundamental areas of
Objectivism here -- I have nothing to say about Rand’s politics or
aesthetics. This is not because I think there is nothing wrong with those
areas of her philosophy, but simply because I am not as interested in those
subjects, and consequently have not thought as much about what Rand said
about them.
---------------------------------
1. Axiomatic concepts (1). “An axiomatic concept,” Rand writes in
_Introduction to Objectivist Epistemology_, Ch. 6, “is the identification
of a primary fact of reality, which cannot be analyzed, i.e., reduced to
other facts or broken into component parts. It is implicit in all facts
and in all knowledge. It is the fundamentally given and directly perceived
or experienced, which requires no proof or explanation, but on which all
proofs and explanations rest.” First, the notion of _proof_ does not apply
to concepts, but only to propositions; one may show that a concept is
correct, or proper, I think, but to do so is not to “prove” the concept.
This is not a very important objection, though. It is only an example of
Rand’s carelessness.
2. Axiomatic concepts (2). I am content to accept that “axiomatic” (I
prefer the more common philosophical term _primitive_) concepts “cannot be
analyzed,” but Rand fails to explain here is _why_ they cannot. One might
think that it is sufficient to say that they are “implicit in all facts and
in all knowledge,” but this too requires explanation: How will we _know_
when we find a concept that is “implicit” in a fact or in knowledge?
Fortunately, Rand has told us what is implicit in all facts; but the
question is what ‘implicit’ means, and based on that meaning, how one may
justifiably conclude that these concepts are “implicit” in all facts.
Alternatively, one might think it an explanation to say that Rand’s
axiomatic concepts are “the fundamentally given and directly perceived,”
but again a critical thinker must ask: How do we know what is to be taken
as _fundamentally_ given and _directly_ perceived? These are simply
crucial questions, since axiomatic concepts are so crucial to her theory of
knowledge; but she has no answers to them, only repetitions of these basic
formulas. Her students may think they “kinda know” what she means; but the
test of understanding, in philosophy, is the ability to explain one’s
concepts in clear (and noncircular) terms. (Unless the concept of
axiomaticity at issue is itself axiomatic. But even that fact would
require explanation.)
3. On existence, identity, and consciousness as the primary axiomatic
concepts. In that same important chapter of _IOE_, Rand writes, “The first
and primary axiomatic concepts are ‘existence,’ ‘identity’ (which is a
corollary of ‘existence’) and ‘consciousness.’ ” I have two objections
here as well. First, it is not very clear what she means by ‘corollary’;
she evidently does not know how the word is ordinarily used. _Concepts_ do
not have corollaries; only theorems (i.e., a kind of proposition) do. It
is also not very clear whether a concept that is a “corollary” of an
axiomatic concept is itself axiomatic. If that is so, then for one concept
to be a “corollary” of another cannot simply be for the first to be defined
in terms of the second; for then all concepts defined in terms of axiomatic
concepts would be primitive, which is absurd, if very many concepts are
supposed to be defined in terms of the axiomatic concepts. So precisely
what the relation is between existence and identity -- or identity and one
of its own “corollaries,” causality -- is another one of those mysterious
areas of Rand’s doctrine. Second, if it is a _sufficient_ condition for a
concept to be axiomatic, that it “cannot be analyzed,” Rand has failed to
state several very important axiomatic concepts. Some of them are at the
foundation of logic, such as the concepts of conjunction, disjunction, and
negation, not to mention quantificational concepts (“all” and “some”);
others are at the foundation of physics, such as the concepts of space,
time, matter, and/or energy.
4. The limited role of axiomatic concepts in Rand’s system. Now, someone
might reply to the latter objection by saying that Rand’s notion of
axiomatic concepts was not intended to include whatever cannot be defined
-- it is meant to include specifically that which is implicit (whatever
this means) in all facts and knowledge. Notions at the foundations of
logic and physics are not “implicit” in this way. Now, I suppose this is
true. But then I think that Rand has axiomatic concepts serving a very
limited role in her system. For obviously she does not mean for them to be
just the concepts in terms of which all other terms may be defined; but
this is what really makes the notion of _primitive_ concepts so important
and useful. So where Rand could and should have augmented her notion of
axiomatic concepts -- so as to make sense of the conceptual structure of
philosophy -- she failed to do so. (By the way, if some Objectivist denies
that each concept in a philosophical system must either be axiomatic or
defined, I enjoin him to say just what the third option is.)
5. Reason as resting on “the Law of Identity” alone. In _PWNI_, p. 63,
Rand writes, “Reason is the perception of reality, and rests on a single
axiom: the Law of Identity.” This is the sort of sweeping claim that makes
it very hard for me to believe that any even slightly critical philosopher,
such as David Kelley, could accept _everything _Rand wrote about
philosophy. First of all, the claim is cryptic. What does it mean for
reason, a faculty, to “rest” on an axiom? Evidently she means that the
validity (whatever validity comes to) of the rational faculty is justified,
in some unspecified way, by the law of identity. But this is all very
vague. Second, it is extremely unlikely that _anyone_ could plausibly
assign a meaning to the claim that would make it true that reason rests on
the _law of identity_, which is simply that A is A. I defy anyone to
actually explain _how_ the validity of the rational faculty rests
_entirely_ upon, in any plausible sense of ‘rests upon’, the claim that A
is A. If you cannot do so, and you call yourself an Objectivist, and if
you are honest, then I think you _must_ admit that Rand has some
formulations that were far too vague for us to be able to assign any
truth-value to them; and thus that not everything Rand said about
philosophy is true. (But this is, of course, just one example out of many
of this sort of vagueness. One ought to be on the lookout for it.)
6. Logic and the “Law of Identity” again. In _PWNI_, p. 15, Rand writes,
“Logic has a single law, the Law of Identity, and its various corollaries.”
The law of identity is that A is A. Again, I enjoin _anyone_ to explain
how _any_ interestingly different rule or theorem of logic follows from A
is A alone. For example, how does modus ponens follow? How does it follow
from A is A that, given that P, and the conditional claim that if P, then
Q, one may conclude that Q? The short and only answer is that this _does
not_ follow from A is A. Rand is at her most absurd in her comments about
logic generally.
7. The definition of ‘logic’. “Logic,” Rand writes (_PWNI_, p. 15), “is
the art or skill of non-contradictory identification.” Among Rand’s
attempts at definition, this must be the worst. First of all, I can look
at a bird, identify it as a bluejay, and do so in a non-contradictory
fashion (I have not also said that it is _not_ a bluejay!); but I have not
used any logic in doing so. If I am skilled in identifying bluejays, I
make no conscious inferences at all; moreover, I doubt that there are such
things as unconscious inferences and that I was engaged in one of those.
Doubtless, somewhere along the line, I must use some sort of inference in
order to make it possible for me to identify various things that I do now;
but that does not make it true that whatever act of non-contradictory
identification I engage in _now_ is perforce an application of logic!
Second, logic ain’t an _art_ or a _skill_ -- it is a set of rules of
inference, together perhaps with some procedures in their application, some
definitions of related terms, and the like. In short, it is a _study_ that
happens to be very useful -- it is the study of logical form, or of the
structure of argument, or of correct inference. Had Rand said it was “the
study or use of non-contradictory inference,” then she would be closer to
the mark.
8. The mind/body problem (1). As explained above, Rand takes
“consciousness” as an axiomatic concept. Now, that entails that it cannot
be analyzed in terms of anything else; hence, it cannot be analyzed in
terms of matter. And that is quite consistent with her frequent
denunciations of materialism. Moreover, I suppose she would also want to
say that “matter” or “energy” or some other basic physical concept could
not be analyzed in terms of anything else. But then we have Rand saying
both that consciousness and matter are irreducible, and certainly not
reducible one to the other. Hence it appears she is committed to dualism,
which may be broadly described as the claim that two fundamentally
different (irreducible) kinds of thing exist (or, if you like, fall under
the single category of existence). But she is constantly denouncing
dualism. So it appears she contradicts herself.
9. The mind/body problem (2). In many places, Rand rails against
materialism, idealism, and dualism. Now, she offers no other option in
explanation of her own theory of mind. But some thinkers may that these
three theories (when each is very broadly construed) exhaust the
possibilities for philosophical theories of the nature of mind. There is
another option, I suppose, namely, neutral monism; but Rand does not
mention it. -- Someone may reply that the relation between mind and body is
a scientific question, and thus need not be considered by philosophers per
se. But this is not exactly what Rand says; she writes (_IOE_, 2nd ed., p.
290), “In asking what’s the relationship between ‘mind’ and ‘brain,’
scientists have to know what they mean by the two concepts. It’s
philosophy that would tell them the [general] definitions of those
concepts. But then actually to find the specific relationship, that’s a
scientific question.” My question here does not concern any specific
relationship, nor even any general _relation_, but the very basic
philosophical question as to what the basic nature of the mind and of
matter is.
Lawrence M Sanger
Objectivism" to a.p.o was substituting R's and S's for double quotes,
and T's and U's for single quotes. I hope this won't be too distracting
for people who actually read this.
Larry Sanger
Betsy Speicher
>I am just trying to support
>my claim that there are minor errors in Objectivism. (And some of the
>errors seem to me not so minor, actually.) ...
> I have discovered, over the years, several errors and omissions of
>some import in Objectivism. Since many of these errors seem to me quite
>glaring, I often find myself disgusted at the seeming dogmatism with which
>Rand's ideas are repeated. ...
>My target is what
>is mistaken about her thinking, and moreover the dogmatism with which it is
>propounded. Those who call themselves Objectivists should, I think, stand
>back and take stock of their consistent adherence to Rand's philosophy
>...
While you were gone, Larry, Sean Saulsbury asked for those who claim to
have found flaws in Ayn Rand's formulations to give specific objections
with their reasoning. I am glad that in your current postings you are
doing so.
As I understand it, Larry, you support David Kelley and his organization,
IOS, but have found fault with and criticize the Ayn Rand Institute.
Sean and others have been trying to sort out the competing claims in the
Kelley vs. Peikoff/ARI dispute. By presenting your reasons for
supporting IOS rather than ARI, perhaps you can help those who are
interested understand the issues better.
Betsy Speicher
Lawrence M Sanger
>As I understand it, Larry, you support David Kelley and his organization,
>IOS, but have found fault with and criticize the Ayn Rand Institute.
>Sean and others have been trying to sort out the competing claims in the
>Kelley vs. Peikoff/ARI dispute. By presenting your reasons for
>supporting IOS rather than ARI, perhaps you can help those who are
>interested understand the issues better.
I don't think I'm the right person to ask -- try Rick Minto or Jimbo
Wales, if you want the views of persons calling themselves Objectivists
who understand the issues involved better than I do.
I can say this much, though. If I tried to become a member of the
ARI (I don't even know if there is such a thing as membership in
ARI) I am quite sure I would fail -- they wouldn't have me. But in
addition to that, I would not _want_ to be a member of ARI, for some
reasons I gave in my "Sixteen Theses." Finally, I support Kelley
and his IOS _primarily_ because he supports scholarly work -- i.e.,
philosophical work done in regular universities. He wants to see
Objectivism spread throughout academia, and so do I, and I think his
ways of going about doing so are far better than any I have heard of
by the ARI. I have the impression that Peikoff really doesn't care
very much about whether or not Objectivists become philosophy prof-
essors and try to insert Objectivist ideas into the world of
academic philosophy. Perhaps I am wrong. But Kelley is quite
explicit about it, and supports it very strongly. As a result, he
has attracted a very fine set of graduate philosophy students to
his organization -- around nine now, I think. In five years, if
these people stay on, there will be probably well over a dozen
philosophy Ph.D.'s in the IOS, maybe 20. (I'm not sure what the
number is at present, but I suspect it's somewhere close to a half-
dozen.) That is not something that I think Peikoff could say. As
far as academic philosophy goes, then, I think the IOS is clearly
on the cutting edge of Objectivism.
Larry Sanger
Brad Aisa
> I have the impression that Peikoff really doesn't care
>very much about whether or not Objectivists become philosophy prof-
>essors and try to insert Objectivist ideas into the world of
>academic philosophy. Perhaps I am wrong.
Dr. Peikoff made a passionate public plea (I think in Debate '84) to
universities to allow even one Objectivist professor amongst their ranks. He
stated that this would be sufficient to (in my words) level the intellectual
playing field against the status quo.
I seem to remember reading that ARI had a seminar program for graduate
students of Objectivism. Dr. Peikoff is a director of ARI.
I would be most interested in an exposition of the epistemological premises
and methods you used to reach your "impression". (Or is intellectual rigour
only applicable to the abstract realm of philosophic ideas, but not the
day-to-day realm of real life?)
:- - - - - - - Brad Aisa - - - - - - -:
: Software Engineer Toronto, CANADA :
: tel (416)423-4075 fax (416)423-8050 :
: - - - - - ba...@hookup.net - - - - :
Michael Hardy
>lsa...@magnus.acs.ohio-state.edu (Lawrence M Sanger) writes:
>> I have the impression that Peikoff really doesn't care
>>very much about whether or not Objectivists become philosophy prof-
>>essors and try to insert Objectivist ideas into the world of
>>academic philosophy. Perhaps I am wrong.
>
>Dr. Peikoff made a passionate public plea (I think in Debate '84) to
>universities to allow even one Objectivist professor amongst their ranks. He
>stated that this would be sufficient to (in my words) level the intellectual
>playing field against the status quo.
>
>I seem to remember reading that ARI had a seminar program for graduate
>students of Objectivism. Dr. Peikoff is a director of ARI.
Harry Binswanger replied thus to a recent query:
<<
The Objectivist Graduate Center of the Ayn Rand Institute offers
*non-degree* graduate-level training in Objectivism for those planning careers
as professional intellectuals. We are completely outside of and opposed to the
current academic world. The OGC is located in New York City and is now near the
end of its first year, with 8 full-time and another 20 part-time students.
For a brochure and/or an application form, contact The Ayn Rand Institute,
4640 Admiralty Way, Marina del Rey, CA 90292. Their email address is
A...@mcimail.com. Phone: (800) 365-6552.
>>
Whether this outfit promotes putting objectivists into philosophy
department faculties I don't know. Maybe someone else here does?
Mike Hardy
Michael Hardy "If you come to a fork
School of Statistics in the road, take it."
University of Minnesota
ha...@stat.umn.edu -- Yogi Berra
Samantha Atkins
In article <lsanger-01...@slip3-10.acs.ohio-state.edu>,
Lawrence M. Sanger <lsa...@magnus.acs.ohio-state.edu> wrote:
13. The problem of universals (2). Rand’s own view is that universals just
>are concepts; as she writes, in the same place, “But concepts are
>abstractions or universals, and everything that man perceives is
>particular, concrete.” But there are several difficulties with the view
>that universals are concepts. Foremost among these difficulties is
>(something along the lines of) the following. Consider volume; having a
>volume of one liter is a universal, if anything is. But it surely sounds
>_bizarre_ to say that volume is a concept! The volume of this container is
>something that exists independently of the mind -- it is not a concept.
>But an Objectivist may reply here that the volume _of this container_ is
>not a universal, but a particular -- it is a particular volume. And so of
>course _it_ is not a concept, and _it_ exists mind-independently. It is
>volume-in-general that is a concept. Consider what sense _these_ claims
>make. On the one hand, the volume of the container, an instance of the
>universal _volume_, exists independently of the mind; on the other, volume
>itself is a concept of the mind. But how can something be an instance of
>another, when the first exists independently of the mind, and the second is
>dependent on the mind? For suppose all minds are destroyed. Then there
>are instances of things that do not exist; and that is absurd. Thus, if
>volume-in-general exists along with particular volumes, it cannot be a
>concept. (My own view is that universals do not exist, and that we may use
>particular volumes, together with the concept of volume that we form based
>on these particular volumes, to explain all we need to explain; and we may
>do away with talk of universals entirely.)
Huh? I am quite lost by this as it looks to me like you stated an apparent
absurdity that follows supposedly from an error AR made and then follow it
by stating "your own view" which is much closer to what she actually said.
It looks like you got caught up in a bit of a game. AR states that concepts
are abstractions formed from perceptions of concretes. Thus the particular
volumes MUST exist before the concept of volume, as an abstraction, could
exist. Similarly, without humans their would still be those concretes that gave
rise to the concept, volume, without the concept existing. My reading of
ITOE is that what Rand said avoids this whole little 'paradox' quite easily.
I agree as I think Rand does that universals do not exist if by universal
you mean some such thing as above where some pattern, if you will, must exist
before any instances of that pattern can exist. I haven't examined it closely
but I believe that the existence of such patterns would lead fairly directly
to the primacy of consciousness.
>
>14. The problem of universals (3). Another rather simple objection is that
>it is incoherent to say that universals are concepts. Take my concept of
Interesting. My reading was that Rand was saying that when people blather
on about universals they really should be talking about concepts. In other
words I read it that she did not believe in universals and thought them a
distortion of concepts.
>volume, for example. This concept is not a concept of any particular
>volume, but of volumes generally. And if universals exist, my concept of
>volume is surely a concept of the universal _volume_; for if universals
>exist, it makes sense to say that concepts are concepts _of_ universals.
>So concepts and universals are two different categories; if they were not,
>then I could sensibly say, "She has a very interesting universal of the
>universal, justice." But this is in fact incoherent. -- These three
This objection is why I think universals should be dropped as a useless
concept. Again, my reading of ITOE is that Rand also has this view.
>objections depend on the assumption that ‘universal’ is to be taken in its
>traditional sense -- that any attempt to change the meaning of this word is
>illegitimate. This is an assumption that I am aware many Objectivists do
>not share. So some Objectivists may find themselves disgusted with these
>objections in particular, since I am in fundamental agreement with them,
>and my objections amount to “word games.” But if these are word games, I
>think they are important word games; one cannot ignore 2000 years of usage.
> It is far better simply to find a new word for the concept one has in
>mind, rather than try to annex old ones.
Well, if you are going to fire that kind of broadside against those who
do not adhere to a "traditional sense" of what we mean by universals then
I think you are obliged to state what the "traditional" meaning is. Please
do so. The point with cleaning up word usage is that 2000 years or however
many of usage is not adequate necessarily to have a word denote a well
defined concept. To judge whether universals have a murky meaning requires
saying what you mean by the term. Is it more or less what I extract from
context above?
>
>15. Measurement-omission (1). Rand’s definition of ‘concept’ is: “_A
>concept is a mental integration of two or more units possessing the same
>distinguishing characteristic(s), with their particular measurements
>omitted._” (_IOE_, ch. 2) But the omission of _measurements_ only is
>hardly sufficient, in many cases, to form a concept. In forming the
>concept of a painting, for example, one must omit not only the size of the
>painting, but also color and the arrangement of shapes on the canvas, and
>so forth. Color and shape-arrangement are _not_ measurements. If an
>Objectivist wants to maintain that they are, then I will reply that one
>cannot just twist the meaning of a fine word like ‘measurement’ to fit
>Rand’s theory. In saying, “A painting must have some arrangement of
>shapes, but may have any,” the Objectivist is not omitting _measurements_.
>Rand should have said, if anything, that the units subsumed by a concept
>have their particular _features_ omitted.
>
Huh? The point is that a concept is an abstraction from the existents it
subsumes. The abstraction is performed by measurement-omission.
Measurement-omission refers to omitting the particular quantities of whatever
qualities are essential to the concept. That is omitting the quantification
of the qualities that would be required to describe a particular instance.
In the case of a painting color and shape-arrangement are possible candidates
for inclusion in the concept, painting. Thus their particular quantification
for any particular painting is omitted in forming the concept. Objecting
that these quantifications are not measurements doesn't seem reasonable.
Perhaps you could substitute _features_ but features is too abstract and
omission of features would leave little to conceptualize.
>16. Measurement-omission (2). Thus she might speak of features, rather
>than measurements; but it is not clear, from her definition of ‘concept’,
>_what_ features may be omitted during concept-formation. For some features
>are obviously essential; one cannot, for example, omit the feature of
>flatness in forming the concept of painting. Thus, while Rand could have
>said that one omits all but the essential features in forming concepts, she
>did not. The account that she does give is very poor.
>
Huh? I can paint a painting on a barrel and most folks will still call it
a painting. Why do you say that flatness is essential? Rand *did* say
that one omits all but the essential features in forming concepts - quite
clearly. So where is the "poor"-ness of her account evident?
>17. Words. In Ch. 2 of _IOE_ Rand writes as though she believes that words
>_just are_ concepts. When asked about this (2nd ed., p. 163) -- whether
>she means literally that words are concepts -- she denies it, and then says
>that actually what she meant was that words “stand for” concepts. But the
>Foreword of the 2nd ed. (see pp. 126-7) would have us take the passages
>from _IOE_ itself as Rand’s actual views. This is, of course, not a very
>damning objection, since Rand obviously never meant to say that words are
>concepts, but it is an example of her extreme carelessness, which often
>gets her into trouble.
Your judgmental attitude is showing big-time here. You admit that your
interpretation is not what Rand meant and that she went through some pains
to close off this misinterpretation. Then you turn around and state that
it is an example of "extreme carelessness". Sorry but you are making what
appear arbitrary judgements in that you are failing to present reasonable
evidence.
>
>18. Meaning (1): word-meaning. Most philosophers today agree, and I agree
>with them, that the theory of meaning is of great and fundamental
>importance. It is disappointing, then, that Rand did not have a more
>completely worked-out theory of meaning. And the theory she did hold is
>certainly flawed. In _IOE_, Ch. 2, she writes, “Every word we use (with
>the exception of proper names) is a symbol that denotes a concept, i.e.,
>that stands for an unlimited number of concretes of a certain kind.”
>First, it is very odd to say that words denote _concepts_. The word ‘dog’,
>in the sentence, “That dog is annoying me,” denotes, if anything, a
>specific _dog_, not a concept. It matters not at all whether we have to
The word dog in that sentence denotes the concept dog. The word, that,
points to a specific instance. Basic grammar really.
>form the concept _dog_ in order to understand this sentence; for the word
>itself in the sentence denotes a dog, not that by which we know to call
>something seen a dog. To put it more succinctly, ‘That dog’ denotes that
Wrong. If what you are saying is true I could have said "that yeyetw is
annoying me". But since yeyetw doesn't denote anything no one would know
what is meant unless I pointed. Even then they would ask what in the hell
a yeyetw is.
>dog; I don’t think I can make it clearer than this. (Someone might answer
>by saying that ‘that dog’ functions as a proper name; and I would agree
>here, but it is _not_ what Rand said.) Second, the part after “i.e.” is
Sorry, but Rand did not commit an error here.
>puzzling. Is the claim, here, that a concept itself is “an unlimited
>number of concretes of a certain kind”? That is how the syntax of the
>claim would have it, but this is certainly the most absurd of views, and
>not even the view that Rand held, since she says clearly elsewhere that
>concepts are _mental integrations_ of concretes. But then, is she saying
>that the meaning of words is mental integrations?
>
This is silly. A word denotes a concept. A concept subsumes an unlimited
number of concretes. The usage may be a bit loose philosophically but the
meaning is quite clear.
I don't have more time for these objections at the moment. Thus far I am
singularly unimpressed though.
- Samantha