Ayn Rand said in ITOE p. 255 -
You know the best example I could give—perhaps this will help. If you brought a dog or a cat into this room, it would be aware of everything that we see here. It would also see the room, the objects, and the people. What it would never be able to grasp is, "I am conscious of this room," although that fact is inherent in its perception.
Then what is the difference between that idea and Kant's idea of apperception?
But all empirical consciousness has a necessary relation to a transcendental consciousness which precedes all special experience, namely, the consciousness of myself as original apperception. It is therefore absolutely necessary that in my knowledge all consciousness should belong to a single consciousness, that of myself. CPR A118.
Showing posts with label Rand. Show all posts
Showing posts with label Rand. Show all posts
Saturday, June 13, 2009
Wednesday, June 25, 2008
analytic-synthetic
"An axiomatic concept is the identification of a primary fact of
reality, which cannot be analyzed, i.e., reduced to other facts or
broken into component parts."
And yet Peikoff railed against the so-called analytic-synthetic dichotomy.
What's ironic is the Objectivist definition of "axiom" - in which you will find
the very idea of analysis itself, and even the word "analyzed." It is
just a short step for them to understand that putting the "broken"
component parts back together again involves nothing more than a
synthesis of those parts.
reality, which cannot be analyzed, i.e., reduced to other facts or
broken into component parts."
And yet Peikoff railed against the so-called analytic-synthetic dichotomy.
What's ironic is the Objectivist definition of "axiom" - in which you will find
the very idea of analysis itself, and even the word "analyzed." It is
just a short step for them to understand that putting the "broken"
component parts back together again involves nothing more than a
synthesis of those parts.
Saturday, May 31, 2008
Kant and Geometry
Here is an example of why the analytic-synthetic distinction is so important
to the history of modern thought.
http://www.friesian.com/kant.htm
"Although it is often claimed, as by the great French mathematician
Poincaré, that the existence of non-Euclidean geometry refutes Kant's
philosophy of geometry, in fact Kant's view of the nature of the
axioms of geometry as synthetic a priori propositions means that Kant
could have predicted the existence of non-Euclidean geometry. This
should be obvious given any clear understanding of the meaning of
'synthetic'."
We need a clear understanding of this meaning. In pursuit of this, the
article on Kant quotes Hume:
"In An Enquiry Concerning Human Understanding, Hume made a distinction
about how subject and predicate could be related:
All the objects of human reason or enquiry may naturally be
divided into two kinds, to wit, Relations of Ideas, and Matters of
Fact. Of the first kind are the sciences of Geometry, Algebra, and
Arithmetic; and in short, every affirmation which is either
intuitively or demonstratively certain [note: these are Locke's
categories]. That the square of the hypothenuse is equal to the square
of the two sides, is a proposition which expresses a relation between
these figures. That three times five is equal to the half of thirty,
expresses a relation between these numbers. Propositions of this kind
are discoverable by the mere operation of thought, without dependence
on what is anywhere existent in the universe. Though there never were
a circle or triangle in nature, the truths demonstrated by Euclid
would for ever retain their certainty and evidence.
Matters of fact, which are the second objects of human reason, are
not ascertained in the same manner; nor is our evidence of their
truth, however great, of a like nature with the foregoing. The
contrary of every matter of fact is still possible; because it can
never imply a contradiction, and is conceived by the mind with the
same facility and distinctness, as if ever so conformable to reality.
That the sun will not rise to-morrow is no less intelligible a
proposition, and implies no more contradiction than the affirmation,
that it will rise. We should in vain, therefore, attempt to
demonstrate its falsehood. Were it demonstratively false, it would
imply a contradiction, and could never be distinctly conceived by the
mind. [Enquiries, Selby-Bigge edition, Oxford, 1902, 1972, pp.25-26]"
This is the distinction between analytic and synthetic propositions
implied by Hume, and finally elucidated by Kant. It is a division,
yes, but not a division of TRUTHS as Hume claimed in the quote above.
Because Hume's example of the sun rising tomorrow does not pack the
same punch as a truth such as Peikoff's "ice floats on water." We can
always dispute what will happen in the future, relegating it to the
realm of probability. But that ice floats on water (not will float, or
has floated, or is floating on water) is an indisputable truth, as
indisputable as "ice is a solid form of water."
And yet, I term the former synthetic, and the latter, analytic,
despite the indisputable nature of both propositions. Indisputability,
or necessity, has nothing to do with it. Rather, indisputability is
relegated to the realm of the a priori, with its necessary and
universal truths. And so, as indisputable, the two truths in question
are both a priori: the former synthetic a priori, and the latter
analytic a priori. Kant has spelled this all out in detail so there
should be no question about it.
The distinction depends on how the two propositions are constructed,
that is, how subject and object are linked in a particular a priori
statement of truth. They are, no doubt, linked with necessity, this
has never been disputed, but they are linked only as necessary a
priori. There is no such thing as a posteriori necessity, only a
posteriori contingency (e.g., the proposition "there could have been
more or less than 50 states in the US"). Contingency brings with it an
element of doubt, it doesn't pack the same punch, and we do not doubt
that ice floats on water any more than we doubt that ice is a solid
form of water.
But "floating" cannot be considered a concept constituent of "ice."
"Solidity" can. That ice is made of water can also. And so to say that
a proposition is analytical is only to say that it elucidates the
constituent elements of a concept, the sine qua nons of any concept
without which the concept would not be.
The danger is always to avoid converting this into an ontological or
metaphysical discussion. I am not talking about all those things the
actual ice can do, or how it is affected by circumstance or "context"
due to the various natures or identities involved. I can only see this
as the source of many synthetic propositions, some a priori and some
a posteriori. But the consideration here is only with that necessity
bound up with types of propositions, not with the necessity bound up
with identities in nature. And so this discussion is really nothing
more than the eludication of rules of method: namely, Kant's synthetic
and analytic methods.
Critique boils down to methodology, primarily, the method by which
philosophy and science are to be constructed, and how their various
and sundry propositions are to be construed. It is important to note
that for Kant the introduction to his Critique did not invoke
philosophy, but science and mathematics. That is, those basic truths
upon which his Critique of philosophy were formed were borrowed from
the truths of science and mathematics, not so much in their content as
in their form, particularly, how the form of their propositions came
to form truths. Borrowing from this, Kant determined that philosophy
itself also utilizes such forms, only historically not as precisely
formulated, mainly because the propositions of philosophy had not been
as intuitive (meaning, they are quite abstracted from the evidence and
the rule of the senses, as is the nature of philosophy).
Not that it was only philosophy that required Kant's help. Science and
mathematics can also benefit from having the form of their truths
elucidated in order to reduce the amount of confusion that is always
involved in any attempt at garnering abstract truths.
to the history of modern thought.
http://www.friesian.com/kant.htm
"Although it is often claimed, as by the great French mathematician
Poincaré, that the existence of non-Euclidean geometry refutes Kant's
philosophy of geometry, in fact Kant's view of the nature of the
axioms of geometry as synthetic a priori propositions means that Kant
could have predicted the existence of non-Euclidean geometry. This
should be obvious given any clear understanding of the meaning of
'synthetic'."
We need a clear understanding of this meaning. In pursuit of this, the
article on Kant quotes Hume:
"In An Enquiry Concerning Human Understanding, Hume made a distinction
about how subject and predicate could be related:
All the objects of human reason or enquiry may naturally be
divided into two kinds, to wit, Relations of Ideas, and Matters of
Fact. Of the first kind are the sciences of Geometry, Algebra, and
Arithmetic; and in short, every affirmation which is either
intuitively or demonstratively certain [note: these are Locke's
categories]. That the square of the hypothenuse is equal to the square
of the two sides, is a proposition which expresses a relation between
these figures. That three times five is equal to the half of thirty,
expresses a relation between these numbers. Propositions of this kind
are discoverable by the mere operation of thought, without dependence
on what is anywhere existent in the universe. Though there never were
a circle or triangle in nature, the truths demonstrated by Euclid
would for ever retain their certainty and evidence.
Matters of fact, which are the second objects of human reason, are
not ascertained in the same manner; nor is our evidence of their
truth, however great, of a like nature with the foregoing. The
contrary of every matter of fact is still possible; because it can
never imply a contradiction, and is conceived by the mind with the
same facility and distinctness, as if ever so conformable to reality.
That the sun will not rise to-morrow is no less intelligible a
proposition, and implies no more contradiction than the affirmation,
that it will rise. We should in vain, therefore, attempt to
demonstrate its falsehood. Were it demonstratively false, it would
imply a contradiction, and could never be distinctly conceived by the
mind. [Enquiries, Selby-Bigge edition, Oxford, 1902, 1972, pp.25-26]"
This is the distinction between analytic and synthetic propositions
implied by Hume, and finally elucidated by Kant. It is a division,
yes, but not a division of TRUTHS as Hume claimed in the quote above.
Because Hume's example of the sun rising tomorrow does not pack the
same punch as a truth such as Peikoff's "ice floats on water." We can
always dispute what will happen in the future, relegating it to the
realm of probability. But that ice floats on water (not will float, or
has floated, or is floating on water) is an indisputable truth, as
indisputable as "ice is a solid form of water."
And yet, I term the former synthetic, and the latter, analytic,
despite the indisputable nature of both propositions. Indisputability,
or necessity, has nothing to do with it. Rather, indisputability is
relegated to the realm of the a priori, with its necessary and
universal truths. And so, as indisputable, the two truths in question
are both a priori: the former synthetic a priori, and the latter
analytic a priori. Kant has spelled this all out in detail so there
should be no question about it.
The distinction depends on how the two propositions are constructed,
that is, how subject and object are linked in a particular a priori
statement of truth. They are, no doubt, linked with necessity, this
has never been disputed, but they are linked only as necessary a
priori. There is no such thing as a posteriori necessity, only a
posteriori contingency (e.g., the proposition "there could have been
more or less than 50 states in the US"). Contingency brings with it an
element of doubt, it doesn't pack the same punch, and we do not doubt
that ice floats on water any more than we doubt that ice is a solid
form of water.
But "floating" cannot be considered a concept constituent of "ice."
"Solidity" can. That ice is made of water can also. And so to say that
a proposition is analytical is only to say that it elucidates the
constituent elements of a concept, the sine qua nons of any concept
without which the concept would not be.
The danger is always to avoid converting this into an ontological or
metaphysical discussion. I am not talking about all those things the
actual ice can do, or how it is affected by circumstance or "context"
due to the various natures or identities involved. I can only see this
as the source of many synthetic propositions, some a priori and some
a posteriori. But the consideration here is only with that necessity
bound up with types of propositions, not with the necessity bound up
with identities in nature. And so this discussion is really nothing
more than the eludication of rules of method: namely, Kant's synthetic
and analytic methods.
Critique boils down to methodology, primarily, the method by which
philosophy and science are to be constructed, and how their various
and sundry propositions are to be construed. It is important to note
that for Kant the introduction to his Critique did not invoke
philosophy, but science and mathematics. That is, those basic truths
upon which his Critique of philosophy were formed were borrowed from
the truths of science and mathematics, not so much in their content as
in their form, particularly, how the form of their propositions came
to form truths. Borrowing from this, Kant determined that philosophy
itself also utilizes such forms, only historically not as precisely
formulated, mainly because the propositions of philosophy had not been
as intuitive (meaning, they are quite abstracted from the evidence and
the rule of the senses, as is the nature of philosophy).
Not that it was only philosophy that required Kant's help. Science and
mathematics can also benefit from having the form of their truths
elucidated in order to reduce the amount of confusion that is always
involved in any attempt at garnering abstract truths.
Sunday, April 20, 2008
"What turned you off of Objectivism?"
The title of this post came from a question asked on the "AynRandContraHumanNature" blog. I know there are basically two answers, one coming from the ex-Objectivist being asked and the other coming from his ex-friends whose personal individualities are still enmeshed in the movement and the aura of Ayn Rand's beliefs. Those who have left the movement will relate various reasons for the break. But those still in the movement think they know the real reason: there is some deep flaw in the ex-Objectivist's premises so profound that not even Objectivism can root it out.
What amazing mind-readers.
I know for me it started slowly, over time. The first awareness I have of breaking away (although I didn't see it coming at that time) occurred when curiosity drove me to find a wider historical context for Objectivism; but it didn't seem to fit in anywhere, it resisted labeling beyond itself. And so the system (such as it is) kind of just hung in mid-air attached to nothing, originating nowhere. This was intellectually dissatisfying, and so Objectivism slowly turned from the focus of my life to an anomaly to be studied from afar, like an insect.
The process was aided along by my eventual realization that Rand and Peikoff were light-years away from an understanding of Immanuel Kant, "the most evil man in mankind's history." Their critique of Critique is so deeply flawed that there is no hope for it. Even Kant's harshest critics do a better job of critiquing than both Rand and Peikoff combined, whose Kant sound-bites were carefully hand-selected and aimed at an audience of converts willing to swallow it all hook, line, and sinker; or simply to those who despise grandiloquent systems of thought anyway, having so recently had them rammed down their throats in college.
Ayn Rand, a philosopher who wrote and spoke about Reality and A is A, had little idea about reality around her. Her break with reality became more evident with the passage of time, culminating in Atlas Shrugged, a novel which is ingenius yet utterly ridiculous, sane in its utter insanity, and gigantic in inverse proportion to the philosophy it attempts to put forth. In this work Rand portrayed a world ripped out of the romantic 19th century and flung into the 20th, consisting of a combination of dazzling, newfangled technology bordering on and then acquiring the status of science fiction, and old-fashioned chutzpah in which politicians sound like 1920s gangsters and leaders of industry behave more like fantasy adventurers of yore. And although Rand admits that this is all dramatization designed to pique the interest of potential fans, and that she never expected anyone to actually recite the oath of egoism ("I swear, by my life and my love of it..."), one begins to wonder how much she really understood that to be the case. Because, in her later essays, characterizations of real people, politicians and such, sadly begin to resemble characterizations from one of her fantasy dramas.
Even more sad is the plight of those whose egos, once their own, are still caught up in the philosophy of a dead cult-leader, having sacrificed their minds and souls to a goddess who most likely did not originally intend to take on such status, but when she did, played it to the hilt and then some.
What amazing mind-readers.
I know for me it started slowly, over time. The first awareness I have of breaking away (although I didn't see it coming at that time) occurred when curiosity drove me to find a wider historical context for Objectivism; but it didn't seem to fit in anywhere, it resisted labeling beyond itself. And so the system (such as it is) kind of just hung in mid-air attached to nothing, originating nowhere. This was intellectually dissatisfying, and so Objectivism slowly turned from the focus of my life to an anomaly to be studied from afar, like an insect.
The process was aided along by my eventual realization that Rand and Peikoff were light-years away from an understanding of Immanuel Kant, "the most evil man in mankind's history." Their critique of Critique is so deeply flawed that there is no hope for it. Even Kant's harshest critics do a better job of critiquing than both Rand and Peikoff combined, whose Kant sound-bites were carefully hand-selected and aimed at an audience of converts willing to swallow it all hook, line, and sinker; or simply to those who despise grandiloquent systems of thought anyway, having so recently had them rammed down their throats in college.
Ayn Rand, a philosopher who wrote and spoke about Reality and A is A, had little idea about reality around her. Her break with reality became more evident with the passage of time, culminating in Atlas Shrugged, a novel which is ingenius yet utterly ridiculous, sane in its utter insanity, and gigantic in inverse proportion to the philosophy it attempts to put forth. In this work Rand portrayed a world ripped out of the romantic 19th century and flung into the 20th, consisting of a combination of dazzling, newfangled technology bordering on and then acquiring the status of science fiction, and old-fashioned chutzpah in which politicians sound like 1920s gangsters and leaders of industry behave more like fantasy adventurers of yore. And although Rand admits that this is all dramatization designed to pique the interest of potential fans, and that she never expected anyone to actually recite the oath of egoism ("I swear, by my life and my love of it..."), one begins to wonder how much she really understood that to be the case. Because, in her later essays, characterizations of real people, politicians and such, sadly begin to resemble characterizations from one of her fantasy dramas.
Even more sad is the plight of those whose egos, once their own, are still caught up in the philosophy of a dead cult-leader, having sacrificed their minds and souls to a goddess who most likely did not originally intend to take on such status, but when she did, played it to the hilt and then some.
Monday, March 17, 2008
For Rand, perception of color and length are only in the subject
This is for you non-believing Randroids I have conversed with who
refuse to accept the idea I've put forth here that color doesn't exist
outside of perception.
The context is a question about the primary-secondary quality
"dichotomy."
AR:
"We perceive light vibrations as color. Therefore you would say the
color is not in the object. The object absorbs certain parts of the
spectrum and reflects the others, and we perceive that fact of reality
by means of the structure of the eye. But then ask yourself: don't we
perceive all attributes by our means of perception - including length?
Everything we perceive is the result of our processing, which is not
arbitrary or subjective." (ITOE2, Appendix, 279)
("Processing"?... as in "I am HAL, pleased to meet you Commander
Data"? Are humans thinking machines? What would be the purpose in
nature evolving a thinking machine...)
First, I would like to get out of the way Rand's comment about
perception not being arbitrary or subjective. Fine. Whatever. It's
never been relevant to any of my points anyway. I am simply interested
in what *is*, not whether it is objective, arbitrary, or subjective.
Those labels are all just ideological blather, used in place of a chip
on one's shoulders in daring some arbitrary, subjectivist skeptic, who
doesn't even exist, to come knock it off. Nothing works like inventing
enemies in order to make one's position seem stronger, even
unbeatable.
But it is not necessary to work on Objectivism via ideological
conflict, that is the illusion she wanted to portray. It is necessary
merely to analyze Rand's writings for factual consistency, accuracy,
or just plain good old-fashioned internal logic (e.g., is it
self-contradictory?). And internal logic is not objective, it is not
anything ontological; neither is it "non-objective" because it
abstracts from all (objective, subjective, arbitrary) content of an
argument and judges only its formal presentation, that is, the formal
manner in which it is presented.
So with regard to the material quoted from the Appendix to ITOE, I
want to highlight the following for examination:
"...don't we perceive all attributes by our means of perception -
including length? Everything we perceive is the result of our
processing..."
The question boils down to asking, "but don't we perceive by means
of perception?" I know, you're thinking that the context is qualities,
or attributes, so I should not have dropped the word "attributes." But
is it relevant?
Not at all. Rand is talking past her interlocutor in her answer.
Because he (known only as "prof. c") specified only qualities such
as color, not attributes such as length. So Rand's example of length
is not relevant to the question, and this question doesn't all boil
down simply to the tautology regarding perception of that which is
perceived, qualities and attributes being held up as equals and not
distinguishable as either primary or secondary. Both are merely the
result of processed sense-data.
In this way, Rand reduced the question to her formula, A is A. And as
a result, implied that, just as color is not in the object, therefore
neither is length. This is why it was necessary for Rand to keep to
the example of color which is a quality and avoid reducing every such
example to perception.
refuse to accept the idea I've put forth here that color doesn't exist
outside of perception.
The context is a question about the primary-secondary quality
"dichotomy."
AR:
"We perceive light vibrations as color. Therefore you would say the
color is not in the object. The object absorbs certain parts of the
spectrum and reflects the others, and we perceive that fact of reality
by means of the structure of the eye. But then ask yourself: don't we
perceive all attributes by our means of perception - including length?
Everything we perceive is the result of our processing, which is not
arbitrary or subjective." (ITOE2, Appendix, 279)
("Processing"?... as in "I am HAL, pleased to meet you Commander
Data"? Are humans thinking machines? What would be the purpose in
nature evolving a thinking machine...)
First, I would like to get out of the way Rand's comment about
perception not being arbitrary or subjective. Fine. Whatever. It's
never been relevant to any of my points anyway. I am simply interested
in what *is*, not whether it is objective, arbitrary, or subjective.
Those labels are all just ideological blather, used in place of a chip
on one's shoulders in daring some arbitrary, subjectivist skeptic, who
doesn't even exist, to come knock it off. Nothing works like inventing
enemies in order to make one's position seem stronger, even
unbeatable.
But it is not necessary to work on Objectivism via ideological
conflict, that is the illusion she wanted to portray. It is necessary
merely to analyze Rand's writings for factual consistency, accuracy,
or just plain good old-fashioned internal logic (e.g., is it
self-contradictory?). And internal logic is not objective, it is not
anything ontological; neither is it "non-objective" because it
abstracts from all (objective, subjective, arbitrary) content of an
argument and judges only its formal presentation, that is, the formal
manner in which it is presented.
So with regard to the material quoted from the Appendix to ITOE, I
want to highlight the following for examination:
"...don't we perceive all attributes by our means of perception -
including length? Everything we perceive is the result of our
processing..."
The question boils down to asking, "but don't we perceive by means
of perception?" I know, you're thinking that the context is qualities,
or attributes, so I should not have dropped the word "attributes." But
is it relevant?
Not at all. Rand is talking past her interlocutor in her answer.
Because he (known only as "prof. c") specified only qualities such
as color, not attributes such as length. So Rand's example of length
is not relevant to the question, and this question doesn't all boil
down simply to the tautology regarding perception of that which is
perceived, qualities and attributes being held up as equals and not
distinguishable as either primary or secondary. Both are merely the
result of processed sense-data.
In this way, Rand reduced the question to her formula, A is A. And as
a result, implied that, just as color is not in the object, therefore
neither is length. This is why it was necessary for Rand to keep to
the example of color which is a quality and avoid reducing every such
example to perception.
a bit more on Rand and class-formation
In my first post I examined class-formation as it related to concept-formation and the ancient problem of universals, in which I stated that Rand did not bother or failed to examine classification theory. There is more detail to that theory than I really need to get into here, I just want to point out that while Rand did not examine class-formation, she did bring it up early on in ITOE.
'A unit is an existent regarded as a separate member of a group of two or more similar members. (Two stones are two units; so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground.) Note that the concept "unit" involves an act of consciousness (a selective focus, a certain way of regarding things), but that it is not an arbitrary creation of consciousness: it is a method of identification or classification according to the attributes which a consciousness observes in reality. This method permits any number of classifications and cross-classifications: one may classify things according to their shape or color or weight or size or atomic structure; but the criterion of classification is not invented, it is perceived in reality. Thus the concept "unit" is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.' (ITOE2, 6-7; emphasis mine.)
There are a number of great points to be made about this theory, sloppy as it is. It takes for granted knowledge of similarity pages before Rand actually goes into the subject in chapter 2.
But as always, it takes for granted concepts already formed, such as "stone" and "ground." And so we are left with the circular notion of classifying units on the basis of their concepts in order to eventually form (the same) concepts out of these units.
It appears that her idea of what classification involves is right on: "one may classify things according to their shape or color or weight or size or atomic structure." So true.
The "act of consciousness" mentioned is "a method of identification or classification according to the attributes which a consciousness observes in reality." What method that is, she doesn't say. Unit-formation?
Strangely enough, when forming a unit it seems that one is really forming a class out of existents: but aren't existents units? Or is "existent" just the general idea of a thing -- which is still a unit?
She used the term "criterion" to describe the attributes found to be similar, but they are not criteria of anything in the proper sense of the word. So it is difficult to know what she means in that passage, except to say that an existent is not an arbitrary creation of the mind. Well, of course it isn't. There's nothing like being able to state a simple fact and making it sound important as hell.
Then there is this odd statement: 'Thus the concept "unit" is a bridge between metaphysics and epistemology,' as if metaphysics had anything to do with this. But the context indicates that Rand is juxtaposing mind (epistemology) and reality (metaphysics). It sounds really cool but in reality it is meaningless jargon.
Finally, Rand leaves us with the following word-salad: 'units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.'
I see. Units do not exist, what exists are things, but units are things.
And what is this about "existing relationships"? Has Rand yet explained how knowledge of existing relationships is acquired? Has she determined whether or not these relationships are "metaphysical" or "epistemological," that is, is the very concept of a "relationship" another idea like a "unit," that doesn't exist, because what exists are things, but relationships are things...um, viewed in certain existing relationships. This is circular.
But then, I've been known to point out in the past that ITOE is a concrete example of the petitio principii in action.
So what is it about classification (or class-formation) that lends so much credence to Rand's argument here? We all know what she's talking about, we take it for granted as a given, it seems to be a scientifically established point. But it is never properly analyzed by Rand.
'A unit is an existent regarded as a separate member of a group of two or more similar members. (Two stones are two units; so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground.) Note that the concept "unit" involves an act of consciousness (a selective focus, a certain way of regarding things), but that it is not an arbitrary creation of consciousness: it is a method of identification or classification according to the attributes which a consciousness observes in reality. This method permits any number of classifications and cross-classifications: one may classify things according to their shape or color or weight or size or atomic structure; but the criterion of classification is not invented, it is perceived in reality. Thus the concept "unit" is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.' (ITOE2, 6-7; emphasis mine.)
There are a number of great points to be made about this theory, sloppy as it is. It takes for granted knowledge of similarity pages before Rand actually goes into the subject in chapter 2.
But as always, it takes for granted concepts already formed, such as "stone" and "ground." And so we are left with the circular notion of classifying units on the basis of their concepts in order to eventually form (the same) concepts out of these units.
It appears that her idea of what classification involves is right on: "one may classify things according to their shape or color or weight or size or atomic structure." So true.
The "act of consciousness" mentioned is "a method of identification or classification according to the attributes which a consciousness observes in reality." What method that is, she doesn't say. Unit-formation?
Strangely enough, when forming a unit it seems that one is really forming a class out of existents: but aren't existents units? Or is "existent" just the general idea of a thing -- which is still a unit?
She used the term "criterion" to describe the attributes found to be similar, but they are not criteria of anything in the proper sense of the word. So it is difficult to know what she means in that passage, except to say that an existent is not an arbitrary creation of the mind. Well, of course it isn't. There's nothing like being able to state a simple fact and making it sound important as hell.
Then there is this odd statement: 'Thus the concept "unit" is a bridge between metaphysics and epistemology,' as if metaphysics had anything to do with this. But the context indicates that Rand is juxtaposing mind (epistemology) and reality (metaphysics). It sounds really cool but in reality it is meaningless jargon.
Finally, Rand leaves us with the following word-salad: 'units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.'
I see. Units do not exist, what exists are things, but units are things.
And what is this about "existing relationships"? Has Rand yet explained how knowledge of existing relationships is acquired? Has she determined whether or not these relationships are "metaphysical" or "epistemological," that is, is the very concept of a "relationship" another idea like a "unit," that doesn't exist, because what exists are things, but relationships are things...um, viewed in certain existing relationships. This is circular.
But then, I've been known to point out in the past that ITOE is a concrete example of the petitio principii in action.
So what is it about classification (or class-formation) that lends so much credence to Rand's argument here? We all know what she's talking about, we take it for granted as a given, it seems to be a scientifically established point. But it is never properly analyzed by Rand.
Friday, March 14, 2008
On Ayn Rand's failure to examine "class-formation"
References to ITOE2 refer to Ayn Rand's "Introduction
to Objectivist Epistemology," second edition.
Let me start off by defining what I mean by a "class."
A class is "a collection of things sharing a common attribute."
http://wordnet.princeton.edu/perl/webwn
An example of this would be the class of red books. Notice that I have
not defined a concept here, only a class. It's distinguishing
characteristic is redness, which is a universal, but not essential to
forming a special concept of red books. (There is also the universal
'bookness' characterizing the books, but let's just discuss redness
for now.)
In order to designate a concept it was necessary for Rand to designate
a special form of class, known as a concept, which integrates two or
more instances by means of certain properties known as essentials.
These essentials are defined as distinguishing characteristics of an
entity, distinguished "from the other entities belonging to the same
genus." (ITOE2, 41)
(I'll ignore the fact that her theory of concept-formation by
essentials illustrates a logical fallacy known as the 'fallacy of
difference,' which states that distinguishing characteristics are not
necessarily essentials, as rationality is not necessarily essential to
manness merely because it is a characteristic used to distinguish
man from animals. Or perhaps let's just say rationality is only
essential to forming the concept, it is not necessarily essential in
the metaphysical sense.)
In class theory it is not necessary to denote two or more instances in
forming the class. A class can consist of one member or even zero, for
example, if someone painted an elephant pink, and it was the only one
in the world, the only member of its class; or if there were no pink
elephants in existence, the class would be empty.
No attribute is essential to forming a class, what matters is that the
uniting characteristic is a universal, that is, the attribute is shared
by all members of the class such that it helps to define the class.
In that case, the attribute is a property, belonging to individual
entities as members of the class, becomes known as a universal.
A universal is held in common by all members of a class, even if the
class consists of only one member, or none.
ITOE consists of some kind of answer to the problem of universals,
accomplished, in Rand's own words, "by presenting my theory of
concepts" (Ibid, 3). And in her mind, universals are equated by Rand
with concepts or abstractions (1), reducing the metaphysical
problem to a problem of concepts.
So as a result of Rand neglecting to examine the issue of classes upon
which is genetically dependent the issue of concepts, she did not
thoroughly examine the issue of universals connected with it, assuming
the problem of universals is only an epistemological one (which it is
not; it is primarily metaphysical at its root). And if a particular
property can be universal to a class consisting of only one member,
then it follows that a concept can be formed from a class consisting
of only one member.
There is an example of such a class found in ITOE2, and that is the
concept or axiom "existence." It seems to violate Rand's rules of
concept-formation, particularly that of the conceptual common
denominator, "The characteristic(s) reducible to a unit of
measurement, by means of which man differentiates two or more
existents from other existents possessing it." (14) In this case there
is only one existent, existence itself. (For those of you who believe
that "existence" is only a concept, Rand believed that concepts are
also existents, indeed, even concrete mental entities.[156])
At one time I was led to believe that the axiomatic concept 'existence'
was no concept at all, that is, by Rand's own rules of concept-formation
(which she rationalized as a "special" exception [58-59]). However,
I now realize that the problem lies with her theory of concept-formation,
most basically, her neglect in examining the wider genus determining the
very notion of a concept, and that is, the class theory behind it.
Rand defined "concept" in one place as "a mental integration of
two or more units which are isolated according to a specific
characteristic(s) and united by a specific definition."(9) However,
"a mental integration" is not specific enough, as "set" or "class"
also constitute mental integrations of material serving as members
distinguished by properties held in common, that is, universals.
("Class" and "set" are often used interchangeably, but "set" is more
of a mathematical expression to which I don't want this analysis to
be limited.)
How does this issue apply to the problem of universals? This problem
does not rely on the issue of class or even concept, but how man has
knowledge of 'redness' despite the fact that, in reality, there is no
particular color that he can distinguish as epitomizing "redness." Or
perhaps many things can serve this function; however, all of them will
vary in their particular shade of red. Thus the question is not "where
is the manness in men" (2), but "How does man's knowledge of manness
arise?" Or, "How does man's knowledge of universals arise from amidst
the great variety of particulars around him?" This is a question of
epistemology, and it is not answered by any theory of
concept-formation.
Geometry can help answer this question, or at least, pose the question
in a more useful way. For example, there are no straight lines in
reality, none at any rate which correspond to man's concept of a
straight line. A straight line is a mental construct, an ideal
concept, used for creating or defining approximations of straight
lines in reality based in utility. Every straight line in reality
instantiates the universal "straightness," without however
substantiating it. There is no substantiating a universal because
there is no substance, no entity in reality equal to this mental
entity, only approximations to it. There is, to put it in terms of
Rand's question (2), straightness in a straight entity, but only
insofar as a mind puts it there. The universal therefore lies a priori
to the judgment of that which is considered straight.
And so, as Aristotle indicated in his Metaphysics II §8, Being and
Unity, the two highest universals, are as one in the same entity, only
I say not in the ontological sense. The being, the whatness, the
universal, is a product of the mind, the unity is universals to any
particular individual in reality (a unit). The product of their
synthesis is variety in experience, without which, in Aristotle's
words, "there is much difficulty in seeing how there will be anything
else besides these, - I mean, how things will be more than one in
number." For if Being and Unity, two universals, existed in
themselves, as properties of an entity, then it would be impossible
to have the concepts of plurality, variety, or many-ness.
And so the properties we designate to individuals, when these
individuals are formed into classes, become universals, but are not
thereby granted existence outside a thinking being qua universals.
Induction only gives the material for creating the universal, but as
essential to its completion there must be concepts borrowed from
metaphysics, that is, metaphysical properties attributed to the
members of the class. For example, Being (Substance), Unity, and
Necessity. Metaphysical concepts grant objective truth to inductive
reasoning, and not merely relative truth.
This class of concepts was not derived from empirical reality, as if
we could somehow intuit its Platonic form, they are nevertheless
metaphysical as deriving from man's primary *form* of cognition which
is rational. Just as man's metaphysical nature demands that he find
straightness in that which is not, as a formal standard to serve
practical building purposes, so his metaphysical form of reasoning
demands that he produce concepts of things from the vastness and
variety of nature, utilizing concepts of his own devising a priori.
to Objectivist Epistemology," second edition.
Let me start off by defining what I mean by a "class."
A class is "a collection of things sharing a common attribute."
http://wordnet.princeton.edu/perl/webwn
An example of this would be the class of red books. Notice that I have
not defined a concept here, only a class. It's distinguishing
characteristic is redness, which is a universal, but not essential to
forming a special concept of red books. (There is also the universal
'bookness' characterizing the books, but let's just discuss redness
for now.)
In order to designate a concept it was necessary for Rand to designate
a special form of class, known as a concept, which integrates two or
more instances by means of certain properties known as essentials.
These essentials are defined as distinguishing characteristics of an
entity, distinguished "from the other entities belonging to the same
genus." (ITOE2, 41)
(I'll ignore the fact that her theory of concept-formation by
essentials illustrates a logical fallacy known as the 'fallacy of
difference,' which states that distinguishing characteristics are not
necessarily essentials, as rationality is not necessarily essential to
manness merely because it is a characteristic used to distinguish
man from animals. Or perhaps let's just say rationality is only
essential to forming the concept, it is not necessarily essential in
the metaphysical sense.)
In class theory it is not necessary to denote two or more instances in
forming the class. A class can consist of one member or even zero, for
example, if someone painted an elephant pink, and it was the only one
in the world, the only member of its class; or if there were no pink
elephants in existence, the class would be empty.
No attribute is essential to forming a class, what matters is that the
uniting characteristic is a universal, that is, the attribute is shared
by all members of the class such that it helps to define the class.
In that case, the attribute is a property, belonging to individual
entities as members of the class, becomes known as a universal.
A universal is held in common by all members of a class, even if the
class consists of only one member, or none.
ITOE consists of some kind of answer to the problem of universals,
accomplished, in Rand's own words, "by presenting my theory of
concepts" (Ibid, 3). And in her mind, universals are equated by Rand
with concepts or abstractions (1), reducing the metaphysical
problem to a problem of concepts.
So as a result of Rand neglecting to examine the issue of classes upon
which is genetically dependent the issue of concepts, she did not
thoroughly examine the issue of universals connected with it, assuming
the problem of universals is only an epistemological one (which it is
not; it is primarily metaphysical at its root). And if a particular
property can be universal to a class consisting of only one member,
then it follows that a concept can be formed from a class consisting
of only one member.
There is an example of such a class found in ITOE2, and that is the
concept or axiom "existence." It seems to violate Rand's rules of
concept-formation, particularly that of the conceptual common
denominator, "The characteristic(s) reducible to a unit of
measurement, by means of which man differentiates two or more
existents from other existents possessing it." (14) In this case there
is only one existent, existence itself. (For those of you who believe
that "existence" is only a concept, Rand believed that concepts are
also existents, indeed, even concrete mental entities.[156])
At one time I was led to believe that the axiomatic concept 'existence'
was no concept at all, that is, by Rand's own rules of concept-formation
(which she rationalized as a "special" exception [58-59]). However,
I now realize that the problem lies with her theory of concept-formation,
most basically, her neglect in examining the wider genus determining the
very notion of a concept, and that is, the class theory behind it.
Rand defined "concept" in one place as "a mental integration of
two or more units which are isolated according to a specific
characteristic(s) and united by a specific definition."(9) However,
"a mental integration" is not specific enough, as "set" or "class"
also constitute mental integrations of material serving as members
distinguished by properties held in common, that is, universals.
("Class" and "set" are often used interchangeably, but "set" is more
of a mathematical expression to which I don't want this analysis to
be limited.)
How does this issue apply to the problem of universals? This problem
does not rely on the issue of class or even concept, but how man has
knowledge of 'redness' despite the fact that, in reality, there is no
particular color that he can distinguish as epitomizing "redness." Or
perhaps many things can serve this function; however, all of them will
vary in their particular shade of red. Thus the question is not "where
is the manness in men" (2), but "How does man's knowledge of manness
arise?" Or, "How does man's knowledge of universals arise from amidst
the great variety of particulars around him?" This is a question of
epistemology, and it is not answered by any theory of
concept-formation.
Geometry can help answer this question, or at least, pose the question
in a more useful way. For example, there are no straight lines in
reality, none at any rate which correspond to man's concept of a
straight line. A straight line is a mental construct, an ideal
concept, used for creating or defining approximations of straight
lines in reality based in utility. Every straight line in reality
instantiates the universal "straightness," without however
substantiating it. There is no substantiating a universal because
there is no substance, no entity in reality equal to this mental
entity, only approximations to it. There is, to put it in terms of
Rand's question (2), straightness in a straight entity, but only
insofar as a mind puts it there. The universal therefore lies a priori
to the judgment of that which is considered straight.
And so, as Aristotle indicated in his Metaphysics II §8, Being and
Unity, the two highest universals, are as one in the same entity, only
I say not in the ontological sense. The being, the whatness, the
universal, is a product of the mind, the unity is universals to any
particular individual in reality (a unit). The product of their
synthesis is variety in experience, without which, in Aristotle's
words, "there is much difficulty in seeing how there will be anything
else besides these, - I mean, how things will be more than one in
number." For if Being and Unity, two universals, existed in
themselves, as properties of an entity, then it would be impossible
to have the concepts of plurality, variety, or many-ness.
And so the properties we designate to individuals, when these
individuals are formed into classes, become universals, but are not
thereby granted existence outside a thinking being qua universals.
Induction only gives the material for creating the universal, but as
essential to its completion there must be concepts borrowed from
metaphysics, that is, metaphysical properties attributed to the
members of the class. For example, Being (Substance), Unity, and
Necessity. Metaphysical concepts grant objective truth to inductive
reasoning, and not merely relative truth.
This class of concepts was not derived from empirical reality, as if
we could somehow intuit its Platonic form, they are nevertheless
metaphysical as deriving from man's primary *form* of cognition which
is rational. Just as man's metaphysical nature demands that he find
straightness in that which is not, as a formal standard to serve
practical building purposes, so his metaphysical form of reasoning
demands that he produce concepts of things from the vastness and
variety of nature, utilizing concepts of his own devising a priori.
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