On definitions and necessity
Chris Cathcart
little thought into the matter of definitions with some clarifying aid
from ITOE. I'm quoting from the page cited in the -Ayn Rand Lexicon-
(p.117):
"A definition is a statement that identifies the nature of the units
subsumed under a concept."
and then, later:
"The purpose of a definition is to distinguish a concept from all
other concepts and thus keep its units differentiated from all other
existents." (ITOE, 52)
Now, keep in mind that Rand also said that "essence" is
epistemological. From p. 118 of the ARL:
"A definition must identify the *nature* of the units, i.e., the
*essential* characteristics without which the units would not be the
kind of existents they are. (ITOE, 55)
How does all this make sense, if for Rand, the *nature* of a thing
(all its characteristics) is not to be confused with its *essential*
(distinguishing) characteristics?
Because while the definition captures what is true of necessity for
all the units -- what is common to the nature of *all* of the units
subsumed under the concept -- the purpose of a definition is to
further identify what is necessarily the case for all the units of the
concept, and to *distinguish* it from all other units for which this
is not necessarily the case.
IOW, the function of a definition is to identify the *nature* of the
units subsumed under the concept in a way that *distinguishes* them
from other sorts of units.
Now, true enough, the *nature* of one apple is such that it is red,
while the nature of another is that it is green. These are the kinds
of differences that a *definition* is not intended to capture as they
do not distinguish apples from non-apples. They are, nonetheless,
differences that are noted and captured under under the *concept*
"apple" in a very open-ended fashion. A concept, in other words, can
subsume vast amounts of information -- only that our means of
economically referencing it is by means of a symbol (term) that we use
to *define* the concept.
The definition only states what by necessity *distinguishes* the
units, but the vast amount of information that can be referenced under
the concept can also capture things that are by necessity true for all
the units.
In the case of ice: the capacity for floating on liquid water does not
*distinguish* ice from all other units, because after all, there are
other, non-ice things that can float on liquid water. The capacity is
therefore not stated in the definition. It is nonetheless contained
in the great amount of information that the concept references, that
ice must float on liquid water in order to be ice.
So it is not the case, per Kant, that by adding "capable of floating
on liquid water" to the term "ice" is adding something new that's not
already contained in the concept of ice. Concepts capture what is
true by necessity for the units subsumed under the concept in an open-
ended, contextual fashion; the only kind of "adding" being done is the
adding that was done *historically* as our knowledge of ice expanded;
given what we *now* know about ice that we may not have known before
*historically speaking*, "floats on liquid water" does not *add*
anything to our concept of ice that isn't already contained in it. We
are not "going outside" of the concept to state truths about ice that
aren't captured in the concept alone. It is merely not captured in
the definition alone.
In sum: there are things necessarily true with regard to a concept and
captured in the concept that are not captured in the definition
alone. The definition only distinguishes -- saying what is
necessarily true *only of these units* and not of other units. The
placement and use of the term "only" here is crucial; people have
gotten confused and thought that a definition states "only what is
necessary to the units." But the difference should be clear.
Malrassic Park
<cath...@gmail.com> wrote:
>In the case of ice: the capacity for floating on liquid water does not
>*distinguish* ice from all other units, because after all, there are
>other, non-ice things that can float on liquid water. The capacity is
>therefore not stated in the definition. It is nonetheless contained
>in the great amount of information that the concept references, that
>ice must float on liquid water in order to be ice.
Yes, and some of this information is synthetic while some of it is
analytic to the concept "ice." These may all be necessary truths
concerning ice, and being synthetic or analytic does not detract from
these as truths.
But what does it mean to be "contained" or "not contained" in a
concept? Let's find out...
>So it is not the case, per Kant, that by adding "capable of floating
>on liquid water" to the term "ice" is adding something new that's not
>already contained in the concept of ice. Concepts capture what is
>true by necessity for the units subsumed under the concept in an open-
>ended, contextual fashion; the only kind of "adding" being done is the
>adding that was done *historically* as our knowledge of ice expanded;
>given what we *now* know about ice that we may not have known before
>*historically speaking*, "floats on liquid water" does not *add*
>anything to our concept of ice that isn't already contained in it. We
>are not "going outside" of the concept to state truths about ice that
>aren't captured in the concept alone. It is merely not captured in
>the definition alone.
This is easy to see by mathematical example. Contained in the concept
of the number 4 (staying with the natural numbers) is the idea of a
combination of numbers, such as 1+1+1+1, or 2+2, or 3+1. The example
most commonly taken from these is 2+2=4.
2+2 is more than just a combination, it is a synthesis (or
integration) of two numbers which equals 4. But it is analytical to
the concept of the number 4 that it consists of adding 2 and 2. This
is just a matter of going backwards (right to left) or forwards (left
to right) in the equation 2+2=4. To go backwards is to divide the
number 4 into two elements by analysis. To go forwards is to
synthesize these two elements back into the number 4.
This formulation is easily applied to the concept 'furniture' in
Rand's example at ITOE 22. Notice that Rand has done part of the work
for us already, by reference to the "constituent concepts" (sometimes
also called "constituent units" or "constituent particulars") of the
concept. Those constituents are nothing more than the various items
of furniture: tables, chairs, beds, armoires, etc. The concept
"furniture" is a product of their synthesis into that concept.
Precisely how this takes place - by differentiation and integration -
is irrelevant in this context, just as the exact mathematical process
was irrelevant to the previous example, although "integration" is
certainly synonymous with "synthesis." And by the same token, a
"constituent concept" or "unit" is the result of analyzing a "wider"
concept into its components.
At one point Rand supported my contention that integration and
synthesis are the same process: "The uniting involved is not a mere
sum, but an integration, i.e., a blending of the units into a single,
new mental entity which is used thereafter as a single unit of thought
(but which can be broken into its component units whenever required)."
(ITOE, 9)
So you have, within Rand's own epistemological context, the very ideas
of synthesis and analysis which are then later attacked by Peikoff, et
al.
The reason 2+2=4 was thought analytical or even tautological was
probably because the answer, 4, was taken for granted, and so 2+2=4
was held equivalent to 4=4. But this ignores the process of synthesis
(or integration) by which the answer 4 was obtained which is why Kant
suggested using much larger numbers on the left side of the equation.
--
" If I had remembered that the name 'Galt' appears
in one of her books, I would have chosen a different
name for my character."
Stephen R. Donaldson, "Gradual Interview"
Chris Cathcart
> This formulation is easily applied to the concept 'furniture' in
> Rand's example at ITOE 22. Notice that Rand has done part of the work
> for us already, by reference to the "constituent concepts" (sometimes
> also called "constituent units" or "constituent particulars") of the
> concept. Those constituents are nothing more than the various items
> of furniture: tables, chairs, beds, armoires, etc.
I don't know why you keep doing this, but the constituent units of a
higher-level concept is a lower-level concept. The units are mental
entities. There are singular tables, singular chairs, etc., but no
singular furnitures. There are singular items that, via abstraction
from abstraction, we come to classify as *items of* furniture. But
nothing like a generic "furniture" is to be found in perception.
There is no generic "item of furniture" in perception, either. There
are only particulars, and those particulars have unique qualities or
characteristics that get them placed in a particular class at a
perceptible level. We don't grasp "furniture" by pointing to
particular things perceptibly or ostensively; it requires a conceptual-
hierarchical cognitive context.
In any event, the claim that the constituent units of a higher-level
concept is the perceptible-level units is so very misleading at best;
understanding the constituent units as being lower-level concepts is
most helpful and straightforward.
I'm still not clear on where you think you're going in your
responses. I keep pointing out that for Kant we don't get necessity
from experience, and that synthesis plays some central role in giving
rise to necessity. Do I have this wrong about Kant? You keep saying
that syntheticity and analyticity are not important to the issue of
necessity. Let's say that for Kant, "synthesis" was necessary to *our
cognition* of things as necessary. This would certainly make sense of
epistemological Kantians like Von Mises who say that our understanding
of economic phenomena rests on "synthetic a priori" judgments that
bring necessity to our statements about those observed phenomena.
Furthermore, I understand them to be saying that it is in virtue of
these synthetic a priori judgments that *we can't cognize the
appearances in any other way than as exhibiting necessity*. That part
I think I get well enough; the *issue*, though, is whether we need
this cognizing in order for there to *be* necessity in what we
experience. I don't see what the point of Kant's response to Hume is
otherwise, if he is not addressing this issue. So of course I see the
issues of analyticity and syntheticity as all closely tied up with the
matter of necessity if we're going to discuss the differences between
a neo-Aristotelian understanding of necessity and a Kantian one.
There's other stuff but I'll leave it at that for now. BTW, are you
familiar with Rothbard's only philosophically useful essay in his
career, "In Defense of 'Extreme Apriorism'" explaining his defense of
Misesian praxeology as a methodological approach to the human
sciences, while rejecting his metaphysics?
Malrassic Park
<cath...@gmail.com> wrote:
>On May 27, 7:09 pm, Malrassic Park <malen...@hotmail.com> wrote:
>
>> This formulation is easily applied to the concept 'furniture' in
>> Rand's example at ITOE 22. Notice that Rand has done part of the work
>> for us already, by reference to the "constituent concepts" (sometimes
>> also called "constituent units" or "constituent particulars") of the
>> concept. Those constituents are nothing more than the various items
>> of furniture: tables, chairs, beds, armoires, etc.
>
>I don't know why you keep doing this,
Because it's the answer, and the next thing you stated did not
contradict me.
>but the constituent units of a higher-level concept is a lower-level
>concept.
I have no issue with that. It's just that Rand calls them
"particulars" and this could mean "particular units," where "units"
refers to whatever they are, concrete or not. I'm not stuck on the
concrete-bound level simply because that's what this one example,
which I got from ITOE, entails. I'm not saying that "furniture" is a
concrete object. None of these side issues even touch on the topic of
syntheticity.
>The units are mental
>entities. There are singular tables, singular chairs, etc., but no
>singular furnitures. There are singular items that, via abstraction
>from abstraction, we come to classify as *items of* furniture. But
>nothing like a generic "furniture" is to be found in perception.
>There is no generic "item of furniture" in perception, either. There
>are only particulars, and those particulars have unique qualities or
>characteristics that get them placed in a particular class at a
>perceptible level. We don't grasp "furniture" by pointing to
>particular things perceptibly or ostensively; it requires a conceptual-
>hierarchical cognitive context.
Grasping the concept "furniture" requires a process of differentiation
and integration. Pointing to various articles of furniture would be
quite helpful in this, it is necessary but not sufficient to the task
of forming the concept. A "cognitive context" is certain necessary
to this, at least psychologically, and that would be a context capable
of differentiating and integrating units.
>In any event, the claim that the constituent units of a higher-level
>concept is the perceptible-level units is so very misleading at best;
>understanding the constituent units as being lower-level concepts is
>most helpful and straightforward.
I never said it was the perceptual level, Rand's example was not
necessarily the only one of its kind.
>I'm still not clear on where you think you're going in your
>responses. I keep pointing out that for Kant we don't get necessity
>from experience, and that synthesis plays some central role in giving
>rise to necessity. Do I have this wrong about Kant?
I defined all this in a previous post. Apparently you didn't see it.
The a priori is, by definition, the source of necessity along with
universality. A synthesis can also be a posteriori, meaning, not
necessary but contingent.
I also explained Kant's ideas about experience. For Kant this
necessity would depend on whether the experience is objective or
subjective. The subjective in experience does not give rise to
necessity. An example of an objective truth, given in experience, is
"ice floats on water." (I also stated this is true only so long as the
ice doesn't far outweigh the water so that their relative densities no
longer matter.)
And so I categorize and describe these in this fashion:
1. Synthetic a priori - objective truths, objective experience,
determined by laws of experience or laws of nature (Kant used both
phrases interchangably).
2. Synthetic a posteriori - subjective ideas and experiences, feelings
and nuances in experience at least in part given by the nature of
human psychology; circumstance given in association, merely by
psychological habit, or simply because it personally 'feels' right.
They are both synthetic simply in the combination of disparate
elements. That sunshine feels warm to the skin is synthetic. But it
feels warm only if you happen to be alive and aware, not asleep or
otherwise insensate, so it is an a posteriori "truth."
>You keep saying
>that syntheticity and analyticity are not important to the issue of
>necessity. Let's say that for Kant, "synthesis" was necessary to *our
>cognition* of things as necessary.
It is also necessarily the case the ice is a solid form of water, yet
this latter is analytical to its being ice.
>This would certainly make sense of
>epistemological Kantians like Von Mises who say that our understanding
>of economic phenomena rests on "synthetic a priori" judgments that
>bring necessity to our statements about those observed phenomena.
The a priori in experience carries along with it necessity, not the
syntheticity.
>Furthermore, I understand them to be saying that it is in virtue of
>these synthetic a priori judgments that *we can't cognize the
>appearances in any other way than as exhibiting necessity*. That part
>I think I get well enough; the *issue*, though, is whether we need
>this cognizing in order for there to *be* necessity in what we
>experience. I don't see what the point of Kant's response to Hume is
>otherwise, if he is not addressing this issue. So of course I see the
>issues of analyticity and syntheticity as all closely tied up with the
>matter of necessity if we're going to discuss the differences between
>a neo-Aristotelian understanding of necessity and a Kantian one.
Analyticity and necessity are tied together, but only because there is
no such thing as an "analytic a posteriori" proposition. So
analyticity is by default a priori, which is therefore necessary.
Syntheticity is allied with necessity only in terms of the synthetic
a priori. If von Mises declared the judgments concerning economic
phenomena to be one and all synthetic a priori, then he must have
considered them as necessary and inevitable as the law of causality,
and as objectifying not only experience but perhaps also predictions
made concerning experience.
>There's other stuff but I'll leave it at that for now. BTW, are you
>familiar with Rothbard's only philosophically useful essay in his
>career, "In Defense of 'Extreme Apriorism'" explaining his defense of
>Misesian praxeology as a methodological approach to the human
>sciences, while rejecting his metaphysics?
I've heard of it.
Chris Cathcart
being the student of Kant, I'm asking you. Does Kant say that all
analytic truths are necessary, and that at least some synthetic truths
are necessary, not in virtue of drawing out the meaning of the concept
itself but in virtue of some apriori thingy we bring to cognition of
appearances?
Malrassic Park
The term "truths" is the only problematic part of your question,
because all truths are necessary truths. I'm not including personal or
subjective "truths" that people lay claim to, such as faith and the
like. And in the post you're replying to, I only called the latter
"ideas and experiences," not truths.
So now that I've clarified that issue, I'll simply repeat that the
a priori is the source of necessarily true judgments, aka truths.
These a priori judgments can be either synthetic or analytic.
But as I understand your previous question, it concerned whether the
a priori is "a kind of knowledge held independently of experience" (to
quote http://www.nutters.org/docs/kant-sap). The context of the whole
question is an argument against Hume, that the a priori is not the
result of constant habitual empirical associations as with causality,
it is part of the cognitive framework which we bring to appearances.
So it is not so much a question of whether or not the a priori is
independent of experience, but whether it is given empirically, or
transcendentally. (That the a priori is given in experience is
therefore not debatable, so it cannot be held independently of
experience.) If the Kantian a priori is empirical, as in Hume's
empiricism, then it cannot be governed by universality and necessity -
it is therefore not a priori, it is a posteriori, which is, as I said
previously, to be governed by contingent, subjective psychological
associations and even social conventions or just plain old faith. The
a priori, in Hume's view, would be given by mathematics which consists
one and all in analytical propositions constructed upon axioms. The
empirical world, on the other hand, only gives material for a
posteriori judgments for Hume who had no concept of a synthetic
a priori element in experience.
Robert J. Kolker
The
> empirical world, on the other hand, only gives material for a
> posteriori judgments for Hume who had no concept of a synthetic
> a priori element in experience.
> --
There is no synthetic a priori necessarily true judgement. All true
synthetic propositions are determined to be true a posteriori.
Every example of the synthetic a priori that Kant gave was subsequently
blown up. Non-Euclidean geometry, the empirical falsity of Newtonian
Mechanics, non-Archemedian number systems etc etc. 7 + 5 = 12 can be
proven by purely analytic deductive means (Peano Axioms and Peano
Arithmetic).
Bob Kolker
Malrassic Park
<robert...@hotmail.com> wrote:
>Malrassic Park wrote:
> The
>> empirical world, on the other hand, only gives material for a
>> posteriori judgments for Hume who had no concept of a synthetic
>> a priori element in experience.
>> --
>
>There is no synthetic a priori necessarily true judgement.
I don't care to discuss this with an algorithm.
Robert J. Kolker
>
> I don't care to discuss this with an algorithm.
That is because you are dead wrong on the matter of the synthetic a
prior, a bogus concept.
How many counterexamples to Kant's concepts do you require before you
admit Kant built his system on slush and quicksand.
Bob Kolker
Malrassic Park
<robert...@hotmail.com> wrote:
>Malrassic Park wrote:
>
>>
>> I don't care to discuss this with an algorithm.
>
>That is because you are dead wrong on the matter of the synthetic a
>prior, a bogus concept.
"That is because" reasoning equals ad hoc fallacy.
Potroast
> Per the discussion going on in the "a body has weight" thread, I put a
> little thought into the matter of definitions with some clarifying aid
> from ITOE. I'm quoting from the page cited in the -Ayn Rand Lexicon-
> (p.117):
>
> "A definition is a statement that identifies the nature of the units
> subsumed under a concept."
>
Most physical nouns (i.e. an apple) are easy. As the expression says a
picture is worth a thousand words, and sounds, and touch, and taste,
and other definitions to guide us. As a kicker physical objects tend
to have a very limited number of properties to remember.
Abstract concepts is where havoc enters the equation when it comes to
understanding essences. Define "justice". Define "truth". Define
"rational". Since there is nothing physical about the concepts the
only way we learn about them is through the words or through emotional
reactions that re-enforce a positive (or negative) reaction to an
experience.
This chaos over abstract definitions is (in my opinion) is one of
primary sources of conflict on this earth.
Potroast
> subsumed under a concept."
I should probably add... a definition of a word as important as
"definition" that oversimplifies its essence... is an inadequate
definition (makes perfect sense :). In practice definitions also have
the important property of conflicting uses... this is to say two (or
more) people can have two distinct understandings of the same sound/
writing that allegedly is a single essence. It can even boil down to
having a different emotional reaction to a word... which essentially
means there is at least 1 unit of difference in essence) . We
sometimes get around this problem by continuing to talk and ironing
out understanding (but sometimes lose patience long before that
happens)
There is an organic aspect to constantly evolving language whose side
effects on a society are rarely investigated empirically. Instead what
often ends up happening is moralistic shouting matches over who's
definition is the correct one... when what should be happening is just
a simple agreements that an apple is an apple, orange is an orange,
reason is reason.
Rand or Kant can unilaterally try to define a definition of
"definition"... but there is always an element of error since not
everyone sticks exactly to it. Part of the problem is
a. abstract concepts are difficult to contain (e.g. define "fairness")
b. we have imperfect memories (there are a great many words... and
many of them abstract concepts with many "units" to consider in their
definition)
c we can be selfish creatures that prefer definitions to suit our
needs ("fairness means equality"... "no fairness means freedom"...)
There may be a way around this problem of solid definitions but it's
very complicated to resolve since to solve it we would use language to
get around it. It's akin to trying to build delicate tools with a
sledgehammer.
Fred Weiss
> Abstract concepts is where havoc enters the equation when it comes to
> understanding essences. Define "justice". Define "truth". Define
> "rational". Since there is nothing physical about the concepts the
> only way we learn about them is through the words or through emotional
> reactions that re-enforce a positive (or negative) reaction to an
> experience.
>
> This chaos over abstract definitions is (in my opinion) is one of
> primary sources of conflict on this earth.
Yes, because the concepts involved are extremely complex and involve a
long chain of referents to prior concepts - and the connection to
reality and their ultimate sensory components is abstract vs. direct
and immediate. This is true even if the sensory referents are very
graphic and emotionally wrenching, such as the lynching of an innocent
man.
"When in doubt about the meaning or the definition of a concept, the
best method of clarification is to look for its referents--i.e., to ask
oneself: What fact or facts of reality gave rise to this concept? What
distinguishes it from all other concepts?
"For instance: what fact of reality gave rise to the concept
"justice"? The fact that man must draw conclusions about the things,
people and events around him, i.e., must judge and evaluate them. Is
his judgment automatically right? No. What causes his judgment to be
wrong? The lack of sufficient evidence, or his evasion of the
evidence, or his inclusion of considerations other than the facts of
the case. How, then, is he to arrive at the right judgment? By basing
it exclusively on the factual evidence and by considering all the
relevant evidence available. But isn't this a description of
"objectivity"? Yes, "objective judgment" is one of the wider
categories to which the concept "justice" belongs. What distinguishes
"justice" from other instances of objective judgment? When one
evaluates the nature or actions of inanimate objects, the criterion of
judgment is determined by the particular purpose for which one
evaluates them. But how does one determine a criterion for evaluating
the character and actions of men, in view of the fact that men possess
the faculty of volition? What science can provide an objective
criterion of evaluation in regard to volitional matters? Ethics. Now,
do I need a concept to designate the act of judging a man's character
and/or actions exclusively on the basis of all the factual evidence
available, and of evaluating it by means of an objective moral
criterion? Yes. That concept is "justice."
"Note what a long chain of considerations and observations is
condensed into a single concept. And the chain is much longer than the
abbreviated pattern presented here--because every concept used in this
example stands for similar chains."
ITOE Chap. 5 - Definitions
This btw also touches on the importance of the "hierarchy of
knowledge". If prior and more basic concepts are unclear, so will be
the later and more complex ones - thus explaining the chronic
philosophical stupidity of TeaCup and The Putz.
Not only are these concepts unclear to them, they are committed to
keeping it that way. That way they can make stupid comments on a
variety of subjects - repeat them over and over again - and not be
held accountable for them.
Fred Weiss
TC
> This btw also touches on the importance of the "hierarchy of
> knowledge". If prior and more basic concepts are unclear, so will be
> the later and more complex ones - thus explaining the chronic
> philosophical stupidity of TeaCup and The Putz.
This from an adherent of a philosophy that advocates nuking cities
for the actions of a few terrorists!
> Not only are these concepts unclear to them, they are committed to
> keeping it that way.
We like not living in medieval societies.
Tom
Robert J. Kolker
>
>
> This from an adherent of a philosophy that advocates nuking cities
> for the actions of a few terrorists!
As long as they are not -our- cities.
Bob Kolker
TC
wrote:
> TC wrote:
You mean we shouldn't have nuked Pendleton NY after
Oklahoma City?
Tom
Potroast
Well this is an interesting development.
We are virtually repeating each other (you independently quoting Rand
no less), we both seem to agree that this abstract definition problem
is no trivial matter, and we both seem to understand why there is a
hierarchy to the intellectual food chain of knowledge.
You know despite our unfortunately current political divide (I try
to keep an open mind when my fat ego lets me :), something about your
candid communism comment awhile back made me consider that we might
connect a little one of these days. I am a firm believer a person is
more likely to understand the true essence of philosophy (as opposed
to "a" philosophy) once they've allowed themselves to emotionally
travel down radically different ideological paths.
It makes sense that a single dimensional being is less likely to
trust there may indeed be a forth and fifth dimension until they've
experienced at least the second. Once one has gotten over the hump
it's far easier to wonder exactly how many more their are? And which
one is the best one currently available? (Not that I know such things
but I think about it :)
Do you have a particular work of Rand you could advise for further
reading on this specific definition issue? I'm coming at this
independently so it would be very interesting to compare notes to see
if she's followed the thought as far (or further) than I have. I can
talk endlessly about this particular problem but few seem interested.
I'd recommend Derrida for his own text-is-dead take on this
definition problem. I know how you feel about post-modernism but IMO
its still worth a look. The main problem with Deconstruction isn't
that it doesn't make a few interesting points. but that it doesn't
arrive to a conclusion. Philosophy needs a punch line or else its only
good use is for other philosophers looking for one.