Tuesday, May 09, 2006
Wednesday, April 12, 2006
Victories Within Ongoing Investigations: 10x+3=11x
accomplishment fiat failed to see
cure for the
solution.
The unattainable horizon kept
lingering.
Not an answer, an indication of
limits or
irregularities of judgment, or
any Thing
countable
or counted.
cure for the
solution.
The unattainable horizon kept
lingering.
Not an answer, an indication of
limits or
irregularities of judgment, or
any Thing
countable
or counted.
Tuesday, April 11, 2006
starting of rain
the heavy squish sound of my heart popping
muffled, almost a burp
a trickled escape leaving my mouth
aimed no where, a message to no one, but
communicated out towards
a repetitive silence
muffled, almost a burp
a trickled escape leaving my mouth
aimed no where, a message to no one, but
communicated out towards
a repetitive silence
seriousness
Seriousness is a mistake of youth that I cannot stop committing.
Morning after morning and into near morning
Seriousness falls over me and I over seriousness.
Tripped up and shut up I squander thoughts that meander
Sequentially through potentiality’s door of void.
I focus to find that door has been closed,
And stare at a piece of white cement.
Morning after morning and into near morning
Seriousness falls over me and I over seriousness.
Tripped up and shut up I squander thoughts that meander
Sequentially through potentiality’s door of void.
I focus to find that door has been closed,
And stare at a piece of white cement.
Friday, March 24, 2006
my conclusion
Conclusion
Where does Dasein end and the world begin?
What Heidegger means by world is the worldhood of the world. Dasein, as Being-in-the-world, is necessarily intertwined with the world. The world is a priori to Dasein and, in this sense, the world also within Dasein. Consequently, part of what Heidegger means by world is Dasein. But, where does Dasein end and the world begin?
We know that this boundary cannot be understood spatially. “Being-in, on the other hand, is a state of Dasein’s Being; it is an existentiale”(SZ 54). My Being-in-the-world is fundamentally different from “the water is ‘in’ the glass, or the garment is ‘in’ the cupboard”(SZ 54). Accordingly, Being-in describes Dasein’s familiarity with the world and comportment towards the world. But still, where do I end and where does my world begin?
This question of boundary is tied into of question identity. It seems that in order for me to know who I am I need to know who I am not. Heidegger often defines the boundary between Dasein and the world negatively. Dasein is not the present-at-hand, the ready-to-hand, or other Daseins. I qua Dasein am not my environment and I am not the They. However, the present-at-hand, the ready-to-hand, others, my environment, and the They are all within my world. That is, all these entities are actively involved in my identity. As Lilian Alweiss puts it in The World Unclaimed: “Dasein cannot be differentiated from its world”(WU 80).
Perhaps there is no boundary. Perhaps the question “Where does Dasein end and the world begin?” is symptomatic of an old and fallible epistemological way of thinking. In following Alweiss again: “Our temptation to locate the distinctiveness of Dasein in its spatiality is erroneous…”(85). Is not a boundary a marker of space? Yet, “in existence, man does not proceed from some inside to some outside; rather, the essence of Existenz is out-standing standing-within the essential sunderance of the clearing of beings”(OA 192). It only appears that a boundary between my world and myself is needed in order for me to retain my individuality, but for Heidegger this is not the case.
In Being-towards-death, my death distinguishes me as an individual. “Death does not just ‘belong’ to one’s own Dasein in an undifferentiated way; death lays claim to it as an individual Dasein”(SZ 263). Quite morbidly, when I die I die and no other Dasein can die for me. Here again the Aristotelian notion of continuity aids us in understanding the where Dasein ends and the world begins. The world is continuous and Dasein is in the world. The world does not stop at some border that is myself. Rather, I am the world too. The world occupies me, but I do not occupy the whole of the world. Again, Being-in ought not to be defined in terms of spatiality; instead Dasein’s existential structure of Being-in-the-world is the condition of possibility for Dasein’s spatiality.
Continuity, infinity, and math:
Aristotle’s definition of continuity in the Physics is helpful, but also complex. Aristotle’s notions of continuity and continua are intimately tied into a handful of other complex terms including indivisibility, distance, time, and movement. Of the four terms, however, it is indivisibility that is most relevant to our topic. Indivisibility is the most relevant for us because this essay does not set out to critically assess Heidegger’s theories on distance, time, and movement. Hence, the way in which I use the term continuity is meant to describe a specific type of unity and relation inherent to what Heidegger means by world. Distance, time, and movement are important for our purposes in so far as they are a part of the world. After all, “the world worlds” and time is obviously an important part of Being and Time. Distance, time, and movement are not irrelevant, but they are heavily reliant on Aristotle’s treatment of indivisibility. Consequently, the term indivisibility gets priority. A full description of Aristotle and Heidegger’s similarities ought to be fully addressed, but is outside the scope of this work.
For Aristotle, “it is impossible for a continuum to consist of indivisible things”(PH 231a21). So, when I claim that my world and the world of my historical people are continuous, does this imply indivisibility? More specifically, does this imply that either Dasein or the peasant woman’s world is indivisible? My answer is: Not necessarily. According to Aristotle, “anything indivisible has no parts” (PH 231a30). Furthermore, “if a continuum were divisible into indivisible parts, that would be a case of indivisible things being in contact, because the limits of continuous things form a unity and are in contact”(PH 231b17). For our purposes, the world can be either infinitely divisible or made up of indivisible parts in contact with one another. Either way, the world is continuous.
Beyond Aristotle, the history of continuums in both math and philosophy is unsettled. From Leibniz’s infinitesimals to D’Alembert’s limit concept and Cantor’s continuum hypothesis, the debate about what a continuum is and how one ought to understand continua is still active. For all the above-mentioned mathematicians and philosophers, the debates about continua are closely tied into debates about infinity as well. For our purposes, we ought to keep these debates and their consequences in mind. It seems that their consequences, however, would enhance our understanding of many details. However, the focus of this essay remains entirely on “What does Heidegger mean by world?” To keep this focus I rely almost entirely on information Heidegger directly gives in only Being and Time and The Origin of the Work of Art. Unfortunately, Heidegger fails to directly address continua within these two works.
A word on intentionality:
In the History of the Concept of Time Heidegger discusses Brentano’s influence on Husserl in terms of intentionality. Within this discussion Heidegger tries “to show that intentionality is a structure of lived experiences as such”(HC 29). The intentio of intentionality “literally means directing-itself-towards”(HC 29). For Heidegger, Dasein is fundamentally Being-towards the world as Being-in-the-world. We witness the direct influence of intentionality upon Heidegger’s philosophy in such phrases as “Being-towards-death”, “the constitutive assignment of the “in-order-to” to a “towards-this”, and “towards-which” [das Wozu] (SZ 74).
Importantly, the intentio has an inherent affinity with the intentum, “whereby intentum, the intended” is “the entity in the how of its being-perceived”(HC 45). These entities are included in Dasein’s environment and are within Dasein’s world. Dasein’s directing-itself-towards is a description of Dasein’s comportment towards the world and the intentum is the world’s status of necessary inclusion. To each lived experience there necessary belongs a world. This concept is reiterated in the phrase “the worldhood of the world”. Worldhood describes Dasein’s comportment as intentional, but already and necessarily included within Dasein’s comportment is the world. Consequently, the “basic constitution of intentionality as a reciprocal belonging-together of intention and intentum”(HC 45) is mimicked in Heidegger’s notion of world. Thereby intentionality plays an active role in what Heidegger means by world.
Undoubtedly intentionality is an important notion, but I describe what Heidegger means by world without it. Thus, I maintain that it is possible to describe what Heidegger means by world without the notion of intentionality. Otherwise, Heidegger ought to of directly mentioned and emphasized intentionality in both Being and Time and The Origin of the Work of Art. Yet, Heidegger does not. Consequently, the word intentionality is mostly absent from this essay. It is not my intention, however, to undermine the importance of intentionality.
Closing thoughts:
Despite my efforts, part of what Heidegger means by world remains outstanding. Yet, it is necessary that part of what Heidegger means by world be left undefined. In a sense, to define is to demarcate, or to set a limit. The world is essentially moving and continually in the process of defining itself. Since time is not at its limit, neither is the world. Therefore, I describe what Heidegger means by world by acknowledging the necessary irresolution of the world’s definition.
Where does Dasein end and the world begin?
What Heidegger means by world is the worldhood of the world. Dasein, as Being-in-the-world, is necessarily intertwined with the world. The world is a priori to Dasein and, in this sense, the world also within Dasein. Consequently, part of what Heidegger means by world is Dasein. But, where does Dasein end and the world begin?
We know that this boundary cannot be understood spatially. “Being-in, on the other hand, is a state of Dasein’s Being; it is an existentiale”(SZ 54). My Being-in-the-world is fundamentally different from “the water is ‘in’ the glass, or the garment is ‘in’ the cupboard”(SZ 54). Accordingly, Being-in describes Dasein’s familiarity with the world and comportment towards the world. But still, where do I end and where does my world begin?
This question of boundary is tied into of question identity. It seems that in order for me to know who I am I need to know who I am not. Heidegger often defines the boundary between Dasein and the world negatively. Dasein is not the present-at-hand, the ready-to-hand, or other Daseins. I qua Dasein am not my environment and I am not the They. However, the present-at-hand, the ready-to-hand, others, my environment, and the They are all within my world. That is, all these entities are actively involved in my identity. As Lilian Alweiss puts it in The World Unclaimed: “Dasein cannot be differentiated from its world”(WU 80).
Perhaps there is no boundary. Perhaps the question “Where does Dasein end and the world begin?” is symptomatic of an old and fallible epistemological way of thinking. In following Alweiss again: “Our temptation to locate the distinctiveness of Dasein in its spatiality is erroneous…”(85). Is not a boundary a marker of space? Yet, “in existence, man does not proceed from some inside to some outside; rather, the essence of Existenz is out-standing standing-within the essential sunderance of the clearing of beings”(OA 192). It only appears that a boundary between my world and myself is needed in order for me to retain my individuality, but for Heidegger this is not the case.
In Being-towards-death, my death distinguishes me as an individual. “Death does not just ‘belong’ to one’s own Dasein in an undifferentiated way; death lays claim to it as an individual Dasein”(SZ 263). Quite morbidly, when I die I die and no other Dasein can die for me. Here again the Aristotelian notion of continuity aids us in understanding the where Dasein ends and the world begins. The world is continuous and Dasein is in the world. The world does not stop at some border that is myself. Rather, I am the world too. The world occupies me, but I do not occupy the whole of the world. Again, Being-in ought not to be defined in terms of spatiality; instead Dasein’s existential structure of Being-in-the-world is the condition of possibility for Dasein’s spatiality.
Continuity, infinity, and math:
Aristotle’s definition of continuity in the Physics is helpful, but also complex. Aristotle’s notions of continuity and continua are intimately tied into a handful of other complex terms including indivisibility, distance, time, and movement. Of the four terms, however, it is indivisibility that is most relevant to our topic. Indivisibility is the most relevant for us because this essay does not set out to critically assess Heidegger’s theories on distance, time, and movement. Hence, the way in which I use the term continuity is meant to describe a specific type of unity and relation inherent to what Heidegger means by world. Distance, time, and movement are important for our purposes in so far as they are a part of the world. After all, “the world worlds” and time is obviously an important part of Being and Time. Distance, time, and movement are not irrelevant, but they are heavily reliant on Aristotle’s treatment of indivisibility. Consequently, the term indivisibility gets priority. A full description of Aristotle and Heidegger’s similarities ought to be fully addressed, but is outside the scope of this work.
For Aristotle, “it is impossible for a continuum to consist of indivisible things”(PH 231a21). So, when I claim that my world and the world of my historical people are continuous, does this imply indivisibility? More specifically, does this imply that either Dasein or the peasant woman’s world is indivisible? My answer is: Not necessarily. According to Aristotle, “anything indivisible has no parts” (PH 231a30). Furthermore, “if a continuum were divisible into indivisible parts, that would be a case of indivisible things being in contact, because the limits of continuous things form a unity and are in contact”(PH 231b17). For our purposes, the world can be either infinitely divisible or made up of indivisible parts in contact with one another. Either way, the world is continuous.
Beyond Aristotle, the history of continuums in both math and philosophy is unsettled. From Leibniz’s infinitesimals to D’Alembert’s limit concept and Cantor’s continuum hypothesis, the debate about what a continuum is and how one ought to understand continua is still active. For all the above-mentioned mathematicians and philosophers, the debates about continua are closely tied into debates about infinity as well. For our purposes, we ought to keep these debates and their consequences in mind. It seems that their consequences, however, would enhance our understanding of many details. However, the focus of this essay remains entirely on “What does Heidegger mean by world?” To keep this focus I rely almost entirely on information Heidegger directly gives in only Being and Time and The Origin of the Work of Art. Unfortunately, Heidegger fails to directly address continua within these two works.
A word on intentionality:
In the History of the Concept of Time Heidegger discusses Brentano’s influence on Husserl in terms of intentionality. Within this discussion Heidegger tries “to show that intentionality is a structure of lived experiences as such”(HC 29). The intentio of intentionality “literally means directing-itself-towards”(HC 29). For Heidegger, Dasein is fundamentally Being-towards the world as Being-in-the-world. We witness the direct influence of intentionality upon Heidegger’s philosophy in such phrases as “Being-towards-death”, “the constitutive assignment of the “in-order-to” to a “towards-this”, and “towards-which” [das Wozu] (SZ 74).
Importantly, the intentio has an inherent affinity with the intentum, “whereby intentum, the intended” is “the entity in the how of its being-perceived”(HC 45). These entities are included in Dasein’s environment and are within Dasein’s world. Dasein’s directing-itself-towards is a description of Dasein’s comportment towards the world and the intentum is the world’s status of necessary inclusion. To each lived experience there necessary belongs a world. This concept is reiterated in the phrase “the worldhood of the world”. Worldhood describes Dasein’s comportment as intentional, but already and necessarily included within Dasein’s comportment is the world. Consequently, the “basic constitution of intentionality as a reciprocal belonging-together of intention and intentum”(HC 45) is mimicked in Heidegger’s notion of world. Thereby intentionality plays an active role in what Heidegger means by world.
Undoubtedly intentionality is an important notion, but I describe what Heidegger means by world without it. Thus, I maintain that it is possible to describe what Heidegger means by world without the notion of intentionality. Otherwise, Heidegger ought to of directly mentioned and emphasized intentionality in both Being and Time and The Origin of the Work of Art. Yet, Heidegger does not. Consequently, the word intentionality is mostly absent from this essay. It is not my intention, however, to undermine the importance of intentionality.
Closing thoughts:
Despite my efforts, part of what Heidegger means by world remains outstanding. Yet, it is necessary that part of what Heidegger means by world be left undefined. In a sense, to define is to demarcate, or to set a limit. The world is essentially moving and continually in the process of defining itself. Since time is not at its limit, neither is the world. Therefore, I describe what Heidegger means by world by acknowledging the necessary irresolution of the world’s definition.
Sunday, March 19, 2006
Wednesday, March 15, 2006
Sunday, March 12, 2006
blinded part
Supple
meant to quiver a
bout these
emptied parts searching for a relation.
Inadequacies are as disposable as
yourself
today
that is to say you
are not
at any person’s disposal at all
No. Instead you are
sheltered in a
broken
moment
meant to quiver a
bout these
emptied parts searching for a relation.
Inadequacies are as disposable as
yourself
today
that is to say you
are not
at any person’s disposal at all
No. Instead you are
sheltered in a
broken
moment
Physis
Generation overflows
Physis
Here comes conflict
Here comes unity sprawling out on top
of surfaces
of shifting pearl.
Monumental sequoia
tongues call
inside the laughter condensation pooling dusty blood.
Un-empty voids birth matter
from a reservoir of none.
going
going
Physis
Here comes conflict
Here comes unity sprawling out on top
of surfaces
of shifting pearl.
Monumental sequoia
tongues call
inside the laughter condensation pooling dusty blood.
Un-empty voids birth matter
from a reservoir of none.
going
going
Tuesday, March 07, 2006
war.
empty space answers by echo.
The distortion is alien and
exposes the contorted
nature of sound.
Pauses stretch for miles and
reach far beyond the
bottom of a red canyon
vortex.
But there is always a movement.
Without touch and without flexibility,
the wind is imperceptible.
Where does clear coercion go?
The emptiness that rings
loudly is just the
call of conscience.
It speaks to remember
nothing much at all.
Imposed interpretation takes
needle-less trees and spins them pine.
But, they were really Aspen after all.
The filters of possibility
forsake all illogical purities.
But, there is nothing perceptible left to distinguish.
A mirror reflection is a repetition.
The image and the object are indifferent.
Illusory opposition comes crawling in
gray shades of admonition.
The echoes grow rougher,
more inane and heartless.
Each replica is less perfect
and farther from the good.
A downward spiral begins
between the real and the projection.
Now there are two instead of just one.
War.
The distortion is alien and
exposes the contorted
nature of sound.
Pauses stretch for miles and
reach far beyond the
bottom of a red canyon
vortex.
But there is always a movement.
Without touch and without flexibility,
the wind is imperceptible.
Where does clear coercion go?
The emptiness that rings
loudly is just the
call of conscience.
It speaks to remember
nothing much at all.
Imposed interpretation takes
needle-less trees and spins them pine.
But, they were really Aspen after all.
The filters of possibility
forsake all illogical purities.
But, there is nothing perceptible left to distinguish.
A mirror reflection is a repetition.
The image and the object are indifferent.
Illusory opposition comes crawling in
gray shades of admonition.
The echoes grow rougher,
more inane and heartless.
Each replica is less perfect
and farther from the good.
A downward spiral begins
between the real and the projection.
Now there are two instead of just one.
War.
unfinished symphony
Knowledge of a manifold unfolding infinitely to be ultimately repeated gains me what? Don’t make the same mistake twice; Don’t make the same mistake twice. I’d like to listen to you Elliot Smith, but you stabbed yourself in the chest. I’m not sure that’s taking your own advice either. And Nick Drake. What’s up with these beautiful geniuses that we all rely on until they disappear? Also, the end of the movie p. Oh, and lets not forget the conclusion of Beatty’s The White Boy Shuffle? Are authors telling us a little wisdom brings a little death?
Black holes are as imaginatively close as our unconsciousness. We know of them, can create actual pictures or pictorials in our minds, but we can prove nothing. Entire lines of thought dedicated to a scientific belief. And science isn’t the new religion? I suppose this is what we all know anyways. How does it feel to have it confirmed? Confirmation originally brought a smile to my face that touched inside the irises. A spherical intuition circulating from my mouth, to my brain, through my belly, and back into my mouth. I blow smoke rings with the feeling.
Welcome to the times. They’re similar to before, but particulars are radically different. Politics are always explosive realities we wear as belts. The players within the game, however, wear different faces. The lineages could easily be the same. It almost seems that eternal truths about life itself are easier to attain than political truths. Ah, but then there are those intellectuals who puncture the very bubble or aristocracy. The revolt. The revolt itself isn’t new, just a circumstantial nuance. Freedom of will navigating towards its destiny through cracks of fate. Room to move, but dictated by the walls of time.
Perhaps meaning itself is outmoded. Evolutionarily unfit. People try to find this meaning thing in life, find there is no “nothing”, and see freedom. Free to terrorize, free for self-condemnation, free to sell their souls to themselves, and free to die. Everyone feels doomed to death, but these very individuals are free to die.
There is another freedom from death. It is that contagious freedom that birthed responsibility. Responsibility carries a negative connotation, but it bestows meaning. Meaning is the same choice as responsibility. Responsibility requires strength.
But what is strength? We know of strength in the physical sense. To be capable of picking up loads, moving objects around, and conquering the physically weaker. “Conquering the physically weaker” here does not refer to war . Reference to war is unnecessary altogether. It refers to a natural definition of strong as found in nature. Responsibility, however, often means a mental load or object. Any natural animal that builds strength tends to survive. When there is a threat towards a species, strongest of the species survive. The physical and natural definition of stronger here is a metaphor for mental strength. Deciding to lift the load of responsibility makes a person stronger, more likely to survive, and therefore equating meaning with life.
A person can deem life meaningless and still choose responsibility. It is difficult to imagine this person being a nihilist. After all, nihilism is the belief in meaninglessness. The nihilist who chooses responsibility unconsciously believes in meaning. There is a meaning attached to avoiding politically negative consequences and accumulation of money. The word “consequence” in itself can be used synonymously with meaning. Whether or not a person believes in meaning or naturally gives meaning they live a life based upon the guidelines of meaning. The person who assumes responsibility towards others and their political state so as to prevent jailing or chaos gives meaning to these acts. Otherwise institutions, laws, and states, within themselves would prove entirely ineffective and obsolete. Their perseverance and strength prove their longevity and lifespan. As said earlier, meaning can be acquainted with life. Whether or not this person believes in meaning or naturally gives meaning they live a life based upon the guidelines of meaning.
There are several ideas in need of elaboration. The first is how can life be self-identical to meaning? The second, what are the guidelines of meaning? In explaining the guidelines to meaning the former question will self-illuminate. Therefore, I will answer the second question and then answer the first.
Guidelines to meaning are not meant as guidelines to how one lives their life. They are not guides to how one ascribes meaning to one’s self as well. These are my axioms for meaning by which I will build an entire geometry.
The word meaning is a more ambiguous word than most. Perhaps the strongest synonym for meaning is the word value. Which objects, either material or cognitive, are those objects that hold, retain, or acquire value ? At times the label value seems subjective, as in the saying “Beauty is in the eye of the beholder”. If objects of beauty can be said to retain value, then this phrase is an excellent example of meaning and value’s ambiguity. It seems value is multifarious, however, as value is also ascribed to many things absent of immediate aesthetics. Beauty can be applied to objects of one’s admiration, despite its appearances. The question of beauty, however, is not the topic of our immediate scrutiny. It is, however, implicitly dealt with in expounding meaning. The above quote is mentioned merely as an example of the ambiguity and seemingly subjective face of meaning and value.
The ancient and oppressive dichotomy of subjectivity and objectivity must be dealt differently now. Instead of dichotomy, perhaps it is helpful to think of symmetry. In eastern philosophy, quantum physics, mathematics, aesthetics, and all general sciences the role of symmetry is present.
Black holes are as imaginatively close as our unconsciousness. We know of them, can create actual pictures or pictorials in our minds, but we can prove nothing. Entire lines of thought dedicated to a scientific belief. And science isn’t the new religion? I suppose this is what we all know anyways. How does it feel to have it confirmed? Confirmation originally brought a smile to my face that touched inside the irises. A spherical intuition circulating from my mouth, to my brain, through my belly, and back into my mouth. I blow smoke rings with the feeling.
Welcome to the times. They’re similar to before, but particulars are radically different. Politics are always explosive realities we wear as belts. The players within the game, however, wear different faces. The lineages could easily be the same. It almost seems that eternal truths about life itself are easier to attain than political truths. Ah, but then there are those intellectuals who puncture the very bubble or aristocracy. The revolt. The revolt itself isn’t new, just a circumstantial nuance. Freedom of will navigating towards its destiny through cracks of fate. Room to move, but dictated by the walls of time.
Perhaps meaning itself is outmoded. Evolutionarily unfit. People try to find this meaning thing in life, find there is no “nothing”, and see freedom. Free to terrorize, free for self-condemnation, free to sell their souls to themselves, and free to die. Everyone feels doomed to death, but these very individuals are free to die.
There is another freedom from death. It is that contagious freedom that birthed responsibility. Responsibility carries a negative connotation, but it bestows meaning. Meaning is the same choice as responsibility. Responsibility requires strength.
But what is strength? We know of strength in the physical sense. To be capable of picking up loads, moving objects around, and conquering the physically weaker. “Conquering the physically weaker” here does not refer to war . Reference to war is unnecessary altogether. It refers to a natural definition of strong as found in nature. Responsibility, however, often means a mental load or object. Any natural animal that builds strength tends to survive. When there is a threat towards a species, strongest of the species survive. The physical and natural definition of stronger here is a metaphor for mental strength. Deciding to lift the load of responsibility makes a person stronger, more likely to survive, and therefore equating meaning with life.
A person can deem life meaningless and still choose responsibility. It is difficult to imagine this person being a nihilist. After all, nihilism is the belief in meaninglessness. The nihilist who chooses responsibility unconsciously believes in meaning. There is a meaning attached to avoiding politically negative consequences and accumulation of money. The word “consequence” in itself can be used synonymously with meaning. Whether or not a person believes in meaning or naturally gives meaning they live a life based upon the guidelines of meaning. The person who assumes responsibility towards others and their political state so as to prevent jailing or chaos gives meaning to these acts. Otherwise institutions, laws, and states, within themselves would prove entirely ineffective and obsolete. Their perseverance and strength prove their longevity and lifespan. As said earlier, meaning can be acquainted with life. Whether or not this person believes in meaning or naturally gives meaning they live a life based upon the guidelines of meaning.
There are several ideas in need of elaboration. The first is how can life be self-identical to meaning? The second, what are the guidelines of meaning? In explaining the guidelines to meaning the former question will self-illuminate. Therefore, I will answer the second question and then answer the first.
Guidelines to meaning are not meant as guidelines to how one lives their life. They are not guides to how one ascribes meaning to one’s self as well. These are my axioms for meaning by which I will build an entire geometry.
The word meaning is a more ambiguous word than most. Perhaps the strongest synonym for meaning is the word value. Which objects, either material or cognitive, are those objects that hold, retain, or acquire value ? At times the label value seems subjective, as in the saying “Beauty is in the eye of the beholder”. If objects of beauty can be said to retain value, then this phrase is an excellent example of meaning and value’s ambiguity. It seems value is multifarious, however, as value is also ascribed to many things absent of immediate aesthetics. Beauty can be applied to objects of one’s admiration, despite its appearances. The question of beauty, however, is not the topic of our immediate scrutiny. It is, however, implicitly dealt with in expounding meaning. The above quote is mentioned merely as an example of the ambiguity and seemingly subjective face of meaning and value.
The ancient and oppressive dichotomy of subjectivity and objectivity must be dealt differently now. Instead of dichotomy, perhaps it is helpful to think of symmetry. In eastern philosophy, quantum physics, mathematics, aesthetics, and all general sciences the role of symmetry is present.
Sunday, March 05, 2006
a million falls.
Leg muscles grew close
ligament
vines overlapped. One plant being indistinguishable from
a green nexus lap
agreeing
to grow out
side
to side alongside
a congregation
of moisture,
hung up in a storm, hangs to dry. Clouds become caves, go inside.
A million falls.
The ticking
clock raindrops
tap
echo notes to take.
Cattiness turns cat-
like, I stretch
out on top of a differentiated more of me. You
see the numbers fade
Our legs end
nowhere at
all
over the bent knee.
ligament
vines overlapped. One plant being indistinguishable from
a green nexus lap
agreeing
to grow out
side
to side alongside
a congregation
of moisture,
hung up in a storm, hangs to dry. Clouds become caves, go inside.
A million falls.
The ticking
clock raindrops
tap
echo notes to take.
Cattiness turns cat-
like, I stretch
out on top of a differentiated more of me. You
see the numbers fade
Our legs end
nowhere at
all
over the bent knee.
Tuesday, February 28, 2006
Sunday, February 26, 2006
Saturday, February 25, 2006
Aristotle's Infinity
Alexis Cohen
February 15, 2006
Infinity in the Physics, Book III4-8
Aristotle begins his explanation of infinity with an appeal to scientific knowledge. If the Physics undertakes the task of illuminating scientific knowledge, then Aristotle is obliged to discuss infinity to this end[1]. For Aristotle, “[s] cientific knowledge of nature involves taking magnitudes and change and time into consideration, and each of them is bound to be either infinite or finite”(202b30). Yet, not everything is either infinite or finite, e.g. qualities and points. Thus, a discussion of infinity does not construct the whole of scientific knowledge.
The Greek word for ‘infinite’, apeiron, is the same word for ‘unlimited’. In its limitlessness, those whom Aristotle calls the “natural scientists”, consider the infinite as neither an origin nor an end. Instead, they think the infinite “is taken not to have an origin, but to be the origin of everything else—to contain everything and steer everything, as has been said by those thinkers who do not recognize any other causes…apart from the infinite”(203b7)[2]. Unlike the natural scientists, both Plato and the Pythagoreans used the word infinite to describe unstructured stuff awaiting an imposed limit in the guise of either a shape or a form[3]. Aristotle, however, differs from all those mentioned above in that he considers the infinite as that “which cannot be traversed”(204a3).
Before attempting to define infinity, Aristotle lays five popular considerations that generally lead people “to infer that something infinite does exist”(203b15). The first two are the infinity of time and the division of magnitudes in mathematics. The last three considerations, however, are less straightforward. Thirdly, Aristotle finds that there is a notion that the persistence of generation and destruction is due to an infinite source “from which anything which is generated is subtracted”(203b17). Aristotle also lists the common notion that there must be a limit to the finite and, hence, no ultimate limit. Lastly, people believe that “number and mathematical magnitudes and the region beyond the heavens seem to be infinite because they do not give out in our thought. And if the region beyond the heavens is infinite, then it seems that body must be infinite too…”(203b22). Aristotle waits till end of the Book III to refute these arguments, however, with the exception that consideration one, that of time, is partly admissible. Aristotle refutes these considerations because they entertain the notion of actual infinity, which only later is proven impossible.
Before refuting the five popular reasons for infinity, Aristotle is compelled to ask whether or not infinity is a substance, an attribute, or neither a substance nor an attribute. In order to answer his own question, Aristotle discusses two different possible meanings of infinity. As mentioned earlier, infinity is that which cannot be traversed or that which “whose nature is such that it might be traversed, but is not in fact traversed or bounded”(204a7). Aristotle then quickly adds one more thought: infinity is either infinite by addition, by division, or by neither.
After posing all these questions, Aristotle declares in his heading for Book III.5 that the infinite is not itself a substance. Also, the infinite cannot stand separation from perceptible things and be just itself. To further defend his views Aristotle asks, “how could there be an independent infinite, if there cannot be independent number and magnitude?”(204a17). Thus, infinity is a property of number and magnitude[4]. Aristotle also declares that it is impossible for infinity to exist both in actuality and “to have substantial existence as a principle”(204a20)[5]. It is here that Aristotle first alludes to the distinction between actual and potential infinity that he will later expound. Before articulating this difference, which is essential for Cantor and his set theory, Aristotle declares infinity as “a coincidental attribute of things”(204a29). Accordingly, the infinite is not a principle. Instead, infinity is an attribute of principles.
In order to later refute the idea of actual infinity, Aristotle debates whether or not there is an infinitely extended body. Ultimately, Aristotle denies the existence of an infinitely extended body because he defines body as “‘that which is bounded by surface’”(20b4). That which is bounded cannot be that which is unlimited, or infinite. Furthermore, Aristotle makes a mathematical claim and states that “[n] or can any number that exists apart from perceptible things be infinite either, because number, and anything which has a number, is countable; anything countable can be counted, and it follows that it would be possible to traverse the infinite”(204b6). It is also important to note that, for Aristotle, it is impossible to simultaneously have an infinitely extended body and a place for this body[6]. Hence, there “is no actually infinite body”(206a7).
Although there is no actually infinite body, Aristotle consents to potential infinity. The verb ‘to be’, here, has two different meanings. ‘To be’ means either ‘to be potentially’ or ‘to be actually’ (206a14). However, ‘being potentially’ does not always refer to a future actuality. In terms of potential infinity, Aristotle uses the ‘to be’ analogously “in the same way that we use it of a day or a contest—that is, because one thing happens after another”(206a21). Here, ‘to be’ can be understood as moving successively as long as that which has passed, qua part, is understood as gone. Consequently, infinity is not “‘that which has nothing beyond itself’”, but rather “‘that which always has something beyond itself’”(206b33). The infinite is seemingly dynamic and, because of this dynamism, the infinite is not whole.
Aristotle defines whole “as that which has no part missing”(207a8). Suggested in the definition of “wholeness” is completeness, and what is complete has reached its end. End, in this sense, is a limit. What is whole is limited and, thus, not infinite. Yet, the whole is similar to the infinite. The infinite, unlike the whole, does not contain all things within it. Instead, “the infinite is matter for the completion of a magnitude and is potentially (not actually) the completed whole…and it takes something else to make it whole and finite, which it is not in its own right; and in so far as it is infinite, it does not contain but is contained”(207a21). The idea that the infinite can be contained, however, is contestable. After all, what is a container other than a type of limit?
Both matter and infinity are contained within things and it is form that does the containing. Accordingly, in terms of the fourfold division of causes, infinity is a material cause. Infinity is also not stable “but is being generated, as time is, and as the number of time is”(207b15). Time is infinite, but only in the sense that the parts of time do not persist. Time, in its successive movement, is always changing and, for Aristotle, time is infinite only “if change is infinite”(207b25).
Question for Consideration:
How can we draw together Aristotle’s definition for infinity with becoming and nature (physis)?
Do we agree that the infinite is matter? What are the consequences of this theory?
[1] The first two sentences of the Physics allude towards Aristotle’s goal of gaining scientific knowledge: “In any subject which has principles, causes, and elements, scientific knowledge and understanding stems from a grasp of these…It obviously follows that if we are to gain scientific knowledge of nature as well, we should begin by trying to decide about its principles”(184a10).
[2] Here, Aristotle is drawing reference to Heraclitus’s 41st Fragment which states: “Wisdom is one thing: to understand with true judgment how all things are steered through all” (Richard Hooker ©1995).
[3] Translator Robin Waterfield alerts readers to this fact in a footnote for 203a4 in the 1996 Oxford World’s Classics addition of the Physics.
[4] “In the second place, how could there be an independent infinite, if there cannot be independent number and magnitude? Infinity is in its own right a property of number and magnitude, so, of the three, an independently existing infinite is the least necessary”(204a17).
[5] Translator Robin Waterfield argues that this argument is a weak one, page 250.
[6] “In short, if place cannot be infinite, and if every body occupies place, then there cannot be an infinite body”(205b35).
February 15, 2006
Infinity in the Physics, Book III4-8
Aristotle begins his explanation of infinity with an appeal to scientific knowledge. If the Physics undertakes the task of illuminating scientific knowledge, then Aristotle is obliged to discuss infinity to this end[1]. For Aristotle, “[s] cientific knowledge of nature involves taking magnitudes and change and time into consideration, and each of them is bound to be either infinite or finite”(202b30). Yet, not everything is either infinite or finite, e.g. qualities and points. Thus, a discussion of infinity does not construct the whole of scientific knowledge.
The Greek word for ‘infinite’, apeiron, is the same word for ‘unlimited’. In its limitlessness, those whom Aristotle calls the “natural scientists”, consider the infinite as neither an origin nor an end. Instead, they think the infinite “is taken not to have an origin, but to be the origin of everything else—to contain everything and steer everything, as has been said by those thinkers who do not recognize any other causes…apart from the infinite”(203b7)[2]. Unlike the natural scientists, both Plato and the Pythagoreans used the word infinite to describe unstructured stuff awaiting an imposed limit in the guise of either a shape or a form[3]. Aristotle, however, differs from all those mentioned above in that he considers the infinite as that “which cannot be traversed”(204a3).
Before attempting to define infinity, Aristotle lays five popular considerations that generally lead people “to infer that something infinite does exist”(203b15). The first two are the infinity of time and the division of magnitudes in mathematics. The last three considerations, however, are less straightforward. Thirdly, Aristotle finds that there is a notion that the persistence of generation and destruction is due to an infinite source “from which anything which is generated is subtracted”(203b17). Aristotle also lists the common notion that there must be a limit to the finite and, hence, no ultimate limit. Lastly, people believe that “number and mathematical magnitudes and the region beyond the heavens seem to be infinite because they do not give out in our thought. And if the region beyond the heavens is infinite, then it seems that body must be infinite too…”(203b22). Aristotle waits till end of the Book III to refute these arguments, however, with the exception that consideration one, that of time, is partly admissible. Aristotle refutes these considerations because they entertain the notion of actual infinity, which only later is proven impossible.
Before refuting the five popular reasons for infinity, Aristotle is compelled to ask whether or not infinity is a substance, an attribute, or neither a substance nor an attribute. In order to answer his own question, Aristotle discusses two different possible meanings of infinity. As mentioned earlier, infinity is that which cannot be traversed or that which “whose nature is such that it might be traversed, but is not in fact traversed or bounded”(204a7). Aristotle then quickly adds one more thought: infinity is either infinite by addition, by division, or by neither.
After posing all these questions, Aristotle declares in his heading for Book III.5 that the infinite is not itself a substance. Also, the infinite cannot stand separation from perceptible things and be just itself. To further defend his views Aristotle asks, “how could there be an independent infinite, if there cannot be independent number and magnitude?”(204a17). Thus, infinity is a property of number and magnitude[4]. Aristotle also declares that it is impossible for infinity to exist both in actuality and “to have substantial existence as a principle”(204a20)[5]. It is here that Aristotle first alludes to the distinction between actual and potential infinity that he will later expound. Before articulating this difference, which is essential for Cantor and his set theory, Aristotle declares infinity as “a coincidental attribute of things”(204a29). Accordingly, the infinite is not a principle. Instead, infinity is an attribute of principles.
In order to later refute the idea of actual infinity, Aristotle debates whether or not there is an infinitely extended body. Ultimately, Aristotle denies the existence of an infinitely extended body because he defines body as “‘that which is bounded by surface’”(20b4). That which is bounded cannot be that which is unlimited, or infinite. Furthermore, Aristotle makes a mathematical claim and states that “[n] or can any number that exists apart from perceptible things be infinite either, because number, and anything which has a number, is countable; anything countable can be counted, and it follows that it would be possible to traverse the infinite”(204b6). It is also important to note that, for Aristotle, it is impossible to simultaneously have an infinitely extended body and a place for this body[6]. Hence, there “is no actually infinite body”(206a7).
Although there is no actually infinite body, Aristotle consents to potential infinity. The verb ‘to be’, here, has two different meanings. ‘To be’ means either ‘to be potentially’ or ‘to be actually’ (206a14). However, ‘being potentially’ does not always refer to a future actuality. In terms of potential infinity, Aristotle uses the ‘to be’ analogously “in the same way that we use it of a day or a contest—that is, because one thing happens after another”(206a21). Here, ‘to be’ can be understood as moving successively as long as that which has passed, qua part, is understood as gone. Consequently, infinity is not “‘that which has nothing beyond itself’”, but rather “‘that which always has something beyond itself’”(206b33). The infinite is seemingly dynamic and, because of this dynamism, the infinite is not whole.
Aristotle defines whole “as that which has no part missing”(207a8). Suggested in the definition of “wholeness” is completeness, and what is complete has reached its end. End, in this sense, is a limit. What is whole is limited and, thus, not infinite. Yet, the whole is similar to the infinite. The infinite, unlike the whole, does not contain all things within it. Instead, “the infinite is matter for the completion of a magnitude and is potentially (not actually) the completed whole…and it takes something else to make it whole and finite, which it is not in its own right; and in so far as it is infinite, it does not contain but is contained”(207a21). The idea that the infinite can be contained, however, is contestable. After all, what is a container other than a type of limit?
Both matter and infinity are contained within things and it is form that does the containing. Accordingly, in terms of the fourfold division of causes, infinity is a material cause. Infinity is also not stable “but is being generated, as time is, and as the number of time is”(207b15). Time is infinite, but only in the sense that the parts of time do not persist. Time, in its successive movement, is always changing and, for Aristotle, time is infinite only “if change is infinite”(207b25).
Question for Consideration:
How can we draw together Aristotle’s definition for infinity with becoming and nature (physis)?
Do we agree that the infinite is matter? What are the consequences of this theory?
[1] The first two sentences of the Physics allude towards Aristotle’s goal of gaining scientific knowledge: “In any subject which has principles, causes, and elements, scientific knowledge and understanding stems from a grasp of these…It obviously follows that if we are to gain scientific knowledge of nature as well, we should begin by trying to decide about its principles”(184a10).
[2] Here, Aristotle is drawing reference to Heraclitus’s 41st Fragment which states: “Wisdom is one thing: to understand with true judgment how all things are steered through all” (Richard Hooker ©1995).
[3] Translator Robin Waterfield alerts readers to this fact in a footnote for 203a4 in the 1996 Oxford World’s Classics addition of the Physics.
[4] “In the second place, how could there be an independent infinite, if there cannot be independent number and magnitude? Infinity is in its own right a property of number and magnitude, so, of the three, an independently existing infinite is the least necessary”(204a17).
[5] Translator Robin Waterfield argues that this argument is a weak one, page 250.
[6] “In short, if place cannot be infinite, and if every body occupies place, then there cannot be an infinite body”(205b35).
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