Excuse the sketchbook format of thought due to limits of interest in literary matter at hand.
Utilitarian language- where purpose is all-important. A path to freedom. However, the mind, or an aspect of the mind, in mistaking its produce for itself, through that very seeking fails to find itself. Being itself, why should it need to find itself in the first place? So the very seeking is self-defeating.
In time, within this self-perpetuating, self-defeating process, lost in language, with the inevitable non-appearance of the hazily imagined goal of reality and happiness, many come to be disillusioned and to doubt the very existence of the exalted goal, but hold fast to the process, but since there is no energy to fuel the process, it all grinds towards a self-consuming halt, with Samuel Beckett being the most obvious incarnation of such proceedings.
Borges as shown in the paradox pieces is an example of the gnostic position, where in the literary field, the mind is lost in the matter of words, but seeks a way out, and the schizophrenic escape route being the falsehood of language itself. Both positions arising from a self trapped within language and a false understanding of that language, and all this completely unnecessary- the mind having no reason to have to entrap itself within one of its emanations.
Showing posts with label borges. Show all posts
Showing posts with label borges. Show all posts
Tuesday, 25 November 2008
Wednesday, 22 October 2008
More on the Paradoxes
Another mentioned paradox by Borges is that if one continuously halves the distance between oneself and the object approached, then one will never arrive at one's destination. Again, however, there is no paradox here. This is simply the internal logic of this mental set-piece. It is simply another way of saying, If you continually get closer to something, you will never reach it. Nothing is being contradicted as the mental framework simply refers to the dynamics of itself.
If movement were made to mirror the given thought of halving teh distance between one point and another, then, yes, the destination would not be reached. But this is movement made to follow the logic. This logic does not mirror movement where the object point is actually reached, but refers to a situation where the object is not reached; and so there is no paradox here. Just childish reasoning.
It is in no sense a rational representation of ordinary external movement for the same reasons given earlier; ie by the specifics of time and distance, as in a simple car speedometer where one travels at fifty miles per hour.
If movement were made to mirror the given thought of halving teh distance between one point and another, then, yes, the destination would not be reached. But this is movement made to follow the logic. This logic does not mirror movement where the object point is actually reached, but refers to a situation where the object is not reached; and so there is no paradox here. Just childish reasoning.
It is in no sense a rational representation of ordinary external movement for the same reasons given earlier; ie by the specifics of time and distance, as in a simple car speedometer where one travels at fifty miles per hour.
Tuesday, 21 October 2008
Zeno's Paradox, Borges
We have dreamt the world...but in its architecture we have allowed tenuous and eternal crevices which tell us it is false.
Borges is writing here of the implications of logical paradoxes where reason betrays its connection to reality; irrefutable logic leading to conclusions contradicting the reality logic purports to reflect.
Borges doesn't quite seem to understand the implications of the paradox correctly here. If logic leads to falseness then the entire edifice of language as an instrument of truth falls apart. There can be no cracks in 'truth', else there is no truth. Nothing is left us which can be intelligently said, including 'the falseness of the edifice.' In other words, nihilistic chaos.
Borges mentions 'perhaps the most elegant of all' paradoxes is where William James denies that 14 minutes can pass, "as first seven minutes must pass, then three and a half minutes, then half this figure, and so on until the invisible end, through tenuous labyrinths of time."
So it is imagined that there is a transgression of truth here, as time- specifically fourteen minutes- most certainly does pass. The 'paradox' here is all rather embarrassing, however. Time passes at the rate of itself, and of course will effortlessly pass all demarcations within the segment being measured. James and Borges are simply confusing - and misusing - the organ of measurement for that which is being measured. All the 'paradox' amounts to is that if one were to count all the imaginable fractions between one whole number and another, this could and would literally take forever as the possible demarcations are infinite. This is the nature of numbers. It bears no relationship, however, to the passage of time. So all this 'paradox' amounts to is a meaningless misuse of logic or reason.
Earlier Borges mentions Zeno's Second Paradox, where Achilles runs ten times faster than a tortoise, giving it a start of ten metres. It proceeds: For every measurement the tortoise travels, Achilles travels ten. Achilles runs ten metres, the tortoise one; Achilles a metre, the tortoise ten centimetres; Achilles ten centimetres, the tortoise one; a centimetre to a millimetre, and so on to infinity without the tortoise ever being overtaken. There is always a gap that cannot be overcome. But in external reality, Achilles does overtake the tortoise, and so logic is seen to be inconsistent with reality.
Is this an intelligent question? Is it an intelligently framed mirror of reality? To measure comparative speed, it is useless simply to say that one is travelling ten times faster than another. It is essential to be specific, and the moment this scenario is specific about the distance travelled, then we find the paradox to fall apart. For if every second, or specific time segment, the tortoise travels one centimetre and Achilles travels ten, then Achilles will, by simple mathematics, overtake the tortoise. And of course the same will occur if the length travelled is a millimetre to ten, or any specific distance. Zeno however keeps changing the terms of reference, leaping from metres to centimetres and so on, with again the more or less identical statement being made as in James' example; ie that one can if one wishes keep splitting the numerical demarcations into smaller and smaller fragments. Again, all the 'paradox' amounts to is faulty reason; the unintelligent framework of a scenario mistakenly imagining the internal logic to refer to something beyond itself.
Borges' position is that of gnosticism or at least gnosticism in the negative sense where, I would say for reasons of timidity before frightening immense and messy reality, a negative value judgement is imposed on life, and this when closely examined, as in the examples, simply amounts to flawed reasoning.
Borges is writing here of the implications of logical paradoxes where reason betrays its connection to reality; irrefutable logic leading to conclusions contradicting the reality logic purports to reflect.
Borges doesn't quite seem to understand the implications of the paradox correctly here. If logic leads to falseness then the entire edifice of language as an instrument of truth falls apart. There can be no cracks in 'truth', else there is no truth. Nothing is left us which can be intelligently said, including 'the falseness of the edifice.' In other words, nihilistic chaos.
Borges mentions 'perhaps the most elegant of all' paradoxes is where William James denies that 14 minutes can pass, "as first seven minutes must pass, then three and a half minutes, then half this figure, and so on until the invisible end, through tenuous labyrinths of time."
So it is imagined that there is a transgression of truth here, as time- specifically fourteen minutes- most certainly does pass. The 'paradox' here is all rather embarrassing, however. Time passes at the rate of itself, and of course will effortlessly pass all demarcations within the segment being measured. James and Borges are simply confusing - and misusing - the organ of measurement for that which is being measured. All the 'paradox' amounts to is that if one were to count all the imaginable fractions between one whole number and another, this could and would literally take forever as the possible demarcations are infinite. This is the nature of numbers. It bears no relationship, however, to the passage of time. So all this 'paradox' amounts to is a meaningless misuse of logic or reason.
Earlier Borges mentions Zeno's Second Paradox, where Achilles runs ten times faster than a tortoise, giving it a start of ten metres. It proceeds: For every measurement the tortoise travels, Achilles travels ten. Achilles runs ten metres, the tortoise one; Achilles a metre, the tortoise ten centimetres; Achilles ten centimetres, the tortoise one; a centimetre to a millimetre, and so on to infinity without the tortoise ever being overtaken. There is always a gap that cannot be overcome. But in external reality, Achilles does overtake the tortoise, and so logic is seen to be inconsistent with reality.
Is this an intelligent question? Is it an intelligently framed mirror of reality? To measure comparative speed, it is useless simply to say that one is travelling ten times faster than another. It is essential to be specific, and the moment this scenario is specific about the distance travelled, then we find the paradox to fall apart. For if every second, or specific time segment, the tortoise travels one centimetre and Achilles travels ten, then Achilles will, by simple mathematics, overtake the tortoise. And of course the same will occur if the length travelled is a millimetre to ten, or any specific distance. Zeno however keeps changing the terms of reference, leaping from metres to centimetres and so on, with again the more or less identical statement being made as in James' example; ie that one can if one wishes keep splitting the numerical demarcations into smaller and smaller fragments. Again, all the 'paradox' amounts to is faulty reason; the unintelligent framework of a scenario mistakenly imagining the internal logic to refer to something beyond itself.
Borges' position is that of gnosticism or at least gnosticism in the negative sense where, I would say for reasons of timidity before frightening immense and messy reality, a negative value judgement is imposed on life, and this when closely examined, as in the examples, simply amounts to flawed reasoning.
Monday, 19 May 2008
Borges, Time, Infinity, Monkeys
To go back to the Borges post earlier, and the idea that "in an infinite period of time all things happen to all men." An example of this notion being the infinite monkeys on typewriters producing the works of Shakespeare given infinite time.
This understanding views time and circumstances as akin to a roulette wheel of time spinning, and with the numbers on the wheel representing what is imagined to be the full possible gamut of circumstances, and that within an infinity of time the ball must eventually fall into each possible slot. However, if all the circumstances can be represented on the roulette wheel, then they must be a finite set of circumstances, not infinite. Infinity cannot be meaningfully spoken of in the inclusive sense of "all that is within infinity." The inclusiveness of 'all' necessarily a notion reserved for use of finite terms.
This lucidly demonstrated by the mathematical parallel of "all the numbers within infinity." Take one of these numbers within the infinity of numbers; this being Pi. Pi- the ratio of any circle's circumference to its diameter- is itself infinite, and so one cannot speak of 'all the numbers of Pi'; 'all' being an inclusive term, whereas infinity spills endlessly beyond 'all'. And this Pi is but one number within an infinity of numbers. Interestingly, Pi is what is described as a transcendental number . It transcends finite representation: though this may have a somewhat different specific meaning in the language of mathematics its linguistic sense holds true.
And any single circumstance of life can be paralleled with Pi. No element within life can be abstracted from the whole of life without falsifying both- there being no life and its consituents distinct from each other, and so each circumstance is itself necessarily an infinity. We cannot cut life into segments or impose limits whereby something is a self-enclosed individual event or circumstance. So, for example, the circumstance of a man standing up exists simultaneously on all kinds of fronts, but to take one element of its existence being the visual. The action could be witnessed from an infinity of points, and such points of perspective could not be exhausted, else they would be a finite number, not infinite. So on that front alone, it is an infinite event, not finite. Though this infinity of points of perspective are infinite, not because of linguistic tautological reasons, but because this is the nature of reality. Every square inch of space is infinite.
So all in all, to talk of 'the infinity of possible things that must happen within infinity' is senseless even on pure linguistic terms. When we try to reach infinity from an assumed starting point of the reality of the finite, we can but end in nonsensical absurdism, but this deluded belief in the solid reality of the finite tends to be the starting point for all discursive thought.
By the way, the mathematical probablitities of the notion of the random creation of Shakespeare's works by undirected intelligences in the form of monkeys is examined here, where the humbler likelihood of the monkeys producing but a single line of Shakespeare is put to the test.
This understanding views time and circumstances as akin to a roulette wheel of time spinning, and with the numbers on the wheel representing what is imagined to be the full possible gamut of circumstances, and that within an infinity of time the ball must eventually fall into each possible slot. However, if all the circumstances can be represented on the roulette wheel, then they must be a finite set of circumstances, not infinite. Infinity cannot be meaningfully spoken of in the inclusive sense of "all that is within infinity." The inclusiveness of 'all' necessarily a notion reserved for use of finite terms.
This lucidly demonstrated by the mathematical parallel of "all the numbers within infinity." Take one of these numbers within the infinity of numbers; this being Pi. Pi- the ratio of any circle's circumference to its diameter- is itself infinite, and so one cannot speak of 'all the numbers of Pi'; 'all' being an inclusive term, whereas infinity spills endlessly beyond 'all'. And this Pi is but one number within an infinity of numbers. Interestingly, Pi is what is described as a transcendental number . It transcends finite representation: though this may have a somewhat different specific meaning in the language of mathematics its linguistic sense holds true.
And any single circumstance of life can be paralleled with Pi. No element within life can be abstracted from the whole of life without falsifying both- there being no life and its consituents distinct from each other, and so each circumstance is itself necessarily an infinity. We cannot cut life into segments or impose limits whereby something is a self-enclosed individual event or circumstance. So, for example, the circumstance of a man standing up exists simultaneously on all kinds of fronts, but to take one element of its existence being the visual. The action could be witnessed from an infinity of points, and such points of perspective could not be exhausted, else they would be a finite number, not infinite. So on that front alone, it is an infinite event, not finite. Though this infinity of points of perspective are infinite, not because of linguistic tautological reasons, but because this is the nature of reality. Every square inch of space is infinite.
So all in all, to talk of 'the infinity of possible things that must happen within infinity' is senseless even on pure linguistic terms. When we try to reach infinity from an assumed starting point of the reality of the finite, we can but end in nonsensical absurdism, but this deluded belief in the solid reality of the finite tends to be the starting point for all discursive thought.
By the way, the mathematical probablitities of the notion of the random creation of Shakespeare's works by undirected intelligences in the form of monkeys is examined here, where the humbler likelihood of the monkeys producing but a single line of Shakespeare is put to the test.
Saturday, 10 May 2008
Borges & Immortality
In Borges' story The Immortal, he writes "They knew that in an infinite period of time all things happen to all men."
This is quite a commonly heard thought: of all things happening within infinity. However the logic doesn't really hold. In an infinite temporal framework there is absolutely no reason I am fated to, for example, cut off my left leg and use it as a tool in a variation of hockey played in the sewers of Rotterdam involving an opposition of asthmatic lepers. Borges is confusing two separate things; time and events. An example of this absurdity being that within his infinity notion, I am also fated to hop a marathon on my left leg, though my left leg is no longer present. But it is an event within the infinity of events. Therefore it must happen. Not, however, if it can't.
Something not happening today, like the leg hockey situation, is in no sense an argument why it should happen tomorrow, or within an infinity of tomorrows. An immortal could simply spend infinity sitting in a cave.
Borges later writes: "If we postulate an infinite period of time with infinite circumstances and changes, the impossible thing is not to compose the Odyssey, at least once."
This second quote is perfectly logical however: that within a universe of infinite circumstances all circumstances one could mention must be contained. However, it is logic simply because it is an exercise in tautology. Of course, if we conjecture a universe of infinite circumstances, then all possible circumstances must be contained within such a universe. That is the nature, the internal logic of the sentence. But this is simply an imposed intellectual framework, the closed system of a thought-piece.
On the other hand, there is no possible reason all possible events must occur within infinite time. It is an unjustified inference; a confusion of the finite with the infinite. This understanding of infinity is merely the finite extended or pushed to a higher power. A mind pushing itself and its boundaries to its limits, but still contained within those limits, and producing absurdities when it imbues those limits with limitlessness, or infinity. The infinite is a beast not so easily captured.
The danger of the joys of abstract thought where one's errors are not demonstrated in reality, though Borges might argue that his is a work of art, and such flaws are cracks within which further creative thought grows. Though that's no excuse.
This is quite a commonly heard thought: of all things happening within infinity. However the logic doesn't really hold. In an infinite temporal framework there is absolutely no reason I am fated to, for example, cut off my left leg and use it as a tool in a variation of hockey played in the sewers of Rotterdam involving an opposition of asthmatic lepers. Borges is confusing two separate things; time and events. An example of this absurdity being that within his infinity notion, I am also fated to hop a marathon on my left leg, though my left leg is no longer present. But it is an event within the infinity of events. Therefore it must happen. Not, however, if it can't.
Something not happening today, like the leg hockey situation, is in no sense an argument why it should happen tomorrow, or within an infinity of tomorrows. An immortal could simply spend infinity sitting in a cave.
Borges later writes: "If we postulate an infinite period of time with infinite circumstances and changes, the impossible thing is not to compose the Odyssey, at least once."
This second quote is perfectly logical however: that within a universe of infinite circumstances all circumstances one could mention must be contained. However, it is logic simply because it is an exercise in tautology. Of course, if we conjecture a universe of infinite circumstances, then all possible circumstances must be contained within such a universe. That is the nature, the internal logic of the sentence. But this is simply an imposed intellectual framework, the closed system of a thought-piece.
On the other hand, there is no possible reason all possible events must occur within infinite time. It is an unjustified inference; a confusion of the finite with the infinite. This understanding of infinity is merely the finite extended or pushed to a higher power. A mind pushing itself and its boundaries to its limits, but still contained within those limits, and producing absurdities when it imbues those limits with limitlessness, or infinity. The infinite is a beast not so easily captured.
The danger of the joys of abstract thought where one's errors are not demonstrated in reality, though Borges might argue that his is a work of art, and such flaws are cracks within which further creative thought grows. Though that's no excuse.
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