TEMPORALPARADIGMS
CNMN
WHAT IS A PARADIGM?
especially : an outstandingly clear or typical example or archetype
… regard science as the paradigm of true knowledge.
— G. C. J. Midgley
the Freudian paradigm of psychoanalysis
broadly : a philosophical or theoretical framework of any kind
ZENO OF ELEA
01
PLATO AND ARISTOTLE
02
ISAAC NEWTON
03
Gottfried Wilhelm von Leibniz
04
IMMANUEL KANT
05
HENRI BERGSON
06
TABLE OF CONTENTS
ZENO
OF ELEA
01
THE ACHILLES PARADOX
Achilles paradox, in logic, an argument attributed to the 5th-century-BCE Greek philosopher Zeno, and one of his four paradoxes described by Aristotle in the treatise Physics. The paradox concerns a race between the fleet-footed Achilles and a slow-moving tortoise.
Zeno's Achilles Paradox attempts to show that motion is impossible. Let's say a tortoise and the Greek hero Achilles were racing. Based on our experiences of how a man and a tortoise move, we would naturally assume that Achilles would win. But consider this: the tortoise has a head start and is constantly moving toward the finish line (Time 1, pictured). Before Achilles can pass the tortoise, Achilles has to reach the spot where the tortoise started, right (A2, Time 2, pictured)? But by the time Achilles reaches the tortoise's starting point, the tortoise has moved on to another location further down the track (T2, Time 2, pictured). So now Achilles has to reach the spot where the tortoise currently is. But by the time Achilles does that, the tortoise has yet again moved on (Time 3, pictured). So, the paradox is that Achilles will always be behind the tortoise and will lose the race.
Today we know that this paradox — Zeno created several that dealt with space and time — has nothing to do with motion being illusory, but we still talk about it because it introduced some interesting math that wouldn't receive thorough treatment until the 17th century A.D., when Gottfried Leibniz invented calculus.
02
PLATO,
ARISTOTLE
PLATO VS. ARISTOTLE
Plato clearly says that time is the wanderings of these bodies - their movement - and not a kind of number that measures such movement. Abstracting time from motion was an innovation of Aristotle's. For Plato, time just is celestial motion. Note that time applies, strictly speaking, only to the realm of becoming.
Aristotle claims that time is not a kind of change, but that it is something dependent on change. He defines it as a kind of 'number of change' with respect to the before and after. It is argued that this means that time is a kind of order (not, as is commonly supposed, that it is a kind of measure).
PLATO
ARISTOTLE
03
ISAAC NEWTON
According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. ... According to Newton, humans are only capable of perceiving relative time, which is a measurement of perceivable objects in motion (like the Moon or Sun).
Newtonian Time
According to its most famous proponent, Sir Isaac Newton, for example, absolute time (which is also sometimes known as “Newtonian time”) exists independently of any perceiver, progresses at a consistent pace throughout the universe, is measurable but imperceptible, and can only be truly understood mathematically. For Newton, absolute time and space were independent and separate aspects of objective reality, and not dependent on physical events or on each other.
Time, in this conception, was external to the universe, and so must be measured independently of the universe. It would continue even if the universe were completely empty of all matter and objects, and essentially represented a kind of container or stage setting within which physical phenomena occur in a completely deterministic way. In Newton’s own words: “absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external”.
Newton’s ideas about absolute time were largely borrowed from Isaac Barrow, his predecessor at Cambridge. Barrow himself described time as a mathematical concept, analogous to a line in that it has length, is similar in all its parts, and can be looked on either as a simple addition of continuous instants, or alternatively as the continuous flow on one instant.
Although absolute time is the “real” time in Newton’s opinion, he cautioned that we mere mortals are not however capable of perceiving it directly. Instead, we are only capable of perceiving what he called “relative, apparent and common time”, which can be observed in the measurement of perceivable objects in motion (like the Moon or Sun) and the ticking of terrestrial clocks, and from which we infer the everyday passage of time. He attributed any discrepancies between absolute and apparent time to such things as irregularities in the motion of the Earth.
04
Gottfried Wilhelm von Leibniz
Leibniz’s positive account of space and time might be thought of as resting on two primary pillars and being filled out by a number of ancillary theses. The first pillar consists in an alternative model, or conception, of space and time offered in conscious opposition to the Newtonian conception absolute space and time. According to Leibniz, space and time are not so much things in which bodies are located and move as systems of relations holding between things. He thus famously tells Clarke in his Third Paper:
05
IMMANUEL KANT
This idea comprises a central piece of Kant's views on space and time, for he famously contends that space and time are nothing but forms of intuition, a view connected to the claim in the Transcendental Aesthetic that we have pure intuitions of space and of time.
06
HENRI BERGSON
Bergson argued that time has two faces. The first face of time is “objective time”: the time of watches, calendars, and train timetables. The second, la durée (“duration”), is “lived time,” the time of our inner subjective experience. This is time felt, lived, and acted.
Living on our own time
Bergson observed that we mostly don’t pay attention to la durée. We don’t need to — “objective time” is far more useful. But we can get a glimpse of the difference between them when they come apart.
The stretch of objective time between 3pm and 4pm is the same as that between 8pm and 9pm. But this does not have to be so with la durée. If the first interval is spent waiting at the dentist’s office and the second at a party, we know the first hour drags and the second just passes by too quickly.
The importance of paradigms
Paradigms are important because they define how we perceive reality and how we behave within it. Everyone is subject to the limitations and distortions produced by their socially conditioned nature. For instance, before Einstein physicists took Newtonian physics for granted.
The primary benefits of a paradigm as identified by Kuhn are a common foundation of assumptions, a canon of accepted ideas, and standards for accepting new research and theories into that canon (Kuhn, II).