heusdens
December 26, 2003, 11:02 AM
The Kalam Cosmological Argument is, that argues that the universe must have had a definite starting point in time, is realy a very old philosophical topic.
The same type of argument can already be found in Immanual Kant's Critique of Pure Reason. Irronically, Kant also gives proof of the contrary, namely that the universe didn't have a begin in time, and makes him conclude that the one can be prooved as convincingly prooved as the other.
History put forward also another defender of the "beginning of time" idea, in the form of Herr Eugen Duhring, who came up with a "world schematism" that would make a clear stance in the philosophical debate and settle these philosophical topics for all time.
For the readers interested in the historical philosophical debate, one has to read the polemic of Friedrich Engels against the "world schematism" of Herr Eugen Duhring in Engels' Anti-Duhring.
The part of interest is Chapter V. Philosophy of Nature. Time and Space (http://www.marxists.org/archive/marx/works/1877/anti-duhring/ch03.htm)
In brief, the main argument of both Herr Eugen Duhring and as put forward by the 'Kalam Cosmological Argument' is that a real (or counted) infinity of time does not and can not exist, and hence time must have had a begin. This position is also known as the contradiction of the counted infinite series.
The error in the argument is realy very simple. Given an infinite time line, and placing two points arbitrarily on the time line and measuering the distance between these two points will always yield a finite measure. However, the points are taken arbitrarily, and given th fact that we deal with a time line which has an end to either side of the line, it can also be shown that no finite number can exist as a boundary to the measurement of time difference between two arbitray points on the time line. Assume that such a measure exists, and the place the leftmost point somewhat to the left, and you just proved that that measure is not a bound to the measurement of time difference on the infinite time line. In this way time is said to be infinite, having no begin or end. Even though when every time measurement taken on the infinite time line, will always yield a definite and finite measurement.
The argument of the contradiction of the infinite counted sereies, which is basically the same argument which is used in the Kalam Cosmological Argument, now claims that the amount of past time can not yield an infinite measure.
The trick in this argument is of course that in order to start measuring or counting time, one has to choose a starting point.
But whatever point one chooses, this always will be an arbitrary point on the time line, and the measurement between that starting point and the point 'now' will yield a finite measurement.
However, on an infinite time line, there is no starting point to begin with, so in fact the proces of counting or measuring time, could not even have started.
The argument therefore smuggles into the premise the thing it has to proof, namely that time did have a beginning.
Stating that on an infinite time line, a line which has no begin or end, one could in fact start counting at the 'begin' is a contradiction in terms, since an infinite time line has no such begin.
What it all comes down to is that infinity itself is a contradiction, since an infinite line is made up entirely of finite parts.
To overcome that contradiction is to get rid of infinity. Infinity therefore can not be conceived of without contradiction.
The consequence of that contradiction is that the universe is unfolding in time endlessly, without a beginning.
For a more detailed treatment of this issue, please read the chapther in the link provided.
The same type of argument can already be found in Immanual Kant's Critique of Pure Reason. Irronically, Kant also gives proof of the contrary, namely that the universe didn't have a begin in time, and makes him conclude that the one can be prooved as convincingly prooved as the other.
History put forward also another defender of the "beginning of time" idea, in the form of Herr Eugen Duhring, who came up with a "world schematism" that would make a clear stance in the philosophical debate and settle these philosophical topics for all time.
For the readers interested in the historical philosophical debate, one has to read the polemic of Friedrich Engels against the "world schematism" of Herr Eugen Duhring in Engels' Anti-Duhring.
The part of interest is Chapter V. Philosophy of Nature. Time and Space (http://www.marxists.org/archive/marx/works/1877/anti-duhring/ch03.htm)
In brief, the main argument of both Herr Eugen Duhring and as put forward by the 'Kalam Cosmological Argument' is that a real (or counted) infinity of time does not and can not exist, and hence time must have had a begin. This position is also known as the contradiction of the counted infinite series.
The error in the argument is realy very simple. Given an infinite time line, and placing two points arbitrarily on the time line and measuering the distance between these two points will always yield a finite measure. However, the points are taken arbitrarily, and given th fact that we deal with a time line which has an end to either side of the line, it can also be shown that no finite number can exist as a boundary to the measurement of time difference between two arbitray points on the time line. Assume that such a measure exists, and the place the leftmost point somewhat to the left, and you just proved that that measure is not a bound to the measurement of time difference on the infinite time line. In this way time is said to be infinite, having no begin or end. Even though when every time measurement taken on the infinite time line, will always yield a definite and finite measurement.
The argument of the contradiction of the infinite counted sereies, which is basically the same argument which is used in the Kalam Cosmological Argument, now claims that the amount of past time can not yield an infinite measure.
The trick in this argument is of course that in order to start measuring or counting time, one has to choose a starting point.
But whatever point one chooses, this always will be an arbitrary point on the time line, and the measurement between that starting point and the point 'now' will yield a finite measurement.
However, on an infinite time line, there is no starting point to begin with, so in fact the proces of counting or measuring time, could not even have started.
The argument therefore smuggles into the premise the thing it has to proof, namely that time did have a beginning.
Stating that on an infinite time line, a line which has no begin or end, one could in fact start counting at the 'begin' is a contradiction in terms, since an infinite time line has no such begin.
What it all comes down to is that infinity itself is a contradiction, since an infinite line is made up entirely of finite parts.
To overcome that contradiction is to get rid of infinity. Infinity therefore can not be conceived of without contradiction.
The consequence of that contradiction is that the universe is unfolding in time endlessly, without a beginning.
For a more detailed treatment of this issue, please read the chapther in the link provided.