8/13/2019 Karl Popper - Infinite Time

http://slidepdf.com/reader/full/karl-popper-infinite-time 1/3

The ritish Society for the Philosophy of Science

On the Possibility of an Infinite Past: A Reply to WhitrowAuthor(s): Karl PopperSource: The British Journal for the Philosophy of Science, Vol. 29, No. 1 (Mar., 1978), pp. 47-48

Published by: Oxford University Press on behalf of The British Society for the Philosophy ofScience

Stable URL: http://www.jstor.org/stable/686391 .

Accessed: 15/02/2014 06:24

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

 .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of 

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact support@jstor.org.

 .

Oxford University Press and The British Society for the Philosophy of Science are collaborating with JSTOR to

digitize, preserve and extend access to The British Journal for the Philosophy of Science.

http://www.jstor.org

This content downloaded from 147.96.1.236 on Sat, 15 Feb 2014 06:24:12 AMAll use subject to JSTOR Terms and Conditions

8/13/2019 Karl Popper - Infinite Time

http://slidepdf.com/reader/full/karl-popper-infinite-time 2/3

8/13/2019 Karl Popper - Infinite Time

http://slidepdf.com/reader/full/karl-popper-infinite-time 3/3

48 Karl Popper

The idea of the actually infinitecan also be explained with the help of this same

sequence. It needs the Cantorian concept of a set. Let us regard instead of the

sequenceof natural numbers the set of all natural numbers. This set is infinite,and it can be described as representing the (smallest) actual infinity.

I now state my assertion against Kant.

We can regard the past time or elapsed time and the future time or impendingtime as symmetricalwith respect to infinity. Both may be regarded as consisting of

infinite sequences of temporal units, and therefore as potential infinities; and

both may be regarded as infinite sets of temporal units, and therefore as actual

infinities.

(The opposite impression is due to viewing the past time (a) as infinite and

at the same time as (b) having a beginning, although one that is infinitely far

away in the past. But it is clear that (b) contradicts (a) and is therefore in-admissible.)

We have only to realise that we must count our units of time (say, years)from some given instant of time (say, the birth of Christ or the year A.D.800).From that given instant we can count units (years) either in the positive direction

(that of the arrow of time ) or in the negative direction. In each case we obtain

a sequence of units which corresponds exactly to the sequence of natural num-

bers: a potential infinity. If, however, we consider the whole past or all

the units of time of the past that is to say, the set of the units of time of the past,then we obtain a Cantorian actual infinity. This is precisely the same whether

we look at the whole or elapsed past or at the whole or not yet elapsedfuture.

The difference between past time and future time is important; but it does not

correspond to the difference between actual or potential infinity.

4 SUMMARY

The attempt to show by a priori reasoning the impossibility of time without

beginning seems to me doomed to failure. There is, of course, one argument,

originally due to Milne, which allows us to transform a time co-ordinate with a

finite beginning into a time co-ordinate without a beginning, and vice versa.And in the absence of any natural unit of time, and even more of any guaranteethat in the distant past there existed events comparable to those events we now

use to define units of time, we may well wonder whether there is an ontologicaldifference corresponding to the difference between a time co-ordinate reachinginto an infinite past and a time co-ordinate with a beginning.

KARL POPPER

Penn, Buckinghamshire

This content downloaded from 147.96.1.236 on Sat, 15 Feb 2014 06:24:12 AMAll use subject to JSTOR Terms and Conditions