We present photometric ISO 60 and 170{mu}m measurements, complemented by some IRAS data at 60{mu}m, of a sample of 84 nearby main-sequence stars of spectral class A, F, G and K in order to determine the incidence of dust disks around such main-sequence stars. Fifty stars were detected at 60{mu}m; 36 of these emit a flux expected from their photosphere while 14 emit significantly more. The excess emission we attribute to a circumstellar disk like the ones around Vega and {beta} Pictoris. Thirty four stars were not detected at all; the expected photospheric flux, however, is so close to the detection limit that the stars cannot have an excess stronger than the photospheric flux density at 60{mu}m. Of the stars younger than 400Myr one in two has a disk; for the older stars this is true for only one in ten. We conclude that most stars arrive on the main sequence surrounded by a disk; this disk then decays in about 400Myr. Because (i) the dust particles disappear and must be replenished on a much shorter time scale and (ii) the collision of planetesimals is a good source of new dust, we suggest that the rapid decay of the disks is caused by the destruction and escape of planetesimals. We suggest that the dissipation of the disk is related to the heavy bombardment phase in our Solar System. Whether all stars arrive on the main sequence surrounded by a disk cannot be established: some very young stars do not have a disk. And not all stars destroy their disk in a similar way: some stars as old as the Sun still have significant disks.