Lee Smolin argues that no scientific law can be applied to the universe since a law has to be based on repeated observation but there is only one universe to observe. If, as he says, if you wanted to judge among various hypotheses like “all children like chocolate more than vanilla” or “children like the first flavor of ice cream they taste.” you need more than one child, but we only have one universe to observe. The problem is that the scientific law itself could only be complete in the context of the universe: anything less than this will abstract from and ignore things that are really affecting the system under study. Science is therefore must necessarily see its perfection in a limit, the attainment of which involves a contradiction.
Dekoninck gave an argument parallel to Smolin’s by starting from the fact that science is based formally on measurement. Every perfect measurement is a relation to some unit that is, as such, indivisible (any division of the unit is really just the specification of a new one) Every unit, however, must have some magnitude, and so necessarily has a margin of error. This margin is not negligible: the difference between Newtonian and Einsteinian systems was vanishingly small; the parallax that finally refuted Ptolemy was so small that we could not measure it till the 19th century; and the confirmation of string theory requires increasing our precision measurements by many orders of magnitude beyond the 16 or 17 we can now measure. The margin of error, in other words, is not minuscule – “minuscule” is a merely relative and anthropocentric term anyway – but something that must be definitely done away with in order for science to be final. But here again, doing away with measurement errors involves contradiction. There are, to be sure, unlimited times when to point out imperfection in measurement is sheer nit-picking and tiresome, but this cannot be universally the case, since if it were we would be saying it makes no difference to prefer Einstein to Ptolemy.
And so the two arguments combine to update Pascal. Human knowledge is caught between two limits, he strives to master them and knows he will be restless and ignorant until he does, and yet reaching either of them involves contradiction.