# Abstract

A thesis is presented here according to which a quantitative measurement
of research output may not be feasible
in consistent terms.

*Introduction: supposing that science’s future progress be rationally predictable.*

If research activities’ output
were measurable in quantitative fashion from within the system where such activities take place, then
innovation scholars belonging to this system might devise deterministic/probabilistic theories of
scientific progress (which would be stated in
mathematical/statistical terms) and, once these general conjectures had
tentatively been tested, the same
scholars may derive from those theories (more or less exact) rational
predictions on the future growth of scientific knowledge.

*1.
**Apparent rejection by K.R. Popper of Hypothesis <<1>>*

But we have been knowing for sure that according to a proof given by Popper in 1982 (Idem, Postscript to the
Logic of Scientific Discovery) it is impossible to make such a prediction.

*A naïve, futile
attempt.*

Someone may perhaps attempt at rejecting the Proof by referring to the
much mooted, and very often denied, Popper’s
criterion of demarcation of science; but, such by a would-be
epistemologist

<<critique>> has no relevance, since, by paying due
attention to the Proof’s content we easily understand
that no theories’ <<falsification>> is referred at in it: rather,
in the Proof, the conditions are discussed for theories’ <<*acceptance*>>.

(The twenty-so pages where the great
Philosopher discusses his Proof are possibly
among the most important
he ever wrote and they deserve
to be studied with the most careful examination.)

*An inescapable conclusion?*

The Proof is essentially tautological: therefore, whenever we accepted the assumptions it is based
upon, we had also to accept
its conclusion. And the crucial assumption made by Popper is that the
prediction of the future growth of rational
knowledge is made from *within the system *such
prediction concerns.

So, in order to reject Popper’s proof one could attempt to say that the
scientific cadre does not form a system.
But such a statement would appear really difficult to be made, considering the
extremely close, rational
connections linking scientists through their thorough reciprocal scrutiny, which
underlies the whole process
of scientific communication (reviewees for publications, citations, conferences etc.).

*A possible relevant
consequence.*

A basic theorem
of formal logic states that:
[ (A —> B) —>
(~B —>~A) ]

namely:

[ if (if A then B)
then (if non B then non A)
] whereby:

{if [ if (the possibility of measuring the research output quantitatively)

entails (the possibility of predicting the increase in scientific knowledge rationally) ]

then [ (the im – possibility
of predicting the increase in scientific knowledge rationally) entails
(the im - possibility of measuring the research output quantitatively)
] }.

*Conclusion:
A last escape route.*

The last line of defense of whom wants to deny the relevance of Popper’s Proof consists in saying that that demonstration concerns the
qualitative, not quantitative, increase in scientific knowledge. But, in fact, that this qualitative content of scientific knowledge will somewhat be boiled down to a quantity is the fundamental idea on which quantitative measurement rests.

# References

Popper
K.R., *THE OPEN UNIVERSE. An Argument for
Indeterminism*; (From the: *POSTSCRIPT TO THE LOGIC OF SCIENTIFIC DISCOVERY*); Routledge, London, 1982: pp.62 – 76.