In the logico-deductive method new knowledge follows old knowledge
(conclusions are made from premises) through the application of sound
arguments. But can we conjure up the new by reassembling the old?

For the phenomenalist, deriving the conclusion and hence bringing it to
perception, brings us new knowledge.

For the realist, a conclusion is not derived by a perceiver, but is
found completely in the premises, which are independent of any perceiver
or logico-deductive process of deduction. If the conclusion is not
immediately apparent then it is only because of intellectual limitations.

CCONCLUSION

For the realist, premises and conclusions are all in the same picture;
for the phenomenalist they are not. The logico-deductive method, which
supposedly brings us new knowledge by deduction, is at least a
phenomenalist's pursuit, but cannot be undertaken by the realist.

This does not square with the standard idea that logical and
mathematical entities are considered as Platonically real, existing
independent of perception.