You ask:
Why can't Popper claim that these basic statements ("present-tense
observation statements about sense-data") are known to be true by
logic inference, either deductive or inductive?
First, you have mis-stated the definition of a basic statement (Section 7 of LScD [Logic of Scientific Discovery]):
What I call a ‘basic statement’or a ‘basic proposition’ is a statement
which can serve as a premise in an empirical falsification; in brief,
a statement of a singular fact.
And to clarify further in note *2 to Section 4:
When I invented the new name ‘basic statement’ (or ‘basic
proposition’; see below, sections 7 and 28) I did so only because I
needed a term not burdened with the connotation of a perception
statement. But unfortunately it was soon adopted by others, and used
to convey precisely the kind of meaning which I wished to avoid.
A basic statement is not a statement about perception. It is a statement that some specific observable thing happened in some specific region of space and time. Further clarification (LScD, Section 28):
Admittedly, it is possible to interpret the concept of an observable
event in a psychologistic sense. But I am using it in such a sense
that it might just as well be replaced by ‘an event involving position
and movement of macroscopic physical bodies’. Or we might lay it down,
more precisely, that every basic statement must either be itself a
statement about relative positions of physical bodies, or that it must
be equivalent to some basic statement of this ‘mechanistic’ or
‘materialistic’ kind.
No statement of any kind can be justified by induction because induction is impossible (Section 1 of LScD):
For the principle of induction must be a universal statement in its
turn. Thus if we try to regard its truth as known from experience,
then the very same problems which occasioned its introduction will
arise all over again. To justify it, we should have to employ
inductive inferences; and to justify these we should have to assume an
inductive principle of a higher order; and so on. Thus the attempt to
base the principle of induction on experience breaks down, since it
must lead to an infinite regress.
In the last two paragraphs of Section 25 of LScD, Popper writes:
In the epistemologies of sensationalism and positivism it is taken for
granted that empirical scientific statements ‘speak of our
experiences’. For how could we ever reach any knowledge of facts if
not through sense perception? Merely by taking thought a man cannot
add an iota to his knowledge of the world of facts. Thus perceptual
experience must be the sole ‘source of knowledge’ of all the empirical
sciences. All we know about the world of facts must therefore be
expressible in the form of statements about our experiences. Whether
this table is red or blue can be found out only by consulting our
sense-experience. By the immediate feeling of conviction which it
conveys, we can distinguish the true statement, the one whose terms
agree with experience, from the false statement, whose terms do not
agree with it. Science is merely an attempt to classify and describe
this perceptual knowledge, these immediate experiences whose truth we
cannot doubt; it is the systematic presentation of our immediate
convictions.
This doctrine founders in my opinion on the problems of induction and
of universals. For we can utter no scientific statement that does not
go far beyond what can be known with certainty ‘on the basis of
immediate experience’. (This fact may be referred to as the
‘transcendence inherent in any description’.) Every description uses
universal names (or symbols, or ideas); every statement has the
character of a theory, of a hypothesis. The statement, ‘Here is a
glass of water’ cannot be verified by any observational experience.
The reason is that the universals which appear in it cannot be
correlated with any specific sense-experience. (An ‘immediate
experience’ is only once ‘immediately given’; it is unique.) By the
word ‘glass’, for example, we denote physical bodies which exhibit a
certain law-like behaviour, and the same holds for the word ‘water’.
Universals cannot be reduced to classes of experiences; they cannot be
‘constituted’.
To understand Popper better you should read what he writes and take it literally. Don't assume that he can't really mean what he's writing. He does mean what he writes.
The Stanford Encyclopedia entry isn't worth much since it doesn't explain Popper's anti-justificationism (see Chapter I of "Realism and the Aim of Science"): justification (showing an idea is true or probably true) is impossible, undesirable and unnecessary. Debating about whether Popper justified this or that is irrelevant without a reply to his criticism of justificationism.
