Are sentences that are neither true nor false still meaningful for some anti-realists, e.g. Dummett, in a
way that they are not for logical positivists?
If so, where do such sentences get their meaning? True and false ones can get their meaning from
truth conditions even if these are just conceived of as verification conditions but those that are not
verifiable/ falsifiable must get their meaning somewhere else.
If not, how can sentences that are neither true or false violate bivalence. Surely a sentence that is
neither true nor false just because it is meaningless is not a problem.
Anti-realists are careful not to say that a sentence is 'neither true nor false'. If 'true' and 'false' are the
only truth values, then 'P is neither true or false' is tantamount to a violation of the law of
non-contradiction. Nor are anti-realists proposing a 'third truth value', in between true and false, a
device that has been used by logicians to deal with problems of vagueness. (So, for example, you
might be unhappy to say about a man with very little hair on top that it is true that he is bald, or that it
is false that he is bald. The truth of the matter is in-between.)
A Dummett-style anti-realist worries over sentences like, 'A tree stood here on this spot a million
hears ago.' Supposing that we could agree what would count as a 'tree', and what we mean by 'here',
this is a statement whose truth value we have no reliable means of discovering, no 'effective decision
procedure'. The anti-realist's view is notthat the sentence is neither true nor false. The anti-realist
merely refuses to assert that the sentence is'either true or false'. According to the Dummett-style
anti-realist, no argument based on the premise, 'Either a tree stood here a million years ago or not'
can be a logically valid argument.
I think this account of anti-realism limps on both feet, but I'm going along with it for the sake of your
question. At least one can say that it is a view that has been held by at least one philosopher of note.
(For my views on Dummett, realism and anti-realism see my answer to Rute and Alan.)
A logical positivist such as the young A.J. Ayer would have no difficulty in accepting that 'A tree stood
here on this spot a million years ago' is a meaningful statement. According to Ayer's verification
criterion of meaning, a statement is meaningful if, and only if, it is verifiable in principle. There are all
sorts of difficulties with this notion. But it is intuitively clear that there is a world of difference between
sentences whose verification is a mere medical or technological impossibility, and sentences for
which it would be impossible even to conceive of circumstances under which they would be
empirically verified. For example, 'The entire universe and all the matter in it is shrinking by half every
ten seconds,' 'In between typing each word of this sentence, every process in the universe came to a
standstill for a million years,' or, more controversially, 'God exists'. According to the logical positivist,
all three statements are equally meaningless.
The short answer to your dilemma is that, yes, statements such as the one about the tree for which
the law of bivalence or law of excluded middle fails are still meaningful according to an anti-realist of
Dummett's persuasion. Our knowledge of their meaning does not give us the capacity to undertake a
decision procedure which would reliably tell us whether the sentence is true or false. By contrast with
decidablestatements, we do not have the ability to recognize the truth or falsity of the statement
whenever it occurs. All the same, we have a knowledge of rules and procedures for making
inferences from present evidence to statements about the past which could conceivably be put to use
were the appropriate kind of evidence to turn up.