1. Dummett about realism and anti-realism
Realism (concerning X) construed as a semantical thesis: it is a certain interpretation of a class of statements (the statements about X – the given class).
Something like this:
The statements in the given class are rendered true or false by reality, independently of our knowing it or even being able to consider it.
Anti-realism: not one, but many.

2. Characteristic features of realism
Necessary (but not sufficient) condition of realism: bivalence in the given class.
Bivalence: Every statement (proposition) is determinately true or false.
Or: Every meaningful sentence is either true or false.
But a realist can use non-classical operators, too:
If p OR q means that we have either a proof for p or a proof for q, then for this OR Law of Excluded Middle does not hold.
LEM: „p or q” is a logical truth.
But we can (should) interpret the metalanguage ̒or’ classically, and we may have a classical ̒or’ in the object language, too.
Another condition: reference-based semantic theory.
Quantified statements are treated virtually as (possibly infinite) conjunctions resp. disjunctions of singular statements.

3. Semantic theory and theory of meaning
A semantic theory is a method to assign semantic value to atomic expressions and calculate the semantic values of the compound ones.
A realist semantic theory determines every statement as true or false. In such a theory, True and False are the only semantic values of a statement.
Example for a non-realist semantic theory: intuitionistic semantics for mathematical statements.
The semantic value of a statement that can be calculated from the semantic values of the component expressions is not its truth value but a relation between the statement and the possible mathematical constructions which holds iff the construction id a proof of the statement.
The statement is true iff there exists a construction which proves it ( ̒exists’ understood constructively).
Objectivist semantic theory: every meaningful sentence is determinately either true or not true (independently of our recognizing etc.)
A „gappy” semantic theory of the Prior-Ruzsa type (Formalisation of the Frege-Strawson idea) is a realist or an objectivist one?

4. ? Meaning and semantic value
A meaning-theory gives account of the knowledge of the speaker/hearer that is needed in order to understand an expression/to grasp its use.
Understanding a sentence involves a grasp of how it is determined as true, if it is true, in accordance with its composition.
Common sense: Whether or not a sentence is true depends both of its meaning and the way the word is.
Given the way the world is, the semantic value of an expression is determined by its meaning.
On an objectivist semantic theory, to know the meaning of an expression consists in knowing the condition for it to have any given semantic value.
Sentences: knowledge of the meaning will consist in a grasp of what has to be the case for it to be true.
Notice: for complete utterances (statements) only!
The same sentence as a constituent of a compound sentence: it contributes to the semantical value of the whole not only with its truth conditions.
Example: modal logic. Truth conditions of ̒Necessarily A’ cannot be calculated simply from the truth conditions of A (in the actual world) but the truth conditions of A in other worlds are also needed. ?

5. Truth conditional theory of meaning
(Classical) two-valued semantics: understanding a sentence as a whole suffices to understand it as a subordinate clause, too. [All sentential operators are truth-functional.]
In particular: the conditions of being false and the conditions of failing to be true fall together.
Truth-conditional meaning-theory: grasp the meaning of a sentence = knowledge of the condition that has to obtain for it to be true.
Anti-realism that repudiates mainly the truth-conditional account of meaning: Wittgenstein about statement ascribing inner sensations.

6. ? Anti-realism, reductionism, reference
Reductionist thesis: statements of the given class have a translation to some reductive class of statements, and this translation confers meaning to the statements of the given class.
Examples: behaviourism, phenomenalism.
Reduction without anti-realism: Frege about directions and paralellism.
Directions are real objects: classes of parallel straight lines.
It eliminates reference (to directions) from statements about directions.
Phenomenalism as anti-realism: just for this reason.
Is it the same case? Can we have explicit definition for physical objects in terms of sense-data?
Three main features of realism:
Bivalence, crucial role of reference, truth-conditional meaning-theory.
Reductionism gives up (?) the second one, but may keep the first and the third. ?