How Does Language Map onto the World? I've edited together my notes on realism and antirealism in an attempt to set out my view.
Speaking very roughly, just to get started, realism holds that ...stuff... is independent of what we say about it; anti-realism, that it isn't.
"Stuff", because the content makes a difference. For instance, if the content is aesthetic, then anti-realism is the view that beauty is in the eyes of the beholder; an aesthetic realist might hold that beauty and ugly are a part of whatever it is we are beholding; an anti-realist, that beauty and ugly are attitudes we adopt, or some such. An ethical realist might say god and bad are as much aspects of the world as matter and volume; and ethical anti-realist, that no observation of the world will reveal good or bad, because they are not 'out there' to be found.
While "realism" has a general use, it's ontology that is often of interest. Stealing blatantly from my Rutledge Encyclopaedia of Philosophy, a realist may hold to things like that correspondence to the facts is what makes a statement true; that there may be truths we do not recognise as such, do not believe and do not know; that the Law of excluded middle holds for things in the world; and that the meaning of a sentence may be found by specifying it's truth-conditions. An anti-realist may in contrast hold that truth is to be understood in sophisticated epistemic terms, perhaps as what a "well-conducted investigation" might lead us to believe; that there can be no unknown truths; that we need include "unknown" as well as true and false in our logical systems; and that the meaning of a sentence is to be found in what it might assert.
I've usually characterised my own ontology as realist. I've argued against typical examples of anti-realism such as pragmatic theory, logical positivism, transcendental idealism and Berkeley's form of idealism. I have however also defended a constructivist view of mathematics, an anti-realist position; and sometimes off-handedly rejected realism in ethics and aesthetics, only to change my mind later.
Changing this to a linguistic argument, realism entails that there are true statements; while an anti-realist would not make that commitment.
So a realist says the ball has a mass of 1kg; the anti-realist might say that saying that it has a mass of 1kg is useful, or fits their perceptions, but will not commit to its being true. The anti-realists failure to commit amounts to a failure to understand how language functions; "the ball" is the ball.
There's a mission to Mercury by the ESA and JAXA. Part of the mission is to decide if there is water at the poles - something hinted at by previous observations. Both the realist and the anti-realist will agree that we do not know that there is water at the poles of Mercury. A realist will say that either there is water at the poles, or there isn't - that either the statement or its negation is true. An anti-realist may say that the statement "There is water at Mercury's poles" is neither true nor not true, until the observation is made. Which is the better approach?
I wonder also if Anscombe's direction of fit works here. It's the difference between the list you take with you to remind yourself of what you want to buy and the list the register produces listing the things you actually purchased. The intent of the first list is to collect the things listed; of the second, to list the things collected. The first seeks to make the world fit the list, the second, to make the list to fit the world. Is it that anti-realism applies to ethics and aesthetics because we seek to make the world as we say, while realism applies to ontology and epistemology because we seek to make what we say fit the world?
We (note the plural) talk in terms of mass and balls and so on. The direction of fit here is that we intend these words to be about whatever it is that is "out there". And when we do this we find that we can construct coherent and useful accounts of what happens. It's not luck, it's a process of eradicating versions that are dysfunctional. A language community in part imposes its language on the world. We talk in terms of balls and stuff that is not balls. Like Anscombe's shopping list, we use the words to pick out things in the world, or we use it to to list the things we have. Both are equally legitimate, and each relies on the other.
How many planets are in our solar system? The number of planets is both an observation and an imposition.
Reality is such that it can be divided up into tables and not-tables. As Davidson (and others…) suggested, the world is always, already interpreted. I would add that the interpretation is put in place by our use of language. We need to put aside the notion of an uninterpreted reality - there is no alternative to imposing an interpretation. In admitting this we deny the dualism of framework versus reality. There are no alternate frameworks. That's a direct consequence of our living in the same world. What look like an alternate frameworks needs must be interpreted in such a way as to merge.
So the world is not what we experience, it is what is the case. That's a difference that few here seem to have picked up on.
Consider Fitch's paradox. Anti-realism holds that stuff is dependent in some way on us, that thinking makes it so. That is, some statement p is true only if it is believed or known to be true. For anti-realism, something's being true is the same as it's being known to be true. Now a direct implication of this is that if something is true, then it is known - that we know everything. Anti-realism is apparently committed to omniscience. The problem does not occur in realism, which happily admits to there being unknown truths.
Consider Fitch's paradox in the case of aesthetics. The anti-realist claim is that beauty is in the eye of the beholder - for all (a), (a) is beautiful if and only if (a) is thought beautiful. It follows, fairly innocuously, that everything that is beautiful is thought to be beautiful. In Ethics, ethical anti-realism holds that what is good is exactly what we know is good. It follows that we know everything that is good.
Consider mathematics. The anti-realist thesis is that for a mathematical proposition to be true is for it to have been proved. So it seems to follow that all true mathematical propositions have been proved. If p is a true mathematical proposition, p has been proved.
An alternate is to adopt a trinary logic. For mathematics, we might borrow from Kripke, and suppose that there are three truth-values for mathematical propositions - true, false and otherwise. We assign "true" to some set of tautologies, "False" to contradictions, and "other" to everything else. When a proof of a proposition is found - a deduction from other truths - we assign "true' to that proposition.
Only proven mathematical propositions get to be called "true" - the main point of constructivism. But I'm guessing the more mathematically literate will find fault with this proposal. The implication is that the conjecture that every prime greater that 2 is the sum of two primes is not true, and it is not false.
I'm amenable to giving consideration to a paraconsistent anti-realism. So I don't think the “middle way” is absurd. The question may be were it is appropriate to apply anti-realism rather than a blanket acceptance or denial. Realism is about there being stuff. Whether our statements about that stuff are true or false is incidental to realism. Whether we understand things about that stuff is also incidental to realism. A realist might well adopt a three-valued logic with regard to statements. Nothing in realism locks the realist into a particular logical system. That is, it seems what is loosely called semantic realism, the view that realism must make use of a correspondence theory of truth, is a bit of a straw man. Or if you prefer, antirealism is a theory about belief, and has little to do with truth.
So the argument usually portrayed as realism vs antirealism is perhaps better thought of as about whether we should best make use of a bivalent logic, or use some paraconsistent logic. And for my money the best way to talk about the various bits and pieces of our everyday use is with a bivalent logic.
That might not be the case in other specific circumstances, nor in ethics, aesthetics or mathematics.