What are the possible sources of knowledge about the world experienced by human beings?

Philosophers call statements about the world we experience "synthetic" and distinguish them from those whose subject is really the meanings of terms, which are called "analytic." Some philosophers (often called "rationalists") have held that it is possible to be justified in believing statements which are about the world we experience, even though experience itself never provides adequate evidence for such statements. Such philosophers argued that "Reason" unaided by experience could justify such statements. Statements which can be thus justified independently of experience are called "a priori" and distinguished from those that can be justified only by appeal to experience, "a posteriori" or "empirical" statements. Rationalists thus hold to the possibility of justifying believing "synthetic a priori" statements.

What is the position of the empiricist consensus regarding the possibility of synthetic a priori knowledge?

Those who belong to the empiricist consensus commonly reject this possibility. For them all justified belief which is not restricted to the meanings of terms, that is, which "escapes the circle of language" and refers to "the world," is only justified by appeal to experience. In other words, we may say that our rational warrant for holding scientific beliefs must always be a certain body of empirical evidence expressed in certain "observation statement" or "basic statements" which are considered to be directly verified by experience. Thus another element of the consensus was its commitment to empiricism against the rationalist view that some things about the world could be known by pure reasoning. This does not mean that the empiricist consensus has no place for reason in determining scientific belief; far from it, the empiricist consensus strongly holds that also scientific explanation and prediction is made possible through deductive reasoning from both general laws and particular observation statements expressing "initial conditions."