Logical Positivism, or sometimes just positivism, was the first real theory of knowledge production. To get started, let's take a brief look at where logical positivism arose from, what if offered, and it's weaknesses that led to its ultimate rejection.

Now we move onto Sir Karl Popper one of the leading critics of logical positivism and its criteria of verification. The excepts below in italics are pulled from Wikipedia - I have left them with their hyperlinks so that you can follow them to additional points if you so desire.

Sir Karl Popper coined the term critical rationalism to describe his philosophy. The term indicates his rejection of classical empiricism, and of the classical observationalist-inductivist account of science that had grown out of it. Popper argued strongly against the latter, holding that scientific theories are abstract in nature, and can be tested only indirectly, by reference to their implications. Logically, no number of positive outcomes at the level of experimental testing can confirm a scientific theory, but a single counterexample is logically decisive: it shows the theory, from which the implication is derived, to be false. The term "falsifiable" does not mean something is made false, but rather that, if it is false, it can be shown by observation or experiment. Popper takes falsifiability as his criterion of demarcation between what is and is not genuinely scientific: a theory should be considered scientific if and only if it is falsifiable.

Popper's falsificationism can be questioned logically: it is not clear how Popper would deal with a statement like "for every metal, there is a temperature at which it will melt." The hypothesis cannot be falsified by any possible observation, for there will always be a higher temperature than tested at which the metal may in fact melt, yet it seems to be a valid scientific hypothesis. These examples were pointed out by Carl Gustav Hempel. Hempel came to acknowledge that Logical Positivism's verificationism was untenable, but argued that falsificationism was equally untenable on logical grounds alone. The simplest response to this is that, because Popper describes how theories attain, maintain and lose scientific status, individual consequences of currently accepted scientific theories are scientific in the sense of being part of tentative scientific knowledge, and both of Hempel's examples fall under this category. For instance, atomic theory implies that all metals melt at some temperature.

Popper maintained that that there is an objective reality, though perhaps separate from our ability to sense it (ontology). He acknowledged that individual beliefs or bias influences the work of individual researchers, but maintained that errors produced by these influences are eventually corrected through the rigorous discourse and consensus building of the researcher community (epistemology). Embedded within this process are two important assumptions: (a) that the consensus, or majority, is always right; and (b) that language itself is a transparent, universally understood and a direct representation of its associated item, concept, etc. Dissatisfaction with this later assumption led to the development of social constructionism, sometimes referred to as relativism.

Recent evidence that assumption (a) above does not always hold up so well
Ridiculed Israeli scientist wins Nobel