We need to properly understand why “justification / verification / confirmation” is considered undesirable, and not blindly accept that it is always wrong.

There are two main logical fallacies that come into play here:

(1) Fallacy of asserting the consequent

(2) Fallacy of denying the antecedent

And their logically valid counterparts:

(3) Modus Ponens

(4) Modus Tollens

Justificationism is said to embody (1) and (2), and therefore accused of being inductive.

Critical Rationalism, on the other hand, is said to uphold (3) and (4), and thereby purports to be deductive.

Bayesian epistemology instead tells us that there is no practical difference between Justificationism and Critical Rationalism. [Having said that, I am aware that Critical Rationalism entails philosophical ideas that Justificationism may not entail. And that’s simply because within Justificationism itself, there are many different streams of thought. The present writer simply wishes to illustrate the practical similarities, and is not particularly interested in the philosophical differences that, realistically, can be held by both a Justificationist and a Critical Rationalist.]

In the real world, things are seldom so straightforward, because the difference between (1) and (3) depends on the existence of plausible alternative theories. The same is true of the difference between (2) and (4).

Bayesian epistemology is a way of assigning concrete probabilities to inform us of whether in a specific situation, (1) or (3) is more likely to be the case, and correspondingly whether (2) or (4) is more likely to be the case.

Additional reading:

http://infoproc.blogspot.sg/2008/12/jaynes-and-bayes.html

To put it in a different way:

Justificationism: Assumes that observation X confirms theory A, while (perhaps) being aware of the existence of plausible alternative theories B, C, etc.

Critical Rationalism: Acknowledges that there exists theories A, B, C, etc. that have yet to be falsified, one of which could explain observation X. In the end, it chooses to use theory A because it is the most well-tested theory amongst the other alternative theories (this is based on the idea of Critical Preference).

Bayesianism: Examines all the available theories A, B, C, etc. [or at least, as many of the most plausible ones as possible to the extent that utility is maximised; Bayesianism represents an ideal that is applicable to varying degrees in practice], and assigns each theory a probability that indicates its plausibility (relative to the other competing theories) of actually being the true theory that explains X.

It is clear that Justificationism and Critical Rationalism (loosely speaking) result in the same thing (all other factors being equal, i.e. assuming that both epistemological approaches are applied—by different people, of course—while adhering to the rule of Critical Preference or some other decision theory that’s practically identical), because they both end up choosing theory A even though the alternative theories B, C, etc., could not be definitely ruled out. [The differences between the two are primarily a matter of perspective, i.e. they are simply two different cognitive interfaces that, given the same variables, produce the same result.]

Bayesianism uses a logical system that is more powerful than both Justificationism and Critical Rationalism, because instead of choosing only one theory, it is able to simultaneously handle all plausible theories by assigning each theory a probability value. [In technical terms, Justificationism and Critical Rationalism traditionally use two-valued logic, whereas Bayesianism uses multi-valued logic.]

http://en.wikipedia.org/wiki/Boolean_algebra#Two-valued_logic

Two-valued logic can be extended to multi-valued logic, notably by replacing the Boolean domain {0, 1} with the unit interval [0,1], in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed. Algebraically, negation (NOT) is replaced with 1 − *x*, conjunction (AND) is replaced with multiplication (), and disjunction (OR) is defined via De Morgan’s law. Interpreting these values as logical truth values yields a multi-valued logic, which forms the basis for fuzzy logic and probabilistic logic. In these interpretations, a value is interpreted as the “degree” of truth – to what extent a proposition is true, or the probability that the proposition is true.

Final thoughts:

In practice, a Justificationist who uses the same philosophy of critical thinking that is advocated by Critical Rationalism, makes decisions that are identical to the Critical Rationalist (all other factors being equal). In fact, the spirit of Critical Rationalism could be said to have been propagated beyond the narrow confines of Critical Rationalism, in the form of Critical Thinking.