Dogma

It is largely arguable what constitutes a reasonable justification for believing something. A common criteria indicates that such a justification should involve at least coherence and evidence.
A belief is coherent if it doesn't contradict other belief, particularly knowledge, and fundamentally, scientific knowledge.
Evidence is any observable that is related with the proposition through a logical connection.
I think however that coherence and evidence are sufficient but not necessary conditions to hold a belief (though they are necessary to promote a belief as formal knowledge)

Most people, specially 'intellectuals', consider irrational to believe what is not evidently true or is evidently false. Though there can certainly be 'irrational' beliefs, that is: a belief that is rooted on anything but reason, IMO, it is often misleading and unfair to externally qualify a belief as irrational, simply because externally is next to impossible to judge the justifications that can hold for such a belief. Most intellectuals judge laymen's beliefs based on the grounds of the accepted scientific knowledge, yet in the case of the Factual Sciences, such a knowledge is still not the ultimate truth, so it is plain dogmatic to defend it up to the point of qualifying as irrational a belief simply because is contradicted by Science.
IMO, it is a lot more useful and fair to qualify a belief from a functional perspective: Having a coherent and evident (even if personally) belief is clearly useful: decisions I base on it have a good chance of turning out right. Having a coherent but poorly evident -or even not evident at all- belief is potentially useful: decisions I base on it have some chance of turning out right. However, having an incoherent belief is unlikely to be any useful at all (recall that incoherent means contradicting with other things we believe or know). But in any case, it is the consequence of holding such a belief what ultimately matters for fair qualification.
If I believe in life after death, in whatever form (with any degree of coherence) and for whatever reason (with any degree of evidence) and, as a consequence, I base all my actions on the principle that everything we do has eternal consequences (eternal meaning as long as time itself exists) because death won't put an end on it, I have a useful and justified belief. It is unlikely, certainly not knowledge, but is nevertheless useful and justified (quite far from irrational)

Since not even scientific knowledge is conclusive, we can only be reasonably justified in believing something up to the boundaries of a given context. A belief can turn out to be false -even after it was rightly held true- for a huge variety of reasons: new contradicting evidence, new contradicting and more fundamental theories, or simply the recognition of a mistake in the logical process or evidence verification. There is no such thing as the ultimate truth, except in the case of the logical virtual structures that exist in our minds, like a mathematical axiom, a lexical significant, etc...

There's nothing wrong in believing something -however unlikely or even contradicting with accepted knowledge- when doing so has useful consequences... what is useless -specially in the long term- is to hold the belief as the ultimate and unquestionable truth. This is dogma.
Yet dogmatism is not about believing what is evidently false or not evidently true (as if such a property could be completely determined); it is about denying the fact that all beliefs are inconclusive. There's dogma in Religion, for sure, but there's dogma also in Sciences (just pick up almost any conversation in sci.physics and you'll clearly see it). It doesn't matter if we're talking about the conservation laws of physics: these are based on a huge amount of evidence and a perfect coherence with every scientific theory, yet all such evidence, however huge, is an insignificant fraction of reality and all the theories such laws are coherent with are rooted in the same extremely partial evidence.
It is ironically dogmatic to hold our so-called "laws of universal physics" unquestionable considering that we've been serious about it for just a few centuries (but been here for a lot lot more) and we're just starting to step out our tiny little planet to get real evidence and not just old EM waves.

Belief, Knowledge and Faith

Conviction is a feeling or awareness of the truth of one's thought. [Merriam-Webster]
Certainty is the quality of something of being certain, and a statement is certain when it is proved to be logically and/or factually correct [Merriam-Webster]

When we're convinced of the truth of something we know it (informally). Since convictions are personal by definition, knowing something (informally) is a personal activity.
Certainty, on the other hand, is a quality given to a statement by a proof. Although a proof does constitute a reason to be convinced of the truth of something, not all such reasons are proofs. The personal reasons I might rightly have can only be regarded as proof if they can be shared so that others can equally and independently realize the same conviction. Formal certainty is therefore an independent measurement of the truth of a statement.

In Logic, formal knowledge is a proposition certainly true.

We can always informally "know something"; that is: be convinced of its truth (for whatever reason), yet we do not formally know it unless it is certainly true.

Although we know, as a personal activity, statements are certain independently.
There are many different formal procedures to assent the certainty of a statement, but they all share a common requirement: anyone should be allowed to carry them out. This assures the independence of the formal certainty attached to a statement.

A belief is a conviction held with or without certainty [Merriam-Webster]
If a belief is a formally certain conviction, it is a formal knowledge.

It is useful, IMO, to draw a distinction between beliefs and (formal) knowledge such that only certainly true convictions are regarded as knowledge and the rest as beliefs. That is, we should consider that we know only what is potentially known by anyone else (has independent certainty) .

Although formal certainty indicates the truth of a statement, factual statements are only certain to a given degree. Therefore, we say that a factual statement is certainly true meaning that is unlikely to be false, but never that is undoubtly true. That's why we say "certainly" true instead of "absolutely" true. Factual sciences, like physics, are ultimately inconclusive because none of its statements are absolutely certain. This means that knowledge, however unlikely, can be false.
On the other hand, a belief (based on the distinction I drew above) is not certain yet it can all the same be true.

Rationalist claim that you should only believe what you know, that is, what is (formally) certain.
I don't agree because you can only formally know what can be independently proven and there are lots of things that cannot. For example, I can be rightly convinced that I love my wife so I can rightly believe it, yet I couldn't possible prove it. (I wouldn't say that I know so, formally, because I like the distinction that knowledge is shareable).

A conviction might be justified. Knowledge, for example, is (very well) justified by its formal proof. Beliefs which cannot be formally regarded as knowledge can be justified too: it is just that such justification cannot be easily shared (more on justified beliefs in my next post).

The most common definition of faith is: firm or unquestioning belief in something for which there is no proof [Merriam-Webster]

although there certainly exist such form of believe, I found sad that the term does not incorporate as one of its many definitions something which IMO is fundamentally important:
There is a motivation that results from believing something. I call such motivation Faith, and the term is colloquially right since it is used in this sense despite its other formal definitions.
In any event, I propose this meaning because the motivation I'm referring to is IMO fundamental, so much that there has to be a term for it, and faith is perfect for it.
There's nothing wrong or irrational in having faith (as in being motivated by one's beliefs); what can be misleading is to believe for the wrong reasons. Faith, in this sense, is what turns a belief or knowledge into a driving force. It is a fundamental and essential human feature.

What is rightly questionable is to be driven by faith to behave wrongly, but faith itself is not to be blamed here since it is not faith alone what results in such bad behavior.

I'm not unaware of the sort of beliefs endured by typical religions, nor that these religions ask their believers to accept those beliefs as an "act of faith". I think, however, that my definition of faith is still correct and that the term is misused by religions because we all need a broad, life-scoping motivation to live, and religions seek to get people to obtain that motivation out of their doctrines, which are claim to be unquestionable. Hence, faith became a synonym for dogma.

All scientists have faith on what they're developing right from the early stages when their belief cannot be considered knowledge. If they hadn't, science would have never developed the way it did.
I can have faith in my own will and potential to reach my goals, and there's nothing wrong with that; I don't know that I will get there (formally speaking) but I rightly believe it and I have faith in this belief. Not only there is nothing irrational in this faith but is also necessary: we humans are driven by motivation; without it, we would be nothing but an organic stone.

The glory and perils of Science

Perhaps the most glorifying achievement of modern mankind is Science, and particularly, the Scientific Method. In a nutshell, the scientific method prescribes how to develop an explanation about some part of reality, how to express it formally, and how to measure its reliability.
In other words, anyone can come up with an explanation for anything; yet if he can put it down formally so that anyone else can understand it (pretty much unambiguously), and anyone else can measure independently how much of a truth the explanation is, then he's formulated a scientific explanation.
If a proposition (a statement about something) is not formally expressed or cannot be independently contrasted in any way, it might be an explanation, but is not scientific.

(Formal) Science, and the scientific method, is probably the most wonderful and fruitful development of the past centuries; however....

Functionally speaking, science and its method is a tool, and all tools ought to be used wisely, yet often, they are not, simply because it is us, humans, who use it.

One of the perils of science is the common misconception, specially among the so-called layman (i.e. us, normal people), that science is bullet-proof and that a scientific statement is guaranteed to be true. It is quite common to heard the expression: "It has been scientifically tested that..." as a way to say: "it is undoubtedly true that..."; yet however common, is wrong.
Science is about producing statements about reality with a known certainty, but known certainty and complete (100%) certainty are quite different things.
Scientific knowledge, in the minds of scientists, is a structured collection of ideas each with a well establish degree of truth; yet in the collective-mind of society, is a corpus of unquestionable laws about everything.
Ironically, most people, including many scientists, pose a dogmatic attitude towards scientific knowledge. The power of science comes from its dynamism, a feature rooted in the fundamental fact that science is always inconclusive. If scientific knowledge were to be considered final word, it would be nothing but dogma.