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.