This involves anything that is found to be logically contradictory. This only applies to deductive logic.
e.g. Black is White
This is the weakest of all non-disprovable beliefs. So much so that you would probably classify it as a 'non-belief'. Reason and logic dictate that the available evidence does not in any way support this idea. In fact it weighs so heavily against it, that it is almost the inductive equivalent of being False.
e.g. Elvis is still alive
There is little or no empirical evidence to support this idea one way or another, thus it is currently impossible to disprove. Therefore one must still be open to the possibility that it could be true, but it is unwise to pursue such a belief without just cause.
e.g. There are lizard men on Mars
The evidence is mainly circumstantial and consists primarily of secondhand accounts or 'biased research'. The weight of evidence is against it, but there is still enough evidence in its favour to at least make it credible.
e.g. Alien Abductions
This is a non-biased starting position for any belief. This position assumes that the evidence is equal i.e. 50/50. It is a position one should adopt when one knows little or nothing about the subject matter, or if after some research you realise that you don’t care either way. It is therefore either a recognised state of ignorance, or one where examination of the evidence, neither supports, or disproves the subject matter sufficiently for you to move to a more biased position on the scale.
The weight of evidence is in its favour, such that you tentatively accept this as a fact, however beliefs at this level are often very mutable and are prone to rapid revision.
e.g. The Big bang
The weight of evidence is heavily in its favour, however it is still not beyond reasonable doubt. Sufficient unanswered questions remain for it to be accepted as an evolving 'fact'.
e.g. Evolution
This is accepted by you as a fact. There is generally no further evidence being gathered and it will often be termed by you as a ‘law’ or ‘rule’. However one must still allow for the 0.1% possibility that you are in some way mistaken.
e.g. The First law of Thermodynamics
This is for anything that is mathematically or logically(deductively) provable
e.g. if a > b and b > c then a > c.