The ineradicabile role of personal subjectivity in all knowledge
One ineradicable fact - one which is often forgotten or lost to sight - is that in the first and last instance, all knowledge of whatever kind can only be understood subjectively. This means that there must be some person(s) - involving their subjective judgements - in the establishment as to what is acceptable as knowledge.
Personal testimony can be reliable, but to be regarded so by others than the experiencer, it has to be checked as far as circumstances allow and evaluated in combination with known circumstantial facts and other evidence. This can of course , include testimonies of others who may or may not have been present to some event or have special knowledge relating to whatever is at issue. Personal experiences count as (circumstantial) evidence not only for those who experienced some given incident or event, when thoroughly tested and shown to be likely to be accurate and truthful. The existence of the same or very similar accounts from other person previously considered reliable can be a deciding factor. Whether statements about personal experience are untrue (or lies) can quite often be determined by circumstantial evidence or known facts surrounding the matter.
The truth about anything is not usually a matter of a simple fact, true or untrue. In most matters of import, to establish the truth is seldom a simple decision about one state of affairs, for many events and circumstances are frequently involved. Otherwise law, science, philosophy and many another complex system of evaluation had all been unnecessary.The likelihood of truth or falsity is the measure used (and may be determined by probability theory). But certainty in matters of truth or falsity is seldom attainable. One can show that specific statements do or do not follow with necessity from given premises (as in logic), but one can not secure the truth or falsity of the premises by such a method. So logic does not itself determine truth (of any other than a formal, non-factual kind known as 'validity' (or 'invalidity). All assertions that have to be established by evidence, whether judicial testimony or empirical observation (as in scientific research). These are not provably certain results, because future discoveries may change the situation. This is known to be highly unlikely in all well-established science,and obviously less unlikely in all evidence that is only subjectively-based as in matters of law, politics, social discourse (i.e. circumstantial evidence, testimony etc.).
The ineradicable fact that all knowledge of whatever kind can only be comprehended as such by one or more subjective minds. This insight embraces everything we learn and come to understand to any degree has begun with subjective experiencing of all the countless elements of experience that go into learning to perceive and know anything in our lives. The resulting 'subjectivity' forms each individual memory, mindset, value predilection, propensity, attitude, and partiality. Of course, a widely shared common mindset develops within a culture, but is most likely hardly ever identical in content, detail, depth or general outline from person to person. There are also very widespread transcultural or global mindsets as regards many areas of life. Without such a common mindset there can be no 'established fact' or knowledge. Even so, the acceptance of information as true knowledge depends on inter-subjective agreement, and it is this that underpins what is widely considered to be firmly established and scientifically-tested knowledge. However many experiments have confirmed a theory, however wide-ranging and effective such a theory is in predicting events and developing technologies, it cannot be considered to be totally objective, since all knowledge depends for its existence and content on subjective decisions - in the very first and last instance. This is the ultimate lesson of philosophy, one which is all too often obscured, unknown or forgotten.
The dialectic of knowing
Persons who pursue knowledge to any serious extent will, through life, reject a very great deal of what they come across as invalid, untrue or plainly 'deranged nonsense' and will probably forget a good deal of it, though remaining aware enough of it to understand why it was not worth considering.
Doubtful claims and theories are put aside, not entirely discarded but preferable retained but within mental brackets, unproven but likely hypotheses likewise.
The process of sorting the mind, organizing one's conceptions of what is feasible, rational, likely, certain and so forth is essential to attaining to genuine knowledge, whether it be of one or more sciences, culture, the humanities, philosophy, literature and art or life experience.
Ideally, the purification of knowledge follows patterns which have been described by the philosopher Hegel as 'dialectical'. In general, this involved facts or theories being confronted by relevant counter-facts and theories until a synthesis of the truth content of each opposing thesis is reached. One retains what one judges to be the 'truth content' and rejects the remainder to the wastepaper basket (or perhaps to a holding tray for eventual retrieval).