A fact is a publicly floated statement which has been certified as valid by a self-appointed authority. Facts are presumed to be verbally expressed relationships of high probability truth value which model our perception of reality. It is tempting to imagine that facts can exist independently of any spoken or written expression of them, but this cannot be the case. Facts are in our heads and are not physical elements of the cosmos. A fact does not have an independent ontological existence any more than a shadow does. There is not a...there is a flying object up there...fact floating around somewhere outside of our awareness. Nature does not know what a balloon, kite, aircraft or seagull is and neither does it know what it is to be flying. All of those concepts dwell in the awareness of the person modeling the perceived situation.

However ephemeral they are, facts can very useful in helping to shape ideas. The...there is a flying object up there...fact, certified by a local reliable aeronautical consultancy, might well function most usefully as part of an overall conceptual model of reality. It might be quite reasonably classified as knowledge for those wanting to estimate wind velocity or explore the physical limitations of flying objects. It might even be archived as evidence for the existence of unidentified flying objects. Thruout this entire process of course, skeptics both nonymous and anonymous will be sending missiles in the direction of the facts in an attempt to bring their shadows back down to earth.

A generally accepted expression of a factual relationship is thus not readily made. The main reasons for this situation are the ambiguity of language, the variable perception capacities of individuals, and the motives of the fact-certification authorities. Existential relationships are often only gradually perceived and linguistically proposed as beliefs or hypotheses which aspire to be facts. As evidence is accumulated, beliefs masquerading as facts should be progressively called into question and reinforced, modified or disputed. There is thus an endless loop of discrimination and comparisons which will have no termination until a general falsification emerges.

Many concepts are reinforced into our awareness from birth by social, cultural and political interests to the extent that they acquire a capsule of self-evident certainty. Such supposed facts seem essentially unquestionable. Yet the basis for such absolute certainty can be fragile. Consider the oft touted claim that...one plus one equals two...is a fact. If it is a conceptual statement of mathematics, contrived from the internal intrinsic definitions, symbols and logic, then to call it a fact is to surreptitiously accept that the conceptual elements of mathematics have the same origins as the conceptions derived from an external reality. But this is like trying and make shadows into things. A shadow is nothing more than the perception that a region of reality has been perceptually modified by an obstruction to a light source. Thus it is with mathematics which exists in a region of reality modified by an awareness and is not about facts at all. The...one plus one equals two...statement, and all similar statements like...one hundred and three plus twenty nine equals one hundred and thirty two..., functions as a sequential manipulative rule for handling counting in bulk. It avoids having to disintegrate each counted value, combine them into a single set, and then recount. It is not a fact that...one plus one equals two... , it is a rule.

If it is to be incorporated as part of a conceptual model about reality and be considered as knowledge, then we must realize that it does not work very well unless careful consideration is given to the meaning of one. One volume of water and one volume of alcohol does not result in two volumes of either. One mass of U₂₃₅ added to another mass of U₂₃₅ can result in a lot more than was bargained for. One dollar at time T₁ added to one dollar at time T₂ will probably not equal two dollars at time T₃.

...one plus one equals two...is not a fact, but an example of a set of numerical rules which we use when we wish to count a number of entities that have been labeled as being members of a convenient category.