Existence
Matter is everything that has a detectable mass. It consists of elementary particles. Some particles form electrons and protons. Those in turn are the basis for atoms. Multiple atoms can form molecules. Matter is what forms the different objects that we can observe around us.
There are also some other particles which do not constitute matter, but are rather considered force carriers, such as a photon which is a carrier for light.
In any case, the existence of an object is broadly defined as its consisting of one or several connected particle(s).
Human Observation
A human being, too, is an object that consists of matter. He can observe and confirm the existence of other objects via his senses of sight, hearing, taste, smell, and touch, if need be aided by certain devices, which are all means to trigger chemical reflexes in his neural system and his brain. Man's consciousness, the sequence of all such reflexes, is an effect of the existence of his brain.
Consciousness allows man to formulate propositions, that is statements about (1) the physical observable properties of an object and (2) its actual movements relative to other objects. It also allows him to group objects with similar observable properties into the same conceptual categories and thus to speak of objects in the form of concepts.
Logic & Validity
Logic is the examination of a proposition's compliance with 3 axioms: the law of identity, the law of non-contradiction, and the law of the excluded middle. These laws are derived directly and objectively from the consistency of reality.
The law of identity says that the statement A = A (at the same time and place) is always true. For example, the statement "that rock on the ground is that rock on the ground" is always true. The statement "I am myself" is also always true in that same regard. The proposition "The law of identity is invalid" implies that A = A is false. This would mean that A = non-A is true. This would imply that the statement "The law of identity is invalid" is identical to saying "The law of identity is valid". Thus anybody who tries to oppose the validity of the law of identity affirms the law of identity in the very process, making it an irrefutable axiom.
The law of non-contradiction says that claiming A AND non-A (at the same time and place) is always false. No proposition can be true and false at the same time. The statement "I am sitting at my desk and I am also not sitting at my desk at the same time" is always invalid. The proposition "The law of non-contradiction is invalid" validates the law of non-contradiction. For if it was invalid, then the proposition "The law of non-contradiction is invalid and valid at the same time" would be correct. But then the person advancing the proposition would always have to affirm as valid the statement "The law of non-contradiction is valid" as well. Thus the law of non-contradiction, too, is an irrefutable axiom.
The law of the excluded middle says that either A OR non-A is always true. This means that, for example, the statement "I am either sitting at my desk or I am not sitting at my desk" is always true, there is nothing in-between. The proposition "The law of the excluded middle is invalid" validates the law of the excluded middle. For if it was invalid, then the statement "The law of the excluded middle is either valid or invalid" would be false. But that would mean that "The law of the excluded middle is invalid AND valid at the same time" would have to be true. But in that case the party advancing that proposition would always have to affirm as valid the statement "The law of the excluded middle is valid".
The logical examination of a proposition is very helpful because it can save you a lot of time. If a proposition fails the test of logic, there is no need to move on and look for evidence. If I say that there are cookies in the jar and these very same cookies are also on the moon, then you don't need to open up the cookie jar, fly out to the moon, search the whole planet for cookies, etc. Since reality is consistent, and logic is just a derivative of reality's consistency, any proposition that fails the logic test is by definition false.
A proposition that passes the logic test is valid. In order for it to be considered true, however, it still needs to pass the test of evidence.
Evidence & Accuracy
Evidence is the sensual, sufficient, and direct observation of objects in reality with the objective of testing the accuracy of a certain proposition. If the observed properties and/or movements of existing objects match those advanced in the proposition then it can be said that evidence exists to corroborate that proposition.
Any proposition that cannot be confirmed by evidence is inaccurate and thus its truth, if any, cannot be confirmed until proven accurate.
Any proposition that is confirmed by evidence can be considered accurate. The more evidence exists to corroborate a proposition the higher its degree of accuracy.
Truth
A proposition that is both valid and accurate can be considered to have been proven to be true. But as humans are fallible in their observations and thinking, they may, at times, make mistakes that lead them to ascribe truth to propositions that are actually false. Thus, there is always room for correction in the pursuit of knowledge. This of course does not mean that reality or truth are in any way relative.
Knowledge vs. Bigotry
One's knowledge is the set of those propositions that one subscribes to that have been proven to be true via logic and evidence. Any activity that involves the discovery of true propositions may be referred to as the pursuit of knowledge.
Bigoted beliefs are the false propositions one subscribes to in spite of missing or even contrary evidence. Any activity that involves the defense of false propositions in the face of missing or even contrary logic and evidence may be referred to as bigotry.
