Consider the law of non-contradiction: Nothing can both have a property and lack it at the same time. For example, one cannot be a bachelor and married at the same time. A binary state cannot be both 1 and 0 at the same time. 

Our universe is governed by physical laws and whatever violates them cannot occur. Hence, although it’s logically possible for a cow to jump over the moon (nothing in the concept of 'cow' makes a 'flying cow' a contradiction), it is not physically possible because of scientific laws relating to gravity and bovine physiology. (Note that many sci-fi creations are simply beings that are currently considered physically impossible.)

As our knowledge of the physical world increases, our understanding of the limits of physical possibility expands. For example, Einstein believed that quantum entanglement of particles—"spooky action at a distance," as he called it—is not physically possible. But we now know that this seemingly impossible phenomenon is real. 

Possibility does not imply actuality. To establish that something is real, we need reliable evidence that it actually exists.

We can’t infer what is from what seems. It is an error in reasoning to conclude that an event or phenomenon (X) is real because it seems real. Questions to ask: Is our experience of X corroborated or shared by others? Does our experience of or conclusion about X contradict all known previous experience? Is it possible that a peculiarity of human perception / cognition (e.g. color constancy) could be operative?

Reasons for doubting include: perceptual construction, memory construction, effects of stress, effects of expectancy and belief, selective attention, misjudgments of probabilities, subjective validation, altered states of consciousness, poor observational conditions, sensory impairments or limitations, and conflicts with other observations / knowledge that we have good reason to believe.

We can’t make something true simply by believing it to be true. The early Greek philosopher Protagoras (c. 490 – c. 421 BC) held that "man is the measure of all things." Today, this subjectivist notion of truth can be seen in various quarters of the New Age movement, where disagreements have been stopped dead in their tracks by statements like "Well, this is my truth, and that’s your truth."

As an elaboration of individual subjectivism, social relativism holds that society, not the individual, determines what is true. But, society used to believe that the Earth was flat, that the sun orbited the Earth, etc. The same problems and contradictions that plague individual subjectivism also befall social relativism.

Neither knowledge nor reasonable belief requires certainty. A proposition is beyond a reasonable doubt when it provides the best explanation of something. But being justified in believing a proposition is no guarantee of its truth.

The quest for knowledge involves eliminating inconsistencies among our beliefs. Sometimes we observe or are informed about things that conflict with our background information—that vast system of well-supported beliefs that we habitually use to guide our thoughts and actions (much of it referred to as "common sense").

The structure of background information can be compared to the structure of a large tree. Bigger branches (beliefs) support smaller ones, which in turn support even smaller ones. Accepting some claims is analogous to pruning small branches—giving up only peripheral beliefs. Accepting others is akin to cutting large branches.

The truth of a claim is established by the amount and type of evidence in its favor—not by the lack of evidence against it. Also, attempting to place the burden of proof on the nonbeliever is asking for the impossible: to prove a universal negative (a claim to the effect that nothing of a certain sort exists). To prove a universal negative, one would have to exhaustively investigate all of time and space.

This is the converse of the preceding principle. Here again, the error in reasoning is an appeal to ignorance (as in the argument that no one has ever proven that alternate universes exist; therefore they don’t).

The more evidence we have for a proposition, the more credence we should give it. The probability of the truth of a contingent or scientific proposition can range from close to 0 (e.g., "Someday, humans will travel faster than the speed of light.") to close to 1. It is generally held that only logical truths warrant such strong belief that their probability values equal 1 (e.g., "Either it is snowing or it isn’t.")

The opinions of experts is superior to our own only in their field of expertise. Just because someone is an expert in one field doesn’t mean that he or she is an expert in another.

Only if we have good reason for believing that they are not functioning properly should we doubt the traditional sources of knowledge: perception (the physical senses), introspection (witnessing dispositional mental states, memory, or reason.

When there is disagreement about a particular state of affairs, the objectivist (moderate realist) believes that it is at least theoretically possible to determine the truth through rational discourse.

Mysticism is just tomorrow’s science dreamed today. –Marshall McLuhan

Not I, but the whole world says it: everything is one. –Heraclitus

When one sees that everything exists as an illusion, one can live in a higher sphere than ordinary man. –The Buddha

…often my body would become so light that it lost all weight. –St. Theresa

The scientific method is our most reliable means of establishing the truth of an empirical proposition beyond a reasonable doubt. Science seeks to understand the world by identifying general principles that are both explanatory and predictive. To minimize the potential for error, inadequacy, or fraud, the scientific method requires repeatable results. In general, any procedure that serves to systematically eliminate reasonable grounds for doubt can be considered scientific. For example, consider this general method:

The process of creating hypotheses (possible explanations) is just as open-ended as the process of artistic creation. Although inductive reasoning can lead to the formulation of a hypothesis, other processes—like direct insight, and imaginative construction—are also sources of useful hypotheses. A good hypothesis must account for all the evidence it is intended to explain.

If a hypothesis can not be tested, there is no way to determine whether it is true or false. Hypotheses have observable consequences only in the context of a background theory. So, to be testable, a hypothesis must predict something more than the background theory alone.

Even in the face of adverse, initial evidence, some hypotheses are attractive because they promise to open new lines of research by making the most novel predictions. E.g., Einstein’s theory of relativity predicts that light waves travelling near massive objects will appear to be bent because space around these bodies is curved. At the time, common wisdom was that light traveled in Euclidean straight lines since photons had no mass.

The more a hypothesis explains and predicts, the more it systematizes and unifies our knowledge. E.g., Einstein’s theory of relativity came to be preferred over Newtonian theories of gravity and motion because the theory of relativity explained and predicted everything that Newton’s theories could and some things that it couldn’t (like variations in Mercury’s orbit).

Although not simple to define, scientific simplicity can be understood as the fewest number of assumptions required by a hypothesis. The simpler the hypothesis, the more it unifies and systematizes our knowledge, and the less likely it is to be false since there are fewer ways for it to go wrong. Hence, Copernicus’s heliocentric theory of planetary motion was considered preferable to Ptolemy’s geocentric theory. This principle is often referred to as Occam’s razor: Do not multiply entities beyond necessity

The hypothesis that fits best with established beliefs is to be preferred. As with all the other criteria of adequacy that can be applied to hypotheses, it may be reasonable to accept a hypothesis that is not conservative if it possesses other criteria of adequacy. And, we can not rank these criteria in order of importance. There are borderline cases where reasonable people can disagree and clear-cut cases where disagreement would be irrational. Hence, although it may not be clear at what point a person becomes bald, it is irrational to consider that a person with a full head of living hair is bald.

The criteria of simplicity and conservatism should lead us to prefer ordinary explanations over unusual and ad hoc (created after the emergence of the phenomena) explanations. It should be noted that with an ad hoc hypothesis, there is no way to test it because no possible data is allowed to count against it. Every apparent counterexample is explained away and no unsuccessful experiments are allowed to count.