Assumptions, assumptions everywhere ...

The difficulty with any attempt to change an organization is that we're full of assumptions. Both as consultant looking into the organization, as well as member of the organization looking out, we filter our perception of reality through a mesh of underlying assumptions. These assumptions will dictate our thoughts and actions. This wouldn't be a big issue if assumptions were either irrelevant or consistent. It becomes an issue when our assumptions are in conflict. But what kind of assumptions do we make?

Axioms ("Base assumptions")

Axioms are fundamental assumptions which we can neither prove nor disprove, so we simply assume they are true. One scientist I respect a lot says that he reduces his axiom system to the following set:

1. Reality exists
2. We can learn something about reality, from which we can form our own model of reality
3. Models with predictive capabilities are better than models without

People may rely on more - or other - axioms.
The principle of Occam's Razor basically states that models requiring fewer assumptions tend to be more accurate.
The problem with relying on a different set of axioms is that basically, we are talking about a different model of reality without even realizing. If you see discussions going in circles, it might be good to establish a common set of axioms and check them for consistency.

Theory ("Scientific Assumptions")

We can to learn something about reality using the Scientific Method. Typically, these are also merely assumptions, because we often rely on tacit knowledge, but we still try to find better explanations with fewer underlying assumptions. The big difference between a scientific theory and an axiom is that a theory can be reinforced by repeating the experiment of the theory. Everyone is encouraged to find an experiment that could disprove the theory and form a more accurate theory. When there is overwhelming evidence for a theory and no valid counter-evidence, the theory is considered proven.
Our theories rely on our axiom system and must be consistent not only with these axioms, but also with one another.

Derivation ("Logical Assumptions")

Often, we derive knowledge rather than proving it with experiment. We often rely such derivate assumptions, such as "Tim is grumpy, therefore it is not a good idea to tease him". The derivation of new assumptions usually relies of further axioms, such as the rule of inference. Logical assumptions are typically considered valid as long as they rely exclusively other assumptions that are considered "valid" and were derived without resorting to a logic fallacy. A derivate assumption is automatically invalid if any underlying assumption turns out to be invalid.

Bullshit ("Made-Up Assumptions")

Sometimes, we just make up an assumption to justify a certain behaviour, in concrete disregard of the reality around us. In many cases, people refer to some form of evidence, ignoring the scientific method. Scrutiny will expose this, and the idea should be rejected. If these assumptions plainly contradict available evidence, there's only one name for that: Bullshit. There's probably not much need to describe what we should do with that.

Dogma ("Religious Assumptions")

One of the worst problems plaguing the world of science, management and news are dogmatic assumptions. But what's a dogma? Dogmas arise whenever a concept is assumed to be valid "because someone said it" (or wrote it) without a tracible line of inference or evidence. Dogmas become problematic in two circumstances. First, if the original idea was already bullshit. In that case, we can also refer to the idea as a hoax. Second, when we need to trace back to the origin in order to discover a potential lever for adjustment. Quite often, tracing back the root busts the assumption: During backtracking, we might discover that we relied on an idea that was not valid to start with. Dogma is not inherently invalid, but whoever adopts dogma runs a risk - Caveat Emptor!

Take-away

Everyone makes assumptions. It is not bad to have assumptions.
However, inconsistent assumptions cause miscommunication and result in poor decisions. 5-Why-Analysis is a method to expose invalid or inconsistent assumptions. Tracing back a thought system to it's underlying assumptions can reveal crucial points of uncertainty.
Exposing the key assumptions in your models can be a powerful mechanism to uncover ways for significant innovations through experimentation, validation and rejection.