Beliefs: Irrational or Rational

In Cognitive Behavioral Therapy, there is a concept of rational or irrational beliefs. What is the difference? Don't all beliefs have both rational and irrational elements? Sometimes I believe all beliefs are fundamentally irrational because there is always an underlying premise that is not provable logically. So aren't all beliefs irrational at some level?

“Don't all beliefs have both rational and irrational elements? Sometimes I believe all beliefs are fundamentally irrational because there is always an underlying premise that is not provable logically.”

At the risk of waxing Clintonian (i.e., “It depends on what the meaning of ‘Is’ is.) it would seem that the full scope of a response would depend on the applicable definition (or at least the context) of ‘Belief’.

One definition of ‘Belief’ - "the feeling of being certain that something exists or is true."

Thus, If you stipulate ‘Belief’ to encompass factual assertions with which you must agree because they are axiomatically truthful, than I fail to see that “all beliefs must be irrational at some level.”

For example, if one approaches Descartes’ classic Cogito ergo sum (I think, therefore I exist") as an assertion of belief, however self-evident, than one surely avoids the caveat “all beliefs must be irrational at some level. ' (Note: this is not to say that Descartes’ assertion does not lack detractors and even an attempted refutation or two; point is, it is not irrational.) Mathematical truisms MAY constitute another branch of non-irrational belief, though this is more complicated.