There are very few sources on the web other than Sean Carroll’s blog that mentions the concept of cognitive instability. In his book “From Eternity to Here” and in his blog posts he credited David Albert for the origination of this concept.
“David Albert  has referred to such a conundrum as cognitive instability – the condition we face when a set of assumptions undermines the reasons we might have used to justify those very assumptions” 
I was intrigued by this concept. Sean Carroll’s example is from Cosmology. I need to find simpler examples. If you can come up with a simple example please kindly let me know (sureshemre at gmail).
I wanted to summarize Carroll’s example here but it is really too complicated. You should read his book instead. I tried to come up with another example for cognitive instability that does not involve false memories and entropy.
It seems to me that classical concepts of “time” and “space” lead us into cognitive instability. Sean Carroll’s example deals with “time” and my example deals with “space.”
The bizarre behavior of particles in confinement led us to quantum mechanics. For electrons confined to an atom the trajectory concept is no longer valid. Position and momentum of that electron cannot be measured simultaneously. The energy of the electron becomes quantized. Quantum mechanics was discovered by studying the characteristics of particles in confinement. I keep saying “confinement” because it is the key concept to understand quantum behavior. Then what happens? The developed theory of quantum physics tells us that space is irrelevant. This is a conundrum. The fully developed theory of quantum mechanics is non-local. There are experimental demonstrations of this claim by preparing a pair of photons in a spin-singlet state and then separating them. The entangled pair acts as if it is a composite particle even though they are separated miles apart. We started out by assuming that space (confinement) is relevant then we discover that space is irrelevant. This is a conundrum. What we find at the end undermines our “space” assumption but in order to discover the non-locality feature of quantum mechanics we had to make the assumption that space was relevant.
 D.Z. Albert, “Time and Change” Harvard University Press (2000)
 Sean Carroll, “From Eternity to Here”, Plume (2010), p:184