How can a distributed system be consistent and available (CA)?
Because I would argue when a network partition occurs, CA cannot be possible in a way where every node of the network, even the partioned nodes that users are connected to, continue to be available and answer with consistent data.
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Dr. Stonebraker says: The guidance from the CAP theorem is that you must choose either A or C, when a network partition is present. As is obvious in the real world, it is possible to achieve both C and A in this failure mode.
See this for thoughts on why CA can exist:
CA is a specification of the operating range: you specify that the system does not work well under partition or, more precisely, that partitions are outside the operating range of the system.
My background is far from these theoretical considerations and I must say it is highly confusing. I am researching distributed Blockchain systems and I don't see why those "generalized" definitions of C, A, P must always apply. If let's say 5% of nodes fail or are otherwise partitioned, the consensus still functions. If an end user is connected to a partitioned node, the node could let the user know it lost connection. I don't even see how any major Blockchain network is CP without defining conditions such as "if a certain amount of nodes fail or get partitioned, the consensus halts".
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As often mentioned, the CAP theorem in its original form is a little misleading. It can be restated as
in the presence of the network partition, a distributed system is either available or consistent
so you are right. Generally, systems cannot be classified as CA, CP or AP only, since partition tolerance is a property of the system, which describes what to choose in case of a network partition. So it is possible that a system can behave according to AP sometimes, and CP other times (however it is not common).
Another interesting part is that RDBMS databases are often at the CA side of the triangle. This is only the case in a single node setup. Even with master (write) - slave (read) setup, the system is not CA (or if it is termed "CA" for some reason, and cannot recover from network partitions, then a split-bran scenario may happen, a new master is elected for the partition, and chaos ensues, possibly breaking the consistency of the system).
Useful read: https://codahale.com/you-cant-sacrifice-partition-tolerance/.
It can, but it won't.
The CAP theorem reasons about guarantees when one or more nodes get isolated from the rest of the cluster. In such cases a node has three options which result in the three known CAP trade-offs: i) it keeps responding to any received requests AP; ii) it no longer responds to received requests until it is again able to reach the others CP; iii) it shuts down before receiving any requests to eliminate the partition along with it CA.
In other words you can achieve CA by having your nodes shutting down instead of tolerating the partition but bear in mind that partitions are likely to keep happening hence this will converge to the scenario in which you have a single node in your cluster and I assume this is the opposite of what you want, i.e. having a cluster with multiple nodes is kind of the whole point.
Therefore in practice you end up choosing between CP and CA. See this answer for more illustrative examples.