Dogma is the unshaken belief that something is true, regardless of proof. The word is frequently misused as interchangeable with doctrine, but doctrine is, rather, the interpretation of dogma. Most frequently, one sees the term applied to religion. Examples in Christianity include the belief in God and the belief that Jesus’ conception was immaculate.
In religions like Hinduism, dogmas express a basic belief in the concept of karma and of reincarnation. A person who does not believe in these ideas could not shake the faith of someone who believes in reincarnation. In essence, dogma derives from faith.
The first dogma, in regards to religion, is the belief in some sort of divine being or beings. Though most religions have diverged from primal religions, they hold the kernel of truth in the sense that humans want to find the divine, and believe in a divine presence. The belief in such a presence or intelligence is the foundation of most religions.
Certain other types of faith are also called dogma. For example, believing in Marxian philosophy, and truly that socialism is the best possible construction for society is dogma. This type of belief assumes certain factors, such as “the worker is oppressed,” and “religion is an opiate of the people.” How these ideas are applied to a society would become political doctrine, or an interpretation of Marxian dogma.
Virtually all schools of philosophy have a set of unproven truths to which they cling. In extreme examples, as per deconstructionist thought, the central dogma is that most text contains multiple contradictions and meanings. Such proofs that are offered, the doctrine of deconstruction, are actually arguments and not proofs.
Dogma also applies to ideas like free education for all. There is an underlying belief structure that it is good for all children to have free education. This is not based on statistics, but on faith that access to education is a basic right and is valuable to all.
Mostly, however, dogma applies to core truths that are based on faith. People in the Judeo/Christian/Islamic religions don’t believe God to exist, they know he exists.