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The first thing to say is that "special revelation" is a useful terminology but not a doctrine like "biblical inspiration". Therefore, the definition of "special revelation" is not set in stone, while the doctrine of "biblical inspiration" is set by a Christian group to guide their reading of the Bible. Being a terminology but not a doctrine, I tried to define "special revelation" from usage (de facto) rather than from what it should have been.
Secondly, what one group considers God's revelation may be different than another group. For example:
For this reason, I will be using the term "authenticated" to mean God's special revelation that has been accepted by a certain group. What's authenticated for Muslims is obviously different for Christians. When reading Christian books about "special revelation", this "authenticated" status is implied, which we should take to mean "authenticated by the group endorsing the book".
For this answer, I'm trying to speak for all mainstream Christian denominations, noting minor variations when applicable.
"Revelation" is God's disclosing of Himself, primarily his character, his plan, his desire, and his law.
The counterpart of "special" is "general", which has to do with both the channel and the mode of disclosure. For general revelation:
Thus we can derive the existence of God from nature, or derive some of his attributes from nature (his power from observing natural forces, his creativity from noticing the variety of plants and animals, his interest in right conduct from our conscience, etc.).
Everything that is not "general" is thus "special", so it's always occassional, one-time event. But the usage of the term "special revelation" is generally restricted to refer to authenticated content (as coming from God) that applies / directed to the community (or all people) for general use and for all time. Therefore:
"biblical inspiration" refers to special features relating to God's providence over hundreds of years to safeguard:
This is a tricky question depending on the doctrine of biblical inspiration. There is a wide spectrum of biblical inspiration doctrines adopted by different Christian camps, ranging from
Two typical middle-of-the-spectrum positions:
Evangelicals who hold the doctrines of plenary verbal inspiration and biblical inerrancy starting with the mid 19th century Princeton Theological Seminary scholars Charles Hodge and Benjamin Warfield, updated in the 1978 Chicago Statement on Biblical Inerrancy. In this model, the content of biblical inspiration is a proper subset of special revelation, PLUS additional special features connected to God's providence.
Christians holding a less strict doctrine of biblical inspiration which allows a biblical author to make factual error (especially relating to scientific facts), although usually God's providence safeguards the final form. For these Christians, they read the Bible using a hermeneutics that does NOT expect the Bible to be treated as science books, using the Framework interpretation for the 6-day creation, for example. In this model of biblical inspiration, some "general revelation" can be part of biblical inspiration.
Biblical inspiration models change over time, even within the evangelicals movement (!). See a 2020 article Inerrancy and Evangelicals: The Challenge for a New Generation.
The following are "special revelation" which are not "biblical inspiration" since they are not included in the Bible:
The following are examples of "biblical inspiration" that are not "special revelation", but (depending on the doctrine of biblical inspiration) MAY have been safeguarded through divine providence (maybe just a subset of the features identified above):
Of course. God can inspire people for various capacities, not just for the purpose of producing the Bible. Whether they are called "special revelation" depends whether it is for authenticated, general use, and for all time. For example, I can be inspired to write music. Many thinks that enduringly renowned artists / poets such as J.S. Bach, Mozart, and Shakespeare are inspired by God, but we don't call their works "special revelation".
God can also inspire people to do special works for Him: