So, hopefully this has at least shown that Reformed theology is not monolithic, meaning that there's a fair amount of diversity of tradition and doctrine. Calvinism, historically has fallen within the Reformed community, but Calvinism itself, is more narrowly defined. There are some elements of what is described as "Calvinism" that you'll have a hard time finding too, within Calvin's own writings. I hinted at this before, but the "L" of the TULIP, limited atonement is not strongly present or clearly defined coming directly from Calvin. Some take that Calvin's initial premises and systematic theology was extended further in some areas, than he himself would have embraced. Even recognizing this, there's some strong common themes within Calvinism.
Chief among these is the theme of God's Sovereignty. Lorainne Boettner, a leading Calvinist theologian who is very well and broadly respected in Calvinist circles, lays out that Calvinism begins with a vision of God that is drawn from the Scripture and is tightly compatable with Philosophical Theism. Bottner says,
"The very essence of consistent Theism is that God would have an exact plan for the world, would foreknow the actions of all the creatures he proposed to create and through His all-inclusive providence would control the whole system." (Boettner, The Reformed Doctrine of Predestination, 23)
Boettner goes further and says
[God] very obviously predetermined every event which would happen" so that "Even the sinful acts of men are included in this plan" (ibid 24)
Calvinism more specifically than just reformed theology, affirms a strong view of God's sovereignty. Calvin himself in the Institutes says,
"We ought undoubtedly to hold that whatever changes are discerned in the world are produced from the secret stirring of God's hand ... what God has determined must necessarily so take place." (John Calvin, Institutes of the Christian Religion, Library of Christian Classics, 20-21)
This is often referred to as devine determinism. Determinism is a term that is shared within both Calvinistic (and some others) theology and is also a Greek Philosphical term. It should be remembered that Calvin, who was indisputably a brilliant man, was a student of Law and Philosophy before he turned to religion and produced, very early in his life, his Institutes. He first published the Institutes when he was 26. There were 5 revisions through his lifetime and he continually expanded them to where the 5th revision was 5 times longer than the first. Calvin's institutes was a seminal work in theology and is still foundational for many. It also represents the first comprehensive Systematic Theology. By that, I mean that this was the first major attempt in Christian History to systematically go through the Bible and organize all of the themes to where the intent was to in a comprehensive manner determine what the Scriptures say collectively on any one theme and then attempt to present doctrinal positions from that exercise. In this manner, Calvin's approach was very consistent with his Legal and Philosophical training foundations before he approached this task. What he taught and based his subsequent work, reasoning and logic on is called Hard Theological Determinism. That means there ultimately are not secondary agents at work making independent choices or taking independent actions that God is taking into account. God is the primary and sole author of all that was, all that is and all that will be and nothing happens that is not a direct result of God's willing it to happen exactly as it has.
It's important to note that this Divine Determinism is not simply stating that God Foreknew all that would happen and has in His Divine providence orchestrated things to where His will, will ultimately come to pass. True Calvinism, holds that God proactively has determined every event that will take place by an active assertion of his infinite power and nothing may deviate from it. There is ultimately nothing that happens in this world or in the life of any person without it having been the declared, direct will of God. Many people who call themselves Calvinists may react to this and seek to tone it down, but if you're going to hold to the tenets as Calvin Himself put them forward that positions is pretty much a non-negotiable.
Calvin's approach, as I mentioned is unquestionably tied to some philosophical themes as well as the methods he developed in logic. This is one primary area where I think Calvinists either are in denial or honestly don't see that this underlying framework, undoubtedly influenced Calvin's system and the results that his approach generated.
Here's a passage from Calvin's own Institutions that gives evidence of what I'm saying,
I, indeed, agree that the things they [the philosophers] teach [about the soul] are true, not only enjoyable, but also profitable to learn, and skillfully assembled by them. And I do not forbid those who are desirous of learning to study them. Therefore I admit in the first place that there are five senses, which Plato preferred to call organs, by which all objects are presented to common sense, as a sort of receptacle. There follows fantasy, which distinguishes those things which have been apprehended by common sense; then reason, which embraces universal judgment; finally understanding, which in intent and quiet study contemplates what reason discursively ponders. Similarly, to understanding, reason, and fantasy (the three cognitive faculties of the soul) correspond three appetitive faculties: will, whose functions consist in striving after what understanding and reason present; the capacity for anger, which seizes upon what is offered to it by reason and fantasy; the capacity to desire inordinately, which apprehends what is set before it by fantasy and sense. (Institutes, I.XV.6.)
Calvinism has been as successful a system of belief as it is, because once it establishes it's presuppositions or premises upon which it's logic rests, it is for the most part internally valid, meaning that it follows closely the rules of logic and comes out to a consistent end or conclusion. Prove that any of these premises are not true, and effectively the entire system falls apart as their are inter-related and inter-dependent. Calvinism presents itself as a Biblical perspective of what the Bible says and only that, free of any outside influences. I disagree with that. I believe Calvinism certainly is Biblical, in the sense that it utilizes proof texting and drawing from Biblical sources in support of what it says, but I think at the foundation are some concepts and approaches to the Bible that the Bible itself doesn't model. This by the way, is not necessarily a problem to Reformed Calvinists to acknowledge and some that I've come accross do acknowledge this. Reformed theology, by definition is a continual process, of reforming to keep the root concepts of truth relevant and applicable within the changes in understanding and culture that may come along. There were several things taking place in Calvin's time that had a profound and direct effect upon how he thought and constructed his reasoning that were decidedly extra-Biblical. One of these would be the great changes in the world that were taking place in the midst of what we now refer to as the Reformation or Rennaisance. In this time, the classics of Roman and Greek literature were rediscovered and had a profound affect and influence on the world around it. Literacy was on the rise as well as printing presses making Scripture available to the masses to where the Churches were no longer the stewards or proprieters of the texts themselves as well as the interpretations. Politically at the time, countries in Europe were in the process of rebelling against Papal Authority and in order to fill that vacuum there had to be a replacement and for many the appeal was to Scripture itself (Sola Scriptura was a cry during this time.) Calvin looking at things from a narrow and structured view as he was trained to in his earlier training also reacted to what he believed was a great deal of allegorizing and over-spiritualizing Biblical texts and he established a much more literal approach that in effect takes what the Bible has to say at face value. I'm not saying that is bad by any means. I do however, take issue from time to time with many of the "proof-texts" that are pulled to support certain concepts that they can at times wrest passages from their form and context and make statements that when you read the entire passage it was originally couched within, you wouldn't come to the conclusion that the statement being drawn out in support of the doctrine cited was making that statement as a focused point.
So anyway, there's some additional foundation. What I'm going to do next is work through the TULIP and present what the points are and how they are generally understood and presented by Calvinists. Again, I'll try to use Calvinist sources and be fair and true to what I think a Calvinist would say. Any who want to correct me in that, feel free, just also keep in mind that there isn't complete agreement between all Calvinists on some of these issues and I'm honestly seeking to be generous in showing these in a positive light, even where I may disagree with something in whole or part.