Is Catholic tradition as important as the Bible?

In order to properly answer this I will have to clarify the terms being used. The answer to the question asked is no, Catholic traditions (please note the lower case "t") are not just as important as the Bible.

The question most people mean to ask is whether Catholic Tradition (likewise, please note the capital "T") is equal to the Bible. The answer to this is a most emphatic yes! Now here's the reasoning:

Sacred Tradition, like the Sacred Scriptures, is considered to be divinely inspired revelation to us, and thus equally important with Sacred Scriptures as a source of revealed Truth. Sacred Tradition, also like Sacred Scriptures, comes from the teachings of Christ and the Apostles/early Church Fathers. The difference between the two is that Sacred Tradition comes from oral teachings, while Scriptures are, of course, written.

In a larger sense, Tradition encompasses both the oral and written components of the Deposit of Faith, especially as much of the Bible is in fact based on oral accounts and eye witness testimony, (NB: this refers to the NT Gospels and Acts, as well as the OT). Much of the Bible was not written simultaneously with Christ performing His actions or living His ministry, but instead after the fact, and there is no absolute certainty that the authors of the Gospels actually were with Christ every step of the way, (certainly only John and Matthew could make such a claim, and there is some dispute as to whether it was the Apostles themselves or their students who wrote their Gospels). But in the more specific sense that we're currently using it, Sacred Tradition refers to the inspired teachings passed down orally and held in the Deposit of Faith as equally inspired revelation with Scriptures.

The next question to be addressed is, of course, how do we know they're inspired?

There are several ways we can recognize Tradition to be equally inspired with Scriptures. The first is Scripture itself tells us so. The end of John's Gospel tells us point blank that not all of Christ's actions were recorded in the Gospels, and that it would be, in fact, impossible to record them all because there were so many. While this may be hyperbole as to the scale, we can certainly rest assured that there are many things Christ said and did that were not recorded in written form. Where can we access these teachings? Obviously though His spoken teachings and the teachings of His Apostles who heard them. Moreover, 2 Thessalonians 2:14 says quite clearly, "Therefore, brethren, stand fast; and hold the traditions which you have learned, whether by word, or by our epistle." And the context of this verse is equally important. It is the culmination of a chapter dealing with the signs of error that are to come, and the mistakes in belief in doctrine that Paul's predicts will become prevalent. His answer to the worries of the Thessalonians is that to avoid these pitfalls, they must hold fast to the traditions which they have learned. The mentioning of both types of traditions demonstrates for us that each is a valuable source of tradition and equally worthy of being held onto. Thus, Scriptures themselves state that both oral teachings and written teachings are to be held to equally.

The next proofs are logical points.

Logical point 1, we know that the teachings of Christ and the Apostles were inspired, thus it stands to reason that if what was written down of their teachings was inspired, what they said in oral instructions was also inspired. Now, of course, for an atheist this won't be particularly satisfactory, but this argument isn't meant for atheists. If a non-Christian wishes to debate this issue, I'll write a separate post.

Logical point 2, oral teachings precede written teachings. It is an important point to note that the written teachings do not exist in a vacuum. And even outside of the compilation of the Bible itself, the vast majority of the works in the New Testament were written after events and teachings took place. This applies not only to the Gospels, but also especially to Acts and most of the Pauline Epistles. The Apostles, especially Paul, were generally not writing to places they hadn't yet visited. In the scattered cases that they were, they certainly weren't writing to places where the faith had not yet spread. In both cases what remains clear is that the oral teachings came first, generally from Paul or one of the other Apostles, and the letters were follow ups (or the occasional advance letter) dictating things that the various communities needed to beware of, or stop doing. In fact, we can directly infer from many of Paul's correctional epistles that they do not present the sum message of the Gospel Paul preached, for they dwell on specific points that many cities needed to improve upon, rather than being treatises and teachings on the entirety of the Christian faith as a whole.

Logical point 3, this is a fine point, and hardly necessary after the others, but I think I'd like to include it. The only authority that is capable of declaring materials as inspired or not has declared Sacred Tradition to be such. This authority is, of course, the Catholic Church, established by Christ, Headed by Christ, His earthly Body of believers, which is constantly guided by the Holy Spirit. This is the same authority that assembled and selected the works found in the Bible, and by that authority declared them inspired. If you are to accept this authority by accepting the Bible's Inspired Truths, then you must accept the same authority which accepts Tradition to be equally inspired.

The final issue to be addressed (at least in my mind) is, are they both necessary?

To this I must give a resounding yes. While most, if not all, of the Truths necessary for salvation are found in the Bible, there are still several problems with taking the Bible alone instead of both. The first problem is that you're still missing part of divine revelation. With an incomplete picture it is impossible to know if you have everything right.

More importantly, while many of the points in both Scripture and Tradition certainly overlap and thus support each other, if we are to take each source separately then we have no way of checking or supporting the message of each. Taking the Bible alone, for example, results in a huge interpretive problem because no individual has another, independent source of Truth with which to compare the Bible, nor the authority of the Church to interpret Scriptures correctly. This results in manifold errors in interpretation, and gives rise to the epidemic of small churches constantly splintering apart because people disagree over how to interpret various passages of the Bible.

This has been illustrated perfectly by modern Christianity in America, but has essentially been present in every single Protestant church since Luther. While the initial Reformers broke with the Church, the vast majority of subsequent breaks have been among the Reformers' groups. The Anglicans and Episcopalians are breaking apart right now. The Lutherans have divided into several synods. Methodism is splintered, the Baptists fragment more every day, and non-denominationalism is on the rise as people realize that they can't mesh their interpretation with anyone else's. The reason this is a problem is because these people don't always agree on what's necessary for salvation, thus even if all the points necessary are present in the Bible, people are still missing them. Moreover these incessant breaks breed ill feelings among those who should be brothers in Christ, and also breeds ignorance of what their fellows believe and teach. Just look at those who denounce Catholics as statue worshipers, or cannibals if you don't believe me.

Moreover, personal interpretation becomes an exercise in egotism instead of guidance from the Spirit. We logically know that the Holy Spirit does not and cannot have multiple personality disorder. Yet we have literally 33,000+ denominations of Christianity, all of which claim their particular version is correct, and inspired by the Holy Spirit. Logically put, this is impossible, and it is dangerous to Christianity as a whole. This problem can be remedied by having another source of Truth with which to compare to the Bible and thus understand it more fully, and an authority which we can deduce is inspired that can guide us in interpreting Scriptures and Tradition so that we avoid the pitfall of interpreting it for ourselves instead of how God meant it.

So yes, Tradition is just as important as the Bible, just as inspired, and just as necessary. But Catholic traditions, not so much.