According to the Calvinist, why "believe" if something is known absolutely true?

Its a matter of simple English. If anything is true we believe it. If its not true we don't believe it. I believe the sun will come up tomorrow morning (unless our Lord returns today). It does not mean I do not know the sun will come up: I know it and so I believe it.

Unfortunately the idea has got around that "believing" something is when you decide you want that something to be true but do not have sufficient evidence to know it is true. In fact, in Biblical language, "believing" is sometimes more than just "knowing", not less. The Devil knows that Jesus is the Son of God, but the Devil does not believe in or on the Son of God, meaning the Devil does not have a loving trust of the Son of God but rather hates the Son of God.

However, we believe many things because we have sufficient evidence to believe them to be true, even though we cannot absolutely prove them to be true. For instance:

1. I believe the sun will come up tomorrow morning, even though I cannot absolutely prove it; but, I am confident enough it will so that I live on the assumption that it will;

2. I believe this chair is reliable to sit on (I do not absolutely know it, but I am confident enough to sit on it, which means I have a very strong confidence in it);

"Believing" and "knowing" can often be considered to have the same meaning. To say you believe something to be true is virtually the same as to say you know something to be true.

You can only be as confident about something as you are confident about the basis for that something. So just as you say, the Christians who believe in the infallibility of scripture believe it, they don't know it like they know that 2 + 2 = 4 or that gravity is real. It's not possible to prove the infallibility of scripture. There's no science that we can do to prove the infallibility of scripture. There's no sound deductive argument to prove the infallibility of scripture. Neither can we prove that the scriptures are inspired by God or are God's word. The best we have is many lines of inductive reasoning that lead us believe that it is most likely that the scriptures are infallible.

If you see Christians saying that they "know" the scriptures are inspired or infallible, don't see that as a scientific or rigid deductive philosophical kind of knowledge, but instead the kind of relational knowledge you have when you say you know your parents or your spouse loves you. This kind of knowledge and belief is grown on the basis of years of experience of reliability.

According to the Calvinist, why “believe” if something is known absolutely true?

Philosophically speaking it is wise to live in agreement with truth. 2 + 2 = 4 is known to be true, so one would be a fool to live life believing that 2 + 2 = 29. Secondly, our values and behaviors are shaped by what we believe whether it's true or not.

To me, God's Word is absolutely the truth. So to me it doesn't need to be believed.

I would argue that this is why it should be believed. Think of all of the negative consequences in life that people experience for not believing what is true. Furthermore God's word being absolutely true is independent of our belief. Believing it's true doesn't make it true.

As a Christian who has come to believe that the Holy Scriptures are inerrant, I would like to explain a point that does not seem to have been raised so far. This hit me with real force only recently when reading a letter written by a Calvinist to a Christian friend. This quoted letter links three crucial truths that are bound up with the inerrancy of the Bible. It uses one illustration to demonstrate the point, and good though your illustration of the ice cube is, this letter takes the matter into the spiritual realms, which all who profess belief in the Bible as the inerrant word of God should grasp.

The illustration is regarding the doctrine of the Trinity, which is a foundational belief of mainstream Christianity, and can only stand on what the Bible states about the being of God. Now, nobody so absolutely knows the truth of the Trinity doctrine as to be able to totally explain it. It won't be until believers are resurrected and stand before the throne of God that things will become much clearer. That, however, does not cause them to doubt the triune nature of the Godhead. They believe it. And that belief only comes from how the Bible which teaches it has been authored by one of the Persons in the Godhead - the Holy Spirit.

It is this authorship that is crucial when considering if the Bible is truly the inerrant word of God, to be totally believed, even though some parts of it cannot be known fully this side of eternity. Consider now how this Calvinist wrote on 19th November 1879 about the vital need for Christians to believe in the inerrancy of the Bible, because of who authored those writings, and why:

"My Dear Friend - Do you understand the state of things in our poor church [in Scotland]? I do not. What I am afraid for is the doctrine of the Trinity... A church's hold on the doctrine of the Trinity is affected by her hold on the doctrine of the inspiration of Scripture. For it is in virtue of a truly inspired Word - His own Word - that the Holy Spirit acts as a person.

It is a degradation to the Third Person of the Godhead to suppose that He would speak by the words or words of any person less than Himself. He does not speak at all as a person by any word less than His own Word, or the Word of the Son, or the Word of the Father, all which are one.

To suppose the Spirit coming by a new and fresh revelation is of course Quakerism, but in His coming by a previously written inspired Word, He acts as a person. As a person He speaks, enlightens, convinces, persuades, and renews. Deal falsely with personality here, then the Holy Spirit does not combine with the Second Person, but falls back upon an impersonal Deity - a Thing. You have merely what is implied in 'God is a Spirit', but Word is gone, Father is gone, Sonship is gone, Messiahship is gone, Mediatorial position is gone, infernal robbery has been committed, and the mists of darkness have settle down upon the church!

Yea, we are not a church at all, for we are robbed of a divine revelation, of a divine record. The privileges and position of a church are given 'chiefly because unto them were committed the oracles of God' (Romans 3:2). Alas! that so many who ought to be teachers deal as falsely and irreverently with the oracles of God as a kitten playing with a cork.

I am sorely afraid that there will be a great decline in our church. If you meet any after I am gone who do courageously stand for all revealed truth, give them my compliments, and tell them to be strong and of a good courage. Let them not yield to the current sentimental Christianity that would convert men's faith in a living, glorious, inexhaustible, infallible Word into empty-headed, empty-hearted speculations no better than Chinese puzzles or acted charades.

God will avenge such trifling. 'The Scripture cannot be broken' (John 10:35) is the testimony of Him who is Himself the eternal Word. And will He suffer it to go unpunished if the divine truth - which He has in infinite condescension been pleased to make known to men by means of an infallibly inspired record - be broken up into bits and shreds, into fragments and fancies? And if the 'Lord will not hold them guiltless who takes his name in vain', (Exodus 20:7) He will not assuredly, hold that church guiltless which tolerates any profaning or abusing of that Word by which He hath made Himself known." Letters of the Late Rev. Hugh Martin, D.D. Free Pesbyterian Magazine, May 1879.

Because Calvinist and all Christians who believe the Bible to be absolutely true (inerrant) due to who its author is, "it effectually works also in you who believe" 1 Thessalonians 2:13. The author reveals the truth of that word, the record of the Word of God where his spoken words are combined with the entire revelation of God to humanity. Confirmation of its inerrancy comes with belief - not the other way around.