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.