In modern usage, yes, that is the definition. In modern usage "belief" is "intellectual assent. I get told that stating that "belief" is not "intellectual assent" is a strawman argument, but that is exactly what you are claiming "belief" is. But that is not the Biblical usage of the word.
No, in every case where "believe" or "belief" is mentioned in reference to salvation, the word used is the Greek "pistis" which means "faith". And faith is not just a mental acceptance. Faith without action is dead, useless, meaningless, impotent (James 2:20, 22, 24, 26). Belief is not just thinking in your head/heart that the Gospel is true, or that Jesus really is God, or that He died for you so that you could live. All of that is true, but "belief/faith" is not just thinking those things. It is taking action because they are true; taking the actions that God commanded that He said LEAD TO/RESULT IN receiving salvation.
Believe (4100) (pisteuo from pistis; pistos; related studies the faith, the obedience of faith) means to consider something to be true and therefore worthy of one’s trust. To accept as true, genuine, or real. To have a firm conviction as to the goodness, efficacy, or ability of something or someone. To consider to be true. To accept the word or evidence of.
Vincent notes that pisteuo "means to persuade, to cause belief, to induce one to do something by persuading, and so runs into the meaning of to obey, properly as the result of persuasion
In secular Greek literature, as well as in the New Testament, pisteuo (pistis, pistos) has a basic meaning of an intellectual assent or a belief that something is true. Michel says that this use arose during the Hellenistic period. During the struggle with skepticism and atheism, it acquired the sense of conviction concerning the existence and activity of the Greek gods. Thayer calls this the intransitive use of the word which conveys the idea of to be sure or be persuaded that something is a fact. This kind of faith does not require any action on the part of the believer but only an intellectual acceptance. As discussed below, James used this type of faith as an example of a dead faith stating that "The devils also believe, and tremble" (Ja 2:19).
The other secular Greek meaning that is the more common use in the New Testament is the transitive or active use which means to "put faith in" or "rely upon" someone or something. Sometimes it has even stronger meaning: "To entrust something to another." In classical usage it denoted conduct that honored a previous agreement, such as the honoring of a truce between opposing armies (Iliad 2.124). The meaning of entrusting something to someone is found in Xenophon (Memorabilia 4.4.17). An example of this use in the New Testament is 2 Timothy 1:12. Paul said
I know whom I have believed, and am persuaded that he is able to keep that which I have committed unto him against that day (see note 2 Timothy 1:12) (Comment: Here pisteuo means to trust in or rely upon Christ to save us)
Pisteuo means to entrust oneself to an entity in complete confidence. To believe in with the implication of total commitment to the one who is trusted. As discussed below Christ is the object of this type of faith that relies on His power and nearness to help, in addition to being convinced that His revelations or disclosures are true.
NIDNTT writes that in classical Greek literature…
pistis means the trust that a man may place in men or the gods (Hesiod, Works, 372; Soph., OT, 1445), credibility (Soph., OC, 611), credit in business (Dem., 36, 57), guarantee (Aesch., Frag. 394), proof (Democ., 125), or something entrusted (IG 14, 2012 A 23).
Similarly, pisteuo means to trust something or someone (Hdt., 1, 24; Aesch., Pers., 800 ff.). It can refer to and confirm legendary tales (Hdt., 4, 96) and mythical ideas (Plato, Grg., 524a). In the construction pisteuo tini ti it means to entrust something or someone to someone (Xen., Mem., 4, 4, 17).
With reference to people, pisteuo means to obey (Soph., OT, 625). The pass. means to enjoy trust (Xen., Anab., 7, 6, 33).
The adj. pistos means trusting (Theognis, 283), trustworthy (Hom., Il., 2, 124). to piston means dependability or the faithfulness of those bound through an agreement (Aesch., Ag., 651; Xen., Anab., 2, 4, 7).
The verb. pistoo has the meaning of binding someone or oneself to be faithful (Soph., OC, 650). In the pass. it means to be sure, to trust (Hom., Od., 21, 217 f.).
The pistis word-group has a special colouring, where it refers to believing doxa (opinion). In such a case dependability is limited (cf. Plato, Phd., 107b). (Brown, Colin, Editor. New International Dictionary of NT Theology. 1986. Zondervan)
The noun pistis and the verb pisteuo, mean an adherence to, committal to, faith in, reliance upon, trust in a person or an object, to be persuaded of or convinced of something, to place one's confidence in, to trust.
John 8:30-32 Believing On Jesus, And Its Counterfeits
Romans 3:3-4 God Justified, Though Man Believes Not
Pisteuo can also mean to be confident about or to be firmly persuaded as to something, and so Paul writes…
One man has faith (pisteuo) that he may eat all things, but he who is weak eats vegetables only. (see note Romans 14:2) (Here the believing conveys the sense of having an opinion, thinking)
As noted above, pisteuo can refer to an
"heart belief" (saving faith, genuine belief that leads to salvation, this believing involves not only the consent of the mind, but an act of the heart and will of the subject) or an intellectual belief (mental assent, "head" knowledge, not associated with bringing salvation if it is by itself), both uses demonstrated by Jesus statement in John 11,
John 11:26 Everyone who lives and believes (refers to genuine saving faith) in Me shall never die. Do you believe (intellectually) this?
John 2:23-24+ Now when He was in Jerusalem at the Passover, during the feast, many believed in His name, observing His signs which He was doing. But Jesus, on His part, was not entrusting (pisteuo) Himself to them, for He knew all men,
See comments on Jesus' "belief" in those who had believed in Him.
James 2:19+ You believe (pisteuo) that God is one. You do well; the demons also believe (pisteuo), and shudder.
Comment: In this passage, James explains that not all believing will result in salvation. The believing he is describing in this passage is a mental or intellectual believing that is not associated in a change in one's heart and thus in one's behavior or actions. Belief in the New Testament sense that effects the new birth denotes more than a "demonic" like, intellectual assent to a set of facts or truths. The demons believe but they are clearly not saved. Genuine belief does involve an intellectual assent and consent of one's mind, but also includes an act of one's heart and will. Biblical saving faith is not passive assent but an active staking of one's life on the claims of God. The respected Greek lexicon author W E Vine defines belief as consisting of
(1) a firm conviction which produces full acknowledgment of God's revelation of Truth - (2Th 2:11+ -"in order that they all may be judged who did not believe [pisteuo] the truth, but took pleasure in wickedness.")
(2) a personal surrender to the Truth (Jn 1:12+ "But as many as received Him, to them He gave the right to become children of God, even to those who believe [pisteuo] in His name") and
(3) a conduct inspired by and consistent with that surrender.
Pisteuo can also refer to a committing of something to someone and so to entrust them. And thus we find pisteuo is translated entrust (entrusted, entrusting) 8 times in the NT. Here are 2 examples of this meaning of pisteuo…
If therefore you have not been faithful (pistos) in the use of unrighteous mammon, who will entrust (pisteuo) the true riches to you? (Luke 16:11+)
Great in every respect (Paul answers his question of what is the advantage of the Jew?). First of all, that they were entrusted (pisteuo) with the oracles of God. (see note Romans 3:2)
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J.