“The whole counsel of God, concerning all things necessary for his own glory, man’s salvation, faith, and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture…” (Westminster Confession of Faith 1:6).
What does this phrase mean and how may it be proved from Scripture? Westminster Divine George Gillespie answers:
A Treatise of Miscellany Questions, ch. 20.
That necessary consequences from the written word of God do sufficiently and strongly prove the consequent or conclusion (if theoretical, to be a certain divine truth which ought to be believed, and if practical, to be a necessary duty which we are obliged unto) jure divino [of divine right].
Statement of the Question
This assertion must neither be so far enlarged as to comprehend the erroneous reasonings and consequences from Scripture which this or that man, or this or that church, apprehend and believe to be strong and necessary consequences; I speak of what is, not of what is thought to be a necessary consequence. Neither yet must it be so far contracted and straightened, as the Arminians would have it, who admit of no proofs from Scripture, but either plain explicit texts, or such consequences as are nulli non obviae [not disputed by anyone], as neither are nor can be controverted by any man who is rationis compos [possessing reason] . By which principle, if embraced, we must renounce many necessary truths which the Reformed Churches hold against the Arians, Anti-Trinitarians, Socinians, and Papists, because the consequences and arguments from Scripture brought to prove them are not admitted as good by the adversaries.
This also I must in the second place premise, that the meaning of the assertion is not that human reason drawing a consequence from Scripture can be the ground of our belief or conscience. For although the consequence or argumentation be drawn forth by men’s reasons, yet the consequent itself or conclusion is not believed nor embraced by the strength of reason, but because it is the truth and will of God. 
Thirdly, let us here observe with Gerhard , a distinction between corrupt reason and renewed or rectified reason; or between natural reason arguing in divine things from natural and carnal principals, sense, experience and the like, and reason captivated and subdued to the obedience of Christ (2 Cor. 10:4-5), judging of divine things not by human but by divine rules, and standing to scriptural principals, how opposite so ever they may be to the wisdom of the flesh. Tis the latter not the former reason which will be convinced and satisfied with consequences and conclusions drawn from Scripture, in things which concern the glory of God, and matters spiritual or divine.
Fourthly, there are two sorts of consequences which Aquinas  distinguisheth. 1. Such as make a sufficient and strong poof, or where the consequence is necessary and certain, as for instance saith he, when reason is brought in natural science to prove that the motion of the Heaven is ever of uniform swiftness, not at one time slower and another time swifter. 2. By way of agreeableness or convenience as in astrology (saith he) this reason is brought for the eccentrics or epicycles, because by these (being supposed) the phenomena or apparentia sensibila [sensible appearances] in the celestial motions may be solved: which he thinks is no necessary proof, because their phenomena may be solved another way, and by making another supposition.
Now the consequences from Scripture are likewise of two sorts, some necessary, strong, and certain, and of these I here speak in this assertion; others which are good consequences to prove a suitableness or agreeableness of this or that to Scripture, though another thing may be also proved to be agreeable unto the same Scripture in the same or another place. This latter sort are in diverse things of very great use; but for the present I speak of necessary consequences.
I have now explained the assertion, I will next prove it by these arguments:
Argument 1: From the Example of Christ and His Apostles.
Christ proved against the Sadducees the resurrection of the dead from the Pentateuch (which was the only Scripture acknowledged by them, as many think, though some others hold there is no warrant for thinking so), “Now that the dead are raised, even Moses shewed at the bush, when he calleth the Lord the God of Abraham, and the God of Isaac, and the God of Jacob. For he is not a God of the dead, but of the living: for all live unto him” (Luke 20:37-38; Mat. 22:31-32).
Again [Christ used good and necessary consequence], John 10:34-36, “Is it not written in your law, I said, Ye are gods? If he called them gods, unto whom the word of God came, and the scripture cannot be broken; Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God?“
The Apostle Paul proved by consequence from Scripture Christ’s resurrection, Acts 13:33-34, “he hath raised up Jesus again; as it is also written in the second psalm, Thou art my Son, this day have I begotten thee. And as concerning that he raised him up from the dead, now no more to return to corruption, he said on this wise, I will give you the sure mercies of David.“
His Godhead is proved from these words, “let all the angels of God worship him” (Heb. 1:6). Divine worship cannot be due, and may not be given to any that is not God.
Argument 2: From the Old Testament.
Although Hooker in his Ecclesiastical Polity, and other prelatical writers, did hold this difference between the Old and New Testament, that Christ and his Apostles hath not descended into all particularities with us as Moses did with the Jews, yet, upon examination, it will be found that all the ordinances and holy things of the Christian Church are no less determined and contained in the New Testament, than the ordinances in the Jewish Church were determined in the Old, and that there were some necessary things left to be collected by necessary consequences from the Law of Moses, as well as now from the New Testament.
If we consult the Talmud, we find there that the law concerning the soul to be cut off for despising the word of the Lord (Num. 15:31) is applied to those who denied necessary consequences from the Law, and (saith the Talmud) “if a man would acknowledge the whole Law to be from Heaven, praeter istam collectionem a majori aut minori, istamve, a pari, is notatur illâ sententiâ, quia verbum Domini aspernatus est” [“except such and such an explanation, such an a fortiori conclusion, such an analogy of expression, they are considered as despising the word of the Lord”] .
So that here are two sorts of necessary consequences from the Law, one is a majori aut minori [from the greater to the lesser] or if ye will, a fortiori [from the stronger thing]; another a pari [from parity or equality]; either of which being refused, the Law itself was despised: yea tis further to be observed with Mr. Selden  that the Karaei or Judaei Scripturarii who reject the additions or traditions of the Talmudical masters, and profess to adhere to the literal and simple sense of the Law, without adding to it or diminishing from it, yet even they themselves do not require express words of Scripture for every divine institution; but what they hold to be commanded or forbidden by the law of God, such commandment or prohibition they draw from the Law three ways,—either from the very words of the Scripture itself, or by argumentation from Scripture, or by the hereditary transmission of interpretations; which interpretations of Scripture formerly received, the following Generations were allowed after to correct and alter upon further discovery or better reason.
The second way, which was by argumentation, was by the principles of the Karaei themselves of two sorts, a pari or a fortiori. Which agreeth with the passage of the Talmud before cited. And herein our writers agree with the Karaei, that all kinds of unlawful and forbidden marriages are not expressly mentioned in the law, but diverse of them to be collected by consequence, that is, either by parity of reason [a pari], or by greater strength of reason [a fortiori]; for instance, Leviticus 18:10, “The nakedness of thy son’s daughter, or of thy daughter’s daughter, even their nakedness thou shalt not uncover: for theirs is thine own nakedness.” Hence the consequence is drawn a pari [from equality]. Therefore a man may not uncover the nakedness of his great grand-child, or of her who is the daughter of his son’s daughter. For that also is his own nakedness, being a descent in linea recta [in a straight line] from himself. From the same text it is collected a fortiori, that much less a man may uncover the nakedness of his own daughter, which yet is not expressly forbidden in the Law, but left to be thus collected by necessary consequence from the very same text. It is likewise a necessary consequence that a man may not uncover the nakedness of her who is daughter to his wife’s son, or to his wife’s daughter. For here the reason holds: it is his own nakedness, his wife and he being one flesh, which gives ground to that general received rule, that a man may not marry any of his wife’s blood nearer than he may of his own, neither may a wife marry any of her husband’s blood, nearer then she may of her own [c.f. WCF 24:4]. Again, Leviticus 18:14, “Thou shalt not uncover the nakedness of thy father’s brother, thou shalt not approach to his wife: she is thine aunt.” Hence it followeth a pari that a man may not uncover the nakedness of his mother’s brother, and by parity of reason (ever since that law was made), it is also unlawful for a woman to marry him who hath been husband to her father’s sister, or to her mother’s sister, the nearness of blood being alike between uncle and niece as between ant and nephew.
Other instances may be given, but these may suffice to prove that what doth by necessary consequence follow from the law, must be understood to be commanded or forbidden by God, as well as that which is expressly commanded or forbidden in the text of Scripture.
Argument 3: From the Infinite Wisdom of God.
If we say that necessary consequences from Scripture prove not a jus divinum [divine right], we say that which is inconsistent with the infinite wisdom of God; for although necessary consequences may be drawn from a man’s word which do not agree with his mind and intention, and so men are oftentimes ensnared by their words; yet (as Camero well noteth) God being infinitely wise, it were a blasphemous opinion, to hold that anything can be drawn by a certain and necessary consequence from his holy Word which is not his will. This were to make the only wise God as foolish man, who cannot foresee all things which will follow from his words. Therefore we must needs hold that it is the mind of God which necessary followeth from the Word of God.
Argument 4: From Absurdities.
Diverse other great absurdities must follow if this truth be not admitted. How can it be proved that women may partake of the Sacrament of the Lord’s Supper unless we prove it by necessary consequence from Scripture? How can it be proved that this or that church is a true church, and the ministry thereof a true ministry, and the baptism ministered therein true baptism? Sure no express Scripture will prove it, but necessary consequence will. How shall this or that individual believer collect from Scripture that to him, even to him, the Covenant of Grace and the promises thereof belong? Will Scripture prove this otherwise than by necessary consequence? How will it be proved from Scripture that the late war against the popish and prelatical party, in defense of our religion and liberties, was lawful, that the Solemn League and Covenant was an acceptable service to God? Necessary consequence from Scripture will prove all this, but express scriptures will not. The like I say of fasting and thanksgiving now and then, upon this or that occasion, God calls us to these duties, and it is his will that we perform them, yet this cannot be proved from Scripture but by necessary consequences.
This fourth Argument will serve for the extension of the present assertion (which I now prove) to its just latitude; that is, that arguments from Scripture by necessary consequence will not only help to prove and strengthen such things which may be otherwise proved from express and plain scriptures, but will be good and sufficient to prove such things to be by the will and appointment of God, or as we commonly say, jure divino, which cannot be proved to be such from any express text of Scripture.
Argument 5: From the Opponents of Necessary Consequences Using Them.
I shall here take notice of the concession of Theophilus Nicolaides, the Socinian.  Although he professeth his dissent, both from the Reformed and Roman churches thus far, that he doth not believe things drawn by consequence from Scripture to be equally necessary to salvation as those things contained expressly in Scripture, yet he yieldeth the things drawn by consequence to be as certain as the other, Quantumuis, saith he, aeque certa sint quae ex sacris literis de ducuntur atque ea quae in illis expresse et ρητώς habentur. [As much as plainly certain things are out of the sacred writings drawn from any number of reasons, it is equally certain of things that are in them expressly and contained].
And generally it may be observed, that even they who most cry down consequences from Scripture and call for express Scriptures, do, notwithstanding, when themselves come to prove from Scripture their particular tenets, bring no other but consequential proofs. So far is wisdom justified, not only of her children, but even of her enemies. Neither is it possible that any Socinian, Erastian, etc. can dispute from Scripture against a Christian, who receiveth and believeth the Scripture to be the Word of God, but he must needs take himself to consequential proofs: for no Christian will deny what is ρητώς [expressly] literally and syllabically in Scripture; but all the controversies of faith or religion in the Christian world, were, and are concerning the sense of Scripture, and consequences drawn from Scripture.
Argument 6: From Human Justice.
If we do not admit necessary consequences from Scripture to prove a jus divinum, we shall deny to the great God that which is a privilege of the little gods, or magistrates. Take but one instance in our own age: when the Earle of Strafford was impeached for high treason, one of his defenses was that no law of the land had determined any of those particulars which were proved against him to be high treason. Which defense of his was not confuted by any law, which literally and syllabically made many of those particulars to be high treason, but by comparing together of several laws, and several matters of fact, and by drawing of necessary consequences from one thing to another, which made up against him a constructive treason. If there be a constructive or consequential jus humanum [human justice], there must be much more (for the considerations before mentioned) a constructive or consequential jus divinum.
 See their Praef Ante Exam. Cens., and their Examen., ch. 25., p. 283.
 which Camero Prael. tom. 1, p. 364, doth very well clear:
Ante omnia hoc tenendum est, aliud esse consequentiae rationem deprehendere, aliud ipsum consequens; nam ut monuimus supra saepenumero deprehenditur consequentiae ratio, cum nec comprehendatur antecedens nec deprehendatur consequens, tantum intelligitur hoc ex illo sequi. I am hoc constituto dicimus non esse sidei proprium sed rationis etiam despicere consequentiae rationem, dicimus tamen fidei esse proprium consequens credere Nec inde tamen sequitur sidem (quia consequens creditur) niti ratione, quia ratio non hic argumentum sed instrumentum est, quemadmodum sides dicitur esse ex auditu, auditus non est argumentum fidei, sed est instrumentum.
 Loc. Thè: de Eccl. num. 252. distinguēdum igitur est inter rationem sibirelictā ac solutam quae sine froeno discurrit, ac suis fertur logismis, quae judicat ac statuit ex suis principiis, quae sunt communes notiones, sensus, experientia, &c. & inter rationem per verbum Dei refrenatam & sub obseqnium Christi redactam, quae judicat an statuit ex proprio Theologiae principio, viz. ex verbo Dei in Scripturis sacris proposito.
 Uxor. Haebraica lib. 1, cap. 3.
 Tractate, de Ecclesia et Missione Ministrorum, cap. 10, p. 121
See also: By Good and Necessary Consequence by Ryan McGraw