Certainty properly is not an affection of an existing thing or of one about to happen, but of the mind certainly knowing or foreknowing that the thing exists or is about to exist: whence a transference is made to the event, -for it is the same that a thing will happen, and that it will certainly happen, -but that it may be signified to another that there is no reason to doubt of the event coming to pass. But necessity is an affection of the being, and adds a mode to the event, by which it is said that a thing will happen necessarily, and is opposed to the mode which is called "contingency". Therefore the same idea is not expressed, when it is said that a thing will happen certainly and necessarily; for the one word is only about futurition, the other about the mode also of futurition. This necessity is that of the consequent, by which a thing exists from its antecedent beginning and cause, so that it cannot not-exist from it: to which is opposed the contingency of the consequent: so that in no respect can these words be used about the same thing. But there is a necessity called by philosophers "the necessity of the consequence," which does not belong to a simple, but to a complex entity, according to syllogistic reasoning; from which cause it is also called syllogistic necessity: and this necessity exists in the whole legitimate arrangement of the syllogism, not i this or that part, whether premise or conclusion; unless it have also what they call the necessity of the matter, which falls in with the necessity of the consequent. The necessity of hypothesis, according to the nature of the hypothesis, will fall in with this or that. If the hypothesis be the antecedent principle and cause of the thing, it will be the same as the necessity of the consequent: but if it be the antecedent principle and cause of the conclusion only, it will be the necessity of the consequence.
But now, if our author wished to denote, from the immutability of the Divine purpose, and the supposition of the destined end, that the salvation or damnation is conlcluded of him who has been predestined to the one or the other, and indeed that they are concluded by a fair consequence; whence certainty may exist in his mind who accounts both premises true, nay, and does exist on account of the premises laid down; I have nothing to say against it. For they for whom salvation has been destined by the immutable purpose of God, will obtain salvation; nor shall it come to pass that they will not obtain salvation. Yet it does not follow from hence that they are necessarily saved: nor shall it come to pass that they will not obtain salvation. Yet it does not follow from hence that they are necessarily saved: for the word "necessarily" cannot be added to the conclusion by the necessity of the consequent. For example: "Whatever God has foretold will come to pass: God has foretold that Christ will die: Therefore Christ will die." The conclusion cannot be drawn, "Therefore Christ will die necessarily", unless the word had been added to the major in this manor "Whatever God has foretold will come to pass necessarily." But now the major will be denied: for it is sufficient to establish the truth of a prediction if that happens which God foretold would happen, even if it does not happen necessarily: nay, since the word "necessarily" adds a mode to the event, the event will not answer to the prediction, unless the necessity be either added in both places, or omitted in both.
But if- as the passage itself seems to require, and the forms of speech familiar to this author and others who concur with him appear to indicate- this be the sense of the author, -that from the presupposition of the immutability of God's purpose and of the destined end the salvation and death of the elect and reprobate necessarily exist, as from the antecedent principle and cause of the matter, which is the necessity of the consequent, that I shall altogether deny: for the predestination of those who are to be saved and damned remains unmoved, with the contingency of the consequent; that is, even if they be contingently saved and damned. Nay if by the Divine decree, no the necessary mode of salvation or damnation, but only salvation and damnation was decreed, then the execution does not answer to the decree, if the predestined are necessarily saved or damned. But, according to the confession of this author, that mode has not been settled beforehand: for, if it had been settled beforehand, the necessity would not now arise from the presupposition of the immutability of the purpose and destined end, but directly form the purpose and decree itself.
In order to make this plain, here are these syllogisms for you to look at: Whatever God had decreed to come to pass, that will come to pass: But God has decreed that this man be saved, that man damned: Therefore this man will be saved, that man damned. Here there is no necessity, except that of the consequence. But let it be in this form: "Whatever God has decreed to come to pass, that will necessarily come to pass: But God has decreed that this man be saved, that man damned: Therefore this man will necessarily be saved, and that one necessarily be damned. Thus is not a necessity of the consequence, but of the consequent; a necessity concluded not from the syllogistic form, but from the necessity of the matter; and that depends not upon any presupposition of the immutability of the decree, and of the destined end, but on the decree itself immediately. But the mayor in that syllogism is false; therefore there is no conclusion. But if anyone wishes to make the major true by this addition, -Whatever God has decreed to take place necessarily, this will take place necessarily, -then the minor will be false: But God has decreed that this man be necessarily saved, that one necessarily damned. Wherefore the conclusion will not follow, -Therefore this man will necessarily be saved, and that one necessarily be damned. The falsity of the minor will appear from my previous remarks, because then God will not save an damn freely. You will say that it does not follow for that God can freely produce an effect, which yet will arise necessarily, God willing to produce the effect by His irresistible omnipotence. I answer, that there is a contradiction in the adjunct, -that God produces an effect freely, and that it arises necessarily.
(James Arminius. Works of James Arminius. 1875 London Edition. Examination of Gomarus on Predestination. Volume 3. p 547-549)