Calvin's reasoning for the doctrine of reprobation

John Calvin was not trained in first-order logic. No one was at his time. Nevertheless, let me analyze his writing on the doctrine of reprobation in Institutes of the Christian Religion. Book III, Chapter 23, Section 1:

The human mind, when it hears this doctrine, cannot restrain its petulance,

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"petulance" is an emotive word. It belongs in rhetoric, not in a formal argumentation setting. I prefer to stick to objective logic when I argue.

but boils and rages as if aroused by the sound of a trumpet.

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He exaggerated the human mind's reaction. Again, it is rhetoric, not logic.

Many professing a desire to defend the Deity from an invidious charge admit the doctrine of election, but deny that any one is reprobated (Bernard. in Die Ascensionis, Serm. 2). This they do ignorantly and childishly

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more emotive words

since there could be no election without its opposite reprobation. God is said to set apart those whom he adopts for salvation. It were most absurd to say, that he admits others fortuitously, or that they by their industry acquire what election alone confers on a few. Those, therefore, whom God passes by he reprobates,

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He did not use the word "therefore" in the FOL sense. I am having trouble following his reasoning. For my taste, he needed to arrange his argument more linearly.

and that for no other cause but because he is pleased to exclude them from the inheritance which he predestines to his children. Nor is it possible to tolerate the petulance of men, in refusing to be restrained by the word of God, in regard to his incomprehensible counsel, which even angels adore.

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Calvin's argument seems to be based on emotive rhetoric and what computer science people call spaghetti logic.

I like to invite modern-day Calvin scholars to express themselves in my subreddit according to its rules.