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All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence.

Why does Hume use the words "demonstrative" and "moral" in this way? Why does he call analytic propositions demonstrative and the synthetic ones moral?

Is by "demonstrative" he meant that the truthfullness/wrongness of the proposition may be demonstrated just by means of logic and math? And about his usage of "moral" I don't have even a clue.

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  • By demonstrative reasoning, he means reasoning that is in a sense apriori and does not rely upon experience and empirical evidence. “Moral” reasoning is reasoning that is aposteriori, based on our experience of the world. Hume postulated that morality may be grounded in senses and emotions.
    – Syed
    Commented Nov 25 at 22:23
  • I understand how to "translate" this words on the modern philosophical language. I'm interested why did he use those words in the first place. But thanks, anyway.
    – Егор Галыкин
    Commented Nov 25 at 23:58
  • You asked how he understands those terms and I answered them. Be more clear in your question if you’re not satisfied by that then
    – Syed
    Commented Nov 26 at 0:00
  • You're right, I've just edited
    – Егор Галыкин
    Commented Nov 26 at 0:03
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    Hume does not use "moral" in the modern sense, see SEP, David Hume:"In his day, “moral” meant anything concerned with human nature, not just ethics, as he makes clear at the beginning of the first Enquiry, where he defines “moral philosophy” as “the science of human nature” (EHU 1.1/5). Hume’s aim is to bring the scientific method to bear on the study of human nature." In this passage, "moral reasoning" is the one based on experience broadly construed rather than on relating concepts (which is broader than just logic and math).
    – Conifold
    Commented Nov 26 at 0:36

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The word moral in our language means right action. Hume does use the same meaning (1), hence his work An Enquiry concerning the Principles of Morals. But he also uses the word moral in two more general senses: (2) Pertaining to human action in general, and (3) Pertaining to the ground and explanation of human action, that is to “human nature”, by which Hume refers to what we would now call human psychology (innate tendencies, habits, mental dynamics).

At the beginning of An Enquiry concerning Human Understanding Hume writes:

Moral philosophy, or the science of human nature, may be treated after two different manners ...

The one considers man chiefly as born for action … pursuing one object, and avoiding another …

That is sense (2) of moral. Then he moves to sense (1).

As virtue, of all objects, is allowed to be the most valuable, this species of philosophers paint her in the most amiable colours …

Then to sense (3)

The other species of philosophers consider man in the light of a reasonable rather than an active being, and endeavour to form his understanding more than cultivate his manners. They regard human nature as a subject of speculation; and with a narrow scrutiny examine it, in order to find those principles, which regulate our understanding, excite our sentiments, and make us approve or blame any particular object, action, or behaviour. (1-2)

As to what Hume writes on the two types of reasoning,

All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. (30)

He uses the word moral in sense (2), pertaining to action in general, as he explains later.

Such is the foundation of moral reasoning, which forms the greater part of human knowledge, and is the source of all human action and behaviour. (132)

In other words, moral reasoning means the kind of reasoning that guides all human actions, at least whenever humans act prudently (hence “rationally”). Even though, as Hume famously argues, unlike “demonstrative” reasoning, “moral” reasoning is to a large extent irrational, grounded in psychology rather than in reason, essentially involving our innate tendencies and habits.

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