"[S]topt short" by this problem, Hume puts the idea of necessary connection on hold and examines two related questions: Why do we accept the maxim 'whatever begins to exist must have a cause'?, and How does the psychological process of probable reasoning work?

Hume begins Part 4 by arguing that "all knowledge degenerates into probability", due to the possibility of error: even the rock solid certainty of mathematics becomes less than certain when we remember that we might have made a mistake somewhere.

And as for why we do not sink into total scepticism, Hume argues that the mind has a limited quantity of "force and activity", and that difficult and abstruse reasoning "strain[s] the imagination", "hinder[ing] the regular flowing of the passions and sentiments".

And since this supposes more regularity than is found in past observation, causal reasoning alone cannot explain it: thus Hume invokes the imagination's tendency to continue in any "train of thinking" inertially, "like a galley put in motion by the oars".

But to explain "so vast an edifice, as... the continu'd existence of all external bodies", Hume finds it necessary to bring constancy into his account, as follows: (1) Identity is characterised as invariableness and uninterruptedness over time.

Turning to the question of the "local conjunction" of mind and matter, he considers and endorses the anti-materialist argument which asks how unextended thoughts and feelings could possibly be conjoined at some location to an extended substance like a body.

Before continuing his "accurate anatomy of human nature" in Books 2 and 3, he anxiously ruminates: the "danger" of trusting his feeble faculties, along with the "solitude" of leaving behind established opinion, make his "bold enterprises" look foolhardy.

Happily, human nature steps in to save him: "I dine, I play a game of back-gammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I wou'd return to these speculations, they appear so cold, and strain'd, and ridiculous, that I cannot find in my heart to enter into them any farther."

Hume finds two ways for something like unexercised power to influence our passions: first, predictions of human behavior are (absent "strong motives") plagued with uncertainty, and we can receive anticipatory pleasure or unease from probable or merely possible exercise of power (tentatively reasoning from our own past conduct to guess what we might do); second, a "false sensation of liberty" presents all feasible courses of action as fully possible to us, giving us an anticipatory pleasure unrelated to any reasoning from experience.

But additional factors play a role: others might be seen as a good judge of character ("authority"), and the very question of one's self-worth is both emotionally heightened and apt to evoke a self-conscious deference to the opinions of others.

Hume finishes by illustrating and confirming his account with a concrete example (viz., a man from a high-class family fallen on hard times leaving home to do manual labour elsewhere), and considering some minor objections.

In these cases, pleasure arises from the sheer stimulating effects of sympathy: family members, neighbors, and acquaintances are a durable source of lively ideas, as are individuals with personal qualities resembling our own.

In general, Hume remarks, the psychological mechanisms at work do not require any sophisticated "force of reflection or penetration": "[e]very thing is conducted by springs and principles, which are not peculiar to man, or any one species of animals".

After a glancing mention of the direct passions and a perfunctory definition of the will as a mere impression we feel, he confronts the hoary philosophical problem of free will and determinism, dedicating two sections to a defense of soft determinist compatibilism.

In the next section, Hume challenges "the doctrine of liberty"—the view that human beings are endowed with a distinctive kind of indeterministic free will—by setting out and debunking "the reasons for [its] prevalence".

As a compatibilist, Hume accepts the latter kind of free will, deeming it "that species of liberty, which it concerns us to preserve" and even "the most common sense of the word"; but he rejects freedom from necessity as either "absurd" (being nothing more than sheer "chance") or else "unintelligible".

Real-world cases also illustrate the idea: close personal relationships bring one's private belongings into common ownership, and free goods like air and water are allowed unrestricted use.

The next four sections see Hume completing his examination of justice as an artificial virtue: he argues that "the three fundamental laws of nature, that of the stability of possession, of its transference by consent, and of the performance of promises" are all based on human convention.

Second, because "rigid stability" would of course bring great disadvantages (resources having been allocated by mere "chance"), we need a peaceful way to induce changes in ownership: thus we adopt the "obvious" rule of transference by consent.

He adds that the "terrible" Catholic doctrine of intention (viz., that a sacrament is invalidated if its minister is in the wrong state of mind) is actually more reasonable than the practice of promising—since theology is less important than promise-keeping, it can afford to sacrifice utility to consistency.

The need for government arises from our short-term thinking: though lawful conduct is clearly in our interest, we get carried away by a dangerous "narrowness of soul, which makes [us] prefer the present to the remote", so that rule violations become more frequent and therefore more strategically advisable.

Hume also appeals to the opinions of everyday people (which in questions of morality and other sentimentalist domains "carry with them a peculiar authority, and are, in a great measure, infallible"), who see themselves as born to obedience independently of any promising, tacit or otherwise, even to authoritarian states—an understanding reflected in legal codes on rebellion.

In a closing discussion of the Glorious Revolution, Hume defends keeping the right of resistance unformulated and out of the legal code, and extending this right from cases of direct oppression to cases of interbranch constitutional encroachment in "mix'd governments", adding two "philosophical reflections": first, Parliament's authority to exclude the heirs of rulers they have deposed, but not the heirs of rulers who simply died, derives from mere imaginative inertia; second, a contested change in authority may acquire legitimacy retroactively from a stable line of successors.

This solution might sound unrealistic in the abstract, but nature has made it a reality: those personally concerned with infidelity have swept along the unconcerned in their disapproval, molded the minds of girls, and extended the general rule into apparently irrational territory, with "debauch'd" men shocked at any female transgression and postmenopausal women condemned for perfectly harmless promiscuity.

Men instead stake their reputation on courage (a partly natural virtue) and enjoy looser sexual norms, fidelity in males (like cooperation among nations) being less important for society.

This explains how we can manage such "extensive sympathy" in morality despite our "limited generosity" in practice: it takes "real consequences" and particular cases to "touch the heart" and "controul our passions", but "seeming tendencies" and general trends are enough to "influence our taste".

Hume finishes by explaining how his system accommodates not only the "moral virtues" but also the "natural abilities" of the mind, and by downplaying the distinction as not very important and largely a matter of mere terminology.

Thus women love a strong man in sympathy with the utility a lover of his could be expected to receive, everyone finds beauty in healthy and useful body parts, and an immediate pleasure or dismay arises from the perception of regular features or "a sickly air", respectively.

So, while Hume presents himself as a theoretical "anatomist" who dissects human psychology into ugly bits, his work is well-suited for the practical "painter" who styles morality into a beautiful and inviting ideal.

This line of thinking had a great influence on my efforts, most specifically Mach and even more so Hume, whose Treatise of Human Nature I studied avidly and with admiration shortly before discovering the theory of relativity.