Section 1b

# The Nature of Probability

by David Hume

We should always correct our first judgment derived from the object’s nature with another judgment derived from the nature of our understanding.

A man of solid sense and long experience should have a greater assurance in his opinions than a foolish and ignorant man.

Our feelings have different degrees of authority, even with ourselves, proportional to our reason and experience. This authority is never entire in a man of the best sense and longest experience.

Since even he must:

• be conscious of many errors in the past, and
• still dread errors in the future.

Here then arises a new species of probability to:

• correct and regulate the first, and
• fix its just standard and proportion.

## Doubt Helps us Correct Our Judgment

Demonstration is subject to probability.

Probability is liable to a new correction by the mind’s reflex act*.

In this reflex, our understanding of the first probability becomes our object.

Every probability has an original uncertainty.

The weakness of the understanding also creates a new uncertainty.

The understanding adjusts the original and new uncertainty together. Our reason obliges us to add a new doubt from the possibility of error in our estimation of the truth of our faculties. This doubt immediately occurs to us. We must decide on this doubt, following our reason. This decision might be favourable to our preceding judgment. But since it is founded only on probability, it must: further weaken our first evidence, and itself be weakened by another doubt of the same kind, and so on to infinity. Until finally, nothing remains of the original probability: no matter how great it may have been, and no matter how small the reduction by every new uncertainty. No finite object can sustain itself under an infinite decrease of probability.

Even the vastest amount in the human imagination will be reduced to nothing in this way. Our initial belief will infallibly perish by passing through so many new examinations. Each examination reduces its force and vigour. When I reflect on my judgment’s natural fallibility, I have less confidence in my opinions, than when I only consider the objects I reason on. My belief totally extinguishes if I further scrutinize my faculties.

• [ Translator’s note: In data science, this reflex act is called backpropagation which corrects the normal flow of thoughts called forward propagation, by averaging initial the probable answers and then running them through the logic in reverse to see which answers survive. The gradual reduction of belief to a neural network is called vanishing gradient.]

Partial Skepticism is Useful, But Total Skepticism is Useless The following questions are entirely superfluous:

Do I sincerely assent to this argument that I am taking such pains to inculcate? Am I really one of those skeptics who think that all is uncertain? No one was ever sincerely and constantly held these opinions.

By an absolute and uncontrollable necessity, Nature has determined us to:

• judge,
• breathe, and
• feel.

We naturally view certain objects in a stronger light from their habitual connection with a present impression, just we think while we are awake.

Whoever takes pains to refute the petty objections of this total skepticism, really:

• disputes without an antagonist, and
• tries to establish a faculty which nature has antecedently:
• implanted in the mind, and
• rendered unavoidable.

The skeptics are a fantastic sect.

I display their arguments so that the reader will know the truth of my hypothesis that: all our reasonings on causes and effects are derived only from custom and habit, and belief is more properly an act of the sensitive part of our natures, than of the meditative part of our natures.

Here I have proven the following:

• The principles which make us decide on any subject are the same principles which correct that decision through our mind’s situation and genius.

When these principles are carried further and applied to every new reflex judgment, they must:

• reduce that judgment to nothing by continually reducing the original evidence, and
• utterly subvert all belief and opinion.

Belief would destroy itself if it were a simple act of the thought, without:

• any peculiar manner of conception, nor
• the addition of a force and vivacity

In such a case, belief would end up to suspending our ability to judge.

In reality, this does not happen because people can still believe, think, and reason as usual. This proves that belief, thought, and reason are based on sensation and conception, which are impossible for mere ideas destroy. But how do these above arguments not stop our judgment?

How does the mind sustain a belief? These new probabilities, whether based on thought or sensation, are based on the same principles as our primary judgment.

They: perpetually reduce the original evidence, equally subvert our primary judgment, reduce the mind to a total uncertainty, through the opposition of contrary thoughts or sensations. A question is asked to me.

I think of an answer. I go over the impressions of my memory and senses. I carry my thoughts from them to the objects commonly conjoined with them. I feel a stronger conception on one side than on the other. I prepare an answer based on this strong conception. I re-examine my answer.

I realize that it is: sometimes correct and sometimes wrong. as regulated by contrary principles or causes. In balancing these contrary causes, I reduce the assurance of my first answer. I prepare a new answer, which is liable to another doubt. This process can go on for infinity. How can we retain belief in philosophy or common life, even after all this?

I answer that, after the first and second answer: the mind’s action becomes forced and unnatural, and the ideas become faint and obscure even if the principles of judgment and the balancing of opposite causes is the same as at the very start. Yet their influence on the imagination and the vigour that they add or remove from the thought are not equal. When the mind reaches its objects with difficulty, the same principles do not have same effect as in our more natural way of thinking.

The imagination does feel the same way as it felt in its common judgments and opinions. The attention is stretched. The posture of the mind is uneasy. The spirits are diverted from their natural course. They move differently from when they flowed in their usual channel. It will not be very difficult to find similar instances if we want them.

Metaphysics will supply us abundantly. The same argument which will convince us in a reasoning on history or politics, has less influence on philosopophical subjects. This is because an effort of thought is needed to understand metaphysical subjects. But this effort of thought disturbs our feelings which the belief depends on. The case is the same in other subjects. The regular flow of our feelings are hindered by the straining of the imagination. We would never feel anything for a tragedy which portrays its heroes as very ingenious and witty in their misfortunes. The soul’s emotions prevent any subtle reasoning and reflection. This makes reasoning and reflection equally prejudicial to the emotions. The mind and the physical body has a precise degree of force, which it employs in one action only at the expense of all the rest. This is more obvious in actions that have different natures. These different natures divert the mind’s force and changes its disposition. It renders us: incapable of a sudden transition from one action to the other, and incapable of performing both actions at once. Conviction from a subtle reasoning decreases the more the imagination struggles to enter into that reasoning. Dogma and Skepticism are Both Based on Doubt, But Operate in Opposite Ways Belief is a lively conception.

It can never be entire if it is not founded on something natural and easy. This is the true state of the question. Some people use an expeditious way to totally reject the arguments of skeptics without examination. We cannot approve of this expeditious way. They say that: if the skeptical reasonings are strong, then it is a proof that reason may have some force and authority, and if the skeptical reasonings are weak, then reason can never be enough to invalidate all the conclusions of our understanding. That argument is not fair.

This is because skeptical reasonings are successively strong and weak, based on the mind’s successive dispositions. Reason initially takes the throne. It prescribes laws and imposes maxims with an absolute authority. Her enemy, doubt, takes shelter under her protection*. It uses rational arguments to prove the fallaciousness and imbecility of reason, producing a patent under her band and seal. This patent initially has an authority proportional to the present and immediate authority of reason, from which it is derived. But as it is contradictory to reason, it gradually reduces the force of reason and its own at the same time. Until finally, they both vanish into nothing, by a regular and just reduction. The skeptical and dogmatical reasons are of the same kind.

But they are contrary in their operation and tendency. Where the skepticism is strong, it has an enemy of equal force in dogma. Their forces were at first equal. They still continue to be equal as long as either of them subsists. None of them loses any force in the contest, without taking as much from its antagonist.

• [ Translator’s note: In data science, this doubt is called the bias that takes shelter in each neuron of a neural network in order to prevent some kinds of data from being processed further. The bias declines or changes depending on factors such as the learning rate. ]

It is happy that nature:

breaks the force of all skeptical arguments in time, and keeps skeptical arguments from having any considerable influence on the understanding. Skeptical arguments never self-destruct.

If nature did not break them, they would have: subverted all conviction, and totally destroyed human reason.

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