Unphilosophical Probability

Four kinds of Probability

All these kinds of probability are:

• received by philosophers, and
• allowed to be reasonable foundations of belief and opinion.

But there are other kinds derived from the same principles, but they were not fortunate to obtain the same sanction.

Probability is Affected by the Reduction of the Impact from the Feelings and Memory

1. The reduction of the impression from our memory or senses also weakens the evidence from the senses.

For example, an argument based on any fact that we remember is convincing depending on the recentness or remoteness of that fact, even if that fact is not philosophically as solid and legitimate.

If the fact is not philosophically solid, its argument would have a different force today compared to next month.

Yet despite the opposition of philosophy, this circumstance:

• has a considerable influence on the understanding, and
• secretly changes the authority of the same argument according to the different times it is proposed to us.

A greater force and vivacity in the impression naturally conveys a greater force to the related idea.

According to the foregoing system, belief depends on the degrees of force and vivacity.

Probability is Affected by the Increase of the Impact from the Feelings and Memory

2. A stronger impression increases our belief and assurance.

This always happens, even if it is disclaimed by philosophers.

A recent experience, fresh in the memory, affects us more than one that is forgotten.

• It has a superior influence on the judgment and the passions.

A lively impression produces more assurance than a faint one.

• It has more original force to communicate to the related idea, which then acquires more force and vivacity.

A recent observation has a like effect because the habit and transition:

• is more entire there, and
• preserves better the original force in the communication.

For example, a drunkard who has seen his companion die of a debauch:

• is struck with that instance for some time, and
• dreads a like accident for himself.

But as its memory decays:

• his former security returns, and
• the danger seems less certain and real.

Probability is Affected by the Number of Ideas Connected to It

3. Our reasonings from proofs often degenerates insensibly into the reasonings from probabilities through many connected arguments.

Our reasonings from proofs and our reasonings from probabilities are different from each other.

When an inference is drawn immediately from an object without any intermediate cause or effect, the conviction is much stronger than when the imagination goes through a long chain of connected arguments, however infallible the connection of each link.

The vivacity of all the ideas is derived from the original impression through the customary transition of the imagination.

This vivacity must:

• gradually decay in proportion to the distance, and
• lose somewhat in each transition.

Sometimes this distance has a greater influence than even the influence of contrary experiments.

A man may receive a more lively conviction from a probable reasoning, which is close and immediate, than from a long chain of consequences which are just and conclusive in each part.

Such reasonings seldom produce any conviction.

One must have a very strong imagination to preserve the evidence to the end, where it passes through so many stages.

A very curious phenomenon has been suggested to us on this.

We can only have an assurance of a point of ancient history by passing through:

• millions of causes and effects, and
• a very long chain of arguments.

Before the knowledge of the fact could come to the first historian, it must be conveyed through many mouths.

After it has been written, each new copy is a new object.

The connection between the two objects is known only by experience and observation.

Therefore, the evidence of all ancient history must now be lost.

Or at least, all evidence will be lost in time, as the chain of causes increases.

But this seems contrary to common sense.

It supposes that if the intellectual world and the art of printing continue, future generations can doubt that Julius Caesar existed. This is an objection to the present system.

If belief consisted only in a certain vivacity, conveyed from an original impression, it:

• would decay by the length of the transition, and
• must finally be extinguished.

Conversely, if belief sometimes does not die out, then it must be something different from that vivacity.

There is a a celebrated argument against Christianity.

It says that the connection between each link of the chain in human testimony has been supposed to:

• not go beyond probability, and
• not be liable to doubt.

But the third kind of probability implies that all histories and traditions must eventually lose its force.

Every new probability reduces the original conviction.

No matter how great that conviction is, it is impossible for it to survive under such re-iterated reductions.

This has one very important exception which will be explained later in Part 4, Section 1.

This objection is against the supposition that historical evidence initially amounts to an entire proof.

To address this, let us consider that there are innumerable links connecting any original fact with the present impression, which is the foundation of belief.

• Yet all these links are of the same kind.

They depend on the fidelity of printers and copiers.

One edition passes into another, into a third, and so on, until we come to the current version.

There is no variation in the steps.

• After we know the latest version, we have no scruple regarding the rest.

By knowing one, we know all.

This circumstance alone:

• preserves historical evidence, and
• will perpetuate the memory of the present age to the future generations.

If the long chain of causes and effects connecting any past event with any volume of history were made of parts different from each other, it is impossible we should preserve any belief or evidence to the end.

But as most of these proofs are perfectly resembling, the mind:

• runs easily along them,
• jumps from one part to another with facility, and
• forms but a confused and general notion of each link.

Through this, a long chain of argument has as little effect in reducing the original vivacity, as a much shorter chain would have, if were made up of parts:

• that were different from each other, and
• where each required a distinct consideration.

Probability is Affected by General Rules

4. Another unphilosophical kind of probability is that derived from general rules, which:

• we rashly form to ourselves, and
• are the source of prejudice.

An Irishman cannot have wit and a Frenchman cannot have solidity.

The conversation of the:

• Irishman may be visibly very agreeable.
• Frenchman may be very judicious.

But we have entertained such a prejudice against them. They are stupid in spite of sense and reason. Human nature is very subject to errors of this kind.

Perhaps Britain is subject to errors as much as any other country.

I think prejudice proceeds from those very principles which all judgments on causes and effects depend on.

Our judgments on cause and effect are derived from habit and experience. When we have been used to see an object united to another, our imagination transits from the first to the second naturally.

This transition:

• precedes reflection, and
• cannot be prevented by reflection.

Habit naturally:

• operates with its full force when the presented objects are exactly the same with those that we have been used to, and
• operates in an inferior degree when we discover objects to be similar but not exact.

The habit loses its force by every difference.

Yet it is seldom entirely destroyed if any considerable circumstances remain the same.

A man who is used to eating fruits, such as pears or peaches, will satisfy himself with melons if he cannot find his favourite fruit.

A man who gets drunk with red wines will get almost as drunk with white wine if given to him.

From this principle, I have accounted for the species of probability which we derive from analogy.

Through analogy, we transfer our experience in past instances to objects which are resembling, but are not exactly the same with those objects we have experienced.

The probability reduces as the resemblance decays.

But still has some force as long as there remain any traces of the resemblance.

We may carry this observation further.

Habit is the foundation of all our judgments.

But sometimes, habit opposes judgement in the imagination.

It produces a contrariety in our feelings on the same object.

In almost all kinds of causes, there is a complication of circumstances.

Some circumstances are essential, others are superfluous.

Some are absolutely needed to the produce an effect. Others are only conjoined by accident.

When these superfluous circumstances are numerous, remarkable, and frequently conjoined with the essential, they have such an influence on the imagination.

Even in the absence of the essential circumstances, they:

• carry us on to the conception of the usual effect, and
• give to that conception a force and vivacity, which make it superior to the mere fictions of the fancy.

We may correct this propensity by a reflection on the nature of those circumstances.

But it is still certain, that habit takes the start and gives a bias to the imagination.

To illustrate this by a familiar instance, let us consider a man who is hung from a high tower in an iron cage.

He cannot refrain from trembling when he surveys the precipice below him, even if he knows he is perfectly secure from falling, by his experience of the iron’s solidity which supports him.

Though the ideas of fall, harm and death are derived solely from custom and experience.

The same habit:

• goes beyond the instances:
  • from which it is derived, and
  • to which it perfectly corresponds.
• influences his ideas of such objects as are in some respect resembling, but fall not precisely under the same rule.

Depth and descent strike so strongly on him.

Their influence cannot be destroyed by the contrary circumstances of support and solidity, which should give him a perfect security.

His imagination runs away with its object, and excites a passion proportioned to it.

That passion returns on the imagination and enlivens the idea.

This lively idea has a new influence on the passion.

It adds the force and violence of that passion. His fancy and affections, mutually supporting each other, cause the whole to have a very great influence on him. Why do we need to seek other instances, when philosophical probabilities offer us an obvious instance in the opposition between the judgment and imagination arising from these effects of custom?