Contrary Events

I propose 3 subtle considerations to justify probability arising fron contrariety.

Just reasoning should retain its force, however subtle, in the same way as matter preserves its solidity:

• in the air, fire, and animal spirits, and
• in the grosser and more sensible forms.

No probability is so great as not to allow of a contrary possibility.

• This is because otherwise it would become a certainty.

The widest probability of causes depends on a contrariety of experiments.

An experiment in the past proves at least a possibility for the future.

The component parts of this possibility and probability are of the same nature.

• They differ in number only, but not in kind.

All single chances are entirely equal.

The only circumstance which can give any contingent event a superiority over another is a superior number of chances.

The uncertainty of causes is discovered by experience, which presents us with a view of contrary events.

When we transfer the past to the future and the known to the unknown, every past experiment has the same weight.

Only a superior number of experiments can throw the balance on any side.

The possibility, therefore, which enters into every reasoning of this kind, is composed of parts.

These parts are of the same nature:

• among themselves, and
• with those that compose the opposite probability.

I establish a maxim: “In all moral and natural phenomena, wherever any cause has a number of parts, and the effect changes according to a change in that number, the effects are a compounded one, and arises from the union of the several effects that proceed from each part of the cause.”

For example, the gravity of a body changes by the change of its parts.

We conclude that each part:

• contains this quality, and
• contributes to the gravity of the whole.

The absence of a part of the cause leads to the proportional absence of a part of the effect.

This constant conjunction proves the one part to be the cause of the other.

Our belief of any event changes according to the number of chances or past experiments.

Our belief is a compounded effect.

Each part of the effect arises from a proportional number of chances or experiments.

There is an opposite possibility to every probability.

This possibility is composed of parts.

These parts have the same nature as the probability.

Consequently, they have the same influence on the mind and understanding.

The belief, which attends the probability, is a compounded effect.

It is formed by the concurrence of the several effects which proceed from each part of the probability.

Each part of the probability contributes to producing the belief.

And so each part of the possibility must have the same influence on the opposite side, since the nature of these parts are the same.

The contrary belief, attending the possibility, implies a view of a certain object, as the probability does an opposite view.

In this, both these degrees of belief are alike.

Only by producing a stronger and more lively view of its object can the superior number of similar parts in the one can:

• exert its influence, and
• prevail above the inferior in the other.

Each part presents a particular view.

All these views unite together to produce one general view.

This view is fuller and more distinct the more causes or principles it is derived from.

The component parts of the probability and possibility are alike in their nature.

They must produce like effects.

The likeness of their effects is that each of them presents a view of a particular object.

These parts are alike in their nature.

But they are very different in their amount.

This difference must appear in the effect and in the similarity.

The view they present in both cases:

• is full and entire, and
• comprehends the object in all its parts, it is impossible that in this particular there can be any difference

There is only a superior vivacity in the probability, arising from the concurrence of a superior number of views distinguishing these effects.