What is Probability?

Probability only discovers the relations of objects, not the relations of ideas.

It must be founded on our perceptions and ideas.

• If there were no perceptions in our probable reasonings, the conclusion would be chimerical.
• If there were no mixture of ideas, the mind’s action in observing the relation would be sensation, not reasoning.

In all probable reasonings, there must therefore be some perception or thing present to the mind, either seen or remembered.

• This something will let us infer something connected with it which is not [yet] seen nor remembered.

Only cause and effect can lead us beyond the immediate perceptions of our memory and senses because only cause and effect can be the basis of just inference from one object to another.

The idea of cause and effect is derived from experience.

• Experience informs us that such objects in all past instances, have been constantly conjoined with each other.

An object similar to one of these objects is supposed to be immediately present in the impression in our experience.

This makes us presume the existence of an object similar to its usual attendant object.

According to this, probability is founded on the presumption of a resemblance between:

• those objects we have experienced, and
• those objects which we have had no experience.

Therefore, our presumption on an existence of a cause or effect can never arise from probability.

The same principle cannot be both the cause and effect of another.

This is perhaps the only proposition on cause and effect that is intuitively or demonstratively certain.

Anyone who eludes this argument without determining whether our reasoning on cause and effect is derived from demonstration or probability, pretends that all conclusions from causes and effects are built on solid reasoning.

This reasoning should be produced for us to examine it.

After we experience of the constant conjunction of objects, we reason in the following way:

1. Object A always produces Object B.

2. Object A is the cause of B by producing it.

3. Therefore, Object A exists or existed if Object B exists.

Object A has a power of producing the effect.

The new production is what we infer from the power and the past production.

But this reasoning is weak if the idea of production is the same with the idea of causation.

Thus, I shall not resort to this

But still, I believe that:

• the production of one object by another implies a power, and
• this power is connected with its effect.

This power does not lie in the sensible qualities of the cause.

Why do you presume in other instances that the same power still exists, merely on the appearance of these qualities?

Your appeal to past experience decides nothing in the present case.

It can only prove that that very object, which produced any other, was at that very instant endowed with such a power.

But it can never prove that the same power must continue in the:

• same object, or
• collection of sensible qualities.

I can much less prove that a like power is always conjoined with like sensible qualities if:

• the same power continues united with the same object, and
• like objects are endowed with like powers.

Why from this experience we form any conclusion beyond those past instances which we experienced?

If you answer this question in the same way as the preceding question, your answer creates a new question to infinity.

This clearly proves that the foregoing reasoning is baseless.