Section 1b

The Nature of Probability

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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 has more 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:

  • have had 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.

Superphysics 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 has 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.

The skeptics are a fantastic sect.

My hypothesis is that:

  • all our reasonings on causes and effects are derived only from custom and habit, and
  • belief is an act of the sensitive part of our natures, more than our meditative part.

Here I have proven that:

  • 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.

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