We should only engage with objects that lead to sure knowledge.

We should only engage with objects which our minds can use to achieve sure knowledge.

All knowledge is certain and evident cognition.

Thus, through this proposition, we:

• reject all merely probable cognitions
• establish that only those fully known and about which there can be no doubt should be believed.

Educated people do not want to admit ignorance.

This is why they have gotten used to embellishing their fabricated arguments, gradually persuading themselves and peddling them as true.

Whenever 2 opinions on the same matter oppose each other, at least one of them is deceived.

Therefore, we cannot acquire perfect knowledge from probable opinions because we cannot hope for more from ourselves than what others have accomplished.

So only Arithmetic and Geometry remain which matches this rule [of using something that applies to all yet itself cannot be doubted].*

We ourselves rejoice that we were once educated in schools.

But we are now released, at a sufficiently mature age, from that oath that bound us to the Master.

Rule 2 is that we should not misuse leisure, as many do, neglecting whatever is easy and only occupying ourselves with difficult matters where we devise the most subtle conjectures which only increase the multitude of doubts without learning any science..

Arithmetic and Geometry alone exist free from any falsehood or uncertainty.

We arrive at knowledge of things by two paths:

1. Experience
2. Deduction

The experiences of things are often deceptive, while deduction or pure inference can be omitted if it is not necessary.

But deduction is never done wrongly by an intellect, even a minimal rational one.

The Dialecticians use chains to control human reason. They are useless for this end, even if they are useful elsewhere.

Every human deception never arises from a bad inference. It can only arise from the fact that certain experiments are assumed little understood or judgments are rashly and without foundation established.

This is why Arithmetic and Geometry are much more certain than other disciplines.

These alone revolve around an object so pure and simple that they assume nothing that experience has made uncertain.

This does not mean that only Arithmetic and Geometry should be learned.

It means that in our search for the truth, we should have the same certainty as from Arithmetic and Geometric demonstrations.