There can never be an entirely explicit reasoning—one has always to be entimematic.
To an unknown degree, as a rule.

* * *

There ain't no such thing as a rigorous proof.

* * *

Logic does not imply rigor—logic needs correctness.

* * *

To deduce anything, one has to introduce at least something.

* * *

There is no scheme without an object. The very human ability to construct schemes is related to certain aspects of human activity.

* * *

Mathematics is never convincing.

* * *

The notion implies understanding. Understanding implies something to understand.

* * *

The principal idea of materialism is to never be scared by the unexpected.
There is always something in the world that has not been comprehended yet,
there is always something beyond the scope of our present experience.
One just has to be prepared to that and not be confused in a critical situation.

* * *

The first definition of an object is its opposedness to another object.
The object "objects" to be identified with anything else.

* * *

All the variety of deductive logical schemes could be generated from two complementary relations,
one antisymmetric ("implication"), and one symmetric ("identity").

* * *

It seems like the notions are first integrated in a sentence, to become differentiated notions.

* * *

A written sentence is not yet a proposition.
Rather, it may be (or not be) a representation of a proposition.

* * *

Since there is only one world, everything can be understood as the world's relation to itself.

* * *

Logical categories are the simplest schemes of activity.

* * *

Refutation does not need justification.
It is only affirmations that must be justified.