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The most precise and complete formulation of the law of higher logic I find in the writing of Plotinus, in his On Intelligible Beauty. I shall quote this passage in the succeeding chapter.
I have called this system of higher logic Tertium Organum because for us it is the third canon — third instrument — of thought after those of Aristotle and Bacon. The first was Organon, the second, Novum Organum. But the third existed earlier than the first.
Man, master of this instrument, of this key, may open the door of the world of causes without fear.
--
Ch. XXI

 

P. D. Ouspensky

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In naming his book Tertium Organum Ouspensky reveals at a stroke that astounding audacity which characterizes his thought throughout — an audacity which we are accustomed to associate with the Russian mind in all its phases. Such a title says, in effect: "Here is a book which will reorganize all knowledge. The Organon of Aristotle formulated the laws under which the subject thinks; the Novum Organum of Bacon, the laws under which the object may be known; but The Third Canon of Thought existed before these two, and ignorance of its laws does not justify their violation. Tertium Organum shall guide and govern human thought henceforth." How passing strange, in this era of negative thinking, of timid philosophizing, does such a challenge sound!

 

P. D. Ouspensky

 

The logical formula: A is both A and Not-A, corresponds to the mathematical formula: A magnitude can be greater or less than itself.
The absurdity of both these propositions shows that they cannot refer to our world. Of course absurdity, as such, is indeed not an index of the attributes of noumena, but the attributes of noumena will certainly be expressed in what are absurdities to us. To hope to find in the world of causes anything logical from our standpoint is just as useless as to think that the world of things can exist in accordance with the laws of a world of shadows or stereometry according to the laws of planimetry.
To master the fundamental principles of higher logic means to master the fundamentals of the understanding of a space of higher dimensions, or of the world of the wondrous.
In order to approach to a clear understanding of the relations of the multi-dimensional world, we must free ourselves from all the "idols" of our world, as Bacon calls them, i.e., from all obstacles to correct receptivity and reasoning. Then we shall have taken the most important step toward an inner affinity with the world of the wondrous.

 

P. D. Ouspensky

 

The ordinary logic has a great deal to say about genera and species, or in our nineteeth century dialect, about classes. Now a class is a set of objects compromising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects compromising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the comtemplation of a fragment of a system to the envisagement of the complete system.

 

Charles Sanders Peirce

 

Under Aristotle the "Reader," whose knowledge of Trojan areté seems conspicuously absent, forms and substances dominate all. The Good is a relatively minor branch of knowledge called ethics; reason, logic, knowledge are his primary concerns. Areté is dead and science, logic and the University as we know it today have been given their founding charter: to find and invent an endless proliferation of forms about the substantive elements of the world and call these forms knowledge, and transmit these forms to future generations. As "the system."

 

Robert M. Pirsig

 

Eventually, Aristotle appeared among the Greeks. He improved the methods of logic and systematized its problems and details. He assigned to logic its proper place as the first philosophical discipline and the introduction to philosophy. Therefore he is called the First Teacher.

 

Ibn Khaldun