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The Development of Laws of Formal Logic of Aristotle

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....If to consider a formal logic of Aristotle from the point of view of its essence , then its center of gravity is its Laws, that were discovered by Aristotle, based on analysis of the different types of syllogism, which Aristotle classified to track down those Laws. In his research, the syllogisms played the same role as the experiments in physics or chemistry for the discovery of regularities, to explain the process of certain events. Once these logical laws of thinking have been discovered, the syllogisms have fulfilled their role. And it would be foolish to assume that our knowledge in any science, is built only on Aristotle's syllogisms or others discovered later. Whatever syllogisms would not have been discovered since Aristotle, none of them had added something new in the laws of formal logic revealed by Aristotle and Leibniz. But philosophers still continue to analyze Aristotle's syllogisms, a historic mission of which ended more than 2000 years ago. Moreover, after the discovering of 4th of law of formal logic, the law of sufficient ground , the legality of any syllogism is easy checked from the viewpoint of the four laws of formal logic, because all our judgments and inferences must be obeyed to these laws, to be true.
Bertrand Russell is the one who belongs to this category of the philosophers, who in his book "History of Western Philosophy", examining the formal logic of Aristotle, has continued to pick weaknesses in his syllogisms, rather than focus his attention on the importance of the laws of formal logic in the human knowledge and to point out to the incompleteness of their definitions....

@IlyaStavinsky,

The connection between The Law of Identity
and the Law of Sufficient Ground
.. Discovered, long time ago, the laws of formal logic, the law of Identity and the law of sufficient ground, are still interpreted with very limited understanding, as evidenced by their contemporary definitions, which is the reason for the existence, in a logical world, of confusion and doubts in existence of perfect formal logic to know the real world.
For Aristotle his logic is not a science, but an instrument (organon) of any science about inference and evidence.

But the law of identity in the form in which Aristotle formulated it, is not quite complete, because he does not say, first, within what borders these unique concepts, judgments and conclusions remain valid - in other words, the limits of its application - and secondly, that all judgments and conclusions, defined uniquely, should be based on true facts, otherwise, all conclusions would be incorrect.

The ancient philosophers took advantage of the first shortcoming of the law and created a series of logical paradoxes that supposedly showed the contradiction of formal logic, i.e. its imperfections. The essence of the paradox is that philosophers in their discussions managed to find a loophole and violate the law of identity described by Aristotle. For example, they determined the judgment as "the truth" in relation to one phenomenon and defined uniquely the same judgment as a "lie" in relation to the other phenomenon. The result is a contradictory conclusions. (A striking example is the Russell's paradox we discussed above).

A second drawback of the definition of the law of identity was noticed by Leibniz, who eliminated it in the 17 th century by discovering of the 4th law of formal logic: the law of sufficient ground. This law states that "not a single event can be valid, not a single statement can be truth without sufficient ground, why it is the case, and not otherwise."

This definition of the law given by Leibniz also is limited, because it only speaks of the real ground, on which claims are based to be valid, and it does not tell about the role of the sufficient ground as a limit, in which law of identity remains in force. But to refer to this property of sufficient ground it is necessary to be familiar with the dialectical logic, which at that time did not exist. In such form the law of sufficient grounds is interpreted and to this day. Currently, the law is as follows: "The true idea must be sufficiently substantiated" or "it is the law - a general logical principle, according to which a position is considered true only if it can be based on sufficient ground. " (Philosophical Dictionary, ed. Ivan T. Frolov. - 4 th izd.-M.: Politizdat, 1981. - 445 pp.).

Incomplete understanding of the law of sufficient ground by earlier and modern philosophers is reflected in the simple fact that so far neither Aristotle's definition of Law of identity has not been amended to reflect its close relationship with the law of sufficient ground, nor the definition of the law of sufficient ground has not been amended to reflect its impact on the Law of Identity in terms of the limits of its applicability.

To eliminate all this shortcomings of the law of sufficient ground, we should formulate it as follows: Law of Sufficient Ground must be not only true but also must be a qualitative basis, in relation to which concepts, judgments and inferences are defined uniquely. As such, the Law includes, on the one hand, the definition given by Leibniz, on the other hand, it sets the boundaries of Law of Identity.
Taking this into consideration, the law of Identity formulated as follows: All concepts, judgments and inferences that are used , should be identified uniquely in relation to the same qualitative ground. As such, the Law includes, on the one hand, the definition given by Aristotle, but on the other hand, its direct relationship with the law of sufficient ground, which sets the boundaries of Law of Identity. Such a formulation of laws of formal logic makes it invulnerable to attack of the philosophers who believe it is not always perfect for a full disclosure of truth.
....

@IlyaStavinsky,

WALL OF TEXT DETECTED

tl;dr

--

In english. If you expect people to read that, then you should have proper formatting.

@Emil,

Emil;137172 wrote:

WALL OF TEXT DETECTED

tl;dr

--

In english. If you expect people to read that, then you should have proper formatting.

In any science people judge an article or a book not by the proper formatting but by their content. The proper formatting just facilitates reading but not understanding.

@IlyaStavinsky,

IlyaStavinsky;172746 wrote:

In any science people judge an article or a book not by the proper formatting but by their content. The proper formatting just facilitates reading but not understanding.

Maybe you should have fun with the content of this too?

Time Cube

@Emil,

That is what I meant in the msg above... "They don't vote in science"
(Ilya Stavinsky)

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