The term “laws of thought” acquired additional meaning through his use of Boole (1815-64) to refer to the theorems of his “algebra of logic”; In fact, he called his second book logical, An Investigation of the Laws of Thought, on which mathematical theories of logic and probability are based (1854). Modern logicians, who almost unanimously disagree with Boole, regard this expression as a misnomer; None of the statements above classified under the “laws of thought” explicitly refer to thought itself, a mental phenomenon studied by psychology, nor does it contain any explicit reference to a thinker or connoisseur, as would be the case in pragmatics or epistemology. The distinction between psychology (as a study of mental phenomena) and logic (as the study of valid inference) is widely accepted. Notice also that the emphasis of the laws of thought was on existence. A common mistake of the deniers of these laws is to consider “non-existence” only as another type of existence, a parallel world or a place beyond space and time, from which new existences come and towards which finite existences go! These people are driven by linguistic habits to reify the word “non-existence”. The latter claims that the logical sum (i.e. ⋁, OR) of a simple sentence p and a predicate ∀xf(x) implies the logical sum of each separately. But PM both derive from six primitive theorems of ❋9, which are rejected in the second edition of PM and replaced by four new “Pp” (primitive principles) of ❋8 (see in particular ❋8.2, and Hilbert derives the first from his “axiom of logical ε” in his 1927 and does not mention the second. How Hilbert and Gödel came to adopt these two axioms as axioms is unclear.

These laws express how we assimilate complex experiences and solve difficulties in the course of thought (concepts, sentences, and arguments). Only through such logic can we “understand” the world around us and within us. By making these truths explicit, Aristotle now allowed people to consciously practice the logic to which they were already unconsciously inclined. Similarly, we can discuss mental objects (i.e. images, sounds, etc.). At first glance, their limitations seem obvious; But when they think about it, they become doubtful – inaccurate and insecure. And since this is the case, we cannot convincingly argue that the limits of material bodies are mental projections. If the boundaries of mental lines are uncertain, then the boundaries of what they are supposed to limit are still uncertain.

From its beginnings, philosophy has always been a study of the first causes and highest principles of all things in the light of logic and reason. Philosophers always seek wisdom by striving to found abstract principles and find their true meaning. To achieve this, we needed a set of laws or principles that organize our thoughts and align them with the path of logic called the laws of thought. So what are the laws of thought and who established them? First of all, it is at least obvious that the word “to be” or “not to be” has some meaning, so that not everything will be “such and not such”. Again, if “man” has any meaning, then it should be “bipedal animal”; If “man” means “X,” then if A is a man, “X” will be what “being a man” means to him. (It makes no difference, even if one were to say that a word has several meanings if they are limited only numerically; for each definition could be assigned a different word. For example, we could say that “man” has not one meaning, but several, one of which would have a definition, namely. “bipedal animal”, although there may be several other definitions if limited in number only; For each of the definitions a particular name could be assigned. If, however, they were not limited, but it were said that the word has an infinite number of meanings, an argument would obviously be impossible; for to have no meaning means to have no meaning, and when words have no meaning, our thinking with each other and even with ourselves has been destroyed; for it is impossible to think of anything if we think of nothing; But if possible, we could give this thing a name.) The generalized law of the excluded medium is not part of the execution of intuitionistic logic, but it is not denied either. Intuitionistic logic simply prohibits the use of the operation as part of what it defines as “constructive evidence”, which is not the same as proving its invalidity (which is comparable to the use of a certain style of construction in which screws are prohibited and only nails are allowed; it does not necessarily refute or question the existence or usefulness of screws, but simply shows what can be built without them). Deductive axioms are also negatively justified by paradoxical logic, that is.