The Three First Principles of Logic - Law of Identity, Principle of Non Contradiction, and the Principle of Excluded Middle - Some Personal Thoughts

Stephen Alexander Beach 

Aristotelian Science 
The word "science" in the much older sense of Aristotle is not our contemporary association with the inductive method of inquiring about the physical world. Science was rather a coherent body of knowledge which was based on first principles. There are all kinds of sciences because there are all kinds of bodies of knowledge. From dog grooming to sailing. Now, what exactly is a first principle? First principles refer to the most universal truths in regard to that body of knowledge. For sailing, for example, a first principle could be that for a boat not to sink, there must be a particular ratio of between the size of the boat and the amount of water it displaces. 

The Science of Sciences

Now we can choose to zoom out from sailing or dog grooming, and ask the question, what is the science that incorporates all other sciences? Or what is the body of knowledge that incorporates all other bodies of knowledge? This would actually be metaphysics, which is the queen of the sciences as it studies being qua being, or being in its universal form, stripped from its specificity. Logic is therefore an expression or codification in human thinking of the science of metaphysics. It applies the metaphysical laws to thinking. And so logic is the science of thinking in accordance with reality. 

Three First Principles of Logic

Now the most fundamental metaphysical truth is that reality does not contradict itself. And so this universal truth of being will also be reflected in the first principles of thinking. And so there are three first principles of thinking that reflect that metaphysical first principle. These are the "Law of Identity," the "Principle of Non Contradiction," and the "Principle of Excluded Middle". The Law of Identity states that "a thing is what it is." The Principle of Non Contradiction that "something cannot both be and not be at the same time and in the same respect." And the Principle of Excluded Middle that "between being and non-being there can be nothing." 

Each expresses an aspect of the metaphysical truth that reality does not contradict. The Law of Identity expresses that a thing retains a concrete identity at any one time and is not relative. The Principle of Non Contradiction that when we hold consistent time and aspect, that reality cannot be contradictory. The Principle of Excluded Middle that when two contradictories are compared, there can be no middle ground. These are boundaries which we can never cross. 

Per Se Nota Negative and Positive Propositions

If we do try to cross them we will always fall into statements of self-refutation. These are statements which disprove themselves in the act of trying to prove themselves. This is because all assertion is a attempt at truth and implies that truth exist, and so to attempt to prove as truth that nothing is true refutes itself immediately. This means that any attempt to disprove truth is per se contradictory. And so the skeptic must not speak or try to assert anything with his words. He must remain silent. But Aristotle is even harder on skeptics, saying that even action in the world implies a practical affirmation of objective truth (I exist the room through the door and not the lightbulb, for example). And therefore, to truly be a skeptic would be to not only remain silent, but to not move or act either. Aristotle compares these to vegetables who cannot speak or act. These types of propositions also become a reduction to absurdity because in doubting truth I must also doubt my understanding of the words that make up the sentence of denying truth. I must also doubt my knowledge of doubt itself, as well as all of my thoughts. Therefore I end in the absurdity of pure nothingness. 

On the opposite side of these self-refuting propositions are self-affirming propositions, also known as "per se nota" propositions (recognized through itself), in which when one knows the meaning of the subject, one immediately is convicted of the truth of the predicate. These do not have to be on the level of first principles, but apply to many things in the world. An example would be "all triangles have three sides." 

Contingent Propositions

Finally, there are a third category of propositions called "contingent propositions". These are statements which could be either true or false. There is nothing inherent in them which would preclude one or the other. And so we must seek evidence or their validity from real life circumstances or situations. 

And so, over all the first principles of logic act as a boundary which we cannot cross, the per se nota propositions likewise are boundaries that we cannot cross, allow us then to genuinely seek for the truth when it comes to contingent propositions about realities in the world which are not necessary but could be or not be. This is the proper realm of logic in which to think and function. Without these boundaries we cannot live.