With the great philosopher Aristotle – who was Alexander the Great’s tutor – we see a general systematisation of philosophy, and a further deepening of the ontological problem. If up to now, we have reasoned starting from the Being in res, it is now a question of analysing the connection between the latter and rationality itself, i.e. the lógos.
In the very first chapters of the book Γ (Gamma) of Metaphysics, the Stagirite exposes these first considerations: the study of the Being qua Being and its attributes, belonging to a single science and this science is the philosopher’s field of study.
Therefore, this naturally also includes the study of the ‘axioms’ and the substance, which pertain to the Being and therefore to everything that is. Since these ‘axioms’ concern the universal par excellence and the whole substance and nature of it, they must also be the most universal and true. The problem of Truth had already been analysed by Aristotle in his Prior Analytics – where the nature of ‘reasoning’ is exposed and the various forms of syllogisms and demonstration are explained; it is evident that a preliminary knowledge of these can be not only useful but, in a certain way, necessary for the understanding of what is being exposed. But since it is not possible to expect the reader to have knowledge of such voluminous and complex texts, an attempt will be made to insert the fundamental notions along the way.
From the Truth’s point of view it proves to be undeniable because any negation that is formulated is self-denial.
Let us therefore start with an Aristotelian quote of fundamental importance:
It is necessary to establish, writes Aristotle, what the principle “regarding which it is impossible to be mistaken” is, that being: whoever enunciates it, at any place or time, can be absolutely certain to enunciate a principle that is true. Furthermore, this has two specific characteristics: it is the best known and it is non-hypothetical. The first characteristic means that although it is possible to know it in other wording, or to have never thought of it in a rational way, it is however, the same principle known and ‘applied’ by anyone (and since we are talking about the Being, we deduce that all things that are also adapt to it); the second characteristic means that the principle cannot be a hypothesis verified through rational reasoning: it is true by its very nature, and receives its truth only from itself.
Such a principle is evidently the fulfilled dream of any thinker who seeks the Truth, because, in some way, it is Truth itself in the form of a principle. But it is still necessary to enunciate it, and Aristotle certainly does not exempt himself from doing so:
This is the first wording of the principle that will later be called ‘of non-contradiction’ (PONC), that is, the foundation and cornerstone of rationality itself. This principle enunciates the impossibility of the contradiction, that is also the impossibility of contradicting oneself. In other words, wecould say that it is impossible for the same object to possess contradictory attributes at the same time and under the same respect. For example, Napoleon may be young and old, but not at the same time (it is possible in different years); Napoleon may be great and small but not under the same respects (he is great general and small in physical stature). What must be kept in mind is the distinction between ‘contrariety’ and ‘contradiction’: black and white are ‘contrary’ because they do not complete the whole field of possibilities (if an object is neither white nor black it can be any other colour), while white and non-white are ‘contradictory’ to each other because they complete the whole field (the ‘non-white’ contains not only ‘black’ but also all other possible colours and the absence of colour). Therefore, a vase can be neither black nor white, but it must necessarily be either white or non-white (tertium non datur).
Once enunciated the PONC, it is necessary to argue whether it really is the principle we were looking for, i.e. whether it really is the one “regarding which it is impossible to be mistaken”. However, there appears to be a dilemma here that seems inextricable: we said that this principle is non-hypothetical, and therefore cannot be verified through normal reasoning, otherwise we would fall into a petition of principle that would render our intent null and void. So how can we ‘prove’ a principle that is true regardless? A peculiar type of demonstration that Aristotle himself calls élenchos, or ‘refutation’ (of the negation of the first principle), should help us. The definition of an élenctic Truth is the following: A Truth that is so because even those who want to deny it would be forced to affirm it. In other words, it is not necessary to show that the principle is true, but simply to show how it is not denied, i.e. that its denial is impossible.
Let us therefore take the PONC’s denial: “it is possible to contradict oneself”, or “it is possible that the same thing is and is not at the same time according to the same respect”; let us call the enunciator of this denial the ‘negator’. Now, the negator expresses a proposition, and it is necessary that he intends to mean something that has meaning. Having a meaning means that it must be possible to distinguish what he means and what he does not mean. The PONC performsthis precise function: if it is possible that something has and has not a certain predicate at the same time and under the same respect, then in reference to that predicate this something will be indeterminate – if a vase is white and not white then neither the colour nor the absence of colour can be determined. In the same way, the negation of the principle must be determined as a negation, that is, it must be a negation of the principle and not anaffirmation of it. At this point two important considerations are given: the first is that evidently any attempt to deny the principle, for the simple sake of achieving a negation (even only as a negative intention), must presuppose it; the second is that the PONC is the principle of determination, and precisely for this reason it is the most universal and the best known of all (according to a famous wording it expresses the reality for which “everything is what it is, and not something else”).
From the principle’s point of view, it is clear that any attempt of denial is not simply doomed to failure, but it is quite impossible; this is why even the mere formulation in the thought of the will to deny the principle presupposes it. On the other hand, from the Truth’s point of view it proves to be undeniable because any negation that is formulated is self-denial. This distinction is indeed complex and would require a separate treatment; here it is sufficient to say that this distinction is only abstract.
Note, however, a very important point (which usually generates a misunderstanding that leads to disastrous consequences in a less shrewd scholar): the PONC negator does not fail because his negation is auto contradictory! In fact, if you accuse the denier of contradicting himself, he could with good reason claim victory, since his intention was precisely to prove that it is possible to contradict one’s self, and for this reason PONC can be denied.
Let’s complete the analysis of the elenctic movement with a notation by Emanuele Severino. In the Aristotelian text it is necessary to distinguish two peculiar dimensions: one being the élenchos of the negation of the first principle (i.e. its refutation) and, the second is the essential diorismós of this principle:
In other words, élenchos is an equivalent to the situation in which the negation of ‘x’ implies the affirmation of ‘x’. While, the diorismós is the fact that the same consciousness cannot be convinced concurrently of two statements that are contradictory (in fact Aristotle writes that no one can be convinced that the same identical thing is to and is not to be). Severino notes that the diorismós is far from being a possible foothold for an accusation of psychologism against Aristotelian thought. It is in fact a particular recognition of the PONC itself; in fact, if two contradictory propositions could be attributed to conscience at the same time and under the same respect, this conscience would be a contradictory entity. But since one does not violate the PONC (because its very negation is its own affirmation), one does not even give contradictory consciences.
One last question remains to be answered: what does all this have to do with the ontological path we have followed so far? In order to answer, it is necessary to move on to another Aristotelian work, and precisely to De Interpretatione, a treatise contained in the Organon. Let us quote it again:
Although the treatise is an analysis of propositions and judgments, it is believed that this step can still be a good clarification of Aristotle’s ontological position. As we can see, here ontology and PONC find their conjunction: it is an exposition of the Being according to its undisputability. What should be clear is how the so-called ‘patricide’ operated by Plato against Parmenides reaches its supreme fulfilment here: it is no longer a matter of preaching the being of the Being as absolute Truth, but of preaching the being of the Being when it is and the non-being of the Being when it is not (otherwise one would run into contradiction). It is not necessary, however, that “all that is, is“, and in fact – when what is, is not – then one will simply have to preach about it that is not, and it will be sufficient to respect the supreme principle, namely the PONC.
Basically, Aristotle admits that there are cases in which the Being is not to be (and one will have to announce that it is not) and cases in which the non-Being is (and one will have to preach its being). This is because everything depends on ‘when’: when the Being is, it is necessary that it is; when it is not, it is necessary that it is not. In other words, Aristotle admits the passage from non-Being to Being and from Being to non-Being, and links this movement (which for Parmenides was the madness of two-headed mortals) to the undeniable, indisputable and uncontested principle: that same principle in which neither gods nor men can make vacillate.
 All quotes present in this article from Aristotle’sOn Interpretation are translated by E. M. Edghill.
 Emanuele Severino, Fondamento della contraddizione [The foundament of contradiction], Adelphi, Milano 2005, pp. 63-64.Translation edited by Dylan Lewis.
 All quotes present in this article from Aristotle’s On Interpretation are translated by E. M. Edghill.