Numerous thinkers have considered the Principle of Non-Contradiction, but none has clearly identified its inherent limitation: that it is itself only a formal principle.

This book shows that negation plays a fundamental role both in the constitution of the principle and in the affirmation of its value, which consists in its undeniability.

1 Introduction.- 2 The formal elenchos appearing in the Principle of Non-Contradiction.- 3 The proof of the Protrepticus as an overcoming of formal elenchus.- 4 Some theoretical implications of the argument.- 5 Conclusion.

“We have the thesis, as radical as it is suggestive, of a syntactic-formal reduction of the principle of non-contradiction (Metaphysics IV), which must transcend itself into the principle of demonstration (Protrepticus). Read through the Aristotelian texts, the irreducibility of the principle of intelligibility to its determination will question and challenge both the theoretician and the historian of philosophy.”

—Carlo Scilironi, Professor of Theoretical Philosophy, University of Padua, Italy.

“The work shows that the authentic principle-ground can neither be determined nor obtained as the result of a proof, not even of the elenchus type, as in Aristotle's Metaphysics, but is that by virtue of which any proof is possible, as in Aristotle's Protrepticus, where it is shown that the necessity of philosophising is the ground even of its attempted negation. It will prove an essential reading for specialists in metaphysics.”

—Ricardo Crespo, Professor of Philosophy of Economics, Austral University, Argentina.

Numerous thinkers have considered the Principle of Non-Contradiction, but none has clearly identified its inherent limitation: that it is itself only a formal principle.

This book shows that negation plays a fundamental role both in the constitution of the principle and in the affirmation of its value, which consists in its undeniability. Since it is a formal negation, it is extrinsic to the negated in such a way that it is configured as a negation only insofar as it is applied to something.

On the basis of this analysis, it is shown that it is possible to reverse the usual philosophical perspective: it makes no sense to speak of proof of the principle, but only of proof by virtue of the principle.

This book is essential reading for all scholars and researchers of theoretical philosophy and Aristotle.

Aldo Stella, former Professor of Philosophy at the University of Urbino, is Professor of Psychology at the University of Perugia, Italy.

Giancarlo Ianulardo is Senior Lecturer in Economics at the University of Exeter, UK.

“While philologists and historians – Jaeger at the forefront – have long seen the Protrepticus as the “place” of Aristotelian Platonism, Stella and Ianulardo, by means of a rigorous theoretical radicalisation, now recognise it as the place simpliciter of the principle, as the ground of the very demonstration contained in Book IV of Metaphysics. Thus, we have the thesis, as radical as it is suggestive, of a syntactic-formal reduction of the principle of non-contradiction (Metaphysics IV), which must transcend itself into the principle of demonstration (Protrepticus, fr. 2). Read through the Aristotelian texts, the irreducibility of the principle of intelligibility to its determination will question and challenge both the theoretician and the historian of philosophy.” (Carlo Scilironi, Professor of Hermeneutic Philosophy and Theoretical Philosophy, University of Padua, Italy)

“This research presents an original rethinking of a classical theme in philosophy, namely the theme of ground and its demonstrability. The work shows that the authentic principle-ground can neither be determined nor obtained as the result of a proof, not even of the elenchus type, as in the Book Gamma of Aristotle's Metaphysics, but is that by virtue of which any proof is possible, as in Aristotle's Protrepticus, where it is shown that the necessity of philosophising is the ground even of its attempted negation. It will prove an essential reading for specialists in metaphysics.” (Ricardo Crespo, Professor of Philosophy of Economics, IAE Business School, Austral University, Argentina)

“For reason to be consistent with itself, there must be a first principle. This will be the principle of non-contradiction. But how is this to be understood? The first principle can never be determined by what it is not. According to Stella and Ianulardo, Aristotle’s Protrepticus and its description of rational inquiry prepare the way for the Metaphysics, according to which I cannot deny the validity of the principle of non-contradiction without positing it. This is not a game of reason, but the recognition of an undeniable reality that thought assumes, albeit without content.” (Paul Gilbert S. I., Professor of Metaphysics, Former Dean of the Faculty of Philosophy, Gregorian Pontifical University, Rome)