Gregory S. Moss: Hegel’s Foundation Free Metaphysics

Hegel’s Foundation Free Metaphysics: The Logic of Singularity Book Cover Hegel’s Foundation Free Metaphysics: The Logic of Singularity
Routledge Studies in Nineteenth-Century Philosophy
Gregory S. Moss
Hardback £120.00

Reviewed by: Alessandro De Cesaris (Università degli Studi di Torino)

In the contemporary philosophical landscape, Gregory S. Moss’s book stands out for many different reasons, and even though it should be considered a major contribution to the understanding of Hegel’s logic, its worth cannot be limited to the narrow boundaries of Hegelian scholarship. In this review I would like to illustrate some of the merits of this book, and I will try to show why Hegel’s Foundation Free Metaphysics can be read as an autonomous philosophical work, an exciting occasion to continue and renew the debate on some fundamental philosophical questions.

The Author’s first monograph on Cassirer’s Philosophy of Symbolic Forms addressed the question of the autonomy of language. While dealing with partially different issues – the nature of language and the philosophy of culture – this book already discusses some topics that are the main focus of Moss’s philosophical work, and shows methodological elements that remain unaltered in his second book. Aside from the general interest in the history of German thought, the book already deals with the problem of autonomy and of universality, discussing the relationship between language and logic and introducing the question about interculturality.

More importantly, in Ernst Cassirer and the Autonomy of Language Moss already showed his deeply theoretical approach to the analysis of the authors of the past. His reconstruction of Cassirer’s philosophy of language does not simply aim at offering an accurate sketch of the author’s thought, but rather it is an attempt to show how that theory can still find a place in the contemporary debate.

Following the same methodological inspiration, Hegel’s Foundation Free Metaphysics offers a monumental reconstruction of Hegel’s metaphysics, often underlining some aspects of his thought that have been lost in the most successful trends of the Hegelian research in the English-speaking world. However, it is also a striking attempt to show why Hegel’s metaphysics continues to be relevant. This may be the greatest achievement of Moss’s work: it does not just illustrate Hegel’s own position, but also and foremost shows what it means to have a Hegelian approach to philosophy today.

Despite its remarkable internal coherence, the impressive size of the book – around 500 pages – makes it almost impossible to provide a comprehensive summary of its content. Instead of doing so, I will start by introducing the main focus of the book – the relation between singularity and absoluteness. After that, I will discuss some pivotal elements of Moss’s interpretation of Hegel’s thought. Finally, I will try to point out some issues that remain open at the end of the analysis, in the attempt to show how this book can be understood as the starting point for a productive debate on Hegel, on the contemporary debate, and on the future of philosophy.

1. Philosophy’s Paradoxical Stance Toward Singularity

Since Plato, the relationship between philosophy and singularity has been complicated, even paradoxical. On the one hand, philosophy has been constantly presented as the kind of knowledge that addresses the universal rather than the singular. The tradition offers us a bunch of formulas in order to clarify this taxonomy: while philosophy is knowledge of the universal, art or history address what is singular. While thought only grasps the universal, only intuition has access to individual things.

On the other hand, however, philosophy has always been obsessed with singularity. The greater part of the philosophical effort since Plato and Aristotle is devoted precisely to understand how singular being (ta ekasta) are structured, how they are generated, how we think and say things about them, how they relate to each other. While the singular is banned from the domain of philosophy, nonetheless philosophy’s main task has always been the discovery and the elaboration of the structure of singularity in itself.

But what is singularity? Even this question, along with the distinction between singular and universal, is quite problematic. We are accustomed to identify singularity as the lower limit of thought, namely as what lies beyond any possible specific difference in the great taxonomy of genera and species. Yet, what is singular is also what lies beyond the upper limit of thought, namely what exceeds any possible genus: it is epekeina tes ousias, to use Plato’s formulation. In a sense, “singular” is the opposite of “universal”; in another sense, it is the opposite of “plural”. I know it is a schematic oversimplification, but this could account for the main difference between Aristotle and Plato: according to Plato, ideas are the true “singulars”: there is only one Beauty, it is one, eternal, and determinate, whereas sensible things are always plural, changing, indeterminate and temporal. In this context, what is most universal is at the same time utterly singular. On the contrary, Aristotle’s attempt to “save phenomena” – a formula used by Simplicius – is precisely the attempt to think sensible things as singular, determinate beings. Universals are plural, they are instantiated and thus have specific, but not numeric unity. Only individual things – both sensible and supra-sensible – are singular. For the sake of discussion, this oversimplification could be useful to identify this basic difference between a Platonic and an Aristotelian attitude towards singularity: on the one side, the singular is the absolute; on the other side, the singular is first and foremost finite, individual being.

2. Hegel’s Thought as a New Theory of Singularity

Now, how do we place Hegel’s philosophy in this frame? First of all, it’s worth mentioning that Hegel’s thought has traditionally been accused of having a complete lack of interest in singularity. Hegel is the “philosopher of universality” par excellence. Universality, necessity and subjectivity are the three key notions that structure most traditional interpretations of Hegel’s idealism, in which singularity, contingency and objectivity are therefore accounted for only as partial and lower steps of a more comprehensive dialectical process.

Already right after Hegel’s death, his first commentators criticized his disregard for singularity. According to Ludwig Feuerbach, the distinction between logical and sensible being is the inescapable mark of Hegel’s failure in thinking the individual: «Die Sprache gehört hier gar nicht zur Sache. Die Realität des sinnlichen einzelnen Seins ist uns eine mit unsern Blute besiegelte Wahrheit» (Sämtliche Werke, II, 212). This is Hegel’s major fault, not recognizing that „reality of singular sensible being” that we cannot help but feel as an immediate truth.

The strongest critic of Hegel’s philosophy of singularity, however, is Kierkegaard, who polemically used the term “Einzelheit” in his philosophy precisely to rescue the singular from Hegel’s monistic and universalistic account. Since idealism is “abstract thought”, Kierkegaard’s aim is to highlight the philosophical significance of existence, whereas what exists is precisely that singular being that abstract thought keeps overlooking.

This interpretation of Hegel’s philosophy has survived up to contemporary philosophy. In particular, French thought used the term “singularity” in order to develop an anti-Platonic and anti-Hegelian concept of individuality. Gilles Deleuze is the philosopher who expresses this critique in the most explicit way: «Hegel substitutes the abstract relation of the particular to the concept in general for the true relation of the singular and the universal in the Idea» (Difference and repetition, 10). Quite ironically, while Hegel is one of the first philosophers to use the word “singularity” as a technical term, clearly distinguishing between a commonsensical and a speculative use of the notion, the whole post-structuralist tradition uses the term “singular” as an anti-Hegelian device, tracing it back to Spinoza in contraposition with Hegelian dialectic.

A second element that is useful to point out, in order to understand the novelty of Gregory S. Moss’s approach, is that this criticism of Hegel’s notion of singularity goes along with a critique of Hegel’s systematic and anti-foundational idea of philosophy. Feuerbach and Kierkegaard, but also many other early commentators of Hegel’s system, such as Karl Werder, Kuno Fischer, Schelling, and Friedrich A. Trendelenburg, criticized Hegel’s disregard for the individual and at the same time stated the impossibility to obtain a complex categorical structure starting from the absolute simplicity of being. In other terms, the impossibility to get difference starting from identity.

Now, this close connection between systematic metaphysics and the problem of singularity is at the core of the theoretical analysis of Hegel’s Foundation Free Metaphysics. The so-called Hegel-renaissance in the English-speaking world has already rediscovered the importance of Hegel’s account of individuality. Paul Redding highlighted in the clearest way how the Pittsburgh school – Robert Brandom in particular – has managed to read Hegel’s philosophy as a semantic theory of individuation. However, these interpretations have systematically underplayed the systematic aspect of Hegel’s thought, along with its strictly metaphysical character. Following the oversimplified frame that I’ve proposed before, Robert Brandom’s inferentialism is – in a way – an Aristotelian reading of Hegel’s theory of singularity, since it understands singular beings only as finite, individual objects.

In this context, Gregory Moss’s book offers a timely and original reading of Hegel’s logic, since it finally highlights some aspects of Hegel’s philosophy that have been structurally neglected by many commentators. Three aspects are particularly worth mentioning.

In the first place, the author clarifies that Hegel’s notion of singularity not only refers to individual, finite beings, but also – and foremost – to that peculiar singular being that is the Absolute. In a way, therefore, Hegel’s speculative use of the notion of singularity overcomes the difference between the Platonic and the Aristotelian approach.

Secondly, Moss shows how it is impossible to understand Hegel’s use of the notion of “singularity” without taking into account the necessary relationship between these two dimensions. There is no account of the singularity of finite being without addressing the singularity of the Absolute, and any account of the Absolute that does not illustrate the metaphysical status of singular finite being is incomplete and partial.

Finally, the book puts a very strong accent on necessity to highlight the general aim of Hegel’s philosophical enterprise. It is impossible to understand Hegel’s use of the notion of “singularity” without considering the metaphysical character of his logic. Here it is important to grasp Hegel’s own understanding of what metaphysics is, rather than applying some contemporary use of the term to the Hegelian text, which forces Hegel into a theoretical frame that does not have much to do with his own methodology.

As I will point out later, these three elements also identify three problematic aspects of Moss’s theoretical and interpretative framework, or at least three questions that are still open after reading the book. However, before going deeper into the critical analysis, I will briefly illustrate the main structure of the book.

3. Thinking the Absolute

One of the most striking elements of Moss’s book is that it emphasizes the strict relationship between infinite and finite thought. While tradition generally accepted that we cannot think the Absolute in the same way we think finite being, one of the key contributions of Classic German Philosophy is the idea that if we fail to think the Absolute, even thinking finite being becomes impossible. If I’m not misunderstood, this is what is at stake in what Moss calls the “problem of nihilism”. I won’t go into it in detail, but a general consequence of this approach is precisely Moss’s attempt to show how Hegel’s philosophy is a unification of Plato’s and Aristotle’s approaches: if the Absolute is absolute, and therefore there is nothing outside of it, then it is impossible to differentiate between two faculties or two different methods, as if, for instance, understanding were to be identified with the faculty of finite being, and reason with the faculty of the Absolute. So, by developing a critical discussion of how the Absolute has been thought in the metaphysical tradition, we are at the same time questioning the way we think finite being. This traditional view is what the Author calls the “duality of principles”, the idea that knowledge – and reality – cannot be grounded on one principle, but rather require at least two: intuitions and concepts, matter and form and so on. Against this position, the Author defends a strongly monistic account of Hegel’s metaphysics, according to which the true Singular – the Absolute – self-differentiates in a way that can be compared to the Neoplatonic One.

The thesis of the duality of principles is grounded on another assumption, namely the impossibility of self-reference. If there is only one principle, then identity and difference must stem from the same source, and this source has no external matter on which to operate. According to Moss, the history of Western thought has mostly rejected this idea because of the undisputed adherence to the principle of non-contradiction. If identity generates difference, then the same thing is at once identical and different, namely contradictory.

These three metaphysical assumptions, the principle of non-contradiction, the rejection of self-reference, and the duality of principles, are presented by the Author as the fundamental argumentative structure that undermines at the basis the very possibility to think the Absolute, and that can be found in the history of Western metaphysics from Plato up to Kant.

For this reason, Moss’s analysis starts with a critical assessment of some basic problem of traditional metaphysics. While the author does not have philological or reconstructive interests, his confrontation with some authors of the past is extremely useful in order to grasp his fundamental orientation. For instance, while Plato, Aristotle and Kant are examples of the duality of principles approach, the brief but intense reconstruction of early German idealism aims at showing that Fichte’s and Schelling’s objective was precisely to overcome Kant’s dualism, and to re-introduce a self-referential first principle as the metaphysical and epistemological ground of a new philosophy. At the same time, this approach is strongly connected by Moss to Plotinus and Neoplatonic philosophy, with a long and dense excursus on ancient philosophy that reveals the Author’s tendency to offer a somewhat Neoplatonist interpretation of Hegel’s logic.

After having offered a critical reconstruction of these three metaphysical assumptions, Moss shows how they inevitably lead to five paradoxes that can be found throughout the history of philosophy.

The Problem of Instantiation: if particulars and universals are indebted to different (epistemological/ontological) principles, it’s impossible to clarify their relationship.

The Missing Difference: if conceptuality is not the source of its own differentiation, then the source of this differentiation is non-conceptual. «The essential difference that distinguishes one thing from another cannot be accounted for by appealing to what the thing is ‘in virtue of itself’» (165).

Absolute Empiricism: since the differentiated content of the conceptual dimension is not conceptual, the source of conceptuality is entirely empirical.

The Problem of Onto-Theology: the most universal notion is indicated as both universal and particular.

The Third Man: if the Concept is not self-differentiating, then every instance of the Concept, as a particular concept, cannot be the Universal Concept. Every attempt to find the universal concept leads to new particular concepts.

The largest part of the book’s first section is devoted to the historic and theoretical analysis of these paradoxes. The second section, instead, shows how – by positing the Concept as one self-referential and dialetheic principle – Hegel’s logic manages to overcome them.

Surprisingly, the book does not use the classic difference between understanding and reason as an instrument throughout this analysis. The question of the difference between understanding and reason is of course present, but it is not always clear whether these issues could be addressed as the result of an intellectualistic and non-speculative understanding of the domain of conceptuality. For instance, and here I’m forcing and radicalizing the issue in order to facilitate the discussion, the problem of the missing difference could be analysed as a specific formulation of a more general issue that concerned British and Italian idealism for a long time, namely the insufficient and contradictory nature of the forms of judgment. In fact, since every judgment, as Kant states, is in the form “The singular is universal”, and since the singular is not universal, an intellectualistic approach to the nature of conceptuality already finds itself entangled in a contradiction.

However, rather than appealing to this methodological instrument, the Author prefers addressing these problems systematically, retracing their origin in the three metaphysical assumptions listed above. This choice gives a very strong conceptual unity to the book, even though it could lead to some forced passages, in particular when it comes to analysing these issues through examples taken from the history of philosophy.

For instance, the first two paradoxes – the problem of instantiation and the missing difference –  are addressed by quoting many passages from Plato’s Parmenides and the Book B of Aristotle’s Metaphysics. Now, while these passages are in fact very good examples of the problems the Author is discussing, both the Parmenides and Metaphysics Beta are, so to say, “partes destruentes”, critical preliminary moments of a new theory. In other words, it is possible to find already in Aristotle’s and Plato’s work – as Hegel himself recognizes in his Lectures on the History of Philosophy – speculative solutions to the problems they raise in some of their texts.

The difference between intellectualistic and speculative thought seems to be a very good way to account for this internal evolution in Plato’s and Aristotle’s thought.  For instance, Plato’s generative account of the koinonia ton genon in the Sophist does not look to be still subject to these paradoxes. In it, for instance, the self-referential character of ideas is no longer problematic, but at the same time it is not trivialized through the reference to empirical concepts as it happens in the Parmenides. Another example is Aristotle’s philosophy: following Ferrarin, Moss concedes that Aristotle’s metaphysics is speculative and belongs to the domain of the concept. But then, how can we integrate this idea with the paradoxes of Aristotle’s account of conceptuality? Isn’t this account, as it is presented in the book, utterly intellectual rather than speculative?

In other words, while the author manages to provide a strikingly coherent and dense systematic account of some fundamental metaphysical issues, a more extensive analysis of Plato’s and Aristotle’s own solutions to these problems, along with a comparison with Hegel’s own interpretation of their works, could give the chance to highlight how there is more than one way to think speculatively. The author does discuss Aristotle’s solutions to some of the problems he listed in Metaphysics Beta, but the historical reconstruction of Aristotle’s approach is not the main focus of Moss’s research, and it is only mentioned in order to highlight some aspect of Aristotle’s thought that the author recognizes in Hegel’s work.

However, given the book’s size, focusing on the systematic aspect of the issue has been a wise choice: this remark only aims at pointing out, once again, that this monumental book must not be interpreted as the end of a research, but rather as an exciting proposition for a new approach to the study of Hegel’s logic, of the history of philosophy and of metaphysics in general.

Four Open Problems

With this spirit in mind, I would like to point out some specific issues that I find of particular importance in Moss’s book. Of course, as already mentioned, this is a monumental piece of scholarship, and there are many topics worth discussing. There are many arguments and analyses that deserve a much deeper discussion than I can provide here. Nevertheless, I will try to avoid discussing specific matters or individual passages of the book, since I would like to keep the debate on a more general and fundamental level, and discuss some structural aspects of Moss’s proposal rather than specific topics. In particular, I will try to propose a brief critical assessment of four questions that remain open.

4a. What Kind of Metaphysics?

In the final part of his critical analysis, the Author thoroughly discusses different metaphysical and non-metaphysical accounts of Hegel’s logic. In particular, he also highlights Hegel’s intention to reform metaphysics beyond any dogmatic understanding of it. The interpretation of Hegel’s own understanding of metaphysics is deeply connected with the relationship between logic, nature and spirit. While Moss does not expressly analyse this aspect of Hegel’s system, the passage from logic to nature is a crucial point of his reading.

As we know, one of the main arguments of the book is that Hegel’s logic introduces a self-referential and self-differentiating account of the Concept. As Roberto Morani has shown in his monumental book on the evolution of Hegel’s dialectics, this aspect of Hegel’s philosophy is also the main focus of the auto-reformation of his own logic in the Second Edition of the Doctrine of being, when he stresses that objective logic already is subjective logic in disguise. This issue is closely related to the question of the “formal” character of logic. According to Hegel, logic is not formal because it has logical forms as its own content: logical forms are at the same time form and content of the logical process, that in this way is truly noesis noeseos:

But logical reason is itself the substantial or real factor which, within itself, holds together all the abstract determinations and constitutes their proper, absolutely concrete, unity. There is no need, therefore, to look far and wide for what is usually called a matter; it is not the fault of the subject matter of logic if the latter seems empty but only of the manner in which this subject matter is grasped. (SL, trans. Di Giovanni, 28)

Elena Ficara has stressed the importance of this passage, which shows Hegel’s opposition to any formalistic understanding of logic as a discipline. However, Moss radicalizes this aspect and points out how this unity of form and matter generates a self-determining progression. But what is the limit of this activity?

The logic is a self-generating process, through which the concept determines itself as concept: while we discover a great variety of conceptual determinations, these determinations never become empirical. In other terms, the logical development of the category of quality never generates the concept of “colour” or of “green”. In other words, what does never happen is what Fichte talks about in his lectures on the Tatsachen des Bewusstseins: if we radicalize this monistic self-generating activity, then everything must be deduced starting from the first principle, even this singular blade of grass. It is the same conception of systematic metaphysics that Wilhelm Traugott Krug presents as a critic to Idealism, and that Hegel ridicules. For instance, when Hegel talks of the ontological proof, the point is that the Concept has logical objectivity. Nevertheless, Moss is right to highlight how important it is to understand the Concept as a creative activity, and by doing so he defends a strong metaphysical interpretation of Hegel’s logic that many passages in Hegel’s work seem to confirm. While the author recognizes that the creative activity of the Concept does not entail the deterministic deduction of all empirical content, establishing the precise nature and the limits of this self-particularizing activity is one of the tasks that remain open after having read his analysis, and it is a crucial element to test the hermeneutical validity of his interpretation.

4b. What Kind of Singularity?

I would like to go back to the notion of singularity, which is the main focus of the book as a whole. In Moss’s book it is clearly stated that each category of the logic cannot be used exclusively to think the Absolute, since the Absolute is not separated from finite being. Therefore, singularity does describe both “limits” of thought—the Absolute and finite being. Nevertheless, Moss’s reconstruction strongly privileges the “Platonic” side of the analysis. In other words, the Author seems to be much more interested in showing how singularity expresses the logical structure of the Absolute, rather than explaining how the same notion can be used to describe the nature of finite being. For instance, Hegel writes that singularity is the principle of every “individuality and personality” (SL, 547). In order to complete the analysis of Hegel’s use of the notion of singularity, it would be very interesting to integrate Moss’s interpretation with a focus on this dimension.

This does not mean, of course, that Moss’s reading is a Platonic one. As I’ve already highlighted, if it is true that Platonism and Neo-Platonism play a pivotal role in the development of his reading of Hegel, Moss aims at showing both the Platonic and Aristotelian aspects of Hegelian dialectics, in particular by emphasising the importance of Aristotle’s notion of the «self-particularizing universal». This interpretation of Aristotle’s notion of Form is also quite interesting, and it would be worth discussing it in a further analysis of Hegel’s own historical sources.

4c. Syllogism

One of the most surprising aspects of Moss’s book is his analysis of syllogism. Usually judgment and syllogism are analysed as logical developments of the abstract concept, and Hegel also expressly indicates them as such in the Science of Logic. Nevertheless, the Author seems to understand judgment and syllogism as a logically impoverished form of the first section, identifying them with a «self-alienated» form of the Concept (374). While this strong accent on the Concept is quite original, it is very hard to explain Hegel’s own statement at the beginning of the section on the syllogism, where he writes that «the syllogism is the completely posited concept; it is, therefore, the rational» (SL, 588). More generally, Hegel repeatedly highlights the syllogistic character of his system: the end of the Encyclopaedia is maybe the strongest example.

This issue leads to another question on the relationship between syllogism and inference. Moss’s critique of Robert Brandom’s account of Hegel’s philosophy as a form of inferentialism is very convincing, and does show the partiality of neo-pragmatist, non-metaphysical readings of Hegel. Nevertheless, by criticizing Brandom, the Author seems to share with him one core assumption, namely that syllogism is inference, and that when Hegel speaks about syllogism, he’s always talking about a formal structure of reasoning. This identification could be the main reason for Moss’s scepticism against the importance of syllogism in Hegel’s thought. For instance, in the Science of Logic Hegel expressly writes that «All things are a syllogism, a universal united through particularity with singularity; surely not a whole made up of three propositions» (SL, 593). Of course, Hegel does heavily criticize the form of inference (even in his Lectures on history of philosophy), but this passage seems to show that we must distinguish the subjective form of inference from the logical, objective form of syllogistic unity. For this reason, while Moss’s interpretation of the relationship between the concept and syllogistic forms is quite original and in some cases very convincing, it does need further discussion.

4d. Contradiction

Finally, I would like to briefly discuss the question of contradiction. One of the structural aspects of the book is to show that, in order to think the Absolute, we must accept dialetheism, namely the position according to which some contradictions are true. In the case of Hegelian thought, this question is closely connected with the meaning of the term “speculative” as Hegel uses it throughout his work. While it is hardly debatable that only speculative thought is able to grasp the Absolute in its concrete and actual form, the question is whether such a way of thinking necessarily entails a violation of the principle of non-contradiction (PNC) in its Aristotelian formulation.

A good start for illustrating the issue is a passage quoted by the Author while analysing the relationship between speculative thought and contradiction:

Speculative thought consists solely in holding on to the contradiction, and thus to itself. Unlike representational thought, it does not let itself be dominated by the contradiction, it does not allow the latter to dissolve its determinations into other ones or into nothing/ (SL, 383)

Right after this passage Hegel does give some examples, and his choice are determinations of relation – above/under, father/son – that can hardly be seen as violation of Aristotle’s PNC. The interpretation of this passage is very contentious and I won’t go into it. Instead, I would like to argue that there are two possible interpretations of the nature of speculative thought. According to the first, speculative thought is necessarily dialetheic, since it requires to accept that the same x is and is not P. Here it is important to clarify that “not being P” is not the same than “being non-P”.

According to the second interpretation, speculative thought generates a new understanding of the predicates and of their reciprocal relationship. In this case, x can be P and non-P, according to a meaning of non-P that does not entail not being P.

For instance: the proposition “the particular is universal” is contradictory only as long as we assume that “being universal” entails “not-being particular”. This implication is different from the simple fact that universal and particular are different concepts, namely that “universal” is not “particular”. I do believe that it is possible to make the case that, in his subjective Logic, Hegel shows how universality, particularity and singularity, as conceptual determinations, are not reciprocally exclusive.

Moss does provide an exhaustive analysis of many different interpretations of Hegel’s account of contradiction. Again, his criticism of Robert Brandom’s strong coherentist reading is very compelling. Nevertheless, while it is clear that, according to Hegel, speculative thought somehow “deals” with contradictions, this statement must be compatible with other two explicit Hegelian theses: that contradiction is a defining aspect of finite being and finite concepts, and that contradiction itself is used throughout the system as a criterion to identify the finite and false character of the categories.

This could mean, in a way, that the Absolute cannot be contradictory in the same way finite concepts and beings are. Moss’s analysis of the difference between explosive and non-explosive contradictions could be a way to express this fundamental difference. However, it seems clear that Hegel’s foundation free metaphysics is an exciting contribution to a debate that is still open and is impossible to close simply by choosing one option over the other, be it coherence or contradiction.

5. Conclusion

At the end of this brief critical assessment of some aspects of the book, there would be much more worth mentioning. Gregory S. Moss’s book offers a compelling reconstruction of Hegelian metaphysics as a form of strong monism and shows how it can be profitably used to discuss some contemporary philosophical positions. Moss is also the translator of the English edition of Markus Gabriel’s Why The World Does Not Exist, and Gabriel’s pluralistic metaphysics is one of the main critical references throughout the book. By using Hegel’s philosophy to debate with Alain Badiou, Quentin Meillassoux, Graham Priest, Robert Brandom and others, Moss brilliantly shows how the study of Classic German Philosophy can still offer a valid contribution to the contemporary debate on metaphysics.

Another aspect that resonates throughout the book is Moss’s interest for intercultural philosophy, as well as for the mystic tradition. There is no doubt that this book is a vital and promising contribution to the contemporary debate on Hegelian philosophy. However, it is also much more than that, since it provides a very compelling theoretical framework for the discussion of many different questions in contemporary continental metaphysics. Finally, it also offers a profitable exchange between philosophy, theology, and the study of other cultures.

Despite its remarkable size, Hegel’s Foundation Free Metaphysics does offer an extremely coherent and well-argued account of some of the most important theoretical issues in the history of metaphysics. By doing so, it succeeds at showing the ground-breaking nature of Hegel’s approach to logic and provides a very original interpretation of the Doctrine of the Concept. It is an ambitious example of Hegelian scholarship, but it is also a very good example of a truly Hegelian approach to philosophy today.

Luca M. Possati: L’ inconsistenza del numero. Ipotesi sulla natura della computabilità

L' inconsistenza del numero. Ipotesi sulla natura della computabilità Book Cover L' inconsistenza del numero. Ipotesi sulla natura della computabilità
I centotalleri
Luca M. Possati
Il Prato
Paperback € 15,00

Reviewed by: Sergio Genovesi (Rheinische Friedrich-Wilhelms-Universität Bonn, Germany)

Nel saggio L’inconsistenza del numero, pubblicato di recente dalla casa editrice “Il Prato”, Luca Possati si propone di elaborare una fenomenologia della computabilità basandosi sull’assunto che l’operazione logica dell’identità è interpretabile. Mettendo in discussione il principio di identità degli indiscernibili e introducendo la logica paraconsistente nel discorso sulla computazione, Possati prende di mira l’idea che la base di ogni calcolo e ragionamento risieda in un’operazione di uguaglianza basilare e univoca e apre la strada a una vera e propria ermeneutica del concetto di identità.

Il lavoro si presenta come un’elaborazione originale e per certi aspetti eterodossa di alcune tematiche controverse molto discusse nel dibattito filosofico attuale sia in ambito analitico che continentale. Da un lato è possibile notare una ripresa delle idee derridiane di différance, traccia e archiscrittura, così come un riferimento alla struttura originaria di differenza e ripetizione descritta da Deleuze e in generale al paradosso dell’iterazione infinita che riecheggia negli scritti di molti autori francesi contemporanei. Questo percorso tematico è stato in passato già ampiamente sviluppato dall’Autore nel saggio La ripetizione creatrice, dove viene trattato il tema dell’analogia in Derrida, Ricoeur e Melandri. Dall’altro lato Possati si distacca dalla tradizione francese e si serve – assieme ad altre fonti provenienti dal pensiero analitico e dalla filosofia della matematica – degli studi di Graham Priest e Francesco Berto sul dialetheism e la logica paraconsistente al fine di costruire un diverso fondamento teorico per la sua trattazione della contraddizione e del paradosso, riuscendo ad apportare nuovo materiale alla critica dell’identità classica intesa come fondamento del pensiero. Il risultato di questa operazione è una trattazione accurata che riesce a trasporre molte delle intuizioni fondamentali che hanno animato la decostruzione della metafisica sostanzialista nel corso del XX secolo sul piano di una fenomenologia del numero e della computazione, congedandosi da un certo lessico e da determinati topoi filosofici tipici del pensiero poststrutturalista francese e dando una diversa consistenza logica alle idee che lo hanno ispirato.

Ripercorriamo adesso nello specifico le principali tappe di questo lavoro. Come indicato dall’Autore stesso, il libro si divide in tre parti: anzitutto viene formulato un approccio ermeneutico alla questione dell’identità; in seguito è fornita una definizione dell’iterazione come trasgressione del principio di identità degli indiscernibili; infine si individua la radice logica del numero e della computazione nell’iterazione (15). Come accennato in prima battuta, Possati mette in questione il principio di identità degli indiscernibili e il suo converso, quello di indiscernibilità degli identici, assieme all’idea generale che l’identità qualitativa sia condizione necessaria e sufficiente per l’identità. Egli riprende l’esempio dell’esperimento mentale di Max Black, nel quale viene mostrato che non vi è nulla di contraddittorio nella discernibilità degli identici: se prendiamo due sfere di metallo identiche in tutto e per tutto, è comunque possibile distinguerle sulla base di coordinate spaziali (8-9). Possati evidenzia che in generale è sempre possibile individuare due oggetti diversi ma qualitativamente uguali – che siano concreti, astratti, reali o finzionali, e che si sovrappongano o meno. Infatti, qualora l’attribuzione di coordinate matematiche non basti a distinguere gli oggetti, il nostro semplice atto di discriminare due items, per esempio chiamando uno di essi x e l’altro y, basta affinché essi non siano esattamente la stessa cosa: l’auto-identità non è condivisa tra oggetti identici (8). Quando asseriamo l’identità di due oggetti, l’operazione che stiamo conducendo può dunque avere significati diversi a seconda del concetto di identità al quale ci stiamo riferendo: potrebbe trattarsi dell’identità di proprietà, di un’identità quantitativa, o ancora di un’identità personale o di genere, etc. Possati mette in luce due sensi principali di identità, la cui confusione porta al paradosso di non riuscire a distinguere due sfere identiche situate in due luoghi diversi: l’identità qualitativa e l’identità numerica. Nella prima «si presuppone un gruppo di qualità per poi, a partire da esse, identificare l’oggetto che le soddisfa. Si va dalle qualità all’oggetto» (23). La seconda «risponde invece al criterio dell’unità o coincidenza. In questa grammatica, “essere identico” vuol dire coincidere con un locus (fisico o teorico) determinato da un frame di coordinate più o meno fisse» (24). Questi due tipi di identità sono inversi ma complementari: senza l’identità numerica non avremmo mai dei singoli e il nostro linguaggio sarebbe puramente aggettivale, senza l’identità qualitativa avremmo solo singoli e classi senza proprietà (28-9). Come sarà chiaro tra breve, le x che questi diversi tipi di identità discriminano sono degli items differenti e proprio per questo si rende necessaria un’ermeneutica del concetto di identità: l’identità qualitativa sembra rimandare a delle x astratte, a esponenti generici e non ben individuati di classi di proprietà; l’identità numerica sembra invece determinare dei singoli non interscambiabili e non confondibili in alcun caso con altre x (che dovrebbero piuttosto essere chiamate y o z).

Possati definisce l’iterazione come «la discrepanza tra le due grammatiche, identità qualitativa e identità numerica» (39). Essa è una struttura logica che ha una natura paraconsistente e dialethetica, vale a dire che ammette la contraddizione e postula l’esistenza di alcune proposizioni vere ma paradossali, dalla forma contraddittoria “A e non A” (47). Questo tipo di contraddizione è proprio ciò che otteniamo se combiniamo i due tipi di identità di cui abbiamo appena parlato, per cui due items x e y possono essere identici qualitativamente, ma non numericamente. Se itero l’item x otterrò un numero grande a piacimento di altri items che hanno allo stesso tempo la proprietà di essere e non essere identici a x. La tesi dell’Autore è che l’iterazione sia la radice logica di ogni possibile concetto matematico: alla base della computazione e del numero ci sarebbero un principio di iterazione e un principio di contraddizione continua secondo i quali a ogni iterazione la contraddizione non distrugge il sistema – come farebbe in una logica tradizionale – ma anzi lo preserva moltiplicando gli item. L’item infatti ha due facce: «è molteplice (x≠x) perché si sviluppa in una serie, differendo sul piano dell’identità numerica; è singolo (x=x) perché la moltiplicazione non aggiunge nulla alla sua identità qualitativa» (53). Il ruolo della contraddizione diventa in questo modo costruttivo e imprescindibile al fine dello sviluppo del sistema e il numero, oggetto iterabile per eccellenza, rappresenta l’emblema di questo principio che sembra governare tutto il dominio della concettualità e dell’astrazione.

Come atto finale del suo lavoro Possati procede dunque nel ripercorrere il processo di costruzione iterativa del numero, scegliendo di seguire la definizione di numero naturale come classe di insiemi aventi uguale cardinalità finita e costruendo i numeri interi e razionali su questa base. Il punto di partenza di questo meccanismo sarà quindi la costruzione dello zero come cardinalità dell’insieme vuoto e l’iterazione dell’insieme vuoto per produrre insiemi di insiemi vuoti con cardinalità corrispondente ai numeri successivi. Per ottenere un numero specifico basterà limitare il processo di iterazione fino al raggiungimento della cardinalità desiderata. Iterazione, contraddizione continua e limite si rivelano così essere «i tre passi che compongono la procedura logica alla radice di ogni possibile numero» (63). In maniera analoga Possati procede alla definizione di somma e prodotto sulla base dell’iterazione (68 sg.). La computazione può dunque definirsi come «la riduzione di un numero alla sua base iterativa» (72): i numeri sono infatti calcolabili fintanto che conservano la loro base iterativa (78) e in generale – potremmo aggiungere – è possibile operare concettualmente con un oggetto fintanto che la sua iterazione è possibile. Questa iterazione può essere concreta, come nel caso della ripetizione di segni su un foglio di carta per scrivere, o astratta, come nel caso dei concetti che pensiamo. Una delle osservazioni conclusive di Possati riguarda proprio questo ultimo punto. L’Autore, seguendo in parte una tesi formulata da Gualtiero Piccinini, sostiene che «all’apparato formale della computazione corrisponda sempre un sistema fisico computazionale che è un’immagine del primo» (81). Una delle osservazioni più interessanti che è possibile fare a proposito dei sistemi computazionali fisici – organici o inorganici – è che la loro esistenza non presuppone una semantica (86). In altri termini, l’emergenza del significato è posteriore all’attuazione dell’iterazione, come già i filosofi poststrutturalisti avevano cercato di mostrare tramite altre vie teoriche, analizzando per esempio il fenomeno della scrittura. Proprio la scrittura, intesa a sua volta come sistema computazionale, rappresenta l’unico modo che un segno ha di parlare di se stesso: iterandosi. Possati chiama principio dell’identità simbolica questa controparte fisica del principio d’iterazione (92).

All’inizio del volume l’Autore ci avverte che lo studio che stiamo leggendo non aspira a essere esaustivo, ma si propone piuttosto di aprire nuove prospettive. Prima di concludere vorrei dunque menzionare due punti critici presenti nel lavoro che meriterebbero un maggiore approfondimento. Non si tratta di passaggi che rischiano di inficiare la validità della trattazione, quanto piuttosto di problematiche che sarebbe bene indagare ulteriormente per orientare gli sviluppi futuri della ricerca. Una prima istanza riguarda la contraddizione nel caso dell’auto-identità. Nel corso dell’opera Possati illustra chiaramente come l’identità qualitativa tra due items sia sempre accompagnata dalla loro non-identità numerica. Tuttavia non è esattamente evidente come l’identità numerica possa a sua volta essere pensata assieme alla non-identità qualitativa. Poniamo un item x considerato in un determinato punto spaziale e istante temporale (o al di fuori di un contesto spaziotemporale o dimensionale in generale): se esso è numericamente identico a se stesso, non dovrebbe esserlo anche qualitativamente? E se per assurdo non fosse identico a se stesso qualitativamente, si tratterebbe sempre dello stesso item singolare? Non si avrebbe forse anche una disuguaglianza numerica? Nella prima parte del saggio Possati adduce alcuni esempi di oggetti numericamente identici che hanno proprietà contraddittorie: in uno spazio curvo, per esempio, un oggetto può essere distante da se stesso. Queste proprietà contraddittorie vengono però mantenute nella relazione di auto-identità e non mettono in questione l’auto-identità qualitativa di un oggetto. In altre parole, se la natura relazionale condivisa da tutti oggetti e l’identità pensata come rete concettuale o cluster (21 sg.) possono evidenziare dei meccanismi di contraddittorietà nel rapporto degli item con se stessi o con altri items, non si capisce se anche l’auto-identità numerica – considerata nel caso puramente astratto dell’assenza di altri fattori di interferenza – possa e sopratutto debba da sola comportare una non auto-identità qualitativa e quindi un’auto-contraddittorietà originaria di un qualsiasi item.

Un secondo punto critico riguarda la costruzione dei numeri sulla base del principio di iterazione e di contraddizione continua: se questo processo risulta ben evidente nel caso dei numeri naturali, interi e razionali, non è chiaro come vada applicato alla costruzione dei numeri reali e complessi. Questi numeri infatti non sono costruibili tramite la cardinalità degli insiemi, né tramite rapporti di altri numeri tra di loro. Come l’Autore stesso ribadisce, è un dato di fatto che questi ultimi tipi di numeri siano computabili (65). Per salvare la validità della teoria avanzata in questo saggio, pena la sua falsificazione, occorre dunque mostrare come i principi di iterazione e contraddizione continua possono essere applicati alla costruzione dei numeri reali e complessi. L’operazione non sembra impossibile: se si sceglie di costruire i numeri reali attraverso le sezioni di Dedekind, è sufficiente osservare che ogni sezione viene individuata da due numeri razionali (a loro volta costruibili tramite i nostri principi); per quanto riguarda i numeri complessi il procedimento va applicato alla costruzione dell’unità immaginaria e alla sua addizione alla parte reale del numero. Questo breve esercizio, assieme alla definizione di «tutte le principali operazioni aritmetiche» tramite l’iterazione (68) – la cui possibilità viene garantita dall’Autore –, dovrebbe essere svolto una volta per tutte nel corso dei futuri sviluppi delle idee avanzate nel saggio.

L’inconsistenza del numero ha sicuramente il merito di trattare il tema ostico delle contraddizioni e dei paradossi che stanno alla base del nostro pensiero attraverso un linguaggio chiaro e uno stile brillante. Senza alcun desiderio di addomesticare la contraddizione o di ingigantirla e mitizzarla, Possati si pone di fronte a essa con un approccio laico e neutrale, evidenziando con grande onestà intellettuale la portata costruttiva dell’incapacità della ragione di pensare univocamente l’identità e dell’indecidibilità fondamentale di questo primo atto del ragionamento logico. Tutto ciò senza voler inneggiare a uno scacco del pensiero: l’apertura verso un’ermeneutica del concetto di identità non intende di certo porsi come una debilitazione della ragione, né si presenta come un manifesto della sua inanità. Al contrario, nel destituire il principio di identità l’Autore pone il principio di iterazione come autentico fondamento della razionalità, un fondo iterativo che sorge proprio dalla crisi dell’identità classica e che si presenta come l’esatto contrario del dogma di un principio assoluto.


Francesco Berto, Teorie dell’assurdo, Roma, Carrocci, 2006.

Max Black, “The Identity of Indiscernibles”, Mind, vol. 61, n. 242, 1952.

Gualtero Piccinini, Physical Computation. A Mechanistic Account, Oxford, Oxford University Press, 2015.

Luca Possati, La ripetizione creatrice. Melandri, Derrida e lo spazio dell’analogia, Milano, Mimesis, 2013.

Idem, L’inconsistenza del numero, Saonara, Il prato, 2017.