There seems to be no concept more obvious and trivial than that of identity: “glasses are glasses”, “thunder is thunder”, even the tedium of reading what follows is without doubt unfailingly identical to itself. After all, the principle of identity marks the determinateness of every thing, whatever it may be. If things, if each entity, were not identical to themselves, reality could not even be regarded as a primordial, undifferentiated broth: we would still be designating it as a certain determinate “broth”, not the one I now and then sip alongside my good lady. The obviousness and uselessness of the principle of identity is acknowledged even by some philosophers, Ludwig Wittgenstein in the first phase of his thought, for instance (the preoccupation returns later), who would like to banish it from intelligible expressions: after all, to say that one thing is identical to itself says nothing, while to say that two things are identical is a glaring nonsense. Other authors, by contrast, have racked their brains over the busillis, deeming it fundamental (our own Emanuele Severino). However the matter stands, I shall not enter into the historical merits of the various theories on the subject, the principle of identity too, like many things dear to philosophers, oscillates between dilemmas verging on imbecility and cornerstones of thought. In what follows I should like, first, to muse a little on some of the ways in which the question of the meaning of the identity sign appears serious, and then to conclude with a possible aspect of the principle that is not only genuinely serious but, at least for me, mysterious.

Let us start, for example, from the well-known formula E = mc2. The expression, at least in its popular version, is usually read as though, from relativistic physics onward, the two quantities can no longer be “distinguished”: energy and mass (multiplied in the usual way, and so on).

Now, starting from the famous equation, the problem one might pose is this: what meaning does that sign actually have? Does it possess a single, specific meaning, or can it be read in many senses? Despite its apparent simplicity, it can in fact be interpreted in various ways. I shall list some of them, with no claim to completeness, in order then to arrive at the one that interests me most and that, whether one realises it or not, ultimately interests everyone, in the literal sense, precisely, that we all are (esse) in the midst (inter) of it.

1) If I state “Luigi is (=) Stefania’s husband,” identity here signifies coreferentiality: “Luigi” and “Stefania’s husband” refer precisely to the same person, the undersigned. This clearly cannot be the meaning of the famous equation, because there is no single event, thing, and so on, to which the two (Energy, etc.) refer.

2) I may then read the sign as ontological identity, as a sort of necessary property of every thing. But quite apart from whether or not there exists a relation of identity in itself (you are identical to yourself), a properly real relation, existing to all intents and purposes, which I doubt is there, how can two different names indicate one and the same thing without returning to point 1)? Were it to exist, this alleged ontological identity would in fact be expressed by A = A.

3) Identity is then used in a diachronic context when I state that Luigi at t¹ is the same Luigi at t², that I am the same at different times. Here the matter is more complex, and I shall return to it at the end; but the two basic theoretical positions on the question, the first called criterial, the second non-criterial, hold: the former, that Claudio is identical at different times, and we are back to the relation of the previous point; the latter, that Claudio is the same F (the same person, biological organism, or whatever the criterion permitting re-identification may be) at the two times. And obviously this cannot be the sense of identity in E = mc2, because either we return to the previous point, or Energy, etc. would be the same substance or characteristic at different times. But there is no third thing, no genus of which the two are the same instance.

4) One may then think that the sign is one of “reduction”. Granted that M = E (where M stands for the mental and E for the physical), if I read the identity from left to right I am a materialist; if I read it from right to left, asserting that a physical event is identical to a mental event, I am an idealist. The sign, if it is not to be used dogmatically, without reasons, requires that in such a case I bring arguments to show how a mental event is in fact a physical event, the only one that exists. Or vice versa! But obviously this cannot be the sense of E = mc2 either, because the expression is not reductionist; indeed I can read it, indifferently, from left to right and from right to left. Bear in mind that some (philosophers) do read it in that sense, even though it does not seem to me to make sense at all.

5) Clearly the expression cannot be a “tautology”. A tautology is a non-atomic formula true in every case, of the type p V ̴ p = not (p and ̴ p), and so on. The expression, by contrast, is made up of constants.

6) Just to mention a possible confusion: the sign “=” does not have, in the physical equation, the sense of “equal” that it possesses, for example, in the expression “Franco and Giovanni (identical twins) really are identical!”. The sign, in this latter case, indicates a three-term relation (and not a reflexive relation) such that “Franco and Giovanni are equal in F” (for example, in somatic features, height, and so on) and therefore necessarily different in something else (they occupy different spaces, and so on). It is not for nothing that in politics, if one leans towards equality in one respect, one leans towards difference in another: if I distribute the total product of a community to everyone in equal parts, to each individual, the diversity of working capacity is not taken into account, and the different, individual abilities to produce are not enjoyed by those who possess them. Giorgio is more intelligent, stronger and generally more capable than I am, but part of his product is distributed among all.

7) We thus come to an important point which, however strange it may seem, sometimes causes confusion. 3 + 2 = 5. Here it is not the case that two numbers, plus the addition sign, are identical to another (that makes no sense). The equation must be read as such. That is to say, 5 is the result of the operation (rule) of addition 3 + 2. Well then, since the identity sign in the natural sciences seems, formally, able to be understood only as an equation, hence as the result of an operation, what it says is that every time I use E, I can replace it with mc2, and vice versa, salva veritate, just as I can replace 3 + 2 with 5 without altering the truth of an equation. But this would mean, a point, as usual, merely formal, given by the meaning of =, not only that the two are not the same quantity, just as 3 + 2 is not the same number as 5, but also, and this is the point I do not understand in the popular version, that they are not at all “indistinguishable”: if I did not distinguish them, and, I would add, if I did not form a concept of them through distinct experiences, I could not even substitute one for the other salva veritate. How does a physicist usually read it? Respecting the indications concerning the given concept of identity, the only way would be analogous to the last, that of the operation. Perhaps I am still musing away, but the point is important for reflecting on the concept of a rule, and for those who believe that numerical entities exist platonically, independently of the minds that think them (mathematical Platonism). That numbers may exist in themselves is, for many, a digestible idea; but that the rule of addition should also exist in itself is much less so. How can a rule exist in itself, independently of being applied? A glorious mystery.

8) Let us now return to a possible reading of point 6), the question that is, for me, mysterious. I am more than convinced that I am, in some sense, the same Luigi from the time I was born to the one now writing. Some philosophers, Hume, for instance, or in our own day Derek Parfit, hold that what I call the permanent subject, little Luigi who is now Luigi, is in reality a plurality of distinct entities, which nonetheless have a series of properties in common. The aforementioned Parfit also thought that awareness of this truth might even be liberating: why on earth should I worry about catching Covid tomorrow and falling to pieces, since the one who falls to pieces is not I! Now, quite apart from the fact that, in Parfitian fashion, I fall to pieces continually anyway, the fact that the “tagliatelli”, as they call them in Perugia, which I am to enjoy this evening, should be eaten by someone else hardly seems a prospect to relish. More seriously, Parfit fails to take account of two facts: a) as a thinking subject I do not have only true or false beliefs about the world, but also intentions. If I intend to eat tagliatelle this evening, I want, causally, to bring it about that an event conforms precisely to my intentional content; I want the world afterwards to conform to what I intend now. Remove the permanent, and intentions vanish! b) if I say, if I utter, the words “today is a fine day” and, nanosecond (one billionth of a second) by nanosecond, losing and gaining atoms, I am not the same, the trivial sentence uttered would make no sense, nor would the words of Parfit’s own texts. “Today”, “is”, “a”, and so on, isolated, independent words, would in fact, in isolation, be linguistic entities devoid of meaning; they express meaning only within the sentence, and the sentence presupposes that, over time, the subject who says or thinks it is the same; c) and then, in what sense, at least at each instant, is the subject a unity? This Parfit takes for granted. If I am not, in some sense, diachronically identical, I am not something determinate, a selfsame thing, even synchronically. Perhaps the idea that the human being is necessarily made of time is not excessively far-fetched.

And yet, and yet, this meagre indication of the necessity of my permanence, of my synchronic and diachronic identity, is very little indeed. Was I not, then, the same when I was a “tiny little thing”, not yet able to think or speak? But above all, the problem is to understand what is identical in me as the days go by. Despite the example just given, in each of us everything changes: biology, thoughts, hopes and emotions. Ever since the philosopher John Locke, the problem has plagued whole ranks of authors, and in the theories of the postwar period it became a constant theme.

I shall not summarise the various conceptions and the attempts to rescue “my dear self”. The fact is that I find none of them truly convincing. Consider: if there is something simple that persists in me throughout my becoming, and that precisely permits the use of the personal pronoun and adjective, then, even if we grant it, it is not clear how it holds together all the rest of the continuous, uninterrupted self-making of my bodily and mental aspects. If, on the other hand, I think that what persists is a complex, the “bodily system” in the broad sense, I shall still have to find an element that persists and, in persisting, holds the system together. In this way, however, we return to the requirement of the simple.

In the ninth and seventh centuries B.C. in the Homeric period (the point comes to me from Donato Lo Scalzo, whom I thank), it seems that the forebears of Western culture used the word “Psyché” to denote the condensed vapour that leaves the mouth in cold weather. Such an archaic attempt to solve the enigma of unity might raise a smile today; in truth it is at least as intelligible as the modern and contemporary attempts to track down the ineffable thing that constitutes the self. “Soma”, moreover, did not then mean “body”, that meaning would begin with Plato, but “corpse”. As if to say: of an individual one denoted the arms, the legs, the head, the parts of what we regard as the body. One did not venture to indicate the “selfsame, permanent material quid”, the substance that for a certain time defies becoming. For these ancient progenitors of ours, that which truly persists, at least for a while, appears, paradoxically, precisely when we are no longer here. Archaic thought very often grasps the crux of a question. Not infrequently, having grasped the crux, human beings spend centuries trying to unravel the skein, losing themselves among its threads. Obviously our ancient progenitors too used, at least from a certain stage of linguistic development onward, personal names and pronouns by which they denoted, at different times, one person or another. The fact is that, one may presume, the essential unity of this or that person, rather than being successfully pinned down by the mind, was humbly wrapped in a vague and sacral atmosphere. Thus even my dear “Self” would be something to which I turn, in Vico’s manner, with a spirit both troubled and moved.

Luigi Cimmino teaches Epistemology and Ethical Paradigms at the University of Perugia.