**Links to**: [[Identity operator]], [[Identity of Indiscernibles]], [[Principle of identity]], [[Aristotle]], [[Difference]], [[Hegel]], [[Equivalence]], [[Equality]], [[Mathematics]], [[Programming]], [[Type theory]], [[Foundation]], [[Principle]], [[Ontology]], [[Analogy]], [[Homotopy]], [[Reflection]], [[Univalence principle]], [[Equivalence and difference]], [[Generalization]], [[Abstraction]], [[Platonism]], [[Lying]], [[Likeness]]. (This entry is a sketch). The concept of identity is generally used for talking about _haecceitas_: the unique, _necessarily unique_,^[Pauli’s exclusion principle holds. But also Kripke’s take on necessary identity. See notes below.] _thisness_ of a thing.^[_Thingness_ in most of this project, unless stated otherwise, is usually defined by the [[Free energy principle]].] Identity, as _haecceity_, can therefore sometimes be equated with _difference_: it is the pure differential pattern that makes _actual_ sameness as equivalence impossible (i.e., no two things can ever be alike, as they must at least differ in being two different things, that is Leibniz’s [[Principle of indiscernibles]] ). As you can read, we are holding difference hostage in order to talk about something else, perhaps much too dialectically.^[Dixit: Lyotard.] This is the conceptual route of most philosophies of difference, according to Deleuze. We seem to capture the concept, but only by subordinating _actual_ difference to other concepts: e.g., identity, sameness, resemblance, opposition, or analogy (the same is true of trying to capture _repetition_). This prevents philosophy from developing a “true” concept of difference in itself (Deleuze 1994 (1968), p. xv). In our view, because neither reality nor thought ever stop, we choose to say that identity (sometimes involving, sometimes excluding other concepts) is **an effect of the predictive tendencies of mind in service of something else**. It is the holding stable of processes so there may be new turns of understanding. Repetition as _difference without a concept_ (Deleuze, ibid.) is in line with our proposal of ratio, [[Rationality]], as the predictive grip which serves to [[Chunk]] and [[Parse]], to segment; to partition the fabric of attention, towards expectable outcomes. Thinking does not gravitate towards accuracy, but towards self-actualization. Thinking, embodied, seeks functions: survivals,^[Not one, but many.] and therefore can only encounter problems, which can only be parsed according to its self-given pattern. We take seriously the proposal that “[a]ll identities are only simulated, produced as an optical ‘effect’ by the more profound game of difference and repetition.” (Deleuze 1994 (1968), p. xix). All perception is self-actualizing hallucination. <div class="page-break" style="page-break-before: always;"></div> ### Some reminders Leibniz’s _Identity of Indiscernibles_ principle states that no two distinct things, or substances, can share exactly all properties. If two things share all properties, we could say they are the same thing. The identity of something is its pure difference versus everything else.^[Deleuze referred to Leibniz and Hegel’s attempt at systematizing difference an attempt at “orgiastic representation,” a kind of totalizing move that subsume all differences into a single conceptual framework, thereby self-defeating in the pursuit of pure difference. For Leibniz, every difference in the universe is contained within and expressed by each monad. For Hegel, this was dialectics, where all differences are ultimately moments of their own self-ovecoming.] _Kripke and (scientific) essentialism by identity_: Something like a person (e.g., Juan) can be identified by properties, but also just _by the person_. This seems pretty Aristotelian (because it can be compared to the proposal that we cannot define an individual). “When we first referred to ‘water’, say, we refer not to whatever satisfies certain characteristic properties (being clear, potable, liquid at standard temperature and pressure, and so on), but to _that stuff_. And when scientists discovered that that stuff was H$_2$O, they discovered _the essence_ of water. Kripke produced an elegant proof that all identities were necessary identities.” (Matthew H. Slater and Andrea Borghini 2011, p. 13). This essence ‘as’ or ‘in the name of’ something, Deleuze designates to the generalizing tendencies, to _repetition_, in all scientific representation. On proper names, the following is worth citing as Deleuze muses over the difference between writing philosophy and history of philosophy: >[When we write philosophy, as opposed to its history, we] try to speak in our own name only to learn that a proper name designates no more than the outcome of a body of work—in other words, the concepts discovered, on condition that we were able to express these and imbue them with life using all the possibilities of language. > >_Difference and Repetition_, preface to the English edition, xv. An outcome—the name of the philosopher attached to their thought—is subject to the very _incomplete_ and variable possibilities of language as this work is consumed by a community. And a name is nothing without this attention-pooling process.^[Regarding _process_ as/and identity: “For Whitehead, process is real, but change and motion are not. For example, according to Whitehead, change is only “the difference between actual occasions comprised in some determined event” (_Process and Reality_ 73) and thus it is “impossible to attribute ‘change’ to any actual entity” (_Process and Reality_ 59). “Thus an actual entity never moves: it is where it is and what it is” (73). Change and motion thus relate to a succession of actual entities and are constituted only by their _differences_. Every entity is “what it is,” and it “becomes” as the whole of reality enters a succession of discretely different states, but no entity ever technically changes or moves. (Nail 2022, p. 18).] This collective learning is bound to inevitable and productive falls.^[See: [[10 Bias, or Falling into Place]].] See also: [[Sameness]], [[Equivalence]], [[Difference]]. %% Read into and summarize: file:///Users/soniadejager/Downloads/AristotleIdentity-FAMuller2023(published).pdf Look into divisor function / sigma function: Wiki: In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities; these are treated separately in the article Ramanujan's sum. "In the Stuttgart Lectures, [[Schelling]] argues that the transition from identity to difference has often been understood as a cancellation of identity; yet that is not at all the case . . . Much rather it is a doubling of the essence, and thus an intensification of the unity [Steigerung der Einheit]" [[Christian Kerslake]] [[Immanence]] p. 24 %% ### Footnotes