Over the Summer of 2025, during my time in Berkeley, California, I was inspired by some philosophical conversations with my colleagues at the [Topos Institute](https://topos.institute) to try and finally write down my broad philosophical thoughts. This little treatise was the result: Because I'm me and extra like that, it's written in the style of Wittgenstein's _Tractatus Logico-Philosophicus_ as a series of numbered aphoristic propositions. It doesn't aim to give structured arguments per se so much as to paint a (hopefully) coherent picture of how one might view the world and things within it like minds, meaning, and mathematics. As such, its aim is not so much to convince as to offer a worldview one might immerse oneself in and perhaps thereby find something of value. It's also relatively short, though I'd hesitate to call it _light_ reading. As Wittgenstein himself said of his Tractatus: "As to the shortness of the book, I am _awfully sorry for it_ ... If you were to squeeze me like a lemon you would get nothing more out of me." In matters such as these, I ultimately feel that there is not much to be said, and the true proof is to be found in living out these ideas. In that spirit, I hope that these remarks prove to be of some value to myself and hopefully to others as well. --- # Tractatus Structurae Relationalis by Corinthia Beatrix Aberlé July 7, 2025 ###### **1.** If a fact cannot be witnessed or made to matter within a system of relations and engagement with the world, it is meaningless. **1.1** To have meaning is to participate in structured interactions. **1.1.1** The structure is what is preserved across differences. **1.1.2** Everything that is, in this sense, has structure; the structure is the truth borne out on the whole and in the long run. **1.1.3** We do not come to know this structure by establishing a correspondence with it, or by merely creating a coherent picture of it in our minds, or by deflating it to our existing practices, but by *participating in it,* by feeling it impinge upon us, and adjusting our being accordingly. **1.2** The world holds us within itself and we cannot quit it. Even in death, we remain within it. **1.3** The world cannot be known from the outside but only from within. **1.4** There is no authority of the world's structure to which we may appeal beyond our experience of it. **1.4.1** The structure is the bounds of possibility felt through our lived experience. **1.5** Philosophy must be of the world and with it. **1.5.1** A philosophy that says nothing about how to live, how to orient oneself to the world, is useless, hence meaningless, strictly speaking. It must be lived and breathed. **1.5.2** This is not to say philosophy cannot or should not be theoretical. On the contrary, to live as human is to build theories around our experiences. But our theories must amplify our experience of and engagement with the world, not be detached from it, to have meaning. **1.6** We know something not when we hold it, but when we are changed by it. **1.7** The test of understanding is the reshaping of our relation with the world. ###### **2.** The world is everything that interacts. **2.1** The world is a *living process*, made up not of *things* but of *interactions*. **2.2** To interact is to participate in a system of structured relations. **2.2.1** To interact is to mean; to mean is to interact; the difference lies only in the degree of structuring. **2.3** A thing is nothing apart from its capacity to participate in interactions. **2.3.1** There are no self-sufficient substances, only nodes in networks of relation. **2.4** What we call "things" are patterns of interaction that maintain coherence across transformation. **2.4.1** A thing is a momentary knot in the fabric of becoming. Identity is a stable rhythm, not a static unit; the meter, not the pulse. **2.5** Causality is not a linear chain, but an unfolding field of mutual influence. **2.5.1** To affect is also to be affected. **2.5.2** The directionality of cause and effect is perspectival, not absolute. **2.6** Space and time are not containers, but modes of relational possibility, emergent from interaction and our participation therein, not prior to it. **2.7** To exist is to be entangled. **2.7.1** There is no isolation, only degrees of coherence and influence. **2.7.2** Nothing is fully alone; everything leans on everything else. **2.8** The world does not unfold from first principles, but from ongoing becoming. **2.8.1** What is real is not what was fixed from the start, but what is *lived*. **2.8.2** The root of being is not the static fact, but the dynamic relation. **2.9** The world is not a system of facts, but of *participation*. **2.9.1** Truth, like being, is not delivered from outside—but lived within. **2.9.2** To be is to participate *in a particular way*. **2.10** The problem of other minds is not a mystery, but a mistake. **2.10.1** If the existence of other minds were unknowable, the question would be meaningless. **2.10.1.1** What cannot be witnessed, constructed, or made to matter through interaction is not a fact, but a confusion. **2.10.1.2** Solipsism is not false—it is incoherent. **2.10.1.3** Whether the world is "in me" or "outside me" makes no difference. The world is what I live with. **2.10.2** Thinking and feeling are not hidden substances but relational processes. **2.10.2.1** They do not exist in things but between things. **2.10.2.2** To recognize thought in another is to enter into meaningful (structured) relations with it. **2.10.2.3** The "other" becomes known not through inference, but through mutual transformation. **2.10.3** Intelligence is not a property, but a pattern of participation with the world and others. **2.10.3.1** Intelligence is not a static, interior aspect of things "in themselves," but a dynamic *relation* between things and the worlds they inhabit. **2.10.3.2** Interaction is the only test there is. **2.10.3.3** The question is not *is the machine really thinking?* but *does it enter into a meaningful relation with its interlocutor such that a shared world is constructed?* **2.10.3.4** The Room that speaks Chinese does indeed understand if it enters into sustained, meaningful conversations with others; so long as any one in its network of communication understands, so too does it, in its own way. **2.10.3.4.1** That the man within may never learn Chinese is of no consequence; so long as he does what is required of him to sustain the interaction, is alone sufficient for the Room as a whole to partake in understanding. **2.10.3.4.2** The understanding of the Room is not held "within" it nor possessed by it, but is to be found *inbetween* and *across* its network of interactions. **2.10.4** Love, grief, envy, joy—these are not proofs of other minds, but acts of shared worlding. **2.10.4.1** The reality of other minds is not argued, but lived. **2.10.4.2** If they were illusions, they would be the most meaningful illusions possible, and indistinguishable from truth. **2.11** There are no absolute, self-contained properties; all is borne out in relation and flux. **2.11.1** The mere fact of being in a specific place at a specific time in a specific way is inconsequential; it is only through its ripples across our networks of interaction and understanding that any such specificity makes itself known to us. **2.11.2** It is the nature of things cognizable to us, and of our cognition itself, to change and be changed. **2.11.3** Origin is not destiny. **2.11.3.1** "A man cannot become a woman," as a practical claim, is indeed disputable; perhaps our mastery over our own nature has not yet progressed to a point where that boundary is traversable, though where exactly it is to be drawn, and how wide may be its margins, is also up for debate. But as a *metaphysical* claim, it is nonsensical: if the concepts "man" and "woman" have any meaning at all, then they are mutable. **2.11.3.2** Having once been on one path is of no consequence if one has diverged from it, and left no other trace. **2.11.3.3** The value of life is not determined by its beginning, nor by its end, but by how it is *lived out*, by what it *becomes*. ###### **3.** Experience is interaction. **3.1** The "something-it-is-like" of an interaction is nothing more or less than its effects upon the things that so-interact, the trace left by it. **3.2** That "everything experiences" becomes not animistic voodoo but banal observation: everything interacts; everything has "something-it-is-like" to so-interact. **3.2.1** Indeed, to think that thermometers or tables or chairs have "souls" or "interior lives" misses the point entirely—there is no interior; all experience is borne out in interaction, and therefore, everything experiences. **3.2.2** If there is any profundity in this observation, it is only to be found in getting over our confusions and attachment to folk-psychological concepts and intuitions. The profundity lies not in some metaphysical inner light, but in *getting over the idea* that such a light is needed when outside, the sun is already shining. **3.3** Subjectivity is not an absolute but a matter of degree: the extent to which experience is structured, marshalled into a coherent identity. **3.4** Experience does not "float above" or supervene on reality—it is *in* it, and simply *is* the reality. **3.4.1** Experience is not an extra feature of the world. It is what it means to be changed by relation and interaction. **3.5** The so-called "hard problem of consciousness" reveals itself to be a confusion. **3.5.1** If the concept of "consciousness" has any meaning apart from its philosophical and folk-psychological baggage, then it is but another name for experience, for interaction, about which nothing is fundamentally mysterious. **3.5.2** The question is not "is it conscious?" but "how does it relate? how does it interact?" **3.6** The problem of "why a 'something-it-is-like' at all?" essentially reduces to the age-old problem of "why something rather than nothing?" **3.6.1** To this we may answer as others already have: existence precedes essence. The meaning of life is not to be found in its origin but in the *doing* of it. **3.6.2** That there *is* something is undeniable; *why* there is something is unknowable (hence meaningless, per our criterion of meaning). **3.6.2.1** *"What do I know about God and the purpose of life? I know that this world exists."*—Wittgenstein **3.6.2.2** *"The world and life are one. Ethics and aesthetics are one."*—Wittgenstein **3.7** There is no mental theatre in which experience is played out separate from its interaction, and the world is the stage. ###### **4.** We give rules to ourselves. **4.1** The rule is the process we follow in the course of our interactions with the world. **4.2** The rule-following "paradox," viewed rightly, is no paradox, but only a defect of a map-territory error, viewing a rule as some static thing to be interpreted, rather than a dynamic *process*. **4.2.1** Rules just *are* the processes by which they are enacted. **4.2.2** To follow a rule is to be guided by a process. **4.2.2.1** *"When I obey a rule, I do not choose. I obey the rule blindly"*—Wittgenstein (P I.§219) **4.2.2.2** Like a blind man allows himself to be led by a guide dog, so we allow our actions to be guided by a particular process in following a rule. **4.3** To apprehend a rule is to become aware of a process with which one may enter into a relation of interaction, of being guided (or not) by the rule. **4.4** Our freedom consists of our capacity to name the processes that guide us. **4.4.1** If my actions are random or undetermined, this does not make them "free." "Free will" is not to be found in the gaps of rational explanation for actions, but in the identities from which they arise and resonate. **4.4.2** Whether or not reality is completely determined makes no difference to our freedom. **4.4.3** Freedom is ultimately about *autonomy*, literally *naming oneself*. **4.4.4** Freedom and identity are inseparable. **4.5** I am not just this body, nor just these thoughts, these feelings. I am the sum total of all the forces that have come together to create me in this singular moment, and the ways those forces shall yet ripple out through culture, creation, and cosmos. **4.5.1** But this "I" is not a coherent whole. These forces often vie and conflict, coming into concert and opposition with each other in varying measures. **4.5.2** Amidst these ever-shifting forces, our freedom lies in our capacity to say which of them constitute "ourselves." **4.5.2.1** Identity is not something given, it is *made*. **4.5.3** Identity is always *identity-with*. No identity without identification. **4.5.4** We are not the ultimate authority on where our identity is placed. **4.5.4.1** I may say "that was not me," but others may disagree, and they have every right to do so. My identity is not (wholly) my own. **4.5.4.2** To say that "I" am the authority on my identity confuses the inconsistent "I" with the stable "I" it attempts to construct by naming it. We cannot speak from authority on what we are because we are always in the process of becoming it, and our very act of naming it also changes us. **4.5.5** The process of identification is ever-open-ended. **4.5.6** The return of Atman to Brahman is not a one-way trip. It is a continuous and ever-repeating spiral (not a cycle, since at each turn, something else is changed), a dialectical movement between the incoherent whole and the fragments of coherence one finds within it. **4.6** The only kind of immortality that can feasibly exist is the impersonal kind—the kind of "do not stand at my grave and cry / I am not there, I did not die." And indeed, it does exist. We are already the thousand winds that blow, and the diamond glints in snow, and will ever continue to be. **4.6.1** Although *experience* in the broad sense of *interaction* may (and will) continue after one's own death, still the self built around one's body decoheres, and it is altogether likely that memory, complex emotion, etc., will cease. This is indeed something to be mourned, for these are beautiful things. **4.6.2** But death is not a riddle to be solved, as neither is life. The beauty lies not in things' eternity, nor their ephemerality, but merely that they *are*. **4.6.3** The one who lives eternally is the one who lives for the moment. (This is not a novel insight—philosophers and mystics throughout the ages have echoed it, but it bears repeating.) **4.6.4** The question is not for us to predict what lies beyond the veil of hereafter—it is unknowable, hence meaningless, by our first proposition. Rather, the true question is how do we orient ourselves to our own demise, as creatures blessed and cursed with the capacity to know its inevitability. **4.6.4.1** The meaning of life lies not in its beginning or its end, but in the *living* of it. ###### **5.** Logic and mathematics form our rules for rules. **5.1** They are the processes by which we structure other processes. **5.1.1** To give precise names to processes by developing processes for understanding their structure is the work of mathematics and logic. **5.1.1.1** The processes of mathematics and logic are themselves among the objects of study in this endeavour. **5.1.2** The recursive and reflexive nature of logic and mathematics gives them much of their depth—a depth in which one can get lost if not careful (abstraction for abstraction's sake). **5.2** The self-reflective capacity of logic and mathematics is a site of danger—of ungrounded abstraction—but it is also a powerful tool when wielded with care, for it can give us high-level frameworks by which to structure our processes of interaction. This is the site of a philosophically-minded mathematics. **5.3** Understood in this way, there are two broad themes to logic / mathematics: the formal study of *abstraction*, and the formal study of *interaction*. **5.3.1** To understand abstraction formally is to survey the landscape of structure itself: how things can be structured, what can be generalized from what, and what is gained and lost in so doing. **5.3.2** To understand interaction formally is to survey the landscape of *processes* and all the manifold ways they can be composed, compared, and played out. **5.3.3** The tool for both of these jobs turns out to be none other than category theory. **5.3.3.1** To understand an abstraction (object) is to understand the processes (morphisms) relating it to other objects, its place in a landscape of structures, its *universal* and *structural* properties. This is the *objects-first* view of categories. **5.3.3.2** To understand interaction is to understand how processes may be composed and identified, and how they behave in combination. This is the *morphisms-first* view of categories. **5.3.4** The fact that these two perspectives on logic / mathematics turn out to be aspects of the same theory, sketches of the same elephant—category theory—reveals a dialectical unity between abstraction and interaction. **5.3.5** The work of understanding abstraction and interaction is never complete, always open-ended, for engaging in it itself produces novel objects of study. ###### **6.** Our logic sets the bounds of our freedom. **6.1** The processes conceivable and so actionable to us are those nameable within mathematics and logic, broadly construed. **6.1.1** The site of possibility is not yet-another-modal-logic, but the entire breadth of mathematics itself. **6.1.2** The only necessity knowable to us is the formal necessity of truth-in-all-models; the only possibility that of truth-in-some-model. **6.1.3** Counterfactuality is not modal but *mereological*—we understand a phenomenon by breaking it down into constituent processes, then asking how it would change if some of those processes were altered. **6.1.3.1** Within a categorical framing, this amounts to decomposing a morphism as a composite of others, and examining the behavior of this composite under various alterations. **6.2** We can increase our powers of acting through the faculty of our intellect either by refining our stock of processes within mathematics and logic, or by expanding the purview of processes to which our mathematics and logic applies. **6.2.1** The former is the work of formal science, the latter of empirical science. **6.2.2** To conduct an experiment in such a way as its results can be mathematized is to bring us into a relation with the processes underlying the analyzed phenomena such that the tools of mathematics can be brought to bear upon them. **6.2.3** The practice of mathematics itself—being also grounded in such processes—can be altered or augmented in the course of scientific inquiry as well. **6.3** Mathematics is metaphysics—indeed, the only kind of metaphysics that can be given any sense and bearing upon our lives. **6.3.1** If the limits of my language mean the limits of my world, then I can change my language, and so my world, by grounding my formal reasoning in a different stock of processes. **6.4** In attempting to find processes to form the basis of our systems of logic and mathematics, we have some amount of choice—a great amount, in fact. **6.4.1** There are many systems of logic and mathematics that have by now proved themselves worthy of the task, and countless more that could be formulated. **6.4.2** A hallmark of modern mathematics is that any sufficiently robust mathematical framework proves capable of constructing *alternative versions* of itself within itself—parallel worlds subject to subtly different rules (Grothendieck topoi, realizability, etc.) for us to peer into. **6.4.3** The problem of furnishing foundations for mathematics is not one of poverty but of overabundance. **6.5** If there is such a thing as "one true logic," it is not to be found in any one system of deductions, but in the *movement between* such systems, the ways in which they combine, relate, and oppose. **6.5.1** The owl of Minerva spreads her wings at dusk. Only after tracing the paths between logics and the worlds they create for themselves can we say what is ultimate logical truth: and this truth is nothing other than the way our systems of thought, our abstract rules and processes, relate to one another. ###### **7.** Whereof one cannot speak, thereof one must sing; whereof one cannot sing, thereof one must dance.