Work #1839
Fragments and Testimonia
Surviving fragments and doxographic reports on Speusippus's mathematical ontology
Speusippus
· c. 347–339 BCE
· Attic Greek
· Prose treatises (fragmentary — surviving in Aristotle, Proclus, Iamblichus, Athenaeus)
Tradition: Academic Platonism / Pythagorean-Platonic synthesis
The One is not the Good — mathematical entities, not transcendent Forms, are the primary realities
Speusippus's writings — reportedly numerous and covering metaphysics, mathematics, biology, and ethics — survive only as fragments and testimonia, principally in Aristotle's Metaphysics (which polemicises against him on several points), Iamblichus's De Communi Mathematica Scientia, and scattered doxographic reports. Three doctrines stand out. First, he rejected Plato's Theory of Forms as separate substances and replaced them with mathematical entities — numbers and spatial magnitudes — as the fundamental realities. Second, he denied that the One (the supreme principle) is identical with the Good, arguing that goodness emerges only at the level of complex, developed beings. Third, he posited distinct principles for each level of reality — one set for numbers, another for geometrical magnitudes, a third for the soul — a "layered ontology" that Aristotle criticised as making the universe "episodic, like a bad tragedy" (Metaphysics 1075b37). His biological work "Homoia" (Similars) classified plants and animals by resemblance, anticipating Aristotle's own taxonomic project.
Author
Editions cited
- Speusippus of Athens: A Critical Study (Leonardo Tarán, Brill, 1981)
- Speusippus: Fragments (Paul Lang, Kleine Texte, 1911; repr. Olms, 1965)
- Aristotle, Metaphysics (W. D. Ross, Oxford, 1924 — principal source of testimonia)
School Embodiments
Speusippus works within the Academy's Platonic framework, even as he revises its central doctrines. His departures are internal critiques.
"Speusippus, being Plato's sister's son, tried to carry out Plato's views." (Proclus, In Parm. 38.32)
Pythagoreanism
30%
The re-Pythagoreanisation of the Academy: numbers and spatial magnitudes as primary realities, with distinct principles for each ontological level.
"Speusippus posited more substances, beginning with the One, and principles for each kind of substance." (Aristotle, Metaphysics 1028b21–24)
Logicism
20%
The attempt to ground reality in mathematical structure anticipates the logicist programme. Number is explanatorily basic, not derived from the Good.
"Speusippus did not think the One was the Good." (Aristotle, Metaphysics 1092a14)
Aristotelianism
15%
Speusippus's biological classification (Homoia) and his bridging of perception and knowledge anticipate and likely influenced Aristotle.
"Speusippus composed a work called Homoia in which he classified things by their resemblances." (Athenaeus, Deipnosophistae 2.68)
Internal Tensions
The governing tension: by positing separate principles for each level of reality, Speusippus risks making the universe "episodic, like a bad tragedy" (Aristotle, Metaphysics 1075b37). What unifies numbers, magnitudes, and soul if there is no single supreme principle (the Good, the One-as-Good) to hold them together? Whether Speusippus had an answer is lost with his writings.
⧖
I. Time
Time is linear and substantival. Mathematical principles are eternal and necessary but "in" the cosmos, not in a separate realm. The temporal world is less fundamental than mathematical structure.
Attributes
Extent: Infinite
Ontological Status: Substantival
Grain: Continuous
Freedom: Deterministic
Traversability: Linear
Direction: Uni-directional
Dimensionality: One
✦
II. Space
Space is finite (the bounded Greek cosmos) and emerges at the level of geometrical magnitudes — the second tier of Speusippus's ontological hierarchy (after numbers).
Attributes
Extent: Finite
Ontological Status: Substantival
Curvature: implicit
Dimensionality: Three
Locality: Local
◉
III. Matter
Matter is relational: its ultimate constituents are mathematical structures. The One and the indefinite dyad generate numbers; numbers generate magnitudes; magnitudes generate physical bodies.
Attributes
Extent: Finite
Ontological Status: Relational
Conservation: Conserved
Dimensionality: Three
Locality: Local
◎
IV. Observer
The observer is both embodied and partly disembodied: the soul has a mathematical nature not reducible to body. "Scientific perception" (epistēmonikē aisthēsis) bridges sense and intellect.
Attributes
Time Instance: Single
Space Instance: Single
Knowledge Extent: Mediated
Knowledge Retainment: Total
Physicality: Both
Agency: Active
Number: Plural
Metaphysical Agency: Cosmic-ordering
⚡
V. Energy
Energy, like matter, is a manifestation of mathematical structure. Conserved and finite within the bounded cosmos. Dispersibility is unaddressed in the surviving fragments.
Attributes
Extent: Finite
Ontological Status: Relational
Conservation: Conserved
Dispersibility: not engaged
⧉
VI. Information
Number is the fundamental informational unit — substantival, discrete, and conserved. Mathematical structure is more basic than matter. Personal information is conserved through the soul's mathematical nature.
Attributes
Ontological Status: Substantival
Cosmic Conservation: Conserved
Personal Conservation: Conserved
Granularity: Discrete
Personas that cite this work
Personas with the nearest attribute fingerprint
Historical figures whose own classification on the same six-dimensional grid lands closest to this work's. Computed by attribute-agreement on coordinates both address.
Computed school proximity
The work's attribute fingerprint scored against all schools using the same quiz scorer. Useful as a sanity check on the hand-curated embodiments above.
How Fragments and Testimonia resolves each dilemma
48 resolved positions across 4 dimensions, including 18 distinctive where the majority of schools go the other way · 9 unaligned.
Each dimension is sorted so minority positions come first. Mainstream positions are folded into an expandable list.
Time · 9 dilemmas · 3 distinctive
Persistence, the future, and the direction of becoming.
Distinctive · only 10% of schools agree
(20/208)
Do you really choose?
If the brain is a physical system and physical systems are governed by laws, then every choice is also a chain of causes — which raises the question of what was really left to choose.
Choice is real within a determined order — agency and determinism aren’t opposites.
On this view, the future is determined and you are genuinely choosing. Those aren't contradictory because the determination runs through you rather than around you: your reasoning, deliberation, and assent are the way the determined outcome gets settled. Choice is what it feels like from …
Roads not taken
The future is open and you are a genuine origin of it. (69%) ·
Choice is structural illusion — every event is fixed by the prior state. (10%) ·
Even if the universe is undetermined, you are not the chooser. (6%)
Distinctive · only 10% of schools agree
(20/208)
Are addicts responsible for their addiction?
Addiction looks from one angle like the textbook case of agency failing — a person doing what they don't, in any meaningful sense, want to do. From another angle it looks like agency at work in hard conditions. Which it is depends on what agency is.
The addict is genuinely responsible within a determined order.
On this view, the addict is acting within a determined order but is genuinely acting — making decisions, endorsing or resisting urges, seeking or refusing help. Responsibility attaches not because some uncaused choice happened, but because the addict is the kind of agent through which …
Roads not taken
The addict could have chosen otherwise — that's why recovery is real. (69%) ·
The addict's behaviour is the outcome of causes; 'responsibility' is a useful fiction, not a metaphysical fact. (10%) ·
Even if the universe is undetermined, the addict isn't the chooser. (6%)
Distinctive · only 10% of schools agree
(20/208)
Should we hold AI systems responsible for what they do?
When an autonomous AI takes an action that harms someone, the question of who or what is responsible — the developer, the operator, the model itself — turns on whether the model is the kind of thing that can be a responsible agent.
The AI can be a genuine agent within determined conditions — and therefore genuinely responsible.
On this view, what makes a being responsible is not indeterminism but the kind of process the being is. An AI that deliberates, considers consequences, can be given reasons, and modifies its behaviour on reflection is doing what responsible agency is, even if its underlying …
Roads not taken
An AI without a free will is not the kind of thing that can be responsible. (69%) ·
An AI's behaviour is fully determined by training and input; 'responsibility' applies if at all to its makers. (10%) ·
Neither AIs nor anyone else are the locus of free agency; the question is the wrong one. (6%)
6 mainstream positions
How much weight do future people deserve?
Future people are as real as you are — and their interests count for as much.
47%
Is regret rational?
The past is as real as the present; regret is a real attitude toward a real thing.
47%
Do we owe extinct species something we cannot give them?
Extinct species are as real as we are; they have standing.
47%
Is the universe running out of usable energy?
Time is unbounded but matter is finite; usable energy can fail without time failing.
47%
Are natural resources fundamentally finite, or only practically so?
Time goes on but matter is bounded; we are eventually constrained even with infinite time.
47%
Could we owe future generations more than is materially possible to provide?
Time is unbounded but matter is not; we can owe more across long time than the matter can provide.
47%
Matter · 7 dilemmas · 5 distinctive
What stuff is — fundamental, relational, or appearance.
Distinctive · only 14% of schools agree
(30/208)
What is money?
The question of what money is — a measured store of real value, an agreed-on practice, a relational ledger of debts, or just a name we apply to many different things — sits behind every argument about inflation, cryptocurrency, debt, and the state.
Money is the ledger of obligations among real people.
On relational views, money is not a substance you have; it is a record of who owes whom what. Debts and credits are real because the relations they track are real — to kin, to community, to ancestors, to land. Money is the form this …
Roads not taken
Money is a real institution with intrinsic features. (55%) ·
Money is a social practice — its content is what we make it. (16%) ·
“Money” names a family of practices — the definition question is nominal. (8%)
Distinctive · only 14% of schools agree
(30/208)
What is a nation?
Whether a nation is a real moral community with intrinsic character, a constructed legal-political artifact, a web of kinship and shared history, an imagined community, or a conventional partition of a deeper unity — these are real ontological positions with sharply different political downstream.
A nation is the web of kinship, ancestry, and shared land that hosts a people.
On relational views, the nation is the relational fabric — extended kinship, ancestral inheritance, shared ecology, communal practice — that hosts a people across generations. Borders matter less than belonging; lineage and land carry the weight that political structures only ratify.
Roads not taken
A nation is a real moral community with intrinsic character. (55%) ·
A nation is a constructed polity — a project, not a discovery. (16%) ·
“Nation” names a family of practices imaginatively held together. (8%)
Distinctive · only 14% of schools agree
(30/208)
What makes someone male or female?
Whether sex is a real biological kind, a constructed social category, a relational identity, a label applied to varied phenomena, or a conventional distinction within a deeper unity is the ontological question the contemporary dispute about gender is mostly about.
Sex and gender are constituted by relations of recognition.
On relational views, identity is not a property a person has alone; it is constituted by the web of recognition the person sits in. What makes someone a man or a woman in any thick sense is the relations of kinship, community, ritual, and recognition …
Roads not taken
Sex is a real biological kind with given content. (55%) ·
Gender is constructed; what counts as male or female reflects practice. (16%) ·
“Male” and “female” are family-resemblance terms — no single essence. (8%)
Distinctive · only 14% of schools agree
(30/208)
Should we edit the human germline?
Whether human nature is a given biological kind, a constructed category, a relational achievement, a family-resemblance cluster, or a conventional distinction within deeper unity is the ontological question the policy debate over heritable gene editing is mostly about.
Personhood is constituted by relations of descent and kinship; germline editing reshapes the relational fabric.
On relational views, what makes someone a person is the web of kinship, ancestry, and community they sit in — not a property the body carries alone. Heritable editing intervenes in exactly this fabric: the lineage that ancestors handed on, the descent that descendants will …
Roads not taken
Human nature is a real biological kind given by reproductive biology or by creation; editing the germline transgresses what is given. (55%) ·
The categories we count as 'human' are emergent from practice; germline editing is a practice-revision like any other. (16%) ·
'Human nature' is a cluster term without a single essence; the editing question is empirical, not metaphysical. (8%)
Distinctive · only 16% of schools agree
(33/208)
Is the world created from nothing?
Creatio ex nihilo is one of the most distinctive Western-theological claims. Whether matter was created from nothing, eternally exists, or is sustained moment-by-moment turns on what kind of thing matter is.
Matter is constituted by relations; the question of 'from what?' presupposes substance.
On this view, matter is not a stuff but a patterning — the standing relations among things, ancestors, processes, and places. The creatio-ex-nihilo question doesn't quite arise, because the ontology has no slot for a free-standing substance to be created or eternal. What persists is …
Roads not taken
Yes — matter was created and is conserved as a real substance. (56%) ·
Matter is real but emerges from something deeper — neither bedrock nor created-from-nothing. (23%) ·
Matter arises and dissolves through cosmic rounds; neither created from nothing nor eternal. (4%)
Observer · 37 dilemmas · 5 distinctive
Mind, agency, and the knower's relation to the known.
Distinctive · only 7% of schools agree
(14/208)
Is reality fundamentally digital?
Pancomputationalism, Planck-scale quanta, simulation theory and Kabbalistic letter-mysticism all say yes — but for very different reasons. The rest of the atlas says no.
Yes — but divinely-discrete: divine letters, momentary cognitions, atomistic theism.
On this view, the world is at bottom discrete, but the units are not bare bits. They are divine names, momentary cognitions, karmic atoms, sacred letters — the elementary acts of a creating or ordering agency. Discreteness is real and fundamental, and so is the …
Roads not taken
No — continuous divine sustaining act, the Tao that knows no joints, the One's self-disclosure. (44%) ·
No — continuous fields, classical limits, analog deep structure. (36%) ·
Yes — bits, quanta, computational substrate. (13%)
Distinctive · only 7% of schools agree
(14/208)
Are there indivisible units of experience?
Whiteheadian actual occasions, Buddhist moments of mind, Kabbalistic letter-cognitions, IIT phi-units — or the unbroken Jamesian stream? The atomism of experience cuts across naturalism and theism alike.
Yes, theistic atomism — actual occasions, divine letters, momentary cognitions.
On this view, the atoms of experience are not bare quanta but agent-laden moments: Whiteheadian actual occasions in which subjectivity and the divine lure meet, Kabbalistic letter-cognitions in which divine names act, Buddhist Abhidharma moments of mind, tantric ksana. The discreteness is real and so …
Roads not taken
No — continuous divine presence; consciousness is the unbroken witness. (44%) ·
No — continuous Jamesian stream, phenomenological lived time. (36%) ·
Yes — naturalist quanta of experience. (13%)
Distinctive · only 7% of schools agree
(14/208)
Is memory stored or reconstructed?
Engrams and traces — or continuous re-narration each time you remember? The cognitive-science debate has a theological cousin: divine memory holding each hair, or the ancestors' continuous remembering.
Stored — in divine memory's discrete particulars, or in karmic-record units.
On this view, memory is held in discrete particulars by an agency: the Lord who knows each hair, the karmic ledger that records each act, the angelic scribe who writes each deed, the Kabbalistic letters that spell each soul. Storage is real; the storer is …
Roads not taken
Held in continuous divine or ancestral remembering — neither stored discretely nor purely reconstructed. (44%) ·
Reconstructed — continuous re-narrating, no fixed engrams. (36%) ·
Stored — discrete engrams, traces, weights. (13%)
Distinctive · only 14% of schools agree
(30/208)
When does a person begin?
The political question of abortion sits atop an older ontological one: at what point does there exist a someone — a being with moral standing — rather than merely the materials from which one will form?
Personhood is conferred by being-in-relation.
On relational views, person was never the name of a thing that exists on its own — it is the name of a node in a web of recognition, obligation, kinship, and ecology. The question of when a being becomes a person is the question …
Roads not taken
A person exists from conception — when a new being comes into existence. (55%) ·
A person comes into being gradually, as the capacities of a mind develop. (16%) ·
The question presupposes a fact of the matter that isn’t there. (8%)
Distinctive · only 14% of schools agree
(30/208)
What is marriage?
Behind every disagreement about how marriage should be defined is a prior disagreement about what kind of thing it is — a given order to be recognized, a practice to be negotiated, or a web of relations to be woven.
Marriage is constituted by the web of relations it creates.
On relational views, marriage is not a thing in itself but a node in a web — a configuration of obligations to children, extended kin, ancestors, ecology, and community. Its definition is what the network of relations is, and any attempt to specify it apart …
Roads not taken
Marriage has a given form — it’s a kind of thing we recognize, not make. (55%) ·
Marriage is a practice we shape — its content is what we make it. (16%) ·
“Marriage” names a family of practices — the definition question is nominal. (8%)
23 mainstream positions
What is our place in nature?
Embedded in a web — partners with the more-than-human world.
14%
Should we colonize space?
Colonisation continues the work that ended the wisdom of seven-generation thinking.
14%
Is genetic engineering of food stewardship or domination?
Editing the genome cuts into the relational fabric; we should be very slow.
14%
Could causation work backwards?
Causation runs one way — the arrow of time is real and structural.
68%
Is the asymmetry between memory and anticipation a real feature of time, or just of us?
The asymmetry is real because time itself has a real direction.
68%
Is the arrow of time a real feature of the cosmos, or only of how we describe it?
The arrow is real and structural; the asymmetry isn't an artifact of description.
68%
Does environmental harm in another country bind me morally?
Moral obligation tracks the relations one is in; distance does matter, structurally.
50%
What happens to "you" when you die?
A soul continues into another mode of being.
38%
Can prayer for someone far away affect them?
Prayer reaches because God or a cosmic ordering acts on the prayed-for.
38%
Are coincidences ever more than coincidence?
What looks like coincidence is providence — there is no such thing as a real coincidence.
38%
Are the dead morally present to the living?
The dead are present through divine memory, communion of saints, or ancestor presence.
37%
Is divine omniscience compatible with human freedom?
The human observer is in time, but God's vantage is not — and foreknowledge is not foreordering.
34%
Does meditation reveal something genuinely timeless?
Meditation participates in a real eternity — divine or cosmic — that the bounded human observer ordinarily cannot reach.
34%
Does prayer change God's mind?
God sees from outside time; prayer doesn't change God's mind, but it is part of how providence is enacted.
34%
Should we trust expert testimony when we can't verify it?
Trust expertise whose conclusions a competent mind can in principle reproduce.
31%
Is religious revelation a real source of knowledge?
Revelation is evaluable by reason — and not above it.
31%
Does an LLM 'know' the things it correctly produces?
An LLM can produce correct outputs but not reason to them; useful, not knowing.
31%
What makes someone the same person over time?
You are a soul — what persists through change is the non-bodily aspect.
30%
Is the late-stage dementia patient still the person their spouse married?
The soul persists; the cognitive change is the body's, not the person's.
30%
If a teleporter copied and destroyed you, would you have survived?
The soul accompanies the person; engineering can't transfer it.
30%
Could an AI have a mind that matters?
An AI’s standing is constituted by the relations it enters.
14%
Do animals have moral standing comparable to humans?
An animal's standing is constituted by its place in the relational fabric.
11%
Could a fetal brain organoid in a petri dish be conscious?
The organoid's standing is constituted by the relations of care around its production.
11%
9 unaligned
Can a civilization recover from collapse?
Schools split: 66% / 18% / 8%
—
Does history have a direction or meaning?
Schools split: 36% / 23% / 19%
—
Does the second law of thermodynamics mean something morally?
Schools split: 66% / 18% / 8%
—
How is knowledge of reality produced?
Schools split: 24% / 17% / 13%
—
Is environmental damage ever truly permanent?
Schools split: 66% / 18% / 8%
—
Is salvation, liberation, or fulfillment individual or communal?
Schools split: 14% / 14% / 4%
—
Is truth universal, tradition-bound, situated, or constructed?
Schools split: 66% / 16% / 10%
—
What kind of religious-theological authority does the tradition recognize?
Schools split: 42% / 16% / 13%
—
Who is the moral primary — the individual, the community, the cosmos, the class, or the species?
Schools split: 38% / 28% / 16%
—
Information · 4 dilemmas, all mainstream
Is anything truly lost when someone forgets?
Information is conserved — the personal pattern is held even when an individual mind loses it.
39%
Does deleting your data online destroy something real?
Information at the cosmic level isn't destroyed; deletion only obscures access.
39%
Could the dead, in principle, be brought back?
The information that constitutes a person is conserved; restoration is in principle possible.
39%
Is forgiveness ontologically possible?
The offense persists ontologically; forgiveness is real moral work, but it doesn't erase what was.
39%