Work #1690 · Mature period
Logical Investigations (fragments)
Chrysippus's 3rd-century BCE foundational works on Stoic propositional logic — the five indemonstrable argument forms and the theory of the lekton
Chrysippus of Soli
· c. 250 BCE
· Ancient Greek
· Philosophical treatises (fragments preserved in later sources)
Tradition: Stoic logic / Hellenistic philosophy
The five indemonstrable argument forms and the foundations of propositional logic
Chrysippus's logical works (of which Diogenes Laertius catalogues over 300 titles on logic alone) survive only in fragments and reports preserved by Diogenes Laertius, Sextus Empiricus, Galen, Alexander of Aphrodisias, and others. The central achievement is propositional logic based on the five indemonstrable argument forms: (1) modus ponens, (2) modus tollens, (3) the denial of a conjunction, (4) exclusive disjunction with one disjunct affirmed, (5) inclusive disjunction with one disjunct denied. Chrysippus also developed the theory of the lekton (the "sayable" or propositional content), which is an incorporeal, providing a sophisticated theory of meaning. These logical innovations were largely forgotten until rediscovered by modern logicians, who recognised Chrysippean logic as a genuine anticipation of propositional calculus.
Author
Editions cited
- Fragments collected in SVF II (von Arnim), Logik; discussed in A.A. Long and D.N. Sedley, The Hellenistic Philosophers (Cambridge UP, 1987), vol. 1, chs. 31, 34-38; Susanne Bobzien, "Chrysippus and the Epistemic Theory of Vagueness" (Proceedings of the Aristotelian Society, 2002); Benson Mates, Stoic Logic (Berkeley, 1953; 2nd edn. 1961)
School Embodiments
Stoicism
35%
Foundational Stoic logical system; Chrysippus's logic defined the Stoic organon.
"The five indemonstrables: (1) If p then q; p; therefore q." (Diogenes Laertius VII.80-81)
The five indemonstrable argument forms are a genuine anticipation of propositional calculus.
"Chrysippus's five indemonstrables correspond to the basic inference rules of modern propositional logic." (Benson Mates, Stoic Logic)
Rationalism
15%
Purely rational analysis of the structure of valid inference.
"Chrysippus held that only what is demonstrable from the indemonstrables is valid." (Sextus Empiricus)
Rediscovered by modern analytic logicians as a genuine anticipation of truth-functional logic.
"Stoic logic, especially Chrysippus's, is a genuine propositional logic." (Benson Mates)
The theory of the lekton (sayable) provides a sophisticated account of propositional content.
"The lekton is what is signified — an incorporeal, neither body nor void." (Sextus Empiricus)
Realism
5%
Realist about logical structure: valid inference tracks objective truth.
"A sound argument leads from true premises to a true conclusion." (Chrysippus, via Sextus)
Internal Tensions
The incorporeal status of the lekton sits uneasily with Stoic corporeal ontology; the relationship between Stoic logic and Stoic physics remains a subject of scholarly debate.
⧖
I. Time
Stoic cyclical cosmic time; logical truths hold across conflagrations.
Attributes
Extent: Infinite
Ontological Status: Substantival
Grain: Continuous
Freedom: Deterministic
Traversability: Cyclical
Direction: Uni-directional
Dimensionality: One
✦
II. Space
The Stoic finite cosmos; logical structure is independent of spatial location.
Attributes
Extent: Finite
Ontological Status: Substantival
Curvature: not engaged
Dimensionality: Three
Locality: Local
◉
III. Matter
Stoic corporeal ontology; the lekton (sayable) is notably incorporeal — a rare exception.
Attributes
Extent: Finite
Ontological Status: Substantival
Conservation: Conserved
Dimensionality: Three
Locality: Local
◎
IV. Observer
The rational agent who grasps propositions and follows valid inferences.
Attributes
Time Instance: Single
Space Instance: Single
Knowledge Extent: Mediated
Knowledge Retainment: Total
Physicality: Embodied
Agency: Both
Number: Plural
Metaphysical Agency: Cosmic-ordering
⚡
V. Energy
Stoic pneuma and conflagration cycle.
Attributes
Extent: Finite
Ontological Status: Substantival
Conservation: Conserved
Dispersibility: Reversible
⧉
VI. Information
Discrete propositions (lekta) as the bearers of logical content; foundational for information-theoretic semantics.
Attributes
Ontological Status: Substantival
Cosmic Conservation: Conserved
Personal Conservation: Non-conserved
Granularity: Discrete
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 Logical Investigations (fragments) resolves each dilemma
51 resolved positions across 4 dimensions, including 15 distinctive where the majority of schools go the other way · 6 unaligned.
Each dimension is sorted so minority positions come first. Mainstream positions are folded into an expandable list.
Time · 9 dilemmas · 5 distinctive
Persistence, the future, and the direction of becoming.
Distinctive · only 9% of schools agree
(18/202)
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 9% of schools agree
(18/202)
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 9% of schools agree
(18/202)
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%)
Distinctive · only 17% of schools agree
(35/202)
How much weight do future people deserve?
If a billion people will exist in the 25th century, do their interests count for as much as the interests of a billion people alive now? The answer turns on what kind of reality the future has.
Past, present, and future are bound in cycles — duties span generations as a matter of course.
On these views, time is not a one-way arrow but a structure of return: cosmic cycles, karmic cycles, the seasons, the succession of generations. To act now is always also to act for the ancestors who shaped your inheritance and for the descendants who will …
Roads not taken
Future people are as real as you are — and their interests count for as much. (47%) ·
Time arises from events or from a deeper substrate — the future is not yet. (32%) ·
The future branches — what we owe depends on which branch we create. (2%)
Distinctive · only 17% of schools agree
(35/202)
Is regret rational?
If the past is fixed and unchangeable, what kind of mental act is regret? An error, a duty, a lesson, a perspective on a moment that is still in some sense present?
The past is part of a cycle one keeps returning to; regret is one of the gates of the cycle.
On cyclical views, the past is not a fixed thing behind you — it is part of the ongoing structure of return: karmic cycles, cosmic cycles, the cycle of seasons and generations. Regret, on these views, is less about an unchangeable past and more about …
Roads not taken
The past is as real as the present; regret is a real attitude toward a real thing. (47%) ·
The past is not a thing now; regret is the present holding what is no longer. (32%) ·
Other branches exist; regret tracks roads not taken that are nonetheless real. (2%)
4 mainstream positions
Do we owe extinct species something we cannot give them?
Past beings are part of the cycle; we owe them what we owe ancestors.
17%
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, all mainstream
Is the world created from nothing?
Yes — matter was created and is conserved as a real substance.
55%
Is the physical world fully real?
Yes — the physical world is fully real, mind-independent, persisting.
55%
Does matter have intrinsic moral standing?
Matter is morally considerable insofar as it is created or conserved good.
55%
What is money?
Money is a real institution with intrinsic features.
54%
What is a nation?
A nation is a real moral community with intrinsic character.
54%
What makes someone male or female?
Sex is a real biological kind with given content.
54%
Should we edit the human germline?
Human nature is a real biological kind given by reproductive biology or by creation; editing the germline transgresses what is given.
54%
Observer · 37 dilemmas · 5 distinctive
Mind, agency, and the knower's relation to the known.
Distinctive · only 6% of schools agree
(12/202)
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. (37%) ·
Yes — bits, quanta, computational substrate. (13%)
Distinctive · only 6% of schools agree
(12/202)
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. (37%) ·
Yes — naturalist quanta of experience. (13%)
Distinctive · only 6% of schools agree
(12/202)
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. (37%) ·
Stored — discrete engrams, traces, weights. (13%)
Distinctive · only 17% of schools agree
(35/202)
Is environmental damage ever truly permanent?
Extinction is forever; soil erosion takes centuries to repair; the carbon we emit will warm the climate for millennia. But whether 'forever' or 'millennia' means what they say depends on what kind of process the universe is.
Loss is part of cycles; what disappears returns in another form.
On cyclical views, what is lost in one phase of the cycle reappears in another. The forest cleared today is the forest that grows back centuries hence; the species extinct now is the niche occupied by a successor species over geological time. Loss is real …
Roads not taken
Damage is real and permanent on the relevant timescales. There is no recovery; there is only limitation. (66%) ·
From the standpoint of the One, the categories of permanence and loss are conventional. (8%) ·
What appears irreversible is reversible by the right action. (5%)
Distinctive · only 17% of schools agree
(35/202)
Can a civilization recover from collapse?
Rome fell; Maya cities emptied; Bronze Age trade networks collapsed in a single generation. Whether what was lost can be recovered — or whether collapse is structurally final — depends on what kind of process civilization is.
Civilization rises and falls in cycles; recovery is structural to history.
On cyclical views, the pattern of rise and fall is itself the structure of historical time. What appears as catastrophic loss in one phase is the condition for emergence in the next. Specific configurations are not preserved across cycles, but the underlying pattern that supports …
Roads not taken
Civilizational complexity is hard to build and easy to lose; recovery is at best partial. (66%) ·
From the One's vantage, civilizational categories are themselves conventional. (8%) ·
Civilization is the kind of order that can in principle be restored. (5%)
26 mainstream positions
Does the second law of thermodynamics mean something morally?
Local entropy increase is part of a cycle; the moral category is participation in the cycle.
17%
Could causation work backwards?
Time is structured as return; 'forward' and 'backward' are local features of the cycle.
17%
Is the asymmetry between memory and anticipation a real feature of time, or just of us?
Memory and anticipation are phases of a cycle that visits both directions.
17%
Is the arrow of time a real feature of the cosmos, or only of how we describe it?
Within a cycle there is a direction; across the cycle there isn't.
17%
When does a person begin?
A person exists from conception — when a new being comes into existence.
54%
What is marriage?
Marriage has a given form — it’s a kind of thing we recognize, not make.
54%
Does environmental harm in another country bind me morally?
Moral obligation tracks the relations one is in; distance does matter, structurally.
50%
What is our place in nature?
Active in a real nature — we cultivate, steward, transform.
48%
Should we colonize space?
Cultivating worlds beyond Earth is the next form of stewardship.
48%
Is genetic engineering of food stewardship or domination?
Genetic modification is cultivation by other means.
48%
What happens to "you" when you die?
A soul continues into another mode of being.
37%
Can prayer for someone far away affect them?
Prayer reaches because God or a cosmic ordering acts on the prayed-for.
37%
Are coincidences ever more than coincidence?
What looks like coincidence is providence — there is no such thing as a real coincidence.
37%
What makes someone the same person over time?
You are your body — continuity is bodily continuity.
36%
Is the late-stage dementia patient still the person their spouse married?
Same body, same person — even when the cognitive pattern has changed.
36%
If a teleporter copied and destroyed you, would you have survived?
Different body, different person — you died in the scanner.
36%
Are the dead morally present to the living?
The dead are present through divine memory, communion of saints, or ancestor presence.
35%
Is divine omniscience compatible with human freedom?
The human observer is in time, but God's vantage is not — and foreknowledge is not foreordering.
33%
Does meditation reveal something genuinely timeless?
Meditation participates in a real eternity — divine or cosmic — that the bounded human observer ordinarily cannot reach.
33%
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.
33%
Should we trust expert testimony when we can't verify it?
Trust expertise whose conclusions a competent mind can in principle reproduce.
32%
Is religious revelation a real source of knowledge?
Revelation is evaluable by reason — and not above it.
32%
Does an LLM 'know' the things it correctly produces?
An LLM can produce correct outputs but not reason to them; useful, not knowing.
32%
Could an AI have a mind that matters?
No — minds are not the kind of thing we engineer.
30%
Do animals have moral standing comparable to humans?
Moral standing comparable to humans requires what only humans have.
29%
Could a fetal brain organoid in a petri dish be conscious?
Without ensoulment, an organoid is tissue, not a person.
29%
6 unaligned
Does history have a direction or meaning?
Schools split: 37% / 23% / 19%
—
How is knowledge of reality produced?
Schools split: 25% / 17% / 13%
—
Is salvation, liberation, or fulfillment individual or communal?
Schools split: 15% / 14% / 4%
—
Is truth universal, tradition-bound, situated, or constructed?
Schools split: 65% / 16% / 10%
—
What kind of religious-theological authority does the tradition recognize?
Schools split: 44% / 16% / 14%
—
Who is the moral primary — the individual, the community, the cosmos, the class, or the species?
Schools split: 40% / 28% / 14%
—
Information · 4 dilemmas, all mainstream
Is anything truly lost when someone forgets?
Information is lost when a mind forgets; matter and energy continue, but the pattern is gone.
51%
Does deleting your data online destroy something real?
Information is genuinely lost when the substrate that hosted it goes; deletion really destroys.
51%
Could the dead, in principle, be brought back?
The information dissipates with the substrate; restoration is in principle impossible.
51%
Is forgiveness ontologically possible?
The offense is locally constituted by its substrate; when the substrate dissolves, the offense genuinely passes away.
51%