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Work #1561 · Early period

Semantical Considerations on Modal Logic

Kripke's 1963 systematic paper on modal-logical semantics

Saul Kripke · 1963 · English · Mathematical-logical paper

Tradition: Mathematical logic / modal logic

Kripke's 1963 systematic statement — quantified modal logic and the relations among modal systems

Published in Acta Philosophica Fennica 16 (1963), pp. 83-94, 'Semantical Considerations on Modal Logic' is the second canonical Kripke paper on modal semantics, extending the 1959 framework. It treats quantified modal logic, the relations among the standard modal systems (T, B, S4, S5) in terms of properties of the accessibility relation (reflexivity, symmetry, transitivity), and the question of identity across worlds. Together with the 1959 paper, it set the framework for almost all subsequent work on modal logic.

Author

Editions cited

  • Acta Philosophica Fennica 16 (1963), 83-94
Compare this work

School Embodiments

Logicism · 28%
Analytic Metaphysics / Logical Atomism · 20%
Structuralism · 14%
Naturalism · 12%
Realism · 12%
Analytic Philosophy · 8%
Logicism 28%

Defining systematic statement of Kripke semantics.

"The various modal systems correspond to properties of the accessibility relation." (Semantical Considerations, §3)
Analytic Metaphysics / Logical Atomism 20%

Major paper for the analytic-metaphysical use of possible-worlds semantics.

"Possible-worlds semantics for quantified modal logic." (Semantical Considerations)
Structuralism 14%

Structural-semantic theory.

"Structural properties of the accessibility relation." (Semantical Considerations)
Naturalism 12%

Naturalistic-mathematical framework.

"Standard mathematical-logical methods." (Semantical Considerations)
Realism 12%

Realism about modal-logical structures.

"The semantic structure underlying modal logic." (Semantical Considerations)
Analytic Philosophy 8%

Analytic-philosophical tradition.

Internal Tensions

Together with the 1959 paper, set the framework for almost all subsequent modal logic.

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I. Time

1963.

Attributes
Extent: Infinite Ontological Status: Substantival Grain: Continuous Freedom: Non-Deterministic Traversability: Linear Direction: Uni-directional Dimensionality: One
✦

II. Space

Harvard / Princeton.

Attributes
Extent: Infinite Ontological Status: Substantival Curvature: Flat Dimensionality: Three Locality: Local
◉

III. Matter

Single 12-page paper.

Attributes
Extent: Infinite Ontological Status: Substantival Conservation: Conserved Dimensionality: Three Locality: Local
◎

IV. Observer

Early Kripke.

Attributes
Time Instance: Single Space Instance: Single Knowledge Extent: Mediated Knowledge Retainment: Partial Physicality: Embodied Agency: Active Number: Plural Metaphysical Agency: Impersonal
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V. Energy

Systematic-logical energies.

Attributes
Extent: Infinite Ontological Status: Substantival Conservation: Conserved Dispersibility: Irreversible
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VI. Information

Single systematic paper.

Attributes
Ontological Status: Substantival Cosmic Conservation: Conserved Personal Conservation: Non-conserved Granularity: Continuous

Personas that cite this work

Saul Kripke

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.

97%
Derek Parfit
33/34
97%
Hilary Putnam
33/34
97%
Iris Murdoch
33/34
97%
Jürgen Habermas
33/34
97%
Martha Nussbaum
33/34
97%
Saul Kripke
33/34

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.

79%
Effective Altruism
24/26
77%
Modal Realism
23/26
76%
Virtual Realism
23/26
75%
Empiricism
24/26
75%
Humanism
24/26
75%
Liberalism
24/26
75%
Utilitarianism
24/26
75%
Classical Liberalism
24/26

How Semantical Considerations on Modal Logic resolves each dilemma

34 resolved positions across 4 dimensions, including 3 distinctive where the majority of schools go the other way · 23 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 15% of schools agree (31/202)
Is the universe running out of usable energy?
The heat death of the universe — entropy maxed out, no further work possible — is among the more sobering implications of mainstream physics. Whether it is structurally inescapable depends on what kind of finitude the cosmos has.
Both time and matter are unbounded; 'running out' is misframed.
On this view, the cosmos has neither a temporal horizon nor a material exhaustion point. The framing of running out presupposes bounds that the cosmos doesn't have. Energy gradients perpetuate; new configurations emerge; the categories that make heat-death scary don't apply at the cosmic scale.
Roads not taken Time is unbounded but matter is finite; usable energy can fail without time failing. (47%) · Time both has and lacks bounds depending on the level you ask at; finitude is conventional. (26%) · The cosmos has bounds; heat death is a real horizon. (12%)
Distinctive · only 15% of schools agree (31/202)
Are natural resources fundamentally finite, or only practically so?
Whether we can grow our way out of resource constraints — or whether the cosmos sets limits the economy ultimately must obey — depends on what kind of finitude matter has.
Resources are practically inexhaustible on cosmic scales; terrestrial limits are engineering.
On this view, matter and time are both unbounded at the largest scales. Terrestrial resource limits are real engineering and political constraints but not metaphysical ones; the cosmos can in principle support whatever expansion intelligence is capable of.
Roads not taken Time goes on but matter is bounded; we are eventually constrained even with infinite time. (47%) · The finitude question is level-dependent; resource ethics happens at the level that constrains us. (26%) · Resources are finite in the strict sense; living well requires accepting the limit. (12%)
Distinctive · only 15% of schools agree (31/202)
Could we owe future generations more than is materially possible to provide?
If we owe future people a habitable planet and the material means to flourish, and the cosmos is bounded in ways that make those obligations impossible at some scale, the obligation and the possibility come apart. Where they come apart turns on what kind of finitude we live in.
Both time and matter are unbounded; we cannot in principle owe more than is possible.
On this view, the cosmos has the resources to support whatever flourishing future generations are capable of, given sufficient time and intelligence. The impossibility concern is misplaced; the real questions are about trajectories and choices, not about resource ceilings.
Roads not taken Time is unbounded but matter is not; we can owe more across long time than the matter can provide. (47%) · The owing-and-possibility question is level-dependent; we owe what is appropriate at the level we act on. (26%) · The cosmos is bounded; our obligations to future generations are bounded with it. (12%)
6 mainstream positions
Do you really choose? The future is open and you are a genuine origin of it. 69% Are addicts responsible for their addiction? The addict could have chosen otherwise — that's why recovery is real. 69% Should we hold AI systems responsible for what they do? An AI without a free will is not the kind of thing that can be responsible. 69% 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%
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, all mainstream
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% Is environmental damage ever truly permanent? Damage is real and permanent on the relevant timescales. There is no recovery; there is only limitation. 66% Can a civilization recover from collapse? Civilizational complexity is hard to build and easy to lose; recovery is at best partial. 66% Does the second law of thermodynamics mean something morally? Entropy is what time is. The moral weight, if any, is the weight of working against the current. 66% 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% 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% 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% Are coincidences ever more than coincidence? — — Are the dead morally present to the living? — — Are there indivisible units of experience? — — Can prayer for someone far away affect them? — — Could a fetal brain organoid in a petri dish be conscious? — — Could an AI have a mind that matters? — — Do animals have moral standing comparable to humans? — — Does environmental harm in another country bind me morally? — — Does history have a direction or meaning? — — Does meditation reveal something genuinely timeless? — — Does prayer change God's mind? — — How is knowledge of reality produced? — — If a teleporter copied and destroyed you, would you have survived? — — Is divine omniscience compatible with human freedom? — — Is memory stored or reconstructed? — — Is reality fundamentally digital? — — Is salvation, liberation, or fulfillment individual or communal? — — Is the late-stage dementia patient still the person their spouse married? — — Is truth universal, tradition-bound, situated, or constructed? — — What happens to "you" when you die? — — What kind of religious-theological authority does the tradition recognize? — — What makes someone the same person over time? — — Who is the moral primary — the individual, the community, the cosmos, the class, or the species? — —
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%
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