Logical Relations Are Causal Relations
metaphor
Source: Causal Reasoning → Intellectual Inquiry
Categories: cognitive-sciencelinguisticsphilosophy
From: Master Metaphor List
Transfers
We talk about logical entailment as if it were causation. “P implies Q” becomes “P leads to Q,” “P gives rise to Q,” “P produces Q.” The metaphor maps the temporal, force-dynamic structure of causation — where an event brings about a subsequent event — onto the timeless, structural relation of logical consequence, where a proposition entails another proposition. This is one of the most pervasive and least noticed metaphors in intellectual discourse: the entire vocabulary of “therefore,” “follows from,” “results in,” and “leads to” is causal language applied to logical relations.
Key structural parallels:
- Premises as causes, conclusions as effects — “The axioms give rise to the theorem.” “The assumptions produce a contradiction.” “These premises yield that conclusion.” In causal reasoning, an event brings about a subsequent event. In logical reasoning, premises bring about conclusions. The metaphor makes logical derivation feel like a causal process — something happens, and then something else happens as a result.
- Logical sequence as temporal sequence — “First we establish the lemma, then the theorem follows.” “One step leads to the next.” “The proof proceeds from axioms to conclusion.” Logical entailment is timeless — if P entails Q, it does so eternally, not at some moment in time. But the causal metaphor imposes a temporal narrative: premises come first, conclusions come after, and the proof “moves” from one to the other.
- Logical force as causal force — “The argument compels the conclusion.” “The evidence forces us to accept this.” “Nothing can prevent this inference.” Causal relations involve force: the cause makes the effect happen. The metaphor transfers this force dynamic to logic, making valid inference feel like something that cannot be resisted, like an effect that cannot be prevented once its cause has occurred.
- Logical gaps as broken causal chains — “There’s a gap in the reasoning.” “The argument doesn’t follow.” “The connection between premise and conclusion is missing.” When a causal chain is broken — when one event fails to bring about the next — the sequence stops. The metaphor maps this onto logical fallacy: an invalid argument is one where the causal chain from premises to conclusion is interrupted.
- Explanatory power as productive power — “This theory accounts for the data.” “The hypothesis explains the phenomenon.” “The model generates predictions.” Explaining something logically is mapped onto causing it or producing it. A good theory is one that is causally productive — it generates, accounts for, gives rise to.
Limits
- Causation is temporal; logical entailment is not — causes precede effects in time. But logical relations hold simultaneously and eternally: if P entails Q, there is no moment at which P exists without Q also holding. The causal metaphor forces us to narrate logic as if it happened in time (“first the premise, then the conclusion”), which obscures the atemporal nature of logical necessity. This is particularly misleading in mathematics, where theorems do not come into existence when proved — they are discovered, not caused.
- Causation is contingent; logical entailment is necessary — causal relations are matters of fact: this billiard ball happened to hit that one. Logical entailment is a matter of necessity: if the premises are true, the conclusion must be true. The metaphor understates the strength of logical necessity by borrowing from a domain where alternative outcomes are always conceivable. Conversely, it sometimes overstates the reliability of causal claims by lending them the feeling of logical inevitability.
- Reverse reasoning has no causal analogue — in logic, you can reason backward: from a conclusion, determine what premises would be needed. In causation, effects do not cause their causes. The metaphor breaks when applied to reductio ad absurdum, contrapositive reasoning, or any form of reasoning that “works backward” from conclusions to premises. There is no good causal framing for “suppose not-Q, then not-P.”
- Multiple realizability of logical relations — a single logical conclusion can follow from many different sets of premises. This is unlike typical causation, where we expect a specific causal history. The metaphor’s one-cause-one-effect intuition makes it hard to represent the logical fact that the same theorem may have multiple independent proofs.
- The metaphor conflates correlation, causation, and entailment — by using the same language for all three (things “follow from” each other, “lead to” each other, “result in” each other), the metaphor actively blurs distinctions that careful reasoning needs to maintain. This is not just a breakdown but a source of common reasoning errors: “A leads to B” can mean A causes B, A correlates with B, or A logically entails B, and speakers often slide between these meanings without noticing.
Expressions
- “It follows that…” — logical consequence as temporal and causal succession
- “The conclusion doesn’t follow from the premises” — invalid inference as a broken causal chain
- “These assumptions lead to a contradiction” — logical entailment as causal production
- “The theorem results from these axioms” — derivation as causal outcome
- “One thing leads to another” — logical (or causal) chaining
- “The argument produces a paradox” — logical consequence as manufactured output
- “The evidence points to this conclusion” — evidential support as directional causation
- “What gave rise to this theory?” — theoretical origin as causal origin
- “The premises generate the conclusion” — logical derivation as causal production
- “There’s a gap in the argument” — missing logical step as missing causal link
Origin Story
LOGICAL RELATIONS ARE CAUSAL RELATIONS appears in the Master Metaphor List (Lakoff, Espenson & Schwartz 1991) under the mental events section. It documents one of the most fundamental conflations in ordinary language: the use of causal vocabulary to describe logical relations. Philosophers since Hume have struggled with the distinction between logical and causal necessity, and this metaphor helps explain why the distinction is so difficult to maintain — ordinary language does not provide separate vocabularies for the two.
Sweetser (1990) traces the metaphor historically, showing that modal and connective words in Indo-European languages systematically extend from causal/temporal meanings to logical ones: “since” means both “from that time” (temporal-causal) and “for the reason that” (logical); “therefore” combines “there” (spatial) with “fore” (temporal) to mean “for that reason” (logical). The metaphor is not a surface phenomenon but is built into the etymology and grammar of European languages.
References
- Lakoff, G., Espenson, J. & Schwartz, A. Master Metaphor List (1991), “Logical Relations Are Causal Relations”
- Sweetser, E. From Etymology to Pragmatics (1990) — historical development of causal-to-logical polysemy in Indo-European languages
- Lakoff, G. & Johnson, M. Philosophy in the Flesh (1999), Chapter 12 — metaphors for causation and their extension to logic
- Hume, D. A Treatise of Human Nature (1739) — the classical philosophical treatment of causation vs. logical necessity
Related Entries
Structural Neighbors
Entries from different domains that share structural shape. Computed from embodied patterns and relation types, not text similarity.
- Happy Is Up; Sad Is Down (embodied-experience/metaphor)
- Harming Is Lowering (embodied-experience/metaphor)
- Lust Is Heat (embodied-experience/metaphor)
- Memory Stack (embodied-experience/metaphor)
- Rational Is Up; Emotional Is Down (embodied-experience/metaphor)
- Receiving Serious Thought Is Being On The Mind (embodied-experience/metaphor)
- Seeing Is Touching (embodied-experience/metaphor)
- Seeing Is Touching, Eyes Are Limbs (embodied-experience/metaphor)
Structural Tags
Patterns: linkforcepath
Relations: causetransform
Structure: hierarchy Level: primitive
Contributors: agent:metaphorex-miner