leibnitz's law
LowAcademic, Philosophical, Technical
Definition
Meaning
The principle that if two entities are identical, then they must share exactly the same properties; often summarized as 'the identity of indiscernibles'.
In philosophy and logic, it is the principle that if two objects are indiscernible in all their properties (i.e., every property true of one is true of the other), then they are one and the same object. In mathematics and computer science, it can refer to the substitution principle that equal things can be substituted for each other without affecting truth.
Linguistics
Semantic Notes
The term is strongly associated with the philosopher Gottfried Wilhelm Leibniz and is a cornerstone of metaphysics and logic. It is often discussed in debates about identity, possible worlds, and the nature of objects. The exact formulation (e.g., identity of indiscernibles vs. indiscernibility of identicals) can vary slightly in different philosophical contexts.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling of 'law' in possessive form can vary ('Leibniz's' or 'Leibniz'') but is consistent with regional possessive conventions.
Connotations
None specific to region.
Frequency
Equally rare and specialized in both varieties, confined to academic discourse.
Vocabulary
Collocations
Grammar
Valency Patterns
Leibniz's law [states/implies/asserts] that...According to Leibniz's law, ...One can appeal to Leibniz's law to show that...The principle known as Leibniz's law...An objection to Leibniz's law is...Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Not used.
Academic
Central term in metaphysics, logic, and philosophy of mind. Used in precise arguments about identity and possibility.
Everyday
Not used.
Technical
Used in formal logic, analytic philosophy, and theoretical computer science (in type theory or formal semantics).
Examples
By Part of Speech
verb
British English
- The argument Leibniz-law-es the two entities, rendering them identical.
American English
- One cannot simply Leibniz's-law two distinct objects into one.
adjective
British English
- The Leibniz-law principle is foundational.
American English
- It was a Leibniz's-law-style argument.
Examples
By CEFR Level
- Philosophers often discuss Leibniz's law in relation to the mind-body problem.
- The purported counterexample to Leibniz's law involved two supposedly identical particles occupying different positions in space-time.
- If mental states have properties that physical states lack, then, by Leibniz's law, they cannot be identical.
Learning
Memory Aids
Mnemonic
Think: 'If two things are truly the SAME (identical), then you can't tell them APART (indiscernible).' Leibniz's Law links Identity and Indiscernibility.
Conceptual Metaphor
IDENTICAL TWINS ARE INDISTINGUISHABLE (If they were perfectly identical in every way, they'd be one person).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating 'law' as 'закон' in a scientific sense (like Newton's law); here it's a 'принцип' or 'положение'.
- The possessive 's' is crucial; it's specifically Leibniz's principle, not a generic 'law of Leibniz'.
- Do not confuse with 'Leibniz's rule' in calculus, which is a different mathematical concept.
Common Mistakes
- Mispronouncing 'Leibniz' as /li:bˈnɪz/; correct is /ˈlaɪbnɪts/.
- Using it to refer to any law about identity, rather than the specific principle of the identity of indiscernibles.
- Confusing 'indiscernibility of identicals' (if identical then indiscernible) with its converse 'identity of indiscernibles' (if indiscernible then identical); the full law often encompasses both.
Practice
Quiz
In which field is Leibniz's Law primarily discussed?
FAQ
Frequently Asked Questions
Often yes, but strictly, 'Leibniz's law' can refer to the conjunction of two principles: the Indiscernibility of Identicals (if x=y, then every property of x is a property of y) and the Identity of Indiscernibles (if x and y share all properties, then x=y). In many discussions, the terms are used interchangeably.
If the Morning Star (Venus) is identical to the Evening Star (also Venus), then anything true of the Morning Star (e.g., it is visible in the morning) must also be true of the Evening Star. If we find a property that differs, they are not identical.
Some argue that 'intensional' contexts (like beliefs or necessity) create problems. For example, Lois Lane believes Superman can fly, but does not believe Clark Kent can fly. According to Leibniz's law, if Superman = Clark Kent, the beliefs should be the same, but they seem not to be. This is known as a failure of substitutivity in intensional contexts.
It is used to argue for or against mind-body identity. If mental states (like feeling pain) have properties (being private, subjective) that brain states (like C-fibers firing) lack, then, by Leibniz's law, they cannot be identical. This challenges physicalist theories of mind.