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The identity of indiscernibles, also known as Leibniz's Law, is an ontological principle first forumlated by German philosopher Göttfried Wilhelm Leibniz. The principle states that if there is no way of telling two entities apart then they are one and the same. That is, two entities x and y are identical if and only if any predicate possessed by x is also possessed by y and vice versa. So "if it looks like a duck, walks like a duck, and quacks like a duck, then it is a duck". In philosophy, ontology (from the Greek ον = being and λόγος = word/speech) is the most fundamental branch of metaphysics. ...
Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ...
An entity is something that has a distinct, separate existence, though it need not be a material existence. ...
Subfamilies Dendrocygninae Oxyurinae Anatinae Merginae Drake Mallard Duck is the common name for a number of types of bird in the family Anatidae. ...
Symbolic expression
In predicate calculus, the identity of indiscernibles may be written as First-order predicate calculus or first-order logic (FOL) is a theory in symbolic logic that permits the formulation of quantified statements such as there is at least one X such that. ...
- (x)(y)(P)(x=y ↔ (Px ↔ Py))
Controversial applications One famous application of the identity of indiscernibles was by René Descartes in his Meditations on First Philosophy. Descartes concluded that he could not doubt the existence of himself (the famous cogito ergo sum argument), but that he could doubt the existence of his body. From this he inferred that the person Descartes must not be identical to his body, since one possessed a characteristic that the other did not: namely, it could be known to exist. René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ...
Meditations on First Philosophy (subtitled In which the existence of God and the real distinction of mind and body, are demonstrated), written by René Descartes (1596 - 1650) and first published in 1641, expands upon Descartes philosophical system, which he first introduced in his Discourse on Method (1637). ...
René Descartes (1596-1650) The Latin phrase cogito, ergo sum (I think, therefore I am) is possibly the single best-known philosophical statement and is attributed to René Descartes. ...
This argument is normally rejected by modern philosophers on the grounds that it derives a conclusion about what is true from a premise about what people know. What people know or believe about an entity, they argue, is not really a characteristic of that entity. Numerous counterexamples are given to debunk Descartes' reasoning via reductio ad absurdum, such as the following: Reductio ad absurdum (Latin for reduction to the absurd, traceable back to the Greek ἡ εις το αδυνατον απαγωγη, reduction to the impossible, often used by Aristotle) is a type of logical argument where we assume a claim for the sake of argument, arrive at an absurd result, and then...
- 1. Bill, an elementary-school student who has just learned division, knows the quotient of .
- 2. Bill has not learned about exponents, so he cannot know what equals.
- 3. Therefore, has a property that does not: its quotient is known to Bill.
- 4. Therefore, does not equal .
Critique Max Black has arqued against the identity of indiscernibles by counterexample. He claimed that in the symmetric universe where only two symmetrical spheres exist, the two spheres are two distinct objects, even though they have all the properties in common.1 Max Black (1909 - 1988) was a distinguished Anglo-American philosopher, who has been a leading influence in analytic philosophy in the first half of the twentieth century. ...
External links
Notes and references - [1] Metaphysics an Anthology. eds. J. Kim and E. Sosa, Blacwell Publishing, 1999
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