Search results
Results from the WOW.Com Content Network
The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa.
From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical (the same) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so ...
The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics – a commentary which is full of the most ingenious and original views, – not only asserts to the law of Identity a coordinate dignity with the law of Contradiction, but, against Aristotle, he maintains that the principle of Identity, and not the principle of ...
The two senses of sameness are linked by two principles: the principle of indiscernibility of identicals and the principle of identity of indiscernibles. The principle of indiscernibility of identicals is uncontroversial and states that if two entities are identical with each other then they exactly resemble each other. [17]
Gottfried Leibniz's Principle of the identity of indiscernibles states that two things are identical if and only if they share the same and only the same properties. This is a principle which defines identity rather than difference, although it established the tradition in logic and analytical philosophy of conceiving of identity and difference as oppositional.
In some contexts one considers the more general notion of order-indiscernibles, and the term sequence of indiscernibles often refers implicitly to this weaker notion. In our example of binary formulas, to say that the triple ( a , b , c ) of distinct elements is a sequence of indiscernibles implies
In metaphysics, identity (from Latin: identitas, "sameness") is the relation each thing bears only to itself. [1] [2] The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles (if x and y share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person ...
This distinction is relevant for the principle of identity of indiscernibles, which states that two things are identical if they are indiscernible, i.e. if they share all their properties. [14] This principle is usually defined in terms of pure properties only.