The transitivity of identity is the logical principle that, if a=b, and b=c, then a=c.
For example, if you know that the Morning Star is the same thing as the Evening Star, and you know that the Evening Star is Venus, you can conclude that the Morning Star is Venus.
The transitivity of identity (like rules concerning identity generally) is not always valid in epistemological, modal, or otherwise opaque contexts. For example, if Oedipus knows that his wife is Jocasta, and you know that Jocasta is the mother of Oedipus, you may not conclude that Oedipus knows that his wife is his mother.
In the discussion of transworld identity in the 1960s and 1970s (when the issue came to prominence as a result of developments in modal logic), it was debated whether the notion of transworld identity is genuinely problematic, or whether, on the contrary, the alleged ‘problem of transworld identity’ is merely a pseudo-problem.
Although a criterion of identity in the second (metaphysical) sense might supply us with a criterion of identity in the first (epistemological) sense, it seems that something could be a criterion of identity in the second sense even if it is unsuited to play the role of a criterion of identity in the first sense.
One such argument is Chisholm's Paradox, which relies on the transitivity of identity to produce the result that a series of small changes in the properties of Adam and Noah leads to a world in which Adam and Noah have swapped their roles.
The transitivity of identity is the logical principle that, if a=b, and b=c, then a=c.
The transitivity of identity (like rules concerning identity generally) is not always valid in epistemological, modal, or otherwise opaque contexts.
Identity, they say, is relative: It is possible for objects x and y to be the same F and yet not the same G, (where F and G are predicates representing kinds of things (apples, ships, passengers) rather than merely properties of things (colors, shapes)).
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