1. “Paris” is equivalent to “the capital of France.”
The referent of the term “Paris” has a fundamental set of characteristics that are the same as those of the referent of the phrase “the capital of France.” Applying the knowledge that two terms are equivalent when their referents have all the same characteristics, we can conclude that “Paris” and “the capital of France” must be equivalent.
2. “Cat” is not equivalent to “dog.”
The fundamental characteristics of the category “cat” are different from those of the category “dog.” Cats meow whereas dogs bark; cats arch their backs whereas dogs bare their teeth, etc. Applying the knowledge that two terms are not equivalent when their referents don’t have all the same characteristics, we can conclude that “cat” and “dog” must be non-equivalent terms.
3. 1+1 = 2
This example illustrates more precisely what is meant by equivalence. As you will have learned in your math classes, 1 added with itself equals 2. In any equation, we could substitute “2” with “1+1” or vice versa. For example:
2+2 = 4 or (1+1)+2 =4
Similarly, in any sentence in which “Paris” occurs, we can replace it with “the capital of France” by the principle of identity.
[Activity]: Come up with your own example of a pair of equivalent terms, as well as a pair of non-equivalent terms. Use the identity principle to explain why these terms are/aren’t equivalent. When you’re done, share your examples with a classmate so that you can check over each other’s work.