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In a recent post I put forward my own preferred version of “Leibniz’s Law,” or more accurately, the Indiscernibility of Identicals. It’s a bit complicated, so as to get around what are some apparent counterexamples to the simpler principle which is commonly held.

Aside for non-philosophers: philosophers are usually after universal principles, truths which hold in all cases, rather than mere non-universal generalizations, i.e. rough rules of thumb which have exceptions. (An example of the latter: Boys love trucks.) Thus, when a philosophers makes a (universal) claim, other philosophers come along and try to show that it is false with “counterexamples” – real, or even merely possible, examples which show the principle to be false (as it doesn’t apply to them). For example, if someone says that all Texans love tacos, a counterexample to this would be a person who is from Texas and doesn’t like them. Just one counterexample is enough to show a universal claim to be false. When provided with a counterexample, of course, one will often refine, as it were, the original claim (e.g. All native Texans love tacos, or All Texans who appreciate Tex-Mex food love tacos) and the game goes on. This is all in the interest of discovering together what is true and what is false. (In my example, of course, those “refinements” would admit of easy counterexamples too.)

So my principle said, to paraphrase, that for any x and y, x just is (=) y, only if they don’t ever intrinsically differ. (I put this in terms of one having a “mode” at a time if and only if the other also has that mode at that time. Others would call these “intrinsic properties.”)

Here our friend, philosopher and blogger Brandon offered a counterexample, Read More »On an alleged counterexample to Leibniz’s Law – Part 1