Though Socrates’ discovery marked the beginning of philosophy as we know it, and is the origin of analytic philosophy in particular, the method of counter-examples hasn’t been hugely important in the history of philosophy. Plato himself turned to reductios (for example in the Parmenides) and Aristotle’s methods are largely constructive. When Descartes wanted to prove the dualism of mind and matter, he didn’t do so by counter-exampling identity theory; similarly Hume and the rationalist theory of causation. The last two authors proceeded from first principles, and this was the dominant method of philosophy even in the heyday of analysis. What are Frege’s great counter-examples? Russell’s?

That example, in the Republic, showed a plausible theory false, but this was not the only use to which Socrates put counter-examples. He used them positively as well: the very fact that the method of counter-examples works shows that analysis (or the answering of ‘What is X?’ questions) is a search for property-identities. Analysis cannot rest content with illumination by convincing paradigms. You cannot answer the question, “What is justice?” simply by pointing to the Supreme Court, or the Constitution. You must designate justice (the property) another way, a way that is easier to understand than designating it as justice. And when you do this, you are open to counter-examples.

The method of counter-examples was introduced to philosophy by that under-achieving gadfly, Socrates, and it was one of Plato’s great achievements that he transcribed some of the conversations in which Socrates used this method. Justice is not the repayment of what you owe, Socrates argued, because it is not an exercise of justice when you return a weapon that you owe to a homicidal maniac.

Today, however, counter-examples are even more rampant than in Plato’s Socratic dialogues. And they often take the form of thought experiments. Consider Kripke. When he wanted to refute the Description Theory of Names, he invited you to imagine that Gödel (whose name you understand as equivalent to "the person who proved the incompleteness of arithmetic") had stolen his ideas from a man named Schmidt. If this were so, would the name ‘Gödel’ designate Schmidt in your dialect? When Judith Jarvis Thompson attacked theories concerning the wrongness of abortion, she asked you to think of a person hooked up to a famous violinist, who would die if disconnected. (Is this person obliged to give up all her mobility on account of the violinist?) When David Chalmers wanted to prove the dualism of mind and matter, he invited you to think about zombies: systems that are physically just the same as a conscious being and which yet lack consciousness. The very fact that one can coherently conceive such a system shows that mind cannot be the same as body. It is worth noting that at bottom, Chalmer’s argument is very like Descartes’—but Descartes didn’t boil it all down to a counter-example. Of course, this probably all goes back to Nelson Goodman, whose grue emeralds constituted “the new riddle of induction” in 1953, and Edmund Gettier, whose three page paper in Analysis (1963) spawned 75% of epistemology as it was conducted in the following quarter century.

Unfortunately, counter-examples now take up a large space in contemporary analytic philosophy. Imagine putting forward a theory of justice, or of consciousness, or of knowledge. Very likely, the theory will contain a property identity claim somewhere, and within months of its publication, the schools will be full of counter-examples. The problem with this is that often the counter-examples are unmotivated. They suck sustenance from theories struggling to find their feet. In science, as we know, many theories survive despite apparent counter-examples. Given time, these theories either find ways to address the counter-example, or die away because there are too many such. Rarely do they struggle with a single counter-example.

In philosophy, it seems to me, counter-examples have not proved uniformly healthy. Sometimes, as I just remarked, they result in the premature demise of theoretical approaches. Sometimes this premature demise stems from the mere conceivability of a counter-example—with no serious effort to set standards for conceivability. (Should we say that something is conceivable merely because somebody claims to have conceived it?) Perhaps even more damagingly, the excessive use of counter-examples has led to the undue verbosity of philosophical theorizing, which relies on multiple clauses unequal to each other in theoretical importance.