The starting point in evaluating an argument for validity is the definition of a valid argument itself: an argument is valid if and only if it is impossible for the premises to be true while the conclusion is false.
Like many other definitions in logic and mathematics, the definition of a valid argument is formulated in such a way as to exclude all other options – options where, for example, both the premises and the conclusion are true but the argument is invalid nevertheless.
An effective way to show that an argument is invalid is simply to find a counterexample – a situation where we can show that even though the premises are true the conclusion cannot be guaranteed to be so. The conclusion is simply false.
A counterexample serves as a knock-down blow. It would follow that we would want to use it whenever an opportunity presents itself, to get the upper hand over our opponent. That depends. A counterexample can reduce conversation to the level of banality or sophistry. Of course, we can blame the opponent for setting up the situation in the first place, but this rarely leads to constructive answers.
Arguing by counterexample comes naturally, even though counterexamples themselves often don’t. That’s another reason not to abuse the technique. Since I can’t find a counterexample every time I would like to, I want to be cautious lest I should walk into a trap myself.
I had this in mind when I followed a debate last week between an Anglican minister, an agnostic and an atheist on Heresy, a BBC comedy show which, being a comedy and of that title too boot, often crosses freely between silliness and seriousness.
The minister (actually, a born-again Christian) related how finding God led him to enlightenment and knowledge. The agnostic countered that Christianity, and religion generally, is responsible for promoting ignorance and superstition. The Middle Ages were mentioned. To this, the minister replied, with a well-practiced air of benevolence and censoriousness typical of his profession, with a question: and who gave us schools and universities?
A pregnant pause had begun to insinuate itself but, fortunately, its force was dissipated amidst the hurly-burly of the debate and general laughter.
What the agnostic didn’t say but could have said is that England gave football to the rest of the world. Look at England now! It doesn’t follow that you should have a monopoly on something just because you started it or that you do it best.
Raising the level of the debate, one might have said: civilization originated in Mesopotamia. Yes, but that particular vine has withered and degenerated, not least because of the hold religion has on the people of this area.
Medicine, too, traces its roots to shamans, witch doctors, and priests, as do many other things. In a primitive society caught between fear and wonder the minds are susceptible of manipulation and all too eager to hand over power and resources to imposters.
So much for counterexamples. The better route to follow would have been to focus on the absurdities taught by the medieval Schoolmen: Abelard, Scotus, Aquinas and company, and conclude, with relief, that we don’t have them to thank for key hole surgery, the aircraft and the telephone. But that would have been nowhere near as effective as, say, the football counterexample.
Like many other definitions in logic and mathematics, the definition of a valid argument is formulated in such a way as to exclude all other options – options where, for example, both the premises and the conclusion are true but the argument is invalid nevertheless.
An effective way to show that an argument is invalid is simply to find a counterexample – a situation where we can show that even though the premises are true the conclusion cannot be guaranteed to be so. The conclusion is simply false.
A counterexample serves as a knock-down blow. It would follow that we would want to use it whenever an opportunity presents itself, to get the upper hand over our opponent. That depends. A counterexample can reduce conversation to the level of banality or sophistry. Of course, we can blame the opponent for setting up the situation in the first place, but this rarely leads to constructive answers.
Arguing by counterexample comes naturally, even though counterexamples themselves often don’t. That’s another reason not to abuse the technique. Since I can’t find a counterexample every time I would like to, I want to be cautious lest I should walk into a trap myself.
I had this in mind when I followed a debate last week between an Anglican minister, an agnostic and an atheist on Heresy, a BBC comedy show which, being a comedy and of that title too boot, often crosses freely between silliness and seriousness.
The minister (actually, a born-again Christian) related how finding God led him to enlightenment and knowledge. The agnostic countered that Christianity, and religion generally, is responsible for promoting ignorance and superstition. The Middle Ages were mentioned. To this, the minister replied, with a well-practiced air of benevolence and censoriousness typical of his profession, with a question: and who gave us schools and universities?
A pregnant pause had begun to insinuate itself but, fortunately, its force was dissipated amidst the hurly-burly of the debate and general laughter.
What the agnostic didn’t say but could have said is that England gave football to the rest of the world. Look at England now! It doesn’t follow that you should have a monopoly on something just because you started it or that you do it best.
Raising the level of the debate, one might have said: civilization originated in Mesopotamia. Yes, but that particular vine has withered and degenerated, not least because of the hold religion has on the people of this area.
Medicine, too, traces its roots to shamans, witch doctors, and priests, as do many other things. In a primitive society caught between fear and wonder the minds are susceptible of manipulation and all too eager to hand over power and resources to imposters.
So much for counterexamples. The better route to follow would have been to focus on the absurdities taught by the medieval Schoolmen: Abelard, Scotus, Aquinas and company, and conclude, with relief, that we don’t have them to thank for key hole surgery, the aircraft and the telephone. But that would have been nowhere near as effective as, say, the football counterexample.