The saying goes that the hardest thing to put up with is a good example. There is actually a harder thing to put up with – a counterexample. In logic, a counterexample works by supposing that our conclusion is the opposite of what it says. Via a series of moves we then show that the opposite cannot hold, so the original conclusion is true. For example:
If elephants are pink, then elephants have dangly trunks.
If elephants have floppy ears, then if they have dangly trunks, then they are either clever or have no feelings.
Elephants are not clever and elephants have feelings.
The conclusion is: Elephants are not pink.
And this conclusion follows from our premises! To show that it does, we can simply negate it: It is not the case that elephants are not pink. The conclusion follows not because ‘Elephants are pink’ (after we cancel double negation) is false, but because the argument a) is not of the kind where the premises are true and the conclusion is false, and b) because the rules of deduction operate is such a way as to yield the conclusion (I leave out the workings here).
In everyday speech we hardly ever use such arguments, but we do use reductio ad absurdum – often unnecessarily and annoyingly, but mostly to sound clever.
It’s a feature of everyday speech that we use rhetoric and hyperbole. With them our speech sounds exaggerated, without them – dull. We have heard this rehearsed many times: - I shall defend to the last my freedom of speech. - So, that means you can go and offend anyone you please because you believe in freedom of speech? The counterexample here is meant to knock down the sweeping claim made by the first speaker.
In such cases the second speaker deserves to be told that freedom of speech is a privilege, not an obligation, and that discretion is the better part of valor, and that failure to draw the distinction is an affliction of small minds.
Another multiply fallacious example is: - I studied philosophy. – No wonder you are poor. Here, a series of hypothetical syllogisms produces the outcome: I studied philosophy. Anyone who studies philosophy is not practically-minded. Anyone who is not practically-minded has no knack for business. Anyone who has no knack for business is poor. So, anyone who studied philosophy is poor. The logic works, but the maxim of cooperation (in communication) doesn’t.
In the end, absurd is as absurd does.
If elephants are pink, then elephants have dangly trunks.
If elephants have floppy ears, then if they have dangly trunks, then they are either clever or have no feelings.
Elephants are not clever and elephants have feelings.
The conclusion is: Elephants are not pink.
And this conclusion follows from our premises! To show that it does, we can simply negate it: It is not the case that elephants are not pink. The conclusion follows not because ‘Elephants are pink’ (after we cancel double negation) is false, but because the argument a) is not of the kind where the premises are true and the conclusion is false, and b) because the rules of deduction operate is such a way as to yield the conclusion (I leave out the workings here).
In everyday speech we hardly ever use such arguments, but we do use reductio ad absurdum – often unnecessarily and annoyingly, but mostly to sound clever.
It’s a feature of everyday speech that we use rhetoric and hyperbole. With them our speech sounds exaggerated, without them – dull. We have heard this rehearsed many times: - I shall defend to the last my freedom of speech. - So, that means you can go and offend anyone you please because you believe in freedom of speech? The counterexample here is meant to knock down the sweeping claim made by the first speaker.
In such cases the second speaker deserves to be told that freedom of speech is a privilege, not an obligation, and that discretion is the better part of valor, and that failure to draw the distinction is an affliction of small minds.
Another multiply fallacious example is: - I studied philosophy. – No wonder you are poor. Here, a series of hypothetical syllogisms produces the outcome: I studied philosophy. Anyone who studies philosophy is not practically-minded. Anyone who is not practically-minded has no knack for business. Anyone who has no knack for business is poor. So, anyone who studied philosophy is poor. The logic works, but the maxim of cooperation (in communication) doesn’t.
In the end, absurd is as absurd does.
This is beyond me but I enjoyed reading it. Patrick
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