`Never said it was,' said Uncle Joe; `it's a Reductio ad Absurdum.'

`An Illicit Process of the Minor!' chuckled Uncle Jim.

That's the sort of way they always go on, whenever I'm with them. As if there was any fun in calling me a Minor!

After a bit, Uncle Jim began again, just as we came in sight of the barber's. `I only hope Carr will be at home,' he said. `Brown's so clumsy. And Allen's hand has been shaky ever since he had that fever.'

`Carr's certain to be in,' said Uncle Joe.

`I'll bet you sixpence he isn't!' said I.

`Keep your bets for your betters,' said Uncle Joe. `I mean'--he hurried on, seeing by the grin on my face what a slip he'd made--`I mean that I can prove it, logically. It isn't a matter of chance.'

`Prove it logically!' sneered Uncle Jim. `Fire away, then! I defy you to do it!'

`For the sake of argument,' Uncle Joe began, `let us assume Carr to be out. And let us see what that assumption would lead to. I'm going to do this by Reductio ad Absurdum.

`Of course you are!' growled Uncle Jim. `Never knew any argument of yours that didn't end in some absurdity or other!'

`Unprovoked by your unmanly taunts,' said Uncle Joe in a lofty tone, `I proceed. Carr being out, you will grant that, if Allen is also out, Brown must be at home?'

`What's the good of his being at home?' said Uncle Jim. `I don't want Brown to shave me! He's too clumsy.'

`Patience is one of those inestimable qualities--' Uncle Joe was beginning; but Uncle Jim cut him off short.

`Argue!' he said. `Don't moralise!'

`Well, but do you grant it?' Uncle Joe persisted. `Do you grant me that, if Carr is out, it follows that if Allen is out Brown must be in?'

`Of course he must,' said Uncle Jim; `or there'd be nobody to mind the shop.'

`We see, then, that the absence of Carr brings into play a certain Hypothetical, whose protasis is "Allen is out", and whose apodosis is "Brown is in". And we see that, so long as Carr remains out, this Hypothetical remains in force?'

`Well, suppose it does. What then?' said Uncle Jim.

`You will also grant me that the truth of a Hypothetical--I mean its validity as a logical sequence--does not in the least depend on its protasis being actually true, nor even on its being possible. The Hypothetical "If you were to run from here to London in five minutes you would surprise people", remains true as a sequence, whether you can do it or not.'

`I can't do it,' said Uncle Jim.

`We have now to consider another Hypothetical. What was that you told me yesterday about Allen?'

`I told you,' said Uncle Jim, `that ever since he had that fever he's been so nervous about going out alone, he always takes Brown with him.'