I recently was told about a conversation in which a Popperian assured his interlocutor that, "The only valid form of reasoning is deductive reasoning, so if someone says, 'I'm not using deductive reasoning,' that means they are admitting they are using invalid reasoning."
Now, the first bit of stupidity present in this argument is that... not one bit of it is deductive! In other words, by the arguer's own argument, his argument is itself invalid.
When it comes to the practical consequences of believing such rubbish, it is difficult to know what to say. Popperians, of course, regularly employ inductive reasoning, or not one of them would be left alive today. I recall one Popperian telling me, on hearing that I was moving to Hackney (in London), "Do you have any idea what the crime rate is there?" Clearly, this Popperian thought the past crime rate in Hackney would be a good predictor of the future crime rate there, about as plainly an inductive argument as we might hope to see.
In any case, I'm presently reading Stephen Toulmin's The Uses of Argument, and he lists the following examples of problems, for each of which defending one's answer to the problem requires different "logical types" of arguments:
"who will be selected to play in the American Davis Cup team against Australia, whether Crippen was justly found guilty of the murder of his wife, whether the painter Piero della Francesca fully deserves the praise which Sir Kenneth Clark bestows upon him, whether Professor Fröhlich's of super-conductivity is really satisfactory, when the next eclipse of the moon will take place, or the exact nature of the relation between the squares on the different side of a right-angled triangle."
Now, the only one of these case for which an appropriate defense of one's answer is deductive in nature is the geometric one; presumably, our insouciant Popperian mentioned above would have to hold that any argument put forward in any of the other cases was invalid; all that one can do in any of those cases is put forward a 'bold conjecture' and see if it falsified.
How would he react if he were in Crippen's shoes, and the judge told him, as he stood in the dock, "Look, there is no deductive method of proving you guilty or not, and any other method of 'reasoning' is merely a defective attempt at deductive reasoning. So I'm just going to put out the bold conjecture that you are guilty, and have you executed. Then I'll wait to see if my conjecture is refuted"? Or what if he and I are planning to travel to Phoenix, and I tell him, "Fine, that train has gotten passengers to Arizona in the past, but that is no reason to think it will continue to do so in the future. Instead, I put forward the bold conjecture that there are magical fairies who will transport us there if we just stand here long enough, clicking our heels together and repeating, "There's no place like Phoenix; there's no place like Phoenix."
No one would entertain this nonsense for a moment but for the fact that it holds out the promise of easy answers for vexing philosophical problems. But, as we know, there ain't no easy answers.