I would take a standard textbook on math, where all the propositions are correct. Write down 99 correct mathematical statements. And then add “Zeus exists”, and compile a text. Then I would argue, that if we have a box, from which we sample randomly 99 balls and they are have the property of being black, we can think with good reason that the next one will be black. And therefore, since 99 of the math propositions in the texts are have the property of being correct, there is good reason to think that “Zeus exists” is also correct. It seems wrong somewhere. But where?

No matter how strong an inductive argument is, it cannot guarantee results the same way a deductive argument can. It is always theoretically possible for the premises of an inductive argument to be true and the conclusion to be false.

In the case you mention, one might make a strong inductive argument to the effect that since the first 99 statements in the book were true, the last would be as well –but that conclusion might still be false. Furthermore, if you are aware of how the book was constructed and you do not include that information in your argument, you are guilty of the fallacy of suppressed evidence, and the argument can no longer be considered “strong.” Clearly, writing a false statement in a book of all true statements does not magically make that last statement true, and your knowledge of that fact must therefore be counted as a factor when judging the strength of the argument.

That may seem hopelessly subjective, but unlike the mathematically precise and assured conclusions of deductive arguments, the conclusions of inductive arguments can never be divorced from the real-world vagaries of context and circumstance.

Related content:

  1. Inductive arguments establish objective facts, so how can they be considered subjective?
  2. Just recently saw the following argument in a logic book: all lions are herbivores all zebras are lions ————– therefore all zebras are herbivores this seems to be logically valid syllogism, but it is disturbing.
  3. 1) The claim “There is extraterrestrial life in the universe, because my father said so” is an example of an appeal to authority. But it can be viewed as an enthymeme, where the hidden assumption is that “my father is always right”. In such a case, there is no logical problem with the argument. Do you agree? 2) Do you think that to say that : “Person A is biased , therefore\what he says is wrong” is fallacious? It can be interpreted as “person A is biased, therefore his information cannot be trusted. Therefore what he says is wrong”. 3) Are errors of logic errors of psychology as well? Or perhaps, only errors of psychology? Appeal to authority besides being a logical fallacy, has a whole psychology and sociology besides it.
  4. Do you think that the following argument is a good one : X says that a certain metaphysical view is correct. X says that if this view M is correct, it should produce certain effects in the psychology of people that realize it. (Make them super-smart, or super-kind for example). It is observed that X has this type of psychology. Thus the metaphysical view M is true.
  5. On one hand, arguments are supposed to be objective – something which is true is always true, for everyone. On the other hand, if person says “P exists because X,Y,Z”, while he personally has seen the evidence (x,y,z) for P, and another person says “P exists because X,Y,Z” and he has only read about X,Y,Z from second sources – their knowledge is actually very different. Where is that difference (crucial one) reflected in logic?
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