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## Induction Notes

This is an extract of our Induction document, which we sell as part of our Metaphysics Notes collection written by the top tier of Cambridge students.

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What is the Problem of Induction? Does it rest on a Misguided Notion of Justification?
In this essay, I intend to argue that the problem of induction rests more on our concept of the function of justification than it does on a problem of knowledge itself. I will first outline the difference between deductive and inductive reasoning, in order to distinguish the latter. I will then go on to dismiss various solutions to the problem of induction, before explaining how all of these disproofs rely on the importance we ascribe to justification, and then reapproaching some of them with this in mind. In doing this I hope to prove that our understanding of justification is the major difficulty to the problem of induction. It can be said that that which we might call knowledge about the world is achieved in two different ways. First, we have deductive reasoning. This exists independent of the current state of the world and is true a priori. Examples of this are the truth that the addition of one thing to another makes their value two, and that the number of sides to a triangle is always three. It is not the case that in observing many more triangles we might come to the conclusion that they can have more or less sides, nor is it true that a more careful analysis of some objects might prove that the addition of another like object would sometimes not increase their total number by one. The information related here is not true in virtue of experimentation or empirical evidence but, rather, by the abstract reasoning of the concepts involved. In this way a deductively valid argument necessarily preserves truth. The second type of reasoning can be called inductive. These are arguments formed a posteriori from our empirical data of the world. This is the type of argument with which the natural sciences concern themselves. By repeating observations on X (let's say) a number of times to an apparently uniform result, they hope to arrive at certain conclusions about the nature of X. The problem of induction is that (it is often argued that), no matter how often an experiment or observation is repeated, the results cannot amount to a conclusive proof of anything besides, perhaps, the fact that in all previous cases of A, B was the result. There is nothing concluded about future cases of A that leads us to the inference that B will be the result then. In this way, we see that there is a difficulty with the certainty of inductive proofs that does not arise from deductive proofs. The underlying assumption of the principle of induction is that the future will resemble the present and past, else the conclusions we drew therein would have no function in that future. As Russell points out, even were we to maintain that in all past cases the future has resembled the past, it doesn't follow that the state of past futures should in any way dictate the nature of future futures. As it happens, we can even observe cases where this has not been the case, often to devastating effect. Consider the terrorist victim, who has taken all cases of her going to work as instances of not being blown up, and so concludes that in all future cases of going to work this will still be the case. This inductive conclusion leads to her death when she arrives at work in a future that does not resemble her past in this respect, and finds that there is a terrorist bomb explosion. Almost every argument that we accept as taking us from things that we directly observe to things that we don't, or possibly can't, observe is of this second type of reasoning and, therefore, its justification is paramount to the truth value of a great amount of that which

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