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  1. #1
    Occasional Member Evan's Avatar
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    Default Hume's problems with induction

    Here's a short essay I wrote in the last 20 minutes for my philosophy class.

    When Hume claims that we have no reason to believe an inference from the observed to the unobserved, he is correct, as long as we’re talking about a certain definition of the word reason. The way he uses the word reason is analogous to whether an inference logically follows from observed data (as in, is deductively valid based on observed data). If we see that A->B has been true any number of times in the past, we cannot logically conclude that A will imply B the next time. For example, if we see the sun rise one time per 24 hour period for our entire lives, we don’t technically have enough data to conclude that it will rise in the next 24 hour period, unless we assume that patterns that have held in the past will continue to hold in the future. Unfortunately, there is no way to prove that past patterns will continue into the future without assuming exactly that. The question “Why will past patterns continue into the future?” can only be answered by claiming something like “well, all past futures have resembled past pasts”, which doesn’t really get us anywhere, or leads to infinite regress, whichever way you want to look at it.

    So does this conflict with my ordinary beliefs about the world? Not at all. In fact, I wonder why Hume’s argument was not stronger. The basic conclusion to be drawn from his argument is that inductive reasoning (reasoning with logical leaps) cannot be logically (deductively) defended. Well, of course that’s true! Otherwise, we wouldn’t have any kind of reasoning other than deduction (why would we make logical leaps if we didn’t have to?). His second claim, that the only way to defend inductive reasoning is to assume the future resembles the past, and that assumption can only be defended by again assuming the future will resemble the past, to infinity, actually seems much weaker than it could be. Any deductive argument is subject to the same kind of reasoning as well. For example, take the argument, “Bachelors are unmarried, Evan is a bachelor, therefore Evan is unmarried”. How do you defend that bachelors are unmarried? How do you defend that Evan is a bachelor? Well, all you can do is say “um, you just have to assume that’s the truth”. Or you can use inductive reasoning, but Hume has already provided good reason for why that would lead to the same problem.

    The truth is that all reasoning has to be based on something. There’s always something you assume to be true in any argument. In deduction, you assume the premises are true, and in induction, you assume that the data you have is valid and the future resembles the past. To use a computer science analogy, if you write a function that adds two numbers together and outputs the answer, the function doesn’t do anything unless it gets two numbers to work with. Before data is passed to it, it is useless. Does the function itself know or care whether the numbers passed into it are somehow “true”? It’s a meaningless question. Just like when you think of the argument: “A->B, A, therefore B”. Does it matter to the actual process of deduction whether A->B is true or whether A is true? No. The process itself just takes what it’s given and gives the answer. The same can be said for induction (reasoning from the observed to the unobserved). If you were to write a computer function that used induction, the first line of it would be something to the effect of “the future resembles the past”. That’s just what induction does. The question of whether or not the future actually resembles the past is irrelevant to the process itself. So Hume is basically saying “Hey, look at that function! It says the future resembles the past! Why?”. Well, the answer is, “uh…that’s just what the function does.”

  2. #2
    veteran attention whore Jeffster's Avatar
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    Brit Hume?
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  3. #3
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by Evan View Post
    Here's a short essay I wrote in the last 20 minutes for my philosophy class.

    When Hume claims that we have no reason to believe an inference from the observed to the unobserved, he is correct, as long as we’re talking about a certain definition of the word reason. The way he uses the word reason is analogous to whether an inference logically follows from observed data (as in, is deductively valid based on observed data). If we see that A->B has been true any number of times in the past, we cannot logically conclude that A will imply B the next time. For example, if we see the sun rise one time per 24 hour period for our entire lives, we don’t technically have enough data to conclude that it will rise in the next 24 hour period, unless we assume that patterns that have held in the past will continue to hold in the future. Unfortunately, there is no way to prove that past patterns will continue into the future without assuming exactly that. The question “Why will past patterns continue into the future?” can only be answered by claiming something like “well, all past futures have resembled past pasts”, which doesn’t really get us anywhere, or leads to infinite regress, whichever way you want to look at it.

    So does this conflict with my ordinary beliefs about the world? Not at all. In fact, I wonder why Hume’s argument was not stronger. The basic conclusion to be drawn from his argument is that inductive reasoning (reasoning with logical leaps) cannot be logically (deductively) defended. Well, of course that’s true! Otherwise, we wouldn’t have any kind of reasoning other than deduction (why would we make logical leaps if we didn’t have to?). His second claim, that the only way to defend inductive reasoning is to assume the future resembles the past, and that assumption can only be defended by again assuming the future will resemble the past, to infinity, actually seems much weaker than it could be. Any deductive argument is subject to the same kind of reasoning as well. For example, take the argument, “Bachelors are unmarried, Evan is a bachelor, therefore Evan is unmarried”. How do you defend that bachelors are unmarried? How do you defend that Evan is a bachelor? Well, all you can do is say “um, you just have to assume that’s the truth”. Or you can use inductive reasoning, but Hume has already provided good reason for why that would lead to the same problem.

    The truth is that all reasoning has to be based on something. There’s always something you assume to be true in any argument. In deduction, you assume the premises are true, and in induction, you assume that the data you have is valid and the future resembles the past. To use a computer science analogy, if you write a function that adds two numbers together and outputs the answer, the function doesn’t do anything unless it gets two numbers to work with. Before data is passed to it, it is useless. Does the function itself know or care whether the numbers passed into it are somehow “true”? It’s a meaningless question. Just like when you think of the argument: “A->B, A, therefore B”. Does it matter to the actual process of deduction whether A->B is true or whether A is true? No. The process itself just takes what it’s given and gives the answer. The same can be said for induction (reasoning from the observed to the unobserved). If you were to write a computer function that used induction, the first line of it would be something to the effect of “the future resembles the past”. That’s just what induction does. The question of whether or not the future actually resembles the past is irrelevant to the process itself. So Hume is basically saying “Hey, look at that function! It says the future resembles the past! Why?”. Well, the answer is, “uh…that’s just what the function does.”
    This is an accurate rendition of Hume's views. However, there is a small, but important part that is missing. Hume argues that we do not have certainty with respect to the knowledge induction yields, yet this does not mean that we should distrust induction.

    In the Treatise on Human nature, Hume mentions that he has many beliefs about the external world and has no regrets about having them. Although he may not have made this claim, the implication of his view is that induction does not create rigorous arguments, but because frequently this is all that we have, we should accept it. After all, he even claimed that deductive reasoning (or fully justified logical reasoning) can be found only in mathematics. That subject he regarded as interesting but secondary in importance. On that note, most of the problems in life and those of greatest importance can be solved only inductively. This is not to say that deductive reasoning will be completely absent in such problem solving endeavors, however, they all will have an inductive component at the very least.
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  4. #4
    Occasional Member Evan's Avatar
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    Quote Originally Posted by SolitaryWalker View Post
    This is an accurate rendition of Hume's views. However, there is a small, but important part that is missing. Hume argues that we do not have certainty with respect to the knowledge induction yields, yet this does not mean that we should distrust induction.

    In the Treatise on Human nature, Hume mentions that he has many beliefs about the external world and has no regrets about having them. Although he may not have made this claim, the implication of his view is that induction does not create rigorous arguments, but because frequently this is all that we have, we should accept it. After all, he even claimed that deductive reasoning (or fully justified logical reasoning) can be found only in mathematics. That subject he regarded as interesting but secondary in importance. On that note, most of the problems in life and those of greatest importance can be solved only inductively.
    Right. I mean, you can't really not use induction.

    Here was the prompt I was responding to:

    What does Hume mean in saying that an inference from the observed to the unobserved does not proceed by "reasoning or any process of the understanding?" Does what he shows conflict with anything you ordinarily believe?
    So yeah I was taking a bit more narrow of a view.

  5. #5
    Occasional Member Evan's Avatar
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    Revised essay:

    Prompt: Does the conclusion that no one ever has reason to believe any unobserved matter of fact conflict with common sense or what we all ordinarily believe? If not, why not? If it does conflict, what should be done? What is the proper response?

    There are a few different ways I can think of to respond to the assertion that “no one ever has reason to believe any unobserved matter of fact”. The first would be to dismiss the statement as altogether too obvious. A second response would mimic Edwards – that we don’t commonly use the term reason to mean the same thing as it does in the assertion. The last way I can think of would combine aspects of the first two responses into an evolutionary argument that negates the problem in the first place. I’ll first outline the problem itself, then respond to it in three different ways.

    We know two ways of coming to conclusions: deduction, which makes conclusions that follow from premises, and induction, which makes conclusions that don’t follow from the premises alone. Hume specifically goes after induction – since the conclusions made from induction do not follow from the premises, they are by definition not logically justified. So in order to justify those conclusions, Hume thinks we make an implicit assumption, that past patterns will continue into the future, or put another way, observed patterns will continue whether or not they are observed. For example, if we see a light turn on every time we flip a light switch, and that’s all the information we have, it’s not justified to conclude that the light will turn on the next time we flip the light switch (because that would be an unobserved matter of fact). But if we assume that observed patterns continue even if they’re not observed, and combine it with the information we have about the light turning on every time we flipped the switch in the past, our conclusion that it will turn on the next time is logically justified.

    The problem with making the assumption about continuing patterns is that it’s impossible to justify. The only way to support the assumption is by pointing to patterns that have continued in the past, which is akin to saying “the observed pattern of [observed patterns continuing] will continue whether or not those patterns continue to be observed”. To make this more clear, we’ll assign the name S to the statement “observed patterns continue when they’re not observed”. In order to justify S, we point to observed evidence. But observed evidence alone is not reason to believe unobserved matters of fact unless we assume S. So in justifying S, we need S itself and some extra evidence. In order to justify the S that justifies the first S, we need another S, and so on to infinity. So we’re now at a point where we can’t justify induction (which is analogous to making conclusions about unobserved matters of fact based on observed matters of fact) whatsoever – the observed is by definition not enough to make conclusions about the unobserved (since induction is by definition not logically justified), and the only way to justify the conclusions is S, which is unjustifiable.

    So, does this conflict with what people ordinarily believe? I think not. In fact, I think the conclusion is actually weaker than what humans actually believe. When Hume attacks induction and not deduction, it might be assumed that he thinks we have no reason to believe in induction but we do have a reason to believe in deduction. That seems to be the counterintuitive part. So I want to extend the argument to deduction as well, showing that it’s impossible to fully justify any conclusion.

    What is deduction? It’s an argument where the premises (or assumptions) entail the conclusion. To put this another way, there is some set of logical statements (we’ll call the set X) that the combination of the premises entails. The conclusion of a deductive argument is limited to X – it can be a subset of X or it can be X itself. (If the conclusion isn’t contained within X, it’s not logically valid.) So how do we justify the assumptions that entail X? All we can do is point to other assumptions that entail X as well – but if two sets of assumptions entail X, those sets of assumptions are logically equivalent. So to justify X, we must assume a set of logical statements that include X. In order to justify the X that justifies the first X, we must assume X again. This problem is equivalent to the problem mentioned before regarding induction: in order to justify S, we must assume S. So both induction and deduction fall prey to the same problem; they are impossible to justify except by assuming they are justified.

    In this sense, we can see that no conclusions are justifiable. To justify a conclusion, we must assume things that entail the conclusion itself: in induction, we must assume our observations are true and that observed patterns continue whether or not they are observed. In deduction, we must assume our assumptions are true. Once you go into justifying those assumptions, you run into problems. But this dilemma of justification seems trivial in the context of common sense. It seems like everyone knows that different assumptions lead to different conclusions. People understand that those with different assumption sets cannot find common ground unless they change their assumptions. People very rarely get into arguments where they question the conclusions someone is making based on their assumptions, they go straight into questioning the assumptions themselves. Because they implicitly understand that no assumptions are logically justifiable, except with other assumptions (which are also not logically justifiable). Mostly, in order to find common ground, people look for assumptions that they have in common, as those assumptions lead to the same set of logical conclusions.

    Here’s a different way of approaching the prompt – “reason” is being used in a way that conflicts with everyday usage of the word. We’ve just seen that no conclusions are justifiable, in other words, we have no “reason” (in the same sense as in the prompt) to believe any conclusion that anyone makes. But usually, when people use the word “reason”, they don’t mean “perfect justification”; if they did, we’d never use the word “reason” in the first place! If someone has “reason” to believe something, it usually means that out of all possible beliefs they could have, some of them are more useful than the rest – so they have reason to believe some of them. The beliefs that are “reasonable” are the same as the beliefs that are useful. We could ask to justify why they are useful, but then we run into the same problem mentioned above. Most people go through the world defining goals, coming up with strategies, dealing with problems, and implementing goals with no second thought as to whether their actions are logically justified. And in going about life that way, a “reason” for doing or believing something just depends on the subjective experience of an individual.

    The final way I want to approach this problem is to give a hypothetical evolutionary account of why people have the beliefs that they do. We’ll think of living beings as belief-holding mechanisms that navigate their environment with limited processing ability. Because of the limited processing, these mechanisms can only have a finite amount of beliefs. The more efficient a belief holding mechanism is (with respect to the environment), the more likely it is that the mechanism will out-compete the rest and eventually replace the less efficient mechanisms through natural selection. There are two ways in which these mechanisms can be efficient – to hold beliefs that accurately predict environmental factors, and to hold simple beliefs that take as little processing as possible, leaving room for more of them. It follows, then, that if two beliefs predict changes in the environment equally, the mechanism with the more simple of those two beliefs is more efficient. Additionally, if two beliefs are equally simple, the mechanism that has the belief that better predicts changes in the environment is more efficient. As time continues, the mechanisms that are left have simple and predictively powerful beliefs about navigating the world.

    We run into a slight problem with this view – what if one extremely simple belief is correct most of the time and an extremely complex alternative belief is correct even more of the time. Which takes precedence? The simple belief or the more predictively powerful belief? There is no easy answer to this question. We can only pit these two mechanisms against each other and see which one outcompetes the other. My guess is that they each win in different situations. This could explain why humans sometimes have very complex representations of objects in the world and sometimes have very simple ones. It also explains why we don’t predict environmental events with 100% accuracy. Sometimes simplicity is favored, as our processing power is limited.

    The powerful conclusion we can draw from viewing beliefs with this framework is that it doesn’t actually make humans more fit to logically justify their beliefs or conclusions. No belief is actually logically better than any other; evolutionary fitness is the only deciding factor in which belief tends to be held. And a mechanism that needs to justify every conclusion wastes belief space on processing information that doesn’t actually help navigate the environment at all.

    In all three of these responses, we see that Hume’s problem of induction isn’t actually much of a problem at all. If induction is not justifiable, then deduction isn’t either, and it’s a waste of time to care about justification at all. If Hume’s use of the word “reason” is different from our everyday use, his conclusion is just a trick with words. And if we view human beliefs as only chosen by natural selection, we’ve already answered the question of why they have the beliefs that they do.

  6. #6
    Tenured roisterer SolitaryWalker's Avatar
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    Post your revised essay in appreciation of contemplation. I should get around to it in a week.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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    Quote Originally Posted by Jeffster View Post
    Brit Hume?
    Well he was British if that's what you mean.

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    Perfect Gentleman! =D d@v3's Avatar
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    Quote Originally Posted by Peguy View Post
    Well he was British if that's what you mean.
    LOL!
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    Hi Evan,

    I largely agree, though I ask: if neither deductive nor inductive inference justifies its conclusion, then what is the use of inductive inference?

    I can see some use in deduction, because we can explore logical consequences, identify testable predictions, and check for consistency.

    But what good is inductive inference? It seems to me that the whole point of induction was precisely to justify universal statements with existential statements. It was felt necessary because sense experience (assumed to correspond to sets of existential statements) was taken to be the only legitimate source of knowledge.

    For the longest time people tried to show that induction (a specific kind of invalid inference) was actually valid afterall. When that goal was given up, attempts were made to make inductive inference partial or probable -- in other words, induction may not be deductively valid, but it can be inductively valid (to which we have discussed objections elsewhere).

    But in the end, this whole chain of problems and attempted solutions arose out of old empiricist philosophy and its desire to justify beliefs with sense experience. If that goal is truly dropped then induction can be dispensed along with it, in my opinion.
    A criticism that can be brought against everything ought not to be brought against anything.

  10. #10
    Occasional Member Evan's Avatar
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    Oh I see what you're saying. If the conclusions of induction aren't justified, why do we even pretend to have some reasoning process behind it; why not just assert the conclusions directly?

    While we could do that, it may not be equivalently useful in all cases. If someone asks why you believe something will happen, they're essentially asking you for a premise of inductive reasoning that could lead to the conclusion they're questioning. Not that the conclusion will ever be fully justified, but sometimes people feel more comfort in approaching guessing in that way.

    OR, you could always use the premise "the unobserved resembles the observed", and then you don't need induction anyway, as you can make a deductive argument for most guesses (of the kind that are usually talked about). That's probably the way I'd go.

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