I have been downloading a cartload of books on my new Kindle lately, since I really enjoy the idea of walking into the subway carrying a rather inconspicuous, very light, yet incredibly large library with me. One of these books is Samir Okasha’s Philosophy of Science: A Very Short Introduction, which I’m reading because I intend to review and promote it. Samir writes very clearly, and this short introduction is very useful for the general curious reader (and, frankly, some scientists of my acquaintance could use it too).Anyway, Samir devotes quite a bit of space in chapter 2 of his book to Hume’s problem of induction, which is fundamental to our understanding of how science -- indeed, reasoning in general -- works. Seems like the kinds of things that readers of this blog enjoy sinking their teeth into, so here we go.
The problem itself is well known: induction is the most common type of reasoning we all use (the other fundamental kind, deduction, is used largely within formal logic and mathematics), and it consists of generalizations from a series of observations. So when we say, for instance, that we are confident that the sun will rise tomorrow, this is not because we have a logical proof that it cannot be otherwise, but because we have seen it rising every day and we have no reason to think that tomorrow it will be otherwise. As Okasha points out, we literally stake our lives on this sort of inductive reasoning, for instance every time we bet that a car will turn to the left if we rotate the steering wheel counterclockwise. (By the way, it won’t do to claim that you expect the sun to rise or the wheels to turn because you understand the mechanism: your understanding of the mechanism is itself built on a series of inductions, it is not that there is a logical necessity for solar systems or cars to work in the particular way they do work.)
The problem is that, according to Hume, there is no rational justification for induction! You see, if I’d asked you why you use inductive reasoning, pretty much the best you can do is to reply that it has worked in the past. Which is an argument based on induction. Which means you are begging the question, in philosophical terms, engaging in circular reasoning.
This may seem yet another example of philosophers engaging in intellectual masturbation, but the more you think about it the more Hume’s problem grows on you, and becomes disturbing. To quote Okasha: “If Hume is right, the foundations on which science is built do not look quite as solid as we might have hoped.” Oops.
Several ways have been proposed out of Hume’s dilemma, none of them particularly successful. I’d like to briefly discuss here the idea -- presented by Okasha in some detail -- that the concept of probability might rescue science and reason from the problem of induction. It goes something like this: granted that induction (unlike deduction) does not guarantee truth. Perhaps, however, we can rephrase what induction allows us to do in terms of probable statements. That is, we don’t really mean that we know that the sun will rise tomorrow, or that the car will turn to the left. We mean to say that, based on past experience, we think there is a high probability that those events will happen again in the future. (Incidentally, since deduction does guarantee truth, why not use it instead? Because deductive reasoning has to start with two or more premises, and at least one of those premises is arrived at via experience, not from first principles. Which means that even deduction itself has to rely on induction, at some point or another. The mystery deepens...)
Now, the problem is that philosophers have pointed out that there are at least three concepts of probability, so we have to see which, if any, of them is going to be helpful to dispel Hume’s ghost. The first way to think about probability is as a measure of the frequency of an event: if I say that the probability of a coin to land heads up is 50% I may mean that, if I flip the coin say 100 times, on average I will get heads 50 times. This is not going to get us out of Hume’s problem, because probabilities interpreted as frequencies of events are, again, a form of induction -- we generalize from a few observations to a broader range of events instead of all possible events, but the type of reasoning is the same.
Secondly, we can think of probabilities as reflecting subjective judgment. If I say that it is probable that the coin will land heads up, I might simply be trying to express my feeling that this will be the case. You might have a different feeling, and respond that you don’t think it's probable that the coin will lend heads up. This is certainly not a viable solution to the problem of induction, because subjective probabilities are, well, subjective, and hence reflect opinions, not degrees of truth.
Lastly, one can adopt what Okasha calls the logical interpretation of probabilities, according to which there is a probability X that an event will occur means that we have objective reasons to believe (or not) that X will occur (for instance, because we understand the physics of the solar system, the mechanics of cars, or the physics of coin flipping). This doesn’t mean that we will always be correct, but it does offer a promising way out of Hume’s dilemma, since it seems to ground our judgments on a more solid foundation. Indeed, this is the option adopted by many philosophers, and would be the one probably preferred by scientists, if they ever gave this sort of thing a moment’s thought. (The statistically savvy among you may have noticed that this concept of probability is not the standard frequentist one common in classical statistical analysis, but more akin to either likelihood or Bayesian methods.)
Okasha warns his readers, however, that even the logical interpretation of probabilities runs into both philosophical and mathematical problems, but we shall leave that for another time. Let me conclude with another quote from Samir’s book, which to me encapsulates the whole point of doing philosophical analysis: “Like most philosophical questions, these questions probably do not admit of final answers, but in grappling with them we learn much about the nature and limits of scientific knowledge.” Indeed.
"The problem is that, according to Hume, there is no rational justification for induction!"
ReplyDeleteMassimo,
Is there some technical definition for the term "rational" here? Am I missing something here? So induction may not lead to some final truth, it may be prone to error, but it is based on something observable, and doesn't make something up out of whole cloth. Why is there no rational justification for induction?
Humanist,
ReplyDeletethe point is that if the only justification for induction is inductive, it is circular. If one cannot find any other justification, then there is no rational basis for induction. It still works, of course, as Hume surely knew...
The only solution that is even close to being intellectually satisfying seems to be the ordinary language solution, which is to say that making intellectual leaps of the kind that we make in making inductions (from particular cases to generalities or from the past to the future) is what we fundamentally mean by being rational. So that asking whether induction is rational is like asking whether it's rational to be rational.
ReplyDeleteAfter all, if induction must have something rationally prior to it, how is it in any worse a state than deduction? If we ask why deduction is rational, then don't we have to employ a prior deduction to do it?--Just like we have to employ a prior induction to justify induction?
Martin,
ReplyDeleteI think the case for deduction is different, because it is amenable to logical proof (indeed, deduction is the only case where one should use the word proof!).
Still, your argument is a good one, and is analogous to one of the solutions listed by Okasha in the book, and on which I did not comment in the post: imagine someone where to ask if the law (in general, not a particular law) is legal. There is no sensible answer to that, because the law is a system within -- but not outside -- which the concept of "legal" makes sense. The same may go for rationality and in particular induction.
Martin:
ReplyDelete... making intellectual leaps of the kind that we make in making inductions (from particular cases to generalities or from the past to the future) is what we fundamentally mean by being rational.
Reminds me of the Einstein quote:
Insanity: doing the same thing over and over again and expecting different results.
Massimo,
ReplyDeleteI agree on the legal example. But how is deduction amenable to logical proof except by deduction? Wouldn't that be just as circular as using induction to argue that induction is logical?
It seems to me that both these cases are just showing us that, at bottom, rationality itself cannot be "proved"--it must merely be intuited. In order to prove proof you have to assume proof.
There is nothing logically prior to it.
Massimo,
ReplyDeleteBy the way, thanks for this post. I was aware of that series of books but was unaware they had published this particular book.
Martin,
ReplyDeleteactually deduction is provable in the sense that the wrong deduction leads to a logical contradiction, which can be shown in formal symbolic logic. That is not the case for induction, which never leads to logical contradiction.
Some years back, an introductory philosophy textbook, written by Elliot Sober, fell into my hands. Sober defined two types of non-deductive, inferential reasoning: the first one is induction, which is the kind of generalization from specifics described here; the second, however, is a kind of hypothetical reasoning, also common in the sciences, which he calls "abduction", otherwise known as an "inference to the best explanation." (Appeals to "Occam's razor", or simplicity or elegance, would be examples of abduction.)
ReplyDeleteIn other words, induction is inferring Y from multiple instances of X; whereas abduction is inferring X as an explanation of Y. The difference may be subtle, but then it seems pretty commonsensical to distinguish: (a) our predictions of future events from past experience; and (b) our assertions that events occur because of some prior conditions or tendencies.
It's been a while since I took a stab at Hume, so I don't know if he had both kinds of non-deductive reasoning in mind when he addressed the "problem of induction."
Very interesting material. Thanks for the heads-up about this book.
ReplyDeleteI look forward to your review. I read Okasha's book last year, but this is a good excuse to read it again!
ReplyDeleteI think the problem is in thinking of induction as a logical principle at all. It isn't. Its an empirical principle. The only good reason to believe that a given induction is true is to continue to observe that it is true. Empiricism is just the process of observing order and pattern around us.
ReplyDeleteScience and math work in opposite directions in a sense. In math you start with a simple set of underlieing assumptions and work out the complex consequences of those assumptions. In science you start with the complex consequences that you observe and assume for the moment as true and try to work backward to the simple set of underlieing principles.
"I have been downloading a cartload of books on my new Kindle lately, since I really enjoy the idea of walking into the subway carrying a rather inconspicuous, very light, yet incredibly large library with me..."
ReplyDeleteArgh! You gotta stop talking about the Kindle - it's driving me crazy. I can't afford one until the price goes down, but I desperately want one. I've got books stacked knee high around my bedroom and already need about two or three large bookshelfs (in addition to the one I already have full) to accomadate them.
Hume's,
ReplyDeletebut think of all the money and space you'll save if you invest in the Kindle... :)
I am, for good reasons or bad, reminded of the Global Warming debate that I am frequently engaged in with my father. I make a probabilistic argument for the correctness of the Anthropogenic argument for global warming, which he tries to assail. I think his counterargument is largely fallacious.
ReplyDeleteMy argument basically goes like this: suppose there is a world with no scientists and there is no "common sense" answer to a question (not like "what color is grass?"). Does anyone have grounds to take a probabilistic stance on this issue? No! There are no scientists; there is no data to work with; there's nothing.
Now, suppose you live in a world with scientists. If one position on an issue happens to be true, then it is more likely that evidence of that truth will get into the hands of scientists than in universes in which that position were false. Since scientists are trained to gather and analyze evidence, they will probably be swayed by the available evidence in the direction of the correct hypothesis, provided that evidence exists.
Global Warming is not an issue in which necessary evidence does not exist. There is a large body of evidence that can be analyzed in order to assess the correctness of various hypotheses regarding Global Warming. As stated earlier, if one position is (in fact) correct, then the evidence will probably sway scientists in the direction of that position.
Scientists, have, by and large, been swayed towards the acceptance of the general hypothesis of Anthropogenic Global Warming. They came to this conclusion through the analysis of evidence. Therefore, this theory is probably true.
My father's objections consistently invoke the "we don't know for sure" fallacy: the idea that one either has absolute knowledge of an issue or one can make no probabilistic statements on this issue. He points out that not all climate scientists agree on global warming. This is true, but it doesn't undermine the probabilistic argument I stated. He points out that scientific consensus does not determine truth. This too is a silly argument: scientists narrow down truth with evidence and analysis. They do not generate, they uncover.
Of course, the arguments go on and on. I would list his more fallacious arguments or non-arguments ("I think it's a big liberal hoax!"). But I was just reminded of these discussions between me and my father by this post regarding science and the nature of probability.
You might imagine a world with no laws, where past experience tell you nothing about the future. In such a world induction would not work. The law of induction is an observation about how our universe works, and as such you wouldn't expect to be able to prove it.
ReplyDeleteI suppose you could try the anthropic principle and note that with no regularity life could almost certainly not evolve and intelligence would be pointless, so the fact that we are here shows that induction must be true.
"but think of all the money and space you'll save if you invest in the Kindle... :)"
ReplyDeleteExcept my collection is largely composed of discount books. My local library sells paperbacks for 50 cents and hardcovers for a dollar, plus a Books-a-Million here also sells hardcover library books for 3 dollars. The city I used to live in had a bargain bookstore near my house that had all books at a minimum half off, and Amazon.com used to have lots of bargain books for a penny plus shipping. Space is an issue, however, and I suppose so is the cost of bookshelves!
Re: the topic of the post:
I'm partial to Susan Haack's crossword puzzle justification for scientific knowledge, myself. Of course, I think its entirely consistent with probalistic escape from Hume's induction problem.
Does the writer use induce or deduce in assuming the article will flow to monitors of others and that there will be someone there to read it and understand the language?
ReplyDeleteMassimo, my understanding is that it is the pragmatic argument that induction just works: this is not a vicious circularity.It is thus a basic warrant unlike Platinga's faith-based one.
ReplyDeleteI use Articulett's definition @ Skeptic Society to make the argument that faith begs the question of its subject. Faith is the we just say so of credulity. Science is acquired knowledge, as Sydney Hook remarks, whilst faith begs the question of being knowledge.
Reason can move mountains of ignorance whilst faith makes mountains of castles in the air.
This is the presumption of rationalism.We have also the presumption of naturalism that natural causes and explanations re not only the efficient causes but also necessary, primary and sufficient; they are the sufficient reason, contrary to Leibniz. This, including Hume's corollary about miracles, neither begs the question nor sandbags theists but is just the demand for evidence.
Then there is the presumption of skepticism and the one of humanism- covenant morality for humanity. We thus have naturalist [positive atheist arguments] to counter theism.
Also, the atelic argument from the weight of evidence that there is no cosmic teleology, thus no cosmic purpose and no need to posit thus the Ground of Being or Being Itself.And thus unplanning natural selection, the anti-chance agency of Nature contradicts teleological God!
The notion for teleological ones derives from theists' use of pareidolia to infer a caring, super mind behind Existence just as some see Yeshua in a tortilla- the argument from pareidolia. This includes their seeing designs when we naturalists see patterns.
The ignostic-Ockham means either that God is a vacuous term or else one requiring convoluted ad hoc assumption's, an useless redundancy, contrary to haughty John Haught.
And Schellenberg's suddenness argument, the problem of Heaven, the evidential argument from evil, the argument from embodied mind: we only know of embodies minds. The disembodied one of God is just another it must be of theologians. And Dawkins's argument from complexity counter's Swinburne's simple God [And he does not fathom the Razor!]
And the [ Angeles's] infinite regress argument that time, event and cause presuppose previous times, events and causes. Furthermore,as Existence is all, there can be no transcendent God.
Logic is the bane of theists.
Si I went beyond induction! Oh, we don't need faith for it. We don't need God to validate our faculites, contrary to Lewis, Fr. Ewing and Platinga the Sophist.
ReplyDeleteMy approach to the problem of induction is based on the fact that there is simply no reasonable alternative to using induction---and when there is no reasonable alternative not employing it would be irrational.
ReplyDeleteIf induction suddenly becomes impossible then any outcome is as likely as any other so we'd just be screwed in such circumstances and probably die within moments if not immediately (for example, if the bonds in the atoms of our bodies no longer held together).
And that isn't an argument that relies on inductive reasoning to validate inductive reasoning.
There are other possible arguments. For example, if the order of the universe is to fundamentally fail at some point such that induction cannot be relied on it must occur at some particular moment X. What are the odds that any particular moment is the moment that inductive unreliability begins. About one in infinity?
Induction then seems at any particular moment the best bet (except for that moment after inductive failure begins---but then we'll almost certainly die anyway so its far from a difficulty for justifying the use of induction.
I suppose you'd call this a pragmatist approach to the problem.
David,
ReplyDeleteyes, that would actually summarize my approach too. Still, it is fascinating to ponder how difficult it is to defend science and basic reasoning, once one begin to think about it more carefully...
Another possible approach is rather than attempting to argue for the probability of induction being reliable in the future to defend induction as part of one's conceptual model of the universe.
ReplyDeleteThat is, we have a conceptual model of the way the world works that includes its being orderly in ways that allow for induction. This model seems to fit the available evidence better than any alternative.
If at some point induction seems to become unreliable (in total or in part) that conceptual model should be revised.
Until then it seems to be the best thing we have to work with.
Does Okasha ever address the Pragmatist answer to the problem of induction? I capitalize the word 'Pragmatist' to indicate Peirce, Dewey, et al rather than David Ellis' informal (but excellent!) response to the problem of induction.
ReplyDelete"Anyway, Samir devotes quite a bit of space in chapter 2 of his book to Hume’s problem of induction, which is fundamental to our understanding of how science -- indeed, reasoning in general -- works."
ReplyDeleteScience is knowledge not reason. The top scientists who founded modern science were theists. God's creation inspired them to study how his creation worked. All the Laws of creation were created by the Creator. Science is not meant to be immoral or separate from God. Science is good and it is fascinating and I loved science in high school, but it has been becoming less interesting to me since people have secularized it and separated it from knowledge and into a relative reasoning, which is not science at all. God makes the scientific Laws and Moral Laws, if one breaks any of those Laws there are consequences.
ReplyDeleteGod makes the scientific Laws and Moral Laws, if one breaks any of those Laws there are consequences.
How would one break a scientific law?
And, as to morality based on laws laid down by God, how do you propose to deal with the Euthyphro dilemma?
The top scientists who founded modern science were theists.
Yes. And Isaac Newton devoted an inordinate amount of time and effort to alchemy.
So what?
Because someone comes up with some good ideas doesn't mean that they weren't also susceptible to bad ones.
David B. Ellis said, "Because someone comes up with some good ideas doesn't mean that they weren't also susceptible to bad ones."
ReplyDeleteYeah I agree. Darwin had a major in Theology in College and even he was susceptible to bad ideas... Evolution.
Massimo,
ReplyDeleteThe problem w/ claiming that deduction is on firm ground because if you make mistakes in deductive logic you can derive contradictions is that, just as with induction, this presumes the truth of the very system you are trying to test.
If you don't believe that given x, and "If x, then y" you can conclude "y" what would convince you of this fact? How is "not-(both x and not-x)" more convincing than that?
I suppose it is true that once one accepts some formal system, and the rules of that system, and commits to rule-following, deduction works, but the question remains how & why one would do any of those things?
Here I am with Martin Cothran -- though tempered with a bit of Wittgenstein. There is nothing "foundational" for induction (or deduction for that matter) to rest on. Rather, there are practices that make sense in the context of our lives. What it *means* to be rational is to be able to give reasons *at the appropriate level*. If you ask "why is it rational to believe that the future will be like the past (with respect to the behavior of the world)" I think you are asking a question at the wrong level, and Martin's reply -- believing that is part of what it *means* to be rational -- is the right way to go.
BTW: David, nice try re: "For example, if the order of the universe is to fundamentally fail at some point such that induction cannot be relied on it must occur at some particular moment X. What are the odds that any particular moment is the moment that inductive unreliability begins. About one in infinity?" but the problem is that if in fact the regularity of the universe is not stable, then probability isn't stable, either. You can't use the past to make predictions about the future is the nature of regularities is up for grabs...
I actually like Thomas' suggestion:
"I suppose you could try the anthropic principle and note that with no regularity life could almost certainly not evolve and intelligence would be pointless, so the fact that we are here shows that induction must be true." You at least show it must have worked in the past. You can then note that if it were to fail, the very meaning of rationality, etc., would fail with it (as well as any chance of survivability, learnability, etc.) so rationality presupposes the continuation of extant order.
Fun stuff!
jk
ReplyDeleteYeah I agree. Darwin had a major in Theology in College and even he was susceptible to bad ideas... Evolution.
Hi. The sky is (usually) blue on my planet.
What color is it on yours?
ReplyDeletebut the problem is that if in fact the regularity of the universe is not stable, then probability isn't stable, either. You can't use the past to make predictions about the future is the nature of regularities is up for grabs...
I consider this the weakest of the three reasons I proposed for employing induction. But the other two seem more than adequate so I can live with that.
I read the Philosophy of Science book as part of an introductory psychology course. I must say that it is quite excellent.
ReplyDeleteThere's also a "very short introduction" book about evolution, which I recommend as well.
Thomas Palm wrote:
ReplyDeleteThe law of induction is an observation about how our universe works ...
Some aspects of our universe, e.g. physics and chemistry, do seem to be very regular. But quantum physics adds a curiously irregular twist to this.
Other aspects of our universe seem quite irregular, e.g. the spots on leopards. Yet (I understand) regularity lurks here. Likewise (I understand) regularity lurks in the apparently chaotic growth of plant leaves.
Regularity and simplicity seem to go together, and it sometimes takes very little complexity to obscure a strong regularity.
Astronomy seems to me a good example of the interplay of regularity and irregularity. The ancients observed clear patterns in the movements of celestial bodies, and yet there were disturbing irregularities. It took thousands of years and more than few geniuses to work things out (and not without some opposition from "heavenly" bodies).
I think induction is the basic tool of science, but to be useful it has to be applied carefully. Ultimately, inductive inference requires a model, whether it is explicit or implicit. But here's the rub: the model itself can only be justified based on past evidence. For a simple, apparently endlessly repeating pattern (e.g. the day follows the night), we can use the model that the probability that the i-th event follows the pattern is w for all i. Then after observing k such confirmatory events, where k is large, we have strong evidence that the pattern always holds, i.e. that w=1, provided the model is true. (Furthermore, we can use statistical methods to quantify this evidence.) If the model is not true, and the probabilities w1, w2, ... vary in some unknown way, then we may be quite wrong. Still, the regularity we have observed is so striking in its simplicity that our simple model is very attractive.
Our modern understanding of astrophysics leads us to believe that there will eventually come a time when the day no longer follows the night. Still, the inductive inference has served us well.
A far more complex example: Newtonian mechanics works very well for objects within a few orders of magnitude of our size, and traveling at modest speeds. The inductive inferences that provided the foundation for Newton's system were extremely valuable. But we now know that beyond the realm of familiar sizes and speeds, these inferences prove inadequate.
Thomas Palm continued:
I suppose you could try the anthropic principle and note that with no regularity life could almost certainly not evolve and intelligence would be pointless, so the fact that we are here shows that induction must be true.
I think this is an appealing argument. But I don't think it's that induction is "true". Rather, it's that there is some regularity in our universe. There is also irregularity. Consider the weather, which is both regular and irregular. We tend to think that the irregularity is simply due to extreme complexity. But, as I noted above, quantum physics puts a curious random element into the picture.
David
ReplyDeleteIf we imagine living in a world where induction is unreliable, how would we find out this but by induction?
It seems to me that we cannot escape question begging precisely because it looks like it is instinctive*, thus inseparable from us.
The only way we could rationaly justify induction would be if we imagined an alternative *strategy* for going about without falling into cliffs. I fail to see how a world inhabited by angels and gods, who see matters of fact as deductively necessary, would look like. In other words, induction cannot be the best bet if it is the only one.
All we could rationaly justify is our preference for good over bad induction, science over myth: Bad induction kills you!
Now the confusion, whether deduction is on firm grounds or not (?), well: deduction IS the ground. That's why it tells you absolutely nothing about the world.
Winstanley,
ReplyDeleteactually, one can imagine a world like the one suggested by David. Take a look at the movie "Dark City" with William Hurt (http://www.imdb.com/title/tt0118929/). In it, the world does change in unpredictable ways (I won't tell you why, in case you'd like to watch it), and the plot is an exploration of what happens when induction is no longer reliable.
Aren't we talking here about Bayesian induction? Start with a prior (subjective) estimate of probability and refine according to experimental observations.
ReplyDeleteI start off with a hypothesis that the laws of physics are constant (50 % probability of being true by subjective estimate). Repeatedly observe that they act in accordance with the hypothesis, and so revise my probability estimate upwards.
It might not meet philosophical standards, but it's how science works.
Lastly, one can adopt what Okasha calls the logical interpretation of probabilities, according to which there is a probability X that an event will occur means that we have objective reasons to believe (or not) that X will occur (for instance, because we understand the physics of the solar system, the mechanics of cars, or the physics of coin flipping). This doesn’t mean that we will always be correct, but it does offer a promising way out of Hume’s dilemma, since it seems to ground our judgments on a more solid foundation
ReplyDeleteI have to admit: I have no idea what this "solution" amounts to. Hume would surely say that to "understand" the solar system or the physics of coin flipping requires (as you've already suggested) faith in the validity of one's prior inductive judgments, and faith in what he calls the the Uniformity of Nature: the idea that the future will resemble the past.
ReplyDeleteIf we imagine living in a world where induction is unreliable, how would we find out this but by induction?
It would be largely irrelevent since a world where induction wasn't reliable to any significant degree would almost certainly not be survivable.
ReplyDeleteIn it, the world does change in unpredictable ways (I won't tell you why, in case you'd like to watch it), and the plot is an exploration of what happens when induction is no longer reliable.
That's not an example of a world with general inductive unreliability. Induction still works quite well in a great many respects (all, in fact, when the missing pieces of information about what is happening in the environment they inhabit are available).
I don't really see that as an example of inductive unreliability but a simple lack of knowledge of vital information.
Great movie though.
Nick,
ReplyDeleteactually Hume would have another problem with the logical interpretation of probability: he wouldn't like the use of the idea of "causation," which he found highly suspicious.
Okasha does get into that, in the following chapter of his book.
I'll definetely watch the movie.
ReplyDeleteAnyway I see your point. But then, I insist, how do we distinguish a world of inductive unreliability (say with miracles every so often) from one about which we lack knowledge?
Do you mean that, since the former is unsurvibable, the fact that we are alive is a proof? It seems that even the most simple organism relies on the regularity of natural laws. Then, could an example be a universe with different fundamental physics, one where we could not survive nor observe?
Which makes me wonder whether inductive reasoning is a purely subjective category or whether it also implies something about the *fabric of the world,... is the anthropic principle anywhere here?
As this gets terribly confusing I remember Hume's words:
"A true sceptic will be diffident of his philosophical doubts as well as of his philosophical convictions; and will never refuse any innocent satisfaction, which offers itself, upon account of either of them". I therefore wish Massimo will keep bringing us many more innocent satisfactions.
Chris: "Yeah I agree. Darwin had a major in Theology in College and even he was susceptible to bad ideas... Evolution."
ReplyDeleteYes, and tho C. Darwin and Abe Lincoln were born on the same day, Abe believed and advanced the idea that ALL MEN were 'CREATED' EQUAL while Darwin believed that men were neither CREATED nor EQUAL.
And who was it that asked what "color" the sky is on your planet???
"David B. Ellis said, "Because someone comes up with some good ideas doesn't mean that they weren't also susceptible to bad ones."
Chris: Darwin had a major in Theology in College and even he was susceptible to bad ideas... Evolution."
ReplyDeleteDarwin, for all his supposed training in theology, had no concept of the value and worth of his own soul. And that fundamental issue alone made him susceptible to every other lie that came after that. A mighty precarious place to be if you ask me.
And welcome fellow Minnesotan. I use to think that Minnesota had some of the brainiest people in the world there until the last few political cycles....
caliana said,
ReplyDelete"And welcome fellow Minnesotan. I use to think that Minnesota had some of the brainiest people in the world there until the last few political cycles.... "
Oh whatever, Governor Jesse Ventura was the best thing that ever happened to this state. And I am proud of our football team who made it to 4 Superbowl's and still didn't win one, and I am especially proud of them for their decision to get caught doing horrible things on their yacht, Go Vikings Go! The only thing I don't like was their decision to make the blueberry muffin Minnesota's state muffin. Raisin oatmeal muffins are so much better.
(all of this is sarcasm to the highest degree)
Well, Chris, at least you're still on top of whats going on in the world and MN.
ReplyDeleteThere use to be a lot of predictability in the social climate (true tolerance & patience) especially at the small town level. Now it anyone's guess why Minnesota just got tired of being "good".
Well, maybe I know in part...
On a trip to Isrl recently, our guide mentions some matters discussed in OT books of the law (which few people seem to understand) i.e. no mixing of fabrics, no mixing of dairy and meat, etc. She explained to us that this alludes to God's way of laying down the concept or precept of "NO MIXING", especially when the Hebrews of various times and places were often surrounded by Greeks and Romans who 'just wanted to have it their OWN way'.
And that's where most of Minnesota is at I think. Flat out tired of being good...just wants to have things (collectively) its own WAY.
There is no other explanation of how more than 5 people would ever vote for Franken or Ventura. Ventura is the craziest most egotistical person... Franken, otoh, is the biggest mocker and slanderer I've seen anywhere....
I am shocked at "US" for tolerating any of that. I guess there is such a thing as being so tolerant one becomes absolutely stupid...
No one has mentioned the "black swan" example of the failure of induction at a low level. If one lived in Britain and never left, one might be justified in believing that "all swans are white", a locally valid induction.
ReplyDeleteBut after travelling the world and seeing black swans, the error would be easily seen.
A new induction would be created for better accuracy: "all swans are either black or white". Induction might not be completely correct, but it can become asymptotic to valid knowledge of the physical universe. Hume's reasoning that it might not be true tomorrow is not really a show stopper for empiricism, which would endeavor to determine why it became "not true". I don't think Hume meant that the universe might stop; I think he meant the issue with the black swans.
This points out another limitation of science that rarely is mentioned: science produces not truth, but factoids that are only contingently valid, until new information causes a correction to be understood to be required.
Also empirical science voluntarily restricts its purvue to observable, measurable, material entities.
This does not address the possibility or probability of non-material entities; Philosophical Materialism makes the error of declaring - without material evidence - that non-material entities do not exist. But Philosophical Materialism is a philosophy, not an empirical science.
Philosphies tend to be purely deductive, without the capability of inductive observation for back-up. This can result in some generic errors that don't really contradict empiricism, but are internally contradictory or non-coherent.
For example starting with an erroneous First Principle leads inexorably to false conclusions. First Principles are known to be true by intuitive inspection; the non-contradiction principle is an example. But if I declare there to be no non-material existences, this is not generally intuitive, and there are reasons for it not to be. For example, the infamous "meme" is not physical, not measurable in x,y,z, dimensions, has no mass, no energy, no reflectivity, no density, no other material characteristics. It is non-material. To argue that it cannot exist is counter-intuitive; thus "no non-material existence" cannot be a First Principle from which deductions can rationally be made.
I have always taken the pragmatists view since first reading of Hume's argument. It may be true from a philosophical perspective that there is tenuous rational for the veracity of induction but as David B. Ellis clearly pointed out, if induction were to be wrong, we all wouldn't survive the break. So accepting it as a fact of our existence in this Universe today, is the best we can do. In mathematics the idea of self derived entities is powerful and used all the time to derive proofs, some of which have been the most powerful in mathematical theory. One obvious example is the symmetry of the integral of the exponential function being an exponential function. Mathematicians don't look at this fact and claim that integration of the function is "circular", it just is and the calculations based on its truth have been theoretically and pragmatically useful. Induction should be considered to be a true and useful artifact of living in a Universe of events of quantized energy mediation.
ReplyDeleteAt least that is how this Engineer tends to look at it. ;)
I've come to this discussion rather late, but I'd like to add my thoughts. Incidentally, I thought of the problem of induction for myself, a few months ago, and was a little disappointed to discover subsequently that it was old hat to philosophers. ;)
ReplyDeleteAs I see it, yes, it's true that induction cannot be rationally justified. But, apart from that, there is no reason or motivation to give it up. Nor is there any alternative on the table. To give up induction is to give up learning from experience. And I doubt we are capable of doing that, even if we wanted to.
(Maybe the lack of an available alternative could be taken as constituting a rational justification for induction. But that would only push the problem back a bit. There cannot be a rational justification for rational thinking itself.)
This is not to say that our use of induction is arbitrary. Our induction-based understanding of the world explains why induction is effective and why we have evolved to use it.
As for deduction, Massimo writes:
ReplyDelete>> actually deduction is provable in the sense that the wrong deduction leads to a logical contradiction, which can be shown in formal symbolic logic.<<
That's right, but you still need deduction in order to "deduce" that wrong deductions lead to contradictions.
I think deduction is one of the irreducibilities we just have to accept - just as induction. If every notion were reducible, we'd end up with an infinity of notions, with a dust of ideas nobody could work with.