-Submitted by David Drumm (Nal), Guest Blogger
Induction is the type or reasoning from specific examples to general statements about reality. Induction is often used to justify the claims regarding the future. The problem of induction was first formulated by David Hume (left), though he didn’t use the term “induction.” The problem of induction occurs when we ask ourselves “how do we know that induction is a reliable rational tool?” The usual answer is that induction has worked in the past. But that answer justifies induction inductively, using circular reasoning (a logical fallacy).
How can we justify using induction to predict the future non-inductively?
Throughout our lives, but particularly during infancy, we learn about reality by perceiving and interacting with it. We form a mental model of reality. One aspect of reality that we learn is that many aspects of reality are not completely random with respect to time. A reality in which events happen randomly from one time interval to the next, would appear very different from the reality as we perceive it.
Reality is a set of random processes. Some of the random processes are completely random from one point in time to another point in time, for example, the flipping of a fair coin. The outcome of a flip at one time is independent of the outcome at another time. There is no correlation between from one point in time to another point in time. Other random processes do possess a high degree of correlation, for example, the rising of the sun from one day to the next. Other random process, like the weather, exhibit some short term (hourly) correlation but less correlation long term (weekly) and then more correlation (yearly). Random processes that display correlations that depends only on the difference between points in time are described as wide-sense stationary (WSS).
Reality is a set of WSS random processes, each with its own correlation. This is a mental model that has been created through experience. How do we know that in the future reality will still maintain its WSS property? We don’t. However, if reality ever lost its WSS property, the effect would be complete and utter chaos. With the loss of the WSS property, events that were previously improbable would become probable.
But aren’t we assuming that the WSS property is an inherent characteristic of reality? Aren’t we assuming the “uniformity of nature” will continue over time? Maybe, but we have shown that the absence of the WSS property would alter reality as we know it.
Using reality’s WSS property, we can predict, with varying degrees of confidence, future events. If there is no independence between present events and past events, for a particular random process, in the set of random process that constitutes reality, the probability that an event (A) will occur given that event (B) occurred, is strictly greater than the probability of event (A). That is, P(A|B) > P(A). Therefore, the probability that the sun will come up tomorrow given that it came up today is greater than the probability that the sun will come up tomorrow. The probability that the sun will come up tomorrow given that it came up today and yesterday is greater still. This can be continued over the millions of sunrises, but it will never equal one. There’s always the chance that a rogue black hole will happen by and ruin our day.
Christian apologists often use the problem of induction to claim that “Science is based on faith too, so there!” However, their justification for using induction, that God did it, is unsatisfying,
James Clerk Maxwell, formulator of classical electromagnetic theory, in 1850 wrote:
The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind.
OK … for a little bit of time I felt like the stupid FBI agent trying to make sense of Charlie Eppes’ plan to uncover the criminal’s hiding place on the program, NUMB3RS.
But I think I’ve got it now … One does not need to assume Christianity to make sense of induction … ?
Mike,
That was clever, on topic and sadly true.
Triple word score.
And for the record, the all-time best third baseman ever to play for the Yankees is not Alex Rodriguez, but Graig Nettles.
The Mets have a Ball club? Since when?
As a lontime Mets, previously Dodgers fan, who hates the Yankees, I can categorically state that Derek Jeter is the greatest Yankee shortstop ever and a Hall of Famer. The problem is that Yankee fans in general are victims of inductive reasoning and so believe that their team must always win and their stars must always be great. When they don’t perform up to past standards the Yankee fan feels betrayed because they’re incapable of understanding that past performance in Baseball can almost never accurately predict future performance, there are far too many variables. Thus it is not their logic that has betrayed them, nor their team, but the individual player who has not performed in line with his past history.
911 was not Bush’s fault. It was the previous administrations inaction’s that lead to Mr. Bush’s comfort.
If you’d been listening to NY sports radio just last week, you would have heard the entire Yankees fan base complaining how Jeter wasn’t producing enough to stay at short.
Spoiled ungrateful bastards.
Me, I’m thrilled with the production and game calling of Russel Martin.
Well . . . it was only against the hapless Rangers.
How about the metaphysics of Derek Jeter hitting back to back home runs?
Buddha,
You know you’re preaching to the choir. Just imagine if the country so much as attempted to think critically about 9/11.
http://www.harpers.org/archive/2004/10/0080234
However, to bring up the topic of induction, in and of itself and not in connection with a question of something like causation or evidence in a case, just seems a tad out of place.
“What harm
athe tonic of informed critical reason except against their foul agendas?”Correcting what happens when you let cats edit.
Two words for you, Bob.
Critical thinking.
How to think is more important than what to think. We can see the consequences of failure to teach people how to think critically simply by tuning in to FAUXNews or by reading the comments of the Trollish. Given that law requires critical thought and that the study of politics (and indeed any subject) is enhanced by critical thought, I’m not sure I see your objection. How many “mini-course” in logic have been given by commentators over the years? Just by me, you and mespo alone it must be in the dozens if not hundreds. I have no issue with general logic topics as subject matter in this forum. Anything to improve the quality of American thought is a good thing at this point. “Above all things I hope the education of the common people will be attended to ; convinced that on their good sense we may rely with the most security for the preservation of a due degree of liberty.” – Thomas Jefferson, letter to James Madison dated December 20, 1787. Since our current lot of pols and corporatists have a vested interest in dumbing down the populace? What harm a the tonic of informed critical reason except against their foul agendas? None I say.
Just out of curiosity, while Hume’s epistemology is interesting, how is the problem of induction a topic for a law blog?
Robert Pirsig:
“To follow Kant one must also understand something about the Scottish philosopher David Hume. Hume had previously submitted that if one follows the strictest rules of logical induction and deduction from experience to determine the true nature of the world, one must arrive at certain conclusions. His reasoning followed lines that would result from answers to this question: Suppose a child is born devoid of all senses; he has no sight, no hearing, no touch, no smell, no taste…nothing. There’s no way whatsoever for him to receive any sensations from the outside world. And suppose this child is fed intravenously and otherwise attended to and kept alive for eighteen years in this state of existence. The question is then asked: Does this eighteen-year-old person have a thought in his head? If so, where does it come from? How does he get it?
Hume would have answered that the eighteen-year-old had no thoughts whatsoever, and in giving this answer would have defined himself as an empiricist, one who believes all knowledge is derived exclusively from the senses. The scientific method of experimentation is carefully controlled empiricism. Common sense today is empiricism, since an overwhelming majority would agree with Hume, even though in other cultures and other times a majority might have differed.
The first problem of empiricism, if empiricism is believed, concerns the nature of “substance.” If all our knowledge comes from sensory data, what exactly is this substance which is supposed to give off the sensory data itself? If you try to imagine what this substance is, apart from what is sensed, you’ll find yourself thinking about nothing whatsoever.
Since all knowledge comes from sensory impressions and since there’s no sensory impression of substance itself, it follows logically that there is no knowledge of substance. It’s just something we imagine. It’s entirely within our own minds. The idea that there’s something out there giving off the properties we perceive is just another of those common-sense notions similar to the common-sense notion children have that the earth is flat and parallel lines never meet.
Secondly, if one starts with the premise that all our knowledge comes to us through our senses, one must ask, From what sense data is our knowledge of causation received? In other words, what is the scientific empirical basis of causation itself?
Hume’s answer is “None.” There’s no evidence for causation in our sensations. Like substance, it’s just something we imagine when one thing repeatedly follows another. It has no real existence in the world we observe. If one accepts the premise that all knowledge comes to us through our senses, Hume says, then one must logically conclude that both “Nature” and “Nature’s laws” are creations of our own imagination.
This idea that the entire world is within one’s own mind could be dismissed as absurd if Hume had just thrown it out for speculation. But he was making it an airtight case.
To throw out Hume’s conclusions was necessary, but unfortunately he had arrived at them in such a way that it was seemingly impossible to throw them out without abandoning empirical reason itself and retiring into some medieval predecessor of empirical reason. This Kant would not do. Thus it was Hume, Kant said, who “aroused me from my dogmatic slumbers” and caused him to write what is now regarded as one of the greatest philosophical treatises ever written, the Critique of Pure Reason, often the subject of an entire University course.”
Robert M. Pirsig,
“Zen And The Art of Motorcycle Maintenance”
These are the shared thoughts and discussions like this that the tea party are afraid of.
IMHO,Education.
Nal,
I think a lot of the value of induction must be viewed in the light of how the user understands uncertainty. Upon reading about the subject of uncertainty, it should be apparent that induction or any sort of forecasting is subject to caveats. Certainty to any degree of reliability is only possible on scales much smaller than the whole, or as Dredd put it, “all truth is local”. This comports with the observations of Einstein’s general relativity (reality is dependent upon point of observation, frames of reference), Heisenberg’s uncertainty principle (observation and the fixing of frames), and with Gödel’s incompleteness theorem (if a system is consistent, it cannot be complete and the consistency of axioms cannot be proven within the system itself).
Can induction be used to predict the future? Yes, it can, but the caveat is that it cannot predict with absolute certainty. The value of induction as a tool is without question, but the key is not to place absolute faith in it. Like all tools, it has functional parameters one must be mindful of. I think any scientist or logician who does not keep induction in the proper perspective is making the same mistake religious thinkers are – faith based reasoning. However, I also think most scientists worth their salt expect the unexpected by training if not (usually) by inclination. For isn’t that part of the joy of discovery itself: the joy of finding the unknown and unexpected? Aye, verily.
Fresh viewpoints on the application of logic are fascinating, its likely origins for me, were born on day one, hour one, of my Logic 101, back in the day. I can still hear our professor’s voice – Dr. Richard Hahn – echoing in my generally empty head. His head wasn’t the slightest bit empty. It was chock full of very cool stuff.
Among other thoughts, Dredd’s mention of “all truths are local” brings to mind what I fear is an erosion of collective reasoning, with respect to what so many of us consider near absolutes. One of those might be, say, human rights. What that originally meant vs what it means today.
Now, it’s a given that “all truths are local” is an expression of the inherent value of viewing reality through the cultural lens. And that’s nifty. But if someone hasn’t already coined a concurrent phrase for an equally logical maxim – something like, “all truths are stitched to the fabric of time” – then I supect we’re missing something important.
We seem to have an irrepressible gene – we educated primates – programmed to stretch common sense thinner than wafer, and yet expect it to hold water across eons. The recent discussion of whether a fruitcake with an attitude had the god-given (actually, man-given) right to “bark” at a restrained police dog, comes to mind.
Must humans stretch logic to absurdity? Is it inherent to our corpuscles?
We step to the edge of a logical precipice and gain a terrific perspective of our world. We take one more step – like forgetting that anointing “rights” to a human baiting a police dog is inherently mad – and down we go.
Gravity usually wins.
So I guess my point is that in the objective, we instinctively know that some things are wrong.
And one of them, it certainly appears to me, is ignoring that “truths” – like Carl Sagan’s cosmos – might very well be bending to the point of no return.
But I know…”To Infinity and Beyond”….Buzz Lightyear…..
Dredd wrote:
“Some things are “unknown” because we don’t want to know them.”
Painfully true…
The metaphor “the Sun rising” means many things, but it is technically imprecise.
In cosmological terms, of course the Sun does not rise.
Instead, the Earth rotates to make the Sun visible to the observer once again.
That requires three things: 1) a Sun, 2) a rotating Earth, and 3) an observer.
The last two are known not to be guaranteed in the long term future, so the speculation of the formula knowingly fails.
Some things are “unknown” because we don’t want to know them.
http://ecocosmology.blogspot.com/2009/11/life-according-to-science.html
Any tool can be misused. For example, a hammer can be used to build or to destroy.
The same holds true for all of the cognitive tools.
Thus, often times it takes work to filter out imperfections or misuses of cognitive tools, but every time that work is done it is well worth it.
There was an official statement in England “the queen has no legs” at one time, which had the force of law.
It was about the same time “the king can do no wrong” official statement gained ground.
The latter is still with us, even with all of our cognitive tools available in the legacy of the practice of law.
http://powertoxins.blogspot.com/2011/04/sovereign-immunity-source-toxins-of.html
There are many lenses pulling and pushing on the way we see induction.
“All truth is local” is a cognitive tool statement that has valid application, because the local lens is one of the more powerful energies always working on the formation of truth.
http://blogdredd.blogspot.com/2011/05/all-truth-is-local.html