The Problem of Induction - N+1 and Penguins
The following is a quotation about the problem of induction by Sextus Empiricus.
"When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars.
But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal: while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite".
Basically the problem of induction is that just because the past is like the past, that does not commit the present and the future to be like the past. We can never practically obtain and sort out all possible facts that can confirm or deny a generality based on our experiences. Using what we have to date may be rendered incorrect as new data which varies from the inductively based theory surfaces.
Consider the following example.
Some scientists study birds. They note that birds have a defining genetic profile. That they fly. Scientists collect data on as many birds as they can. The number of species and birds in each one numbers well into the hundreds of millions. In every case, the birds fly. Using inductive reasoning, they theorize that if some creature is a bird by DNA structure, it will fly.
Let N equal the number of birds studied to date. Let's say for sake of example that the number of birds that fly is 600,000,000.
One scientist goes to Antarctica. The scientist encounters a family of penguins. They appear to be birds. Yet they do not fly. The adult Penguin is the N+1 (600,000,001) that disproves the induction based theory. It looks bird like. It has bird DNA. It does not fly. None of the penguins observed do.
Perhaps as the climate change over the course of time the penguins who once may have flown evolved to adapt to an extremely cold climate at the bottom of the world. So they put on enough weight from fat to insulate themselves, and store sufficient energy to survive such brutal cold.
How does the theory based on inductive empirical evidence that to be a bird the creature must possess bird DNA and fly be handled?
Is the theory wrong because we now have a counter example to it?
Do we dismiss Penguins as bird like creatures because they do not fly?
Are Penguins the exception that prove the rule?
Is the definition of what it means to be a bird to be changed to exclude birds who fly not? Is that fudging? Ignoring evidence simply by changing a definition?
Can the theory be amended to state that all birds fly, unless they need to evolve to adapt to changing conditions where flying cannot be done? Whether by the creature's weight to wing flap ratio necessary to overcome gravity and go up, up and away or some other adaptation affecting flight?
One of a number of ways to handle counter examples is to say that induction provides the basis upon which to generalize. Such generalizations yield working hypotheses. When evidence surfaces that disproves the working hypothesis, a new working hypothesis must be created to accommodate new evidence.
A protocol sentence in the bird case may state that based on past data collected D, class of entities studied C at time T in place P using methods M and instruments I should yield the same result (plus or minus 5 - 10 % for standard deviation) tell us that creatures with certain characteristics and DNA genomes are birds and fly; unless they evolve out of flying to adapt to climate change. Genetic modification is another way to express evolution.
What are your thoughts on the problem of induction?
How to handle it?
Feel free to use this example, or any one you choose.
Kindly define what you think the problem of induction is.
You may want to read the following authors for other formulations of the problem, beyond that of Sextus Empiricus above.
David Hume, Jayarasi Bhata, Duns Scotus, William of Ockham, Nelson Goodman, David Stove, Donald Williams, Keith Campbell, Claudio Costa, Karl Popper, Wesley C. Salmon and David Miller.
This is only a partial list of people who wrote on the topic.
We look forward to your thoughts on this topic.
Please follow site, room rules, and the Four B's.
Be On-Point.
Be Respectful.
Be Positive.
Or Be Gone!
That said, its an interesting topic.
How do you propose we handle it?
P&AB.
Enoch.
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Enoch.
All categorization methods seek to cluster on common characteristics so as to distinguish items of interest. In this case, the items of interest are birds.
Thing is, we are constantly learning. As such, a categorization scheme that currently works well might not be so ideal when new data is made available. It is up to us to refactor our categories to best fit the data. In other words, the data is the truth, the categories are simply a way to organize things for analysis and general comprehension. ( On comprehension: our brains favor clumps - categories. )
Scientists work very hard to come up with good defining characteristics for each category. They seek stable, measurable properties because even though categories can and do evolve as we learn, the change in categories is disruptive. People have to relearn the meaning of categories and there is a bit of short term confusion. For example, Pluto was declassified as a planet because the defining characteristics for the category 'planet' changed. A bit disruptive.
That established:
The category is not technically wrong, per se. The question is if it should be expanded or if a new category is more appropriate. The answer depends on the strength (the importance) of the defining characteristics in the Bird category. If flight, relative to other characteristics, is not considered strong then Penguins would be included as Birds. However a sub-category of 'flightless' would likely be included (especially as new species of flightless birds are discovered).
However if flight was one of the major defining characteristics for the Bird category we would not see Penguins classified as birds. ( Of course, we know that they are classified as birds and that means that flight was a weaker characteristic. )
Dear Friend T1G: Your thumb is clearly on the pulse.
Astute contributions here.
Excellent.
We are grateful.
E.
But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal: while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite".
Such could be written of the universe, for in order to make universal statements about uniformity, mankind would be required to search the entirety of the universe at least once. After which, mankind would be expected to repeat looking over the universal for any new changes.
Dear Brother CB: Precisely the case!
Bulls eye.
In David Hume's, Treatise on Human Nature he sees the problem of induction as one of how humans need to structure their experiences, sensory and instrument enhanced ones in order for us to interpret and make sense of them.
His take is that this doens't reflect objective external reality.
It tells us more about how we perceive than what we perceive and how that interacts.
For this reason he argues that the social sciences should be A Posteriori, empirically and inductively not A Priori, rationally and deductively based in approach.
Great point.
Thanks.
P&AB.
E.
Let's try this. Speaking of love. Experience has shown that generic sets of two people can fall into passionate love for one another and these relationships in the millions endure lifetimes (unto death). There is some general law at work in these 'couples.'
Happens everyday somewhere on the planet.
However, it is equally clear that two people passionately in love - planning to stay together for a lifetime - can without any distinguishable explanation, fall out of their love relationship, deciding to walk separate, single paths (again) at some point. Unexplainable exceptions to the rule.
Not sure this strictly adheres with the subject matter; so looking forward to yours and others thoughts on induction.
Dear Brother CB: Since falling in and out of love happens, it is an observable phenomenon.
Generalizations as to why in both cases can occur.
The problem is that human relations, human interactions have so many variables that it is not at all inconceivable that there will be more counter-example to inductively based working hypotheses than rules which overcome the exceptions.
Psychology, Sociology and Anthropology are referred to as "soft" sciences, since the variables are so great that a reductionist epistemological model so prevalent in the "hard" sciences, Physics, Chemistry and Biology seem not to work nearly as well.
Great question posited.
I wish I had something more constructive than this to post.
Hopefully other cogitators can muck in on this.
All wisdom welcomed.
P&AB.
Enoch.
I can see your point. Stellar explanation!
Thanks, Brother CB.
E.
In many cases the particulars (observed facts) are conditional. Applying an observed fact to different conditions requires an assumption that the facts are applicable under all conditions. So, induction involves both particulars and assumptions. IMO testing an inductive conclusion is more about testing assumptions than it is about testing the particulars.
In the examples of penguins, flight is a behavior (an activity made possible by the physical anatomy of birds). The physical characteristic that makes flight possible are wings covered with feathers. If I observe a dead penguin that has wings covered with feathers, I can deductively conclude that the penguin is a bird.
The inductive conclusion would be that the dead penguin has wings covered with feathers; therefore, penguins fly like any other bird since that is a common behavior of birds. Testing that inductive conclusion (based on an assumption) would require observing the behavior of penguins.
Dear Friend Nerm_L: Alfred North Whitehead once write that the most interesting thing about any system or methodology of thought are the assumptions upon which they rest.
You are right in the thick of Professor Whitehead's ideological constructs.
Good show!
Thanks for your contribution.
You are most welcome in my articles any time.
Peace and Abundant Blessings.
Enoch.
Thanx!
Unfortunately the inductive corollary would be:
Great minds make the same mistakes.
Dear Friend Nerm_L: Indeed it would.
Smiles.
E.
Dear Brother Enoch,
A wonderful and enlightening article, from which I have learned a good deal.
Thank you for sharing it with us. (smile)
Dear Sister Raven Wing: What I do is done by us both.
It is our honor to further the goals of T1G's room on Critical Thinking.
You and I , we are one.
P&AB
E.
Ostriches, Enoch! Emus!
As the Wise Man said, "All generalizations are worthless... including this one!"
Inductive collation of facts breeds generalities, which have the advantages and defaults of all generalities: usually true, and occasionally false.
It's perfectly acceptable to build hypotheses on these possibly erroneous "rules"... but knowing that an hypothesis is built on uncertainty should lead to caution from the holder. Biologists today are pretty careful when using the term "species".
Dear Friend Bob: Great points all.
We are deeply indebted to you.
For your contribution here.
For all you do and bring to this on-line community.
Thanks.
P&AB.
E.
Dear Brother Bob Nelson:
Ostriches and Emus are perfect counter examples to the bird theory used for this article.
Great choice.
Well done.
E.
The inductive principle, however, is equally incapable of being proved by an appeal to experience. Experience might conceivably confirm the inductive principle as regards the cases that have been already examined; but as regards unexamined cases, it is the inductive principle alone that can justify any inference from what has been examined to what has not been examined. All arguments which, on the basis of experience, argue as to the future or the unexperienced parts of the past or present, assume the inductive principle; hence we can never use experience to prove the inductive principle without begging the question.
Thus we must either accept the inductive principle on the ground of its intrinsic evidence, or forgo all justification of our expectations about the future. If the principle is unsound, we have no reason to expect the sun to rise to-morrow, to expect bread to be more nourishing than a stone, or to expect that if we throw ourselves off the roof we shall fall. When we see what looks like our best friend approaching us, we shall have no reason to suppose that his body is not inhabited by the mind of our worst enemy or of some total stranger. All our conduct is based upon associations which have worked in the past, and which we therefore regard as likely to work in the future; and this likelihood is dependent for its validity upon the inductive principle. — Bertrand Russell.
Source:
Dear Brother CB: Hence the term, "working hypothesis".
Theories work until they do not.
Back to the drawing board then, to utilize new facts that came to light.
E.
Enoch, as you may have observed, I am not inherently a joiner of groups.
Yet you pose a good question. It is true, in any given situation, the possibilities are infinite. Yet, in my mind, it makes sense to start at point zero, or point of origin, being that which we know and be willing to expand from there. We know history (hopefully) but no one can definitively know the future.
Little busy and will have to return later.
Thank you.
Dear Friend Dave: We look forward to your return.
We learn from and are inspired by your sagacity and humanity in all forms and forums expressed.
By the bye, you are most welcomed and encouraged to join the new on-line resource room for pastoral care which Raven wing and I co-created and manage.
T1G and Perrie Halpern have been and shall continue to be instrumental in this project for the greater good of our on-line community, all its members and non-member visitors.
There is no obligation to join in order to use.
There is no requirement to visit or contribute.
That said, knowing what are caring and deep thinking person you are, it costs nothing to join.
Who knows when you may want to use it for research, personal use and use for the assistance you can provide to others.
P&AB Always to You and Yours.
Enoch.
Observation can be used in many ways in science. Looking at physical characteristics is one way. But since we can now look at DNA, I think that is the most accurate way of defining a species. In the case of a penguin, it is a bird, by it's DNA.
This has happened with a few other species of animals.
Take the Panda. First, the classified it as a bear. Then they classified it in the raccoon family. Then after looking at the DNA, it went back to a subspecies of bear.
I hope I am not missing the point here.
Dear Friend Perrie: You are precisely on-point here.
The Panda example is a very strong and good one.
I think advances in DNA, and when necessary Mitochondrial DNA (Mitochondria and the Golgi bodies) make this at the moment the best way to classify a genus and species.
Social Security number and passwords a close second.
Smiles.
P&AB.
E.
Perhaps... but at the same time, you're illustrating it.
When we use inductive reasoning - draw conclusions from limited data - those conclusions may be correct... or may not be.
Speciation is a good example. When I was a kid, a species was "mutually fertile" - full stop. Things have gotten s-o-o-o-o much more complicated since then!
There was the problem of terns that were perfectly compatible, genetically... but never interbred. Their species were not physically separated, but rather "socially".
Now, as you say, there's DNA... Dogs are wolves are coyotes are.......
The definition of "species" wasn't "wrong"... but incomplete because it was based on insufficient data.
We do the same thing, all the time. We must, because we usually have insufficient data. It's not a problem... unless we "forget" that our data was incomplete...
Dear Brother Bob: Precisely the point of a discussion on the problem of induction.
We get better by being open to new data.
Great post.
Thanks.
E.