Induction is badly misunderstood. Here is an abridged and augmented excerpt (how’s that!) from Uncertainty’s Chapter 3.
There is no knowledge more certain than that provided by induction. Without induction, no argument could, as they say, get off the ground floor; this is because induction provides that ground floor. No argument could even be phrased if it were not for induction, because phrasing requires language and language requires induction. When we say apple, we know it applies to all apples via a form of induction.
All arguments must trace eventually back to some foundation. This foundational knowledge is first present in the senses. Through noesis or intellection, i.e. induction, first principles, universals, and essences are discovered. Induction is what accounts for our being certain, after observing only a finite number of instances or even one and sometimes even none, that all flames are hot, that all men are mortal, that white is always white, that for all natural numbers x and y, if x = y, then y = x, and for the content and characteristics of all other universals and axioms. Because we know these indubitable propositions more surely than any other, induction produces greater certainty than deduction.
Mistakes in induction occur, as they do in every area of intellectual activity. When a man sees several white swans and reasons, “All swans are white”, he is proved wrong when a black swan in sighted (as in Australia). It would be a gross mistake to condemn induction because of this error. It would be like throwing out algebra because middle schoolers miscalculate.
Since at least Hume it has been fashionable to pretend mystification about why induction is “justified”, or to claim that it is not. Hume said, “We have no reason to believe any proposition about the unobserved even after experience!” The prominent Bayesians Howson & Urbach say that there is no “solution” to induction and that this sad fate “is no longer controversial.” Karl Popper asked, “Are we rationally justified in reasoning from repeated instances of which we have experience [like the hot flames] to instances of which we have had no experience [this flame]?” His answer: “No”.
Fisher was not of the same skeptical bent, but he agreed in principle with Popperian ideas and used these beliefs to build his system of statistics. Theories (propositions) could only be “rejected” and never verified and so on (hell, p-values and hypothesis testing).
One reason induction is widely misunderstood, even considered a “problem” in the academic sense, is because it is analogical. Here, I largely follow Louis Groarke’s wonderful An Aristotelian Account of Induction, which is must reading. There is no way to adequately summarize the entire work, which is long and deep. Only a few highlights sufficient to dispel the sense that induction is “problematic” are given here.
“The goal of induction,” Groarke tells us, “is not simply to prove that something is the case but to provoke an understanding of the general case.” Induction moves from the particularities collected by the senses, and moves to unobservable, unsensible generalities or universals, such as knowledge of a thing’s essence. Induction starts with the finite and progresses to the infinite; so although we can never entirely grasp the infinite, we can and even must know part of it.
According to Groarke’s view, induction is “the cognitive/psychological mechanism that produces the leap of insight” necessary for all understanding. He gives five flavors, aspects, or facets of induction. These are (in my modified terms more useful for probability) (1) induction-intellection, (2) induction-intuition, (3) induction-argument, (4) induction-analogy, and (5) the most familiar induction-probability. The order is from that which provides the most to the least certainty.
(1) Induction-intellection is “induction proper” or “strict induction”. It is that which takes “data” from our limited, finite senses and provides “the most basic principles of reason.” Our senses provide information of the here-and-now (or there-and-then), but induction-intellection tells us what is always true everywhere and everywhen. We move with certainty from the particular to the general, from the finite to the infinite. Without this kind of induction, no argument can ever get anywhere, no argument can ever even start; without it language would not be possible.
Induction-intellection produces “Abstraction of necessary concepts, definitions, essences, necessary attributes, first principles, natural facts, moral principles.” In this way, induction is a superior form of reason than mere deduction, which is something almost mechanical. The knowledge provided by induction-intellection comes complete and cannot be deduced: it is the surest knowledge we have. Numbers come from this form of induction. We see one apple, two apples, three. And then comes 1, 2, 3, … Deduction has much to say about that “…”, but knowing that we can reason deductively comes from this form of induction.
(2) Induction-intuition is similar to induction-intellection. It “operates through cleverness, a general power of discernment of shrewdness” and provides knowledge of “any likeness or similitude, the general notion of belonging to a class, any discernment of sameness or unity.” Axioms arise from this form of induction. Axioms are of course the ground of all mathematical reasoning. We have to be careful because some use the word axiom loosely, and merely mean assumption, a proposition which is not necessarily believed but is desirable. By axiom I mean those base propositions which are fundamental and believed by all those who consider them (like Peano’s axioms, etc.).
The foundational rules of logic are provided to us by this form of induction. We observe that our mom is now in this room and now she isn’t, and from that induce the principle of non-contradiction, which cannot be proven any other way. No universal can be known except inductively because nobody can ever sense every thing. Language exists, and works, because induction-intuition.
(3) Induction-argument, given by inductive syllogisms, is the “most rigorous form of inductive inference” and provides knowledge of “Essential or necessary properties or principles (including moral knowledge)”. An example is when a physicist declines to perform an experiment on electron number 2 because he has already performed the experiment on electron number 1, and he claims all electrons are identical. Induction-argument can provide conditional certainty, i.e. conditional truth.
(4) Induction-analogy is the least rigorous but most familiar (in daily life) form of induction and provides knowledge of “What is plausible, contingent or accidental; knowledge relating to convention, human affairs.” This form of induction explains lawyer jokes (What’s the difference between a good lawyer and a bad lawyer? A bad lawyer makes your case drag on for years. A good lawyer makes it last even longer).
(5) Induction-probability of course is the subject of most of this book. It provides knowledge of “Accidental features, frequency of properties, correlations in populations” and the like. It is, as is well known by anybody reading these words, the most prone to error. But the error usually comes not in failing to see correlations and confusing accidental properties with essences, but in misascribing causes, in mistaking correlation for causation even though everybody knows the admonition against it.
See also the articles on the so-called problem of grue.
Not really sure I see what Induction-intuition is. An example would have been nice.
Induction-analogy and Induction-probability are really the same thing: when I get this situation then X probably happens (even if probably at times implies always). It’s the basis for all hypotheses and is the operating principle for everyday life. In fact, we seem to be wired for it, hence, lucky charms. It goes wrong when the situation is not really the same as the exemplar.
Popper had it right for falsifiable. It means testable. It is the basis for independent verification. Without it (as in deduction), you are running open-loop without any feedback. How do you know when you’ve gone astray?
I used induction-analogy instead of induction-argument. Cursed internet.
Sometime ago I was the Marketing Plans Manager of one of the Big Three automobile companies trying to understand why our share of pick-up trucks remained around 8% while the two top brands each had around 40% of the market. A study was made of our brands sales percent of availability (stock + sales) versus market share of pickup segment. The data showed that when sales percent of availability peaked both sales and share declined. Conclusion: our pickup stock was insufficient to gain market share. Note: dealers tend to increase price as stock declines.
The second element of study the size of the disloyal market of each of our competitive which turned out to be 25% of the total industry. What was happened was that the customers of the two top brands where switching back and forth. This information indicated there was a significant disloyal market that presumably would consider another brand. With our brand at only 8% the opportunity seemed obvious. But these disloyal buyers were nearly impossible to obtain because of insufficient inventory.
I presented this study to top sales management who were not convinced enough to take the risk. A couple of weeks later I showed it to the Controller of our company who took it to the President who made the decision to double shift the truck plant. Sales improved as expected and now have doubled.
Conclusions: Inductive statistics help make decisions and some decision makers lack courage.
“Induction produces greater certainty than deduction.” Is a somewhat bizarre assertion, particularly as we have known since Popper that one process is truth-preserving and the other fictitious.
That no one has ever successfully formulated a Principle of Induction should raise some alarm bells, particularly as it must rely on certain metaphysical assertions about reality, such as a principle of “uniformity of nature”.
Contrast this with the success of Scientific Method, which as elucidated by Popper, does not employ induction in any way.
Tom,
The claim is not only has somebody “successfully formulated a Principle of Induction”, but that somebody was Aristotle, and that an entire book about that formulation has been written. See the link above; buy the book; read the book.
“Here is an abridged and augmented excerpt (how’s that!) from Uncertainty’s Chapter 3.”
Are you joking that you abridged it and then augmented it, so that the result is that it’s unchanged?
William,
“The goal of induction,” Groarke tells us, “is not simply to prove that something is the case…”
Therefore it is possible to use induction to prove that Newton’s Laws are true?
‘induction is “the cognitive/psychological mechanism that produces the leap of insight” necessary for all understanding.’
So, induction not only proves that something is the case, but it also “produces leaps of insight”. I wonder what other amazing properties this process has? Had Einstein really accumulated observations that produced the leap of insight that was General Relativity?
The scientific method deals with how ideas are treated, not how they are obtained.
Actually, natural science is built on induction. It consists of generalizing from a finite number of observations to a universal. Hume’s inconsiderate trashing of induction (and his consequent replacement of causation with correlation) pulled the conceptual rug out from under natural science. No matter how many times one measures the charge of an electron, there is no guarantee that the next electron won’t measure differently. Yet, physicists constantly rely upon that induction.
Ye Olde Statistician,
“Actually, natural science is built on induction”. No it is not. Induction has no place in the Scientific Method.
“It consists of generalizing from a finite number of observations to a universal”. Perhaps, but as we know, that is a fallacy. Science does not, and cannot work that way. Science is about EXPLANATION.
“No matter how many times one measures the charge of an electron, there is no guarantee that the next electron won’t measure differently. Yet, physicists constantly rely upon that induction.”
Really, physicists don’t rely on that or any other induction. Induction is not just a fallacy, it is a myth.
Oh boy…
Consider: “(1) Induction-intellection is “induction proper” or “strict induction”. It is that which takes “data” from our limited, finite senses and … tells us what is always true everywhere and everywhen. We move with certainty from the particular to the general, from the finite to the infinite.”
Data from our “limited, finite senses” … from which we “move with certainty”…
How does one self-assess one’s own senses, and then one’s own analytical capacity, to ensure they are truly credible?
Tom, as a physicist, I don’t consider your statements about science adequate or, to put it more kindly, only partially applicable. As a practicing scientist the general model that I think fits how science is done best is that of Lakatos, where there is a core of fundamental principles, an inner layer of fundamental theories, an outer layer of derived theories, and an outer shell of experimental data. To indulge in some shameless self-promotion, to illustrate how these considerations might be applied see
http://rationalcatholic.blogspot.com/2017/04/whos-winning-scientism-or-our-catholic.html
and
http://rationalcatholic.blogspot.com/2016/02/peeling-back-onion-layers-gravitational.html
Briggs, your comments about the principles of logic being derived by induction are interesting. What about the situation for quantum logic, wherein the distributive law of Boolean logic is not observed; i.e. A*(B+C) is not equal to A*B + A*C, (I’d use logic symbols but they aren’t available), as shown in the double slit experiment. Again, I link to one of my blog posts:
http://rationalcatholic.blogspot.com/2016/03/the-resurrection-of-dead-and-quantum.html
Bob,
“as a physicist, I don’t consider your statements about science adequate or, to put it more kindly, only partially applicable.”
Here’s the thing. None of my statements conflict with the scientific method as elucidated by Popper. He described THE method of science, which just happens to avoid fallacies such as induction. Science is spectacularly successful, and it does not involve induction, or any other fallacious method, in any way. How could it?
“As a practicing scientist the general model that I think fits how science is done best is that of Lakatos, where there is a core of fundamental principles, an inner layer of fundamental theories, an outer layer of derived theories, and an outer shell of experimental data.”
So, as a physicist, and given your core of fundamental principles, what accumulated observations do we need to make in order to induce the theory that unifies quantum mechanics and general relativity?
If Groarke’s book is TL:DR for you, a sympathetic, brief account of Groarke’s argument about induction can be found here:
http://ndpr.nd.edu/news/an-aristotelian-account-of-induction-creating-something-from-nothing/
Groarke’s attempted revival of induction resolves the ‘problem’ of induction by understanding it to be not a problem, but rather a (historically relatively recent) self-generated paradox. Returning to former understandings removes the faulty premises and logic that generated the ‘problem’ of induction, so the ‘problem’ disintegrates.
In short, Groarke makes the meta-case that more recent thinking is not necessarily superior to former conceptions. In effect, Groarke argues that induction is recently on trial not due to a better, superior understanding, but to an inferior understanding whose only virtue is that it is more recent.
It is worthwhile noting that Groarke’s full title is: An Aristotelian Account of Induction: Creating Something from Nothing.
I believe that part of Matt’s fondness for this account of induction, which gives induction pride of place, arises because he senses the need for an impetus, a motion or eros, that must exist prior to, or at least, in conjunction with, intellection — something that gets things going. This is close to Groarke’s ‘induction-intellection’. There is a kind of ‘something from nothing’ about this process we call thought.
Also, Matt has discovered how infallibly frequentist statisticians become inductivists, when the time comes to actually do something.
Finally, we are all inductivists; Matt’s question at the head of his post: “Would you stick your hand into this flame?” is apt.
One is tempted to say that induction is the key process of thought, and that deduction is really a secondary process of thought, operating as a kind of check of induction; one induces a Major — but does the minor, where we begin, really follow from that Major?
To be bold, understanding just is induction, informed by, checked by, deduction.
JohnK
“Groarke’s attempted revival of induction resolves the ‘problem’ of induction by understanding it to be not a problem, but rather a (historically relatively recent) self-generated paradox. Returning to former understandings removes the faulty premises and logic that generated the ‘problem’ of induction, so the ‘problem’ disintegrates.”
So, let’s take you at your word. Einstein must have accumulated sufficient observations in order to induce General Relativity. Once General Relativity is induced – i.e. proved and justified by accumulated observations – what is the point of String Theory?
We can “split hairs” with Tom’s remarks:
“Actually, natural science is built on induction”. No it is not. Induction has no place in the Scientific Method. …
…“No matter how many times one measures the charge of an electron, there is no guarantee that the next electron won’t measure differently. Yet, physicists constantly rely upon that induction.” [Briggs, quoted] …
“… Really, physicists don’t rely on that or any other induction. Induction is not just a fallacy, it is a myth.”
REAL WORLD: Induction . Syllogism can lead to some very wrong conclusions even when each successive premise in a line of reasoning are correct up to the conclusion, for example:
‘The coin I pulled from the bag is a penny. That coin is a penny. A third coin from the bag is a penny. Therefore, all the coins in the bag are pennies.’
or
‘Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald.’
Tom is very correct in saying that induction has no place within the scientific method, however, overreaches in saying physicists (and, presumably, scientists, etc.) do not rely on induction — Induction is routinely used by this ilk as a basis for formulating hypotheses/theories (speculations that appear to have merit, but which warrant further rigorous study to refine/reject one way or other). Tom is correct in saying physicists, etc. don’t “rely” on induction…but they do use and apply it up to a tentative point. “The scientific method deals with how ideas are treated, not how they are obtained.” The distinction is worth emphasizing
What seems absolutely bizarre is this bit from Briggs in response to Tom’s reference to the Scientific Method:
“The claim is not only has somebody “successfully formulated a Principle of Induction”, but that somebody was Aristotle, and that an entire book about that formulation has been written.”
Briggs in that remark is making an Appeal to Authority — a kind of emotional reasoning … side-stepping Tom’s main point; a curious evasion because as much as one must concede Aristotle was profoundly brilliant, Aristotle’s logic falls far & away short of the rigor of the Scientific Method, which didn’t come to exist for millennia and which supplanted such limited analytical approaches as inductive reasoning. Even the Vatican’s astronomer has gone on record about making such illogical associations!
If one is inclined to pursue induction as a means of reaching a conclusion, distinct from merely serving as a springboard of an idea regarding which more rigourous and reproducible research might be conducted, one ought to be pausing to reflect if there’s some ulterior motive(s) prejudicing the analytical outcome.
In this regard, induction is very much like metadata and survey data — not necessarily very credible or compelling, but often enough a sufficient pattern emerges to justify a theory/hypothesis against which more rigorous study might prove or disprove. Curiously, Briggs routinely dismisses wholesale such early evidence [especially when it points to an unpleasant conclusion] and in other instances is quite willing to entertain the apparent principles described [that when it supports a cherished viewpoint].
If one does not self-assess one’s own clarity of interpretation and account for one’s implicit biases, preconceptions and so forth, one is sure to fail in the actual application of the analytical/logical tools. Just like a Marine might be considered a weapon, and the gun an extension of the Marine, the logical tool (e.g. induction) is an extension of the person applying it. All this blather about Popper, Groerke, and whoever about whatever they said is like some kid learning about windage, recoil, drop and so forth in their bedroom and then thinking when they get out on a firing range they’ll be effective at putting the bullet on target because they know “about” using the tool. Any of the analyses saying Carbon 14 dating methods are no good or that Earth is 6000 yrs old & sedimentation strata arose from a single great flood are examples of this kind of failure.
Even in science there is induction from what we believe to be true (with high confidence) to what we believe to be true (with less confidence). This is always true, even when what we believe is logically implied by high-confidence propositions. It’s just that rejection of an implied proposition normally forces us to reconsider the premises.
Science attempts to increase our confidence by testing “what we believe” in conditions where we might find evidence that would contradict our belief. That’s the basis of Popper, and I find it unobjectionable. Science allows us to deductively *reject* beliefs as being universally true (because we have observed a contrary case), but does not allow us to deductively *accept* them as such. All science is subject to rejection. Even “fusion will occur if [such and such conditions are met]” is inductive, and subject to falsification.
And even Popper would (I believe – too late to ask him) admit that our rejection owes something to induction. We have to trust that we correctly observed that which caused us to reject, and that we are correct about the logical implications.
How do we know that every electron, even those unobserved, has the same charge? How do we know that the next time we combine sodium and chlorine, we will get salt?
++++
A logical “fallacy” does not mean that the proposition is false.
https://lastedenblog.wordpress.com/2017/03/11/fallacies-arent-what-you-think-they-are-and-they-arent-very-useful/
Thus, Popper and his proteges held that while one may be fearful of walking out of a high window, the outcomes of earlier defenestrations did not provide a basis for that fear! Empirical evidence not only fails to increase the likelihood that a theory was true, it does not supply any basis whatsoever for believing it.
That is, a scientific theory is never deducible from the observational evidence for it. Popper and his followers deny, with Hume, that propositions about the observed can ever be a positive reason to believe a scientific theory. One may as well invent a theory from pipe dreams and political necessities. It has no less support than one with a pile of empirical observations.
But the EXPLANATION is what we call “physical theories,” and they just are what induction produces.
Wait. Physicists do not rely on all electrons having the same charge? Or that the laws of physics might not apply over there? That seems bizarre.
If it is, then the References at the end of every scientific paper is a bundle of appeals to authority. Citing a source for an argument is not an appeal to authority.
An appeal to authority is not a formal fallacy. It is a material fallacy. A material fallacy is such because of the subject matter, not its form. E.g., If one were to cite R. Dawkins in support of an argument on the existence of God, that would be a fallacious appeal to authority, for the excellent reason that he is not an authority. But to cite A. Einstein in support of an argument in relativity would be valid, since in that theater, Einstein really was an expert.
Aristotle was cited as the source for reasoning by induction. http://classics.mit.edu/Aristotle/posterior.html
Which scientific method is that? There are so many.
One syllogism given by Aristotle is what is called modus tollens, which has the form:
M. p?q
m. not-q
/:. not-p
This is precisely the reasoning employed by Popper for his falsification doo-dah. So be careful what you denounce as “limited” and “supplanted.”
Aristotle’s approach, perfected by Grosseteste in the Middle Ages was that we start with observations (quia) and proceed inductively to an explanation (propter quid). In the “work of the intellect (negotiatio intellectus) different propter quid are considered and discarded until the best is identified. Then one proceeds deductively from the propter quid to the quia, but these quia must not be the same ones used to induce the theory in the first place. That is, the theory must predict new observations. That is: induction from the facts up to the theory; then deduction from the theory down to new facts.
Naturally, all theories derived from evidentia naturalis, as Nicholas of Autrecourt said in the 14th cent., might be shown wrong by new facts. (He used the example of “grass is green” by pointing out that somewhere there might be grass which in its natural and flourishing state was yellow.)
With one exception, propositions based on empirical data could only be known probably. (The exception was self-existence, which is known by direct empirical experience.) Only propositions demonstrated by evidentia potissima could be held with certainty.
+++
The “problem” of induction: plato.stanford.edu/entries/induction-problem/#DemArgShoSouInd
Critique of irrationalism in science can be found here:
ontology.buffalo.edu/stove/preface.html
Esp. Part 2:
ontology.buffalo.edu/stove/part-two.html
Ye Olde Statistician,
“How do we know that every electron, even those unobserved, has the same charge?”
We know all electrons have the same charge because we have explanatory theories that tell us electrons have certain properties. While we’re on the subject of fundamental particles, I wonder how much induction went into the discovery of the Higgs, particularly as it was discovered in 60s and not observed for 50 years.
“Thus, Popper and his proteges held that while one may be fearful of walking out of a high window, the outcomes of earlier defenestrations did not provide a basis for that fear! Empirical evidence not only fails to increase the likelihood that a theory was true, it does not supply any basis whatsoever for believing it. ”
If you want to do science, then you seek theories that explain the phenomenon you are interested in. If all you seek is a justification for your fear, I suspect you’ll discover something to your satisfaction.
I’m sure you’re aware of the intellectual history of theories of why objects fall, which is a fascinating tale. I have never come across any account of the set of accumulated observations that caused Einstein to induce his explanation of gravity. It seems, from all accounts, that Einstein was trying to solve a problem that was not motivated by observation in any way, but rather by requirements of theoretical consistency.
“That is, a scientific theory is never deducible from the observational evidence for it.”
I don’t think even hard-core inductivists believe that.
“Popper and his followers deny, with Hume, that propositions about the observed can ever be a positive reason to believe a scientific theory. One may as well invent a theory from pipe dreams and political necessities. It has no less support than one with a pile of empirical observations. ”
That is non sequitur. You ARE free to invent a theory however you wish, and it will enjoy no less support than its competitors. Subject your theory to the Scientific Method and see how it fares.
In fact, why don’t you induce a theory?
Interesting post! However, the distinction between “induction intellection” and “induction intuition” seemed to be vague without much difference if any. It seems that the Law of Non-Contradiction could be classified as your first form of induction if it’s about inducing commonsense principles of reason. Also what about the theory of innate ideas? Are there certain notions that are innate as some philosophers have argued?
I make that bowled out for a duck.
This post has cleared up why induction is a problem. The fact that it isn’t a problem is the problem. Those who don’t think they do anything by faith first and those who know that everybody does, every time they take a step and their reflexes and automatic movement don’t fail. Some things have to be assumed or trusted as what is known until now based on experience.
An appeal to authority is no guarantee. That is an example of induction.
Like Thomas Aquinas was wrong about the humours and Aristotle about flies and teeth.
They are fallible. So what about why they were wrong. It’s the truth that is of interest.
Faith trust and respect in the authority underpin the appeal to authority or the theory or argument can just be taken on it’s own without the merit of the expert who holds the theory to be true.
People use induction all the time in clinical reasoning. The thing can’t run without it. Unlike how some seem to think things run, on paper results and research in the minute detail of every possible decision scenario. That’s not what happens except in well defined examples. At least in most cases people do use their common sense and do not put undue faith on a mechanical system of truth seeking. They are, for the most part outside of social science and politics, doing the right thing. They do so despite ‘Papers’ muddying the waters telling them this works or that works best. Sorry but when a decision is to be made you have a few moments or minutes. Those decisions are only as good as the information to hand. Once that’s gathered, ‘scientific method’ doesn’t come into it except indirectly. They still call the discipline science.
Induction must be prime or people are throwing away their own mind and judgement in the aim of trying to be dispassionate and it is not necessary to be one or the other. The operator or the scientist is only as good as their ability to rule out bias.
I was always plagued by the thought did it work for the reason you thought? Like Doug M’s confidence in the theory. There is always the chance that the theory is wrong but the outcome was good. like the dog who barks at the postman and learns that it works, he goes away! In the dog’s world that’s al that matters. When the mind is expanded and more truth is revealed more thinking is required and for that more induction is required from what is observed or sensed from the world around.
At least this above discussion has made a simple thing simple. Perhaps by accident but a happy one.
What a waste of time! Just to tread water. Sod Grue to hades.
Where did the theory come from? Who observed the theory?
“It has become clear that the desired objective reality of the elementary particle is too crude an oversimplification of what really happens.” … [T]he atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.” –Werner Heisenberg
That’s called “induction.”
That was one of the charges that the Aryan physicists laid against relativity. However, I think the precession in the nodes of Mercury’s orbit was at least one such fact. He also believed the speed of light was constant regardless of observer, though this was the result of an induction, not of empirical facts. Who has ever observed any such thing?
Of course not. That was Popper’s stance and he was under the spell if Hume.
No, Popper and the other irrationalists held explicitely that there was no connection whatsoever between the facts and the theory.
I can’t. According to Hume, Popper et al., observed facts have no relationship to the theory, and the scientific methods — at least the classical one used by inductionists — relied on facts.
We did it all the time in math. Prove that IF p is true for k, then it is true for k+1. The prove that it is true for k=1. It then follows inductively that p is true for all values of k.
Galileo proved both that the moon is a sphere and that it had mountains on it by induction. In the former case, he considered every geometric shape and determined whether that shape could account for the observed phases and other patterns in the data. (This was a true induction: he went through all possible shapes that might present a circular face to observers on earth: a bowl, a cylinder seen head on, a plate, etc. When all alternatives have been eliminated, whatever remains, however improbable, must be the truth.) He did not observe mountains on the moon. The telescopes of the time did not allow sufficient focus, magnification, or field of view; nor was it yet established (by induction) that instrument-mediated observations were true. What he (and Harriot before him) observed was a pattern of light and darkness near the limb of the moon. Because Galileo had trained as an artist, he immediately recognized the chiaroscuro and inferred that these were the peaks of mountains still receiving sunshine that the valleys were not.
YOS, I’m enjoying and learning from your comments, but I would like to emend your comment about Galileo’s inference that the moon had mountains and seas by looking at shadows cast at various angles with the sun’s rays. This, I believe, is an example of “retroductive reasoning”, i.e. using a model to represent an actual situation. The same sort of modeling is used, for example, in representing molecular vibrations as simple harmonic motion following the differential equations corresponding to point masses attached to a weightless spring. See, for example, Ernan McMullin, “A Case for Scientific Realism”, at
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.542.950&rep=rep1&type=pdf
Bob,
Are you referring to C.S.Peirce’s retroduction (aka abduction or “inference to the best explanation in it’s A.I. incarnation)? Peirce had three forms of inference: deduction, retroduction, and induction. Much of this discussion seems to be confusing the second and third forms. If one claims there is only deduction, how does one justify, say, a likelihood function or any form of pooling data (e.g across experiments).
@ Bill R… As I’ve learned it, abduction is what “Inference to the best explanation”, i.e. as Sherlock Holmes said, (paraphrasing) “if all explanations have to be discarded, except an improbable one, then that is the one to be accepted”. Retroduction is using a model to explain a more complicated one, e.g. point mass attached to a massless spring to explain molecular vibrations. I didn’t know about C.S. Pierce’s work, but as I’ve read it (I’m trying to remember where), abduction and retroduction are different forms of rational inquiry. I’ve gone through this in more detail in a blog post, “Why do we believe…” at
http://rationalcatholic.blogspot.com/2017/07/why-do-we-believe-and-why-doesnt-god.html
@ Bob Kurland
Thanks for your reply. Peirce’s explanation evolved and he changed the label several times, but retroduction was a term he used, along with both abduction and hypothesis for the same form of reasoning to generate explanations for “odd” events. IBE seems to be the CompSci version (e.g. Josephson and Josephson’s book.)
Abduction/Retroduction doesn’t limit you to a single hypothesis, being more of a “how can I explain this weird result” exercise, while induction, as I use it, becomes a “does this explanation allow me to repeat the effect under varying circumstances?”, using deduction to fill in the details. Narrowing this to IBE requires the addition of some ordinal or better metric for “best” (e.g. a logical probability.)
In any event Peirce (a fallibist himself) was quite clear that it was fallible, like induction. This seems to confound the deduction types, and seems to lie at the root of the ongoing “p-value” controversy.
Thanks Bill for your explanation. As long as the two modes of rational inquiry, IBE and using a model are distinct, I’d like to continue using different names for the two. I’m still trying to find out where I got the difference–I got the term retroductive from Ernan McMullin’s essay (linked in a previous comment), but I don’t remember where the “abductive” link to IBE came from… maybe Stephen Meyer’s book, “The Signature in the Cell”?
@Bill R. I now remember where I picked up the bit about abductive and retroductive methods of inquiry: “Labyrinths of Reason…” by William Poundstone.
Bob,
In my retirement, I’ve been trying to read Peirce, and Patrick Laurie Davies.
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Gonna try to see how this division of induction matches the “at least six different kinds of induction” in Part XIV of Peter Kreeft’s Socratic Logic.
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