Let us have the following:
(P1)For each theory H, there is always another theory G such that G and H are empirically equivalent in the ‘weak sense’, (they are empirically equivalent in the weak sense if potential future observations may break this equivalence); (P2) if G and H are empirically equivalent in a weak sense, there is no reason to believe in H and not in G; (C) To contest this argument, it seems necessary to refer to extra-empirical reasons. It must attempt to show how, despite the empirical equivalence, there are other reasons for preferring one theory to another. For example, Popper proposed two preference criteria; he argued that G should be ignored if it were ‘ad hoc’ or did not imply predictions empirically falsifiable. A representative case is that the evolutionary theories are preferable to creationist ones.
Of course, both are compatible with the collected evidence (although the supporters of both parties argue that it is only his own) because they were built in compliance with it. Evolutionary theory, however, allowed to make some predictions (later proved correct): assume that men and chimpanzees are closely related species implied that morphologically intermediate species should be found and this is what happened with the discovery of Australopithecus. Nowadays the forecasts confirmed by the evolutionary theories are numerous and go beyond this simple example. By contrast, the creationist theories do not seem to have ever made falsifiable predictions and seem built ad hoc. Another way to build an ad hoc theory is the following:
G asserts that all what has been observed so far is compatible with H, but that the next observation will be different. In this case, what helps to choose in favor of H is induction. As past experience has never shown cases of sudden change of natural laws, inductively speaking we believe that the next observation will confirm H.
A simple argument to consider the possibility of underdetermination is that of the adjustment of the curve. It should be pointed out, incidentally, that in general we have the phenomenon of underdetermination when there is a situation where there is no true description, because information is not sufficient. The empirical underdetermination of scientific theories (due in part to Duhem and in part to Quine), according to which different theories can be compatible with the same set of observational data, result that the choice between theories would be based on pragmatic considerations of simplicity and comfort rather than on their capacity to provide a true representation of reality.
Let us return to the adjustment of the curve and assume that some scientists have derived experimentally a number of data that have been placed on a graph. If they had to draw the curve (function) that connects two quantities (for example), they will be inclined to use the one that best suits the results, even considering simplicity, elegance, consistency with other formulas and theories (what philosophers call ‘super-empiric virtues’). However, from a purely theoretical point of view, given a finite set of points (the data on the graph) there are infinite curves that pass by each of them. We call these curves or theories empirically equivalent in the weak sense.
Dear Gianrocco Tucci,
If two theories are empirically equivalent on a given set of data, it does not mean that they will predict similar results in general. The Ptolemy model and the Copernican model at the time were empirically equivalent for the prediction of the stars and planets movements in the night sky but the Copernican model was far simpler for the same prediction and had far wider domain of applicability (the implications of the model were not limited to the movement of the planets and fixed stars in the night sky) and it is the later feathure that really distinguish the two models.
So two theories may be empiriclly equivalent on a given set of data but vasly different in domain of applicability. A screw driver is design to screw/unscrew screws but can be used to so many other purposes and thoses might be more important than screwing/unscrewing. So two different design of screw drivers migh be equivalent for screwing/unscrewing but one of them might be a wounderfull general tool and the other not.
‘’Copernicus and his followers were guided by the heliocentric system to their enguiries. They pursued the problems suggested by the Copernican layout of the Universe. Kepler’s Third Law, relating the square of planetary periods inversely to the cube of planetary distances from the sun, also elaborated a problem set by Copernicus, by observing how orbital periods steadily increase with the planet’s distance from the sun. The First and Second Laws introducing the elliptic paths, with the sun in one focus of them, could hardly have been conceived by anyone who ignored the heliocentric system; for it made no sense in the Ptolemaic system. And it was of course Kepler’s laws, combined with findings of Galileo, that set Newton his task and preapared his triump.’’ http://polanyisociety.org/Duke/Duke1.pdf
The above celebrated case illustrate that a theory is not simply an encapsulation of data but a thinking tool and two empirically equivalent theory may be two totally different thinking tools and choice between them could often be made on the fruitfullness in terms of thinking tools and here aesthetic considerations play a big role for a scientist although they cannot be used to convince others. For that only concrete discoveries sudgest by that aesthetic choice will vindicate this choice..
Dear Gianrocco Tucci,
If two theories are empirically equivalent on a given set of data, it does not mean that they will predict similar results in general. The Ptolemy model and the Copernican model at the time were empirically equivalent for the prediction of the stars and planets movements in the night sky but the Copernican model was far simpler for the same prediction and had far wider domain of applicability (the implications of the model were not limited to the movement of the planets and fixed stars in the night sky) and it is the later feathure that really distinguish the two models.
So two theories may be empiriclly equivalent on a given set of data but vasly different in domain of applicability. A screw driver is design to screw/unscrew screws but can be used to so many other purposes and thoses might be more important than screwing/unscrewing. So two different design of screw drivers migh be equivalent for screwing/unscrewing but one of them might be a wounderfull general tool and the other not.
‘’Copernicus and his followers were guided by the heliocentric system to their enguiries. They pursued the problems suggested by the Copernican layout of the Universe. Kepler’s Third Law, relating the square of planetary periods inversely to the cube of planetary distances from the sun, also elaborated a problem set by Copernicus, by observing how orbital periods steadily increase with the planet’s distance from the sun. The First and Second Laws introducing the elliptic paths, with the sun in one focus of them, could hardly have been conceived by anyone who ignored the heliocentric system; for it made no sense in the Ptolemaic system. And it was of course Kepler’s laws, combined with findings of Galileo, that set Newton his task and preapared his triump.’’ http://polanyisociety.org/Duke/Duke1.pdf
The above celebrated case illustrate that a theory is not simply an encapsulation of data but a thinking tool and two empirically equivalent theory may be two totally different thinking tools and choice between them could often be made on the fruitfullness in terms of thinking tools and here aesthetic considerations play a big role for a scientist although they cannot be used to convince others. For that only concrete discoveries sudgest by that aesthetic choice will vindicate this choice..
To Gianrocco Tucci
There is an article ‘Z-Theory. Foundation and Frame’ (downloadable from my profile) that explains way of creation of every theory in comparison with the theoretical framework of Z-Theory.
Suppose now that they have two theories H and G that explain the same phenomenon. But those theories use different ways of explanations. To make comparison of those theories they should study basic assumptions used as the basis of both theories. Different basic assumptions lead to different explanations of the same phenomenon.
Usually, each theory has some ‘ground-level’ assumptions. Therefore, as long as those Ground Level Assumptions (GLA) have not any difference those theories are generally compatible and explain phenomena without much difference.
However, it is quite possible for two theories to use different GLA. In that case, those theories become incompatible at the ground level and explain the same phenomena by incompatible ways. Obviously, that is the most intriguing situation because acceptance of any given theory from any set of such theories means acceptance of all GLA of a given theory also!
However, there is a critical problem here. Suppose that there are two GLA-incompatible theories H and G. They chosen theory H and decline theory G. What does happen that way? The result is obvious. The entire science goes by the only one “right way” predicted by the theory H and every evidence of theory G will be declined as well even they appear later and stronger.
That situation lasts as long as a new theory F appears and covers the same area but uses a different GLA and gives answers on many questions that were “unanswerable” ever before. In that case, GLA of any older theory become wrong and the theory becomes falsified.
That is a Standard Circle of Comprehension Improvement (SCCI). It appears again and again in science. As a result, older theories become falsified and new theories take their places regardless of any “imaginable power” of those old theories.
Have we any example of such situation today?
Yes we have. There is a theory that uses a postulate at Ground Level Assumptions about inability of an observer to detect his motion relative to light. That postulate was proposed in 1905 (more than 100 years ago) and based on the assumption that rests on some experiments known that time (Michelson-Morley Experiment, MME).
Today, we have a patent application WO/2015/040505 that describes some technology that exceeds limitation caused by the old postulate. Many scientists think that the device contradicts a “well established theory”. That is incorrect point of view because the technology was developed by different Ground Level Assumptions and physical operability of the device supports all of them.
Dear Professor Tucci,
In my eyes, out of the four classical types of mathematical proofs - deduction, induction, contradiction and counter example, induction is the strongest kind of proof.
C. Hemanta K. Baruah "In my eyes, out of the four classical types of mathematical proofs - deduction, induction, contradiction and counter example, induction is the strongest kind of proof."
A. The question was about different theories that describe indistinguishable properties of the same set of experiments.
In that case, there is not any methodology that can help researchers.
For example, suppose that there are two points A and B. An observer observes motion of an object between those points on a round-trip motion (an object moves from A to B and from B to A).
The easiest conclusion from the experiment is this duration of the round-trip experiment has two equal parts of motion by AB-Trajectory and BA-Trajectory. Therefore, full duration of that experiment is equal for doubled duration of each on-way motion.
D = 2 DAB; D = 2 DBA (1)
Everything looks fine but the problem has another solution
D = (DAB + NAB )+ (DBA – NBA )= DAB + DBA = 2 DAB (or 2 DBA) (2)
If something using round-trip between points A and B has some influence that increases its speed (+NAB) in one direction and decreases speed (-NAB) in the opposite direction, the full duration of the experiment has not any changes (like motion of a boat up and down the stream along the same distance measured on the river shore).
As long as the observer is able to detect only dull duration of the experiment he keeps the inclusion (1) and ignores possibility (2). Therefore, he uses a theory that uses only assumption about equality of durations of motion in two opposite directions and declines any other theories and explanations because they “contradict” his theory based on the assumption (1).
That is the current situation in physics. There is a long lasting theory of Relativity that was born on the assumption (1) of light (two-way) propagation. They used two-way experiments like Michelson-Morley type experiments to build the theory. Obviously, any one-way experiment “contradicts” the theory because it shows a different result (2).
However, in reality, that theory contradicts correct experiments. Full explanation of the situation is given in the paper ‘The Epistemological concept of the True Space-Velocity Detector’ (downloadable from my profile)
Article The Epistemological concept of the True Space-Velocity Detector
Dear Zade,
No, no! I just said that induction is a very strong kind of proof. With reference to certain examples, my statement may actually be wrong. Not everything can be proved by the method of induction after all.
Dear Gianrocco, I am not sure that I really understand the terms you use to formulate the question (especially "theory" and "induction"). They are very deep. But let me try anyway to elaborate on your interesting question, hoping we use these terms in a similar manner and referring to the case of "physics" that I understand a bit more.
In my understanding, physics is deductive-inductive science, so this case is quite pertinent. Induction is a (or perhaps the) way to formulate new hypotheses, that can be later exploited, tested, used to get predictions. Induction is a very subtle moment of the investigation; there is no general rule, and Newton himself warned us to be cautious--recall "hypotheses non fingo".
Anyhow suppose we reach some hypothesis, by using empirical or also extra-empirical information. We have to keep track of the validation steps; I mean, if this hypothesis leads us to failures over failures, the rule of science is: put it aside (example: aether theory). If it works, we continue to use it (example: relativity). If we have two hypotheses with similar predictive power, we devise tests to decide in the favour of one or the other; and sometimes we will keep both of them using them were appropriate and were convenient. (examples: classical and quantum mechanics; non-relativistic and relativistic physics).
While it is important to take hypotheses very seriously (I mean, to follow induction till its bitter end) in my view we have to be fair and just when we test them against reality, in order to avoid to trick ourselves. I love as Feynman says this and this is the reason why I put below the link to a famous commencement address of him.
http://neurotheory.columbia.edu/~ken/cargo_cult.html
Caro Vissani,
credo di poter usare l’Italiano per essere più breve. A conforto di quanto lei scrive, vorrei citare alcuni riferimenti che penso riflettano il suo pensiero. I primi due scritti sono reperibili su ResearchGate nella Sezione: ‘Question asked’ e sono rispettivamente:
1) Is induction of any help in choosing among theories empirically equivalent?;
2) What is your opinion on the relationship between science and culture?
A quest’ultimo riguardo, parlando della cultura, sulla scorta degli insegnamenti ricevuti dal Prof. Gismondi, scrivevo: “
Sapere e attività scientifica operano sui valori culturali, non direttamente, ma per induzione pratica. Ciò indica che i criteri dapprima ispirano implicitamente gli atteggiamenti e i comportamenti degli operatori scientifici (rigore, oggettività, criticità, esattezza, ecc.). Poi vengono resi espliciti mediante le continue discussioni su metodi e principi. Infine, così rielaborati, sono assorbiti dalla società, come valori e norme che ispirano comportamenti e azioni”.
Avrei altro da aggiungere, per esempio un mio libro scritto sotto l’egida della Sapienza (purtroppo esaurito non perché sia stato un best-seller, ma per distribuzione alle varie biblioteche italiane. Il titolo è : “La riduzione dell’invidia in Economia – equità, evoluzione culturale e ‘selezione di gruppo’.
La ringrazio per l’attenzione, sperando di poterla leggere su ResearchGate o altrove. (Pazienza per chi non conosce l'Italiano) Gianrocco Tucci
Thanks to you Gianrocco,
for the stimulating discussion and the precious occasion of exchange of views.
The attitude toward science you describe is admirable, I believe we should do all we can to make it work, despite the fact that in everyday life we see so many other-meaner-attitudes.
I hope I will have an occasion to read your book in future, in Italian of course, and to meet you the first useful occasion.
Care cose, Francesco
C. F. Vissani “If we have two hypotheses with similar predictive power, we devise tests to decide in the favour of one or the other; and sometimes we will keep both of them using them were appropriate and were convenient.”
A. The original question was about possible way to distinguish two theories that have the empirical equivalences.
In that caseб any attempt of induction is useless because all of them use the same set of empirical data from experiments.
Therefore, there is the only one possible way to distinguish those theories. We need to make an extra experiment that shows some extra data. Analysis of that extra information helps us to make strong distinguish between competitive theories.
F. Vissani “While it is important to take hypotheses very seriously (I mean, to follow induction till its bitter end) in my view we have to be fair and just when we test them against reality, in order to avoid to trick ourselves.”
Very well! Do you like to prove your words and make such experiment by instrumental test of Relativity by one-way experiment by the technology proposed by the WO/2015/040505 patent application?
In case of positive answer, you have the official license from the patent holder to build and use the device.
Dear Vissani,
there is a comment by Allan Zade that concerns your contribution. I do not know if it has been sent also to you. Best regards, Gianrocco Tucci
You need to use both induction and the law of contradiction--if two theories are contradictory they cannot both be correct--you can use deduction if they have different causal implications--you can take new measurements, collect new data--in the end there was lots of evidence in favor of the heliocentric system--but since science is most fundamentally inductive, this leaves open the possibility of new discoveries-science is a building process-
C. Edwin A. Locke “You need to use both induction and the law of contradiction -- if two theories are contradictory they cannot both be correct”
A. Usually, they use the law of contradiction for statements (not for theories). Obviously, “contradictory statements cannot both be true in the same sense at the same time”.
However, that law is not applicable for two theories because each theory has many statements and it is not obligatory that each statement of theory A has contradictory statement from theory B.
In case of theory-to-theory contradiction we need to find a way to falsify one of them (!) Therefore, all new evidences mentioned above can be used against booth theories and it is quite possible that both theories become falsified by new evidence/data etc. (that is a general case).
If only one theory survive, that theory possesses advantage of support by new evidence(s).
Many theories have weakness on the Ground Level Assumptions (GLA) because they use postulates. A theory exists as long as full set of its postulates remains correct. Therefore, destruction (falsification) of any postulate leads to destruction (falsification) of entire theory.
For example, there is a famous postulate from Relativity “The speed of light is ever the same for every observer regardless of any relative mouton of the observer and light”.
When does the theory become falsified?
It happens as soon as anyone shows that “the speed of observer-to-light relative motion depends on the speed of the observer”.
I do not agree with Popper. Falsification is not the main method of science-that is backwards. To prove a theory you need positive evidence. You do need to rule out alternative explanations, of course. If more than one theory seems to be consistent with the evidence, it is almost always possible to design a new study to see which is right. If the theory is so vague that it can accommodate anything, then it is not a good theory. Or, in some cases, the technology is not available so you have to wait.
Edwin,
By putting falsification as an important critera for a theory to be scientific allow to eliminate rubber band theory, theory that are so vague that they are always right. Those one get kick out by the requirement for a theory to be falsifiable.
If a theory is very vague you cannot falsify it but more importantly you cannot support it--so it is not really a theory at all-
There is no such thing as inductive logic so what are you all talking about?
To Lawrence A. Boland
Inductive logic means Inductive arguments intend to support their conclusions only to some degree; the premises do not necessitate the conclusion. Traditionally, the study of inductive logic was confined to either arguments by analogy or else methods of arriving at generalizations on the basis of a finite number of observations. A typical argument by analogy proceeds from the premise that two objects are observed to be similar with respect to a number of attributes to the conclusion that the two objects are also similar with respect to another attribute. The strength of such arguments depends on the degree to which the attributes in question are related to each other.
from logic. (2008). Encyclopædia Britannica. Encyclopaedia Britannica 2008 Deluxe Edition. Chicago: Encyclopædia Britannica.
Science is possible only with Inductive logic.
Edwin A. Locke “Falsification is not the main method of science-that is backwards.”
The original question of this thread relates for two theories. In that case, it is quite possible that new evidence can be used to falsification of one of those theories. That way eliminates a weaker theory.
Allan,
David Hume refuted this nonsense 200 years ago. Inductive logic is not logic, it is sophisticated jumping to conclusions.
Sorry but I totally reject Hume--if you look at the history of science, such as David Harriman's The Logical Leap you will see that science progressed by induction. Induction must precede deduction--I also disagree with Popper that you should make deductions totally arbitrarily-
Stefan is making some good points here that induction comes up today when choosing a theory or model. My only problem with this is simply, why are we suppose to choose? True, engineers choose all the time, but the exact truth of their theories is not at issue, only convenience. Engineers are instrumentalists. So, why choosing? One might reject a model for being non-falsifiable, but beyond that, why?
I do not agree, Stefan. There is no need to choose if one cannot prove one's choice is true. And there is no inductive proofs. As Quine said, the only deductive proof amounts to a tautology which is, of course, uninformative. Think of the wave and phase theories of light.
Sorry but I do not agree that truth does not matter--if it does not, throw science out--and how could a theory be convenient unless it actually works in application? Of course, something can work for a different reason that one thinks--that is part of scientific detective work (and induction)--and, as I have said, causal explanations are discovered in layers--and, as I have said falsifiability is not the real issue- I want to use an example from Freudians here: let's say you reject the Oedipus complex (wanting to kill your father and rape your mother)--if you oppose it they would say your are being defensive so what would be evidence against it? Yes, it would be unfalsifiable but the real issue is not that; the real issue is: what is your evidence?--and then you find it is case studies with totally arbitrary interpretations--it can be thrown out on that basis alone--
Who said truth does not matter? I just said if you can not prove a theory or model is true, why choose?
Mainz, Germany
Dear Tucci et al.,
Regarding Popper's view, I here borrow a short passage from the article "The Problem of Induction" in the Stanford Encyclopedia of Philosophy (which I regard as generally very good):
One of the most influential and controversial views on the problem of induction has been that of Karl Popper, announced and argued in The Logic of Scientific Discovery (LSD). Popper held that induction has no place in the logic of science. Science in his view is a deductive process in which scientists formulate hypotheses and theories that they test by deriving particular observable consequences. Theories are not confirmed or verified. They may be falsified and rejected or tentatively accepted if corroborated in the absence of falsification by the proper kinds of tests:
[A] theory of induction is superfluous. It has no function in a logic of science.
The best we can say of a hypothesis is that up to now it has been able to show its worth, and that it has been more successful than other hypotheses although, in principle, it can never be justified, verified, or even shown to be probable. This appraisal of the hypothesis relies solely upon deductive consequences (predictions) which may be drawn from the hypothesis: There is no need even to mention “induction”. (LSD, 315)
---end quotation
As I say, the Popperian view seems to me well worth considering, though many disagree--whether explicitly or explicitly. In any case, you may find the entire article of some use in exploring the related topics. See:
http://plato.stanford.edu/entries/induction-problem/#KarPopVieInd
H.G. Callaway
Rather than deal any more on short posts I am posting here a section of my 2007 article in the J. of Management on Popper,
Influenced by Kant’s views, modern philosophers of science such as Kuhn and Popper claimed that scientific certainty about the real world was impossible and that induction was invalid: “A principle of induction is superfluous, and it must lead to logical inconsistencies” (Popper, 2003: 5). The problem for Popper (2003) was that making a universal statement from specific experiences would require further experiences, thus leading in the end to an infinite regress. (Of course, it would only be a theory of experiences, not facts, because reality was unknowable.) To him, “Theories are . . . never empirically verifiable” (p. 18). Instead, Popper argues that empirical “testing” of a scientific theory can involve no more than seeing if it can be falsified. Nor does Popper embrace the notion of causality, “I shall, therefore, neither adopt nor reject the ‘principle of causality’; I shall be content simply to exclude it as ‘metaphysical’,from the sphere of science”(p. 39). Metaphysical means pertaining to the basic nature of reality, which, as noted, Kant said was unknowable. Popper also rejected the idea of objective concept formation: “It is widely believed that it is possible to rise by a process called ‘abstraction’from individual concepts. This view is a near relation to inductive logic. . . . Logically these procedures are equally impracticable” (p. 45).
In sum, Popper (2003) rejected not only induction but everything that makes induction possible: reality (specifically, the ability to know it), causality, and objective concept formation. Popper rejected the whole concept of proof and claimed that science “advances” only by disproving theories. This brings up a question: Where do theories come from, if not from integrating observations and discoveries by induction? Popper had no real answer to this: “There is no such thing as a logical method of having new ideas, or a logical reconstruction of this process. My view may be expressed by saying that every discovery contains ‘an irrational element’, or ‘a creative intuition’” (p. 8). Observe the Platonic element in this theory, although Plato would have argued that rational intuitions can be made by philosophers.
Popper’s (2003) replacement for induction was deduction. Because there was no rational method of formulating a theory inductively, one could, in effect, start from anywhere one wanted because one theoretical starting point was as good as another—deduce a theory, and then try to falsify it.
Popper’s (2003) views were reinforced in an influential article written by Platt in 1964 called, ironically, “Strong Inference.” It claimed to explain the rapid progress made in some fields of science like biology by identifying the method involved. Step 1 involved making “intellectual inventions” from which hypotheses were then deduced (Step 2). Then they were tested and the theories or hypotheses were adjusted accordingly, the erroneous ones being falsified (Step 3). Platt stresses the process of testing competitive hypotheses, but he gives virtually no account of how one develops theories or hypotheses in the first place. For example, he writes, “But if you stop doing experiments for a little while and think how proteins can possibly be synthesized, there are only about 5 different ways, not 50! And it will take only a few experiments to distinguish these” (Platt, 1964: 348).
But how could one know there could be only 5 ways and not 50 unless it was based on evidence gained from prior research? Otherwise such a claim would be totally arbitrary. How does one formulate these hypotheses or theories in the first place? Platt (1964) never says; presumably he agrees with Popper (2003) that “intellectual inventions” represent some intuitive process. Although Platt himself claims to be advocating an inductive process, the process of testing hypotheses, competitively or otherwise, can only occur after one has gathered evidence from which the predictions are deduced. Thus, there can be a rational use of intuition based on previously gained knowledge stored in the subconscious, but the subconscious must contain material based on reality for it to be potentially useful. Nor can the subconscious substitute for the hard work of thinking and discovering.
Furthermore, once we have falsified a hypothesis, where are we? Unfortunately, nowhere. Platt (1964) even undermines his own method in agreeing with Popper that “there is no such thing as proof in science—because some later alternative explanation may be as good or better—so science advances only by disproofs” (p. 350). This means that science advances, in effect, by showing theories not to be true.
The falsifiability approach falls apart even on its own terms. Your falsification might itself be false. After all, there is no certainty even in falsification, because it involves gathering actual evidence that disproves a theory. But how do you know whether that evidence is valid? You would need to see if you can falsify your falsification and so on. Logically, the falsification approach must lead to an infinite regress—the very problem that Popper (2003) claimed was the fatal weakness of induction.
More fundamentally, however, how could science ever advance by showing that something is not true? What would we gain by showing that genes were not controlled by fourleaf clovers or that the planets were not kept in orbit by tiny gold strings? The history of science clearly shows that it advances by discovering things that are true. If this were not the case, we would still be living in the dark ages. In reality, science has not, and could not have, progressed by the process of falsification; it progressed only by the process of making positive discoveries.
When dealing with causal relationships, one does have to rule out alternative explanations (by controlling variables), but that is what the experimental method is for. However, ruling out alternatives is virtually useless unless there is something positive to account for the relationship. Ruling out 1,000 hypothesized causes of the plague may be slightly helpful, but this does not explain what actually causes the plague or how, that is, an infection by the bacterium Yersinia pestis through personal contact or flea bites. When Thomas Edison found that hundreds of different materials failed to work as light bulb filaments, this was useful to know because those materials could then be ignored. But he still had to find a filament (a cotton thread coated with carbon) that did work (Josephson, 1959). The invention of a practically workable light bulb represented true scientific progress.
Dear Callaway,
thank you for the precious information, I should get the Stanford Encyclopedia, an excellent 'instrument' of knowledge.
I'll try to go through the article. I presume it will take some time. If possible, I'll skip the mathematics as I am of a literary formation and not very familiar with that 'language'. I must confess I always had preference for humanistic studies. Consequently, I placed the 'classics' to the root of my cultural identity.
Best regards, G.Tucci
Mainz, Germany
Dear Locke,
If Popper was wrong about many things, and he has certainly been widely disputed (and in some points in my own writings as well), it does not follow that one can easily disregard what he says about induction, or the generally skeptical Popperian approach.
The best answer to Popperian skepticism, I suppose, would be a clear formulation of what it is that "induction" amounts to, with some clear illustrations or paradigm cases of induction. Surely, there is much successful practice in the sciences and in other empirically based studies. So, one, rather less skeptical approach, is to say that "induction" is whatever the practitioners do which leads them from empirical evidence, to a justification or acceptability of generalizations of relevance. If one takes this approach, then there will surely be much of interest to examine and detail --in the history of science which would illustrate the relevant "inductive" practices.
It strikes me that you chiefly launch into a generalized criticism of Popper rather than a defense of induction against Popperian skepticism. Whatever the value of your remarks in their original context, they strike me as not exactly to the point here. In any case, it was not the point of my prior posting to defend arbitrarily selected elements of Popper's views, but to point out that there has been reasoned criticism of the very idea of "induction." That should at least make the point that it has not been easy to formulate, with any precision, exactly what induction is supposed to be. As, I say, perhaps the best reply to Popper would be to simply and compellingly state what induction is and how it works.
H.G. Callaway
Edwin, I think you are talking about Lakatos's version of Popper. As Popper himself has said, falsificationism is not his view of the philosophy of science. As I have pointed out many times in my publications, Popper's view is nothing more than an updated version of the view of the Socrates of early Plato. One learns by discovering one's errors. For Popper, this is learning from criticism. The followers who understand Popper call his view Critical Rationalism.
Dear Dr. Gallaway:
Aside from my own theory building work (over 45 years) what would I recommend as an alternative to Popper? I have posted this recommendation several times: David Harriman's book The Logical Leap. It presents a theory of induction and shows how progress in physics and related fields was achieved through induction. It shows what induction is and how it works.
Lawrence: My view of Popper (and my quotes) are from Popper's own book. Rationalism is the right word for him and it does come from Plato--and that is the problem. Plato divorced concepts from the senses and he was really the founder of mysticism. Rationalism is reason divorced from reality--the intellectual's disease. That is why of the ancients I am pro-Aristotle, though he did make mistakes.
Edwin, I did not just say Plato, I said early Plato. Early Plato usually refers to the few short early dialogues. Note also, Popper wrote more books than just the LSD.
Mainz, Germany
Dear Locke,
You have referenced a favorite source on induction, so why don't you briefly describe the matter of induction, as it appears in your favorite account? Are you here to convince the participants or merely to tell us that you are convinced and stand on your authority?
You wrote:
Aside from my own theory building work (over 45 years) what would I recommend as an alternative to Popper? I have posted this recommendation several times: David Harriman's book The Logical Leap. It presents a theory of induction and shows how progress in physics and related fields was achieved through induction. It shows what induction is and how it works.
---end quotation
Like artist performing and creating art, somewhat, scientists are often better at constructing theories than they are at telling how they do it, or what they do when they do it. So, the details of the actual work of science are of interest in answering Popper's skepticism, in ways that a mere reference to someone disagreeing with Popper is not.
I notice that you go on in polemics against Popper. Since he is no longer around to answer, that's easy enough to do.
But what is induction? You don't say. If it were so easy and obvious to answer this question, then I don't see how Popper could have got away with a career, over many decades, based on his skepticism about induction.
BTW. "Callaway" (notice the initial "C") is an English family name of some thousand years' standing. It is Anglo-Norman and derives from a place name in Normandy, according to the best theory I know. Its Anglicized, from Norman French, and the original meaning suggests a stream or path of white stones. All the variations in spelling exist in England and around the world in the English-speaking countries. If you look in the telecom phone books, you will find the name "Callaway" concentrated in south-central England, near to the Norman landing place and the Battle of Hastings.
H.G. Callaway
Mainz, Germany
Dear all,
Here follows a short quotation from the opening summary of the Stanford Encyclopedia's article on "The Problem of Induction," which may facilitate the discussion here:
In recent times inductive methods have fissioned and multiplied, to an extent that attempting to define induction would be more difficult than rewarding. It is however instructive to contrast induction with deduction: Deductive logic, at least as concerns first-order logic, is demonstrably complete. The premises of an argument constructed according to the rules of this logic imply the argument's conclusion. Not so for induction: There is no comprehensive theory of sound induction, no set of agreed upon rules that license good or sound inductive inference, nor is there a serious prospect of such a theory. Further, induction differs from deductive proof or demonstration (in first-order logic, at least) not only in induction's failure to preserve truth (true premises may lead inductively to false conclusions) but also in failing of monotonicity: adding true premises to a sound induction may make it unsound.
The characterization of good or sound inductions might be called the characterization problem: What distinguishes good from bad inductions? The question seems to have no rewarding general answer, but there are nevertheless interesting partial characterizations, some of which are explored in this entry.
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Surely, part of what is involved in the present question is to characterize what is meant by "induction." If we are going to decide whether induction will be helpful for particular purposes, then we need to know what induction is. But the suggestion of the above quotation is that there is no general or generally agreed answer to this question. This suggests, in turn, starting with a consideration of the "interesting partial characterizations." Some of these are illustrated in the article.
Kind regards to all.
H.G. Callaway
Dear H.G. Callaway,
Is there any chance that we share some relative in Normandy? My ancestor, Antoine Brassard (1609-1668) was a normand master mason. He is among the first 100 persons who immigrated in New France, Quebec city in 1637.
It would not be fair to try to summarize Harriman's The Logical Leap--but I will note a few highlights--induction starts with perception (sorry Hume) and the development of concepts. Induction is strongly related to the process of concept formation as described by Ayn Rand, which is a book in itself. The process is tied to mathematics. Harriman traces critical discoveries in science such as Newton's Laws, the atomic theory, the theory of gasses. He shows how Popper went wrong and the causes of inductive errors. using verious examples. This is all I can do in a brief summary. I think it is a stunningly brillaint book but everyone has to decide that for himself.
Here are a few quote of Poincaré from chapter titled “Mathematical Creation” from his 1904 tome The Foundations of Science: Science and Hypothesis, the Value of Science, Science and Method. Poincaré observes a process profoundly applicable not only to mathematics, but to just about any creative discipline:
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I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate; the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and succeeded without difficulty in forming the series I have called theta fuchsian.
Just at this time, I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidian geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’ sake, I verified the result at my leisure.
I turned my attention to the study of some arithmetical questions apparently without much success and without a suspicion of any connection with my preceding researches. Disgusted with my failure, I went to spend a few days at the seaside and thought of something else. One morning, walking on the bluff, the idea came to me, with just the same characteristics of brevity, suddenness and immediate certainty, that the arithmetic transformations of indefinite ternary quadratic forms were identical with those of non-Euclidian geometry.
Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable, and traces of it would be found in other cases where it is less evident. Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind. It might be said that the conscious work has been more fruitful because it has been interrupted and the rest has given back to the mind its force and freshness.
One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. It seems, in such cases, that one is present at his own unconscious work, made partially perceptible to the over-excited consciousness, yet without having changed its nature. Then we vaguely comprehend what distinguishes the two mechanisms or, if you wish, the working methods of the two egos.
There is another remark to be made about the conditions of this unconscious work: it is possible, and of a certainty it is only fruitful, if it is on the one hand preceded and on the other hand followed by a period of conscious work. These sudden inspirations (and the examples already cited sufficiently prove this) never happen except after some days of voluntary effort which has appeared absolutely fruitless and whence nothing good seems to have come, where the way taken seems totally astray. These efforts then have not been as sterile as one thinks; they have set agoing the unconscious machine and without them it would not have moved and would have produced nothing.
''The subliminal self is in no way inferior to the conscious self; it is not purely automatic; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed.''
Gianrooco: I disagree that evolution and creationism were compatible with evidence. Creationism belongs in the category of being totally arbitrary: a non-perceivable ghost in the sky whose existence and actions are to be accepted on faith. Give me a break. Such an argument is properly dismissed out of hand and belongs in the realm of fantasy, not science. The issue of falsifiability would not even properly come up. The arbitrary does not have to be refuted, because, in reality, nothing has been said. In contrast, evolution theory is based on actual evidence.
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