In his book on Opticks (1704) Newton clearly described the method he used to proceed from particulars to more universal conclusions with this strong rejection of hypotheses. And it has been clearly shown by Ducheyne (2005) that he was following the Bacon’s method of Induction, even if he rarely mentioned his name.
In his Novum Organum (1620) Bacon described two ways of searching and discovering truth: There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgement and to the discovery of middle axioms. And this way is now in fashion. The other derives from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms at last of all. This is the true way, but as yet untried.
In the second way, Bacon substitutes observation to hypothesis, in order to develop a true method of Induction. According to him, we should never proceed from particular to universals directly (i.e. simple enumerative induction, which he considers as childish), but to do so by establishing progressive stages of certainty. Newton’s argument follows the same way: he proceeds from particular to mediate axioms to arrive at the phase of synthesis testing the generality of the general principles, as well in opticks as in universal gravitation.
However, from Mill (1843) and his followers induction is taken as a generalization from particular facts. About this induction Bacon wrote: For the induction which proceeds by simple enumeration is childish; its conclusions are precarious and exposed to peril from a contradictory instance; and it generally decides on too small a number of facts, and on which are at hand. It is against this induction that Einstein (1936) wrote: There is no inductive method which could lead to the fundamental concepts of physics. Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century. This sense of the term induction is very often only considered nowadays.
Popper (1959) with his falsificationism, even if he rejected also this kind of induction, substituted his hypothetico-deductivism to Bacon’s inductivism. For him a hypothesis is the point of departure of any research. But doing this will not permit to establish a true scientific way of reasoning as there will be as many scraps as there are hypotheses to verify and that this will restrict a research to a task of validation. The falsification of a theory occurs after the mechanism which generates the observed properties has been identified, and will confirm the advanced formal structure, or indicates that we need to revise it (Franck, 2002).
I already had a discussion about Newton’s argument with H.E. Lehtihet and I think that it is interesting to open a specific thread on this topic in order to have Research Gate members’ advice on it.
References
Bacon F. (1620). Novum Organum. J. Bill.
Ducheyne S. (2005). Bacon’s idea and Newton’s practice of induction. Philosophica, 76, 115-126.
Einstein A. (1936). Physics and reality. Journal of the Franklin Institute, 221, 348-382.
Franck R. ed. (2002). The explanatory power of models. Kluwer.
Mill J.S. (1843). A system of logic. Harrison.
Newton I. (1704). Opticks. Sam. Smith and Benj. Walford.
Popper K. (1959). The logic of scientific discovery. Hutchinson & Co.
George,
Your answer as a mathematician and a statistician is quite interesting for me, as during the beginning of the last century mathematicians were searching for the axiomatic foundations of probability. For example, Hilbert at the International Congress of Mathematicians in Paris (1900) set the sixth problem to be solved as follows: The investigations on the foundation of geometry suggest the problem to treat in the same manner, by mean of axioms, those physical sciences in which mathematics play an important part; in the first rank are the theory of probabilities and mechanics. When Kolmogorov (1933) wrote his book on the axiomatic of probability he devoted an entire section to spelling out the links between the world of experience and the axioms. In 1934 Feller was commenting enthusiastically Kolmogorov: The calculus of probability is constructed axiomatically, with no gaps in the greatest generality, and for the first time systematically integrated, fully and naturally, with abstract measure theory. However this axiomatic approach of objective probability is not the only one and de Finetti (1937) proposed axioms for subjective probability and Jeffreys (1939) for logical probability. Such a search for axioms is perfectly in the line of Bacon’s induction. Has it been abandoned nowadays by mathematicians to follow Popper’s way of reasoning? I would like to have the advice of other mathematicians.
Dear Daniel, Newton's practice seems to contradict his statement about hypotheses, because he does use hypotheses to deduce his laws - this is what I heard from a professor who analysed his book Principia Mathematica
I am on Holidays. Yet, your question is interesting. Let us have some fun then.
According to Peter Urbach (his book on Bacon), Francis Bacon recognized induction but preferred deduction and hypothesis.
Yet, I would like to avoid unnecessary confusion and typical conflicts with people, particularly with the mathematicians. They often presume that they are performing nothing of what we mortals could ever understand: a kind of intuitive, ingenious procedures to arrive at their illuminating shorthand descriptions of the World. If a description does not fit, they look for a section of the world where their strings of gibberish could be squeezed to fit. Luckily, for them, Wold is large enough, so sooner or later they will find what they are looking for, more or less, of course. If needed, they will even extend their theory of numbers or introduce another set of axioms and virtual spaces to make their solutions possible. But this is no problem for them. When they find it, they claim that they applied an ingenious, indescribable research method and if something is still incongruent, this is the world that is not perfect! I will therefore prefer to respond when I will return home and have more time to construct some down to Earth, friendlier response.
Dear Alfredo,
Even if what you heard was true, why in this case Newton wrote this sentence? Can you also tell us what your professor means under the term hypothesis, as we need to be cautious about the exact meaning of the terms we use? Newton clearly said: For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. He was taking his conclusions from observation and experiment and not from hypotheses as he defines them.
Dear Dragan,
Thank you for your contribution to this debate even from your Holydays paradise!
There were so many books written about Bacon that unfortunately I did not read the book of Peter Urbach on Francis Bacon’s philosophy of science (1987). However I read that Urbach noted many parallels between Bacon and Popper, portraying Bacon as a precursor of Popper: such a paternity may lead to think that Bacon preferred deduction and hypothesis to induction. However Popper, in the Logic of scientific discovery, describes Baconian induction as an industrious gathering of the ‘countless grapes, ripe in season’, from which he expected the wine science to flow and as his myth of a scientific method that starts from observation and then proceeds to theories. This appears to support my thesis of the rejection by Popper of Baconian induction. Conversely it appears to me that Bacon and Newton were rejecting hypotheses.
Ah, no Daniel. Urbach is explicit: Francis Bacon held that induction is primitive and unreliable. Popper misunderstood Bacon's point on induction. Popper really did not grasp quite complex language of Bacon. I do not know what was Popper's reaction when Urbach published it, but believe that he accepted it. Believe me when I read it already in 1987 I examined all the citations of Bacon's " Novum Organum " that Urbach gives in his book and I remember very well those points. When back in Paris I will give you the references and point out the places in the "Novum Organum". The famous book is available in PDF on the Internet:
https://rosswolfe.files.wordpress.com/2015/05/francis-bacon-the-new-organon.pdf
Bacon also defines two different forms of deduction, one is what we now call "hypothesis" and he - as I can remember now - held it to be superior. But I do not have a book in front of me and have not much time to look it up on the screen. It should be somewhere after Paragraph 100 or so.
Dear Dragan,
For me as for many other readers, Baconian induction is clearly defined and developed in many parts of his work as the only scientific way of reasoning. In his New Organon Book I, we can read in Aphorism XIV: The only hope is true induction; in Aphorism XL: Formation of notions and axioms by means of true induction is certainly an appropriate way to banish idols and get rid of them; in Aphorism CV: But the induction which will be useful for the discovery and proof of sciences and arts, should separate out nature, by appropriate rejections and exclusions; etc. In the same Aphorism CV he rejects the other form of induction: For the induction which proceeds by simple enumeration is a childish thing, its conclusions are precious, and it is exposed to the danger of the contrary instance.
He never used, to my knowledge, the terms deduction and hypothesis and they don’t appear in the index of he Cambridge edition, while experience and observation are vey often cited. For example in Aphorism LVIII he said: Let such be the care in observation which will banish and get rid of idols of the cave.
So that I don't see where Urbach found that Bacon prefered deduction and hypothesis to induction.
Please read the entire Aphorism CV again and further. That form of "induction" that Bacon accepts, he calls "demonstration" - which is in fact "hypothesis", he posits the "consequent"! This is a deductive mode of inference, more precisely inversed modus ponens, where we affirm the consequent, or what was later recognized as Pierce's abduction. Peter Urbach really explains this with more examples, but I have not the copy here on the beach of the Aegean sea.
I will continue this discussion in 2 weeks, when I will be in Paris.
Dear Dragan,
Here is the English translation of Aphorism CV in its entirety:
In forming an axiom we need to work out a different form of induction from the one now in use; not only to demonstrate and prove so-called principles, but also lesser and intermediate axioms, in fact all axioms. For the induction which proceeds by simple enumeration is a childish thing, its conclusions are precarious, and it is exposed to the danger of the contrary instance; it normally bases its judgement on fewer instances than is appropriate, and merely on available instances. But the induction which will be useful for the discovery and proof of sciences and arts should separate out a nature, by appropriate rejections and exclusions; and then, after as many negatives as are required, conclude on the affirmatives. This has not yet been done, nor even certainly tried except only by Plato, who certainly makes use of this form of induction to some extent in settling on definitions and ideas. But any number of things need to be included in a true, legitimate account of this kind of induction or demonstration, which have never occurred to anyone to think about, so that more effort needs to be put into this than has ever been spent on the syllogism. It is this kind of induction whose help we must have not only to discover axioms but also to define concepts. And we may certainly have the greatest hopes for this kind of induction.
And here the original Latin text:
CV. In constituendo autem axiomate, forma inductionis alia quam adhuc in usu fuit excogitanda est; eaque non ad principia tantum (quae vocant) probanda et invenienda, sed etiam ad axiomata minora et media, denique omnia. Inductio enim quae procedit per enumerationem simplicem res puerilis est, et precario concludit, et periculo exponitur ab instantia contradictoria, et plerumque secundum pauciora quam par est, et ex his tantummodo quae praesto sunt, pronunciat. At inductio, quae ad inventionem et demonstrationem scientiarum et artium erit utilis, naturam separare debet, per rejectiones et exclusiones debitas; ac deinde, post negativas tot quot sufficiunt, super affirmativas concludere; quod adhuc factum non est, nec tentatum certe, nisi tantummodo a Platone, qui ad excutiendas definitiones et ideas hac certe forma inductionis aliquatenus utitur. Verum ad hujus inductionis, sive demonstrationis, instructionem bonam et legitimam quamplurima adhibenda sunt, quae adhuc nullius mortalium cogitationem subiere; adeo ut in ea major sit consumenda opera, quam adhuc consumpta est in syllogismo. Atque hujus inductionis auxilio, non solum ad axiomata invenienda, verum etiam ad notiones terminandas, utendum est. Atque in hac certe inductione spes maxima sita est.
I think that Urbach made a mistake while thinking that demonstationis was a substitute to hypothesis in Popper’s sense. As Robert Franck said in The explanatory power of models (2002, p. 290): It will have been noticed that induction, such as it was conceived in the 17th century, is not compatible with the empiricism of Hume or Mill, or with the covering law approach. It is hard to see how a law-like generalization could be implied by particular statements! It is the case that empiricist philosophy rejected classical induction, revived he traditional meaning of induction (as generalization) which Bacon had rejected, and restored the deductive conception of explanation which came from Scholastic metaphysicians. And Popper’s falsificationism is evidently in the line of Hume or Mill.
Good Holidays on the beach of the Aegean Sea!
Dragan, I found this citation about Peter Urbach’s interpretation of the thought of Bacon, in Markku Peltonen Introduction to The Cambridge companion to Bacon (1996, p. 44-45): After about thirty years Peter Urbach puts an end to the imaginary Bacon which was invented by Popper and Popperian epistemologists. However, having the tendency to take the community of epistemologists for the whole scholarly community, Urbach holds the Popperian interpretation of Bacon as a standard interpretation (“standard” for what, we are tempted to ask) and does not care to compare this interpretation with other comments, articles, or books published outside the parochial community of English-speaking epistemologists, during the fashion of such interpretation. This view seems to permit a more clear comparison of your interpretation and mine. I however, in view of my previous arguments, I still think that Bacon’s induction is not based on deduction and hypothesis.
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